Non-invasive analysis of electrophysiological processes using imaging and deep learning

Abstract

This invention provides new and useful methods for accurately imaging heart rhythm disorders. Novel panoramic optical mapping methods, and recent advances in machine learning techniques, are used to create a mechano-electrical model effective in predicting electrical activity of a tissue based on motion of the tissue. Deep learning techniques for constructing three-dimensional intramural electrical wave patterns from surface data, imaging chambers for performing panoramic optical mapping methods, and deep learning techniques for motion tracking tissue via optical and / or ultrasound data are also provided. The optical mapping and deep learning techniques of the disclosure may be applied in a plurality of different ways, individually or in combination, to improve the diagnosis and treatment of heart rhythm disorders. Also provided are systems for performing the methods described herein as well as non-transitory computer readable storage media and computer products.

Description

Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 NON-INVASIVE ANALYSIS OF ELECTROPHYSIOLOGICAL PROCESSES USING IMAGING AND DEEP LEARNING STATEMENTREGARDINGFEDERALLYSPONSOREDRESEARCHThis invention was made with government support under Grant No. DP2HL168071 awarded by the National Institutes of Health. The government has certain rights in the invention. CROSS-REFERENCE TO RELATED APPLICATION Pursuant to 35 U.S.C. § 119 (e), this application claims priority to the filing dates of United States Provisional Patent Application Serial No.63,465,826 filed May 11, 2023, and United States Provisional Patent Application Serial No.63,613,466 filed December 21, 2023, the disclosures of which applications are herein incorporated by reference in their entirety. INTRODUCTIONHeart disease is a major cause of morbidity and mortality worldwide. Understanding the origins and underlying mechanisms of heart rhythm disorders is pivotal in the planning of therapeutic interventions. Yet, despite decades of research, the driving mechanisms underlying complex heart rhythm disorders (such as, e.g., atrial or ventricular fibrillation) remain poorly understood. This is due, at least in part, to the major technological and scientific challenges inherently associated with the imaging of heart rhythm disorders. Although cardiovascular imaging has significantly progressed over the past several decades, imaging the heart’s physiological processes still has major limitations. Currently, heart rhythm disorders, including atrial fibrillation (AF) and ventricular tachycardia (VT), are routinely diagnosed using catheter-based mapping. Unfortunately, in addition to being invasive and time-consuming, catheter-based measurements typically only provide information about the heart’s abnormal electrical activity on its surface. It is not presently possible to map the three-dimensional morphology of electrical waves throughout the entire heart muscle using catheter-based approaches,Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 especially during arrhythmias such as ventricular tachycardia. However, the electrical wave phenomena associated with abnormal cardiac rhythms (e.g., arrhythmias, such as atrial arrhythmias or ventricular arrhythmias) are inherently three-dimensional phenomena evolving deep within the cardiac muscle, where they often interact with an arrhythmogenic substrate (e.g., scar tissue) in locations that are inaccessible to standard catheter mapping. Better imaging technology is greatly needed to improve diagnostics and therapies. SUMMARY Thus, there is a need for improved and useful methods and systems for accurately imaging (e.g., measuring and visualizing) heart rhythm disorders. In particular, there is a need for methods and systems useful in visualizing the heart’s intramural electrical activity. This invention provides such new and useful methods and systems, addressing the limitations mentioned above. To accomplish this, the invention pursues the highly unconventional approach of calculating or predicting electrical activity from the heart’s motion (captured via, e.g., 4D ultrasound or MRI). To enable such an approach, the invention leverages recent advances in machine learning techniques (including, e.g., deep learning techniques), and generates high-resolution training data via novel optical mapping methods, in order to train a model to predict three-dimensional electrical wave dynamics from deformation mechanics (e.g., cardiac deformation mechanics, such as ventricular or atrial deformation mechanics). The methods and systems of the invention, e.g., as described in greater detail below, find use in a variety of applications where it is desirable to improve the diagnosis and treatment of heart rhythm disorders—or other cardiac pathophysiology. As discussed above, conventional cardiovascular mapping techniques are invasive and do not capture the three-dimensional morphology of electrical waves in the heart. As such, existing methods of creating electrophysiological and mechanical movement cardiac data are incapable of producing training data-sets of sufficient size, quality, or heterogeneity to train a model capable linking electrophysiological cardiac tissue dynamics to mechanical cardiac tissue dynamics. In order to generate training data sufficient for the creation of a robust model effective in predicting three-Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 dimensional electrical wave dynamics from deformation mechanics (e.g., cardiac deformation mechanics, such as ventricular or atrial deformation mechanics), novel deep learning techniques and models for constructing three-dimensional intramural electrical wave patterns from surface data, novel imaging techniques and apparatuses for fully panoramic stereoscopic imaging of contracting hearts, and novel deep learning techniques and models for motion tracking cardiac tissues via optical and / or ultrasound data are also presented in this disclosure. The aforementioned models, apparatuses, and techniques useful for the generation of sufficient mechano-electrical model training data may be combined (e.g., via networks or iterative improvement loops) in order to enhance or refine the training data and / or the mechano-electrical model. Alternatively, as these models, chambers, and techniques each possess utility in their own right, they may be individually presented and applied, e.g., in order to improve the diagnosis and treatment of heart rhythm disorders or other cardiac pathophysiology. Accordingly, embodiments of the present invention may comprise one or more of the following aspects: 1. Deep learning- based reconstruction of electrical maps from catheter or optical mapping data including calculation of activation maps, phase maps and rotor cores.2. Deep learning-based reconstruction of three-dimensional intramural electrical wave patterns from surface data.3. Training data generation or model refinement via panoramic and / or stereoscopic imaging of contracting hearts.4. Deep learning-based motion tracking of tissues via ultrasound, MRI, and / or optical data.5. Deep learning-based reconstruction of surface or three-dimensional intramural electrical wave patterns from the motion of the heart.6. Deep learning-based localization of myocardial fibrosis or scarring from the motion of the heart. Also provided are systems for performing the methods described herein as well as non-transitory computer readable storage media and computer products. BRIEF DESCRIPTION OF THE DRAWINGS FIG.1 provides a flow diagram for practicing methods of modeling mechanical movement patterns and electrophysiological activation patterns of a tissue in accordance with an embodiment of the disclosure.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIG.2 provides a flow diagram for practicing methods of modeling mechanical movement patterns and electrophysiological activation patterns of a tissue in accordance with an embodiment of the disclosure. FIGS.3A to 3C depict a distribution matching of in silico, ex vivo and clinical electromechanical data with sparse, heterogeneous, and out-of-distribution data to achieve generalization in accordance with an embodiment of the disclosure. FIGS.4A to 4B depict training data generation using electromechanical simulations in accordance with an embodiment of the disclosure. FIGS.5A to 5B illustrate both the ‘forward’ and the ‘inverse’ mechano-electrical problem. FIGS.6A to 6B provide block diagrams of a mechano-electrical model and a data set used to train the model in accordance with an embodiment of the disclosure. FIGS.7A to 7B illustrate a self-supervised deep learning-based approach for solving the ‘inverse’ mechano-electrical problem in accordance with an embodiment of the disclosure. FIGS.8A to 8C depict computer simulations used to generate training data for a mechano-electrical model in accordance with an embodiment of the disclosure. FIGS.9A to 9C show reconstruction of electrical excitation waves from mechanical deformation using both a deep neural network and numerical modeling. FIGS.10A to 10B illustrate electrical 3D activation patterns causing unique time- varying 3D contraction patterns. FIGS.11A to 11B provide block diagrams illustrating the use of an electrical wave dynamics model and an optical motion tracking model to train a mechano- electrical model in accordance with an embodiment of the disclosure. FIGS.12A to 12B provide block diagrams illustrating the use of an ultrasound motion tracking model to train a mechano-electrical model and the use of an optical motion tracking model to train an ultrasound motion tracking model in accordance with an embodiment of the disclosure. FIGS.13A to 13E illustrate ex vivo electromechanical imaging of arrhythmias to obtain training data for AI in accordance with an embodiment of the disclosure.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIG.14 depicts electromechanical high-resolution imaging of arrhythmias ex vivo using panoramic fluorescence and 4D ultrasound imaging in accordance with an embodiment of the disclosure. FIGS.15A to 15D show ex vivo electromechanical imaging of arrhythmias, using 16-camera high-speed panoramic fluorescence imaging, highspeed 4D ultrasound, and an imaging chamber, to obtain training data for an inverse mechano-electrical model in accordance with an embodiment of the disclosure. FIG.16 depicts ultrasound imaging during catheter ablation procedures in humans in accordance with an embodiment of the disclosure. FIGS.17A to 17B depict block diagrams of stereoscopic multi-camera optical mapping being used to train and / or validate a mechano-electrical model, and to train an optical motion tracking model in conjunction with an ultrasound motion tracking model, in accordance with an embodiment of the disclosure. FIGS.18A to 18B show models and experiments connected together in a training network or training loop in order to iteratively refine a mechano-electrical model in accordance with an embodiment of the disclosure. FIGS.19A to 19B show models and experiments connected together in a training network or training loop in order to iteratively refine a mechano-electrical model in accordance with an embodiment of the disclosure. FIG.20 illustrates deep learning-based reconstruction of scroll wave chaos inside a three-dimensional volume from partial observations of the dynamics on its surface in accordance with an embodiment of the disclosure. FIGS.21A to 21D provide surface observations and projections of three- dimensional scroll wave chaos (‘turbulent’ parameter regime) in a bulk medium in accordance with an embodiment of the disclosure. FIG.22 depicts observations of three-dimensional scroll waves (‘laminar’ parameter set) on the top and bottom surfaces of an opaque medium, and in the projection of the full dynamics in a transparent medium in the bulk’s z-direction (depth). FIGS.23A to 23C provide predictions of three-dimensional ‘laminar’ scroll wave dynamics from two-dimensional observations using deep convolutional encoding-Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 decoding neural network (U-Net) in an anisotropic excitable medium in accordance with an embodiment of the disclosure. FIGS.24A to 24D provide predictions of three-dimensional scroll wave dynamics (‘laminar’ parameter set) and their vortex filaments from either single- or dual-surface observations in a thick, opaque, anisotropic excitable medium using a deep learning model in accordance with an embodiment of the disclosure. FIGS.25A to 25C depict different electrical wave patterns as seen in the top layer, bottom layer, and projection of all layers of a three-dimensional bulk. FIG.26 illustrates bulk thickness and transmurality of scroll wave dynamics (‘turbulent’ scroll wave chaos). FIGS.27A to 27D provide predictions of (‘turbulent’) electrical scroll waves in subsurface layers of anisotropic (left) and isotropic (right) bulk tissue using U-Net in accordance with an embodiment of the disclosure. FIGS.28A to 28B provide predictions of electrical scroll waves within subsurface layers of a bulk-shaped ‘turbulent’ anisotropic excitable medium using U-Net in accordance with an embodiment of the disclosure. FIGS.29A to 29F show average reconstruction error over bulk depth in opaque or transparent excitable media with anisotropy using a U-Net model in accordance with an embodiment of the disclosure. FIGS.30A to 30B provide a comparison of reconstruction errors obtained with different imaging configurations in opaque anisotropic excitable medium using a U-Net model in accordance with an embodiment of the disclosure. FIG.31 depicts average reconstruction error per layer (depth) over time in an anisotropic excitable medium for 5 different depths using a deep learning model in accordance with an embodiment of the disclosure. FIGS.32A to 32B illustrate deep learning-based reconstructions on ‘laminar’ scroll wave dynamics in the presence of various noise levels in accordance with embodiments of the disclosure. FIGS.33A to 33B show reconstruction errors obtained with different neural network architectures for ‘turbulent’ scroll wave chaos in accordance with embodiments of the disclosure.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIGS.34A to 34E provide predictions of bulk thickness from surface observations of scroll wave chaos for various media using either a regression or a classification neural network in accordance with embodiments of the disclosure. FIGS.35A to 35C provide prediction errors at various bulk depths for isotropic excitable media using a deep learning model in accordance with an embodiment of the disclosure. FIGS.36A to 36B provide a comparison of deep learning-based reconstruction of scroll waves with a naive reconstruction in isotropic excitable media. FIGS.37A to 37D illustrate diffusion-based generative modeling of electrical wave dynamics in cardiac tissue in accordance with embodiments of the disclosure. FIGS.38A to 38B show diffusion-based reconstruction of scroll wave dynamics inside a three-dimensional bulk from two-dimensional observations of the dynamics on the bulk’s top and bottom surface in accordance with embodiments of the disclosure. FIGS.39A to 39B provide transmural reconstruction error per layer number or depth with diffusion, U-Net or diffusion + U-Net models in accordance with embodiments of the disclosure. FIGS.40A to 40E illustrate hallucination of diffusion model during inpainting of electrical spiral wave dynamics. FIGS.41A to 41E illustrate diffusion-based modeling of reentrant electrical waves in heart-shaped bi-ventricular geometries in accordance with embodiments of the disclosure. FIGS.42A to 42C depict data-driven modeling of spiral wave dynamics using diffusion models in accordance with embodiments of the disclosure. FIGS.43A to 43C provide a comparison of spiral wave dynamics generated in computer simulations using a biophysical model (ground-truth) and ‘fake’ diffusion- generated spiral wave dynamics. FIGS.44A to 44E illustrate parameter-specific generation of spiral wave dynamics using diffusion generative modeling in accordance with embodiments of the disclosure. FIGS.45A to 45B show generation of 1,000 different bi-ventricular heart geometries for generation of an electromechanical training dataset consisting of tens ofAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 thousands of training samples of ventricular arrhythmias, according to an embodiment of the disclosure. FIGS.46A to 46B show computer simulation of ventricular deformation during reentrant arrhythmia, according to an embodiment of the disclosure. FIGS.47A to 47B illustrate deep learning-based prediction of electrical arrhythmia circuits from mechanical deformation in simulations of the heart’s ventricles, according to embodiments of the disclosure. FIGS.48A to 48C depict simulated training data of focal and reentrant ventricular arrhythmias generated with electromechanical computer simulations, according to embodiments of the disclosure. FIGS.49 shows spatial heterogeneity and scar tissue in the ventricles automatically generated for each simulation, according to embodiments of the disclosure. FIG.50 depicts neural network architecture and training samples for inverse mechano-electrical prediction of electrical arrhythmia circuits from ventricular deformation according to embodiments of the disclosure. FIGS.51A to 51B show deep learning-based predictions of focal electrical (action potential) waves from ventricular mechanical deformation. FIGS.52A to 52B provide electrical activation maps computed from the sequence of electrical wave patterns predicted using a deep learning-based approach, in accordance with embodiments of the disclosure. FIGS.53A to 53I show deep learning-based predictions of reentrant electrical (action potential) waves from ventricular motion, in accordance with embodiments of the disclosure. FIGS.54A to 54B provide deep learning-based prediction of electrical (action potential) waves from ventricular mechanical deformation in the presence of scar tissue, in accordance with embodiments of the disclosure. FIGS.55A to 55B illustrate training of a deep learning model on simulated data generated with the smoothed particle hydrodynamics (SPH) method, and application of the trained model to simulated data generated with the finite element method (FEM), in accordance with embodiments of the disclosure.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIGS.56A to 56C provide prediction accuracies of deep learning-based inverse reconstruction of electrical waves from ventricular deformation of the heart on synthetic simulated data with different models in accordance with embodiments of the disclosure. FIG.57 provides experimental results demonstrating that the prediction accuracy of a neural network of the disclosure stays the same over a wide parameter range. FIGS.58A to 58C illustrate optical mapping combined with numerical motion tracking for measurement of an action potential or calcium waves in moving and deforming cardiac tissues, such as an isolated heart, during voltage-sensitive optical mapping, according to embodiments. FIG.59 provides a flow diagram depicting the sequential order of the fully automatic numerical pre- and post-processing and tracking of optical mapping data, according to embodiments. FIGS.60A to 60F show typical examples of optical mapping data acquired with 4 different high-speed cameras, according to embodiments. FIGS.61A to 61E depict the performance of the Farnebäck GPU algorithm with sinus rhythm data imaged in an isolated, contracting rabbit heart, according to embodiments. FIGS.62A to 62E depict performance of the numerical motion tracking and motion-stabilization procedure on optical mapping data showing a rabbit heart during ventricular fibrillation, according to embodiments. FIGS.63A to 63D show numerical motion tracking and motion-stabilization procedures using the Farnebäck motion tracking algorithm with cell culture data, according to embodiments. FIGS.64A to 64E provide examples of sinus rhythm in a contracting mouse and rabbit heart, according to embodiments of the disclosure. FIGS.65A to 65B show a comparison of the processing speeds with low- resolution (128 × 128 pixels) voltage-sensitive optical mapping data, according to embodiments. FIGS.66A to 66B show a comparison of the processing speeds with 128 × 128, 256 × 256, 512 × 512, and 1,024 × 1,024-pixel video images, according to embodiments of the disclosure.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIGS.67A to 67C depict the accuracy of GPU-based motion tracking algorithms applied to synthetic voltage-sensitive optical mapping data, according to embodiments of the disclosure. FIGS.68A to 68C provide optical traces obtained from contracting heart surface during ventricular fibrillation (VF) in voltage-sensitive optical mapping recordings, according to embodiments of the disclosure. FIGS.69A to 69C provide a comparison of motion tracking error of 5 different GPU-accelerated motion tracking algorithms, according to embodiments. FIGS.70A to 70C show contrast-enhancement with different kernel diameters k for three different optical mapping recordings, according to embodiments. FIG.71 provides an illustration of the synthetic-to-real approach, according to embodiments of the disclosure. FIG.72 shows a comparison of PWC-Net architecture and a classical coarse-to- fine approach, according to embodiments. FIG.73 provides results on the validation dataset using PWC-Net, according to embodiments of the disclosure. FIGS.74A to 74B provide a tracking accuracy comparison between deep learning-based and conventional motion tracking algorithms, according to embodiments. FIGS.75A to 75I show seven samples of a validation dataset and predicted optical flow vector fields by a neural network according to embodiments of the disclosure. FIGS.76A to 76B illustrate tracking accuracy of deep learning-based motion tracking versus conventional motion tracking on experimental video data with added gaussian noise, according to embodiments. FIGS.77A to 77G depict an imaging setup, according to embodiments of the disclosure. FIG.78 shows camera poses and three-dimensional reconstruction of an isolated rabbit heart, according to embodiments. FIGS.79A to 79E depict an imaging configuration for panoramic voltage- sensitive optical mapping of the entire contracting ventricular surface, according to embodiments of the disclosure.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIGS.80A to 80B show sinus rhythm imaged in a contracting rabbit heart with voltage-sensitive multi-camera optical mapping, according to embodiments. FIGS.81A to 81D illustrate ventricular wall motion during sinus rhythm imaged with an optical mapping system, according to embodiments of the disclosure. FIGS.82A to 82C illustrate ventricular wall motion during sinus rhythm imaged with an optical mapping system, according to embodiments. FIGS.83A to 83D depict action potential wave fronts following a pacing stimulus, according to embodiments. FIGS.84A to 84F show ventricular fibrillation imaged across the entire surface of a contracting isolated rabbit heart using voltage-sensitive 3D optical mapping according to embodiments of the disclosure. FIGS.85A to 85C illustrate that action potential waves cause rotating mechanical motion of the ventricular surface in a fibrillating and contracting rabbit heart. FIGS.86A to 86C show action potential vortex waves and mechanical vortices on the three-dimensional, deforming ventricular surface during ventricular fibrillation in a rabbit heart, according to embodiments. FIGS.87A to 87C provide optical traces from the ventricular surface of a fibrillating, contracting rabbit heart measured with a multi-camera optical mapping system, according to embodiments of the disclosure. FIGS.88A to 88C present overviews of a panoramic imaging setup according to an embodiment of the disclosure. FIGS.89 provides a schematic representation of a computer-controlled optical mapping system’s electrical components, according to embodiments. FIGS.90A to 90C illustrate ventricular segmentation from B-mode ultrasound data, according to embodiments. FIGS.91A to 91C show optical flow-based motion tracking of the ventricles in 4D ultrasound data, according to embodiments. FIG.92 shows a particle-based representation of ventricles from 4D ultrasound data, according to embodiments of the disclosure. FIG.93 illustrates action potential wavefront propagation across a beating rabbit heart over time following electrical stimulation, according to embodiments.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIG.94 illustrates inverse mechano-electrical prediction with a neural network, according to embodiments of the disclosure. FIG.95 depicts how 4D ultrasound and computed three-dimensional motion vectors of tissue movement may be used to predict electrical wavefront propagation and calculate electrical activation maps, according to embodiments of the disclosure. FIG.96 illustrates how 3D optical surface reconstructions and electrophysiology, in combination with 3D ultrasound, is used to map a surface mesh onto ultrasound datapoints of the heart and compute three-dimensional motion vectors of tissue movement, according to embodiments of the disclosure. DETAILED DESCRIPTION Methods and systems for accurately imaging heart rhythm disorders are provided. Embodiments of the methods leverage panoramic optical mapping approaches and recent advances in machine learning techniques to create (e.g., train or configure) a mechano-electrical model effective in predicting or calculating electrical activity of a tissue based on motion of the tissue (e.g., in combination with the localized characteristics of the tissue, such as fibrosis or scarring). Deep learning and differentiable simulation techniques for constructing three-dimensional intramural electrical wave patterns from surface data or partial data, imaging chambers for performing panoramic optical mapping methods, and deep learning or gradient descent- based techniques for motion tracking tissue via optical and / or ultrasound data are also provided. The optical mapping and deep learning techniques of the disclosure may be applied in a plurality of different ways, individually or in combination, to improve the diagnosis and treatment of heart rhythm disorders and other cardiac pathophysiology such as, e.g., hypertrophic cardiomyopathy, bundle branch block, long QT syndrome, and / or heart failure. Also provided are systems for performing the methods described herein as well as non-transitory computer readable storage media and computer products.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Before the present invention is described in greater detail, it is to be understood that this invention is not limited to particular embodiments described, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting, since the scope of the present invention will be limited only by the appended claims. Where a range of values is provided, it is understood that each intervening value, to the tenth of the unit of the lower limit unless the context clearly dictates otherwise, between the upper and lower limit of that range and any other stated or intervening value in that stated range, is encompassed within the invention. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges and are also encompassed within the invention, subject to any specifically excluded limit in the stated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the invention. Certain ranges are presented herein with numerical values being preceded by the term "about." The term "about" is used herein to provide literal support for the exact number that it precedes, as well as a number that is near to or approximately the number that the term precedes. In determining whether a number is near to or approximately a specifically recited number, the near or approximating unrecited number may be a number which, in the context in which it is presented, provides the substantial equivalent of the specifically recited number. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although any methods and materials similar or equivalent to those described herein can also be used in the practice or testing of the present invention, representative illustrative methods and materials are now described. All publications and patents cited in this specification are herein incorporated by reference as if each individual publication or patent were specifically and individually indicated to be incorporated by reference and are incorporated herein by reference to disclose and describe the methods and / or materials in connection with which the publications are cited. The citation of any publication is for its disclosure prior to the filing date and should not be construed as an admission that the present invention is notAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 entitled to antedate such publication by virtue of prior invention. Further, the dates of publication provided may be different from the actual publication dates which may need to be independently confirmed. It is noted that, as used herein and in the appended claims, the singular forms “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise. It is further noted that the claims may be drafted to exclude any optional element. As such, this statement is intended to serve as antecedent basis for use of such exclusive terminology as “solely,” “only” and the like in connection with the recitation of claim elements, or use of a “negative” limitation. As will be apparent to those of skill in the art upon reading this disclosure, each of the individual embodiments described and illustrated herein has discrete components and features which may be readily separated from or combined with the features of any of the other several embodiments without departing from the scope or spirit of the present invention. Any recited method can be carried out in the order of events recited or in any other order which is logically possible. While the apparatus and method has or will be described for the sake of grammatical fluidity with functional explanations, it is to be expressly understood that the claims, unless expressly formulated under 35 U.S.C. §112, are not to be construed as necessarily limited in any way by the construction of "means" or "steps" limitations, but are to be accorded the full scope of the meaning and equivalents of the definition provided by the claims under the judicial doctrine of equivalents, and in the case where the claims are expressly formulated under 35 U.S.C. §112 are to be accorded full statutory equivalents under 35 U.S.C. §112. METHODS As summarized above, methods for accurately imaging heart rhythm disorders are provided. Embodiments of the methods leverage panoramic optical mapping approaches and recent advances in machine learning techniques to create (e.g., train or configure) a mechano-electrical model effective in predicting or calculating electrical activity of a tissue based on motion of the tissue. Details of embodiments of the present invention, including the deep learning techniques and models for constructing three-Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 dimensional intramural electrical wave patterns from surface data, the imaging chambers for performing panoramic and / or stereoscopic optical mapping methods, the deep learning techniques and models for motion tracking tissue via optical and / or ultrasound data, and the machine learning techniques and models for constructing three-dimensional intramural electrical wave patterns or tissue characteristics from the motion (i.e., mechanical movement or deformation patterns) of the heart, and aspects thereof, are described below. Also described are methods of enhancing or refining the mechano-electrical training data and / or the mechano-electrical model by combining (e.g., via networks / webs or iterative improvement loops) the aforementioned models, chambers, and techniques. Machine Learning Models and Experimental Setups As described above, embodiments of the methods include methods of training an electrical wave dynamics (EWD) model for, e.g., constructing three-dimensional intramural electrical wave patterns from cardiac tissue surface data. The cardiac tissue surface data may comprise any type of electrophysiological activation patterns correlated with the electrical waves of the heart that induce the mechanical deformation of cardiac tissue (that occurs, e.g., during a heartbeat or heart pulsation). For example, the cardiac tissue surface data may comprise electrical data such as, e.g., voltage measurements or calcium concentration measurements associated with action potential (AP) waves. The surface data may be obtained through any number of means including, e.g., through conventional catheter-based cardiac mapping approaches and / or the panoramic stereoscopic multi-camera optical mapping techniques of this disclosure described below. In some embodiments, the EWD model may be able to construct the three-dimensional (3D) intramural electrical wave patterns occurring during normal heart function (e.g., sinus rhythm) from cardiac tissue surface data. In some embodiments, the EWD model may be able to construct the 3D intramural wave patterns that occur during abnormal heart function. For example, the EWD model may be able to generate or construct 3D intramural focal wave and / or reentrant wave (e.g., scroll and / or spiral wave) dynamics from measurements of action potential waves taken at the surface ofAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 the heart. In some embodiments (e.g., of the EWD model and / or the mechano-electrical model below), the electrical wave dynamics and mechanical response to it may depend on tissue heterogeneities such as fibrosis or scarring. In some embodiments, the EWD model is able to construct or generate the 3D intramural electrical wave patterns that occur during both normal and abnormal heart function from cardiac tissue surface data. In order to train the EWD model, a training dataset sufficient for training the EWD model to perform one or more specific tasks is generated or obtained. By ‘sufficient’ in this context is meant the training data has a size, quality, and heterogeneity that enables training a model to perform one or more desired tasks with a predetermined threshold level of accuracy. In some cases, the predetermined threshold level of accuracy is calculated or determined for a trained (e.g., EWD or mechano-electrical) model in a manner that ensures less frequently occurring phenomena (e.g., abnormal heart function dynamics) are accurately reproduced or generated (e.g., from cardiac tissue surface data). In some embodiments, EWD model training datasets may comprise high-resolution in silico, ex vivo, and / or in human (e.g., clinically obtained) data. In silico training data may be generated using computer simulations of, e.g., electrical numerical models. In some embodiments, multiple different numerical models are used to ensure sufficient heterogeneity such as, e.g., an Aliev-Panfilov model, a Fenton-Karma model, a Mitchell-Schaeffer model, and / or a Bueno-Orovio model (as described in, e.g., Example 3, below). In these cases, the parameters used to run each simulation of each model may also be varied, e.g., randomly, within a specific range of values. In some embodiments, synthetic noise is introduced into the in silico training data simulations. The synthetic noise may be configured to recreate or capture the noise phenomena occurring in the measurements of cardiac tissue surface data that are intended to be input into the trained EWD model during use (i.e., the noise naturally occurring in the surface data measurements the trained EWD model will be applied to). For example, synthetic noise that accurately captures or recreates the noise of catheter- based measurements of cardiac tissue surface data may be introduced or injected into simulated training data, e.g., when the trained EWD model is intended to construct 3D intramural electrical wave patterns from said catheter-based measurements.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 In some embodiments, ex vivo training data may be generated from optical mapping experiments, such as, e.g., the panoramic / stereoscopic optical mapping experiments of this disclosure, discussed below. In some cases, ex vivo training data may be generated from mechanical movement patterns of cardiac tissue (e.g., obtained from optical mapping experiments) that are input into a mechano-electrical model of this disclosure in order to construct or generate electrical wave dynamics of the tissue. In human (e.g., clinically obtained) training data may be obtained via, e.g., conventional catheter-based cardiac mapping approaches. In some embodiments, the training dataset includes a combination of in silico, ex vivo, and clinical data sufficient to ensure that the dataset is of adequate size, quality, and heterogeneity for its intended purpose. In some embodiments, the training data input during training of the EWD model is augmented by, e.g., adding random noise to the input values, randomly rotating or flipping the data, removing a random section of the input data, scaling the data randomly, blurring the input data, and / or adding artifacts to the input data in order to ensure that the dataset is of sufficient size, quality, and heterogeneity for its intended purpose. The training data may be generated based on the task the EWD model is trained to perform. In some embodiments, the EWD model may be trained to reconstruct 3D waves from 2D measurements, as discussed above. In these instances, the EWD model may be applied in order to create a training dataset for the electro-mechanical model of this disclosure from, e.g., clinical catheter-based measurements (performed in conjunction with, e.g., ultrasound or MRI measurement generation) (see, e.g., FIG. 11A). In some embodiments, the EWD model may be trained to predict future three- dimensional intramural electrical wave patterns from cardiac tissue surface data. In these embodiments, the EWD model may be used in conjunction with the mechano- electrical model in order to, e.g., predict future three-dimensional intramural electrical wave patterns from mechanical movement patterns, or to create a training dataset such that the mechano-electrical model of this disclosure may be trained to do so directly. In some cases, the EWD model may be trained (or fitted) to detect the presence of, or to localize, fibrosis or tissue scarring from cardiac tissue surface data. In some embodiments, the EWD model may be a machine learning model including an artificialAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 neural network (NN). In some embodiments, the machine learning model is a deep learning model. In these cases, the model may be three or more layers deep, such as five or more layers deep, or ten or more, or twelve or more, or thirty or more, or fifty or more, or one hundred or more. In some cases, the EWD model is a diffusion-based generative model, or a differentiable simulation fitted to data (e.g., fitted to the training dataset discussed above). As described above, embodiments of the methods include methods of training a motion tracking model, e.g., for tracking fluorescing tissues of an optical mapping experiments using optical measurements (e.g., an array of sequential images) (i.e., an optical motion tracking model) or for tracking tissues of in human or ex vivo experiments and procedures from ultrasound measurements (i.e., an ultrasound motion tracking model). By ‘tracking’ in this context is meant generating or determining the position and / or motion of one or more discrete areas or voxels of the tissue in relation to all the other areas / voxels of the tissue (e.g., obtaining mechanical movement patterns of the tissue). In order to train the optical or ultrasound motion tracking model, a training dataset sufficient for training the motion tracking model to perform one or more specific tasks is generated or obtained. In some embodiments, motion tracking model training datasets may comprise high-resolution in silico, ex vivo, and / or in human (e.g., clinically obtained) data. In silico training data may be generated using computer simulations of, e.g., optical mapping experiments (such as, e.g., the panoramic optical mapping experiments of the disclosure). For example, numerical models of optical mapping experiments, in conjunction with virtual cameras, may be used in order to generate training data for the optical motion tracking models of the disclosure. Similarly, synthetic ultrasound data may be generated using numerical models of optical mapping experiments and / or using actual experimental data obtained by the panoramic optical mapping experiments of this disclosure discussed below (e.g., by adjusting in silico synthetic ultrasound data generating models to better capture real ultrasound measurements). Synthetic noise may be introduced into the motion tracking model training data similar to as was discussed for the EWD model above.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 In some embodiments, the optical motion tracking model may be applied in order to create a training dataset for the mechano-electrical model of this disclosure from, e.g., optical measurements (e.g., images) obtained during optical mapping experiments such as, e.g., the panoramic optical mapping experiments of this disclosure (see, e.g., FIG.11B). In some embodiments, the optical motion tracking model may be applied in order to create a training dataset for the ultrasound motion tracking model of this disclosure, e.g., from optical measurements coupled with ultrasound measurements obtained via the panoramic optical mapping experiments of the disclosure (see, e.g., FIG.12B). In some instances, the ultrasound tracking model may be used in conjunction with the mechano-electrical model in order to, e.g., predict three- dimensional electrical wave dynamics from clinically obtained ultrasound data, or to create a training dataset such that the mechano-electrical model of this disclosure may be trained to do so directly (see, e.g., FIG.12A). As described above, embodiments of the methods include methods of training a mechano-electrical model for, e.g., linking electrophysiological cardiac tissue dynamics to mechanical cardiac tissue dynamics (e.g., predicting three-dimensional electrophysiological activation patterns from mechanical movement patterns) (see, e.g., FIG.6A). The mechanical dynamics data (or, i.e., mechanical movement pattern data or mechanical deformation data) may comprise any type of spatial measurement of the cardiac tissue such as, e.g., an ultrasound, MRI, or optical measurement. The electrophysiological dynamic data (or, i.e., electrophysiological activation pattern data or electrical dynamic data) may comprise any type of electrophysiological activation patterns correlated with the electrical waves of the heart that induce the mechanical deformation of cardiac tissue (that occurs, e.g., during a heartbeat or heart pulsation). For example, the cardiac tissue surface data may comprise electrical data such as, e.g., voltage measurements or calcium concentration measurements associated with action potential (AP) waves. The mechanical movement pattern data may be obtained through any number of means including, e.g., through ultrasound, MRI, or optical measurements. The surface data may be obtained through any number of means including, e.g., through conventional catheter-based cardiac mapping approaches and / or the panoramicAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 stereoscopic multi-camera optical mapping techniques of this disclosure, described below. In some embodiments, the mechano-electrical model may be able to construct the 3D intramural electrophysiological activation patterns occurring during normal heart function (e.g., sinus rhythm) from mechanical movement pattern data. In some embodiments, the mechano-electrical model may be able to construct the 3D intramural electrophysiological activation patterns that occur during abnormal heart function. In some embodiments, the mechano-electrical model is able to construct or generate the 3D intramural electrical wave patterns that occur during both normal and abnormal heart function, e.g., from ultrasound data. In some embodiments, the mechano-electrical model may be able to generate or construct mechanical movement pattern data, e.g., from 2D or 3D electrophysiological activation patterns of cardiac tissue. In order to train the mechano-electrical model, a training dataset sufficient for training the mechano-electrical model to perform one or more specific tasks is generated or obtained. In some embodiments, mechano-electrical model training datasets may comprise high-resolution in silico, ex vivo, and / or in human (e.g., clinically obtained) data. In silico training data may be generated for the mechano-electrical model in a similar manner as to the training data of the EWD model discussed above. For example, to ensure sufficient heterogeneity, simulations may be run using multiple different electrical numerical models coupled to multiple different mechanical models (such as, e.g., the Holzapfel-Ogden, Goktepe-Ogden, Wang et al., and Eriksson et al. models discussed in Example 3 of the disclosure) and using multiple different computational techniques (such as, e.g., finite-difference method (FDM), finite element method (FEM), finite volume method (FVM), smoothed-particle hydrodynamics (SPH), and / or boundary-element method (BEM)) (see, e.g., FIG.6B). The parameters used to run each simulation of each model may also be varied, e.g., randomly, within a specific range of values to ensure sufficient heterogeneity. In some embodiments, synthetic noise is introduced into the in silico training data simulations. The synthetic noise may be configured to recreate or capture the noise phenomena occurring in the measurements of the mechanical movement patterns, or electrophysiological activation patterns, that are intended to be input into the trained mechano-electrical model duringAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 use (e.g., the noise naturally occurring in ultrasound measurements the trained mechano-electrical model will be applied to). In some embodiments, ex vivo training data may be generated from optical mapping experiments, such as, e.g., the panoramic / stereoscopic optical mapping experiments of this disclosure discussed below. In some cases, ex vivo training data may be generated from electrophysiological activation patterns on the surface of cardiac tissue (e.g., obtained from optical mapping experiments) that are input into an EWD model of this disclosure in order to construct or generate 3D electrophysiological activation pattern data of the training dataset. In some cases, ex vivo training data may be generated from optical or ultrasound measurements that are input into an optical or ultrasound motion tracking model of this disclosure in order to construct / generate mechanical movement pattern data of the training dataset. In human (e.g., clinically obtained) training data may be obtained via, e.g., conventional catheter-based cardiac mapping measurements in conjunction with ultrasound or MRI measurements. In some embodiments, in human training data may be obtained using an EWD or motion tracking model of this disclosure. In some embodiments, the training dataset includes a combination of in silico, ex vivo, and clinical data sufficient to ensure that the dataset is of a size, quality, and heterogeneity sufficient for its intended training purpose. In some embodiments, the training data input during training of the mechano-electrical model is augmented in a similar manner as was discussed for the EWD model above. The training data may be generated based on the task the mechano-electrical model is trained to perform. In some embodiments, the mechano-electrical model may be trained to construct or generate electrophysiological activation patterns from mechanical movement patterns of a tissue that are obtained, e.g., via ultrasound. In some cases, the mechano-electrical model may be trained to identify a heart rhythm disorder from a temporally consecutive sequence of ultrasound measurements obtained from a patient. In some instances, the mechano-electrical model may be trained to predict future mechanical movement pattern data from one or more measurements of mechanical movement patterns and / or electrophysiological activation patterns. In some cases, the mechano-electrical model may be trained to predict futureAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 electrophysiological activation pattern data from one or more measurements of mechanical movement patterns and / or electrophysiological activation patterns. In some cases, the mechano-electrical model may be trained (or fitted) to detect the presence of, or to localize, fibrosis or tissue scarring from one or more measurements of mechanical movement patterns and / or electrophysiological activation patterns. In some cases, the mechano-electrical model may be trained to compute myocardial fibrosis or scarring maps from ultrasound data and / or catheter data. In these instances, the myocardial fibrosis or scarring maps may be used for diagnosis and / or to guide treatment, e.g., in the form of ablation procedures. In some cases, the (e.g., ground truth) training data used to train the mechano-electrical model regarding tissue fibrosis and / or scarring associated tasks may be generated using one or more of: MRI with a gadolinium-based contrast agent (commonly called late gadolinium enhancement), MRI without contrast agents (called T1 mapping), and / or PET / CT with fibroblast activation protein inhibitor radiotracers. In some embodiments, the mechano-electrical model may be used in order to, e.g., guide tissue ablation (or another tissue modification technique). For example, methods of the disclosure might include: imaging the heart of a subject using 4D ultrasound in order to generate spatio-temporal mechanical deformation data of the subject’s heart during one or more contractions; inputting the mechanical deformation data into a mechano-electrical model of the disclosure, wherein the output of the model is used to locate tissue associated with an abnormal electrical wave, an abnormal electrical pathway, or scar tissue; and ablating tissue associated with the abnormal electrical wave, the abnormal electrical pathway, or the scar tissue in order to disrupt formation or propagation of the abnormal electrical wave. In some embodiments, the output of the mechano-electrical model is used to locate the origin of an abnormal electrical wave. In some instances, the electrical circuits which give rise to an abnormal electrical wave (e.g., an arrhythmia) may be extremely complex. In these cases, the mechano-electrical model may not be able to locate a single origin and instead may, e.g., identify or locate one or more tissue locations which may be ablated or otherwise modified in order to block the propagation of electrical waves and break up the abnormal pathway / abnormal electrical wave.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 In some embodiments, the mechano-electrical model is trained to simulate a patient’s heart from mechanical movement pattern data, electrophysiological activation pattern data, and / or patient specific data obtained from the patient. Patient or subject specific data may comprise, e.g., demographic data, genetic information, patient history data, structural imaging data, and / or quantitative medical data. In some embodiments, a trained mechano-electrical model may be configured to perform its task in real time as it receives input data. For example, a mechano-electrical model trained to identify heart rhythm disorders from a temporally consecutive sequence of ultrasound measurements may identify heart rhythm disorders in real-time as it receives ultrasound measurements or, e.g., may identify heart rhythm disorders 10 minutes or less after it receives ultrasound measurements including, e.g., 5 minutes or less, or 2 minutes or less, or 1 minute or less, or 10 seconds or less. In some embodiments, several heart beats (e.g., heart contractions) are averaged and / or analyzed to improve temporal resolution. In some embodiments, cardiac gating based on, e.g., ECG signals is used to improve temporal resolution and / or to minimize imaging artifacts caused by cardiac motion. In some embodiments, the mechano-electrical model may input ECG signals and / or may input data from several heart beats to improve temporal resolution and / or to minimize imaging artifacts. In some embodiments, temporal resolution improvement and / or imaging artifact minimization (via, e.g., averaging / analyzing several heart beats and / or ECG signals) may be performed by a separate model (e.g., the optical or ultrasound motion tracking models of the disclosure), and the separate model may feed into the mechano-electrical model in order to improve the performance of the mechano-electrical model. In some embodiments, the mechano-electrical model is trained to work in conjunction with a numerical model in order to simulate a heart (e.g., for drug discovery). In some embodiments, the mechano-electrical model comprises physics- informed neural networks (PINNs). In some embodiments, the mechano-electrical model may be a machine learning model including an artificial neural network (NN). In some embodiments, the machine learning model is a deep learning model. In these cases, the model may be three or more layers deep, such as five or more layers deep, or ten or more, or twelve or more, or thirty or more, or fifty or more, or one hundred orAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 more. In some cases, the mechano-electrical model comprises attention or convolutional mechanisms. In some cases, the mechano-electrical model may be a numerical model and, e.g., the training data of the mechano-electrical model discussed above is used to fit the model or adjust the parameters of the model. For example, the mechano-electrical model may be a differentiable simulation model fitted to data (e.g., fitted to the training dataset discussed above) using, e.g., gradient descent techniques. In some embodiments of the present invention, simulations of focal and reentrant electromechanical activation dynamics in idealized bi-ventricular geometries are generated, and the generated data is used to train a mechano-electrical model (including, e.g., a neural network) to analyze ventricular deformation mechanics and, subsequently, to predict the three-dimensional electrical wave pattern(s) that caused the deformation. Accordingly, next to focal wave patterns, even complicated three- dimensional electrical scroll wave patterns can be reconstructed using the deep learning techniques of this disclosure, even if, e.g., the trained mechano-electrical model has never seen the particular arrhythmia or heart geometry and was trained on a different electrophysiological or mechanical model. Mechano-electrical models, such as deep learning models, of the present invention have the ability to generalize through training on data generated, e.g., with one computational technique (e.g., smoothed particle hydrodynamics (SPH) method) and, subsequently, being applied to data generated with a different computational technique (e.g., finite element method (FEM)). Predictions can be performed in the presence of scars and with significant heterogeneity. With adequate (i.e., sufficient) training data, embodiments of the present invention can be used to calculate intramural action potential wave patterns from imaging data of the motion of the heart muscle. As described above, embodiments of the methods include imaging techniques and apparatuses (e.g., chambers) for fully panoramic stereoscopic imaging of contracting hearts. By ‘fully panoramic’ is meant that all 360° of the surface of the heart (apart from the surface covered, e.g., by mechanisms used to mount or stimulate the heart) is imaged, e.g., while the heart is in motion. By ‘stereoscopic’ is meant each voxel or region of the surface of the heart is imaged from multiple perspectives simultaneously, e.g., using multiple cameras (such that, e.g., stereoscopic algorithmsAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 may be applied for motion tracking the voxels / regions of the surface). The panoramic / stereoscopic optical mapping techniques of this disclosure may generate electrophysiological activation pattern data (obtained via, e.g., imaging of voltage- or calcium-sensitive dyes introduced into the heart) temporally and spatially coupled with mechanical movement pattern data (obtained via, e.g., optically imaging the surface of the heart and / or via 3D ultrasound imaging of the intramural regions of the heart). In some embodiments, the coupled electrophysiological activation pattern data and mechanical movement pattern data may be used to generate training date for, validate the performance of, and / or refine parameters of a mechano-electrical model of this disclosure. In some embodiments, the panoramic and / or stereoscopic optical mapping methods of the disclosure are performed using an imaging apparatus including: an enclosed interior volume into which a tissue is introduced; a substrate on which the tissue is mounted; an electrode for electrically stimulating the tissue; a perfusion subsystem configured to support physiological conditions of the tissue; a plurality of light sources configured for optically illuminating the tissue; an imaging system comprising an optical imaging subsystem configured for obtaining optical images of the tissue; and a plurality of mounts configured for mounting the light sources and claims of the imaging system such that the tissue is evenly illuminated, and the imaging system obtains optical images of the tissue from a plurality of different perspectives. In some cases, the imaging system of the imaging apparatus further includes an ultrasound imaging subsystem configured for obtaining ultrasound images of the tissue. In some embodiments, the imaging apparatus further includes a plurality of electrodes configured to detect electrophysiological activation patterns of the tissue, e.g., by measuring electrocardiograms from the tissue. In some cases, the plurality of mounts are configured for mounting aspects of the imaging system such that every point of the surface of the tissue is imaged from two or more perspectives (i.e., such that stereoscopic motion tracking techniques may be used). In some cases, the imaging apparatus comprises a rig or chamber. The chamber may have a soccer ball geometry or a truncated icosahedron shape and may include, e.g., a plurality of penta- or hexagonal surfaces. In some cases, the imaging apparatusAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 includes a shape with angles of optical axes between two adjacent surfaces of 37.4° or 41.8°. In some embodiments, the optical imaging subsystem includes 6 or more cameras such as, e.g., 10 or more cameras, or 12 or more, or 15 or more, or 20 or more. In some cases, the angle between neighboring cameras is between 35 and 45°. In some embodiments, the optical imaging subsystem comprises a plurality of CCD or CMOS cameras. In some instances, the optical imaging subsystem is configured for measuring changes in fluorescence of aspects of the tissue such including, e.g., in response to a physiological change of the tissue. The physiological change may include a change in transmembrane potential of the tissue. In some embodiments, the ultrasound imaging subsystem is configured for obtaining ultrasound images of the tissue at extremely rates such as, e.g., a rate of 100 volumes per second or more, or 200 volumes per second or more, or 500 volumes per second or more, or 100 volumes per second or more, or 2000 volumes per second or more, or 300 volumes per second or more, or 5000 volumes per second or more, or 5200 volumes per second or more. some embodiments, the ultrasound imaging subsystem is configured for obtaining ultrasound images of the tissue with high spatial resolution. As discussed above, existing methods of creating electrophysiological and mechanical movement cardiac data are incapable of producing training data-sets of sufficient size, quality, or heterogeneity to train a mechano-electrical model of this disclosure (e.g., a model capable linking electrophysiological cardiac tissue dynamics to mechanical cardiac tissue dynamics). In order to generate training data sufficient for the creation of a robust and effective mechano-electrical model, the panoramic and / or stereoscopic optical mapping methods of the disclosure may be used (see, e.g., FIG. 17A). In this way, the panoramic / stereoscopic optical mapping methods of the disclosure may be compared to, e.g., the final piece of a puzzle enabling the creation of the mechano-electrical models of this disclosure. In some cases, the EWD models, optical motion tracking models, and ultrasound motion tracking models of the disclosure may be used to further enhance the performance of mechano-electrical models of this disclosure (see, e.g., FIGS.18 and 19). For example, the EWD models, optical motion tracking models, and ultrasound motion tracking models, in combination with the panoramic stereoscopic optical mapping methods, may be combined via, e.g., a trainingAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 network or web, or an iterative improvement loop, in order to enhance or refine mechano-electrical model training data and / or mechano-electrical model performance. Further, similar to the enabling nature of the panoramic / stereoscopic optical mapping techniques for the mechano-electrical model, the panoramic / stereoscopic optical mapping techniques discussed above may enable the creation of training data sufficient for the creation of the optical motion tracking models and / or ultrasound motion tracking models of the disclosure (see, e.g., FIG.17B). FIGS.1 and 2 provide flow diagram for practicing methods of modeling mechanical movement patterns and electrophysiological activation patterns of a tissue in accordance with an embodiment of the disclosure. FIGS.3A to 3C depict a distribution matching of in silico, ex vivo and clinical training data with sparse, heterogeneous, and out-of-distribution data to achieve generalization in accordance with an embodiment of the disclosure. In some cases, training data (such as, e.g., electromechanical data, electrophysiological data, fluorescence data, mechanical deformation data, and / or ultrasound data, depending on the model) may be combined based, e.g., on observations of the panoramic stereoscopic optical mapping experiments of the disclosure. The combined data set is adjusted, combined, refined, and augmented in order to generalize a model or, i.e., to enable the model to learn underlying dynamics of a phenomena rather than simply the dynamics of a specific data generating modality. FIGS.4A to 4B depict training data generation for the mechano-electrical model using electromechanical simulations with randomized initialization of focal or reentrant ventricular arrhythmias. The training data enables the mechano-electrical model to reconstruct cardiac excitation waves from tissue deformation. FIGS.5A to 5B illustrate both the ‘forward’ (FIG.5A) and the ‘inverse’ (FIG.5B) mechano-electrical problem addressed by the mechano-electrical models of this disclosure. FIG.6A provides a block diagram of a mechano-electrical model and a training data set of paired electrophysiological data (including, e.g., electrophysiological activation patterns) and mechanical deformation data (including, e.g., mechanical movement patterns) used to train the mechano-electrical model. The electro-Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 physiological data and mechanical deformation data varies depending on the function of the mechano-electrical model (i.e., the task the mechano-electrical model will be applied to perform). For example, the mechanical deformation data may comprise consecutive ultrasound measurements when training the mechano-electrical model to predict future deformation states and / or future electrical wave states from mechanical or electrophysiological wave measurements. FIG.6B demonstrates an example of potential in silico data that may be included in a mechano-electrical model training dataset. Multiple different electrical models (e.g., numerical electrical models and / or EWD models of this disclosure) are used to generate electrophysiological data. The electrophysiological data is then used by multiple different mechanical models (e.g., numerical mechanical models and / or motion tracking models of this disclosure) to generate mechanical deformation data. In embodiments where the mechano-electrical model is applied to ultrasound measurements, training data may be generated via an ultrasound motion tracking model used in conjunction with a numerical mechanical model. For example, the ultrasound motion tracking model may be used to generate synthetic ultrasound data from the mechanical deformation data output by the numerical mechanical model. FIGS.7A to 7B illustrate a self-supervised deep learning-based approach for solving the ‘inverse’ mechano-electrical problem in accordance with an embodiment of the disclosure. FIG.7A depicts a deep neural network (AI) for the reconstruction / prediction of electrical excitation waves (right) from deformation (left). FIG.7B illustrates Training with many thousands of pairs of mechanical and electrical data. The neural network memorizes many different electrical patterns, which caused corresponding deformation patterns, and can then subsequently be applied to new data. FIGS.8A to 8C depict computer simulations used to generate training data for a mechano-electrical model in accordance with an embodiment of the disclosure. FIG.8A shows 1,000 different ventricular geometries used to perform 50,000 unique simulations. FIG.8B illustrates the cardiac excitation-contraction-coupling mechanism that connects electrical and mechanical dynamics in the heart. FIG.8C shows a mechano-electrical model that may be used, e.g., to predict subsequent mechanical or electrical states from measured deformation data. Left: 3D motion of the heart. Center:Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Predictions of electrical waves (dark: depolarized phase of action potential) obtained with AI (NN: neural network). Right: Ground-truth generated in simulations. The ground- truth was used to compute the deformations and motion vectors on the left. FIGS.9A to 9C show reconstruction of electrical excitation waves from mechanical deformation using both a deep neural network and numerical modeling. FIG.9A illustrates a deep neural network (AI) (i.e., a mechano-electrical model) for the reconstruction of electrical excitation waves from deformation. FIG.9B provides a numerical reconstruction of focal excitation wave from deformation in 2D, the reconstruction being visually indistinguishable from the original. FIG.9C depicts reconstruction of 3D scroll wave chaos (VF) with very good match between reconstructed (black) and original (gray) vortex filaments. FIGS.10A to 10B illustrate electrical 3D activation patterns causing unique time- varying 3D contraction patterns. FIG.10A shows an electrical 3D activation pattern (action potential wave) causing FIG.10B unique, fingerprint-like time-varying 3D contraction patterns (displacement vectors indicating motion), from which in turn a specially trained mechano-electrical model of the disclosure will be able to compute the original action potential wave. FIG.11A provides a block diagram illustrating the use of an electrical wave dynamics (EWD) model to train a mechano-electrical model in accordance with an embodiment of the disclosure. In these instances, the EWD model may be applied in order to create a training dataset for the electro-mechanical model of this disclosure. For example, the EWD model may be used to generate 3D electrical wave mechanics from 2D clinical catheter-based measurements, fill in missing data obtained from clinical imaging techniques, adjust experimental data, inpaint randomly deleted sections of electrical numerical model simulations, generate electrophysiological activation patterns (such as, e.g., scroll waves), etc. FIG.11B provides a block diagram illustrating the use of an optical motion tracking model to train a mechano-electrical model in accordance with an embodiment of the disclosure. In these instances, the optical motion tracking model may be applied in order to create a training dataset for the electro-mechanical model of this disclosure. For example, the optical motion tracking model may be applied to optical measurementsAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 (e.g., images) obtained during optical mapping experiments (such as, e.g., the panoramic optical mapping experiments of this disclosure) in order to obtain more accurate ground-truth mechanical deformation data. FIG.12A provides a block diagram illustrating the use of an ultrasound motion tracking model to train a mechano-electrical model in accordance with an embodiment of the disclosure. For example, clinically obtained ultrasound measurements may be input into the ultrasound tracking model in order to generate or determine the position and / or motion of a discrete area or voxel of a tissue in relation to all the other areas / voxels of the tissue (i.e., mechanical deformation data). The positions and / or motions of the areas / voxels output by the ultrasound tracking model may be coupled with electrophysiological data obtained from catheter-based measurements simultaneously generated with the ultrasound measurements in order to obtain paired electromechanical training data. In some cases, the ultrasound tracking model may be used to generate synthetic ultrasound data, e.g., from numerical mechanical model simulations (e.g., as discussed above) in order to train the mechano-electrical model to predict electrophysiological cardiac tissue dynamics (e.g., intramural electrical waves) directly from ultrasound measurements. FIG.12B provides a block diagram illustrating the use of an optical motion tracking model to train an ultrasound motion tracking model in accordance with an embodiment of the disclosure. In some embodiments, the optical motion tracking model may be applied in order to create a training dataset for the ultrasound motion tracking model. For example, optical measurements temporally coupled with ultrasound measurements obtained, e.g., via the panoramic optical mapping experiments of the disclosure may be used to generate ‘ground truth’ training data for the ultrasound motion tracking model. FIGS.13A to 13E illustrate ex vivo electromechanical imaging of arrhythmias to obtain training data for AI in accordance with an embodiment of the disclosure. FIGS. 13A-13B show 3D-printed heart chamber with 16, 24 or 32 windows for multi-camera optical mapping. FIG.13C depicts a CMOS camera with LEDs. FIGS.13D illustrates stereoscopic 3D optical mapping of ventricles. FIG.13E provides ventricular contractions imaged using 4D ultrasound at high speeds in order to produce a 3DAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 reconstruction of cardiac tissue (which may, e.g., then be used to predict an electrical activation sequence or overlay an imaged / observed electrical activation sequence over the 3D reconstruction). FIG.14 depicts electromechanical high-resolution imaging of arrhythmias ex vivo using panoramic fluorescence and 4D ultrasound imaging in accordance with an embodiment of the disclosure. FIGS.15A to 15D show ex vivo electromechanical imaging of arrhythmias, using 16-camera high-speed panoramic fluorescence imaging and highspeed 4D ultrasound, to obtain training data for an inverse mechano-electrical model in accordance with an embodiment of the disclosure. FIGS.15A, 15C and 15D depict a 16-camera high-speed panoramic fluorescence imaging setup and FIGS.15B, 15C and 15D illustrate highspeed 4D ultrasound to obtain training data for inverse AI (i.e., training an mechano-electrical model of the present disclosure). FIG.16 depicts ultrasound imaging during catheter ablation procedures in humans in accordance with an embodiment of the disclosure. FIG.17A depicts a block diagram of stereoscopic panoramic multi-camera optical mapping being used to train and / or validate a mechano-electrical model in accordance with an embodiment of the disclosure. In some cases, stereoscopic multi- camera optical mapping is used to produce paired electrophysiological data (e.g., measurements of action potential (AP) waves or wave fronts, calcium waves or wave fronts, etc.) and mechanical deformation data (e.g., measurements of motion including, e.g., three-dimensional motion vectors of tissue movement) used to train the mechano- electrical model. In some embodiments, paired electrophysiological and mechanical deformation data (i.e., electromechanical data) is used to evaluate or validate a trained mechano-electrical model. For example, mechanical deformation data of an experimentally obtained electromechanical dataset may be input into the mechano- electrical model in order to predict electrophysiological data. The predicted electrophysiological data may then be compared with the corresponding electrophysiological data of the electromechanical dataset (i.e., the experimentally obtained electrophysiological data corresponding with the input mechanical deformation data) in order to evaluate or validate the mechano-electrical model. The evaluation of the mechano-electrical model may then be used to, e.g., alter the distribution of in silico,Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 ex vivo and clinical training data used to train the mechano-electrical model. In some cases, the evaluation of the mechano-electrical model may be used to adapt or configure the stereoscopic panoramic multi-camera optical mapping to generate data better suited for mechano-electrical model training or refinement. For example, certain pacing regiments may be applied by a stimulation electrode of the stereoscopic panoramic multi-camera optical mapping methods based on the evaluation in order to better train the mechano-electrical model to capture, e.g., a specific electrical wave dynamic. In some embodiments, electromechanical data obtained via panoramic stereoscopic multi-camera optical mapping may be used to, e.g., adjust parameters of numerical simulations used to generate the mechano-electrical training data, adjust augmentation of the mechano-electrical training data (e.g., refine synthetic noise to better capture experimentally observed phenomena), and / or otherwise refine or curate the mechano-electrical training data. FIG.17B depicts a block diagram of stereoscopic multi-camera optical mapping being used to train and / or validate an optical motion tracking model in conjunction with an ultrasound motion tracking model, in accordance with an embodiment of the disclosure. In some embodiments, stereoscopic multi-camera optical mapping may be used to produce optical measurements temporally coupled with ultrasound measurements, which may be used to generate ground truth training data (comprising, e.g., mechanical deformation data paired with ultrasound data) for the ultrasound motion tracking model. The ground truth training data of the ultrasound motion tracking model may be generated using, e.g., numerical stereoscopic motion tracking techniques or the optical motion tracking model. In some embodiments, stereoscopic multi-camera optical mapping may be used to produce optical measurements temporally coupled with mechanical deformation data, which may be used to generate ground truth training data for the optical motion tracking model. The ground truth training data of the optical motion tracking model may be generated using, e.g., numerical stereoscopic motion tracking techniques. In some embodiments, the numerical (e.g., stereoscopic) motion tracking techniques are accelerated by leveraging the capabilities of modern graphics processing units (GPUs).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIG.18A shows an optical motion tracking model, an ultrasound motion tracking model, and panoramic stereoscopic optical mapping connected together in a training network or training loop in order to iteratively refine a mechano-electrical model in accordance with an embodiment of the disclosure. In a similar manner as described for FIG.17A, the stereoscopic panoramic multi-camera optical mapping may be used to train and / or validate the mechano-electrical model, and in a similar manner as described for FIG.17B, the stereoscopic panoramic multi-camera optical mapping may be used to train and / or validate the optical motion tracking model and / or the ultrasound motion tracking model. Further, in a similar manner as described for FIGS.11B and 12B, the ultrasound motion tracking model and the optical motion tracking model may be used to train the mechano-electrical model. In some embodiments, each model achieves better performance every time the stereoscopic panoramic multi-camera optical mapping is performed, which, in turn further elevates downstream models (i.e., models wherein training is affected by a different model, e.g., the ultrasound motion tracking model relative to the optical motion tracking model in FIG.18A), culminating in significant improvements to the mechano-electrical model each iterative performance of the stereoscopic panoramic multi-camera optical mapping. Further, although not depicted in FIG.18A, the mechano-electrical model may be used to train the ultrasound motion tracking model and / or the optical motion tracking model. Accordingly, the training network or training loop formed by the models may include synergistic effects that improve the performance of each model relative to what could be accomplished if each model were to be evolved or refined separately. FIG.18B shows an ultrasound motion tracking model, an EWD model, and panoramic stereoscopic optical mapping connected together in a training network or training loop in order to iteratively refine a mechano-electrical model in accordance with an embodiment of the disclosure. In a similar manner as described for FIG.17A, the stereoscopic / panoramic multi-camera optical mapping may be used to train and / or validate the mechano-electrical model, and in a similar manner as described for FIG. 17B, the stereoscopic / panoramic multi-camera optical mapping may be used to train and / or validate the ultrasound motion tracking model. Further, in a similar manner as described for FIGS.11A and 12B, the ultrasound motion tracking model and the EWDAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 motion tracking model may be used to train the mechano-electrical model. In some embodiments, the stereoscopic panoramic multi-camera optical mapping may be used to train and / or validate the EWD model. For example, a plurality of detecting / measuring electrodes may be positioned within a tissue of an optical mapping experiment such that surface electrophysiological data (obtained via, e.g., imaging voltage- or calcium- sensitive dyes) paired with intramural electrophysiological data (obtained via the plurality of measuring electrodes) may be used to generate ground truth training data for the EWD model. In some embodiments, each model achieves better performance every time the stereoscopic / panoramic multi-camera optical mapping is performed, which, in turn further elevates downstream models, culminating in significant improvements to the mechano-electrical model each iterative performance of the stereoscopic / panoramic multi-camera optical mapping. Further, although not depicted in FIG.18B, the mechano-electrical model may be used to train the ultrasound motion tracking model and / or the EWD model. Accordingly, the training loop formed by the models may include synergistic effects that improve the performance of each model relative to what could be accomplished if each model were to be evolved or refined separately. FIG.19A shows an embodiment of a training network or training loop formed by an EWD model, an optical motion tracking models, an ultrasound motion tracking model and panoramic / stereoscopic optical mapping and used in order to iteratively refine a mechano-electrical model in accordance with an embodiment of the disclosure. Similar to as was described for FIGS.11-12 and 17-19, the training loop formed by the models may include synergistic effects that improve the performance of each model relative to what could be accomplished if each model were to be evolved or refined separately. FIG.19B shows an alternate configuration of the ultrasound tracking model being used with the mechano-electrical model in order to, e.g., predict three-dimensional electrical wave dynamics from clinically obtained ultrasound data. In this instance, clinically obtained ultrasound data may be input into the ultrasound tracking model in order to generate or determine the position and / or motion of each discrete area or voxel of a tissue in relation to all the other areas / voxels of the tissue. The positions and / or motions of the areas / voxels output by the ultrasound tracking model may then be input into theAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 mechano-electrical model in order to for the mechano-electrical model to, e.g., predict three-dimensional electrophysiological activation patterns from the ultrasound data. FIG.95 depicts how 4D ultrasound and computed three-dimensional motion vectors of tissue movement may be used in order to predict electrical wavefront propagation and calculate electrical activation maps. For example, optical flow estimation techniques or differentiable motion estimation techniques (including, e.g., the optical motion tracking models discussed above) may be applied, e.g., to compensate for tissue movement and / or to generate optical motion vectors from optically obtained data (obtained via, e.g., the panoramic stereoscopic mapping techniques of the disclosure). The mechano-electrical model may then be applied, e.g., in order to predict electrical wavefront propagation and calculate electrical activation maps from the 4D ultrasound data and / or the three-dimensional motion vectors of tissue movement. In some embodiments, the 4D ultrasound data may be used to compute three-dimensional motion vectors of tissue movement. FIG.96 illustrates how 3D optical surface reconstructions and electrophysiology, in combination with 3D ultrasound, is used to map a surface mesh onto ultrasound datapoints of the heart and compute three-dimensional motion vectors of tissue movement. In some embodiments, the 3D optical surface reconstructions, electrophysiology, and / or 3D ultrasound data may be generated, e.g., using the panoramic stereoscopic mapping techniques of the disclosure. The generated data (including, e.g., the mapped surface mesh and computed three-dimensional motion vectors) may be used in order to train a mechano-electrical model of the disclosure (or, similarly, fit a differentiable simulation mechano-electrical model of the disclosure) Applications and Training Schemes Mechano-Electrical Reconstructions Using 4D Ultrasound: Embodiments of the present invention comprise training a machine learning model (i.e., an AI) that can recognize the electrophysiological processes underlying heart rhythm disorders based on, for example, ultrasound videos—an approach that is highly unconventional. The AI may be trained with high-resolution training data of heart rhythm disorders generated in a laboratory with intact, isolated hearts. Using unique exAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 vivo imaging setup, electrophysiological and tissue-mechanical phenomena can be measured at unprecedented resolutions, which are currently unattainable in humans. In other words, embodiments of the present invention relate to an approach that is comparable to the approach used by developers of self-driving cars. These developers generate training data for AI-assisted driving, collecting extensive video and other sensor data. Based on the data, the AI then learns to ‘drive a car’. Machine learning models in embodiments of the present invention learn to predict the underlying electrophysiology of cardiac arrhythmias. Trained with high-resolution data, the AI will become highly specialized in recognizing the spatio-temporal organization of heart rhythm disorders and visualizing their dynamics in 3D over time (= 4D) at rapid speeds throughout the entire organ. Based on its training in a laboratory, the AI can then be applied ‘in the wild’ and visualize the same processes in human patients during ultrasound examinations. The heart’s contractions are triggered by electrophysiological waves, or action potential waves, which propagate rapidly through the heart muscle and initiate the release of intracellular calcium, which in turn is involved in the generation of active contractile stress in cardiac muscle cells via the so-called cellular ‘excitation-contraction coupling mechanism’. Traditionally, cardiologists are interested in the electrophysiological wave phenomena because they reveal potential causes of heart rhythm disorders, and their visualization can guide therapies such as catheter ablation. However, it is difficult and time-consuming to visualize the heart’s electrical activity because it requires inserting electrodes into a patient’s heart and measuring the activity point by point across the heart surface. This procedure can take up to several hours and is invasive. By contrast, embodiments of the present invention are based on the idea that, because the heart’s contractions and deformations are triggered by electrophysiological waves, inversely these waves can be computed by analyzing the heart’s contractions and deformations. The heart’s motion can be visualized routinely non-invasively using high-speed three-dimensional (3D + t = 4D) ultrasound. However, thus far ultrasound cannot visualize electrophysiological waves, but merely display motion. Embodiments of the present invention change that. Recent work has found i) that the heart’s global electrophysiological and mechanical dynamics are highlyAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 correlated even during complex heart rhythm disorders and ii) that ultrasound can be used to visualize the mechanical fingerprints of electrophysiological vortex phenomena during cardiac fibrillation (see, e.g., Example 1 of this disclosure, provided below). Even more importantly, it has been found iii) that deep learning can accurately ‘predict’ electrophysiological wave phenomena from simulated tissue deformation at high resolutions (see, e.g., Example 3 of this disclosure, provided below), even if the deformations exhibited by the heart muscle during heart rhythm disorders are highly complex. The latter aspect is particularly exciting, because the three-dimensional electrophysiological wave phenomena, that are underlying heart rhythm disorders such as atrial or ventricular fibrillation, degenerate into complex spatio-temporal electrical chaos and cause very irregular and complex deformation patterns. Embodiments of the present invention are able to solve this ‘inverse problem’ with computer simulations. They can do so because the machine learning models have been trained with tens of thousands of examples of heart rhythm disorders from which they learned to associate an electrical state with a given deformation. After training, machine learning models of embodiments of the present invention can predict any ‘electrical circuit’ underlying a particular rhythm from the heart’s motion, even if it has never seen this individual rhythm and although the relationship between tissue deformation and electrophysiology is highly complex, the arrhythmia potentially chaotic, and in each individual case unique. The central hypothesis underlying embodiments of the present invention is that the motion and deformation of the heart contains a wealth of information, which - if captured in a 4D measurement and analyzed properly - is unique enough to be able to compute the 4D electrophysiological dynamics causing the heart rhythm disorder. Subsequently, training a machine learning model (i.e., an AI) to learn the complex relationship between cardiac electrics and tissue mechanics from a well-curated 4D imaging dataset obtained under laboratory conditions and undergirded by clinical and simulated data, will enable the AI to predict any electrical activation pattern from any deformation in any heart. Just as AI can recognize objects, faces, speech or handwritten text and any other complex high-dimensional feature in data, embodiments of the present invention comprising a specially trained AI will also be able to recognizeAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 any heart rhythm disorder solely by observing 4D ultrasound data. Embodiments of the present invention are developed with intact isolated hearts. A first training dataset with isolated (rabbit, pig, and human) hearts using 4D ultrasound and panoramic voltage- sensitive fluorescence imaging have been developed in connection with embodiments of the present invention. Both modalities generate ex vivo training data, which can be mixed with in silico and human training data generated in computer simulations and in the clinical setting. Embodiments of the present invention may be useful in providing diagnostics that could be performed non-invasively and in real-time (compared to 30-90 minutes) and the approach could be used complementarily to conventional electrical catheter mapping to guide catheter ablation or other forms of therapy. AI-enabled 4D ultrasound-based mapping of electrical ventricular tachycardia circuits Embodiments of the present invention establish an entirely novel ultrasound- based imaging technique utilizing artificial intelligence (AI) for the non-invasive, transmural visualization and diagnosis of the 3D morphology of ventricular arrhythmias. The imaging will supersede existing mapping techniques, as it will produce 3D visualizations of heart rhythm disorders in real-time and provide novel insights into the origins and driving mechanisms of heart rhythm disorders. Despite significant progress in the field of biomedical imaging, imaging of heart rhythm disorders remains a major technological and scientific challenge. Understanding the origins and underlying mechanisms of heart rhythm disorders is pivotal in the planning of therapeutic interventions. Currently, heart rhythm disorders, such as atrial fibrillation (AF) or ventricular tachycardia (VT), are routinely diagnosed using catheter- based mapping. Catheter-based measurements are time-consuming and typically provide information about the heart’s abnormal electrical activity on its surface. However, the electrical wave phenomena associated with ventricular arrhythmias are inherently three-dimensional phenomena evolving deep within the cardiac muscle, where they often interact with an arrhythmogenic substrate (e.g. scar tissue) in locations that are inaccessible to standard catheter mapping.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Embodiments of the present invention comprise a novel AI-enabled and 4D (time-varying 3D) ultrasound-based imaging approach for the non-invasive and in-depth visualization of heart rhythm disorders. The imaging approach is based on the idea that, because the heart’s contractions and deformations are triggered by electrical activity, inversely this electrical activity can be computed by analyzing the heart’s deformations. The imaging approach is enabled by AI, which will learn and translate this complex relationship; embodiments of the present invention utilize high-resolution multi-modal optical mapping of voltage, calcium and strain in intact, isolated hearts, and are combined with 4D ultrasound. With this powerful methodological approach, embodiments of the present invention are able to correlate electrophysiological and mechanical tissue dynamics at high resolutions and develop an inverse computational reconstruction technique that is able to decipher the heart’s complex deformations. Based on this analysis, the imaging approach will provide high-resolution numerical reconstructions of the arrhythmic electrical phenomena throughout the ventricular heart muscle. The central hypothesis underlying embodiments of the present invention is that the motion and deformation of the heart contains a wealth of information, which can serve like a fingerprint of an arrhythmia, and which – if captured in a 4D measurement and analyzed properly - is unique enough to be able to compute the 4D morphology of the electrical dynamics causing the arrhythmia. Subsequently, training a machine learning model (i.e., an AI) to learn the complex relationship between cardiac electrics and mechanics from a well-curated 4D imaging dataset obtained ex vivo under laboratory conditions and undergirded by synthetic data generated in computer simulations, will enable the AI to predict any electrical activation pattern from any deformation in any heart. Just as AI can recognize objects, faces, speech or handwritten text and any other complex high-dimensional feature in data, embodiments of the present invention comprising a specially trained AI will also be able to recognize any arrhythmia morphology or electrical circuit solely by observing 4D ultrasound data. The AI will be able to recognize the 3D arrhythmia morphology even though arrhythmias are chaotic in nature and will be different and unique in each patient.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Background: The heart’s contractions are triggered by action potential waves, which propagate rapidly from cell to cell and through the heart muscle and lead via the excitation-contraction coupling mechanism to macroscopic deformations of the heart muscle. Heart rhythm disorders are caused by abnormal electrical waves, which may degenerate into complicated, disorganized, self-sustained wave patterns that initiate irregular and persistent contractions of the heart muscle. These waves are conjectured to take on the shapes of rotating scroll waves or ‘rotors’ during reentrant ventricular arrhythmias. However, the precise origin of triggers and the three-dimensional morphology of arrhythmic electrical circuits remains often insufficiently understood, because imaging technology able to resolve the waves throughout the heart muscle does not exist. Modern ultrasound imaging can provide high-speed 4D videos of the entire heart at resolutions sufficient to resolve even the rapid, small irregular contractions during ventricular fibrillation. However, ultrasound provides solely images of the motion of the heart and does not provide electrical information. Current State-of-the-Art: The current state-of-the-art for the imaging of heart rhythm disorders is electro-anatomic catheter-mapping, which provides measurements of electrical activity in locations sparsely distributed across the heart surface. Catheter mapping is time-consuming as the mapping needs to be performed sequentially, point- by-point to obtain high-resolution maps. Procedural times are typically 30-90 minutes to map an arrhythmia. The measurements are superficial and prone to motion-related artifacts and maps cannot distinguish epi-, endo- or intracardial signal. Intramural measurements using needle electrode catheters are performed in specialized cardiac electrophysiology laboratories to identify intramural, often isthmus-related origins of VTs in patients with ischemic cardiomyopathies (ICM) but are not routinely done in most electrophysiology laboratories because these catheters are not commercially available and require significant time and expertise to perform. An alternative imaging technique is inverse electrocardiography, which involves recording body surface electrical potentials to calculate potentials on the heart surface. However, the technique provides indirect measurements and requires further validation. Both techniques require 3D location sensors or imaging data (e.g. CT or MRI) to create electro-anatomic maps. In the laboratory, heart rhythm disorders can be studied with optical mapping, whichAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 provides highly detailed visualizations of the heart’s electrical activity but fails to image activity deep within the cardiac muscle, similarly as clinical techniques. Optical mapping is limited by low penetration depths of light in tissue and involves toxic substances and can therefore not be used in patients. Embodiments of the present invention address a very significant challenge within cardiovascular medicine, and a long-standing problem within biomedical engineering: the non-invasive and in-depth visualization of cardiac arrhythmias. Currently, no experimental method exists that can visualize three-dimensional, transmural electrical activity of the heart non-invasively. The inventors have shown that 4D ultrasound imaging can resolve the electromechanical phenomena underlying cardiac fibrillation, and that this technique could - if combined with AI - provide high-resolution, three- dimensional visualizations of heart rhythm disorders non-invasively, in real-time and with high precision (see, e.g., Examples 3, 6 and 7 of this disclosure, provided below). The proposed 4D imaging approach is expected to supersede existing cardiac mapping approaches and could greatly advance the diagnosis of heart rhythm disorders and be used to guide therapeutics, such as catheter ablation, more reliably and effectively. For example, while simple reentrant arrhythmias (e.g. “AVNRT”, “AVRT”, atrial flutter) are easily mapped and ablated with high success, complex reentrant arrhythmias (e.g. ischemic VT, polymorphic VT, persistent AF or VF) are not easily mapped and ablated clinically. In some cases, the imaging technique could provide highly detailed live 4D visualizations of these heart rhythm disorders, while guiding more targeted, intracardial ablation procedures. Independent of its potential transformative clinical impact, embodiments of the present invention will open doors to a novel field with extraordinary potential in unraveling cardiac arrhythmia mechanisms. High-Resolution 4D Ultrasound-based Imaging of Electromechanical Rotors during Ventricular Fibrillation (VF) Ex Vivo: The inventors have demonstrated ex vivo that it is possible to image and characterize the electrical and mechanical phenomena underlying ventricular fibrillation (VF) at unprecedented resolutions using 4D ultrasound and panoramic optical mapping. By imaging the fibrillating heart with both imaging techniques simultaneously, the inventors were able to show that the heart’s mechanical strain and electrophysiological dynamics are very similar during VT, polymorphic VTAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 and VF. More specifically, the inventors found that rotating action potential and calcium waves observed on the heart’s ventricular surface cause similarly rotating strain waves, suggesting that the cellular excitation-contraction coupling mechanism can lead to highly correlated electrophysiological and mechanical phenomena on the tissue and organ scale. The experimental findings suggest that it is possible to compute electrophysiological wave phenomena from the heart’s muscle deformations. AI for Solving the ‘Inverse Mechano-Electrical Problem’: Recently it has been demonstrated in computer simulations that it is possible to cross-estimate or predict electrical excitation wave phenomena from tissue deformation that was caused by the electrical wave phenomena. In these proof-of-principle studies, two inverse numerical approaches were developed, one knowledge- or physics-based and one self-supervised deep learning-based approach, to solve the ‘inverse mechano-electrical problem’, in simulated 2D and 3D bulk-shaped tissues. While the physics-based approach employed a replicate biophysical model that assimilates mechanical observation data to drive an internal reproduction of the original electrical dynamics, the deep learning approach employed an encoder-decoder-like convolutional neural network (CNN) that was trained on many thousands of pairs of mechanical and corresponding electrical data. While both approaches can successfully compute electrical wave phenomena from tissue deformation, the inventors found that deep learning outperforms the physics-based approach (90-95% vs.75-85% accuracy). Key to embodiments of the present invention, a self-supervised deep learning algorithm trained on a large electromechanical dataset can easily associate the underlying electrical pattern with an observed deformation pattern although their relationship is highly complex, and the dynamics are chaotic and in each individual case unique. The inventors found that a neural network can reliably predict even complicated electrical scroll wave chaos, the type of wave dynamics conjectured to underlie VF, with high precision even with measurement noise and at low spatial resolutions. The results suggest that an AI may equally be able to predict the 3D morphologies of electrical circuits during VT from the heart’s rapid deformations. 4D Ultrasound Imaging during Ventricular Tachycardia (VT) in Humans: It has been demonstrated that 4D ultrasound can be applied during VT ablation procedures in human patients. It was found that with transthoracic 4D ultrasound the spatial andAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 temporal resolutions and image quality are sufficient to resolve arrhythmic ventricular wall motion and deformation during VT, while mapping the heart’s endocardial surface using basket catheters (unpublished). Simultaneous Imaging of Voltage, Calcium and Strain in Contracting Cardiac Tissue using Optical Imaging and Computer Vision: Optical mapping of the heart using voltage-and / or calcium-sensitive fluorescent dyes is widely used in basic cardiovascular research. However, until recently it was not possible to perform optical mapping with contracting hearts. Instead, the heart’s contractile motion had to be inhibited using pharmacological excitation-contraction uncoupling agents such as Blebbistatin. Embodiments of the present invention relate to optical and computer vision techniques, with which it is possible to measure action potential and calcium waves together with tissue strain at high spatial resolutions on the strongly contracting 3D deforming heart surface using multi-camera optical mapping systems. Embodiments of the present invention combine computational, cardiovascular and bioengineering methods and clinical imaging. Embodiments of the present invention will consist of i) generating high-resolution in silico, ex vivo and in human electromechanical data of the heart’s arrhythmic electrical and mechanical 4D dynamics to identify and characterize a universal mapping between these two dynamics and ii) developing an AI algorithm, which can translate 4D cardiac mechanics into electrophysiological activation dynamics. The algorithm will ultimately be able to predict these electrical dynamics from 4D imaging data produced with a commercial ultrasound system. Solving the Inverse Mechano-Electrical Problem in Computer Simulations of Ventricular Arrhythmias: Using a combination of computer simulations and inverse numerical reconstruction techniques, embodiments of the present invention compute electrophysiological wave phenomena, such as action potential or calcium waves, from the 3D deformations of the ventricles of a simulated heart. Embodiments of the present invention may be used to explore first i) in simplified ventricular geometries, which deform due to focal and reentrant ventricular arrhythmias (VT) created with phenomenological models, and next ii) in more realistic ventricular and whole heart geometries and models with more complex arrhythmias (e.g. poly-morphic VT or VF)Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 and pathophysiology created with more detailed models. Embodiments of the present invention may apply the AI-enabled inverse numerical re-construction technique to the simulated data and aims at further refining the technique. Embodiments of the present invention may i) Provide a proof-of-concept in silico for ventricular arrhythmias to compute 3D electrophysiological morphologies of arrhythmias, as well as locate arrhythmia origins from tissue motion in real-time. ii) Perform these computations in or close to real-time2 (data rate and voxel numbers in computer simulations are comparable to ultrasound imaging) using state-of-the-art GPU (graphics processing unit) hardware. Embodiments of the present invention may be used to generate synthetic simulated training data for the training of a deep learning model (e.g. encoder-decoder-like 3D-CNN), which is consequently specialized in computing 3D electrical activation dynamics from the heart’s 3D / 4D tissue motion and deformation. In embodiments, it is possible to generate sufficiently large training data sets (2-4TB, >10,000 samples) with phenomenological computational models within 3-5 days computing time. The simulations will initially exclude heterogeneity and other tissue abnormalities to focus solely on the mapping between mechanics and electrics given a particular arrhythmia morphology in an otherwise idealized situation. As the project progresses, simulations will include more intricate scenarios (e.g. scar tissue, slow conduction channels, dissociation phenomena between voltage and calcium, etc.) and the simulations will be refined to match experimental data. High-Resolution Ex Vivo Training Data Generation and First Proof-of-Principle in Intact Excised Porcine Hearts: One of the central goals of embodiments of the present invention is to produce high-resolution optical mapping data of arrhythmic hearts in a unique ex vivo imaging environment as training or development data. Intact, isolated porcine hearts (N=50) may be imaged in a Langendorff-perfusion and / or working heart setup. Hearts may be imaged from all sides with up to 32 high-speed CMOS cameras at speeds of 500 fps, measuring voltage and / or calcium. Simultaneously, the hearts may be imaged at speeds of up to 180 volumes per second using high-speed 4D ultrasound (Siemens Acuson SC2000). The two imaging data types may be cross-registered, such that the 3D voltage- and / or calcium-sensitive optical maps can be compared with the volumetric ultrasound data showing the heart’s 3D wall motion within the sameAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 coordinate system. Embodiments of the present invention may be used to generate 4D high-resolution electromechanical data of the arrhythmic heart ex vivo. Embodiments of the present invention may be used to process data in such a way that it can i) be used to create and be assimilated into biophysical computer models, ii) be used to create data-driven computer models and, ultimately, be iii) used to develop an AI-based reconstruction technique. Ultimately, embodiments of the present invention may comprise training an AI with a mix of in silico and ex vivo data and apply the AI to unseen ex vivo or in human data to predict electrical activation patterns from the mechanical deformations with the same precision and at the same high resolutions that are attainable with optical mapping. The high-resolution optical mapping measurements may be used as the ‘ground truth’ to cross-validate the estimated reconstruction results. A secondary goal will be to extrapolate missing electrical data within the volume of the heart from surface observations during polymorphic VT or VF with epi-endocardial dissociation. First Application In Human: Embodiments of the present invention may be used to gather in human data during VT ablations (N=60). The data may be acquired together with cardiologists using transthoracic or transesophageal 4D ultrasound (Siemens Acuson SC2000 system used for ex vivo imaging is also available in the clinic) as well as electro-anatomical catheter-mapping. The in human data may be cross-registered with electrical mapping data to compare electrical and mechanical arrhythmia morphologies and to use the data for the development and training of an AI-based reconstruction approach. Embodiments of the present invention may be used: i) to explore the feasibility of the approach in a clinical setting, ii) to determine whether the in silico, ex vivo and in human data can be pooled in a general training dataset and iii) to provide a proof-of-principle in humans for VT. Embodiments of the present invention may be used to show that it is possible to reconstruct arbitrary VT morphologies from 4D ultrasound data in patients with structural or ischemic heart disease (e.g. ICM). Embodiments of the present invention may be used to determine to what extent AI that was trained either solely on in silico data or a mixture of in silico, ex vivo and / or in human data can make accurate predictions about the underlying arrhythmia circuit.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 AI-assisted imaging & prediction of cardiac arrhythmia origins using 4D ultrasound Embodiments of the present invention establish an entirely novel ultrasound- based imaging technique utilizing artificial intelligence (AI) for the non-invasive, transmural visualization and diagnosis of heart rhythm disorders in real-time that will supersede existing imaging techniques and provide novel insights into the origins and driving mechanisms of heart rhythm disturbances. Heart disease is the major cause of morbidity and mortality worldwide. Despite significant progress in the field of biomedical imaging, imaging of heart rhythm disorders remains a major technological and scientific challenge. Understanding their origins and underlying mechanisms is pivotal in the planning of therapeutic interventions. Currently, cardiologists rely on catheter-based contact electrode measurements when diagnosing heart rhythm disorders, such as atrial fibrillation (AF) or ventricular tachycardia (VT). Catheter-based measurements are invasive, time-consuming and typically provide information about the heart’s abnormal electrical activity on its endo- or epicardial surface. However, the electrophysiological wave phenomena causing heart rhythm disorders are inherently three-dimensional phenomena evolving deep within the tissue, where they often interact with an arrhythmogenic substrate (e.g. scar tissue) in locations that are inaccessible to standard catheter mapping. Embodiments of the present invention comprise a novel AI-assisted and 4D (time-varying 3D) ultrasound-based imaging approach for the non-invasive and in-depth visualization of heart rhythm disorders. The imaging approach may be based on the idea that, because the heart’s contractions and deformations are triggered by electrical activity, inversely this electrical activity can be computed by analyzing the heart’s deformations even during complex arrhythmias. The imaging approach will be enabled by AI, which will learn and translate this complex relationship, 4D imaging and embodiments of the present invention’s use of high-resolution multi-modal fluorescence imaging of intact, isolated hearts. With this powerful methodological approach, embodiments may be able to link electrophysiological and mechanical tissue dynamics at high resolutions and develop an AI-based inverse reconstruction technique that are able to decipher the heart’s complex deformations and provide high-resolution predictions of the arrhythmic electrical phenomena throughout the entire heart muscle.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Background: The heartbeat is triggered by nonlinear waves of electrical excitation, which propagate rapidly through the heart muscle and activate the cellular contractions of heart muscle cells via the excitation-contraction coupling mechanism. Heart rhythm disorders are caused by abnormal electrical waves, which may degenerate into disorganized, self-sustained wave patterns that initiate irregular and persistent contractions of the heart muscle and underlie cardiac fibrillation. These waves are conjectured to take on the shapes of rotating spiral and scroll waves or ‘rotors’. However, their precise origin and three-dimensional morphology remains insufficiently understood, because imaging technology able to resolve the waves throughout the heart muscle’s volume does not exist. Modern ultrasound imaging can provide high-speed 4D videos of the entire heart at resolutions sufficient to resolve even the rapid, small irregular contractions during fibrillation. However, ultrasound provides solely images of the motion of the heart and does not provide electrical information. Current State-of-the-Art: The current state-of-the-art for the imaging of heart rhythm disorders is electro-anatomic catheter-mapping. Catheter-based mapping is invasive, time-consuming and provides information only from local measurements sparsely distributed across the heart surface. Even with multi-electrode catheters (e.g. multi-arm- or basket-catheters with 256 electrodes) the mapping needs to be performed sequentially, point-by-point to obtain high-resolution maps and, accordingly, the procedural times are typically 30-90 minutes to map an arrhythmia. The measurements are superficial and prone to motion-related artifacts and maps cannot distinguish epi-, endo- or intracardial signal. Intramural measurements are performed in specialized cardiac electrophysiology laboratories using needle electrode catheters to identify intramural, often isthmus-related origins of VTs in patients with ischemic cardiomyopathies (ICM) but are not routinely done in most electrophysiology laboratories because these catheters are not commercially available and require significant time and expertise to perform. An alternative imaging technique for the diagnosis of heart rhythm disorders is inverse electrocardiography, which involves recording electrical potentials from the patient’s body surface and using inverse computational techniques to calculate potentials on the heart surface. However, the technique provides indirect measurements and requires further validation. BothAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 techniques require 3D location sensors or imaging data (e.g., CT or MRI) to create electro-anatomic maps of the abnormal electrical activity during heart rhythm disorders. In the laboratory, heart rhythm disorders can be studied using voltage-sensitive fluorescence imaging, which provides highly detailed visualizations of the heart’s electrical activity but fails to image activity deep within the cardiac muscle, similarly as the techniques used in the clinical setting. Fluorescence imaging is limited by low penetration depths of light in tissue and involves toxic substances and can therefore not be used in patients. Significance: Embodiments of the present invention address a very significant challenge within cardiovascular medicine, and a long-standing problem within biomedical engineering: the non-invasive and in-depth visualization of cardiac arrhythmias. Currently, no experimental method exists that is capable of visualizing three-dimensional, transmural electrical activity of the heart non-invasively. The inventors have shown that 4D ultrasound-based imaging can resolve the electromechanical phenomena underlying cardiac fibrillation, and that the technique could - if combined with AI - provide high-resolution, three-dimensional visualizations of heart rhythm disorders and their origins non-invasively, in real-time and with high (see, e.g., Examples 3, 6 and 7 of this disclosure, provided below). The proposed 4D imaging approach is expected to supersede existing cardiac mapping approaches and could greatly advance the diagnosis of heart rhythm disorders and be used to guide therapeutics, such as catheter ablation, more reliably and effectively. For example, while simple reentrant arrhythmias (e.g. “AVNRT”, “AVRT”, atrial flutter) are easily mapped and ablated with high success, complex reentrant arrhythmias (e.g. ischemic VT, persistent AF or VF) are not easily mapped and ablated clinically. In embodiments, imaging techniques could provide highly detailed live 4D visualizations of these heart rhythm disorders, while guiding more targeted, intracardial ablation procedures using, for instance, focused ultrasound, microwaves or electroporation. Independent of its potential transformative clinical impact, embodiments of the present invention may open doors to a novel field with extraordinary potential in unraveling the mysteries underlying heart rhythm disorders and will provide novel insights into their transmural dynamics.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 High-Resolution 4D Ultrasound-based Imaging of Electromechanical Rotors during Ventricular Fibrillation (VF) Ex Vivo: The inventors have previously demonstrated in intact isolated pig hearts ex vivo that it is possible to image and characterize the electrical and mechanical phenomena underlying ventricular fibrillation (VF) at unprecedented resolutions using 4D ultrasound and panoramic fluorescence imaging (see, e.g., Examples 4-7 of this disclosure, provided below). By imaging the fibrillating heart with both imaging techniques simultaneously, the inventors showed, for the first time, that the heart’s mechanical strain dynamics are very similar to the electrophysiological dynamics during VT, polymorphic VT and VF. More specifically, the inventors have found that rotating action potential and calcium waves observed on the heart’s ventricular surface cause similarly rotating strain waves, suggesting that the cellular excitation-contraction coupling mechanism can lead to highly correlated electrophysiological and mechanical phenomena on the tissue and organ scale and produces ‘electro-mechanical rotors’. Using 4D ultrasound, the inventors demonstrated that the rotating electrical waves produce mechanical filament-like phase singularities, which evolve through the heart muscle and indicate the rotational centers of mechanical scroll waves, which in turn are likely produced by electrical scroll vortex waves during VF. The experimental findings are an indirect measurement of 3D electrophysiological wave phenomena and suggest that it is possible to compute electrophysiological wave phenomena from the heart’s muscle deformations during arrhythmias. Inverse AI- and Physics-based Computational Techniques for Solving the ‘Inverse Mechano-Electrical Problem’: In recent studies, the inventors have demonstrated in computer simulations that it is possible to cross-estimate or predict electrical excitation wave phenomena from tissue deformation that was caused by the electrical wave phenomena. In these proof-of-principle studies, the inventors developed two inverse numerical approaches, one knowledge- or physics-based and one deep learning-based approach, to solve the ‘inverse mechano-electrical problem’, in simulated 3D bulk-shaped tissues. While the physics-based approach employed a replicate numerical model that assimilates mechanical observation data to drive an internal reproduction of the original electrical dynamics via synchronization, the deep learning approach employed a convolutional neural network (CNN) with an encoder-Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 decoder-like architecture that was trained on many thousands of pairs of mechanical and corresponding electrical data. While both approaches can successfully compute electrical wave phenomena from tissue deformation, the inventors found that deep learning outperforms the physics-based approach (90-95% vs.75-85% accuracy). Key embodiments of the present invention, a self-supervised deep learning algorithm trained on a large electromechanical dataset can easily associate the underlying electrical pattern with an observed deformation pattern although their relationship is highly complex, and the dynamics are chaotic and in each individual case unique. A neural network can reliably predict even complicated electrical scroll wave chaos, the type of wave dynamics conjectured to underlie VF, with high precision even with measurement noise and at low spatial resolutions. The results suggest that an AI may equally be able to predict spatio-temporal electrical wave phenomena from the heart’s rapid arrhythmic deformations imaged with 4D ultrasound, based on its vast knowledge of arrhythmic electromechanics acquired through extensive training. 4D Ultrasound Imaging during Ventricular Tachycardia (VT) in Humans: It has been demonstrated that 4D ultrasound can be applied during VT ablation procedures in human patients (N=6). It was found that with transthoracic 4D ultrasound the spatial and temporal resolutions and image quality are sufficient to resolve arrhythmic ventricular wall motion and deformation during VT, while mapping the heart’s endocardial surface using basket catheters. Simultaneous Imaging of Voltage, Calcium and Strain in Contracting Cardiac Tissue using Optical Imaging and Computer Vision: Fluorescence imaging of the heart using voltage- and / or calcium-sensitive fluorescent dyes has been widely used in basic cardiovascular research for over 30 years. However, until recently, it was not possible to image action potential or calcium waves propagating across the contracting heart surface. Instead, the heart’s contractile motion had to be inhibited using pharmacological excitation-contraction uncoupling agents such as Blebbistatin. Embodiments of the present invention utilize optical and computer vision techniques, with which it is possible to measure action potential and calcium waves together with tissue strain at high spatial resolutions using multi-camera measurement systems on the strongly contracting 3D deforming heart surface.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Embodiments of the present invention comprise i) generating high-resolution in silico, ex vivo and in human electromechanical data of the heart’s arrhythmic electrical and mechanical 4D dynamics to identify and characterize a universal mapping between these two dynamics and ii) developing an AI-based and / or physics-based inverse algorithm, which can translate 4D cardiac mechanics into electrophysiological activation dynamics. The algorithm will ultimately be able to predict these electrical dynamics from 4D imaging data produced with a commercially available ultrasound system. Solving the Inverse Mechano-Electrical Problem in Computer Simulations of Atrial and Ventricular Arrhythmias: Using a combination of computer simulations and inverse numerical reconstruction techniques, embodiments of the present invention may be used to show that it is possible to compute electrophysiological wave phenomena, such as action potential or calcium waves, from the 3D deformations of a simulated heart. In this purely computational aspect, the feasibility of the approach may be explored first i) in simplified ventricular geometries, which deform due to focal and reentrant ventricular arrhythmias (VT) created with phenomenological models, next ii) in more realistic ventricular and whole heart geometries and models with more complex arrhythmias (e.g. polymorphic VT or VF) and pathophysiology created with more detailed models, and finally iii) in simulated atria and atrial arrhythmias, such as atrial flutter or AF. Embodiments of the present invention may be utilized to apply two different inverse numerical re-construction techniques to the data, one AI- or deep learning-based and one physics-based data assimilation technique, and may be used in connection with advancing and further refining these techniques or developing new hybrid versions. Embodiments of the present invention may be used to provide a proof- of-concept in silico for ventricular and subsequently for atrial arrhythmias to compute the electrophysiological activation dynamics and 3D arrhythmia morphologies, as well as locate arrhythmia origins such as scars or isthmus locations, from tissue motion in a wide range of scenarios accurately, robustly and in real-time. Using the AI-based approach, embodiments of the present invention may be used to demonstrate that reconstructions can be performed in or close to real-time (data rate and voxel numbers in computer simulations are comparable to ultrasound imaging) in bulk-shaped tissues using state-of-the-art GPU (graphics processing unit) hardware.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Embodiments of the present invention may involve the generation of synthetic simulated training data for the training of the AI-based approach or a deep neural network (e.g. encoder-decoder-like 3D-CNN), which is consequently specialized in computing 3D electrical activation dynamics from the heart’s 3D / 4D tissue motion and deformation. It is possible to generate sufficiently large training data sets (2-4TB, >10,000 samples) of ventricular arrhythmias with phenomenological computational models within 3-5 days of computing time. The simulations may initially exclude heterogeneity and other abnormalities to focus solely on the mapping between mechanics and electrics given a particular arrhythmia morphology in an otherwise idealized situation. The simulations may include more intricate scenarios (e.g. ischemia, scar tissue, isthmuses or macro- reentrant circuits, fibrosis, heterogeneous active tension, dissociation phenomena between voltage and calcium, electrical abnormalities, etc.) and the simulations may be refined to match experimental data and to create synthetic 4D ultrasound data. Lastly, the relationship between substrate or arrhythmia origins and mechanical activation dynamics during sinus rhythm will be explored. High-Resolution Ex Vivo Training Data Generation and First Proof-of-Principle in Intact Excised Porcine Hearts: Embodiments of the present invention may be used to produce high-resolution fluorescence imaging data of arrhythmic hearts in a unique ex vivo imaging environment as training or development data. Intact, isolated porcine hearts (N=50) may be imaged in a unique Langendorff-perfusion and / or working heart setup at speeds of 500 frames per second using a custom 3D panoramic fluorescence imaging system with 16 or 32 high-speed CMOS cameras, measuring the transmembrane potential and / or calcium across the entire 360º contracting heart surface. Simultaneously, in embodiments, the hearts may be imaged at speeds of up to 180 volumes per second using high-speed 4D ultrasound (Siemens Acuson SC2000 system, also certified for clinical use). The two imaging data types will be cross- registered, such that the 3D voltage- and / or calcium-sensitive fluorescent maps of the electrophysiological phenomena on the heart surface can be compared with the volumetric ultrasound data showing the heart’s 3D wall motion within the same coordinate system. Using the panoramic fluorescence and ultrasound imaging system, embodiments may generate 4D high-resolution electromechanical data of theAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 arrhythmic heart ex vivo. The data may be processed in such a way that it can i) be used to create and be assimilated into biophysical computer models, ii) be used to create data-driven computer models and, ultimately, be iii) used to train or develop an AI or physics-based mechano-electrical reconstruction technique, respectively. Ultimately, embodiments may comprise training train an AI either i) solely with in silico data or ii) with a mix of in silico and ex vivo data and apply the AI to unseen ex vivo 4D ultrasound data to predict electrical activation patterns from the mechanical deformations with the same precision and at the same high resolutions that are attainable with fluorescence imaging. The high-resolution fluorescence measurements will be used as the ‘ground truth’ or validation data to cross-validate the estimated reconstruction results. A secondary goal will be to extrapolate missing electrical measurement data within the volume of the heart from the surface observations, for instance, during polymorphic VT, VF or AF with epi-endocardial dissociation. First Application of AI-assisted 4D Ultrasound-based Mapping In Human: Embodiments of the present invention may be used in connection with gathering in human training and development data during ablation procedures of arrhythmias in patients (N=100). The data may be acquired using transthoracic or transesophageal 4D ultrasound (Siemens Acuson SC2000 system used for ex vivo imaging is also available in the clinic) as well as electro-anatomical high-density catheter-mapping during VT or AF ablation procedures. As with the ex vivo data, the in human data will be cross- registered with electrical mapping data to be able to compare electrical and mechanical arrhythmia morphologies and to use the data for the training or development of an AI- or physics-based reconstruction approach. Embodiments of the present invention may be used in connection with the following: i) to explore the feasibility of the approach in a clinical setting, ii) to determine whether the in silico, ex vivo and in human data can be pooled in a general training and development dataset and iii) to provide a proof-of- principle in humans for both ventricular and atrial arrhythmias. The data may be used to guide and refine the computer simulations and numerical reconstruction techniques. Embodiments may be used to show that it is possible to reconstruct, for instance, arbitrary VT morphologies from 4D ultrasound data in patients with structural or ischemic heart disease (e.g. ICM). Embodiments may be used to determine whetherAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 and to what extent AI that was trained either solely on in silico data or a mixture of in silico, ex vivo and / or in human data can make accurate predictions about the underlying arrhythmia circuit. Embodiments may further be used in connection with establishing 4D ultrasound-based imaging of heart rhythm disorders such as VT or AF as a routinely, clinically used imaging technique. The imaging may produce visualizations of short arrhythmic episodes (5-10 sec.) and locate arrhythmia origins, such as intramural scars, isthmuses or fibrotic regions, either in real-time or at least within less than 2-3 minutes using GPU hardware. Development of Tracking and Segmentation Algorithms and Generation of Synthetic 4D Ultrasound Data: To be able to analyze the ultrasound data and measure wall motion accurately, embodiments may comprise developing numerical tools and algorithms for 3D motion tracking, deformation quantification, segmentation and visualization. Embodiments of the present invention may comprise a numerical computer vision framework, with which the applicant and his team will be able to extract, quantify and analyze kinematic information about the 3D motion of the heart, even with poor ultrasound image quality. In some cases, in embodiments: 1) An AI-based approach may not “generalize”, or, in other words, might fail to make accurate predictions reliably, for instance, i) across a larger or ii) in a distinctly different cohort of patients (in silico vs. ex vivo vs. in vivo, different disease, etc.). In embodiments, this issue, and the issue of eventually having too few clinical samples, may be addressed by iterative refinement of the computer simulations and addition of synthetic and eventually ex vivo training data (e.g. obtained with explanted human hearts from heart transplants). Alternatively, a hybrid or a purely physics-based reconstruction technique may be employed in some embodiments.2) In some patients, poor image quality during transthoracic ultrasound imaging might prevent numerical analysis. In this case, skipping numerical motion tracking and performing training and reconstruction directly in an image-based fashion might circumvent these issues in embodiments. Lastly, the approach could alternatively be pursued with MRI.3) In some cases, with severe disease progression (e.g. severe scarring, severely reduced ejection fraction, late-stage heart failure) the inverse mechano-electrical problem may not be able to be solved in some embodiments.4)Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Dissociation of the excitation-contraction coupling mechanism may, in some patients, compromise the imaging approach. Currently, heart rhythm disorders are diagnosed by measuring and analyzing the heart’s electrical activity during catheter-based contact mapping procedures. Embodiments of the present invention comprise a radically different approach to diagnose heart rhythm disorders by imaging the heart’s deformations using high- resolution 4D ultrasound and predicting the underlying electrical activity and arrhythmia origins from the deformations with precisions and at unprecedented resolutions, which are otherwise only attainable in direct electrical measurements in a cutting-edge research laboratory ex vivo. The central hypothesis of embodiments of the invention is that the motion and deformation of the heart contains a wealth of information, which can serve like a fingerprint of an arrhythmia, and which - if captured in a 4D measurement and analyzed properly - is unique enough to be able to compute the 4D morphology of the electrical dynamics causing the arrhythmia. Subsequently, training an AI to learn the complex relationship between cardiac electrics and tissue mechanics from a well- curated 4D imaging dataset obtained under laboratory conditions and undergirded by clinical and synthetic data, may enable the AI to predict any electrical activation pattern from any deformation in any heart. Just as AI can recognize objects, faces, speech or handwritten text and any other complex high-dimensional feature in data, embodiments of the present invention comprising a specially trained AI will also be able to recognize any arrhythmia morphology solely by observing 4D ultrasound data, although arrhythmias are chaotic in nature and will be different and unique in each patient. A self- supervised deep learning algorithm in silico may be provided in support of this hypothesis. The central assumption that a solution for the ‘inverse mechano-electrical problem’ or, in other words, that a unique mapping between cardiac mechanics and electrophysiology exists and is robust enough that it can be exploited by an AI universally in various conditions is highly innovative and extends far beyond the current frontiers in arrhythmia research. In embodiments, the proposed data-driven approach rejects all conventions to describe cardiac deformation mechanics using human-defined characteristics, such as strain or anatomical length changes, but instead processes spatio-temporal patterns of cardiac motion.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 SYSTEMS & COMPUTER READABLE MEDIA Aspects of the present disclosure further include systems, such as computer- controlled systems, for practicing embodiments of the above methods. In some instances the systems further include one or more computers for complete automation or partial automation of the methods described herein. In some embodiments, systems include a computer having a computer readable storage medium with a computer program stored thereon. In embodiments, the system includes an input module, a processing module and an output module. The subject systems may include both hardware and software components, where the hardware components may take the form of one or more platforms, e.g., in the form of servers, such that the functional elements, i.e., those elements of the system that carry out specific tasks (such as managing input and output of information, processing information, etc.) of the system may be carried out by the execution of software applications on and across the one or more computer platforms represented of the system. Systems may include a display and operator input device. Operator input devices may, for example, be a keyboard, mouse, or the like. The processing module includes a processor which has access to a memory having instructions stored thereon for performing the steps of the subject methods. The processing module may include an operating system, a graphical user interface (GUI) controller, a system memory, memory storage devices, and input-output controllers, cache memory, a data backup unit, and many other devices. The processor may be a commercially available processor or it may be one of other processors that are or will become available. The processor executes the operating system and the operating system interfaces with firmware and hardware in a well-known manner, and facilitates the processor in coordinating and executing the functions of various computer programs that may be written in a variety of programming languages, such as Java, Perl, C++, other high level or low level languages, as well as combinations thereof, as is known in the art. The operating system, typically in cooperation with the processor, coordinates and executes functions of the other components of the computer. The operating system also providesAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 scheduling, input-output control, file and data management, memory management, and communication control and related services, all in accordance with known techniques. The processor may be any suitable analog or digital system. In some embodiments, processors include analog electronics which allows the user to manually align a light source with the flow stream based on the first and second light signals. In some embodiments, the processor includes analog electronics which provide feedback control, such as for example negative feedback control. The system memory may be any of a variety of known or future memory storage devices. Examples include any commonly available random access memory (RAM), magnetic medium such as a resident hard disk or tape, an optical medium such as a read and write compact disc, flash memory devices, or other memory storage device. The memory storage device may be any of a variety of known or future devices, including a compact disk drive, a tape drive, a removable hard disk drive, or a diskette drive. Such types of memory storage devices typically read from, and / or write to, a program storage medium (not shown) such as, respectively, a compact disk, magnetic tape, removable hard disk, or floppy diskette. Any of these program storage media, or others now in use or that may later be developed, may be considered a computer program product. As will be appreciated, these program storage media typically store a computer software program and / or data. Computer software programs, also called computer control logic, typically are stored in system memory and / or the program storage device used in conjunction with the memory storage device. In some embodiments, a computer program product is described comprising a computer usable medium having control logic (computer software program, including program code) stored therein. The control logic, when executed by the processor the computer, causes the processor to perform functions described herein. In other embodiments, some functions are implemented primarily in hardware using, for example, a hardware state machine. Implementation of the hardware state machine so as to perform the functions described herein will be apparent to those skilled in the relevant arts. Memory may be any suitable device in which the processor can store and retrieve data, such as magnetic, optical, or solid-state storage devices (includingAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 magnetic or optical disks or tape or RAM, or any other suitable device, either fixed or portable). The processor may include a general-purpose digital microprocessor suitably programmed from a computer readable medium carrying necessary program code. Programming can be provided remotely to processor through a communication channel, or previously saved in a computer program product such as memory or some other portable or fixed computer readable storage medium using any of those devices in connection with memory. For example, a magnetic or optical disk may carry the programming, and can be read by a disk writer / reader. Systems of the invention also include programming, e.g., in the form of computer program products, algorithms for use in practicing the methods as described above. Programming according to the present invention can be recorded on computer readable media, e.g., any medium that can be read and accessed directly by a computer. Such media include, but are not limited to: magnetic storage media, such as floppy discs, hard disc storage medium, and magnetic tape; optical storage media such as CD-ROM; electrical storage media such as RAM and ROM; portable flash drive; and hybrids of these categories such as magnetic / optical storage media. The processor may also have access to a communication channel to communicate with a user at a remote location. By remote location is meant the user is not directly in contact with the system and relays input information to an input manager from an external device, such as a computer connected to a Wide Area Network (“WAN”), telephone network, satellite network, or any other suitable communication channel, including a mobile telephone (i.e., smartphone). In some embodiments, systems according to the present disclosure may be configured to include a communication interface. In some embodiments, the communication interface includes a receiver and / or transmitter for communicating with a network and / or another device. The communication interface can be configured for wired or wireless communication, including, but not limited to, radio frequency (RF) communication (e.g., Radio-Frequency Identification (RFID), Zigbee communication protocols, WiFi, infrared, wireless Universal Serial Bus (USB), Ultra Wide Band (UWB), Bluetooth® communication protocols, and cellular communication, such as code division multiple access (CDMA) or Global System for Mobile communications (GSM).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 In one embodiment, the communication interface is configured to include one or more communication ports, e.g., physical ports or interfaces such as a USB port, an RS-232 port, or any other suitable electrical connection port to allow data communication between the subject systems and other external devices such as a computer terminal (for example, at a physician’s office or in hospital environment) that is configured for similar complementary data communication. In one embodiment, the communication interface is configured for infrared communication, Bluetooth® communication, or any other suitable wireless communication protocol to enable the subject systems to communicate with other devices such as computer terminals and / or networks, communication enabled mobile telephones, personal digital assistants, or any other communication devices which the user may use in conjunction. In one embodiment, the communication interface is configured to provide a connection for data transfer utilizing Internet Protocol (IP) through a cell phone network, Short Message Service (SMS), wireless connection to a personal computer (PC) on a Local Area Network (LAN) which is connected to the internet, or WiFi connection to the internet at a WiFi hotspot. In one embodiment, the subject systems are configured to wirelessly communicate with a server device via the communication interface, e.g., using a common standard such as 802.11 or Bluetooth® RF protocol, or an IrDA infrared protocol. The server device may be another portable device, such as a smart phone, Personal Digital Assistant (PDA) or notebook computer; or a larger device such as a desktop computer, appliance, etc. In some embodiments, the server device has a display, such as a liquid crystal display (LCD), as well as an input device, such as buttons, a keyboard, mouse or touch-screen. In some embodiments, the communication interface is configured to automatically or semi-automatically communicate data stored in the subject systems, e.g., in an optional data storage unit, with a network or server device using one or more of the communication protocols and / or mechanisms described above. Output controllers may include controllers for any of a variety of known display devices for presenting information to a user, whether a human or a machine, whetherAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 local or remote. If one of the display devices provides visual information, this information typically may be logically and / or physically organized as an array of picture elements. A graphical user interface (GUI) controller may include any of a variety of known or future software programs for providing graphical input and output interfaces between the system and a user, and for processing user inputs. The functional elements of the computer may communicate with each other via system bus. Some of these communications may be accomplished in alternative embodiments using network or other types of remote communications. The output manager may also provide information generated by the processing module to a user at a remote location, e.g., over the Internet, phone or satellite network, in accordance with known techniques. The presentation of data by the output manager may be implemented in accordance with a variety of known techniques. As some examples, data may include SQL, HTML or XML documents, email or other files, or data in other forms. The data may include Internet URL addresses so that a user may retrieve additional SQL, HTML, XML, or other documents or data from remote sources. The one or more platforms present in the subject systems may be any type of known computer platform or a type to be developed in the future, although they typically will be of a class of computer commonly referred to as servers. However, they may also be a main-frame computer, a workstation, or other computer type. They may be connected via any known or future type of cabling or other communication system including wireless systems, either networked or otherwise. They may be co-located, or they may be physically separated. Various operating systems may be employed on any of the computer platforms, possibly depending on the type and / or make of computer platform chosen. Appropriate operating systems include Windows, iOS, Oracle Solaris, Linux, IBM i, Unix, and others. Aspects of the present disclosure further include non-transitory computer readable storage mediums having instructions for practicing the subject methods. Computer readable storage mediums may be employed on one or more computers for complete automation or partial automation of a system for practicing methods described herein. In certain embodiments, instructions in accordance with the method described herein can be coded onto a computer-readable medium in the form of “programming”, where the term "computer readable medium" as used herein refers to any non-transitoryAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 storage medium that participates in providing instructions and data to a computer for execution and processing. Examples of suitable non-transitory storage media include a floppy disk, hard disk, optical disk, magneto-optical disk, CD-ROM, CD-R, magnetic tape, non-volatile memory card, ROM, DVD-ROM, Blue-ray disk, solid state disk, and network attached storage (NAS), whether or not such devices are internal or external to the computer. A file containing information can be “stored” on computer readable medium, where “storing” means recording information such that it is accessible and retrievable at a later date by a computer. The computer-implemented method described herein can be executed using programming that can be written in one or more of any number of computer programming languages. Such languages include, for example, Python, Java, Java Script, C, C#, C++, Go, R, Swift, PHP, as well as any many others. The non-transitory computer readable storage medium may be employed on one or more computer systems having a display and operator input device. Operator input devices may, for example, be a keyboard, mouse, or the like. The processing module includes a processor which has access to a memory having instructions stored thereon for performing the steps of the subject methods. The processing module may include an operating system, a graphical user interface (GUI) controller, a system memory, memory storage devices, input-output controllers, cache memory, a data backup unit, and many other devices. The processor may be a commercially available processor, or it may be one of other processors that are or will become available. The processor executes the operating system and the operating system interfaces with firmware and hardware in a well-known manner, and facilitates the processor in coordinating and executing the functions of various computer programs that may be written in a variety of programming languages, such as those mentioned above, other high level or low-level languages, as well as combinations thereof, as is known in the art. The operating system, typically in cooperation with the processor, coordinates and executes functions of the other components of the computer. The operating system also provides scheduling, input-output control, file and data management, memory management, and communication control and related services, all in accordance with known techniques.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 UTILITY The methods and systems of the invention, e.g., as described above, find use in a variety of applications where it is desirable to understand the origins and underlying mechanisms of heart disease in general, including, for example, heart rhythm disorders such as, e.g., atrial fibrillation (AF) or ventricular tachycardia (VT) in particular. In some embodiments, the methods and systems described herein find use when it is desirable to improve the diagnosis and treatment of heart rhythm disorders in order to improve patient outcomes. In some embodiments, the subject methods and systems find use in diagnosing a heart rhythm disorder and / or diagnosing other cardiac abnormalities. In some embodiments, the subject methods and systems find use in treating a heart rhythm disorder, e.g., by guiding or directing cardiac ablation. In some embodiments, the methods and systems described herein find use in drug discovery, e.g., by performing or enabling drug discovery simulations. EXAMPLES OF NON-LIMITING ASPECTS OF THE DISCLOSURE Aspects, including embodiments, of the present subject matter described above may be beneficial alone or in combination, with one or more other aspects or embodiments. Without limiting the foregoing description, certain non-limiting aspects of the disclosure numbered 1-232 are provided below. As will be apparent to those of skill in the art upon reading this disclosure, each of the individually numbered aspects may be used or combined with any of the preceding or following individually numbered aspects. This is intended to provide support for all such combinations of aspects and is not limited to combinations of aspects explicitly provided below: 1. A method of configuring a model to reflect electrical and mechanical behavior of a tissue, the method comprising: collecting initial data comprising corresponding electrophysiological activation patterns of a tissue and mechanical movement patterns of the tissue; and configuring a model of the tissue based on the corresponding electrophysiological activation patterns of the tissue and mechanical movement patterns of the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 2. The method of aspect 1, wherein the initial data comprises dynamic structural imaging data. 3. The method of aspects 1 or 2, wherein the initial data comprises model training data. 4. The method of any one of one the previous aspects, wherein the initial data comprises model configuration data. 5. The method of any one of the previous aspects, wherein the initial data reflects an initial state of tissue electrophysiology and mechanical movement. 6. The method of any one of the previous aspects, wherein the electrophysiological activation patterns comprise one or more of: electrical, optical, acoustical, and / or photo- acoustical measurements of electrical excitation of the tissue and / or structure of the tissue. 7. The method of any one of the previous aspects, wherein the initial data is obtained from a subject. 8. The method of aspect 7, wherein the initial data comprises subject-specific data. 9. The method of aspect 8, wherein the subject-specific data comprises one or more of: demographic data, genetic information, patient history data, structural imaging data, and / or quantitative medical data. 10. The method of aspects 8 or 9, wherein the method further comprises configuring the model of the tissue based on the subject information. 11. The method of aspect 10, wherein the model of the tissue is configured based on the subject information after the model is configured based on the electrophysiological activation patterns and mechanical movement patterns of the tissue. 12. The method of any one of the previous aspects, wherein the dynamic structural imaging data comprises ultrasound imaging data, magnetic resonance imaging (MRI) data, and / or computed tomography (CT) imaging data. 13. The method of aspect 12, wherein the ultrasound imaging data reflects mechanical movement patterns. 14. The method of any one of the previous aspects, wherein the dynamic structural imaging data comprises optical data.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 15. The method of aspect 14, wherein the optical data reflects electrophysical activation patterns. 16. The method of any one of the previous aspects, wherein the dynamic structural imaging data comprises fused imaging and optical data. 17. The method of any one of the previous aspects, wherein the dynamic structural imaging data comprises imaging data over time. 18. The method of any one of the previous aspects, wherein the initial data comprises synthetic data. 19. The method of any one of the previous aspects, wherein the initial data comprises data generated using a numerical model configured to represent intra- and / or extra-cellular processes of the tissue. 20. The method of any one of the previous aspects, wherein the initial data comprises data generated using a computational technique. 21. The method of aspect 20, wherein the computational technique comprises one or more of: finite-difference methods (FDM), finite element method (FEM), finite volume method (FVM), smoothed-particle hydrodynamics (SPH), and boundary-element method (BEM) and / or a differentiable version of such technique, optionally comprising a differential SPH simulation fitted to data. 22. The method of any one of the previous aspects, wherein the model is trained using training data comprising electrophysiological data and mechanical deformation data or fitted to such data using gradient descent techniques. 23. The method of any one of the previous aspects, wherein electrophysiological activation patterns comprise one or more of: action potential (AP) waves or wave fronts, calcium waves or wave fronts, AP activation maps, calcium activation maps, calcium concentrations or changes in calcium concentrations, oxygenation or changes in oxygenation, and / or pH or changes in pH. 24. The method of any one of the previous aspects, wherein the electrophysiological activation patterns comprise intramural electrical activity of the tissue. 25. The method of any one of the previous aspects, wherein the electrophysiological activation patterns comprise electrical activity on the tissue surface.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 26. The method of any one of the previous aspects, wherein the electrophysiological activation patterns comprise a sinus wave pattern, a focal wave pattern, and / or a reentrant wave pattern. 27. The method of any one of the previous aspects, wherein the electrophysiological activation patterns comprise a three-dimensional wave pattern. 28. The method of any one of the previous aspects, wherein the mechanical movement patterns comprise tissue deformation. 29. The method of any one of the previous aspects, wherein the mechanical movement patterns comprise tissue deformation triggered by the electrical activation patterns. 30. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate an electrophysiological activation pattern of a tissue of a subject by: inputting experimental data to the model, wherein the experimental data comprises one or more mechanical movement patterns; and receiving estimated electrophysiological activation patterns output from the model. 31. The method of any one of the previous aspects, wherein the model infers electrical activity of the tissue from mechanical deformation of the tissue. 32. The method of any one of the previous aspects, wherein the model infers internal electrical activity of the tissue from mechanical deformation of the tissue. 33. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate a mechanical movement pattern of a tissue of a subject by: inputting experimental data to the model, wherein the experimental data comprises one or more electrophysiological activation patterns of the tissue; and receiving estimated mechanical movement patterns output from the model. 34. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate electrophysiological activation patterns of a tissue of a subject by:Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 inputting data to the model, wherein the input data comprises one or more electrophysiological activation patterns of the tissue; and receiving estimated subsequent electrophysiological activation patterns output from the model. 35. The method of aspect 34, wherein the electrophysiological activation pattern input to the model comprises experimental data. 36. The method of aspects 34 or 35, wherein the electrophysiological activation pattern input to the model comprises electrode-recordings. 37. The method of any one of the previous aspects, wherein the electrophysiological activation pattern input to the model comprises an incomplete measurement of electrical activity of the tissue. 38. The method of any one of the previous aspects, wherein the electrophysiological activation pattern input to the model comprises sparse measurement data or data with low spatial resolution. 39. The method of any one of the previous aspects, wherein the electrophysiological activation pattern input to the model comprises simulated data. 40. The method of any one of the previous aspects, wherein the estimated subsequent electrophysiological activation patterns comprise chaotic wave phenomena. 41. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate a mechanical movement pattern of a tissue of a subject by: inputting experimental data to the model, wherein the experimental data comprises one or more mechanical movement patterns of the tissue; and receiving estimated subsequent mechanical movement patterns output from the model. 42. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate electrophysiological activation patterns and mechanical movement patterns of a tissue of a subject by: inputting experimental data to the model, wherein the experimental data comprises one or more electrophysiological activation patterns of the tissue or mechanical movement patterns of the tissue; andAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 receiving estimated electrophysiological activation patterns and mechanical movement patterns output from the model. 43. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate the presence of abnormal electrophysiological activation patterns of a tissue of a subject by: inputting experimental data to the model, wherein the experimental data comprises one or more electrophysiological activation patterns of the tissue or mechanical movement patterns of the tissue; and receiving an estimate of a presence of abnormal electrophysiological activation patterns of the tissue output from the model. 44. The method of aspect 43, wherein the abnormal electrophysiological activation patterns comprise electrophysiological activation patterns associated with an arrythmia, tachycardia, and / or the presence of scar tissue. 45. The method of any one of the previous aspects, wherein the method further comprises: obtaining ultrasound imaging data of the tissue; applying the model to the obtained ultrasound imagining data; and receiving an estimate from the model of the presence of an abnormal physiological symptom. 46. The method of aspect 45, wherein the abnormal physiological symptom comprises one or more of: an abnormal electrical circuit, an abnormal tissue characteristic, scar tissue, diseased tissue, tissue comprising a discontinuity, and / or fibrotic tissue. 47. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate a location of and / or a particular morphology associated with an electrical circuit causing an abnormal electrophysiological activation pattern. 48. The method of any one of the previous aspects, wherein the method further comprises applying the model to identify tissue associated with an abnormal electrophysiological activation pattern.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 49. The method of any one of the previous aspects, wherein the method further comprises applying the model to identify a location for tissue ablation or other tissue modification to remove an abnormal electrophysiological activation pattern. 50. The method of any one of the previous aspects, wherein the model is further configured based on subject information comprising one or more of: demographic data, genetic information, patient history data, structural imaging data, and / or quantitative medical data. 51. The method of any one of the previous aspects, wherein data input to and / or data output from the model comprises spatio-temporal data. 52. The method of any one of the previous aspects, wherein data input to and / or data output from the model comprises a sequence of images. 53. The method of any one of the previous aspects, wherein data output from the model comprises a single image. 54. The method of any one of the previous aspects, wherein data input to the model and data output from the model each comprise three-dimensional representations of the tissue over time. 55. The method of any one of the previous aspects, wherein the initial data comprises the experimental data. 56. The method of any one of the previous aspects, wherein the experimental data is distinct from the initial data. 57. The method of any one of the previous aspects, wherein the model is first configured using the initial data before being subsequently trained using experimental data. 58. The method of any one of the previous aspects, wherein the experimental data comprises dynamic structural imaging data. 59. The method of aspect 58, wherein the dynamic structural imaging data comprises ultrasound imaging data. 60. The method of aspect 58 or 59, wherein the dynamic structural imaging data comprises optical data. 61. The method of any one of aspects 58-60, wherein the dynamic structural imaging data comprises fused imaging and optical data.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 62. The method of any one of aspects 58-61, wherein the dynamic structural imaging data comprises imaging data over time. 63. The method of any one of the previous aspects, wherein the experimental data comprises one or more of: ultrasound, MRI, and / or CT scan data. 64. The method of any one of the previous aspects, wherein the method further comprises generating synthetic data for use configuring or training the model. 65. The method of any one of the previous aspects, wherein the initial data comprises synthetic data. 66. The method of any one of the previous aspects, wherein the model is trained using synthetic data. 67. The method of any one of aspects 64-66, wherein the synthetic data comprises data generated based on a mechanical model of the tissue or an electrophysiological model of the tissue. 68. The method of any one of aspects 64-67, wherein generating the synthetic data comprises: generating variations of tissue models in silico; and applying such variations of tissue models to generate synthetic data. 69. The method of any one of aspects 64-68, wherein the synthetic data comprises data generated by applying a mass-spring model (MSM), a finite-element model (FEM), and / or a smoothed-particle hydrodynamics (SPH) framework, and / or a differentiable simulation version thereof, optionally comprising a differentiable simulation version of MSM, SPH, and / or FEM. 70. The method of any one of aspects 64-69, wherein the synthetic data comprises data generated by applying an electromechanically coupled simulation. 71. The method of any one of the previous aspects, wherein the method further comprises: generating a plurality of models of structures of the tissue, wherein each of the structures varies in at least one aspect; and applying the plurality of models to generate synthetic data comprising electrophysiological activation patterns of the tissue and / or mechanical movement patterns of the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 72. The method of aspect 71, wherein each of the structures varies in one or more of: tissue shape, tissue thickness, tissue stiffness, contractile force, fiber orientations, interconnections between regions of tissues, velocities of electrical activation patterns, durations of electrical activation waves, and / or spatial heterogeneity. 73. The method of any one of the previous aspects, wherein the method further comprises using numerical simulations of tissue behavior to generate synthetic data. 74. The method of any one of the previous aspects, wherein the synthetic data is configured to mimic experimental data. 75. The method of any one of the previous aspects, wherein data used to configure or train the model is augmented by one or more of: adding random noise to the data, randomly rotating or flipping the data, removing a random section of the data, randomly scaling the data, blurring the data, and / or adding artifacts to the data. 76. The method of any one of the previous aspects, wherein the synthetic data comprises electrophysiological activation patterns exhibiting a sinus wave, a focal wave, and / or a reentrant wave. 77. The method of any one of the previous aspects, wherein data used to configure or train the model comprises electrophysiological activation patterns exhibiting a sinus wave, a focal wave, and / or a reentrant wave. 78. The method of any one of the previous aspects, wherein the method further comprises: generating ground-truth electrical activation patterns of the tissue; using the ground-truth electrical activation patterns to estimate mechanical movement patterns of the tissue; applying the model to the estimated mechanical movement patterns to estimate the electrical activation patterns. 79. The method of any one of the previous aspects, wherein the model is trained using training data generated from a plurality of electrophysiological models and mechanical deformation models. 80. The method of any one of the previous aspects, wherein the data generated by the plurality of electrophysiological models is applied to the plurality of mechanicalAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 deformation models to generate data comprising corresponding electrical activation and mechanical movement patterns. 81. The method of any one of the previous aspects, wherein the model comprises a model of electrophysiological activation patterns of the tissue. 82. The method of any one of the previous aspects, wherein the model comprises a model of calcium concentrations, oxygenation, and / or pH of the tissue or changes in one or more of calcium concentrations, oxygenation, and / or pH of the tissue. 83. The method of any one of the previous aspects, wherein the model comprises a model of mechanical movement of the tissue. 84. The method of any one of the previous aspects, wherein the model comprises a model of three-dimensional images or three-dimensional motion vectors of the tissue. 85. The method of any one of the previous aspects, wherein mechanical movement of the tissue is represented based on three-dimensional images or three-dimensional motion vectors. 86. The method of any one of the previous aspects, wherein the model is trained to learn mechanical movement of the tissue based on three-dimensional images or three- dimensional motion vectors. 87. The method of any one of the previous aspects, wherein the method comprises estimating electrical activity of the tissue based on three-dimensional images or three- dimensional motion vectors representing tissue movement using the model. 88. The method of any one of the previous aspects, wherein the model comprises a deep learning model. 89. The method of any one of the previous aspects, wherein the model comprises one or more of: a convolutional neural network, a U-Net, a sparse Res U-Net, a denoising diffusion neural network, a sparse denoising diffusion neural network, a transformer, a graph neural network, and / or a large language model. 90. The method of aspect 89, wherein the model comprises convolutional or attention mechanisms. 91. The method of any one of the previous aspects, wherein the model comprises a sparse encoding-decoding convolutional neural network.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 92. The method of any one of the previous aspects, wherein the model comprises a virtual vector model. 93. The method of any one of the previous aspects, wherein the model comprises a numerical simulation. 94. The method of any one of the previous aspects, wherein the model comprises a mass-spring model (MSM), a smoothed-particle hydrodynamics (SPH) model, or a finite element method (FEM) model. 95. The method of any one of the previous aspects, wherein the model comprises a differentiable electrical, mechanical, or electromechanical tissue model. 96. The method of any one of the previous aspects, wherein the model comprises a simulation core component. 97. The method of any one of the previous aspects, wherein the initial data comprises tissue motion data, tissue geometry data, and / or other subject-specific data. 98. The method of any one of the previous aspects, wherein the model is trained using gradient descent optimization. 99. The method of any one of the previous aspects, wherein the model comprises a numerical model configured to represent intra- and extra-cellular processes of the tissue. 100. The method of any one of the previous aspects, wherein the model comprises a computational technique comprising one or more of: finite-difference methods (FDM), finite element method (FEM), finite volume method (FVM), smoothed-particle hydrodynamics (SPH), and / or boundary-element method (BEM). 101. The method of any one of the previous aspects, wherein the model comprises an idealized model of the tissue. 102. The method of any one of the previous aspects, wherein the model comprises a subject-specific model of the tissue. 103. The method of any one of the previous aspects, wherein the model comprises a model of the tissue comprising one or more of: a fiber-architecture model of the tissue, scar placement within the tissue, and / or fibrosis placement within the tissue. 104. The method of any one of the previous aspects, wherein the method further comprises applying the model for drug screening.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 105. The method of any one of the previous aspects, wherein the method further comprises of applying the model for treatment of a subject. 106. The method of any one of the previous aspects, wherein the model comprises a digital twin of a subject. 107. The method of any one of the previous aspects, wherein the method further comprises generating a virtual simulation of the tissue using the model. 108. The method of any one of the previous aspects, wherein the configuring comprises simulating a tissue function as the model learns the contractile motion and electrophysiological wave pattern associated with the tissue. 109. The method of any one of the previous aspects, wherein the configuring comprises simulating a pumping heart as the model learns the contractile motion and electrophysiological wave pattern associated with the tissue. 110. The method of any one of the previous aspects, wherein the method further comprises using the model to evolve the behavior of a simulated tissue over time. 111. The method of any one of the previous aspects, wherein the electrical behavior of the tissue is integrated with the mechanical behavior of the tissue in the model. 112. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate a sequence in which different tissue locations are electrically activated. 113. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate an electrical activity activation map of the tissue. 114. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate a location of scar tissue on the tissue. 115. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate a location of tissue that exhibits an abnormal electrical property. 116. The method of aspect 115, wherein the abnormal electrical activity comprises one or more of abnormal conductivity and / or abnormal conduction speed for the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 117. The method of any one of the previous aspects, wherein the method further comprises applying the model to estimate a location of tissue that exhibits an abnormal mechanical property. 118. The method of aspect 117, wherein the abnormal mechanical property comprises abnormal contractility for the tissue. 119. The method of any one of the previous aspects, wherein the method further comprises validating the model based on clinical treatment of a subject. 120. The method of any one of the previous aspects, wherein the method further comprises validating the model, wherein validating the model comprises: using the model to estimate an electrical activation pattern of the tissue based on an observed movement pattern of the tissue; and confirming the electrical activation pattern is associated with the observed movement pattern of the tissue. 121. The method of any one of the previous aspects, wherein the method further comprises validating the model, wherein validating the model comprises: obtaining an electrical activation pattern of a tissue or a mechanical activation pattern of a tissue; estimating an electrical activation pattern or a mechanical activation pattern by applying the model to the electrical activation pattern or a mechanical activation pattern; using a second model to estimate an electrical activation pattern or a mechanical activation pattern by applying the second model to the electrical activation pattern or a mechanical activation pattern, wherein the second model comprises a physics-based model; and assessing the accuracy of the model by comparing the estimates from the model against the estimates from the second model. 122. The method of any one of the previous aspects, wherein the method further comprises collecting ultrasound imaging data of an in vivo tissue of a subject; applying the collected imaging data to the model to estimate electrical activation patterns within the tissue of the subject; and identifying one or more aspects of an abnormal electrophysiological activation pattern of the tissue of the subject.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 123. The method of any one of the previous aspects, wherein the method is a method of non-invasively analyzing electrophysiological processes of the tissue. 124. The method of any one of the previous aspects, wherein the method is a method of non-invasively mapping a heart’s electrical activity. 125. A method of observing mechanical movement patterns and corresponding electrophysiological activation patterns of a tissue, the method comprising: introducing a tissue into an imaging apparatus configured to image electrophysiological activation patterns and mechanical movement patterns of the tissue, wherein the imaging apparatus comprises: an enclosed interior volume into which the tissue is introduced; a substrate on which the tissue is mounted; an electrode for electrically stimulating the tissue; a perfusion subsystem configured to support physiological conditions of the tissue; a plurality of light sources configured for optically illuminating the tissue; an imaging system comprising an optical imaging subsystem configured for obtaining optical images of the tissue; and a plurality of mounts configured for mounting the light sources and aspects of the imaging system such that the tissue is evenly illuminated, and the imaging system obtains optical images of the tissue from a plurality of different perspectives; electrically stimulating the tissue with the electrode; imaging of the tissue by applying the imaging system in response to a stimulation of the tissue, wherein tissue stimulation comprises one or more of electrical, optical, and / or pharmacological stimulation of the tissue; imaging electrophysiological activation patterns of the tissue by applying the imaging system to obtain voltage- or calcium-sensitive optical mapping images in response to the stimulation of the tissue; and combining the obtained images of mechanical movement patterns and electrophysiological activation patterns to reconstruct movement of the tissue in response to the stimulation.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 126. The method of aspect 125, wherein the imaging system of the imaging apparatus further comprises an ultrasound imaging subsystem configured for obtaining ultrasound images of the tissue. 127. The method of aspect 126, wherein the mechanical movement patterns of the tissue are imaged by applying the ultrasound imaging subsystem in response to a stimulation of the tissue. 128. The method of aspect 125 to 127, wherein the imaging apparatus further comprises a plurality of electrodes configured to detect electrophysiological activation patterns of the tissue. 129. The method of aspect 128, wherein the plurality of detection electrodes are configured to measure electrocardiograms from the tissue. 130. The method of aspect 125 to 129, wherein the imaging apparatus further comprises a power source configured to supply power to the imaging system and / or the plurality of light sources. 131. The method of aspects 125 to 130, wherein the plurality of mounts are configured for mounting aspects of the imaging system such that every point of the surface of the tissue is imaged from two or more perspectives. 132. The method of aspects 125 to 131, wherein the method further comprises optically stimulating the tissue using the plurality of light-sources. 133. The method of any one of aspects 125 to 132, wherein the method further comprises pharmacologically stimulating the tissue using pharmacological compounds or drugs. 134. The method of any one of aspects 125 to 133, wherein the method further comprises pharmacologically immobilizing aspects of the tissue using pharmacological compounds or drugs. 135. The method of any one of aspects 125 to 134, wherein the imaging apparatus comprises an imaging chamber or an imaging rig. 136. The method of aspect 135, wherein the imaging chamber or rig comprises a plurality of windows configured for illuminating the tissue and obtaining images of the tissue from a plurality of different perspectives.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 137. The method of any one of aspects 125 to 136, wherein the optical imaging subsystem comprises a multi-camera high-speed imaging system. 138. The method of any one of aspects 125 to 137, wherein the method comprises obtaining panoramic images of the tissue. 139. The method of aspect 138, wherein every point on the surface of the tissue is imaged. 140. The method of any one of aspects 125 to 139, wherein the method further comprises: repeatedly obtaining representations of corresponding electrophysiological activation patterns of the tissue and mechanical movement patterns of the tissue; and combining such representations into a data set for configuring a model according to aspects 1 to 124. 141. The method of aspect 140, wherein the method further comprises: collecting electrical activation patterns and associated mechanical movement patterns for the tissue present in the imaging chamber; and applying the electrical activation patterns and associated mechanical movement patterns as training data for the model. 142. The method of any one of aspects 125 to 141, wherein the method further comprises applying a numerical motion compensation technique to images of the tissue. 143. The method of any one of aspects 125 to 142, wherein the method further comprises applying an optical mapping technique combined with a numerical motion tracking technique to measure an electrical activation pattern in the tissue moving in the imaging apparatus. 144. The method of any one of aspects 125 to 143, wherein every point of the surface of the tissue is imaged from two or more perspectives and the method further comprises applying a stereoscopic motion tracking technique to measure an electrical activation pattern and / or a mechanical movement pattern in the tissue moving in the imaging apparatus. 145. The method of any one of aspects 125 to 144, wherein the method comprises applying a GPU-based motion tracking algorithm to process imaging data of the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 146. The method of any one of aspects 125 to 145, wherein the method further comprises: collecting a plurality of raw images of the tissue; applying an optical flow estimation technique or differentiable motion estimation technique to the raw images to compensate for tissue movement; and generating a plurality of compensated images of the tissue to estimate tissue deformation. 147. The method of aspect 146, wherein every point of the surface of the tissue is imaged from two or more perspectives and the optical flow estimation technique is a stereoscopic optical flow estimation technique or a multi-view differentiable rendering technique used for tracking three-dimensional motion. 148. The method of any one of aspects 125 to 147, wherein the method further comprises applying one or more optical flow estimation techniques, differentiable motion estimation techniques, or motion compensation techniques to images of the tissue moving to mitigate motion artifacts. 149. The method of any one of aspects 125 to 148, wherein the method comprises imaging the tissue without applying a pharmacological excitation-contraction uncoupling agent to the tissue. 150. The method of any one of aspects 125 to 149, wherein the method comprises imaging electrophysiological activation patterns of the tissue or mechanical movement patterns of the tissue without a fiducial marker. 151. The method of any one of aspects 125 to 150, wherein the method comprises imaging electrical activation patterns across a tissue surface as the tissue deforms. 152. The method of any one of aspects 125 to 151, wherein the method comprises imaging electrical activation patterns across a surface of the tissue (optionally comprising an atrial or a ventricular surface) as the tissue contracts. 153. A method comprising validating a model according to any one of aspects 1 to 124 based on imaging obtained using the imaging apparatus according to any one of aspects 125 to 152. 154. The method of any one of the previous aspects further comprising: validating the model, wherein validating the model comprises:Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 using the model to estimate an electrical activation pattern of the tissue based on an observed movement pattern of the tissue; and confirming the electrical activation pattern is associated with the observed movement pattern of the tissue. 155. The method of any one of the previous aspects further comprising validating the model, wherein validating the model comprises: obtaining an electrical activation pattern of a tissue or a mechanical activation pattern of a tissue; estimating the electrical activation pattern or the mechanical activation pattern by applying the model to the electrical activation pattern or a mechanical activation pattern; using a second model to estimate the electrical activation pattern or the mechanical activation pattern by applying the second model to the electrical activation pattern or a mechanical activation pattern, wherein the second model comprises a physics-based model; and assessing the accuracy of the model by comparing the estimates from the model against the estimates from the second model. 156. The method of any one of the previous aspects further comprising: collecting ultrasound imaging data of an in vivo tissue of a subject; applying the collected imaging data to the model to estimate electrical activation patterns within the tissue of the subject; and identifying one or more aspects of an abnormal electrophysiological activation pattern of the tissue of the subject. 157. The method of any one of the previous aspects, wherein the method is a method of non-invasively analyzing electrophysiological processes of the tissue. 158. The method of any one of the previous aspects, wherein the method is a method of non-invasively mapping a heart’s electrical activity. 159. The method of any one of the previous aspects, wherein the tissue comprises electrically excitable tissue. 160. The method of any one of the previous aspects, wherein the tissue comprises anisotropic tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 161. The method of any one of the previous aspects, wherein the tissue comprises cardiomyocytes. 162. The method of any one of the previous aspects, wherein the tissue is cardiac tissue, lung tissue, intestinal tissue, or uterine tissue. 163. The method of aspect 162, wherein the tissue is cardiac tissue. 164. The method of any one of the previous aspects, wherein the tissue comprises one or more of: left ventricle tissue, right ventricle tissue, left atrium tissue, and / or right atrium tissue. 165. The method of aspect 164, wherein the tissue comprises left and right ventricles. 166. The method of any one of the previous aspects, wherein the tissue comprises a biventricular heart geometry. 167. The method of any one of the previous aspects, wherein the tissue is human tissue, rabbit tissue, pig tissue, sheep tissue, dog tissue, mouse tissue, rat tissue, or guinea pig tissue. 168. The method of aspect 167, wherein the tissue is human tissue or pig tissue. 169. The method of any one of the previous aspects, wherein the tissue comprises a discontinuity. 170. The method of aspect 169, wherein the discontinuity is scar tissue or fibrotic tissue. 171. The method of any one of the previous aspects, wherein the tissue comprises an isolated organ. 172. The method of any one of the previous aspects, wherein the tissue comprises cultured tissue. 173. The method of any one of the previous aspects, wherein the tissue comprises elastic excitable media. 174. The method of any one of the previous aspects, wherein the tissue exhibits muscle fiber anisotropy. 175. A method of assessing a model, the method comprising: generating ground-truth electrical activation patterns of a tissue; using the ground-truth electrical activation patterns to estimate mechanical movement patterns of the tissue;Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 applying a model of the tissue to the estimated mechanical movement patterns of the tissue to estimate associated electrical activation patterns; comparing the estimated associated electrical activation patterns with the ground-truth electrical activation patterns; and assessing the accuracy of the model’s predictions based on results of comparing the estimated and ground-truth electrical activation patterns. 176. A method of training a model to estimate electrophysiological activation patterns based on mechanical movement patterns, to estimate mechanical movement based on electrophysiological activation patterns, and / or to estimate a future electromechanical state based on electrophysiological activation patterns or mechanical movement patterns, the method comprising: collecting a plurality of training data comprising corresponding electrophysiological activation patterns of a tissue and mechanical movement patterns of the tissue; representing the electrophysiological activation patterns of the tissue as voltages, calcium concentrations, oxygenation, pH, and / or a temporal change thereof over a volume representing the tissue; representing the mechanical movement of the tissue as three-dimensional images and / or motion vectors over the volume representing the tissue; training a model using the electrophysiological activation patterns and corresponding mechanical movement. 177. The method of aspect 176, wherein the model is trained to estimate electrophysiological activation patterns, given a representation of mechanical movement of the tissue. 178. The method of any one of aspects 176 to 177, wherein the model is trained to estimate electrophysiological activation patterns, including abnormal patterns and locations, over a time period. 179. The method of any one of aspects 176 to 178, wherein the training data comprises a sequence of images of corresponding electrophysiological activation patterns of the tissue and mechanical movement patterns of the tissue at consecutive times.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 180. The method of any one of aspects 176 to 179, wherein the training data comprises simulation data. 181. The method of aspect 180, wherein the simulation data comprises results of electromechanical simulations. 182. The method of any one of any of aspects 176 to 181, further comprising augmenting the training data with simulation data. 183. The method of aspect 182, wherein augmenting the training data with simulation data comprises: generating a plurality of computer-based models of structures of the tissue, wherein each of the structures varies in at least one aspect; and using the plurality of tissue models to generate simulated results of corresponding electrical activation patterns of the modeled tissue and mechanical movement of the modeled tissue. 184. The method of aspect 183, wherein each of the structures varies in one or more of: tissue shape, tissue thickness, tissue stiffness, contractile force, fiber orientations, interconnections between regions of tissues, velocities of electrical activation patterns, durations of electrical activation waves, and / or spatial heterogeneity. 185. The method of aspect 184, wherein each of the structures varies in spatial heterogeneity, the spatial heterogeneity varied comprising one or more of: tissue shape, tissue thickness, tissue stiffness, contractile force, fiber orientations, interconnections between regions of tissues, velocities of electrical activation patterns, and / or durations of electrical activation waves. 186. The method of any one of aspects 183 to 185, wherein the plurality of computer- based models of structures of the tissue comprise numerical simulations comprising one or more of: finite-difference methods (FDM), finite element method (FEM), finite volume method (FVM), smoothed-particle hydrodynamics (SPH), and / or boundary-element method (BEM). 187. The method of any one of aspects 183 to 186, wherein augmenting the training data with simulation data further comprises: simulating the introduction of electrophysiological activation patterns, action potential waves, or calcium waves into the modeled tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 188. The method of aspect 187, wherein the electrophysiological activation patterns comprise one or more of a sinus wave, focal wave, and / or reentrant wave. 189. The method of any one of aspects 176 to 188, wherein the volume representing the tissue comprises an idealized or patient-specific computer-based model of the tissue, optionally comprising one or more of a fiber-architecture model of the tissue, scar or fibrosis placement within the tissue of the tissue. 190. An imaging apparatus for imaging electrophysiological activation patterns and mechanical movement patterns of a tissue, wherein the imaging apparatus comprises: an enclosed interior volume configured to receive biological tissue; a perfusion subsystem configured to support physiological conditions of the tissue; a substrate on which the tissue is mounted; a plurality of light sources configured for illuminating the tissue; an imaging system comprising an optical imaging subsystem configured for obtaining optical images of the tissue; and a plurality of mounts configured for mounting the light sources and aspects of the imaging system such that the tissue is evenly illuminated, and the imaging system obtains optical images of the tissue from a plurality of different perspectives. 191. The imaging apparatus of aspect 190, wherein the imaging system further comprises an ultrasound imaging subsystem configured for obtaining ultrasound images of the tissue. 192. The imaging apparatus of aspect 190 or 191, wherein the imaging apparatus comprises a plurality of windows configured for illuminating the tissue and obtaining images of the tissue from a plurality of different perspectives. 193. The imaging apparatus of any one of aspect 190 or 192, wherein the imaging apparatus further comprises a plurality of electrodes configured to detect electrophysiological activation patterns of the tissue. 194. The imaging apparatus of aspect 193, wherein the plurality of detection electrodes are configured to measure electrocardiograms from the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 195. The imaging apparatus of any one of aspects 190 to 194, wherein the imaging apparatus further comprises a power source configured to supply power to the imaging system and / or the plurality of light sources. 196. The imaging apparatus of any one of aspects 190 to 195, wherein the imaging apparatus comprises a truncated icosahedron shape. 197. The imaging apparatus of any one of aspects 190 to 196, wherein the imaging apparatus comprises a soccer ball geometry. 198. The imaging apparatus of any one of aspects 190 to 197, wherein the imaging apparatus comprises an open top and an open bottom. 199. The imaging apparatus of any one of aspects 190 to 198, wherein the open top and open bottom comprise fluidic pathways. 200. The imaging apparatus of any one of aspects 190 to 199, wherein the imaging apparatus comprises 24 penta- or hexagonal surfaces. 201. The imaging apparatus of any one of aspects 190 to 200, wherein the imaging apparatus comprises a shape with angles of optical axes between two adjacent surfaces of 37.4° or 41.8°. 202. The imaging apparatus of any one of aspects 190 to 201, wherein the surfaces comprise windows configured for mounting cameras. 203. The imaging apparatus of any one of aspects 190 to 202, wherein the imaging apparatus comprises a plurality of windows present at vertices between surfaces of the imaging apparatus and configured to receive LEDs to illuminate the interior of the imaging apparatus. 204. The imaging apparatus of any one of aspects 190 to 203, wherein the interior of the imaging apparatus is configured to be uniformly illuminated. 205. The imaging apparatus of any one of aspects 190 to 204, wherein the optical imaging subsystem comprises six or more cameras. 206. The imaging apparatus of any one of aspects 190 to 205, wherein the optical imaging subsystem comprises 12 or more cameras. 207. The imaging apparatus of any one of aspects 190 to 206, wherein an angle between neighboring cameras is between 35 and 45°.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 208. The imaging apparatus of any one of aspects 190 to 207, wherein the optical imaging subsystem comprises a plurality of CCD or CMOS cameras. 209. The imaging apparatus of any one of aspects 190 to 208, wherein the optical imaging subsystem is configured for measuring changes in fluorescence of aspects of the tissue. 210. The imaging apparatus of any one of aspects 190 to 209, wherein the optical imaging subsystem is configured for measuring changes in fluorescence of aspects of the tissue in response to a physiological change of the tissue. 211. The imaging apparatus of aspect 210, wherein the physiological change comprises a change in transmembrane potential of the tissue. 212. The imaging apparatus of any one of aspects 190 to 211, wherein the optical imaging subsystem is configured to image from the plurality of cameras simultaneously. 213. The imaging apparatus of any one of aspects 190 to 212, wherein the optical imaging subsystem comprises a plurality of filters configured to block excitation light originating from the plurality of light sources. 214. The imaging apparatus of any one of aspects 190 to 213, wherein the perfusion subsystem comprises a constant-pressure Langendorff-perfusion subsystem. 215. The imaging apparatus of any one of aspects 190 to 214, wherein the volume of the imaging apparatus is approximately 5L. 216. The imaging apparatus of any one of aspects 190 to 215, wherein the imaging apparatus further comprises an electrode configured for electrically stimulating the tissue. 217. The imaging apparatus of aspect 216, wherein the stimulation electrode is configured to introduce regular pacing of electrical stimulation to the tissue. 218. The imaging apparatus of aspect 216 or 217, wherein the stimulation electrode is configured to introduce burst pacing of electrical stimulation to the tissue. 219. The imaging apparatus of any one of aspects 190 to 218, wherein the imaging apparatus is configured to obtain 360° imaging of the tissue. 220. The imaging apparatus of any one of aspects 190 to 219, wherein the imaging apparatus is configured to simultaneously obtain images of every point on the surface of the tissue from two or more perspectives.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 221. The imaging apparatus of any one of aspects 190 to 220, wherein the imaging apparatus is configured to simultaneously obtain images of every point on the surface of the tissue from four or more perspectives. 222. The imaging apparatus of any one of aspects 190 to 221, wherein the imaging apparatus is configured to obtain images of the tissue while the tissue moves. 223. The imaging apparatus of any one of aspects 190 to 222, wherein the imaging apparatus is configured to obtain images of the tissue while the tissue deforms. 224. The imaging apparatus of any one of aspects 190 to 223, wherein the imaging apparatus comprises a 3D-printed substrate. 225. The imaging apparatus of any one of aspects 190 to 224, wherein the imaging apparatus further comprises a temperature-regulation subsystem. 226. The imaging apparatus of any one of aspects 190 to 225, wherein the imaging apparatus a processor comprising memory operably coupled to the processor, wherein the memory comprises instructions stored thereon, which, when executed by the processor, cause the processor to control the imaging apparatus. 227. A system for utilizing a model of a tissue, the system comprising: a processor comprising memory operably coupled to the processor, wherein the memory comprises instructions stored thereon, which, when executed by the processor, cause the processor to implement the steps of a method of any one of aspects 1 to 189. 228. The system of aspect 227, wherein the system further comprises an imaging apparatus according to any of aspects 190 to 226, wherein the imaging apparatus is operably connected to the processor and memory. 229. The system of aspect 227 or 228, wherein the memory further comprises instructions store thereon, which, when executed by the processor cause the processor to: control the imaging apparatus to collect images; and apply a numerical motion tracking algorithm to mitigate motion artifacts present in the images. 230. A non-transitory computer readable storage medium comprising instructions stored thereon, the instructions comprising an algorithm configured to implement the steps of a method of any one of aspects 1 to 189.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 231. A method for identifying a subject as having a heart rhythm disorder, the method comprising: imaging the heart of the subject using 4D ultrasound in order to generate spatio- temporal mechanical deformation data of the subject’s heart during one or more contractions; and inputting the mechanical deformation data into a model according to any one of claims 1 to 124, wherein the output of the model is used to determine if the subject has a heart rhythm disorder. 232. A method for performing catheter ablation on the heart of a subject having a heart rhythm disorder, the method comprising: imaging the heart of the subject using 4D ultrasound in order to generate spatio- temporal mechanical deformation data of the subject’s heart during one or more contractions; inputting the mechanical deformation data into a model according to any one of claims 1 to 124, wherein the output of the model is used to locate tissue associated with an abnormal electrical wave, an abnormal electrical pathway, or scar tissue; and ablating tissue associated with the abnormal electrical wave, the abnormal electrical pathway, or the scar tissue in order to disrupt formation or propagation of the abnormal electrical wave.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 The following is offered by way of illustration and not by way of limitation: EXPERIMENTAL Embodiments of methods of the present invention were applied in connection with obtaining experimental results described below. The experimental results described below relate to observing, visualizing, configuring, training, and implementing aspects of cardiac tissue models. As demonstrated in the above disclosure, the present invention has a wide variety of applications. The following is put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how to make and use the present invention and are not intended to limit the scope of what the inventors regard as their invention nor are they intended to represent that the experiments below are all or the only experiments performed. Those of skill in the art will readily recognize a variety of noncritical parameters that could be changed or modified to yield essentially similar results. Efforts have been made to ensure accuracy with respect to numbers used but some experimental errors and deviations should be accounted for. Example 1: Reconstruction of Three-Dimensional Scroll Waves in Excitable Media from Two-Dimensional Observations Using Deep Neural Networks 1.0. Overview Scroll wave dynamics are thought to underly life-threatening ventricular fibrillation. However, direct observations of three-dimensional electrical scroll waves remain elusive, as there is no direct way to measure action potential wave patterns transmurally throughout the thick ventricular heart muscle. Here whether it is possible to reconstruct simulated scroll waves and scroll wave chaos using deep learning is studied. Encoding-decoding convolutional neural networks were trained to predict three- dimensional scroll wave dynamics inside bulk-shaped excitable media from two- dimensional observations of the wave dynamics on the bulk's surface. Whether observations from one or two opposing surfaces would be sufficient and whether transparency or measurements of surface deformations enhances the reconstruction was tested. Further, the approach's robustness against noise was evaluated and the feasibility of predicting the bulk's thickness was tested. Isotropic and anisotropic, as wellAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 as opaque and transparent, excitable media were distinguished as models for cardiac tissue and the Belousov-Zhabotinsky chemical reaction, respectively. While it was demonstrated that it is possible to reconstruct three-dimensional scroll wave dynamics, it was also shown that it is challenging to reconstruct complicated scroll wave chaos and that prediction outcomes depend on various factors such as transparency, anisotropy, and ultimately the thickness of the medium compared to the size of the scroll waves. In particular, it was found that anisotropy provides crucial information for neural networks to decode depth, which facilitates the reconstructions. This work indicates deep neural networks could be used to visualize intramural action potential wave patterns from epi- or endocardial measurements. 1.1. Introduction Scroll wave dynamics occur in excitable reaction diffusion systems, termed ’excitable media’. They are conjectured to underly life-threatening heart rhythm disorders, such as ventricular fibrillation. In the heart, nonlinear waves of electrical excitation propagate through the cardiac muscle and initiate its contractions. The electrical waves are conjectured to degenerate into electrical scroll wave chaos via a cascade of wavebreaks during the onset of ventricular fibrillation. However, direct evidence for the existence of scroll waves in the heart is lacking. While the dynamics of scroll waves have been studied extensively in computer simulations [1–3], the direct visualization of scroll waves throughout the depths of the heart muscle remains a challenge. Spiral wave-like action potential waves can be imaged on the heart surface during ventricular tachycardia or fibrillation using voltage-sensitive optical mapping [4– 8], and the surface observations are in agreement with simulated three-dimensional scroll wave dynamics [3]. Otherwise, only few, and indirect experimental evidence of scroll waves in the heart exists. Voltage-sensitive transillumination imaging was used to measure projections of scroll waves on the surface of the isolated right ventricle of porcine and sheep hearts [9–11]. The right ventricles are thinner than the left and can therefore be penetrated (∼0.5 cm) by near-infrared light, making them semi-transparent. Consequently, it was possible to locate focal wave sources inside the volume of theAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 right ventricle using transillumination imaging [12, 13]. More recently, it was shown that ultrasound imaging can reveal mechanical vortices in the ventricles of whole isolated porcine hearts, which co-exist with electrical vortices on the epicardial surface, suggesting that the heart’s mechanical dynamics reflect electrical scroll wave dynamics [7, 14]. However, it remains difficult to extrapolate the measured projections or surface observations of the electrical dynamics into the depths of the cardiac muscle, and eventually correlate them with mechanical measurements. Fully three-dimensional reconstructions of scroll waves were obtained using optical tomography in the transparent Belousov-Zhabotinsky chemical reaction [15–18], which is an excitable medium that shares very similar wave dynamics with cardiac tissue. In contrast, three- dimensional action potential waves have been directly measured in small rat and zebrafish hearts using laminar optical tomography

[0019] or light-sheet microscopy

[0020] . However, attempts to obtain three-dimensional visualizations of scroll waves inside the optically dense cardiac muscle of large mammalian hearts have not yet attained a similar quality, and better measurement and reconstruction techniques are needed. Multiple numerical approaches for the reconstruction of scroll waves from surface observations have previously been proposed: Berg et al.

[0021] attempted to recover simulated scroll wave chaos from single-surface observations using a synchronization- based data-assimilation approach. However, while the approach was successful at recovering scroll wave chaos from sparse measurements within the medium, (e.g.,

[0022] ), it was not suited to extrapolate scroll wave dynamics into the three-dimensional bulk-shaped medium from surface observations. Hoffman et al. [23, 24] analyzed dual- surface observations (comparable to measuring both the epi- and endocardium) using a different data-assimilation approach, the local ensemble transform Kalman filter

[0025] , to successfully reconstruct simulated scroll waves. The question remains if it is possible to reconstruct truly complex three-dimensional scroll wave chaos from single- or dual- surface observations. More recently, neural networks were used to predict cardiac dynamics from sparse or partial observations with promising results [26–28]. However, the task of predicting scroll wave dynamics from surface observations using neural networks has not yet been established.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Here, a numerical proof-of-principle that deep encoding-decoding convolutional neural networks, under certain conditions, can be used to reconstruct three-dimensional scroll wave dynamics, including complicated scroll wave chaos, from two-dimensional observations of the dynamics is provided (FIG.20). It is shown that scroll waves can be recovered fully when the size of the waves is in the order of the thickness of the medium, or when analyzing projections of dynamics with more and smaller waves in transparent anisotropic excitable media. Several deep convolutional neural network architectures were tested, and their reconstruction performance was analyzed depending on opacity, thickness, and anisotropy of simulated excitable media. FIG.20: Deep learning-based reconstruction of scroll wave chaos inside a three- dimensional volume from partial observations of the dynamics on its surface. Scroll wave chaos is a model for the electrophysiological dynamics underlying ventricular fibrillation. Computer simulations were performed in isotropic and anisotropic bulk- shaped excitable media. A neural network (NN) predicts scroll wave dynamics underneath the bulk’s surface from a short temporal sequence (t1, …, t5) of two- dimensional observations (here shown for top layer). 1.2. Methods Simulations of three-dimensional electrical and electromechanical scroll wave dynamics were performed in bulk-shaped isotropic and anisotropic (elastic) excitable media, respectively, and neural networks were used to predict the three-dimensional wave patterns from a short sequence of two-dimensional observations of the dynamics on the bulk’s surface. ‘Laminar’ scroll wave dynamics, consisting of 1-3 meandering scroll waves, and ‘turbulent’ scroll wave chaos was distinguished. 1.2.1. Scroll Wave Dynamics in Elastic Excitable Media Electrical scroll wave dynamics were simulated in bulk-shaped excitable media of size 128×128×dz voxels with varying thicknesses or depths dz ∈ {8, …, 40}. The phenomenological Aliev-Panfilov model

[0029] was used to simulate nonlinear waves of electrical excitation: ^^ = ^ · − ^^ − − − ^^Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 ^^ ^^= ^(^, ^)(^^(^ + 1 − ^) − ^) (2) The dynamic variables u and r represent the local electrical excitation (voltage) and refractory state, respectively, and are dimensionless, normalized units. Together with the term (u, r) = ∈0 + µ1r / (u + µ2), the partial differential equations describe the local excitable kinetics and diffusive dynamics. The parameters k, a, ∈0, µ1 and µ2, listed in Table 1, influence the properties of the excitation waves. The partial differential equations were integrated using the forward Euler method in a finite differences numerical integration scheme and Neumann (zero-flux) boundary conditions were used. ^ = ^^^^^ (3) Both isotropic and anisotropic excitable media werewith locally varying fiber direction with diffusion coefficients for the parallel D∥fiber direction and perpendicular D⊥1, D⊥2 to it [1]: ^## ^#$ 0^=^%%= ^.$Here, the fiber organization represents ventricular muscle tissue with muscle fibers aligned in sheets in the x–y plane and the sheet-fiber orientation rotating throughout the thickness of the bulk. D⊥1 is the diffusivity perpendicular to the fiber axis in the x–y plane and D⊥2 transmurally, for simplicity D⊥ = D⊥1 = D⊥2 was set. A varying fiber angle θ(z) ranging from 0° to 90° was usedthe top and bottom layer of the bulk for the simulation depth dz = 24 voxels: +(,) = , · ∆+ (5)Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 For the other depths, dz∈ {8, 12, 16, 20, 28, 32, 40}, the same ∆θ was used as in the dz = 24 case. The ratio between the parallel D∥ and perpendicular D⊥ diffusion coefficients was set to 4:1. D⊥ = Diso = 0.05 was chosen, and ∆t was adapted for the Euler integration such that 500 simulation time steps correspond to about 0.5 − 1.0 scroll wave rotations. The simulation time steps required for one scroll wave rotation fluctuates and depends on the parameter values as well as an / -isotropy. To save disk space, only every 80th simulation time step was stored as one ‘snapshot’, such that 5 snapshots covered about a half to one scroll wave rotation, see also FIG.22. In addition to the purely electric simulations, electromechanical scroll wave dynamics in deforming excitable media were also simulated, as described in

[0022] . In short, a three-dimensional mass-spring damper system with hexahedral cells and tunable fiber anisotropy

[0030] was coupled to the electric simulation. Each cell in the mechanical part of the simulation corresponded to one cell or voxel in the electrical part of the simulation. Active tension generation in each cell was modelled using an active stress variable Tathat is directly dependent on the excitation variable u, as described in

[0031] : ^23^^= ∈ (^) · (^2^ − 45) (6)The force could be pointed into an arbitrary direction, and, throughout the bulk, the axis alignment matched the rotating orthotropic fiber alignment already defined in the electrical part of the simulation. The mechanical parameter kT and other parameters shown in Table 1 influence the magnitude of contraction and the properties of the elasticity of the mass- spring damper system. The elastic medium’s boundaries were non-rigid and confined by elastic springs acting on the medium’s boundary

[0022] . In general, the electromechanical simulation produces three-dimensional deformation patterns that are highly correlated with the electrical scroll wave chaos.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Table 1: Electrical (top) and mechanical (bottom) parameters used to simulate two different regimes of scroll wave dynamics: a ‘laminar’ regime (see FIGS.23, 24) and a fully ‘turbulent’ scroll wave chaos regime (see FIGS 25, 26 and 28). Electro-mechanical simulations were only performed with the ‘turbulent’ parameter set. Parameter ‘Laminar’ Set ‘Turbulent’ Set k 8 8 a 0.05 0.05 ε0 0.002 0.002 µ1 0.8 0.2 µ20.3 0.3 kT— 3 kij— 5 kj — 0.5 kf — 4 cf— 10 Two different regimes of scroll wave dynamics were simulated: 1) a ‘laminar’ regime with 1−3 meandering scroll waves with wavebreaks as shown in FIGS.23 and 24 and 2) a fully ‘turbulent’ scroll wave chaos regime as shown in FIGS.26-28 (see Table 1 for the respective parameter values). For both parameter regimes, 125 isotropic and anisotropic simulations of electrical scroll wave chaos were performed for different bulk depths – dz∈ {16, 24, 32, 40} voxels for the ‘laminar’ regime and dz∈ {8, 12, 16, 20, 24, 28, 32} for the ‘turbulent’ regime.100 simulations were used during generation of the training dataset and 25 simulations were exclusively used for evaluation. Furthermore, 125 simulations of electromechanical scroll wave chaos were performed for a thickness of dz= 24, with the same split between training and evaluated dataset. The electrical and mechanical parameters were identical in each simulation. However, the initial conditions ut = 0(x, y, z), rt = 0(x, y, z) were randomized and therefore different in each simulation. Cross-field stimulation was used to set ut = 0, rt = 0 such that two scroll waves are induced at random positions (x1, y1), (x2, y2). Additionally a small amount of Gaussian noise (standard deviation σ = 0.1) was added to the initialAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 conditions ut= 0, rt= 0. With both parameter sets, the dynamics quickly diverged. The first 75 snapshots of each simulation were discarded (approximately 15 scroll wave rotation periods) and the remaining 500 snapshots were used (approximately 100 scroll wave rotation periods) for generating the training or evaluation data, respectively. If the excitation in a simulation decayed (ut≈ 0 ∀(x, y, z)), the simulation was restarted with new initial conditions ut= 0, rt= 0. The training dataset consists of 20,000 randomly selected samples from the 100 training simulations, and the evaluation dataset uses 5,000 randomly chosen samples from the 25 evaluation simulations. Consequently, training and evaluation datasets were completely separate datasets. The numerical simulation was implemented in C++, and the source code for the simulations is available in

[0022] . FIGS.21A-21D: surface observations and projections of three-dimensional scroll wave chaos (‘turbulent’ parameter regime) in a bulk medium. A) Observation of the top surface of the bulk (layer 1) in single-surface mode. B) Observation of the top and bottom surfaces of the bulk (layers 1 and 24) in dual-surface mode. C) Observation of the electrical activity and mechanical motion on the top surface of the bulk (layer 1) in single-surface mode (red: motion vectors). In a-c), the medium is opaque and does not allow observations of the dynamics inside the medium below the top layer. D) Observation of the projection (transillumination) of the three-dimensional dynamics along the depth of the bulk. The projection is calculated by summing the values in all 24 layers along the z-axis for a specific (x, y)-coordinate and dividing the sum by the number of layers. All layers 1−24 are cross-sections in the x−y plane. FIG.22: Observations of three-dimensional scroll wave (‘laminar’ parameter set) on the top and bottom surfaces of an opaque medium, and in the projection of the full dynamics in a transparent medium in the bulk’s z-direction (depth). In each case, the neural network analyzes a short sequence of 5 snapshots, which are sampled at discrete times (red) over the period of the scroll wave from the simulation data, see section II B for details. In the simulations, one rotational period corresponds to about 500 simulation time steps.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 1.2.2. Deep Learning-based Reconstruction of Scroll Wave Dynamics Deep neural networks were implemented and tested, which each analyze a short temporal sequence of 5 subsequent two-dimensional snapshots of electrical wave patterns ũt(x, y) to reconstruct a single fully three-dimensional snapshot ut(x, y, z) of scroll wave dynamics: (ũ#(=, >), ... , ũ?(=, >)) → ^#(=, >, ,) (7) It was empirically found that 5 snapshots provide sufficient information about the dynamics (see, e.g.,

[0026] or

[0032] ). Reconstructing the dynamics with a series of 10 snapshots was also tested and no improvement in performance was observed compared to 5 snapshots. Consequently, 5 snapshots was used by default. Further, it was found that the reconstruction accuracy does not depend on whether the network analyzes the current snapshots plus 4 snapshots sampled in the past or in the future with respect to the current snapshot, or whether 2 are sampled in the past and 2 in the future, respectively. The two-dimensional snapshots (see FIGS.21, 22 and 25) are either i) the top surface layer (single-surface mode, FIG.21A): ũ^(=, >) = ^^(=, >, 1) (8) ii) both the top and bottom surface layer (dual-surface mode, FIG.21B): ũ^(=, >) = (^^(=, >, 1), ^^(=, >, A,)) (9) iii) both the electrical wave dynamics and the mechanical displacements A = (dx, dy) which occur in corresponding electromechanical simulations from the top surface layer (single-surface mode), see FIG.21C): ũ^(=, >) = (^^(=, >, 1), A=(=, >, 1), A>(=, >, 1)) (10) or iv) a projection of all u-values along the z-direction (depth) of the bulk (FIG. 21D): ũ#^(=, >) = ∑C^FD# ^^(=, >, / ) (11)Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 For the top+bottom case (iii) and the mechanical displacement case (iv), the snapshots were interleaved. The neural network architectures chosen require three- dimensional input samples ((128, 128, 5) for case (i) and (ii)), whereas in cases (iii) and (iv) the sample shape is (128, 128, 5, 3) and (128, 128, 5, 2) respectively. Their shape was changed to be three-dimensional by stacking the components: e.g., in case (iv) the resulting shape is (128, 128, 10) using the top layers for the even indices and bottom frames for the odd indices (u1(x, y, 1), u1(x, y, dz), u2(x, y, 1) … u5(x, y, dz)). Four different neural network architectures were evaluated with basic and more intricate designs for the three-dimensional bulk prediction task (Eq.7). While a U-Net

[0033] architecture was primarily use, it was validated against a simple Encoder-Decoder architecture, TransUNet

[0034] and MIRNet

[0035] . The Encoder-Decoder convolutional neural network (CNN) is similar to the architecture used in [26, 32]. It consists of an encoder stage where the spatial resolution is progressively decreased, a latent space, and a decoder stage where the spatial resolution is progressively increased back to the original resolution. The encoding and decoding steps consist of three steps, in each two padded two-dimensional convolutional layers (2D-CNN) with filter size 3×3 and rectified linear unit

[0036] (ReLU) activation are applied, followed by batch normalization

[0037] and maxpooling (encoder) or upscaling (decoder), respectively. The number of filters in 2D- CNN layers in order are 128, 128, 256, 256, 512, 512, 256, 256, 128 and 128. The U- Net architecture is identical to the Encoder-Decoder CNN architecture, except that skip connections are added between the encoder and decoder stages (see

[0033] ). The TransUNet combines the U-Net architecture with self-attention mechanisms of Transformers

[0038] in its latent space. The MIRNet architecture is different from the other evaluated architectures, as it contains parallel multi-resolution branches with information exchange, as well as spatial and channel attention mechanisms

[0035] . It aims at maintaining spatially precise high-resolution representations through the entire network, while simultaneously receiving strong contextual information from the low-resolution representations. For all neural network architectures the generalized Charbonnier loss function was use [39, 40]: G(^, ^H) = I(^H − ^)$+∈$(12)Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 where u is the three-dimensional ground truth, ^H the prediction and ∈ = 0.001 was chosen. The Charbonnier loss function behaves like L2 loss (mean squared error) when u ≈ ^H and like L1 loss (mean absolute error) otherwise. The accuracy of the predictions was evaluated on the evaluation datasets with the root mean squared error (RMSE) on each z-axis layer: JKLM(,) = N# $O ∑Q,R,^(^H(=, >, ,, P) − ^(=, >, ,, P)) (13) To validate the findings, it was studied if a neural network can accomplish a simpler task than the three-dimensional prediction: estimate the depth dz of the simulation bulk from 5 two-dimensional observations. Both a depth regression and a depth classification neural network were tested, which each predict the depth dz of the simulation bulk: (^S#(=, >), ... , ^S?(=, >)) → AT(14) The depth regression network predicts the depth dz as a continuous value, while the depth classification network predicts the depth dzas one of {8, 12, 16, 20, 24, 28, 32}. For this task the encoder part from the Encoder-Decoder architecture was used, followed by a global average pooling layer, two dense layers with 1024 filters with batch normalization and ReLU activation, and ultimately an output dense layer with one filter (for regression) or seven filters (for classification). For the depth classification neural network a categorical cross-entropy loss function was used with a softmax activation function for the last layer, and for the depth regression network mean squared error as loss function and ReLU as activation function. The datasets for the depth estimation was generated from the bulk prediction task datasets.4,000 random samples were used for each depth for the training dataset and 500 samples for the evaluation dataset (in total 28,000 training samples and 3,000 evaluation samples). The networks were trained using the Adam

[0041] optimizer with a learning rate of 10−3for the bulk prediction tasks and 10−5for the depth regression and classification task for 20 epochs. A batch size of 32 was used for the Encoder-Decoder and U-Net architectures and a batch size of 4 was used for TransUNet and MIRNet. All neuralAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 network models were implemented in Tensorflow

[0042] using Keras

[0043] . Training and reconstructions were performed on NVIDIA RTX 24000 graphics processing units (GPUs). Table 2: Different neural network architectures used in this study and their respective number of trainable parameters and training times for 20 epochs. Training was performed on a single NVIDIA RTX 24000 GPU. Model Parameters Training Time Encoder-Decoder 6,829,309 44 min U-Net 8,278,168 55 min TransUNet 406,899,608 19 hours MIRNet 145,358,026 17 hours dz Regression 426,593 5 min dz Classification 432,743 5 min FIGS.23A-23C: Predictions of three-dimensional ‘laminar’ scroll wave dynamics from two-dimensional observations using deep convolutional encoding-decoding neural network (U-Net) in an anisotropic excitable medium (128 × 128 × 24 voxels). A) Ground- truth scroll wave dynamics (5 random representative snapshots). The simulations exhibit scroll waves with meandering and curved vortex cores (see also FIG.24D), wavebreak, and dissociation between the top and bottom surface dynamics (see FIG. 25). B) Predictions from two-dimensional wave pattern visible only on the top surface of the bulk when the medium is completely opaque. The reconstruction accuracy decreases slightly with increasing depth (wave pattern becomes fuzzy towards the bottom). C) Predictions from two-dimensional projection of the whole three-dimensional dynamics along the z-axis in a transparent medium. The prediction accuracy is slightly better than in B), particularly towards the bottom layers of the bulk. Overall, the predictions and the ground-truth are visually difficult to distinguish from each other. The data was not seen by the network during training. FIGS.24A-24D: Predictions of three-dimensional scroll wave dynamics (‘laminar’ parameter set) and their vortex filaments from either single- or dual-surfaceAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 observations in a thick, opaque, anisotropic excitable medium (128×128×40 voxels). A) Ground-truth scroll wave dynamics. B) Prediction from the top surface only. C) Prediction from both the top and bottom surfaces. In dual-surface mode, the network is able to recover the dynamics sufficiently well. Arrow indicates direction of cross- sectional view. D) Ground-truth vortex filaments (gray) and vortex filaments calculated from predicted scroll wave dynamics (red). In single-surface mode, predictions become unreliable (wave pattern becomes fuzzy / vortex filaments do not match) towards the bottom of the bulk. Reconstructions performed with U-Net. FIGS.25A-25C: Different electrical wave patterns as seen in the A) top layer, B) bottom layer and C) projection of all layers of a three-dimensional bulk. Bulk sizes are 128×128×24 voxels (left and right) and 128×128×40 voxels (center), respectively. With increasing bulk thickness or smaller scroll waves, the top and bottom layers are dissociated because the dynamics become increasingly three-dimensional. The projection is calculated for a given (x, y)-coordinate by averaging the u-values (u ∈ [0, 1]) along the depth (z-direction) of the bulk. Data (from left to right) shown in FIGS.23, 24 and 28, respectively. The left and center snapshots are from the ‘laminar’ parameter regime, while the ones on the right are from the ‘turbulent’ chaotic parameter regime. 1.3. Results Using deep convolutional neural networks, it is possible to reconstruct three- dimensional scroll wave dynamics inside an excitable medium when the medium’s thickness is not much thicker than the scroll wave (see, e.g., FIG.23 and section 1.3.1 below). Reconstructions become increasingly difficult in thicker excitable media or with smaller scroll waves and more complicated dynamics (see, e.g., FIGS.24, 28A and sections 1.3.1-1.3.3 below). However, complicated scroll wave chaos can be reconstructed in transparent anisotropic excitable media (see FIGS.27D, 28B, 29C and 29F), or with dual-surface observations in thinner opaque excitable media (see FIGS. 24C, 27B and section 1.3.2 below). 1.3.1. Medium Thickness vs. Scroll Wave Size The thickness of the excitable medium and the size of the scroll waves with respect to the thickness of the medium determine to what extent and with whichAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 accuracy scroll wave dynamics can be reconstructed. To test the reconstruction performance with different size ratios, ‘laminar’ scroll waves (see FIGS.23 and 24) and ‘turbulent’ scroll wave chaos (see FIGS.26, 27C and 28A) were simulated in bulks with varying thicknesses. While the reconstructions from single surface observations are very accurate for the ‘laminar’ scroll wave dynamics in the thinner bulk (with thickness dz = 24) shown in FIGS.23A-23B, reconstructions become increasingly inaccurate with increasing thickness and prediction depth. The reconstructions of the ‘laminar’ scroll wave dynamics in the thicker bulk (with thickness dz= 40), shown in FIG.24A-24B, exhibit artifacts towards the bottom half of the bulk. Accordingly, the vortex filaments computed from the predicted scroll wave dynamics (red) exhibit substantial mismatches compared to the ground-truth vortex filaments (gray) in the lower half of the bulk, see FIG.24D. With increasing bulk thickness, the three-dimensional character and complexity of the wave dynamics increases, which is reflected by the dissociation of the top and bottom layers (see FIGS.25 and 26) and also by the various orientations of the vortex filaments in FIG.24D. The degree of dissociation and the average scroll wave size relative to the medium’s thickness ultimately determine the prediction accuracy at deeper layers. The ’horizon’ up to which the predictions are successful appears to be approximately one scroll wavelength, also compare the bottom half of the thick bulk with ‘laminar’ scroll wave dynamics in FIG.24B to the bottom half of the thinner bulk with ‘turbulent’ scroll wave chaos in FIGS.27B and 27A. In general, the reconstructions become increasingly difficult the deeper one aims to predict in opaque excitable media, and they do not succeed beyond the first layer of scroll waves. Correspondingly, the plots in FIG.29A-29D show how the prediction error increases in opaque excitable media with increasing depth z (in bulks with different depths dz= 8, 12, … , 40) with ‘laminar’ and ‘turbulent’ scroll wave dynamics, respectively. The error increases approximately linearly with increasing depth and increases faster with thicker bulks and faster with ‘turbulent’ than with ‘laminar’ scroll wave dynamics. The error profiles obtained with the deep learning-based reconstruction were compared with a naive reconstruction in which the top layer is simply repeated in each following layer in FIG.36. The naive reconstruction produces significantly steeper error curves with both ‘laminar and ‘turbulent’ scroll wave dynamics. The curves in FIG.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 29A and 29D indicate that the average reconstruction accuracies in FIG.23B and FIG. 24B are approximately 0.05 and 0.15 (RMSE) at midwall, respectively, while the deepest layers shown in FIG.24B yield reconstruction errors in the order of 0.2−0.5 (RMSE). By comparison, the worst average reconstruction error at the maximal depth of the ‘laminar’ scroll wave shown in FIG.25B is about 0.1 (RMSE) (see blue curve in FIG. 30B). Note that a root mean squared error of 0.1 (RMSE) corresponds to about 0.05 mean absolute error (MAE). The average single-surface reconstruction error for the ‘laminar’ scroll wave in FIG.25B is better than 95%. Overall, the reconstruction error fluctuates moderately over time, remains small at smaller depths, and increases as the reconstruction error increases with larger depths (see FIG.31). Videos demonstrating the reconstructions for ‘laminar’ and ‘turbulent’ scroll wave dynamics and giving an impression of the temporal stability of the reconstructions were produced. FIG.26: Bulk thickness and transmurality of scroll wave dynamics. ‘Turbulent’ scroll wave chaos with different bulk thicknesses dz= {8, 12, 16, 20, 24}, also shown in corresponding cross-sections. The dynamics are quasi two-dimensional with dz= 8. Dissociation between top and bottom layers starts to emerge at dz = 12 as the dynamics become increasingly three-dimensional. At dz> 12 the dynamics are fully three- dimensional. FIGS.27A -27D: Predictions of (‘turbulent’) electrical scroll waves in subsurface layers of anisotropic (left) and isotropic (right) bulk tissue with dimension 128×128×24 voxels. A) Ground-truth scroll wave dynamics (representative snapshots). B) Prediction in dual-surface mode analyzing the top and bottom layers of an opaque bulk tissue. C) Prediction in single-surface mode analyzing the top surface layer of an opaque bulk. D) Prediction analyzing the z-projection of the dynamics along its depth (or z-axis) in a transparent bulk. The depth-profile of the prediction error (RMSE: root mean squared error) along the z-axis is shown to the right of each prediction. The reconstruction is successful in anisotropic transparent media, but fails in isotropic transparent media, as shown in D). In opaque media, the reconstruction performs sufficiently well in dual- surface mode with larger errors emerging at midwall of the bulk, as shown in B). In transparent isotropic media, the subsurface prediction fails because the network isAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 unable to infer the depth of the layers. Cross-sections intersect the bulk at its center. All reconstruction with U-Net. FIG.31: Average reconstruction error per layer (depth) over time in an anisotropic excitable medium with thickness dz= 24 shown for 5 different depths. Left: In opaque media and single-surface mode, the prediction error increases and fluctuates more with increasing depth. Right: In transparent media, the prediction error stays small throughout the different depths. Both plots derived for the ‘laminar’ scroll wave dynamics as shown in FIG.23. 1.3.2. Single-Surface vs. Dual-Surface Observations Low prediction depths in opaque excitable media can be overcome by analyzing both the top and bottom surface layers in dual-surface mode rather than single-surface mode, respectively. FIGS.24C and 27B demonstrate how the reconstruction improves in a thick bulk with the ‘laminar’ scroll wave and in a thin bulk with ‘turbulent’ scroll wave chaos, respectively. The vortex filaments (red) in the thick bulk in FIG.24C match the ground-truth vortex filaments (gray) much better in dual- than in single-surface mode. The plots in FIGS.29B, 29E and 30 show how the profile of the reconstruction error changes in dual-surface mode. Surprisingly, the network does not appear to benefit from the additional information from both surfaces of the bulk in dual-surface mode with scroll wave chaos: the steep linear increase in the error persists on both sides and the network is not able to significantly reduce the error at midwall (see FIG.29B). Nevertheless, it is possible to slightly reduce the error at midwall when reconstructing larger scroll waves (see FIGS.24C, 29B and 30B). The data suggests that it could be possible to reconstruct scroll waves in the heart using epi- and endocardial optical mapping recordings if the scroll wavelength is not much shorter than the thickness of the ventricular wall. 1.3.3. Transparent vs. Opaque Excitable Media While it is challenging to reconstruct scroll wave dynamics or scroll wave chaos in thicker opaque excitable media, the reconstructions succeed in transparent excitable media of any thickness (of the thicknesses tested). However, the reconstructions only succeed under the condition that the excitable media are anisotropic. FIGS.27 and 28Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 show a comparison of reconstructions obtained in an opaque and transparent excitable medium, respectively. FIG.27 shows cross-sections along the depth of the bulk (z- direction) whereas FIG.28 shows layers parallel to the surface in the x-y plane of the bulk. Comparing FIGS.27C and 27D and FIGS.28A and 28B, it becomes immediately apparent that it is possible to obtain highly accurate reconstructions of scroll wave chaos in transparent, anisotropic excitable media, while it would not be possible to obtain similar reconstructions in opaque media (see also plots in FIG.35 with isotropy). FIG.29C shows that the reconstruction error stays small transmurally throughout the entire bulk if the excitable medium is transparent and anisotropic. The prediction error is < 0.1 (RMSE) with various bulk depths (dz = 8 − 32) and with the ‘laminar’ and ‘turbulent’ scroll wave dynamics. Importantly, as can be seen in the right panel in FIG. 27D, the reconstruction completely fails in isotropic transparent excitable media (see also FIG.35). The effect of anisotropy on the prediction is discussed in more detail below. FIGS.28A -28B: Predictions of electrical scroll waves within subsurface layers of a bulk-shaped ‘turbulent’ anisotropic excitable medium from observing either A) the top layer of the bulk or B) the projection of the three-dimensional wave pattern in a transparent bulk along its depth (or z-axis). The bulk’s dimensions are 128×128×24 voxels and predictions were performed with the U-Net architecture. Predictions are shown for the 24 layers along the z-axis of the bulk, where the first layer is the top layer and the 24th layer is the bottom layer. First row: The five two-dimensional frames (t1, … , t5) which are the input for the neural network prediction. Second row: Ground truth (GT) electrical excitation wave pattern within cross-sectional layers (1-24), of which layers 2-24 cannot be observed. Note that the pattern changes from layer to layer throughout the bulk. Third row: Prediction of the current cross-sectional layer (1-24) by the neural network. Fourth row: Absolute difference per voxel between prediction and ground-truth. FIGS.29A-29F: Average reconstruction error over bulk depth (RMSE: root mean squared error along z-axis) in opaque (A, B, D, E) or transparent (C, F) excitable media with anisotropy (with varying bulk depths of dz ∈ {8, 12, … , 40}). All reconstructions were performed with U-Net. A-C) ‘Laminar’ scroll wave dynamics as shown in FIGS.23Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 and 24: A) Single-surface mode (see also FIGS.25B and 24B). B) Dual-surface mode. C) Projection (see also FIGS.25C and 24C). ‘Turbulent’ scroll wave chaos as shown in FIG.26: D) Single-surface mode (see also FIGS.27C and 28A). E) Dual-surface mode (see also FIGS.21B and 27B). F) Projection (see also FIGS.27D and 28B). An error of 0.1 (RMSE) corresponds to a mean absolute error (MAE) of about 5%. In opaque excitable media, the reconstruction error increases approximately linearly with depth. In transparent media with anisotropy the error remains flat and below 0.1. Separate U-Net neural networks were trained for each combination. See also FIG.35 for a comparison with isotropic excitable media and FIG.36 for a comparison of the deep learning-based reconstruction with a naive reconstruction in which the top layer is simply repeated in each following layer. 1.3.4. Anisotropy While ventricular muscle tissue is highly anisotropic (orthotropic muscle fiber organization), the Belousov-Zhabotinsky chemical reaction is isotropic. Both systems exhibit scroll waves, but the scroll wave morphology can be very different in anisotropic versus isotropic excitable media. In anisotropic media, scroll waves are elongated in fiber direction as they propagate faster along the fiber direction. This phenomenon can often be observed in optical mapping recordings. In the simulated anisotropic bulk, the waves are elongated differently at different depths, which is presumably why the reconstructions succeed in transparent excitable media as shown in FIGS.29C and 29F. By contrast, in isotropic excitable media the scroll waves are similarly shaped throughout the bulk, and therefore the network cannot distinguish scroll waves closer to the surface from scroll waves deeper in the bulk (see also FIG.36). Anisotropy does not affect the reconstructions in opaque excitable media, as the reconstruction does not rely on depth information. 1.3.5. Analyzing Surface Deformation If the network analyzes the mechanical deformation of the surface in addition to the excitable wave patterns visible on the same surface, the reconstruction improves slightly (see plot ‘Top + Motion’ in FIG.30A). This behavior was tested with ‘turbulent’ scroll wave chaos (the U-Net architecture and the single-surface configuration shown inAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIG.21C) and it was found that the reconstruction improves slightly, but not substantially. This is a surprising finding, because deformation on the surface may also occur due to contractile activity within the bulk. The reconstruction error does not increase as steeply with increasing depth as when analyzing electrics in single-surface mode alone. The reconstruction accuracy improves by roughly 25% at midwall (with a bulk thickness of dz = 24 layers). It was found that there was no significant difference between analyzing only two-dimensional in-plane displacements ^U = (ux, uy) with x- and y-components versus three-dimensional displacements with also a z-component (see also eq. (10) in section 1.2.2). That the latter finding is specific to the methodology of this example and the mechanical boundary conditions that were used in the simulations cannot be excluded. FIGS.30A-30B: Comparison of reconstruction errors obtained with different imaging configurations in opaque anisotropic excitable medium (with thickness dz= 24 layers) with A) ‘turbulent’ scroll wave chaos and B) ‘laminar’ scroll wave dynamics. In the different configurations, the network (U-Net) analyzes i) in single-surface mode the electrics on the top layer (blue), ii) in single-surface mode the electrics and motion on the top layer (green), iii) in dual-surface mode the electrics on both top and bottom layers (orange), and iv) the z-projection of the three-dimensional electrics (red). All reconstruction errors were calculated per depth as root mean squared error (RMSE). 1.3.6. Noise Reconstructions can be performed with noise (see, e.g., FIG.32) if the network was previously trained with noise, similarly as described in

[0026] and

[0032] . The noise can be present in either the surface observations or projections. FIGS.32A and 32B show reconstructions of scroll wave dynamics with noise in an opaque and a transparent anisotropic excitable medium (thickness: dz= 24 layers), respectively. In the opaque bulk in single-surface mode, the slope of the reconstruction error is slightly steeper with noise than without. In the transparent bulk, the error profile remains flat and stays below 0.1 (RMSE) with noise. This behavior was tested with Gaussian noise and noise levels of up to σ = 0.2, shown in FIG.32 (top right in each panel). FIGS.32A-32B: Noise does not pose a limitation for the deep learning-based reconstructions (performed with U-Net on ‘laminar’ scroll wave dynamics).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Reconstructions succeed in the presence of various noise levels (σ = 0.05, … , 0.2) in both A) opaque and B) transparent anisotropic excitable media. Top: Gaussian noise with standard deviation σ was added onto the input images. Bottom: Error profiles along depth increase only slightly (light pink curve: σ = 0.0, black curve: σ = 0.2). 1.3.7. Network Types Several deep neural network architectures were tested (basic Encoder-Decoder, U-Net, TransUNet and MIRNet, see also section 1.2.2) on the ‘turbulent’ scroll wave chaos prediction task and it was found that the prediction behavior is very similar across the different architectures (see FIG.33). It was observed that the MIRNet architecture produces the lowest reconstruction error, while Encoder-Decoder, U-Net, and TransUNet all have similar but slightly higher reconstruction errors. In opaque excitable media, the prediction error (RMSE: mean root squared error) rises linearly and steeply with deeper layers equally with all networks, as seen for the single-surface reconstructions shown in FIG.33A for anisotropic scroll wave chaos in a bulk with thickness dz= 24. The prediction error saturates equally with all networks at depths dz> 10 where they produce maximal prediction errors of about 0.3 (RMSE). MIRNet provides a slightly lower maximal error than the other networks. All networks achieve small prediction errors of < 0.1 (RMSE) in transparent excitable media with anisotropy, as seen for the projection reconstructions shown in FIG.33B for anisotropic scroll wave chaos in a bulk with thickness dz = 24. MIRNet provides the lowest error of less than 0.05 (RMSE), whereas the other networks produce errors ranging between 0.06−0.1 (RMSE). All networks produce the same characteristic error profile. Note that an RMSE of 0.1 corresponds to a mean absolute error (MAE) of about 5%. Therefore, all networks achieve reconstruction accuracies of greater than 95% in transparent excitable media. MIRNet even achieves reconstruction accuracies in the order of 97%−98%. As described in section 1.2.2, U-Net differs from the Encoder-Decoder architecture in the inclusion of long skip connections, while TransUNet is a U-Net with a Transformer as the latent space. MIRNet is different in that it has multi-resolution branches with information exchange as well as self-attention mechanisms. The training times for 20 epochs and the number of trainable parameters for each network architecture are listed in Table 2. Given that TransUNet and MIRNet provided either noAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 or incremental improvements in prediction accuracy, while requiring significantly longer time to train, U-Net was primarily used in this study. U-Net required about an hour to train, while being competitive with the accuracy of MIRNet, which required almost a full day to train. All other results in FIGS.23-28 were obtained with the U-Net architecture, if not stated otherwise. Several U-Net sizes were tested: a small model with 0.5M parameters, a medium network with 2M parameters and a large model with 8M parameters, it was determined that larger models perform significantly better, and subsequently the largest model was used. In some circumstances U-Net and TransUNet exhibited a significantly better reconstruction performance than the Encoder- Decoder network, but significant differences in accuracy between U-Net and TransUNet was not observed. FIGS.33A-33B: Reconstruction errors obtained with different neural network architectures for ‘turbulent’ scroll wave chaos in a bulk with thickness of dz = 24. A) Steep increase of reconstruction error with all networks (Encoder-Decoder, U-Net, TransUNet, MIRNet) in opaque excitable media from a single surface (top). B) Low and relatively flat reconstruction errors (below 10%) with all networks in transparent anisotropic excitable media (projection). MIRNet performs slightly better than the other networks. All reconstruction errors stated as root mean squared error (RMSE). 1.3.8. Depth Estimation It is possible to estimate the thickness or depth dz of transparent bulks from projections of the corresponding scroll wave dynamics using either a regression or classification neural network. By contrast, it is not possible to reliably predict the thickness of opaque bulks using either approach. FIG.34A shows predictions obtained with a regression neural network in transparent media, which estimates the depth accurately with floating point precision (with a certain degree of uncertainty). FIG.34C shows a confusion matrix with depth predictions obtained with a classification neural network also in transparent media, which performs better than the regression. Out of ∼500 predictions per thickness, only few attempts falsely classify the thickness (off- diagonal values). For both panels 34A and 34C, predictions were made from two- dimensional observations as shown in FIGS.25C and 34E. In particular, FIG.34E shows how the contrast of the waves decreases with increasing bulk thickness as moreAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 and more waves are superimposed and the signal is averaged along the z-axis. The neural network presumably associates the bulk’s thickness with the contrast. Both the regression and classification neural networks are unable to predict the depth of opaque media correctly, as shown in FIGS.34B and 34D. The classification neural network predicts random thicknesses and fails completely at correctly classifying the bulk’s actual thickness. For both panels 34B and 34D, predictions were made from two-dimensional observations as shown in FIG.25A or 25B. The data demonstrates that predicting the extend of scroll wave chaos is challenging with opacity, at least with the methodology used as discussed in this example. While scroll wave dynamics can vary qualitatively with different bulk thicknesses, in particular with thinner bulks, as shown in FIGS.25-27, there is a critical thickness beyond which the dynamics are dominated by the intrinsic excitable kinetics and are less influenced by the bulk’s geometry and its boundaries, thus making depth predictions from surface observation challenging. FIGS.34A-34E: Prediction of bulk thickness from surface observations of scroll wave chaos in A,C) transparent bulk medium with projection observations and B,D) opaque bulk medium with top surface observations. The bulk thickness was predicted using either A,B) a regression (black line shows ideal prediction dprediction = dtrue) or C,D) a classification neural network, respectively (all in anisotropic media). In transparent media, the thickness can be predicted from observations as shown in FIG.25C, whereas in opaque media neither the regression nor classification neural networks predict the thickness correctly. E) Exemplary projection images for bulk thicknesses or depths dz = 8, dz = 16, and dz = 32. Due to the averaging, the contrast of the waves decreases with increasing depths. 1.4. Analysis and Conclusions It was demonstrated that deep neural networks can be used to reconstruct three- dimensional scroll wave dynamics from two-dimensional observations of the dynamics on the surface of excitable media. Reconstructions succeed throughout fully opaque excitable media when the scroll wave size is not much smaller than the medium’s thickness. In that case, scroll waves can take on complex shapes with their vortexAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 filaments being arbitrarily oriented in space, producing significant dissociation between the surface dynamics on two opposing surfaces of the medium. However, multiple layers of scroll waves are challenging to reconstruct using encoding-decoding convolutional neural networks in opaque media, even when the dynamics are analyzed from two opposing surfaces of the medium. Reconstructions can be performed particularly well in transparent anisotropic excitable media, in which it is possible to reconstruct complicated scroll wave chaos far into the medium. That encoding-decoding convolutional neural networks can reconstruct three- dimensional dynamics from two-dimensional observations is facilitated by their training on tens of thousands of similar examples. Further generalization can be achieved by diversifying the training dataset, e.g., by adding simulations with a broad range of parameters to the training data or by performing data augmentation. The amount of information that encoding-decoding convolutional neural networks can extract from the short sequence of snapshots to perform the 2D-to-3D prediction task is remarkable. However, it is also revealing that the dual-surface reconstruction does not provide any benefit or synergistic effects over the single-surface reconstruction. It is as if the network performs two separate reconstructions from either side. This highlights fundamental limitations of convolutional encoding-decoding neural networks in this particular application. One interesting detail that was found is that in transparent excitable media the reconstruction outcomes are very good with anisotropy, but poor with isotropy. Scroll wave chaos cannot be reconstructed at all in transparent isotropic excitable media, and reconstructions of simpler scroll wave dynamics exhibit artifacts. These findings show that anisotropy is crucial because it implicitly encodes depth. The neural network learns to associate the alignment of the waves with the underlying fiber alignment which varies with depth. Moreover, it is able to decode this encoding even when multiple waves are superimposed in the projections (see FIGS.25C, 28B and 34E). Accordingly, the reconstructions exhibit artifacts or fail entirely in isotropic transparent excitable media as the network lacks depth information. Presumably, it would equally fail in anisotropic excitable media with uniform linearly transverse anisotropy. Unfortunately, this means that this feature cannot be exploited and is neither directly applicable to ventricularAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 fibrillation, because the ventricular muscle is opaque, nor to the Belousov-Zhabotinsky reaction, which is transparent but isotropic. Nevertheless, the methodology of this example discussed above could still be used to reconstruct intramural action potential waves including scroll waves inside cardiac tissue: 1) Transillumination imaging [9–13], near-infrared optical mapping

[0044] , or other optical techniques [19, 20], which allow imaging of action potential waves deeper inside cardiac tissue, could be used in the transilluminated right ventricle, in the atria or in small animal hearts such as mouse or zebrafish hearts. The muscle fiber architecture in the projections of the transilluminated translucent tissues could enable the depth encoding.2) Dual-surface imaging with superficial electrode mapping or fluorescent dyes lacking the penetration depth (such as Di-4-ANEPPS) could be used to reconstruct ‘laminar’ episodes of ventricular tachycardia or atrial fibrillation. The wavelengths of single scroll waves or macro-reentries during ventricular arrhythmias are larger than the thickness of the right and left ventricular walls. The atria, which exhibit epi- and endocardial dissociation during atrial fibrillation [45–49], are presumably thin enough for dual-surface reconstructions to succeed. However, the training data would have to account for the complex anatomy of the atria

[0050] as well as the particular wave dynamics. Whether it will be possible to create ground-truth data or to train a neural network on simulated data and subsequently apply it to experimental data needs to be determined in future research. It was found that the latter approach is in principle feasible. Lastly, the deep learning-based reconstructions can be performed very efficiently within milliseconds on a graphics processing unit, and they do not require the collection of long time-series data. Similar encoding-decoding convolutional neural networks were used for the prediction of electrical scroll wave chaos from three-dimensional mechanical deformation

[0032] , as well as for the prediction of phase maps and phase singularities from two-dimensional electrical spiral wave chaos

[0026] . While the networks performed very well in these applications, some of the results presented in this study, particularly the results for scroll wave chaos, are more sobering. This study is another example of the more general notion that cardiac dynamics, and chaotic dynamics more generally, are challenging to predict [27, 51–55]. It is well known that classical deep learningAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 approaches excel at interpolating, but do not perform well at extrapolating, which is what this study aimed to do. Therefore, the complete reconstruction of complicated fine- scaled scroll wave dynamics from surface observations in opaque excitable media will require more sophisticated techniques than encoding-decoding convolutional neural networks. It was demonstrated that it is possible to reconstruct three-dimensional scroll wave dynamics from two-dimensional observations using deep encoding-decoding convolutional neural networks. Reconstructions succeed under two conditions: either i) the medium is transparent and anisotropic with spatially varying anisotropy or ii) the medium is opaque, and the dynamics are observed on two opposing surface layers while the scroll wavelength is not much shorter than the medium’s thickness. In the future, the above discussed methodology of this example could be used to reconstruct transmural action potential wave dynamics from epicardial or endocardial measurements. 1.5. References The numbering related to the following references apply with respect to the experimental results presented in Example 1: [1] F. Fenton and A. Karma, Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation, Chaos: An Interdisciplinary Journal of Nonlinear Science 8, 20 (1998). [2] R. H. Clayton, Vortex filament dynamics in computational models of ventricular fibrillation in the heart, Chaos: An Interdisciplinary Journal of Nonlinear Science 18, 043127 (2008). [3] P. Pathmanathan and R. A. Gray, Filament dynamics during simulated ventricular fibrillation in a high-resolution rabbit heart, BioMed Research International 2015, 10.1155 / 2015 / 720575 (2015). [4] J. M. Davidenko, A. V. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife, Stationary and drifting spiral waves of excitation in isolated cardiac muscle, Nature 355, 349 (1992).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 [5] A. M. Pertsov, R. Davidenko, J. M. Salomonsz, W. T. Baxter, and J. Jalife, Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle, Circulation Research 72, 631 (1993). [6] A. Winfree, Electrical turbulence in three-dimensional heart muscle, Science 266, 1003 (1994). [7] J. Christoph, M. Chebbok, C. Richter, J. Schroder-Schetelig, P. Bittihn, S. Stein, I. Uzelac, F. H. Fenton, G. Hasenfuss, R. J. Gilmour, and S. Luther, Electromechanical vortex filaments during cardiac fibrillation, Nature 555, 667 (2018). [8] I. Uzelac, S. Iravanian, N. K. Bhatia, and F. H. Fenton, Spiral wave breakup: Optical mapping in an explanted human heart shows the transition from ventricular tachycardia to ventricular fibrillation and self-termination, Heart Rhythm (2022). [9] W. T. Baxter, S. F. Mironov, A. V. Zaitsev, J. Jalife, and A. M. Pertsov, Visualizing excitation waves inside cardiac muscle using transillumination, Biophysical Journal 80, 516 (2001).

[0010] O. Bernus, K. S. Mukund, and A. M. Pertsov, Detection of intramyocardial scroll waves using absorptive trans-illumination imaging, Journal of Biomedical Optics 12, 014035 (2007).

[0011] B. G. Mitrea, M. Wellner, and A. M. Pertsov, Monitoring intramyocardial reentry using alternating trans-illumination, in 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society(2009) pp.4194–4197.

[0012] V. D. Khait, O. Bernus, S. F. Mironov, and A. M. Pertsov, Method for the three- dimensional localization of intramyocardial excitation centers using optical imaging, Journal of Biomedical Optics 11, 34007 (2006).

[0013] B. J. Caldwell, M. L. Trew, and A. M. Pertsov, Cardiac response to low-energy field pacing challenges the standard theory of defibrillation, Circulation: Arrhythmia and Electrophysiology 8, 685 (2015).

[0014] A. Molavi Tabrizi, A. Mesgarnejad, M. Bazzi, S. Luther, J. Christoph, and A. Karma, Spatiotemporal organization of electromechanical phase singularities during high-frequency cardiac arrhythmias, Phys. Rev. X 12, 021052 (2022).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0

[0015] B. J. Welsh, J. Gomatam, and A. E. Burgess, Three-dimensional chemical waves in the Belousov–Zhabotinskii reaction, Nature 304, 611 (1983).

[0016] T. Bansagi and O. Steinbock, Three-dimensional spiral waves in an excitable reaction system: Initiation and dynamics of scroll rings and scroll ring pairs, Chaos: An Interdisciplinary Journal of Nonlinear Science 18, 026102 (2008).

[0017] P. Dahmlow, S. Alonso, M. Bar, and M. J. B. Hauser, Twists of opposite handedness on a scroll wave, Phys. Rev. Lett.110, 234102 (2013).

[0018] C. Bruns and M. J. B. Hauser, Dynamics of scroll waves in a cylinder jacket geometry, Phys. Rev. E 96, 012203 (2017).

[0019] E. M. C. Hillman, O. Bernus, E. Pease, M. B. Bouchard, and A. Pertsov, Depth- resolved optical imaging of transmural electrical propagation in perfused heart, Opt. Express 15, 17827 (2007).

[0020] L. Sacconi, L. Silvestri, E. C. Rodriguez, G. A. Armstrong, F. S. Pavone, A. Shrier, and G. Bub, KHz-rate volumetric voltage imaging of the whole zebrafish heart, Biophysical Reports 2, 100046 (2022).

[0021] S. Berg, S. Luther, and U. Parlitz, Synchronization based system identification of an extended excitable system, Chaos: An Interdisciplinary Journal of Nonlinear Science 21, 10.1063 / 1.3613921 (2011).

[0022] J. Lebert and J. Christoph, Synchronization-based reconstruction of electromechanical wave dynamics in elastic excitable media, Chaos: An Interdisciplinary Journal of Nonlinear Science 29, 10.1063 / 1.5101041 (2019).

[0023] M. J. Hoffman, N. S. LaVigne, S. T. Scorse, F. H. Fenton, and E. M. Cherry, Reconstructing three-dimensional reentrant cardiac electrical wave dynamics using data assimilation, Chaos: An Interdisciplinary Journal of Non-linear Science 26, 013107 (2016).

[0024] M. J. Hoffman and E. M. Cherry, Sensitivity of a data-assimilation system for reconstructing three-dimensional cardiac electrical dynamics, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, 20190388 (2020).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0

[0025] B. R. Hunt, E. J. Kostelich, and I. Szunyogh, Efficient data assimilation for spatiotemporal chaos: A local ensemble transform kalman filter, Physica D: Nonlinear Phenomena 230, 112 (2007), data Assimilation.

[0026] J. Lebert, N. Ravi, F. H. Fenton, and J. Christoph, Rotor localization and phase mapping of cardiac excitation waves using deep neural networks, Frontiers in Physiology 12, 10.3389 / fphys.2021.782176 (2021).

[0027] S. Herzog, R. S. Zimmermann, J. Abele, S. Luther, and U. Parlitz, Reconstructing complex cardiac excitation waves from incomplete data using echo state networks and convolutional autoencoders, Frontiers in Applied Mathematics and Statistics 6, 10.3389 / fams.2020.616584 (2021).

[0028] C. H. Martin, A. Oved, R. A. Chowdhury, E. Ullmann, N. S. Peters, A. A. Bharath, and M. Varela, EP-PINNs: Cardiac electrophysiology characterisation using physics- informed neural networks, Frontiers in Cardiovascular Medicine 8, 10.3389 / fcvm.2021.768419 (2022).

[0029] R. R. Aliev and A. V. Panfilov, A simple two-variable model of cardiac excitation, Chaos, Solitons & Fractals 7, 293 (1996).

[0030] D. Bourguignon and M. Cani, Controlling anisotropy in mass-spring systems, Computer Animation and Simulation, Springer , 113 (2000).

[0031] M. Nash and A. Panfilov, Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias, Progress in Biophysics and Molecular Biology 85, 501 (2004).

[0032] J. Christoph and J. Lebert, Inverse mechano-electrical reconstruction of cardiac excitation wave patterns from mechanical deformation using deep learning, Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 123134 (2020).

[0033] O. Ronneberger, P. Fischer, and T. Brox, U-net: Convolutional networks for biomedical image segmentation, in Lecture Notes in Computer Science (Springer International Publishing, 2015) pp.234–241.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0

[0034] J. Chen, Y. Lu, Q. Yu, X. Luo, E. Adeli, Y. Wang, L. Lu, A. L. Yuille, and Y. Zhou, Transunet: Transformers make strong encoders for medical image segmentation, CoRR abs / 2102.04306 (2021), 2102.04306.

[0035] S. W. Zamir, A. Arora, S. Khan, M. Hayat, F. S. Khan, M.-H. Yang, and L. Shao, Learning Enriched Features for Real Image Restoration and Enhancement, in Computer Vision – ECCV 2020 , Lecture Notes in Computer Science, edited by A. Vedaldi, H. Bischof, T. Brox, and J.-M. Frahm (Springer International Publishing, 2020) pp.492– 511.

[0036] V. Nair and G. E. Hinton, Rectified linear units improve restricted boltzmann machines (Omnipress, Madison, WI, USA, 2010) p.807–814.

[0037] S. Ioffe and C. Szegedy, Batch normalization: Accelerating deep network training by reducing internal covariate shift, in Proceedings of the 32nd International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol.37, edited by F. Bach and D. Blei (PMLR, Lille, France, 2015) pp.448–456.

[0038] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin, Attention is all you need, in Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, USA, edited by I. Guyon, U. von Luxburg, S. Bengio, H. M. Wallach, R. Fergus, S. V. N. Vishwanathan, and R. Garnett (2017) pp. 5998–6008.

[0039] A. Bruhn, J. Weickert, and C. Schnorr, Lucas / Kanade meets Horn / Schunck: Combining local and global optic flow methods, Int. J. Comput. Vis.61, 211 (2005).

[0040] J. T. Barron, A General and Adaptive Robust Loss Function, in 2019 IEEE / CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2019) pp.4326– 4334.

[0041] D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, in 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, edited by Y. Bengio and Y. LeCun (2015).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0

[0042] M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Man´e, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Largescale machine learning on heterogeneous systems, https: / / www.tensorflow.org (2015).

[0043] F. Chollet et al., Keras, https: / / keras.io (2015).

[0044] B. J. Hansen, N. Li, K. M. Helfrich, S. H. Abudulwahed, E. J. Artiga, M. E. Joseph, P. J. Mohler, J. D. Hummel, and V. V. Fedorov, First in vivo use of high- resolution near-infrared optical mapping to assess atrial activation during sinus rhythm and atrial fibrillation in a large animal model, Circulation: Arrhythmia and Electrophysiology 11, e006870 (2018).

[0045] R. B. Schuessler, T. Kawamoto, D. E. Hand, M. Mitsuno, B. I. Bromberg, J. L. Cox, and J. P. Boineau, Simultaneous epicardial and endocardial activation sequence mapping in the isolated canine right atrium., Circulation 88, 250 (1993).

[0046] J. Eckstein, B. Maesen, D. Linz, S. Zeemering, A. van Hunnik, S. Verheule, M. Allessie, and U. Schotten, Time course and mechanisms of endo-epicardial electrical dissociation during atrial fibrillation in the goat, Cardiovascular Research 89, 816 (2010).

[0047] J. Eckstein, S. Zeemering, D. Linz, B. Maesen, S. Verheule, A. van Hunnik, H. Crijns, M. A. Allessie, and U. Schotten, Transmural conduction is the predominant mechanism of breakthrough during atrial fibrillation, Circulation: Arrhythmia and Electrophysiology 6, 334 (2013).

[0048] N. de Groot, L. van der Does, A. Yaksh, E. Lanters, C. Teuwen, P. Knops, P. van de Woestijne, J. Bekkers, C. Kik, A. Bogers, and M. Allessie, Direct proof of endo- epicardial asynchrony of the atrial wall during atrial fibrillation in humans, Circulation: Arrhythmia and Electrophysiology 9, e003648 (2016).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0

[0049] T. E. Walters, G. Lee, A. Lee, R. Sievers, J. M. Kalman, and E. P. Gerstenfeld, Site-specific epicardium-to-endocardium dissociation of electrical activation in a swine model of atrial fibrillation, JACC: Clinical Electrophysiology 6, 830 (2020).

[0050] J. Zhao, B. J. Hansen, T. A. Csepe, P. Lim, Y. Wang, M. Williams, P. J. Mohler, P. M. Janssen, R. Weiss, J. D. Hummel, and V. V. Fedorov, Integration of high- resolution optical mapping and 3-dimensional microcomputed tomographic imaging to resolve the structural basis of atrial conduction in the human heart, Circulation: Arrhythmia and Electrophysiology 8, 1514 (2015).

[0051] J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach, Phys. Rev. Lett.120, 024102 (2018).

[0052] J. Pathak, A. Wikner, R. Fussell, S. Chandra, B. R. Hunt, M. Girvan, and E. Ott, Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model, Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 041101 (2018).

[0053] S. Herzog, F. Worgotter, and U. Parlitz, Data-driven modeling and prediction of complex spatio-temporal dynamics in excitable media, Frontiers in Applied Mathematics and Statistics 4, 10.3389 / fams.2018.00060 (2018).

[0054] S. Shahi, C. D. Marcotte, C. J. Herndon, F. H. Fenton, Y. Shiferaw, and E. M. Cherry, Long-time prediction of arrhythmic cardiac action potentials using recurrent neural networks and reservoir computing, Frontiers in Physiology 12, 10.3389 / fphys.2021.734178 (2021).

[0055] S. Shahi, F. H. Fenton, and E. M. Cherry, A machine learning approach for long- term prediction of experimental cardiac action potential time series using an autoencoder and echo state networks, Chaos: An Interdisciplinary Journal of Nonlinear Science 32, 063117 (2022).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Example 2: Dreaming of Electrical Waves: Generative Modeling of Cardiac Excitation Waves using Diffusion Models 2.0. Overview Electrical waves in the heart form rotating spiral or scroll waves during life- threatening arrhythmias such as atrial or ventricular fibrillation. The wave dynamics are typically modeled using coupled partial differential equations, which describe reaction- diffusion dynamics in excitable media. More recently, data-driven generative modeling has emerged as an alternative to generate spatio-temporal patterns in physical and biological systems. Here, denoising diffusion probabilistic models were explore for the generative modeling of electrical wave patterns in cardiac tissue. Diffusion models were trained with simulated electrical wave patterns to be able to generate such wave patterns in unconditional and conditional generation tasks. For instance, inpainting tasks, such as reconstructing three-dimensional wave dynamics from superficial two- dimensional measurements, and evolving and generating parameter-specific dynamics were explored. The diffusion-generated solutions were characterized and compared to solutions obtained with biophysical models and it was found that diffusion models learn to replicate spiral and scroll waves dynamics so well that they could serve as an alternative data-driven approach for the modeling of excitation waves in cardiac tissue. For instance, it was found that it is possible to initiate ventricular fibrillation (VF) dynamics instantaneously without having to apply pacing protocols in order to induce wavebreak. The VF dynamics can be created in arbitrary ventricular geometries and can be evolved over time. However, it was also found that diffusion models ‘hallucinate' wave patterns when given insufficient constraints. Regardless of these limitations, diffusion models are an interesting and powerful tool with many potential applications in cardiac arrhythmia research and diagnostics. 2.1. Introduction Waves in excitable media exhibit complex spatiotemporal dynamics [1, 2]. In two- dimensional media, they form linear, focal, or rotating spiral-shaped waves or compositions thereof. In three-dimensional media, they manifest as planar or spherical focal waves, or take on more complicated rotational shapes referred to as scroll waves.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Spiral and scroll wave dynamics have been studied for many decades, as they are associated with heart rhythm disorders, such as atrial fibrillation, polymorphic ventricular tachycardia, or ventricular fibrillation [2–12]. In the heart, electrical excitation initiates the contraction of the heart muscle, and it is hypothesized that the abnormal rapid and irregular contractions during tachyarrhythmias are caused by spiral- and scroll-shaped waves of electrical excitation. The electrical waves can be reproduced and studied in computer simulations using biophysical models [13–15]. These models consist of coupled partial differential equations (PDEs), which describe the electrical excitability u and refractoriness r of cardiac muscle cells and the coupling between them (see eqs. (1–2) of this example). The equations model reaction-diffusion dynamics, where the exchange of currents through ion channels between cells are modeled as a diffusive process and the cells as nonlinear oscillators. Integrating these equations in time and over space in a spatially extended system using, for instance, the finite difference or finite element method produces nonlinear waves of electrical excitation mediated via diffusion. Diffusion, on the other hand, is a term that has recently emerged in the field of artificial intelligence (AI), referring to a class of generative neural networks which employ a diffusive process to generate data [16–18]. During the training procedure, noise is iteratively added to the training data and the neural networks, termed denoising diffusion probabilistic models (DDPMs)

[0018] or diffusion models, learn to reverse this process, ultimately enabling them to create data from noise, see FIG.37. Diffusion models are very successful in generating data such as images [19–21], videos

[0022] , and audio

[0023] , and they are increasingly also used for technical applications in physics, engineering, medicine, and biology [24–27]. Diffusion models likely also have many useful applications in cardiology that have yet to be explored. For example, they could be used in electrophysiological studies to generate synthetic action potential wave patterns and arrhythmia morphologies, either to fill in or reconstruct missing measurement data, or to simulate cardiac dynamics in a data-driven fashion. Diffusion- generated solutions could be particularly useful in situations in which measurements can only be obtained partially or indirectly, or when biophysical model equations or parameters are lacking.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Here, diffusion models were explored for their application in cardiac electrophysiology and arrhythmia research. In this numerical study, whether diffusion models can be used to reconstruct or simulate electrical impulse phenomena, such as spiral and scroll waves, in computer simulations of excitable media was investigated. Electrical spiral and scroll waves were simulated in two- and three-dimensional square-, bulk- and heart-shaped tissues with isotropic and anisotropic diffusive spread of the excitation, and trained different diffusion models to i) inpaint spiral wave dynamics (see section 2.3.2), ii) reconstruct three-dimensional scroll wave dynamics from two- dimensional observations (see section 2.3.1), iii) generate parameter-specific wave dynamics (see section 2.3.7), and iv) predict the evolution of wave dynamics over time in analogy to integrating the dynamics (see section 2.3.5). It was determined how reliable diffusion models are when generating such spatio-temporal physiological dynamics. Generative neural networks, such as diffusion models, generative adversarial networks (GANs), or large language models (LLMs) are known to be capable of producing a continuum of output including false or undesired output, which is often referred to as ’hallucination’. It was shown that diffusion models can generate electrical waves in many different ways: out of the blue in an unconstrained generative process or when the generative process is guided or constrained by parameters or boundary conditions such as partial data, or a recent dynamical state of the system. In particular, the latter generative mode corresponds to diffusion-based data-driven modeling of cardiac dynamics. It was found that hallucination occurs when the generation task is insufficiently constrained, which raises concerns over the reliability of diffusion models in diagnostic applications. FIGS.37A-37D: Diffusion-based generative modeling of electrical wave dynamics in cardiac tissue. A) Forward diffusion process and generative reverse denoising process. The training data consists of spiral and scroll wave dynamics in excitable media. B) General diffusion model architecture for processing image data with underlying U-Net architecture. C) ResNet Attention block. D) Diffusion model for generating scroll waves in heart-shaped geometries represented as pointclouds with corresponding scalar-valued data (Point-Voxel Diffusion

[0028] ).Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 2.2. Methods 2.2.1. Simulations of Electrical Wave Dynamics in Heart Muscle Tissue Nonlinear waves of electrical excitation were simulated in i) two-dimensional rectangular-shaped, ii) three-dimensional bulk-shaped, and iii) three-dimensional heart- shaped geometries, respectively. In all three cases, the phenomenological Aliev- Panfilov model

[0015] was used to simulate nonlinear waves of electrical excitation: ^^ ^^= ^ · (^^^) − ^^(^ − ^)(^ − 1) − ^^ (1) Theexcitation and refractoriness in dimensionless, normalized units, respectively. The parameters k, a, ^0, µ1 and µ2 determine the properties of the waves (e.g. excitability, wavelength, conduction speed, number of waves, etc.). The parameters k and ^0were varied to change the properties of the excitation waves and produce different training data for different tasks (Task 1-6), (see Table 3 and sections 2.2.1-2.2.6). The simulations in the simplified (rectangular, bulk) and heart-shaped geometries were performed as described in

[0029] and

[0031] , respectively. Correspondingly, the system of equations (1-2) was integrated using the forward Euler method and the smoothed particle hydrodynamics method [32, 33], respectively. The two-dimensional simulations were isotropic, whereas the three-dimensional simulations were anisotropic with a locally varying fiber direction and faster wave propagation along the fiber direction. The fiber architectures were created as described in [29, 31]. In particular, the bi-ventricular heart geometries and underlying rule-based fiber architectures were randomly initialized as described in

[0031] . The model parameters were chosen specifically for each task (see Table 3). Scroll wave dynamics were simulated in a bulk with 128×128×40 voxels as shown in FIG.38 using a fixed set of parameters (Task 1). Two different regimes of spiral wave dynamics were simulated, as shown in FIGS.40 and 42, using two different parameter sets: one with few (Task 2a, 5a) and one with more spiral waves (Tasks 2b, 5b). A range of parameter-specific spiral wave dynamics were simulated (Task 6), as seen inAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 FIG.44A and 44B, by varying the parameters k and ^0. For each task, hundreds of simulations were performed to generate sufficient training data. For example, for Task 1, 125 simulations were performed, where 100 simulations were used for training and 25 for evaluation, as described in

[0029] . The initial conditions u0, r0were randomized and therefore different in each simulation, see also

[0031] . If the spiral or scroll wave dynamics self-terminated prematurely, the simulation was restarted. Using the simulation data, different training datasets were generated for each task, see Tasks 1-6 in section 2.2.2 for details. Each training dataset consisted of thousands of samples randomly chosen from the different training simulations. Correspondingly, each evaluation dataset consisted of thousands of samples randomly chosen from the evaluation simulations. Training and evaluation datasets were completely separate datasets. FIGS.38A-38B: Diffusion-based reconstruction of scroll wave dynamics inside a three-dimensional bulk from two-dimensional observations of the dynamics on the bulk’s top and bottom surface. The bulk is fully opaque, and measurements can only be obtained from its surface. A) Illustration of diffusion process over denoising iterations. B) Scroll wave dynamics (left: ground-truth) and reconstructed scroll waves with diffusion (center left), U-Net (right) and U-Net refined with diffusion (center right). While diffusion produces smoother wave patterns than U-Net, particularly at deeper layers, the overall reconstruction accuracies are not significantly different across the three approaches (see also FIG.39). White squares highlight slight differences between reconstructions and ground-truth. The bulk is 128×128×40 voxels (aspect ratio was altered to emphasize transmural wave morphology), see also

[0029] . The simulation parameters are shown in Table 3 (Task 1). 2.2.2. Denoising Diffusion Model A denoising diffusion probabilistic modeling

[0018] neural network architecture was used, which is referred to as diffusion model in this study for simplicity. Diffusion models consist of a forward diffusion process and a reverse diffusion process (see FIG.37). During the forward diffusion process, gaussian noise is added incrementally to an input image until it is indistinguishable from random noise. This produces a sequence of samples (x0, … , xT) with increasing noise, starting from the data point x0from the realAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 data distribution q(x) and ending with what is indistinguishable from an isotropic Gaussian distribution. \(x^|x^_#) = N(x^;I1 − b^x^_#, b^I) (3) Theby a variance schedule βt. \(x#:2|xW) = ∏2^F#\(=^|=^_#) (4) Whenpθis learned to estimate q(xt−1|xt), which is also approximated by a gaussian distribution. This is referred to as the reverse diffusion process. fg(=W:2) = f(x2)∏2^F#fg(xh|xh_#) (5)This allows the model pθ to only have to estimate the two parameters µ and σ of the estimated denoising step. Commonly, σθis fixed to a constant variance schedule and is not learnable. This means that in order to estimate pθ, a model needs to learn µθ(xt, t). Electrical wave dynamics can be treated as image-like data and the U-Net architecture from Dhariwal and Nichol

[0034] is used to estimate the noise at each step of the reverse diffusion process. The model is trained using pairs taken from the forward diffusion process xt, xt−1 and taking the mean squared error (MSE) between the noise estimated by the model and the true noise at that step. Different versions of diffusion models for different tasks were implemented, as described in the following sections. The conditioned diffusion models for sections 2.2.2, 2.2.5, and 2.2.6 were implemented following Saharia et al.

[0020] using an implementation by L. Jiang and Y. Belousov

[0035] . The unconditioned diffusion model for section 2.2.3 was implemented following Ho et al.

[0018] using the Diffusers library

[0036] . The diffusion model for section 2.2.4 was implemented following Zhou et al.

[0028] using the official codebase. All diffusion models include a U-Net

[0037] architecture and were implemented in PyTorch

[0038] . Table 3: Parameters of biophysical model

[0015] used to simulate electrical wave patterns. Task 1: Scroll wave dynamics in anisotropic 3D bulk shown in FIG.38. Tasks 2, 3, 5:Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Spiral wave dynamics in 2D isotropic medium (see FIGS.40, 42, 43). Task 4: Scroll wave dynamics in (bi-ventricular) heart-shaped medium (see FIG.41). Task 6: Parameter-specific generation of spiral waves (see FIG.44). Da is an anisotropic diffusion tensor (see also [29, 31]). Param. Task 1 Task 2a / 5a Task 2b / 5b Task 3 Task 4 Task 6 D Da 1 1 1 Da 1 k 8 8.5 7.5 8 8 k’ a 0.05 0.1 0.1 0.05 0.2 0.1 ε0 0.002 0.003 0.001 0.002 0.002 ε’0 µ1 0.8 0.16 0.16 0.2 0.2 0.16 µ20.3 0.3 0.3 0.3 0.3 0.3 Task 1: Reconstruction of 3D Scroll Wave Dynamics A diffusion model was trained to predict three-dimensional scroll wave dynamics inside a bulk from two-dimensional observations of the dynamics on the surface of the bulk (Task 1), as described in

[0029] and shown in FIG.38. The model was trained to predict a single three-dimensional snapshot of the excitatory variable ut (x, y, z) at a given time t at every voxel in a bulk with 128×128×40 voxels from 5 subsequent two- dimensional snapshots of the dynamics on the bulk’s surface: (^#(=, >), ... , ^?(=, >)) → ^S?(=, >, ,) (7)truth). The snapshots were measured either i) on the top surface only (single-surface mode) resulting in a spatio-temporal measurement consisting of 5 snapshots (u1(x, y, 1), … , u5(x, y, 1)) or ii) on the top and bottom surface (dual-surface mode) resulting in 2 · 5 snapshots (u1(x, y, 1), u1(x, y, 40), u2(x, y, 1), … , u5(x, y, 40)), as described in

[0029] . The 5 snapshots were sampled at equidistant times t1, t2, t3, t4, t5 = t−4τ, t−3τ, t−2τ, t−τ, t with ui = u(ti) over about one rotational period T of the scroll wave dynamics (τ = t − t−τ ≈ T / 5), which were found to provide sufficient information to reconstruct the dynamics, as described in, e.g.,

[0029] . Accordingly, the diffusion model was conditioned by concatenating these sequences asAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 additional channels in the U-Net inputs (interleaved in dual-surface mode, odd indices for the top layer and even indices for the bottom layer). To explore an alternative extension of the reconstruction approach, the diffusion model was conditioned using the output of a generic U-Net model, which was trained and applied as described in

[0029] , to create a combined model that potentially can take advantage of the strengths of both the U-Net and diffusion models (see also FIG.39). Accordingly, the combined model was conditioned with the sequences of 5 (or 2 · 5) two-dimensional snapshots and 1 three-dimensional prediction ^S(x, y, z) of the U-Net model, which analyzed in turn also 5 snapshots as input. The two- and three-dimensional inputs were concatenated to obtain (128 × 128 × 45) or (128 × 128 × 50) samples in single- vs. dual-surface mode as conditions, respectively. This leads to a total of 4 conditioning modes that were tested (single- vs. dual-surface, diffusion vs. combination of diffusion + U-Net). Generally, the different model versions required three-dimensional input samples, e.g. (128×128×5) or (128×128×45). To denoise a 128 × 128 × 40 volume image with 5 · 128 × 128 snapshots as conditioning, the model corresponds to an R(128 × 128 × 45) → R(128 × 128 × 40) function. However, internally, because the denoising diffusion process works on the intermediate noisy bulk data, the overall data consists of the conditioning data concatenated to the noisy data which then results in an array size of, for example, 128 × 128 × 80. Training was performed with 20,000 training samples, which were generated in 100 simulations (see also section 2.2.1), and the model was evaluated on 5,000 separate samples. The same simulation data and parameters were used as in

[0029] (see also Table 3). Task 2: Inpainting of 2D Spiral Wave Dynamics A diffusion model was trained to inpaint missing data of two-dimensional spiral wave dynamics (Task 2), as shown in FIG.40. Data from a square region at the center of the 128×128-pixel simulation domain was masked or left out and the network was trained with corresponding pairs of masked um(x, y) and ground-truth data u(x, y) to reconstruct the missing parts of the spiral wave pattern: (^j,#(=, >), ... , ^j,?(=, >)) → ^S?(=, >) (8)Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 where ^S is a prediction of the ground-truth dynamics u and the model reads a short spatio-temporal sequence of 5 two-dimensional snapshots as above. Masked pixels were replaced by zeros. How the reconstruction accuracy of the network changes with different mask sizes m ∈ [0.05, … , 0.8] (percentage masked area vs. total area from 5% to 80% in increments of 5%) and with less and more complex wave patterns (see section 2.3.2) was tested. Two spiral wave regimes were simulated, and two separate models were trained: i) one with largely only one spiral wave (Task 2a) and ii) one with multiple, more chaotic spiral waves (Task 2b), see Table 3 for the corresponding simulation parameters. Both models were trained equally with a range of masks with uniform distribution (of the percentage of masked area vs. total area). Training and evaluation was performed with 27,500 and 6,000 samples, respectively. Task 3: Unconditional Generation of Spiral Wave Patterns a diffusion model was trained to generate two-dimensional spiral wave patterns in an unconditional fashion (Task 3), as also shown in FIG.43. This means that the model can dream up any spiral wave pattern it can come up with (depending on what data it was trained on) starting from random noise ξ: k(=, >) → (^S, ^̃)(=, >) (9) The model is completely unrestricted in that it is not trained to perform certain tasks, such as inpainting, nor conditioned by certain boundary conditions, such as top or bottom layers, or parameters which guide the generative process, as in Task 6 (below). The model was trained with 50,000 training samples generated from spiral wave patterns simulated in an isotropic excitable medium with a fixed parameter set from

[0042] (see also Table 3). Each training sample consisted of a single spiral wave pattern defined by its dynamical variables (u, r)t (x, y) in a 128×128-pixel simulation domain. The training samples were sampled from the last 300 timesteps of 1,000 simulations which ran for a fixed simulation time and were randomly initiated following a random pulse protocol (similarly as used in

[0042] ). After training, the diffusion model outputs a pair of two-dimensional (^S, ^̃)^(=, >) −fields or a snapshot of the system’s dynamical state. The output together with the parameters and boundary conditions (no-flux) defines a complete current dynamical state of the spiral wave dynamics. The diffusionAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 model outputs were then used as initial states for the biophysical model defined in eqs. (1-2) and 5,000 simulations were initiated with these diffusion-generated initial conditions with identical model parameters as during training data generation and measured the time until each simulation self-terminated over the ensemble of simulations (see section 2.3.6). Task 4: Generation of Scroll Waves in Heart-shaped Geometries A diffusion model was trained to generate scroll waves in bi-ventricular-shaped geometries (Task 4), similarly as described in the above Task 3 and as shown in FIG. 40. Both the shape and the wave pattern were generated by the diffusion model simultaneously. This means that the diffusion model outputs an arbitrary bi-ventricular geometry as well as a corresponding anisotropic scroll wave pattern, the anisotropy reflecting the underlying fiber architecture. The generation was unconditional as described in the previous Task 3. The simulated training data (see Task 1) consists of pointclouds of (∼32,000) vertices f(=)^located within bi-ventricular heart shapes and scalars representing the excitatory variable uiper vertex with index i (see FIG.41). The data was down-sampled to 16,000 points and Point-Voxel Diffusion

[0028] was used trained on 5,000 training samples obtained from the simulations. The model was trained to output 16,384 points (with a latent dimension of 512). Task 5: Generation of Spiral Wave Dynamics and Integration of their Spatio- Temporal Evolution A diffusion model was trained to calculate an immediate future time step of a given spatio-temporal excitation wave pattern (Task 5): (^, ^)(=, P) → (^S, ^̃)(=, P + m) (10) where (u, r) are the dynamic variables from eqs. (1-2) and τ is an infinitesimal temporal increment or the integration time step. In other words, a diffusion model was trained to be able to evolve cardiac excitation wave dynamics. More precisely, the model was trained to predict the next 5 timesteps from the previous 5 timesteps of the dynamics, resulting in a temporal integration scheme that updates a brief spatio- temporal pattern instead of a static spatial pattern. This approach was found to be moreAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 stable than auto-regressively integrating the dynamics, e.g., updating the dynamics one time step at a time and predicting the next time step from the previous 5 timesteps. With this spatio-temporal integration eq.(10) corresponds to: (^, ^)(=, P_n, ... , PW) → (^S, ^̃)(=, P#, ... , P?) (11)steps and t1, … , t5are the next 5 future timesteps (see FIG.42A). The model was trained and evaluated with 15,000 and 5,000 samples, respectively, showing two-dimensional spiral wave dynamics with the simple and complex parameter sets from Task 2 (see FIGS.42B and 42C). Task 6: Parameter-specific Generation of Spiral Waves A diffusion model was trained to generate parameter-specific spiral wave dynamics (Task 6), as shown in FIG.44: (k(=, >), ^, ^W) → (^S, ^̃)(=, >, P#, Pn, Po, P#W, P#%) (12) where k and ^0are parameters of the biophysical model in eqs.(1-2) of this example and (^S, ^̃) is a short sequence of 5 predictions of the dynamical state of the spiral wave patterns at future times t1, t4, t7, t10, t13 given in simulation time steps (see detailed explanation below). The diffusion model generates spiral wave patterns from the initial noise ξ(x, y) and this generation process was refer as ‘conditioned by the parameters k and ^0’. The model generates a sequence of 5 subsequent spiral wave patterns for validation purposes (see section 2.3.7). A training dataset was generated in which the parameters k and ^0were varied systematically and spiral wave dynamics were initiated with these parameters for 20 different parameter pairs (k, ^0) (see FIGS.44A and 44B).200 simulations were run over the 20 parameter pairs on the grid k = [7, 7.5, 8, 8.5, 9] and ^0 = [0.0001, 0.001, 0.003, 0.015] with 10 simulations per parameter combination, and data was selected from 15 of the 20 parameter sets to train the model and the remaining 5 for testing, as shown in FIGS.44A and 44B. The diffusion model was then conditioned by concatenating the parameters to the initial noisy distribution ξ(x, y), adding two channels to the input of the underlying U-Net (2 × 128 × 128 pixels). Aside from the parameterAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 conditioning, the generation was unconditioned allowing the diffusion model to dream up any spiral wave pattern, as described in Task 3 above. To test the specificity of the parameter-specific generations, the training and prediction process were set up as follows: for each simulation, 150 frames were extracted and every 15 frames were grouped into one training sample {(u, r)1, … ,(u, r)15}. Of these 15 frames, only 5 frames were used per training sample, subsampling the data in time by a factor of 3: {(u, r)1, (u, r)4, (u, r)7, (u, r)10, (u, r)13}. Using this data as the target during training, the diffusion model was trained to predict a short spatio-temporal sequence of spiral wave dynamics consisting of 5 frames with an offset of 3 frames (see eq.(12) of this example). Whether the diffusion model can generate different parameter- specific dynamics was then evaluated by loading the first predicted dynamical state (^S, ^̃)#created with a specific parameter pair (k*, ^0*) and evolving it using the biophysical model (integrating the PDEs) for 15 simulation timesteps using either the same parameter pair (k*, ^0*) or a different one (k, ^0). This process was repeated with all 20 parameter pair combinations and the 5-th diffusion-generated frame (^S, ^̃)13 (x, y) was compared to the output of the simulation at time step 13 by calculating the error (RMSE) between the two frames (see FIG.44D). 2.2.3. Training Details The networks were trained using the Adam

[0043] optimizer with a learning rate of 10−4for the bulk prediction tasks and 10−3for all other tasks. A batch size of 8 was used for the bulk prediction tasks and a batch size of 32 was used for all the other tasks. All neural network models were implemented in PyTorch

[0038] . Training and reconstructions were performed on a NVIDIA RTX 24000 graphics processing unit (GPU). Table 4: Different model sizes (trainable parameters) and training times used in this study. Training was performed on a single NVIDIA RTX 24000 GPU. Model Trainable Parameters Training Time Task 1 965,266,792 9 days Task 1 62,640,193 1.5 days Task 1 113,673,219 1.5 days Task 1 31,092,676 1 daysAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 Task 1 62,644,805 1.5 days Task 1 250,430,474 4 days Classification 11,689,512 5 min 2.2.4. Evaluation The diffusion model’s accuracies were evaluated using the root mean squared error (RMSE), the mean absolute error (MAE), or the multi-resolution perceptual error (MR)

[0041] depending on the model and ta...

Claims

Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 WHAT IS CLAIMED IS:

1. A method of configuring a model to reflect electrical and mechanical behavior of a tissue, the method comprising: collecting initial data comprising corresponding electrophysiological activation patterns of a tissue and mechanical movement patterns of the tissue; and configuring a model of the tissue based on the corresponding electrophysiological activation patterns of the tissue and mechanical movement patterns of the tissue.

2. The method of claim 1, wherein the initial data comprises dynamic structural imaging data.

3. The method of claims 1 or 2, wherein the initial data comprises model training data.

4. The method of any one of one the previous claims, wherein the initial data comprises model configuration data.

5. The method of any one of the previous claims, wherein the initial data reflects an initial state of tissue electrophysiology and mechanical movement.

6. The method of any one of the previous claims, wherein the electrophysiological activation patterns comprise one or more of: electrical, optical, acoustical, and / or photo-acoustical measurements of electrical excitation of the tissue and / or structure of the tissue.

7. The method of any one of the previous claims, wherein the initial data is obtained from a subject.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 8. The method of claim 7, wherein the initial data comprises subject-specific data.

9. The method of claim 8, wherein the subject-specific data comprises one or more of: demographic data, genetic information, patient history data, structural imaging data, and / or quantitative medical data.

10. The method of claims 8 or 9, wherein the method further comprises configuring the model of the tissue based on the subject information.

11. The method of claim 10, wherein the model of the tissue is configured based on the subject information after the model is configured based on the electrophysiological activation patterns and mechanical movement patterns of the tissue.

12. The method of any one of the previous claims, wherein the dynamic structural imaging data comprises ultrasound imaging data, magnetic resonance imaging (MRI) data, or computed tomography (CT) imaging data.

13. The method of claim 12, wherein the ultrasound imaging data reflects mechanical movement patterns.

14. The method of any one of the previous claims, wherein the dynamic structural imaging data comprises optical data.

15. The method of claim 14, wherein the optical data reflects electrophysical activation patterns.

16. The method of any one of the previous claims, wherein the dynamic structural imaging data comprises fused imaging and optical data.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 17. The method of any one of the previous claims, wherein the dynamic structural imaging data comprises imaging data over time.

18. The method of any one of the previous claims, wherein the initial data comprises synthetic data.

19. The method of any one of the previous claims, wherein the initial data comprises data generated using a numerical model configured to represent intra- and / or extra-cellular processes of the tissue.

20. The method of any one of the previous claims, wherein the initial data comprises data generated using a computational technique.

21. The method of claim 20, wherein the computational technique comprises one or more of: finite-difference methods (FDM), finite element method (FEM), finite volume method (FVM), smoothed-particle hydrodynamics (SPH), and boundary- element method (BEM), and / or a differentiable version of such technique, optionally comprising a differential SPH simulation fitted to data.

22. The method of any one of the previous claims, wherein the model is trained using training data comprising electrophysiological data and mechanical deformation data, or fitted to such data using gradient descent techniques.

23. The method of any one of the previous claims, wherein electrophysiological activation patterns comprise one or more of: action potential (AP) waves or wave fronts, calcium waves or wave fronts, AP activation maps, calcium activation maps, calcium concentrations or changes in calcium concentrations, oxygenation or changes in oxygenation, and / or pH or changes in pH.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 24. The method of any one of the previous claims, wherein the electrophysiological activation patterns comprise intramural electrical activity of the tissue.

25. The method of any one of the previous claims, wherein the electrophysiological activation patterns comprise electrical activity on the tissue surface.

26. The method of any one of the previous claims, wherein the electrophysiological activation patterns comprise a sinus wave pattern, a focal wave pattern, and / or a reentrant wave pattern.

27. The method of any one of the previous claims, wherein the electrophysiological activation patterns comprise a three-dimensional wave pattern.

28. The method of any one of the previous claims, wherein the mechanical movement patterns comprise tissue deformation.

29. The method of any one of the previous claims, wherein the mechanical movement patterns comprise tissue deformation triggered by the electrical activation patterns.

30. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate an electrophysiological activation pattern of a tissue of a subject by: inputting experimental data to the model, wherein the experimental data comprises one or more mechanical movement patterns; and receiving estimated electrophysiological activation patterns output from the model.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 31. The method of any one of the previous claims, wherein the model infers electrical activity of the tissue from mechanical deformation of the tissue.

32. The method of any one of the previous claims, wherein the model infers internal electrical activity of the tissue from mechanical deformation of the tissue.

33. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate a mechanical movement pattern of a tissue of a subject by: inputting experimental data to the model, wherein the experimental data comprises one or more electrophysiological activation patterns of the tissue; and receiving estimated mechanical movement patterns output from the model.

34. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate electrophysiological activation patterns of a tissue of a subject by: inputting data to the model, wherein the input data comprises one or more electrophysiological activation patterns of the tissue; and receiving estimated subsequent electrophysiological activation patterns output from the model.

35. The method of claim 34, wherein the electrophysiological activation pattern input to the model comprises experimental data.

36. The method of claims 34 or 35, wherein the electrophysiological activation pattern input to the model comprises electrode-recordings.

37. The method of any one of the previous claims, wherein the electrophysiological activation pattern input to the model comprises an incomplete measurement of electrical activity of the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 38. The method of any one of the previous claims, wherein the electrophysiological activation pattern input to the model comprises sparse measurement data or data with low spatial resolution.

39. The method of any one of the previous claims, wherein the electrophysiological activation pattern input to the model comprises simulated data.

40. The method of any one of the previous claims, wherein the estimated subsequent electrophysiological activation patterns comprise chaotic wave phenomena.

41. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate a mechanical movement pattern of a tissue of a subject by: inputting experimental data to the model, wherein the experimental data comprises one or more mechanical movement patterns of the tissue; and receiving estimated subsequent mechanical movement patterns output from the model.

42. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate electrophysiological activation patterns and mechanical movement patterns of a tissue of a subject by: inputting experimental data to the model, wherein the experimental data comprises one or more electrophysiological activation patterns of the tissue or mechanical movement patterns of the tissue; and receiving estimated electrophysiological activation patterns and mechanical movement patterns output from the model.

43. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate the presence of abnormal electrophysiological activation patterns of a tissue of a subject by:Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 inputting experimental data to the model, wherein the experimental data comprises one or more electrophysiological activation patterns of the tissue or mechanical movement patterns of the tissue; and receiving an estimate of a presence of abnormal electrophysiological activation patterns of the tissue output from the model.

44. The method of claim 43, wherein the abnormal electrophysiological activation patterns comprise electrophysiological activation patterns associated with an arrythmia, tachycardia, and / or the presence of scar tissue.

45. The method of any one of the previous claims, wherein the method further comprises: obtaining ultrasound imaging data of the tissue; applying the model to the obtained ultrasound imagining data; and receiving an estimate from the model of the presence of an abnormal physiological symptom.

46. The method of claim 45, wherein the abnormal physiological symptom comprises one or more of: an abnormal electrical circuit, an abnormal tissue characteristic, scar tissue, diseased tissue, tissue comprising a discontinuity, and / or fibrotic tissue.

47. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate a location of, or particular morphology associated with, an electrical circuit causing an abnormal electrophysiological activation pattern.

48. The method of any one of the previous claims, wherein the method further comprises applying the model to identify tissue associated with an abnormal electrophysiological activation pattern.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 49. The method of any one of the previous claims, wherein the method further comprises applying the model to identify a location for tissue ablation or other tissue modification to remove an abnormal electrophysiological activation pattern.

50. The method of any one of the previous claims, wherein the model is further configured based on subject information comprising one or more of: demographic data, genetic information, patient history data, structural imaging data, and / or quantitative medical data.

51. The method of any one of the previous claims, wherein data input to and / or data output from the model comprises spatio-temporal data.

52. The method of any one of the previous claims, wherein data input to and / or data output from the model comprises a sequence of images.

53. The method of any one of the previous claims, wherein data output from the model comprises a single image.

54. The method of any one of the previous claims, wherein data input to the model and data output from the model each comprise three-dimensional representations of the tissue over time.

55. The method of any one of the previous claims, wherein the initial data comprises the experimental data.

56. The method of any one of the previous claims, wherein the experimental data is distinct from the initial data.

57. The method of any one of the previous claims, wherein the model is first configured using the initial data before being subsequently trained using experimental data.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 58. The method of any one of the previous claims, wherein the experimental data comprises dynamic structural imaging data.

59. The method of claim 58, wherein the dynamic structural imaging data comprises ultrasound imaging data.

60. The method of claim 58 or 59, wherein the dynamic structural imaging data comprises optical data.

61. The method of any one of claims 58-60, wherein the dynamic structural imaging data comprises fused imaging and optical data.

62. The method of any one of claims 58-61, wherein the dynamic structural imaging data comprises imaging data over time.

63. The method of any one of the previous claims, wherein the experimental data comprises one or more of: ultrasound, MRI, and / or CT scan data.

64. The method of any one of the previous claims, wherein the method further comprises generating synthetic data for use configuring or training the model.

65. The method of any one of the previous claims, wherein the initial data comprises synthetic data.

66. The method of any one of the previous claims, wherein the model is trained using synthetic data.

67. The method of any one of claims 64-66, wherein the synthetic data comprises data generated based on a mechanical model of the tissue or an electrophysiological model of the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 68. The method of any one of claims 64-67, wherein generating the synthetic data comprises: generating variations of tissue models in silico; and applying such variations of tissue models to generate synthetic data.

69. The method of any one of claims 64-68, wherein the synthetic data comprises data generated by applying a mass-spring model (MSM), a finite-element model (FEM), and / or a smoothed-particle hydrodynamics (SPH) framework, or differentiable versions thereof, optionally comprising a differentiable simulation version of MSM, SPH, and / or FEM).

70. The method of any one of claims 64-69, wherein the synthetic data comprises data generated by applying an electromechanically coupled simulation.

71. The method of any one of the previous claims, wherein the method further comprises: generating a plurality of models of structures of the tissue, wherein each of the structures varies in at least one aspect; and applying the plurality of models to generate synthetic data comprising electrophysiological activation patterns of the tissue and / or mechanical movement patterns of the tissue.

72. The method of claim 71, wherein each of the structures varies in one or more of: tissue shape, tissue thickness, tissue stiffness, contractile force, fiber orientations, interconnections between regions of tissues, velocities of electrical activation patterns, durations of electrical activation waves, and / or spatial heterogeneity.

73. The method of any one of the previous claims, wherein the method further comprises using numerical simulations of tissue behavior to generate synthetic data.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 74. The method of any one of the previous claims, wherein the synthetic data is configured to mimic experimental data.

75. The method of any one of the previous claims, wherein data used to configure or train the model is augmented by one or more of: adding random noise to the data, randomly rotating or flipping the data, removing a random section of the data, randomly scaling the data, blurring the data, and / or adding artifacts to the data.

76. The method of any one of the previous claims, wherein the synthetic data comprises electrophysiological activation patterns exhibiting a sinus wave, a focal wave, and / or a reentrant wave.

77. The method of any one of the previous claims, wherein data used to configure or train the model comprises electrophysiological activation patterns exhibiting a sinus wave, a focal wave, and / or a reentrant wave.

78. The method of any one of the previous claims, wherein the method further comprises: generating ground-truth electrical activation patterns of the tissue; using the ground-truth electrical activation patterns to estimate mechanical movement patterns of the tissue; applying the model to the estimated mechanical movement patterns to estimate the electrical activation patterns.

79. The method of any one of the previous claims, wherein the model is trained using training data generated from a plurality of electrophysiological models and mechanical deformation models.

80. The method of any one of the previous claims, wherein the data generated by the plurality of electrophysiological models is applied to the plurality of mechanicalAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 deformation models to generate data comprising corresponding electrical activation and mechanical movement patterns.

81. The method of any one of the previous claims, wherein the model comprises a model of electrophysiological activation patterns of the tissue.

82. The method of any one of the previous claims, wherein the model comprises a model of calcium concentrations, oxygenation, and / or pH of the tissue or changes in one or more of calcium concentrations, oxygenation, and / or pH of the tissue.

83. The method of any one of the previous claims, wherein the model comprises a model of mechanical movement of the tissue.

84. The method of any one of the previous claims, wherein the model comprises a model of three-dimensional images or three-dimensional motion vectors of the tissue.

85. The method of any one of the previous claims, wherein mechanical movement of the tissue is represented based on three-dimensional images or three- dimensional motion vectors.

86. The method of any one of the previous claims, wherein the model is trained to learn mechanical movement of the tissue based on three-dimensional images or three-dimensional motion vectors.

87. The method of any one of the previous claims, wherein the method comprises estimating electrical activity of the tissue based on three-dimensional images or three-dimensional motion vectors representing tissue movement using the model.

88. The method of any one of the previous claims, wherein the model comprises a deep learning model.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 89. The method of any one of the previous claims, wherein the model comprises one or more of: a convolutional neural network, a U-Net, a sparse Res U-Net, a denoising diffusion neural network, a sparse denoising diffusion neural network, a transformer, a graph neural network, and / or a large language model.

90. The method of claim 89, wherein the model comprises convolutional or attention mechanisms.

91. The method of any one of the previous claims, wherein the model comprises a sparse encoding-decoding convolutional neural network.

92. The method of any one of the previous claims, wherein the model comprises a virtual vector model.

93. The method of any one of the previous claims, wherein the model comprises a numerical simulation.

94. The method of any one of the previous claims, wherein the model comprises a mass-spring model (MSM), a smoothed-particle hydrodynamics (SPH) model, or a finite element method (FEM) model.

95. The method of any one of the previous claims, wherein the model comprises a differentiable electrical, mechanical, or electromechanical tissue model.

96. The method of any one of the previous claims, wherein the model comprises a simulation core component.

97. The method of any one of the previous claims, wherein the initial data comprises tissue motion data, tissue geometry data, and / or other subject-specific data.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 98. The method of any one of the previous claims, wherein the model is trained using gradient descent optimization.

99. The method of any one of the previous claims, wherein the model comprises a numerical model configured to represent intra- and extra-cellular processes of the tissue.

100. The method of any one of the previous claims, wherein the model comprises a computational technique comprising one or more of: finite-difference methods (FDM), finite element method (FEM), finite volume method (FVM), smoothed-particle hydrodynamics (SPH), and / or boundary-element method (BEM).

101. The method of any one of the previous claims, wherein the model comprises an idealized model of the tissue.

102. The method of any one of the previous claims, wherein the model comprises a subject-specific model of the tissue.

103. The method of any one of the previous claims, wherein the model comprises a model of the tissue comprising one or more of: a fiber-architecture model of the tissue, scar placement within the tissue, and / or fibrosis placement within the tissue.

104. The method of any one of the previous claims, wherein the method further comprises applying the model for drug screening.

105. The method of any one of the previous claims, wherein the method further comprises of applying the model for treatment of a subject.

106. The method of any one of the previous claims, wherein the model comprises a digital twin of a subject.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 107. The method of any one of the previous claims, wherein the method further comprises generating a virtual simulation of the tissue using the model.

108. The method of any one of the previous claims, wherein the configuring comprises simulating a tissue function as the model learns the contractile motion and electrophysiological wave pattern associated with the tissue.

109. The method of any one of the previous claims, wherein the configuring comprises simulating a pumping heart as the model learns the contractile motion and electrophysiological wave pattern associated with the tissue.

110. The method of any one of the previous claims, wherein the method further comprises using the model to evolve the behavior of a simulated tissue over time.

111. The method of any one of the previous claims, wherein the electrical behavior of the tissue is integrated with the mechanical behavior of the tissue in the model.

112. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate a sequence in which different tissue locations are electrically activated.

113. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate an electrical activity activation map of the tissue.

114. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate a location of scar tissue on the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 115. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate a location of tissue that exhibits an abnormal electrical property.

116. The method of claim 115, wherein the abnormal electrical activity comprises one or more of abnormal conductivity and / or abnormal conduction speed for the tissue.

117. The method of any one of the previous claims, wherein the method further comprises applying the model to estimate a location of tissue that exhibits an abnormal mechanical property.

118. The method of claim 117, wherein the abnormal mechanical property comprises abnormal contractility for the tissue.

119. The method of any one of the previous claims, wherein the method further comprises validating the model based on clinical treatment of a subject.

120. The method of any one of the previous claims, wherein the method further comprises validating the model, wherein validating the model comprises: using the model to estimate an electrical activation pattern of the tissue based on an observed movement pattern of the tissue; and confirming the electrical activation pattern is associated with the observed movement pattern of the tissue.

121. The method of any one of the previous claims, wherein the method further comprises validating the model, wherein validating the model comprises: obtaining an electrical activation pattern of a tissue or a mechanical activation pattern of a tissue;Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 estimating an electrical activation pattern or a mechanical activation pattern by applying the model to the electrical activation pattern or a mechanical activation pattern; using a second model to estimate an electrical activation pattern or a mechanical activation pattern by applying the second model to the electrical activation pattern or a mechanical activation pattern, wherein the second model comprises a physics-based model; and assessing the accuracy of the model by comparing the estimates from the model against the estimates from the second model.

122. The method of any one of the previous claims, wherein the method further comprises collecting ultrasound imaging data of an in vivo tissue of a subject; applying the collected imaging data to the model to estimate electrical activation patterns within the tissue of the subject; and identifying one or more aspects of an abnormal electrophysiological activation pattern of the tissue of the subject.

123. The method of any one of the previous claims, wherein the method is a method of non-invasively analyzing electrophysiological processes of the tissue.

124. The method of any one of the previous claims, wherein the method is a method of non-invasively mapping a heart’s electrical activity.

125. A method of observing mechanical movement patterns and corresponding electrophysiological activation patterns of a tissue, the method comprising: introducing a tissue into an imaging apparatus configured to image electrophysiological activation patterns and mechanical movement patterns of the tissue, wherein the imaging apparatus comprises: an enclosed interior volume into which the tissue is introduced; a substrate on which the tissue is mounted; an electrode for electrically stimulating the tissue;Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 a perfusion subsystem configured to support physiological conditions of the tissue; a plurality of light sources configured for optically illuminating the tissue; an imaging system comprising an optical imaging subsystem configured for obtaining optical images of the tissue; and a plurality of mounts configured for mounting the light sources and aspects of the imaging system such that the tissue is evenly illuminated, and the imaging system obtains optical images of the tissue from a plurality of different perspectives; electrically stimulating the tissue with the electrode; imaging of the tissue by applying the imaging system in response to a stimulation of the tissue, wherein tissue stimulation comprises one or more of electrical, optical, and / or pharmacological stimulation of the tissue; imaging electrophysiological activation patterns of the tissue by applying the imaging system to obtain voltage- or calcium-sensitive optical mapping images in response to the stimulation of the tissue; and combining the obtained images of mechanical movement patterns and electrophysiological activation patterns to reconstruct movement of the tissue in response to the stimulation.

126. The method of claim 125, wherein the imaging system of the imaging apparatus further comprises an ultrasound imaging subsystem configured for obtaining ultrasound images of the tissue.

127. The method of claim 126, wherein the mechanical movement patterns of the tissue are imaged by applying the ultrasound imaging subsystem in response to a stimulation of the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 128. The method of claim 125 to 127, wherein the imaging apparatus further comprises a plurality of electrodes configured to detect electrophysiological activation patterns of the tissue.

129. The method of claim 128, wherein the plurality of detection electrodes are configured to measure electrocardiograms from the tissue.

130. The method of claim 125 to 129, wherein the imaging apparatus further comprises a power source configured to supply power to the imaging system and / or the plurality of light sources.

131. The method of claims 125 to 130, wherein the plurality of mounts are configured for mounting aspects of the imaging system such that every point of the surface of the tissue is imaged from two or more perspectives.

132. The method of claims 125 to 131, wherein the method further comprises optically stimulating the tissue using the plurality of light-sources.

133. The method of any one of claims 125 to 132, wherein the method further comprises pharmacologically stimulating the tissue using pharmacological compounds or drugs.

134. The method of any one of claims 125 to 133, wherein the method further comprises pharmacologically immobilizing aspects of the tissue using pharmacological compounds or drugs.

135. The method of any one of claims 125 to 134, wherein the imaging apparatus comprises an imaging chamber or an imaging rig.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 136. The method of claim 135, wherein the imaging chamber or rig comprises a plurality of windows configured for illuminating the tissue and obtaining images of the tissue from a plurality of different perspectives.

137. The method of any one of claims 125 to 136, wherein the optical imaging subsystem comprises a multi-camera high-speed imaging system.

138. The method of any one of claims 125 to 137, wherein the method comprises obtaining panoramic images of the tissue.

139. The method of claim 138, wherein every point on the surface of the tissue is imaged.

140. The method of any one of claims 125 to 139, wherein the method further comprises: repeatedly obtaining representations of corresponding electrophysiological activation patterns of the tissue and mechanical movement patterns of the tissue; and combining such representations into a data set for configuring a model according to claims 1 to 124.

141. The method of claim 140, wherein the method further comprises: collecting electrical activation patterns and associated mechanical movement patterns for the tissue present in the imaging chamber; and applying the electrical activation patterns and associated mechanical movement patterns as training data for the model.

142. The method of any one of claims 125 to 141, wherein the method further comprises applying a numerical motion compensation technique to images of the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 143. The method of any one of claims 125 to 142, wherein the method further comprises applying an optical mapping technique combined with a numerical motion tracking technique to measure an electrical activation pattern in the tissue moving in the imaging apparatus.

144. The method of any one of claims 125 to 143, wherein every point of the surface of the tissue is imaged from two or more perspectives and the method further comprises applying a stereoscopic motion tracking technique to measure an electrical activation pattern and / or a mechanical movement pattern in the tissue moving in the imaging apparatus.

145. The method of any one of claims 125 to 144, wherein the method comprises applying a GPU-based motion tracking algorithm to process imaging data of the tissue.

146. The method of any one of claims 125 to 145, wherein the method further comprises: collecting a plurality of raw images of the tissue; applying an optical flow estimation technique or a differentiable rendering technique to the raw images to compensate for tissue movement; and generating a plurality of compensated images of the tissue to estimate tissue deformation.

147. The method of claim 146, wherein every point of the surface of the tissue is imaged from two or more perspectives and the optical flow estimation technique is a stereoscopic optical flow estimation technique or a multi-view differentiable rendering technique used for tracking three-dimensional motion.

148. The method of any one of claims 125 to 147, wherein the method further comprises applying one or more optical flow estimation techniques or differentiableAtty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 motion estimation techniques or motion compensation techniques to images of the tissue moving to mitigate motion artifacts.

149. The method of any one of claims 125 to 148, wherein the method comprises imaging the tissue without applying a pharmacological excitation-contraction uncoupling agent to the tissue.

150. The method of any one of claims 125 to 149, wherein the method comprises imaging electrophysiological activation patterns of the tissue or mechanical movement patterns of the tissue without a fiducial marker.

151. The method of any one of claims 125 to 150, wherein the method comprises imaging electrical activation patterns across a tissue surface as the tissue deforms.

152. The method of any one of claims 125 to 151, wherein the method comprises imaging electrical activation patterns across a surface of the tissue (optionally comprising an atrial or a ventricular surface) as the tissue contracts.

153. A method comprising validating a model according to any one of claims 1 to 124 based on imaging obtained using the imaging apparatus according to any one of claims 125 to 152.

154. The method of any one of the previous claims further comprising: validating the model, wherein validating the model comprises: using the model to estimate an electrical activation pattern of the tissue based on an observed movement pattern of the tissue; and confirming the electrical activation pattern is associated with the observed movement pattern of the tissue.

155. The method of any one of the previous claims further comprising validating the model, wherein validating the model comprises:Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 obtaining an electrical activation pattern of a tissue or a mechanical activation pattern of a tissue; estimating the electrical activation pattern or the mechanical activation pattern by applying the model to the electrical activation pattern or a mechanical activation pattern; using a second model to estimate the electrical activation pattern or the mechanical activation pattern by applying the second model to the electrical activation pattern or a mechanical activation pattern, wherein the second model comprises a physics-based model; and assessing the accuracy of the model by comparing the estimates from the model against the estimates from the second model.

156. The method of any one of the previous claims further comprising: collecting ultrasound imaging data of an in vivo tissue of a subject; applying the collected imaging data to the model to estimate electrical activation patterns within the tissue of the subject; and identifying one or more aspects of an abnormal electrophysiological activation pattern of the tissue of the subject.

157. The method of any one of the previous claims, wherein the method is a method of non-invasively analyzing electrophysiological processes of the tissue.

158. The method of any one of the previous claims, wherein the method is a method of non-invasively mapping a heart’s electrical activity.

159. The method of any one of the previous claims, wherein the tissue comprises electrically excitable tissue.

160. The method of any one of the previous claims, wherein the tissue comprises anisotropic tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 161. The method of any one of the previous claims, wherein the tissue comprises cardiomyocytes.

162. The method of any one of the previous claims, wherein the tissue is cardiac tissue, lung tissue, intestinal tissue, or uterine tissue.

163. The method of claim 162, wherein the tissue is cardiac tissue.

164. The method of any one of the previous claims, wherein the tissue comprises one or more of: left ventricle tissue, right ventricle tissue, left atrium tissue, and / or right atrium tissue.

165. The method of claim 164, wherein the tissue comprises left and right ventricles.

166. The method of any one of the previous claims, wherein the tissue comprises a biventricular heart geometry.

167. The method of any one of the previous claims, wherein the tissue is human tissue, rabbit tissue, pig tissue, sheep tissue, dog tissue, mouse tissue, rat tissue, or guinea pig tissue.

168. The method of claim 167, wherein the tissue is human tissue or pig tissue.

169. The method of any one of the previous claims, wherein the tissue comprises a discontinuity.

170. The method of claim 169, wherein the discontinuity is scar tissue or fibrotic tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 171. The method of any one of the previous claims, wherein the tissue comprises an isolated organ.

172. The method of any one of the previous claims, wherein the tissue comprises cultured tissue.

173. The method of any one of the previous claims, wherein the tissue comprises elastic excitable media.

174. The method of any one of the previous claims, wherein the tissue exhibits muscle fiber anisotropy.

175. A method of assessing a model, the method comprising: generating ground-truth electrical activation patterns of a tissue; using the ground-truth electrical activation patterns to estimate mechanical movement patterns of the tissue; applying a model of the tissue to the estimated mechanical movement patterns of the tissue to estimate associated electrical activation patterns; comparing the estimated associated electrical activation patterns with the ground-truth electrical activation patterns; and assessing the accuracy of the model’s predictions based on results of comparing the estimated and ground-truth electrical activation patterns.

176. A method of training a model to estimate electrophysiological activation patterns based on mechanical movement patterns, to estimate mechanical movement based on electrophysiological activation patterns, and / or to estimate a future electromechanical state based on electrophysiological activation patterns or mechanical movement patterns, the method comprising: collecting a plurality of training data comprising corresponding electrophysiological activation patterns of a tissue and mechanical movement patterns of the tissue;Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 representing the electrophysiological activation patterns of the tissue as voltages, calcium concentrations, oxygenation, pH, and / or a temporal change thereof over a volume representing the tissue; representing the mechanical movement of the tissue as three-dimensional images and / or motion vectors over the volume representing the tissue; training a model using the electrophysiological activation patterns and corresponding mechanical movement.

177. The method of claim 176, wherein the model is trained to estimate electrophysiological activation patterns, given a representation of mechanical movement of the tissue.

178. The method of any one of claims 176 to 177, wherein the model is trained to estimate electrophysiological activation patterns, including abnormal patterns and locations, over a time period.

179. The method of any one of claims 176 to 178, wherein the training data comprises a sequence of images of corresponding electrophysiological activation patterns of the tissue and mechanical movement patterns of the tissue at consecutive times.

180. The method of any one of claims 176 to 179, wherein the training data comprises simulation data.

181. The method of claim 180, wherein the simulation data comprises results of electromechanical simulations.

182. The method of any one of any of claims 176 to 181, further comprising augmenting the training data with simulation data.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 183. The method of claim 182, wherein augmenting the training data with simulation data comprises: generating a plurality of computer-based models of structures of the tissue, wherein each of the structures varies in at least one aspect; and using the plurality of tissue models to generate simulated results of corresponding electrical activation patterns of the modeled tissue and mechanical movement of the modeled tissue.

184. The method of claim 183, wherein each of the structures varies in one or more of: tissue shape, tissue thickness, tissue stiffness, contractile force, fiber orientations, interconnections between regions of tissues, velocities of electrical activation patterns, durations of electrical activation waves, and / or spatial heterogeneity.

185. The method of claim 184, wherein each of the structures varies in spatial heterogeneity, the spatial heterogeneity varied comprising one or more of: tissue shape, tissue thickness, tissue stiffness, contractile force, fiber orientations, interconnections between regions of tissues, velocities of electrical activation patterns, and / or durations of electrical activation waves.

186. The method of any one of claims 183 to 185, wherein the plurality of computer-based models of structures of the tissue comprise numerical simulations comprising one or more of: finite-difference methods (FDM), finite element method (FEM), finite volume method (FVM), smoothed-particle hydrodynamics (SPH), and / or boundary-element method (BEM).

187. The method of any one of claims 183 to 186, wherein augmenting the training data with simulation data further comprises: simulating the introduction of electrophysiological activation patterns, action potential waves, or calcium waves into the modeled tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 188. The method of claim 187, wherein the electrophysiological activation patterns comprise one or more of a sinus wave, focal wave, and / or reentrant wave.

189. The method of any one of claims 176 to 188, wherein the volume representing the tissue comprises an idealized or patient-specific computer-based model of the tissue, optionally comprising one or more of a fiber-architecture model of the tissue, scar or fibrosis placement within the tissue of the tissue.

190. An imaging apparatus for imaging electrophysiological activation patterns and mechanical movement patterns of a tissue, wherein the imaging apparatus comprises: an enclosed interior volume configured to receive biological tissue; a perfusion subsystem configured to support physiological conditions of the tissue; a substrate on which the tissue is mounted; a plurality of light sources configured for illuminating the tissue; an imaging system comprising an optical imaging subsystem configured for obtaining optical images of the tissue; and a plurality of mounts configured for mounting the light sources and aspects of the imaging system such that the tissue is evenly illuminated, and the imaging system obtains optical images of the tissue from a plurality of different perspectives.

191. The imaging apparatus of claim 190, wherein the imaging system further comprises an ultrasound imaging subsystem configured for obtaining ultrasound images of the tissue.

192. The imaging apparatus of claim 190 or 191, wherein the imaging apparatus comprises a plurality of windows configured for illuminating the tissue and obtaining images of the tissue from a plurality of different perspectives.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 193. The imaging apparatus of any one of claim 190 or 192, wherein the imaging apparatus further comprises a plurality of electrodes configured to detect electrophysiological activation patterns of the tissue.

194. The imaging apparatus of claim 193, wherein the plurality of detection electrodes are configured to measure electrocardiograms from the tissue.

195. The imaging apparatus of any one of claims 190 to 194, wherein the imaging apparatus further comprises a power source configured to supply power to the imaging system and / or the plurality of light sources.

196. The imaging apparatus of any one of claims 190 to 195, wherein the imaging apparatus comprises a truncated icosahedron shape.

197. The imaging apparatus of any one of claims 190 to 196, wherein the imaging apparatus comprises a soccer ball geometry.

198. The imaging apparatus of any one of claims 190 to 197, wherein the imaging apparatus comprises an open top and an open bottom.

199. The imaging apparatus of any one of claims 190 to 198, wherein the open top and open bottom comprise fluidic pathways.

200. The imaging apparatus of any one of claims 190 to 199, wherein the imaging apparatus comprises 24 penta- or hexagonal surfaces.

201. The imaging apparatus of any one of claims 190 to 200, wherein the imaging apparatus comprises a shape with angles of optical axes between two adjacent surfaces of 37.4° or 41.8°.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 202. The imaging apparatus of any one of claims 190 to 201, wherein the surfaces comprise windows configured for mounting cameras.

203. The imaging apparatus of any one of claims 190 to 202, wherein the imaging apparatus comprises a plurality of windows present at vertices between surfaces of the imaging apparatus and configured to receive LEDs to illuminate the interior of the imaging apparatus.

204. The imaging apparatus of any one of claims 190 to 203, wherein the interior of the imaging apparatus is configured to be uniformly illuminated.

205. The imaging apparatus of any one of claims 190 to 204, wherein the optical imaging subsystem comprises six or more cameras.

206. The imaging apparatus of any one of claims 190 to 205, wherein the optical imaging subsystem comprises 12 or more cameras.

207. The imaging apparatus of any one of claims 190 to 206, wherein an angle between neighboring cameras is between 35 and 45°.

208. The imaging apparatus of any one of claims 190 to 207, wherein the optical imaging subsystem comprises a plurality of CCD or CMOS cameras.

209. The imaging apparatus of any one of claims 190 to 208, wherein the optical imaging subsystem is configured for measuring changes in fluorescence of aspects of the tissue.

210. The imaging apparatus of any one of claims 190 to 209, wherein the optical imaging subsystem is configured for measuring changes in fluorescence of aspects of the tissue in response to a physiological change of the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 211. The imaging apparatus of claim 210, wherein the physiological change comprises a change in transmembrane potential of the tissue.

212. The imaging apparatus of any one of claims 190 to 211, wherein the optical imaging subsystem is configured to image from the plurality of cameras simultaneously.

213. The imaging apparatus of any one of claims 190 to 212, wherein the optical imaging subsystem comprises a plurality of filters configured to block excitation light originating from the plurality of light sources.

214. The imaging apparatus of any one of claims 190 to 213, wherein the perfusion subsystem comprises a constant-pressure Langendorff-perfusion subsystem.

215. The imaging apparatus of any one of claims 190 to 214, wherein the volume of the imaging apparatus is approximately 5L.

216. The imaging apparatus of any one of claims 190 to 215, wherein the imaging apparatus further comprises an electrode configured for electrically stimulating the tissue.

217. The imaging apparatus of claim 216, wherein the stimulation electrode is configured to introduce regular pacing of electrical stimulation to the tissue.

218. The imaging apparatus of claim 216 or 217, wherein the stimulation electrode is configured to introduce burst pacing of electrical stimulation to the tissue.

219. The imaging apparatus of any one of claims 190 to 218, wherein the imaging apparatus is configured to obtain 360° imaging of the tissue.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 220. The imaging apparatus of any one of claims 190 to 219, wherein the imaging apparatus is configured to simultaneously obtain images of every point on the surface of the tissue from two or more perspectives.

221. The imaging apparatus of any one of claims 190 to 220, wherein the imaging apparatus is configured to simultaneously obtain images of every point on the surface of the tissue from four or more perspectives.

222. The imaging apparatus of any one of claims 190 to 221, wherein the imaging apparatus is configured to obtain images of the tissue while the tissue moves.

223. The imaging apparatus of any one of claims 190 to 222, wherein the imaging apparatus is configured to obtain images of the tissue while the tissue deforms.

224. The imaging apparatus of any one of claims 190 to 223, wherein the imaging apparatus comprises a 3D-printed substrate.

225. The imaging apparatus of any one of claims 190 to 224, wherein the imaging apparatus further comprises a temperature-regulation subsystem.

226. The imaging apparatus of any one of claims 190 to 225, wherein the imaging apparatus a processor comprising memory operably coupled to the processor, wherein the memory comprises instructions stored thereon, which, when executed by the processor, cause the processor to control the imaging apparatus.

227. A system for utilizing a model of a tissue, the system comprising: a processor comprising memory operably coupled to the processor, wherein the memory comprises instructions stored thereon, which, when executed by the processor, cause the processor to implement the steps of a method of any one of claims 1 to 189.Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 228. The system of claim 227, wherein the system further comprises an imaging apparatus according to any of claims 190 to 226, wherein the imaging apparatus is operably connected to the processor and memory.

229. The system of claim 227 or 228, wherein the memory further comprises instructions store thereon, which, when executed by the processor cause the processor to: control the imaging apparatus to collect images; and apply a numerical motion tracking algorithm to mitigate motion artifacts present in the images.

230. A non-transitory computer readable storage medium comprising instructions stored thereon, the instructions comprising an algorithm configured to implement the steps of a method of any one of claims 1 to 189.

231. A method for identifying a subject as having a heart rhythm disorder, the method comprising: imaging the heart of the subject using 4D ultrasound in order to generate spatio-temporal mechanical deformation data of the subject’s heart during one or more contractions; and inputting the mechanical deformation data into a model according to any one of claims 1 to 124, wherein the output of the model is used to determine if the subject has a heart rhythm disorder.

232. A method for performing catheter ablation on the heart of a subject having a heart rhythm disorder, the method comprising: imaging the heart of the subject using 4D ultrasound in order to generate spatio-temporal mechanical deformation data of the subject’s heart during one or more contractions;Atty. Docket No.: UCSF-737WO SF-2023-190-3-PCT-0 inputting the mechanical deformation data into a model according to any one of claims 1 to 124, wherein the output of the model is used to locate tissue associated with an abnormal electrical wave, an abnormal electrical pathway, or scar tissue; and ablating tissue associated with the abnormal electrical wave, the abnormal electrical pathway, or the scar tissue in order to disrupt formation or propagation of the abnormal electrical wave.

Images