A method of constructing maps of dynamical variables on a cardiac surface

Abstract

A computer implemented method of training a model for constructing maps of cardiac dynamical variables is described. The method comprises receiving a training dataset comprising dynamical variables from a first region of a cardiac surface and dynamical variables from a plurality of points, the plurality of points located within a subregion of the first region. The method further comprises calculating a predicted dynamical variable at a point on the cardiac surface using the dynamical variables from the plurality of points located within the subregion. The method further comprises calculating a reconstruction error by comparing the calculated predicted dynamical variable with the received dynamical variable from the cardiac surface at the same point. The method further comprises using the reconstruction error to update the model, and storing the trained model.

Description

[0001] A method of constructing maps of dynamical variables on a cardiac surface

[0002] Field

[0003] The present invention relates to a method of constructing maps of dynamical variables on a cardiac surface.

[0004] Background

[0005] Atrial fibrillation (AF) is the most prevalent cardiac arrhythmia, associated with significant morbidity and mortality globally. Catheter ablation is the cornerstone of AF treatment, but it consists of a one-size-fits-all intervention in the form of pulmonary vein isolation, with limited efficacy, especially in persistent AF. Pulmonary vein isolation by catheter ablation has limited effectiveness in treating AF because we cannot map AF dynamics with sufficient resolution and coverage provided by sequential contact mapping catheters. This limitation prevents effective patient phenotyping for personalised, targeted ablation.Summary

[0006] According to a first aspect of the invention, there is provided a computer implemented method of training a model for constructing maps of cardiac dynamical variables, the method comprises receiving a training dataset. The training dataset comprises dynamical variables from a first region of a cardiac surface and dynamical variables from a plurality of points, the plurality of points located within a subregion of the first region. The method further comprises calculating a predicted dynamical variable at a point on the cardiac surface using the dynamical variables from the plurality of points located within the subregion, calculating a reconstruction error by comparing the calculated predicted dynamical variable with the received dynamical variable from the cardiac surface at the same point, using the reconstruction error to update the model, and storing the trained model.

[0007] In other words, ground truth measurements or simulations of dynamical variables for a first region of a cardiac surface area are received, a subset of these dynamical variables are selected within the first region of the cardiac surface and used to predict a dynamical variable at a selected point on the cardiac surface. The selected point may be within the first region or the subregion. The ground truth or simulated dynamical variable at the selected point is compared with the predicted dynamical variable and a reconstruction error is calculated. This reconstruction error is used to update the model.

[0008] The cardiac dynamical variables may be from a healthy heart (cardiac dynamical variables), a heart experiencing arrythmia (cardiac arrhythmia dynamical variables). If the dynamical variables are from a heart experiencing arrythmia, the arrythmia may be any sort of arrythmia, for example, fibrillation (cardiac fibrillation dynamical variables) or regular tachycardia (cardiac tachycardia dynamical variables). The dynamical variables may be atrial or ventricular dynamical variables.

[0009] The subregion may be continuous or comprise two or more discrete or separated regions. The subregion may include the plurality of points used to calculate the predicted dynamical variable.The dynamical variables may be one or more of unipolar voltage, dipolar voltage, omnipolar voltage, dipole density, or phase measurements, for example, voltage electrograms.

[0010] The dynamical variable, e.g., voltage, may be recorded as a function of time and position or location on the cardiac chamber.

[0011] The cardiac surface may be the atrial surface or the ventricular surface.

[0012] The predicted dynamical variable may be a point-wise estimate, or may be a probabilistic estimate (distribution of possible values). Thus, the method may construct maps of predicted dynamical variables and their confidence (prediction uncertainty). The uncertainty may be helpful when interpreting the maps.

[0013] The constructed maps may use or be based on the predicted dynamical variables.

[0014] A first region of the cardiac surface may be all, substantially all, or the whole cardiac surface.

[0015] The point on the cardiac surface where the dynamical variable is being predicted may be outside the subregion.

[0016] A map may refer to the visual representation showing how different dynamical variables change across the heart's (cardiac) surface and over time for a healthy heart, and / or, for example, during arrythmia (fibrillation or tachycardia). A map may aid with understanding and analysis of the complex dynamics of cardiac arrythmia (fibrillation or tachycardia), or the dynamics of a healthy heart, by displaying how these variables are distributed spatially and temporally.

[0017] The first region may be a first area, and the subregion may be a subarea. That is, they are regions or areas of the surface of a heart chamber, be that an atrial or ventricular chamber.

[0018] The model can then be used to construct a map or other visualisation of the dynamical variables on the cardiac surface.The method may further comprise iteratively: using the updated model to calculate the predicted dynamical variable, calculating an updated reconstruction error by comparing the calculated dynamical variable with the received dynamical variable, and using the updated reconstruction error to update the updated model.

[0019] The predicted dynamical variable may include or be associated with a prediction confidence value which indicated the level of confidence the learned model has about the predicted dynamical variable being a true representation of what would be a measured or simulated dynamical variable at the same point.

[0020] The dynamical variables from the first region of the cardiac surface may be obtained from one or more of: cardiac activity measured from direct contact with the cardiac surface, cardiac activity measured while not in direct contact with the cardiac surface, or simulated cardiac activity measurements directly or indirectly from the cardiac surface.

[0021] Cardiac activity measured from direct contact with the cardiac surface may be acquired using electrodes on the cardiac surface which can directly measure a dynamical variable.

[0022] Cardiac activity measured while not in direct contact with the cardiac surface may be acquired using and received from an imaging and mapping system which uses high-resolution 3D cardiac chamber reconstructions using ultrasound and cardiac electrical activity, e.g., the AcQMap system. The dynamical variables may be unipolar voltage electrograms.

[0023] Simulated cardiac activity may be measurements simulated from physics theory of cardiac conduction, e.g. from the Fenton-Karma model.

[0024] The dynamical variables from the whole cardiac surface maybe used as ground truth measurements to train the model.

[0025] At least one of the dynamical variables from the whole cardiac surface may be unipolar voltage electrograms.

[0026] At least one of the dynamical variables from the whole cardiac surface may be directly measured from the cardiac surface using an electrode.The at least one of the dynamical variables is directly measured from the cardiac surface using an electrode may be measured at 70 Hz. The electrode may be a grid catheter electrode.

[0027] At least one dynamical variable may be measured or obtained using an invasive technique or procedure, or the at least one dynamical variable is simulated as if an invasive technique or procedure was being used. That is, an invasive or surgical procedure or technique may be required to measure or obtain at least one dynamical variable, or the simulation of the dynamical variable is a simulation of measuring or obtaining the dynamical variable using an invasive technique or procedure. Non-invasive procedures include electrocardiogram measurements where electrodes are places on the body surface (e.g., skin), whereas invasive procedures may include accessing the chambers of the heart directly and taking or simulating surface measurements from these surfaces.

[0028] The model may be a non-linear state-space and / or a spatio-temporal model for propagating information from the plurality of points located within the area of the cardiac surface to points outside of the area of the cardiac surface.

[0029] The model may be a graph recurrent neural network (GRNN), for example, a gated GRNN. The model may be bidirectional. The model may be point-wise (e.g. GRNN) or probabilistic (e.g. denoising diffusion probabilistic model) to estimate the value and / or distribution of dynamical variables in space and time: to estimate a map of the variable and its uncertainty.

[0030] The plurality of points located within the subregion of the cardiac surface may be determined by sampling over at of least part of the cardiac surface.

[0031] Sampling may be, sequential sampling, random walk, etc. The random walk may be over the whole atria surface. The random walk may be a self-avoiding random walk.

[0032] The plurality of points located within the subregion of the cardiac surface may be representative of the electrode arrangement on a grid catheter.For example, the plurality of points located within an area of the cardiac surface may be in a regular gird or be evenly spaced along a first and / or a second axis.

[0033] The cardiac surface may be an atrial surface and / or a ventricular surface.

[0034] The dynamical variables from the first region of the cardiac surface comprise a dynamical variable which has been measured from a subject.

[0035] The subject may be a human, for example a human patient undergoing a cardiac treatment, for example, for cardiac (e.g., atrial) fibrillation, or ventricular tachycardia.

[0036] The dynamical variable measured from a subject may be acquired from an electrode catheter.

[0037] The dynamical variable measured from a subject may be used to train part of the model.

[0038] For example, the dynamical variable measurement from a subject may be used to optimise node and subject-specific embedding parameters using an observed patch reconstruction loss while the remaining parameters of the model are fixed after training on the dynamical variables from the whole cardiac surface and the dynamical variables from a plurality of points, the plurality of points located within an area of the whole cardiac surface. That is, while all received dynamical variables may be used to train the global model relevant to all patients, dynamical variable measurements from a single subject can be used to train subject-specific parameters or embedding of the model, improving the model for each subject.

[0039] In addition to subject-specific embeddings, other patient-specific parameters alongside subject-specific embeddings (e.g. age, height, weight, BMI, blood pressure, coronary artery disease data, heart failure data, and valvular heart disease data) and if the subject or patient was prescribed anti-arrhythmic drugs (e.g., yes / no and dosage) etc.).

[0040] The computer implemented method may further comprise calculating a second reconstruction error by comparing the calculated dynamical variable with themeasured dynamical variable, and using the second reconstruction error to update the model.

[0041] At least one of the dynamical variables from the whole cardiac surface may be dynamical variables from discrete points on the cardiac surface.

[0042] That is, at least one of the dynamical variables is from a node on the area of the cardiac surface.

[0043] The dynamical variables from the first region may be associated with a graph.

[0044] The graph may be a connectivity graph. The graph may include spatial information, the spatial information may include proximity information. The spatial information may include the absolute and / or relative location of the of the dynamical variable on the cardiac surface.

[0045] The dynamical variables from the first region may comprise dynamical variables from a plurality of subjects.

[0046] For example, the dynamical variables may be measured or recorded from a first subject and a second subject and measurements or recordings may be used to train the model.

[0047] The dynamical variables may span a time period.

[0048] That is, the dynamical variables may be measured or recorded for a period of time, for example, less than 20 seconds, for example, between 1-20 seconds, or more preferably, 5-20 seconds. Measuring dynamical variables for longer can achieve better results, and therefore the dynamical variables may be measured for more than 20 seconds, for example between 20 and 30 seconds, or between 30 and 50 second. The dynamical variables may be measured for longer than 50 seconds to get more accurate measurements of the dynamical variables. The dynamical variables may be measured or recorded at a frequency of between 2000 and 6000 Hz, preferably between 3000-6000 Hz. Higher frequencies may generate higher resolution dynamical variable data, and therefore higher frequencies may be used and preferred.According to a second aspect of the invention, there is provided a computer implemented method of imputing a dynamical variable at a point on a cardiac surface, the method comprising: receiving a measurement of a dynamical variable at a first point on the cardiac surface, using the trained model the first aspect and the received measurement to impute a dynamical variable at a second point on the cardiac surface.

[0049] The second point may be, or be at a different location to, the first point. There may be more than one dynamical variable received.

[0050] The dynamical variable may have a time component and / or a duration component.

[0051] The received measurement of a dynamical variable may be used to update subjectspecific parameters of the model.

[0052] The computer implemented method may further comprise using the imputed dynamical variable to phenotype a or the subject.

[0053] For example, the imputed dynamical variable or variables may be used to assign a subject to a group or groups which all have similar dynamical variables behaviours.

[0054] The computer implemented method may further comprise using the imputed dynamical variable to diagnose and / or treat a condition or disease for a or the subject.

[0055] That is, the imputed dynamical variable or variables may be used to determine a phenotype, a condition, or a disease that a subject under investigation may have. Further, the imputed dynamical variable or variables may be used to determine where to treat on the cardiac surface, for example, where to ablate on the cardiac surface to destroy tissue that causes irregular heartbeats.

[0056] The subject may be a patient, for example a human patient. The imputed dynamical variables may be used solely or in combination with other information (which may be subject-specific information) to diagnose the subject with a condition or a disease (for example a cardiovascular disease), treat the disease or condition, or assign the subject to a phenotype which may aid further monitoring or investigations.According to a third aspect of the invention, there is provided a system comprising: an electrode for measuring dynamical variables from a cardiac surface, and a processor for receiving the dynamical variables and processing received and / or measured dynamical variables from the electrode, using the trained model of the first aspect.

[0057] The electrode may be a grid catheter electrode.

[0058] The system may further comprise a controller. The controller may comprise the processor, system memory, and an interface.

[0059] According to a fourth aspect of the invention, there is provided a computing device performing the method of either the first or the second aspect.

[0060] The computing device may include a memory, and at least one processor for performing the method.

[0061] According to a fifth aspect of the invention, there is provided a computer readable medium having program instructions for performing the method of the first or second aspects.

[0062] The non-transitory computer readable medium (CRM), may store one or more programs for execution by one or more processors of a computing device, the one or more programs including instructions for performing the method.Brief description of the drawings

[0063] Certain embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

[0064] Figure 1 is a schematic of the observation mask and the evaluation mask on a cardiac surface for training and fine-tuning the model;

[0065] Figure 2A is a schematic diagram of the inputs to the model;

[0066] Figure 2B is a schematic diagram of the architecture of the model generation;

[0067] Figure 3A is a plot of the reconstruction loss over the number of epochs;

[0068] Figure 3B is a plot of test set reconstruction performance (mean absolute error) of all models considered;

[0069] Figure 3C is a plot of test set performance as true positive rate for phase singularity detection;

[0070] Figure 4A is a series of snapshots of the model's imputation maps versus the ground truth AcQMap phase maps for two different patients;

[0071] Figure 4B is a plot of node-level temporal reconstructions of voltage for two different patients;

[0072] Figure 5A is a sliding window cross-correlation analysis between AcQMap and the present model output phase signals produced from multipolar catheter measurements;

[0073] Figure 5B are plots of kernel density estimates of pairwise cross-correlations computed between AcQMap and the present model output maps (produced from multipolar catheter measurements) from the same patient (intra), different patients (inter) and a random baseline (shuffled);

[0074] Figure 5C are plots of cross correlation across sliding window durations for intra-and inter-patient comparison and comparison with a random baseline (shuffled); Figure 5D are representative snapshots of phase maps from highly correlated windows, comparing AcQMap recordings with the present model's output maps derived from real multipolar catheter measurements covering <10% of the atrial surface per time;

[0075] Figure 6A are three-dimensional bar charts of the reconstruction error over grid catheter area and dwell time;

[0076] Figure 6B are line plots of the reconstruction error over imputation horizon for patients grouped by entropy of AF dynamics;

[0077] Figure 7 are plots which show how FibMap's hidden state and patient-specific node parameters are interpreted. Ai) Trajectory of the hidden state of a node in the test set, where the state space has been reduced to 3D using TSNE dimensionalityreduction. Trajectories are coloured by their position in the state space by converting the 3D coordinate to RGB. Aii) The imputed and true voltage electrograms are plotted for the same node, coloured by their position in the state space. The absolute error between the imputed and true electrograms is also shown. Aiii) A recurrence plot summarising the state space trajectory, where different dynamical structures are observed over time. B) Node embeddings in the test set coloured by (i) patient, (ii) dominant frequency and (iii) Shannon entropy; Figure 8 is a system block diagram of a catheter ablation system;

[0078] Figure 9 is a process flow diagram for training and implementing a model of reconstructing global cardiac dynamical variables from sparse measurements; Figure 10 is a process flow diagram for training a model for constructing maps of cardiac dynamical variables;

[0079] Figure 11 is a qualitative reconstruction of rat ventricular fibrillation from simulated sparse sequential contact mapping; and

[0080] Figure 12 is qualitative reconstruction of human atrial fibrillation from simulated sparse sequential contact mapping.

[0081] Detailed description of certain embodiments

[0082] Introduction

[0083] Atrial fibrillation (AF) is the most common cardiac arrhythmia with a lifetime risk of one in three. AF is estimated to affect 37.5 million people worldwide - 0.5% of the global population - with a 60% projected rise by 2050. The arrhythmia underpins much of global morbidity and mortality as a major cause of stroke, heart failure and death. Global healthcare systems experience a significant and rising cost burden managing AF, with direct patient costs alone estimated to be 2.4% of the United Kingdom's £182 billion healthcare budget.

[0084] Catheter ablation is a common treatment for AF. Catheter ablation aims to aid the maintenance of sinus (normal) rhythm through the controlled destruction of cardiac tissue via heating or freezing. In this way, it is possible to electrically isolate regions of the atria that initiate or sustain AF. Pulmonary vein isolation, which isolates AF triggers in the pulmonary veins from the left atrium, is central to AF ablation, yet its success rates are as low as 50% at five years in persistent AF, with effectiveness diminishing over time. Other ablation targets, such as linear lesions to compartmentalise the atria and targeted ablation of putative AF drivers have not significantly improved outcomes. These approaches fail to tailor interventions to theunique electrophenotypes within the spectrum of AF observed in patients, leaving a one-size-fits- all treatment plan for a highly heterogeneous disorder.

[0085] A major limitation in applying tailored ablation strategies within the invasive electrophysiology laboratory is the inability to map AF effectively, that is, reconstruct AF dynamics on the surface of the heart. Sequential contact mapping is routinely used to record electrical signals from the atria, wherein a multipolar electrode catheter is inserted into the atrial chamber and placed in contact with the endocardial surface of the atrial chamber during the invasive procedure. The chamber is scanned sequentially with voltage recorded as a function of time and position, and the results are computationally stitched together. This approach is powerful for organised arrhythmias, such as focal tachycardias, where the regularity of the dynamics allows for accurate stitching and thereby precise localisation of the arrhythmic source, resulting in a curative targeted ablation procedure that lasts minutes rather than hours.

[0086] However, this approach is ineffective in AF due to its highly disorganised nature, with beat-to-beat variations in wavefront propagation, meaning the non-continuous recordings cannot be sensibly stitched together. While there have been attempts at continuous whole atria mapping, these typically require different modalities such as non-contact catheters that are not routinely used in the clinic since they often lack the spatial resolution and coverage necessary to effectively target AF drivers, are expensive and increase procedural complexity and risk.

[0087] Further, for healthy patients, or those experiencing organised arrhythmic beats, while it is possible to "computationally stitch together" the recordings using existing methods mentioned above. However, this process is time consuming and can have significant errors. For these patients, the methods detailed here offer an alternative approach which may be faster, easier to process, and result in a more accurate representation of their heart performance.

[0088] To address this a novel artificial intelligence imputation mapping model is provided (hereinafter also referred to as FibMap) that can reconstruct cardiac dynamical variables (e.g., AF dynamics) from sparse measurements. FibMap is a graph recurrent neural network model tailored to reconstruct whole atria dynamics via imputation. Trained and validated on 51 non- contact whole atria recordings, FibMap demonstrates state-of-the-art performance in reconstructing voltageelectrograms across a spectrum of AF dynamics and efficiently generalises to new and unseen patients in real time. FibMap reconstructs whole atria dynamics from just 10% surface coverage, achieving a mean absolute error of 0.0574 (± 0.0005) and tracking phase singularities with a true positive rate of 0.8924 (± 0.0342), outperforming baselines by 210% and an order of magnitude, respectively.

[0089] FibMap's clinical utility is showcased on real examples of sequential contact mapping recorded with a grid mapping catheter, showing its ability to reconstruct personalised AF dynamics with fidelity comparable to whole-atria non-contact mapping, using data from less than 10% surface coverage. Sensitivity analysis shows that FibMap performs better with rapid surface coverage and organised AF patterns, while analysis of its state spaces and patient-specific parameters offer potential insights for electrophenotyping of AF. By integrating imputation mapping into clinical practice to provide personalised and potentially real-time dynamical variable maps (e.g., AF maps) to the catheter laboratory, FibMap may allow for personalised cardiac disease or condition (e.g., AF) care and potentially improve clinical outcomes. FibMap can also be used to reconstruct dynamical variables for healthy patients with healthy hearts and cardiac tissue, and dynamical variables for patients with different types of arrythmia, for example, ventricular fibrillation (VF) or atrial / ventricular tachycardia.

[0090] Methods

[0091] FibMap aims to reconstruct the dynamics of cardiac dynamical variables (e.g., AF) from partial measurements collected during sequential contact mapping using a Graph Recurrent Neural Network (GRNN). This task is formulated using a spatiotemporal time series imputation framework, which models the propagation of electrical signals across the atrium via spatiotemporal message passing on a graph.

[0092] To become a feasible clinical solution, the design of FibMap solves several technical challenges of the task: 1) how to effectively propagate information from highly sparse sets of observations where only ~10% of the atrium is observed per time with sequential contact mapping; 2) how to manage possibly unknown parameters which could affect the dynamics, such as the spatial properties of the tissue and patient-specific covariates; 3) how to efficiently train and use a single model within the duration of the clinical procedure, whilst balancing the trade-off between personalised reconstruction and generalising across a spectrum of AF dynamics; and 4) how to quantify the uncertainty of the estimated reconstruction — an essential factor for ensuring a utile and trustworthy clinical tool in practice. In thissection, we describe the framework behind FibMap, our solution for achieving accurate reconstruction of AF dynamics while considering the technical challenges detailed above.

[0093] Background and related work

[0094] The field of graph signal processing has emerged in the last decade to generalise digital signal processing methods, such as convolutional filters, to the graph domain. A graph, G, is defined as a set of N nodes, w e for / = 1,..., N, and a set of E edges denoting the pairwise connections between them, eu = (Vi, Vj) e E, for / = 1, N and j = 1, N. Graph signal processing focuses on analysing signals on graphs, where a multivariate signal on a graph is defined as Xf 'xc, which assigns a real-valued signal of c channels to each node, X v H> IRC.

[0095] Building on graph signal processing methods, graph deep learning has generalised successful deep learning architectures, such as convolutional neural networks, to the graph domain. Spatio-Temporal Graph Neural Networks (ST-GNNs) refer to the class of deep learning architectures designed to analyse time-varying graph signals. ST-GNNs can be categorised into time-then-space or time-and-space models which denote separate or joint processing of the space and time dimensions, respectively. A notable example of a time- and-space ST-GNN is the GRNN, which replaces the fully connected layers in a recurrent neural network with graph convolutions. ST-GNNs have achieved state-of-the-art performance in tasks such as forecasting and missing data imputation.

[0096] ST-GNNs are inherently global models, sharing parameters across space and assuming a stationary process over time. Global ST-GNNs can be used for zero-shot transfer and inductive learning on unseen graphs, however, they might fail to account for spatial variations in dynamics. Node embeddings have been recently introduced to learn these local effects in ST- GNNs. Whilst hybrid global-local models often outperform global architectures, recent research has focussed on improving their performance in an inductive setting using transfer learning.

[0097] Inputs to FibMap

[0098] A graph adjacency matrix for each patient p, A(p)e ^N, is created by discretising the atrial surface into N nodes and triangulating the surface to create edges. The adjacency matrix A is constant over time. A sequence of graphs is formed as a tuple Gt:P)= Mt:P), A(p)), whereby partial electrical voltage signalsn^wxiareobserved via sequential contact mapping, and the observation mask Mt: 'p)e {0,l}Wxlspecifies the indices of the valid measurements.

[0099] To manage the patient's latent spatial and global parameters which could affect the dynamics of AF, trainable embeddings are used as an additional input. Specifically, trainable node embeddings, V(p)e IRWXC / , are used to learn the latent spatial properties of the patient's tissue, and trainable patient embeddings, g r, will be used to learn the latent global properties of the patient. In this way, the sequence of graph data for each patient can be expressed as a tuple Gt: L(p)= XCL(P), MCL(P), A(p), y(p)fg(p) FOrefficient processing, input sequences are formed by splitting the sequence of length L into windows of length W, processed with a stride M.

[0100] Furthermore, if there are observed spatial and global parameters of the patient, these features can be accounted for by concatenating them to l ^and g(p)as additional non-trainable parameters, respectively.

[0101] Architecture

[0102] FibMap is instantiated as a bidirectional gated-GRNN, a non-linear state space model designed to propagate information from valid observations across space and time. Our solution is composed of two spatiotemporal encoder blocks and a decoder. The spatiotemporal encoders operate in two different directions, processing the sequence in both a forward (fwd) and backward (bwd) direction, respectively. FibMap’s architecture can be interpreted as an extension of the framework proposed in Cini, A., Marisca, I. & Alippi, C. Filling the g_ap_s: multivariate time series imputation by graph neural networks in Proceedings of the International Conference on Learning Representations (2022). FibMap incorporates local and global embedding parameters to enable generalisation across patients and efficient transfer to new patients via fine-tuning (see Cini, A., Marisca, I., Zambon, D. & Alippi, C. Taming local effects in graph-based spatiotemporal forecasting in Proceedings of the 37th International Conference on Neural Information Processing Systems, 55375-55393 (2024)), adapting the original framework to address the AF mapping problem at hand.

[0103] To balance the trade-off between personalised reconstruction and generalisation across a spectrum of AF dynamics with a single model, FibMap is designed to perform personalised reconstruction by providing patient-specific parameters, V(p)and g(p), as additional input to the encoder and decoder components of the architecture. All other model parameters are shared across patients to learn thecommon aspects of the dynamics (such as the physics of the problem). We begin by defining the spatiotemporal encoder block of the architecture, before explaining the decoder.

[0104] The spatiotemporal encoder

[0105] First, the observed data at time t is encoded as

[0106] Ht° = MLPenc([ Xt(P) O Mt(Pi 11 Mt(Pi 11 G(p)11 V(Pi ]),

[0107] where the symbols O and 11 denote the Hadamard product and concatenation operator, respectively, and G(p)e lNxris a matrix where copies of g(p)are stacked across nodes. The encoding step constructs a representation of the observed and missing values alongside the patient-specific parameters in a common embedding space, Ht°e ^Nxd. Next, the embedded data is processed sequentially using a gated-GRNN, where the -th layer is given by

[0108] Ztk= Htk 1

[0109] Rtk= a( MPrk([Ztk| \Ht-ik], E) ),

[0110] Utk= O( MPuk ([Ztk| \Ht-ik], E) ),

[0111] Ctk= tanh( MPck([Ztk11 RtkO Ht-ik], E) ),

[0112] Htk= UtkO Ht-ik+(1- Utk) O Ctk.

[0113] MPrk, MPukand MPckdenote the MPNN layers for the reset, update, and candidate gates, respectively, and the activation functions o and tanh denote the sigmoid and hyperbolic tangents. The hidden state of the gated-GRNN at each layer k is initialised as a linear function of the node embeddings

[0114] Ht=0k= V(Pi Winitk+ binitk,

[0115] where Winitke Tqxdand binitke lRd, which takes the different characteristics of each time series into account when initialising the state, thus reducing the need to rely on a long observation history.Message passing layers. The MPNN layers for each gate in the GRININ, denoted as MP, compute the hidden state of each node / as

[0116] ht+1= yk(htk, J JVW {pk(Oik, ok, eg)}),

[0117] where ( e ^2drepresents the input of the gate at layer k. Specifically, the function pkis implemented as

[0118] mijk= MLPmsgk([OikI I Ojk]),

[0119] gijk= O’ (Wmsg-gk(m ) ),

[0120] mik= gikmijk,

[0121] where the messages are weighted according to an inferred scalar value gg, which resides on the interval [0, 1]. The scalar value ggkallows for anisotropic message passing, which assists in learning latent edge attributes such as the coupling strength between nodes. Messages are then aggregated at node i using the summation, m,k= je ) mk. Finally, the update function ykis implemented with a residual skip connection as

[0122] u = MLPuPk([ h,k11 n ]),

[0123] ht,k+1= uk+ Wskipkok,

[0124] where WSkiPedx2dand h +1 n Note that the parameters of the MPNN layers, MP, are defined separately for each gate and layer.

[0125] Iterative imputations. To learn effective state space representations while processing the data sequentially, missing values must be accounted for. To do this, first and second-stage imputations are performed iteratively within the spatiotemporal encoder block. The first stage imputation performs one-step-ahead prediction via a linear readout as

[0126]

[0127] t+1 ~ "t Wastage-! + b stage-lrwhich is used in place for the missing values. The second stage imputation acts as a type of regularisation, estimating the value at node / by using the previous hidden states, as well as the masks and first-stage imputations at the neighbouring nodes. The second stage imputation involves first computing an intermediate representation of each node, given by

[0128] S

[0129]

[0130] t+l,i = Ystage-2 (Jit,*, Zje.vfi) Pstage-2([~^t+l,]'1^ | | htjK| |, Gij)),

[0131] where St+i n^ and the message passing is implemented using a diffusion graph convolution. Next, a linear readout layer performs the second stage imputation as

[0132] (2) K

[0133] X

[0134]

[0135] t+i = [St+1\ \Ht] Wstage.2+ b stage-2 / S

[0136] which is used again in place of the missing values in Xt+i.

[0137] The process detailed so far in the spatiotemporal encoding block is repeated for Xt+i, to learn representations

[0138]

[0139] and so forth, until a set of representations St:t+w and Ht:t+W, and imputations Xt:t+w(1)andX / .r+j / ^ are calculated for the whole window length W. To summarise the spatiotemporal encoding block detailed in this section, we use the following shorthand notation

[0140] (

[0141]

[0142] St:t+ir, Xt:t+w(1), X:t^2)} = ST-Encoder (Xtt+w®, g(p), V(pJ).

[0143] The FibMap decoder

[0144] The sequences are encoded in both the forward and backward directions, to form

[0145] Sfwd, HfwdK, Xfwdw, Xfwd(2)) = ST-Encoder

[0146]

[0147] g<p\ V<p''),

[0148] and

[0149] {

[0150]

[0151] Sbwd, HbwdK, X^1), Xbwd(2)) = ST-Encoder {Xt+w:tfp), Mt+w:t(p), g(p), V(p)),

[0152] respectively, where t+W:t denotes the time reversed I backward sequence. The next stage is to decode the hidden state representations from the encodings in bothdirections, to perform a final imputation at time t'. This is done with the following function

[0153] Y

[0154]

[0155] t' = MLPdec([SfWd < t' 11 Hfwd < t'K11 SbWd > r 11 HbWd < t'K11 MtM11 11 g™ ]),

[0156] where the notation fwd < t' refers to an index of the hidden states at time t' (which includes information from times < tQ and similarly, bwd > t' refers to index at time t' (which includes information from times > tQ. The decoder takes a form like that in except patient-specific parameters are also provided to facilitate personalisation. We denote the final imputed values for the entire window length as Yt:t+w.

[0157] FibMap optimisation

[0158] To quantify the uncertainty for the reconstructed dynamics, FibMap is formulated as a quantile regression. In general, a quantile regression aims to estimate the conditional quantile function QY (T | B), which represents the T-th quantile of the response variable Y given the predictor variables B, and is given by QY (T | B) = inf { yeR | P(Y < y | B) > T }, where P(Y < y | B) is the conditional cumulative distribution function of the response variable Y given the predictors B, and inf represents the infimum of the set.

[0159] In this work, conditional quantile functions for TEC, where

[0160]

[0161] C are predicted for each of the imputed values. This is done by computing the following masked quantile / pinball loss function

[0162] ( Yt:t+T, Yt:t+T, Mt:t+T) = [ Xh=tt+Tmt,, (yt,„ yt,t) ] / / 2), / 72' / vm^],

[0163]

[0164] (1)

[0165] where Yt lRWx|ei, Yt lRWxl, and Mte{0,l}Wxl, represent the predicted values, target values, and the evaluation mask, respectively, at time t. The function Lt,i computes the average pinball loss computed at time t and node i, which is given by

[0166] Tt,i (yt,i, yt,i) = (1 / |C|) Zc=l|C |) ( yt,i - yt,i[c])(TC - 1{ yt,i - yt,i[c] < 0}), (2)

[0167] where c refers to the channel of yt,i (prediction vector at time t and node / ') which contains the prediction of the c-th conditional quantile Qyt,i ( TC|... ), and 1{ yt,i -Yt,i[c] < 0} represents the indicator function, which is equal to 1 if yt,i - yt,i[cj < 0, else it is equal to 0. In practice, we modify the decoder to predict a value for eachquantile (rather than a single value) and compute the average pinball loss from each predicted quantile value as in Equation 2.

[0168] For FibMap, the following loss function is minimised

[0169] S£loss—S£ (Yt:t+T, Xt:t+T, M^t+r)

[0170] + £ (Xt:t+^W Xt:t+T, Mt:t+T) + &(Xt:t+7™’ Xt:t+T, Mt:t+T)

[0171] + £ (Xt:t+T^hwd, Xt:t+T, M,t+T) + S£ (Xt:t+T(2)’hwd, Xt:t+T, Mt:t+T),

[0172]

[0173] (3) where £ is given in Equation 1 and each component of the loss is specific to a different imputation stage and processing direction. The specification of the evaluation mask M differs depending on training and fine-tuning as detailed in the next sections.

[0174] Dataset

[0175] The dataset comprises recordings from 51 patients with persistent AF, obtained using the AcQMap system. This system provides non-contact simultaneous unipolar voltage electrograms for the entire atria (~3500 nodes at 3000 Hz for 5-20 seconds). The AcQMap system reconstructs voltage electrograms on the atrial surface from non-contact measurements sampled from the centre of the chamber, offering a ground truth of human AF dynamics with reasonable fidelity. All recordings were obtained prior to pulmonary vein isolation at two United Kingdom centres between 2016 and 2023. The patient cohort (mean age 64 ± 11 years, 69% male) had standard cardiovascular risk factors and were on guideline-directed medical therapy (see Table 1).

[0176] Table 1: Characteristics of the study patients. Values are mean ± SD or n (%). The asterisk denotes the presence of missing values; the number missing is shown as n* Acronyms: Body Mass Index (BMI).

[0177] Total N=51

[0178] Demographics

[0179] Mean age (years) 64 ± 11

[0180] Male 35 (69%)

[0181] Mean BMI 29 ± 5

[0182]

[0183] Comorbidities

[0184] Hypertension 20 (39%)

[0185] Diabetes Mellitus 5 (10%)

[0186] Heart failure 17 (33%)

[0187] CHA2DS2-VASC score >2 14 (27%)

[0188] Medications

[0189] Antiarrhythmics: Beta-blockers 33* (87%, n* = 13) Antiarrhythmics: Amiodarone 11* (29%, n* = 13) Anticoagulants 38* (100%, n*=13)

[0190] Statins 16* (42%, n* = 13)

[0191]

[0192] For pre-processing, these signals are first resampled spatially to a resolution consisting of 500 nodes. This is done by k-means clustering of the 3D node coordinates into k=500 non- overlapping clusters, where signals are resampled using the mean average signal within each cluster for each time point. Temporal resampling to 70 Hz is conducted through a combination of low-pass filtering and downsampling. Low-pass filtering is applied to each time series at 70 Hz to prevent aliasing, and then the filtered signal is downsampled by reducing the sampling rate proportionally. Finally, the time series are normalised across space and time by applying min- max normalisation, where the minimum and maximum values are determined across all nodes and times, ensuring that the amplitude of the resampled signals is scaled consistently between 0 and 1.

[0193] The dataset was stratified to ensure a spectrum of AF dynamics within training (70%), validation (10%), and test (20%) sets. The Shannon entropy was first computed for the resampled time series at each node to do this. The cumulative distribution function (CDF) of Shannon entropy across the atrium was then created for each patient, serving as a measure to compare the similarity of the spatiotemporal dynamics between patients. The similarity between patients was assessed by computing Kolmogorov-Smirnov (KS) distance between CDFs for each pair of patients, where a smaller KS distance represents more similar entropy distributions / spatiotemporal dynamics. From this, groups of similar patients were identified by clustering a Laplacian eigenmap embedding using k-means, where the number of clusters was determined using the elbow method. This involved forming a weighted adjacency matrix by applying a radial basis function kernel to thereciprocal of the KS distances and thresholding. Finally, the training, validation, and test sets were formed by performing stratified sampling across these clusters, maintaining a consistent spectrum of AF dynamics within each set.

[0194] Simulating sequential contact mapping

[0195] A sequential contact mapping strategy is simulated from the non-contact recordings as a self- avoiding walk of the multipolar catheter (represented as a patch of observations) on the atrial surface; whereby the catheter surface area, dwell time, and spatial overlap, could be controlled. The self-avoiding walk is defined by first providing the catheter surface area as a fraction of the total area, where its reciprocal (1 / area) is rounded up to the nearest integer to give the number of patches required to sample the whole atrium. Then, the atrium is split into disjoint patches by k- means clustering the 3D node coordinates, with k equal to the number of patches. Spatial overlap between patches is simulated by adding additional clusters between adjacent patches and sharing node sets in proportion to the overlap required. A self-avoiding random walk ensures the path does not revisit the same region twice. This is simulated by sampling a patch randomly, then sampling the remaining patches without replacement with a probability proportional to the distance between the current and remaining patches. The resulting sequence of patches is converted to an observation mask, M, by assigning a unity value if nodes are within the observed patch, zero otherwise, and repeating these values such that each patch is observed for a duration equal to the specified dwell time. Except during the sensitivity analysis, the sequence of patches is repeated until the length of the available recording is met.

[0196] Training

[0197] The training procedure of FibMap leverages the whole atria ground truth signals of each patient to learn a robust function for reconstructing whole atrium dynamics from data collected in a sequential contact mapping fashion. To do this, a selfsupervised approach is employed, wherein self-avoiding walks of the multipolar catheter are sampled at random to form the observation mask, M, and observed input data, X, of each training sample, alongside a range of catheter surface areas (2.5 - 50% of the atrium), dwell times (0.2 - 4 seconds) and spatial overlaps (0 - 3 additional clusters between adjacent patches). At each training iteration, batches of size B are formed by collating samples from different patients, whereby B inputs Xt:W(p), A(p), V(p), g(p)are collated for a temporal input window size, W,sampled from the original time series following a sliding window approach with unit stride.

[0198] Imputation is performed within the temporal window and a whole atria reconstruction loss is used to optimise FibMap during training, whereby Equation 3 is optimised using an evaluation mask, Mt: W, with all nodes and times in the input window equal to unity (see Figure 1 for an illustration of the observation and evaluation mask used during training). This approach ensures a robust function for reconstructing whole atria maps that generalise across the distribution of multipolar catheter paths and parameters of sequential contact mapping such as dwell time.

[0199] A hyperparameter search is conducted for the parameters shown in Table 2, by first splitting the time series of each patient sequentially, with the first 85% of time steps being used for training, the second 5% for validation, and the final 10% for testing. For the validation and test sequences, a fixed self-avoiding walk of the multipolar catheter is used with a surface area of 10%, a dwell time of 1 second, and no spatial overlap. Each configuration in the hyperparameter search is conducted for 100 epochs, whereby the Mean Absolute Error (MAE) across the remaining atria for the validation sequence is monitored with early stopping. All experiments were performed on a NVIDIA RTX A5000 graphics processing unit. The best- performing set of hyperparameters is chosen by computing the MAE loss across the remaining atria for the test sequence and selecting the minimum loss. The best-performing configuration for training FibMap was found to be B=16, W=40, d=64, q=64, r=16, K=1, and 1024 hidden layer neurons. This configuration was retrained for 500 epochs, where a learning rate of 0.0009 and a cosine scheduler were used. Training took a total of 31 hours. The result is a pre-trained FibMap model, which performs accurate and robust whole atria reconstruction from partial observations across a spectrum of dynamics found in patients and variations in multipolar mapping.

[0200] Table 2: Hyperparameter values tested during FibMap training. Acronyms: MultiLayer Perceptron (MLP), Encoder (enc) and Decoder (dec).

[0201] Hyperparameter Range tested

[0202] Batch size, B [16, 32, 64]

[0203] Input window length, W (timesteps) [20, 30, 40, 50]

[0204] Hidden size, d [64, 128, 256]

[0205]

[0206] Node embedding size, q [16, 32, 64]

[0207] Patient embedding size, r [16, 32, 64]

[0208] Layers, K [1, 2, 3]

[0209] Hidden layer neurons in MLPenc and [128, 256, 512, 1024]

[0210] MLPdec

[0211]

[0212] Fine-tuning: validation and testing

[0213] In clinical practice, only the patches of multipolar catheter measurements are available from sequential contact mapping. The rest of the atrium remains unobserved. To make FibMap a feasible clinical solution for imputation mapping, a fine-tuning procedure is introduced to enable accurate whole atria reconstruction on new and unseen patients when only partial observations of the dynamics are available.

[0214] Our fine-tuning procedure preserves essential knowledge for whole atria reconstruction acquired during training by fixing the parameters of the pre-trained FibMap model, while quickly personalising the model to new patients by optimising only the node and patient embedding parameters using an observed patch reconstruction loss (see Figure 1 for an illustration of the observation and evaluation masks used during fine-tuning, which are defined to be equal). The observed patch reconstruction loss is defined using this evaluation mask in Equation 3. This restricts the optimisation during fine-tuning to only the patches of multipolar catheter measurements.

[0215] Our fine-tuning procedure was configured on the validation set, which also has ground truth whole atria signals available for patients. Validation of the fine-tuning procedures aims to evaluate the relationship between the observed patch and whole atria reconstruction losses. Again, the time series of each patient was split sequentially, with the first 85% of time steps being used for training, the second 5% for validation, and the final 10% for testing.

[0216] A random hyperparameter search was conducted across learning rates [0.0005, 0.005] and batch sizes [16, 32, 64, 128]. Each learning rate in the hyperparameter search was conducted for 100 epochs, whereby the MAE across the remaining atria for the validation sequence was monitored with early stopping. For the validation and test sequences, a fixed self-avoiding walk of the multipolar catheter was used with a surface area of 10%, a dwell time of 1 second, and no spatial overlap. Thebest- performing set of hyperparameters was chosen by computing the MAE across the remaining atria for the test sequence and selecting the minimum loss. The best- performing configuration for fine-tuning FibMap was found to have a learning rate of 0.005 and a batch size of 16.

[0217] Finally, the performance of FibMap imputation mapping on new and unseen patients, through our fine-tuning setup, was quantified on the test set patients. A sequential time series split was not used during testing, instead, all observed measurements were used. FibMap was fine-tuned for 100 epochs using the configuration found in validation, and the observed patch reconstruction loss was monitored to perform early stopping. The performance metrics, detailed next, were computed across the remaining atria to assess test set performance.

[0218] Performance metrics

[0219] Quantitative assessment of the reconstructed imputation maps was performed using several metrics: MAE, Mean Square Error (MSE), Mean Relative Error (MRE) and Mean Absolute Percentage Error (MAPE). These metrics evaluate the fidelity of the reconstructed whole atria maps, Y, against the ground truth, X, for the mask, M, which represents the logical binary complement of the observation mask, M. The averaged performance metrics were computed via Equation 1, where £t,i was computed using each of our evaluation metrics. Metrics were computed for each model trained or fine-tuned across 5 different seeds. The average and standard deviation across these seeds were reported for each metric.

[0220] Additionally, the Phase Singularity (PS) True Positive Rate (TPR) was used to evaluate the accuracy of tracking PSs in the reconstructed phase maps compared to the ground truth. For each patient in the test set and each imputation model, PSs were manually labelled by two independent trained observers using a custom graphical user interface. Annotating each frame for each patient and model is labour-intensive, so only the central 70 frames (1 second) of each reconstructed phase map were annotated. Annotating PSs for each model seed is also infeasible, so the mean and standard deviation were computed from 1000 bootstrap samples. A PS is considered detected if its location in the reconstructed map falls within a specified tolerance of 0.1 seconds and a 4-hop neighbourhood in space compared to its location in the ground truth map.

[0221] Baseline modelsWe introduce additional baseline models for the imputation mapping task: 1) Mean, which performs imputation using the node-level average; 2) MF with rank = 10; 3) univariate Recurrent Neural Network (RNN), which performs imputation based solely on the node-level signals; and 4) univariate Bidirectional (Bi-)RNN. Mean and MF baseline models are employed solely on the test set due to their transductive nature. Both the univariate RNN and Bi-RNN models were trained using MAE loss function and followed identical hyperparameter settings and training-test protocols as FibMap. Unlike FibMap, these models did not require fine-tuning due to their inductive nature.

[0222] Imputation mapping from EnSite Precision HD Grid recordings

[0223] From our test cohort, three AF patients had both EnSite Precision HD Grid and AcQMap recordings collected non-contemporaneously before ablation. For these patients, AcQMap recordings were 20 seconds in duration, while EnSite Precision HD Grid recordings were significantly longer (14, 19, and 20 minutes). EnSite Precision HD Grid data consists of sequential contact mapping recordings from 16 electrodes arranged in a grid array, along with the roving 3D coordinates of each electrode within the atrium.

[0224] To ensure compatibility with FibMap, the EnSite Precision HD Grid recordings were pre- processed. Sparse electrogram recordings were first mapped to a uniform discretisation of the atrial surface using a nearest-neighbour approach with a 3 mm radius to interpolate the signals between electrodes. An observation mask identified active recording periods, after which signals were normalised using the maximum peak-to-peak voltage. The data was then resampled spatially to a resolution of 500 nodes using k-means clustering and resampled temporally to 70 Hz using a combination of low-pass filtering and downsampling. A final min-max normalisation ensured all signals fell within 0 and 1. From these processed measurements, imputation maps were generated using our fine-tuning procedure, whereby the observed patch reconstruction loss was monitored to perform early stopping.

[0225] We developed a sliding window cross-correlation framework to compare FibMap reconstructions against AcQMap 'ground truth' recordings. While temporal alignment was not possible between the non-contemporaneous recordings, spatial alignment was achieved between AcQMap and imputation map by centring the vertices of the geometries around the origin, applying rigid registration using the iterative closest point algorithm, and projecting data between geometries using a k=5 nearest-neighbours regression. Using sliding window lengths from 0.5 to 4.0seconds and a constant stride of 0.1 seconds, we computed the Pearson correlations between Hilbert phases of processed signals across all nodes and times within window pairs. This generated a cross-correlation matrix characterising the spatiotemporal similarity between recordings, which were flattened and plotted as distributions for analysis.

[0226] To validate that FibMap captured patient-specific dynamics, we performed three types of correlations: intra-patient comparisons between AcQMap and FibMap from the same patient; inter-patient comparisons between AcQMap and FibMap from different patients; and random baseline intra-patient comparisons between AcQMap and a spatiotemporally shuffled imputation map. For each patient, the 99th percentile of the intra, inter and shuffled distributions were plotted and statistical significance was assessed by computing the confidence intervals via bootstrapping (n = 1000 rounds of 10000 resamples).

[0227] Results

[0228] FibMap performs accurate whole atria imputation mapping for AF

[0229] Leveraging spatiotemporal message passing on a dynamical graph representation of the input, FibMap effectively propagates information from valid measurements across the atrial surface and time to accurately perform imputation mapping. Our solution personalises the reconstruction of AF dynamics through unique node and patient embedding parameters, akin to word embeddings in natural language processing; conversely, shared parameters are utilised across patients to capture common elements of the dynamics such as the physics of wave propagation. The input representation and architecture of FibMap are detailed in Figures 2A and 2B.

[0230] The dataset used comprises non-contact recordings from 51 patients with persistent AF, obtained during an AF ablation procedure using the AcQMap system before pulmonary vein isolation. Each recording samples approximately 3500 nodes across the entire atria at 3000 Hz for 5-20 seconds. Patients were treated between 2016 and 2023 at two centres in the United Kingdom: The Royal Brompton Hospital, London, and the John Radcliffe Hospital, Oxford. The cohort (mean age 64 ± 11 years, 69% male) had a mean BMI of 29 ± 5 kg / m2, with comorbidities including hypertension (39%), heart failure (33%), and diabetes mellitus (10%) (see Table 1). The procedure involved left atrial mapping, followed by pulmonary vein isolation, and in some cases further adjunctive linear ablations (anterior, posterior, septal) and cardioversion to restore sinus rhythm. The AcQMap system provides non-contact simultaneous unipolar voltage electrograms for the entireatria by inversely mapping non-contact measurements sampled from the chamber centre to the chamber surface, offering a ground truth of human AF dynamics with fidelity suitable for developing and validating FibMap. After resampling these signals spatially to ~500 nodes, temporally to 70 Hz, and normalising the electrograms, the dataset was stratified to ensure a spectrum of AF dynamics within training (70%), validation (10%), and test (20%) sets.

[0231] Continuous whole atria mapping with systems such as AcQMap are not routinely used in the clinic since they have not demonstrated efficacy. Instead, contact mapping catheters are routinely used to precisely measure electrical signals from the atria, with the limitation that they provide sparse measurements across the surface. To emulate routine clinical data collection within the invasive electrophysiology laboratory, a sequential contact mapping strategy was simulated from the whole atria non-contact recordings as a self-avoiding walk of the multipolar catheter (represented as a patch of observations) on the atrial surface; whereby the catheter surface area, dwell time (duration of recording at each location), and spatial overlap, could be controlled (see Figure 4A). During training, FibMap was optimised for imputation mapping through a whole atria reconstruction loss and a self-supervised learning approach, wherein various multipolar catheter paths were sampled, and parameters augmented (see Training section of Methods for more details). As a result, the pre-trained FibMap model, adept at reconstructing a spectrum of AF dynamics from sparse measurements, remains robust against variations in multipolar mapping.

[0232] This model is efficiently adapted to new patients through a fine-tuning transfer learning procedure, designed to enable accurate whole atria reconstruction from sequential contact mapping data. Our fine-tuning approach preserves essential knowledge for whole atria reconstruction acquired during training by fixing model parameters, while quickly personalising the model by optimising only the patientspecific parameters using an observed patch reconstruction loss (see Training section of Methods for more details). The fine-tuning procedure was configured on the validation set, whereby a strong correlation (Pearson's r=0.97, p<0.0001) between the observed patch and whole atria reconstruction loss curves was found (see Figure 3A). This indicates that our fine-tuning procedure enables accurate whole atria reconstruction and generalises effectively to new patients without overfitting to the signals in the observed patches.The performance of FibMap imputation mapping on new and unseen patients, through our fine- tuning procedure, was quantified on the patients in the test set. Testing involved simulating sequential contact mapping for test set patients with a catheter surface area of 10% of the atrium, a dwell time of 1 second, and no spatial overlap between successive patches (as shown in Figure 4A). FibMap was finetuned using the configuration found in validation, with the observed patch reconstruction loss monitored to perform early stopping. Test set fine-tuning took a total of 3 hours and 40 minutes, averaging just 22 minutes per patient. After fine-tuning, FibMap's performance was confirmed through various metrics against ground truth whole atrium signals. FibMap significantly outperformed baseline models in predicting whole atrium signals from simulated sequential contact mapping measurements. Figure 3B illustrates these performances, with the complete set of results shown in Table 3. Specifically, FibMap achieved an MAE of 0.0574 ± 0.0005, a 2.1x improvement compared to the best baseline imputation model, Matrix Factorisation (MF), which had an MAE of 0.1205 ± 0.0012. In Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE), FibMap scored 0.0069 ± 0.0001 and 16.7715 ± 0.4589, respectively, compared to MF's 0.0254 ± 0.0005 and 32.5598 ± 0.5609.

[0233] Table 3: Imputation results for 10% observed area, dwell time of 1 second, and no spatial overlap. Acronyms: Recurrent Neural Network (RNN), Bidirectional (Bi), Matrix Factorisation (MF), Mean Absolute Error (MAE), Mean Squared Error (MSE), Mean Relative Error (MRE), Mean Absolute Percentage Error (MAPE), Phase Singularity (PS) and True Positive Rate (TPR).

[0234] Model MAE MSE MRE MAPE PS TPR Mean 0.1734 ± 0.0507 ± 35.0833 ± 47.7258 ± 0.0126 ± 0.0005 0.0003 0.1043 0.3260 0.0035 Univariate 0.1393 ± 0.0298 ± 28.1724 ± 44.0633 ± 0.0369 ± RNN 0.0001 0.0000 0.0213 0.2098 0.0121 Univariate 0.1368 ± 0.0290 ± 27.6553 ± 42.8590 ± 0.0803 ± Bi-RNN 0.0001 0.0001 0.0251 0.1856 0.0309 MF 0.1205 ± 0.0254 ± 24.3715 ± 32.5598 ± 0.0552 ± 0.0012 0.0005 0.2434 0.5609 0.0207 FibMap 0.0574 ± 0.0069 ± 11.5868 ± 16.7715 ± 0.8924 ± 0.0005 0.0001 0.1098 0.4589 0.0342

[0235]

[0236] In addition, the performance of the imputation models was assessed by their ability to track the Phase Singularities (PS) present in the recordings, a characteristic of fibrillation dynamics. These points, where the phase of electrical activity is undefined, mark the tips of rotating spiral waves that could drive and maintain AF, representing potential ablation targets and providing crucial insights into the underlying fibrillation mechanisms. Two independent trained observers manually labelled the PSs in the central 1-second segment (70 frames) of each map from the different imputation models and patients. FibMap excelled in tracking PSs, achieving a True Positive Rate (TPR) of 0.8924 ± 0.0342, an 11.1x improvement upon the next closest competitor

[0237] TPR of 0.0803 ± 0.0309, as illustrated in Figure 3C and Table 3. These results demonstrate FibMap's capability to accurately reconstruct AF dynamics across space, time, and patients, significantly improving upon existing imputation methods.

[0238] Our empirical results confirm FibMap's capability to reconstruct the complex dynamics of AF accurately. Figure 4B illustrates FibMap's reconstructions of voltage electrograms at individual nodes compared to baseline methods (columns) across two test patients (rows), highlighting its ability to reconstruct the temporal dynamics of AF. While small variations in voltage amplitudes are observed between FibMap's reconstruction and the ground truth recordings, the true signal often resides within FibMap's predicted confidence intervals (90th - 10th quantiles, see FibMap optimisation section of Methods for more details). Furthermore, FibMap's reconstruction maintains phase coherence with the ground truth recordings, allowing for the accurate visualisation of phase maps across the atrium.

[0239] Figure 4A provides a snapshot of FibMap's phase maps derived from the predicted voltage electrograms, demonstrating its precise reconstruction of AF spatial dynamics for two different patients (rows). These maps reveal characteristic features of complex AF dynamics such as multiple wavefronts and rotational activity that were otherwise not visible in the observed patches. In comparison, our empirical findings in Figure 4B underscore the limitations of the baseline models. While MF could in principle be used here, it fails in capturing the complex spatiotemporal dynamics that characterise AF, as evidenced by reconstruction errors in both amplitude and phase in Figure 4B which result in poor phase map reconstruction in Figure 4A.FibMap reconstructs personalised AF dynamics from real clinical sequential contact mapping data

[0240] FibMap's ability to reconstruct whole atria dynamics from real sequential contact mapping data was validated retrospectively using recordings from the Advisor™ HD Grid Mapping catheter (16 electrodes arranged in a grid and evenly spaced 3mm apart, referred to as HD Grid) and the EnSite Precision mapping system (Abbott Laboratories, Lake County, Illinois, United States). This system is routinely used for mapping cardiac arrhythmia and guiding ablation procedures in the invasive electrophysiology laboratory. For three AF patients in the test set, both EnSite Precision contact mapping and non-contact AcQMap recordings of different durations (tens of minutes vs. seconds) were collected in sequence (non-contemporaneously) before ablation was performed. EnSite Precision HD Grid recordings were resampled to ~500 nodes at 70 Hz, electrograms were normalised, and imputation maps were created from the EnSite Precision HD Grid using our fine-tuning procedure (see Imputation mapping from EnSite Precision HD Grid recordings section of Methods for more details).

[0241] A comparative approach was developed to assess FibMap imputation maps from the EnSite Precision HD Grid against the whole atria "ground truth" provided by AcQMap. The non- contemporaneous nature of these recordings and their varying durations present analytical challenges. AF wavefront patterns vary beat-to-beat, preventing direct temporal alignment and direct comparison between the imputed maps from the EnSite Precision HD Grid versus the ground truth of the global AcQMap recordings. To overcome this, a sliding window analysis was implemented (Figure 5A) to cross-correlate segments of ground truth AcQMap and imputed FibMap phase signals, quantifying the overall dynamical similarity between these non-contemporaneous recordings without requiring exact temporal matching. This approach enables fair and meaningful comparison between the two data modalities (imputed maps vs. ground truth). The resulting cross-correlation distributions were analysed to determine whether FibMap captures patient-specific dynamics and distinguishes genuine electrophysiological patterns from arbitrary correlations expected by random chance.

[0242] To investigate patient specificity, distributions of cross-correlation were computed by comparing AcQMap recordings (ground truth) to FibMap (imputed maps) of the same (intra-) patient and different (inter-) patients using a sliding window ofduration 0.5 seconds. To compute the cross- correlation, recordings were projected between source and target surfaces using a nearest- neighbours approach (see Imputation mapping from EnSite Precision HD Grid recordings section of Methods for more details). Cross-correlation distributions were plotted as kernel density estimates in Figure 5Bi-iii for all three patients, revealing consistently wider tails for intra-patient correlations between AcQMap and FibMap, with 99th percentiles ranging from 0.19-0.22 compared to 0.16-0.17 for inter-patient correlations. The higher frequency of strong correlations within the same patient demonstrates FibMap's ability to capture patient-specific dynamics rather than generic patterns common across patients.

[0243] To assess whether these correlations were meaningful, we compared them against a random baseline created by spatiotemporally shuffling the FibMap imputation maps and then performing an intra-patient comparison with AcQMap. The significant separation between intra-patient and random distributions (99th percentiles shown by vertical dashed lines in Figure 5Bi-iii) confirms that the similarities between AcQMap and FibMap are not due to chance, validating FibMap's ability to impute AF dynamics. If this were due to chance, the observed 99th percentile for intra-patient correlations would lie at approximately 0.02 for each patient, an order of magnitude lower than the observed values of 0.19-0.22 (see Figure 5Bi-iii).

[0244] To test the robustness of these findings, sliding window durations were varied from 0.5 to 4.0 seconds (Figure 5Ci-iii). The 99th percentiles of the cross-correlation distributions were plotted against window duration, showing that while these values generally decreased with longer windows, the 99th percentiles for intra-patient correlations consistently remained higher than both inter-patient and shuffled comparisons. For each patient, confidence intervals were computed via bootstrap sampling (see Imputation mapping from EnSite Precision HD Grid recordings section of Methods for more details), revealing non-overlapping intervals between intra-patient, inter-patient, and shuffled distributions across all window durations, confirming the statistical significance of these differences. Representative phase maps (Figure 5D) visually confirm the agreement between FibMap imputations and AcQMap ground truth recordings to reveal complex AF dynamics such as multiple wavefronts and rotational activity, which were otherwise not visible by the EnSite Precision HD Grid which covers less than 10% of the atrial surface.These findings demonstrate that FibMap, through our fine-tuning procedure, can reconstruct personalised whole atria AF dynamics from real examples of multipolar catheter contact recordings collected in the invasive electrophysiology laboratory with fidelity comparable to AcQMap. This demonstrates the capacity of imputation mapping to integrate with and significantly enhance the capabilities of routinely used multipolar catheter mapping systems.

[0245] The sensitivity of FibMap to variations in multipolar mapping and AF organisation Returning to our analysis of simulated sequential contact mapping, a sensitivity analysis was conducted to assess FibMap's practical application by evaluating its reconstruction performance of whole atria dynamics across various catheter areas, dwell times, and levels of AF organisation. Spatial overlap was fixed at zero for this analysis. AF organisation was quantified by computing the average Shannon entropy across the ground truth electrograms of each patient, where lower values indicate more organised dynamics. Patients were then divided into two groups of low and high entropy based on the median average Shannon entropy value.

[0246] Figure 6A illustrates the MAE of the whole atria reconstruction for both groups across varying catheter areas and dwell times. The low entropy group (more organised forms of AF) consistently exhibited lower MAE values, with 0.065 on average compared to 0.071 of the high entropy group. Furthermore, both groups demonstrated improved reconstruction performance with increased catheter surface area and reduced dwell time, achieving a minimal MAE of 0.045 in the low entropy group with a 20% catheter surface area and a 0.5s dwell time. A shorter dwell time enables faster sampling of the whole atrium, allowing it to be covered multiple times within the finite duration of our recordings. For each combination of dwell time and catheter surface area depicted in Figure 6A, we ensure that each patient's atrium is covered at least once.

[0247] Combinations that do not meet this criterion are not shown. While these results could guide the optimal use of FibMap, we were unable to evaluate its performance for longer durations due to the limited length of our recordings. However, in practice, sampling duration is not restricted.

[0248] Performance was assessed based on the imputation horizon to reveal insights into FibMap's capabilities and their implications for practical application. The imputation horizon, defined as the spatiotemporal distance from the closest observed node and time point (measured in hops on a spatiotemporal graph), measures how far (inspace and time) FibMap can reliably predict beyond the observed data points.

[0249] Figure 6A demonstrates that the high entropy group experienced a sharper increase in MAE with increasing imputation horizon compared to the low entropy group, where MAE eventually plateaued, possibly due to FibMap's predictions losing phase coherence with the ground truth. Concurrently, Figure 6B demonstrates a corresponding increase in predicted confidence intervals with the imputation horizon. This underscores FibMap's capability to capture uncertainty in long-range predictions, emphasising the importance of uncertainty quantification in interpreting whole atria imputation maps. Such insights into regions of confidence and uncertainty could guide clinical assessments effectively.

[0250] Revealing structure in FibMap's state- and embedding-spaces

[0251] FibMap is designed as a non-linear state-space model, enabling the visualisation of hidden state dynamics at each node over time for patients. These states exhibit chaotic dynamics, characterised by diverging trajectories around fixed points in state space, effectively capturing the inherent chaos of AF. In Figure 7Ai, TSNE dimensionality reduction 30 has been employed to depict the state-space trajectory of a given node in a 3D space. Trajectories are colour-coded by converting the 3D coordinates to RGB values, highlighting orbital patterns across different regions of space with observable transitions.

[0252] To explore whether distinct regions of state space correspond to varied temporal dynamics, Figure 7Aii displays the imputed and ground truth electrograms coloured by their state-space positions. The absolute error between these electrograms is also shown to investigate how error varies depending on the state. Whilst the duration within each state and the absolute error varies, changes in the dynamics between states are subtle. To provide a different view, Figure 7Aiii shows a recurrence plot 31 derived from the state space trajectory, highlighting substantial structure underpinning the dynamics within and between states. For example, several parallel lines to the main diagonal are observed at later times, which is a characteristic of deterministic dynamics as trajectories repeatably progress through the same sequence of states.

[0253] These findings demonstrate that FibMap's formulation as a state-space model inherently captures important information about AF dynamics. Moreover, this approach suggests the potential application of non-linear dynamics analysis tools, such as recurrence plots, to uncover additional insights from FibMap. These insightscould aid in electrophenotyping patients, to categorise AF patients into broad subgroups, and potentially be useful for predicting the probability of benefit from ablation as well as guiding ablative strategy.

[0254] The learned patient and node embedding parameters in FibMap can also be analysed for structural insights. Figure 7B illustrates the node embeddings for each patient in the test set in a 2D space using TSNE dimensionality reduction 30, revealing significant structure. Figure 7Bi uniquely colours each node (marker) for each patient, revealing small clusters. Other nodes appear distributed across the space, indicating similarity between the nodes of different patients. To interpret these embeddings, Figures 7Bii and 7Biii show the voltage electrogram's dominant frequency and Shannon entropy for each node, respectively. The node embeddings capture this information in a complex manner, with dominant frequency generally lower at the bottom and Shannon entropy increasing toward the centre of the space. Interpreting the node embedding spaces could enable a systematic comparison of tissue properties across patients and anatomical locations, while an interpretation of the patient embeddings could identify individuals with similar global dynamics.

[0255] These findings suggest that, alongside FibMap's state spaces, the embedding parameters may hold potential for electrophenotyping patients. However, since follow-up information or spatial properties of the tissue were not available for our dataset, further research is needed to fully interpret and validate the information contained within the patient and node embeddings.

[0256] Discussion

[0257] The inability to map AF effectively in the invasive electrophysiology laboratory limits the application of tailored ablation strategies and potentially hinders curative treatment outcomes. To tackle this problem, we introduce imputation mapping to reconstruct AF dynamics from noncontinuous recordings collected through sequential contact mapping. Until now, these recordings could not be effectively stitched together due to AFs highly disorganised nature. Our solution, FibMap, employs a novel GRNN-based non-linear state-space model for personalised reconstruction of AF dynamics.

[0258] FibMap was trained and rigorously validated on a dataset of 51 persistent AF patients using continuous non-contact whole atria recordings from the AcQMapsystem as ground truth and simulated sequential contact mapping to replicate clinical data collection. Our results show that FibMap outperforms the baseline imputation models in whole atria reconstruction, achieving over 2x improvement in MAE and more than an order of magnitude improvement in PS detection rates with only 10% of the atrium observed per imputation. Empirical results demonstrate that FibMap accurately captures both amplitude and phase relations of voltage across the atria, reconstructing complex features of AF dynamics such as rotational activity and multiple wavefronts. Beyond simulated contact mapping, we crucially showed that FibMap successfully transfers to real clinical examples of sequential contact mapping collected with the multipolar HD Grid catheter to reconstruct AF dynamics with high fidelity to those captured by global AcQMap. This demonstrates FibMap's ability to stitch the clinical non-continuous AF recordings into a coherent imputation map. Further improvements in reconstruction quality are likely when the sampling collection / placement of the sensor catheter is guided prospectively (possibly by the results of our sensitivity analysis). Finally, we showed that the state and embedding spaces of FibMap can be visualised to reveal significant structure, suggesting potential for future electrophenotyping studies.

[0259] In summary, FibMap provides a comprehensive solution for imputation mapping by 1) capturing the rich dynamical variables of cardiac tissue for each patient, 2) effectively reconstructing whole chamber maps from sequential contact measurements, 3) producing uncertainty estimates to facilitate a clinical interpretation, 4) efficiently generalising to new patients for clinical use through our fine-tuning procedure, and 5) parameterising phenotypes (e.g., new AF phenotypes, but also other phenotypes for other conditions or diseases), offering the opportunity for downstream work to investigate its potential in personalising cardiac care (e.g., AF care).

[0260] While methods for whole atria mapping exist, such as the AcQMap system and non-invasive electrocardiographic imaging, these approaches have not demonstrated sufficient efficacy for routine clinical use, due in part to their non-contact nature. These non-contact methods suffer from having to calculate the electrograms on the heart surface rather than recording true contact electrograms. Imputation mapping offers a novel approach to obtaining whole atria maps from routinely collected sequential contact mapping data, efficiently integrating with existing mapping multipolar catheters (such as EnSite Precision HD Grid) to reconstruct AF dynamics in a real-time or post hoc manner.Non-contact data provides a realistic ground truth for human AF, which is essential for accurate model training and validation. Using these measurements, FibMap can learn an empirical model of AF dynamics (or other arrythmia, or the dynamics of a healthy heart), ensuring an accurate representation of human AF. In contrast, using simulated whole atria signals could bias the model towards simplified and debated mathematical models of fibrillation, arrythmia, tachycardia, or health hearts. While this approach proved effective for our proof-of-concept validation on AcQMap and EnSite Precision HD Grid recordings, if future work did identify limitations, FibMap could be trained on a mixture of real and simulated fibrillation data (or health heart data, or arrythmia data, e.g., tachycardia data) to enhance its robustness.

[0261] However, we emphasise that FibMap's current design incorporates a pre-trained model component that permits continual learning, potentially improving accuracy over time as it is applied to and fine-tuned on contact mapping recordings from new patients across the spectrum of AF. Imputation mapping, as demonstrated by FibMap, offers a promising integrative approach for reconstructing whole atria dynamics from routinely collected sparse sequential contact mapping data.

[0262] Refinements to FibMap's architecture could be considered to further improve imputation accuracy. For example, hierarchical architectures could be adopted to improve the imputation performance at longer horizons. By effectively bridging the gap between sequential contact mapping and continuous whole atria mapping systems, imputation mapping allows clinicians to see more with less. Its integration with existing mapping systems has the potential to transform our interpretation of complex AF dynamics, ultimately standing to improve the precision and effectiveness of AF ablation.

[0263] Referring to Figure 8, an electrode catheter system 1 comprises a controller 2 and an electrode catheter 3. The controller 2 comprises one or more processors 4, system memory 5, and one or more interfaces 6 which can allow a user to view recordings, or to pass them to an additional device (not shown). The electrode catheter 3 can record dynamical variable signals form a cardiac surface, for example, an atrial surface, or a ventricular surface. These recording can be sent to the controller 2 and, if required, be processed by the processor 4. The electrode catheter 3 may be a grid catheter electrode.The grid catheter may be a high-density mapping catheter. There may be a plurality of electrodes in the grid catheter which may be evenly, unevenly, regularly, or irregularly, spaced apart in a grid or a suitable non-grid arrangement. Possible gird arrangements may include a square or orthogonal grid, a rectilinear grid, a non-orthogonal grid, a triangular grid, a hexagonal grid, a curvilinear grid, a spiral grid, an irregular spaced grid. More than one grid type may be used for the grid catheter and / or for the measurements or simulations. For example, the grid catheter may include 16 electrodes in a 4 × 4 square or orthogonal grid. Additional electrodes outside of the grid arrangement may also be used.

[0264] Referring to Figure 9, an overview of how to train and implement the FibMap model is outlined. To train the model for constructing maps of cardiac dynamical variables, training data is received by a computer (step SI). The training data includes dynamical variables from a first region of a cardiac surface and, dynamical variables from a plurality of points which are located within a subregion of the first region. The first region may be the whole cardiac surface being analysed or may be a portion of that surface. These dynamical variables may be one or more of unipolar voltage, dipolar voltage, omnipolar voltage, dipole density, or phase measurements, for example, voltage electrograms. The dynamical variable, e.g., voltage, may be recorded as a function of time and position or location on the cardiac chamber. Optionally, clinically measured dynamical variables are also received by the computer and can augment or at least partially replace part of the training data (step S2). The cardiac surface may be an atrial surface, or a ventricular surface.

[0265] At least one dynamical variable may be measured or obtained using an invasive technique or procedure, or the at least one dynamical variable is simulated as if an invasive technique or procedure was being used. That is, an invasive or surgical procedure or technique may be required to measure or obtain at least one dynamical variable, or the simulation of the dynamical variable is a simulation of measuring or obtaining the dynamical variable using an invasive technique or procedure. Non-invasive procedures include electrocardiogram measurements where electrodes are places on the body surface (e.g., skin), whereas invasive procedures may include accessing the chambers of the heart directly and taking or simulating surface measurements from these surfaces.A graph of the dynamical variables of the atrial surface is generated from the training and / or clinical data (step S3). Intra-patient model parameters (embeddings) are then generated (step S4). One or more dynamical variables are then either received from either clinical measurement, or from the training data (step S5). The FibMap model (that is, the GRNN to process the dynamical variables of the atrial surface) is then trained by calculating a predicted dynamical variable at a point on the cardiac surface using the dynamical variables from a plurality of points on the cardiac surface within a subregion of the cardiac surface, then calculating a reconstruction error between the calculated predicted dynamical variable and a ground truth dynamical variable from the cardiac surface at the same point. The reconstruction error is then used to update the model (step S6).

[0266] If implementing an already trained model, a binary mask of the dynamical variables can be generated based on atrial surface measurements of the dynamical variables and the model (step S7).

[0267] Optionally, a spatio-temporal imputation model may be applied to the (simulated) binary mask (step S8). Parameters of the updated model can then be shared across different patients (step S9) allowing for further training and the optimisation of inter and intra- patient model parameters by minimising reconstruction error on the ground truth measurements (step S10).

[0268] During implementation of the model, it may be that the intra patient model parameters are optimised by minimising reconstruction error on the partial measurements (step S11). These guide measurements may then be provided to train the model further in steps S5 and S6. (step S12).

[0269] Referring to Figure 10, the method of training the model for constructing maps of cardiac dynamical variables may include receiving a training dataset comprising dynamical variables from a first region of a cardiac surface and dynamical variables from a plurality of points, the plurality of points located within a subregion of the first region (step S21).

[0270] The method further comprises calculating a predicted dynamical variable at a point on the cardiac surface using the dynamical variables from the plurality of points located within the subregion (step S22). Then, a reconstruction error is calculated by comparing the calculated predicted dynamical variable with the receiveddynamical variable from the cardiac surface at the same point (step S23). The calculated reconstruction error is used to update the model (step S24) and the trained model is stored (step S25).

[0271] In other words, ground truth measurements or simulations of dynamical variables for a first region of a cardiac surface area are received, a subset of these dynamical variables are selected within the first region of the cardiac surface and used to predict a dynamical variable at a selected point on the cardiac surface. The selected point may be within the first region or the subregion. The ground truth or simulated dynamical variable at the selected point is compared with the predicted dynamical variable and a reconstruction error is calculated. This reconstruction error is used to update the model.

[0272] The subregion may be continuous or comprise two or more discrete or separated regions. The subregion may include the plurality of points used to calculate the predicted dynamical variable.

[0273] The dynamical variables may be one or more of unipolar voltage, dipolar voltage, omnipolar voltage, dipole density, or phase measurements, for example, voltage electrograms. The dynamical variable, e.g., voltage, may be recorded as a function of time and position or location on the cardiac chamber.

[0274] The cardiac surface may be the atrial surface or the ventricular surface, but any suitable cardiac surface may be used. The first region of the cardiac surface may be all, substantially all, or the whole cardiac surface. The point on the cardiac surface where the dynamical variable is being predicted may be outside the subregion. The first region may be a first area, and the subregion may be a subarea. That is, they are regions or areas of the surface of a heart chamber, be that an atrial or ventricular chamber. Dynamical variables from the whole cardiac surface may be used as ground truth measurements to train the model.

[0275] The predicted dynamical variable may be a point-wise estimate, or may be a probabilistic estimate (distribution of possible values). Thus, the method may construct maps of predicted dynamical variables and their confidence (prediction uncertainty). The uncertainty may be helpful when interpreting the maps. The constructed maps may use or be based on the predicted dynamical variables.A map may refer to the visual representation showing how different dynamical variables change across the heart's (cardiac) surface and over time, for example, during fibrillation, or during arrhythmia, e.g., tachycardia, or during a normal / healthy heart performance. A map may aid with understanding and analysis of the complex dynamics of cardiac activity (e.g., arrythmia (fibrillation or tachycardia)) by displaying how these variables are distributed spatially and temporally. The model can be used to construct a map or other visualisation of the dynamical variables on the cardiac surface.

[0276] The method may have an iterative component, for example, the method may include iteratively using the updated model to calculate the predicted dynamical variable,

[0277] calculating an updated reconstruction error by comparing the calculated dynamical variable with the received dynamical variable; and using the updated reconstruction error to update the updated model.

[0278] The predicted dynamical variable may include or be associated with a prediction confidence value which indicated the level of confidence the learned model has about the predicted dynamical variable being a true representation of what would be a measured or simulated dynamical variable at the same point.

[0279] The dynamical variables from the first region of the cardiac surface may be obtained from one or more of: cardiac activity measured from direct contact with the cardiac surface, cardiac activity measured while not in direct contact with the cardiac surface; or simulated cardiac activity measurements directly or indirectly from the cardiac surface.

[0280] Cardiac activity measured from direct contact with the cardiac surface may be acquired using electrodes on the cardiac surface which can directly measure a dynamical variable.

[0281] Cardiac activity measured while not in direct contact with the cardiac surface may be acquired using and received from an imaging and mapping system which uses high-resolution 3D cardiac chamber reconstructions using ultrasound and cardiac electrical activity, e.g., the AcQMap system. The dynamical variables may be unipolar voltage electrograms. Simulated cardiac activity may be measurements simulated from physics theory of cardiac conduction, e.g. from the Fenton-Karmamodel. At least one of the dynamical variables from the whole cardiac surface may be directly measured from the cardiac surface using an electrode. If a directly measured dynamical variable is used, it may be measured at 70 Hz. The electrode may be a grid catheter electrode.

[0282] As described earlier, the model is a non-linear state-space and / or a spatio-temporal model for propagating information from the plurality of points located within the area of the cardiac surface to points outside of the area of the cardiac surface. The model may be a graph recurrent neural network (GRNN), for example, a gated GRNN. The model may be bidirectional. The model may be point-wise (e.g. GRNN) or probabilistic (e.g. denoising diffusion probabilistic model) to estimate the value and / or distribution of dynamical variables in space and time: to estimate a map of the variable and its uncertainty.

[0283] The plurality of points located within the subregion of the cardiac surface may be determined by sampling over at of least part of the cardiac surface. Such sampling may be, sequential sampling, random walk, etc. and may be over the whole atria surface. The random walk may be a self-avoiding random walk. The plurality of points located within the subregion of the cardiac surface may be representative of the electrode arrangement on a grid catheter. For example, the plurality of points located within an area of the cardiac surface may be in a regular gird or be evenly spaced along a first and / or a second axis.

[0284] The dynamical variables from the first region of the cardiac surface may include a dynamical variable which has been measured from a subject. The subject may be a human, for example a human patient undergoing treatment for cardiac (e.g., atrial) fibrillation. The dynamical variable measured from a subject may be acquired from an electrode catheter and may be used to train part of the model. For example, the dynamical variable measurement from a subject may be used to optimise node and subject-specific embedding parameters using an observed patch reconstruction loss while the remaining parameters of the model are fixed after training on the dynamical variables from the whole cardiac surface and the dynamical variables from a plurality of points, the plurality of points located within an area of the whole cardiac surface. That is, while all received dynamical variables may be used to train the global model relevant to all patients, dynamical variable measurements from a single subject can be used to train subject-specific parameters or embedding of the model, improving the model for each subject.In addition to subject-specific embeddings, other patient-specific parameters alongside subject-specific embeddings (e.g. age, height, weight, BMI, blood pressure, coronary artery disease data, heart failure data, and valvular heart disease data) and if the subject or patient was prescribed anti-arrhythmic drugs (e.g., yes / no and dosage) etc.).

[0285] The model may be further updated or refined by calculating an additional reconstruction error(s) by comparing the calculated dynamical variable with the measured dynamical variable and using the second reconstruction error to update the model.

[0286] The dynamical variables from the whole cardiac surface may be dynamical variables from discrete points on the cardiac surface. That is, at least one of the dynamical variables is from a node on the area of the cardiac surface.

[0287] The dynamical variables from the first region may be associated with a graph. The graph may be a connectivity graph. The graph may include spatial information, the spatial information may include proximity information. The spatial information may include the absolute and / or relative location of the of the dynamical variable on the cardiac surface.

[0288] The dynamical variables from the first region may include dynamical variables from a plurality of subjects. For example, the dynamical variables may be measured or recorded from a first subject and a second subject and measurements or recordings may be used to train the model.

[0289] The dynamical variables may span a time period. That is, the dynamical variables may be measured or recorded for a period of time, for example, less than 20 seconds, for example, between 1-20 seconds, or more preferably, 5-20 seconds. Measuring dynamical variables for longer can achieve better results, and therefore the dynamical variables may be measured for more than 20 seconds, for example between 20 and 30 seconds, or between 30 and 50 second. The dynamical variables may be measured for longer than 50 seconds to get more accurate measurements of the dynamical variables. The dynamical variables may be measured or recorded at a frequency of between 2000 and 6000 Hz, preferably between 3000-6000 Hz. Higher frequencies may generate higher resolutiondynamical variable data, and therefore higher frequencies may be used and preferred.

[0290] A dynamical variable at a point on a cardiac surface may be imputed by receiving a measurement of a dynamical variable at a first point on the cardiac surface, using the trained model and the received measurement to impute a dynamical variable at a second point on the cardiac surface. The second point may be, or be at a different location to, the first point. The dynamical variable may have a time component and / or a duration component. Further, the received measurement of a dynamical variable may be used to update subject-specific parameters of the model.

[0291] Additional Datasets

[0292] A fundamental challenge in developing imputation mapping methods is obtaining high-fidelity ground truth data that captures the complete spatiotemporal dynamics of cardiac fibrillation while remaining clinically relevant. Clinical contact mapping provides the sparse measurements that motivate this work, yet training and validating reconstruction algorithms requires dense, simultaneous observations across the entire chamber surface (a capability not available in routine clinical practice).

[0293] This challenge is addressed using three complementary datasets with increasing clinical relevance: 1) High-resolution ex vivo optical mapping of rat ventricular fibrillation (VF) provides gold-standard ground truth with simultaneous measurements across the ventricular surface, enabling rigorous validation of the imputation approach under controlled conditions; 2) Clinical non-contact mapping of human AF using the AcQMap system offers clinically relevant human AF data from actual patients, though with the acknowledged limitations of inverse-reconstructed signals and 3) Real contact mapping recordings from clinical procedures demonstrate practical translation to routine clinical workflows

[0035] . This multi-dataset approach establishes generalisability across species, arrhythmia types, and recording modalities.

[0294] High-resolution ex vivo optical mapping of rat VF

[0295] Optical mapping recordings of VF from 17 ex vivo Sprague-Dawley rat hearts with durations of 4 seconds were used for initial validation, yielding approximately 67,000 temporal frames simultaneously across 94,000 spatial nodes and totalling over 6.3 billion unique spatiotemporal data points. Optical mapping recordsfluorescence signals proportional to action potentials using a 128×80-pixel camera (~0.2 mm pixel spacing) at 1000 Hz, providing high-resolution recordings of chaotic fibrillation dynamics. While VF differs from AF in chamber and substrate, both exhibit complex spatiotemporal propagation patterns (multiple wavefronts, rotational activity, chaotic dynamics), making VF recordings valuable for validating our core methodology.

[0296] Raw optical signals underwent established preprocessing, spatial and temporal filtering, baseline drift removal, and min-max normalisation to emphasise propagation patterns and ensure equal training contribution across spatial locations. Signals were downsampled to 42×26-pixel resolution (~0.6 mm spacing) at 200 Hz to preserve fine-scale fibrillatory dynamics while maintaining computational tractability. For each heart, a graph was constructed by connecting each pixel (node) to its 8 nearest neighbours, representing ventricular surface connectivity.

[0297] Clinical non-contact mapping of human AF with AcQMap

[0298] Non-contact recordings from 51 persistent AF patients with durations of 5-20 seconds were obtained using the AcQMap system (Acutus Medical, Inc.) prior to ablation, yielding over 2.3 million temporal frames across 183,000 spatial nodes (433 billion unique spatiotemporal data points). The AcQMap system uses noncontact electrodes within the atrial cavity to sense intra -cavitary unipolar electrograms at 3000 Hz, from which dipole density measurements (charge density in Coulombs / cm) are inversely derived to reconstruct electrical activity across approximately 3500 nodes on the atrial surface simultaneously. This inverse reconstruction approach provides whole-atrial coverage without direct tissue contact, though with acknowledged spatial resolution limitations due to the ill-posed nature of the inverse problem and necessary regularisation. Despite these limitations and the system's limited clinical adoption, these recordings provide realistic human AF dynamics for assessing FibMap's feasibility on clinical data.

[0299] Raw dipole density signals were preprocessed: spatially resampled to 500 nodes via k-means clustering, temporally filtered and resampled to 200 Hz, and min-max normalised at the node level to emphasise propagation patterns. This resolution preserves clinically relevant AF dynamics (phase singularities, wavefront propagation) while ensuring computational feasibility. For each patient, a graph was constructed by triangulating the discretised atrial surface.Clinical sequential contact mapping of human AF with the HD Grid Sequential contact mapping was obtained from three patients using the an HD Grid catheter (16 electrodes, 4x4 grid, 3 mm spacing) and EnSite Precision system (Abbot) for proof-of-concept clinical translation assessment. Both HD Grid and AcQMap recordings were collected non-contemporaneously before ablation. HD Grid recordings (2035 Hz, 13-20 minutes) yielded 1.6-2.4 million temporal frames across 1100-4600 spatial points per patient.

[0300] Electrograms were preprocessed following a similar pipeline: spatial interpolation to the atrial surface, identification of active recording periods, voltage normalisation, spatial resampling to 500 nodes, and temporal resampling to 200 Hz. Graphs were constructed by triangulating the atrial surface.

[0301] Experimental setup

[0302] Dataset partitioning

[0303] Datasets (optical and AcQMap) were partitioned at two levels. First, hearts / patients were split into training (70%), validation (10%), and test (20%) subsets, stratified by Shannon entropy to ensure diverse fibrillation dynamics. Second, training and validation hearts had their time series further split sequentially into training (85%), validation (5%), and test (10%) temporal segments for model optimisation and selection, while held-out test hearts retained complete time series for fine-tuning and evaluation.

[0304] Model training and validation

[0305] Two separate FibMap models were trained: one for rat VF using optical mapping data and one for human AF using AcQMap data. To train FibMap on datasets with complete spatiotemporal ground truth while preparing it for sparse clinical data, sequential contact mapping was simulated. A multipolar catheter was represented as a spatial patch of observations that moves sequentially across the chamber surface, with configurable parameters including patch size (catheter surface area), dwell time (recording duration at each location), and spatial overlap between successive positions. For optical mapping, patches were defined as rectangular pixel regions traversing the ventricular surface. For the AcQMap dataset, patches were defined using k-means clustering with catheter movement simulated as a selfavoiding random walk to mimic realistic navigation patterns.Training employed a self-supervised learning approach with augmented catheter parameters (varying patch sizes, spatial overlaps, and dwell times) to reflect clinical variability and improve model robustness. During training, the model optimised a whole-surface reconstruction loss where all spatial locations and time points contributed regardless of whether they were observed or unobserved. This training objective forced the network to propagate information from observed patches across unobserved regions, learning universal fibrillation propagation patterns through shared parameters while capturing patient-specific characteristics through embedding parameters.

[0306] Deployment via fine-tuning

[0307] To simulate clinical deployment where only sparse contact measurements are available, the trained model was adapted to new test patients through fine-tuning. During fine-tuning, sequential contact mapping was simulated using fixed catheter parameters to ensure consistent evaluation: optical mapping used 9×9 pixel patches (~10% surface coverage) with 10-frame (50 ms) dwell times and nonoverlapping placement, while AcQMap used patches representing ~10% atrial surface area with 1-second dwell times and no spatial overlap.

[0308] Unlike training, fine-tuning optimised only patient-specific embedding parameters while keeping shared model parameters fixed. The optimisation used an observedpatch reconstruction loss that restricted the loss computation to only the spatiotemporal locations where measurements were available, enabling rapid patient-specific adaptation from sparse observations. Fine-tuning hyperparameters (learning rate, number of epochs) were determined on validation hearts by monitoring the relationship between patch-level fitting and whole-surface reconstruction accuracy. For both optical and AcQMap datasets, a strong correlation (Pearson's r ≥ 0.97, p < 0.05) was observed between observed-patch and wholesurface reconstruction losses, confirming that improvements in patch-level optimisation translated to accurate whole-surface reconstruction without overfitting. For final evaluation, the pre-trained FibMap model was then fine-tuned on held-out test hearts using the optimal hyperparameter configuration.

[0309] FibMap's performance on the optical mapping and AcQMap test sets was benchmarked against five baseline imputation methods and evaluated using reconstruction accuracy metrics (MAE, Mean Squared Error (MSE), Mean RelativeError (MRE)) and phase singularity (PS) detection F1-scores across multiple precision thresholds.

[0310] Clinical translation to HD Grid

[0311] The human AF model pre-trained on AcQMap data was transferred to real-world HD Grid contact mapping recordings from three test patients using the fine-tuning procedure described in earlier. Since HD Grid and AcQMap recordings were collected non-contemporaneously from the same patients (minutes apart) and AF exhibits beat-to-beat variability, direct temporal alignment was not feasible. Clinical translation was therefore assessed by quantifying the dynamical similarity between FibMap-imputed phase maps (reconstructed from sparse HD Grid observations) and AcQMap "ground truth" recordings using sliding-window cross-correlation analysis. Intra-patient correlations (same patient) were compared against inter-patient correlations (different patients) and spatiotemporally shuffled baselines to validate patient-specific pattern capture and distinguish genuine electrophysiological patterns from arbitrary correlations expected by chance.

[0312] Additional Results

[0313] Performance was evaluated through three validation studies: high-fidelity experimental validation using optical mapping of rat VF, clinical validation with noncontact mapping of human AF, and proof-of-concept translation to real-world contact mapping.

[0314] High-resolution ex vivo validation with optical mapping of rat VF

[0315] On the test set, FibMap accurately reconstructed complete ventricular activity from simulated sparse sequential contact mapping observations, with reconstruction losses plateauing rapidly during fine-tuning shows representative reconstructions for three test hearts. From 10% surface coverage, FibMap reconstructed full spatiotemporal activity, capturing multiple wavefronts and rotational activity invisible in partial observations. Reconstructed phase maps (Figure 11A) revealed the characteristic chaotic VF dynamics, with FibMap preserving both spatial propagation patterns and temporal dynamics across the entire chamber. FibMap's signal reconstructions at the pixel level demonstrated high fidelity to ground truth (Figure 11B), maintaining accurate amplitude and phase even in unobserved regions. Prediction intervals (shaded regions, 10th-90th quantiles) widened when phase coherence was lost (circled region in Figure 11B), demonstrating the model's ability to quantify reconstruction confidence.Referring to Figure 11, qualitative reconstruction of rat ventricular fibrillation from simulated sparse sequential contact mapping is shown. A) Representative phase map reconstructions for three test hearts (i-iii) showing partial observations (left, ~10% surface coverage), ground truth optical mapping (centre-left), FibMap reconstructions (centre-right), and next-best baseline Bi-RNN+FT (right). FibMap accurately reconstructs complete spatiotemporal dynamics from sparse observations, capturing complex fibrillation features including multiple wavefronts (yellow arrows) and rotational activity (green arrows) that remain invisible in partial observations. The next-best baseline fails to capture these dynamics, producing phase maps with substantial errors. Simulated catheter parameters: ~10% surface area, no spatial overlap, 50 ms dwell time. B) Pixel-level signal reconstructions at representative nodes for the three test hearts, showing FibMap predictions (red lines), ground truth (black lines), prediction intervals (pink shaded regions, 10th-90th quantiles), and observed time periods (blue shaded regions). FibMap maintains high signal fidelity in unobserved regions, with prediction intervals appropriately widening during regions of high uncertainty (circled for heart i), demonstrating effective uncertainty quantification. The next-best baseline (Bi-RNN+FT, right panels) shows poor reconstruction fidelity with incorrect amplitude and phase relationships during unobserved periods.

[0316] Quantitatively, FibMap significantly outperformed all baseline imputation methods (Table 4):

[0317] Table 4:

[0318] Quantitative reconstruction performance on rat VF optical mapping test set. Models evaluated using simulated sequential contact mapping (9×9 pixel patches, ~10% surface coverage, 50 ms dwell time, no spatial overlap). Reconstruction metrics: Mean Absolute Error (MAE), Mean Squared Error (MSE), and Mean Relative Error (MRE). Phase singularity (PS) detection evaluated using Fl-score at standard precision threshold (~1.8 mm, 45 ms). Models include transductive baselines (Trans.), pre-trained inductive baselines, and fine-tuned variants (FT). Best performing method in bold, second best underlined. Results reported as mean ± standard deviation across 5 random seeds.Model MAE 1 MSE 1 MRE (%) 1 PS F1-score Trans. FT

[0319] Mean 0.2141 ± 0.0717 ± 44.94 ± 0.004 ± 0.000

[0320] 0.0000 0.0000 0.00

[0321] MF 0.2164 ± 0.0733 ± 45.40 ± 0.351 ± 0.012

[0322] 0.0005 0.0002 0.10

[0323] RNN 0.2059 ± 0.0587 ± 43.16 ± 0.591 ± 0.000

[0324] 0.0000 0.0000 0.00

[0325] Bi-RNN 0.1874 ± 0.0503 ± 39.26 ± 0.645 ± 0.000

[0326] 0.0000 0.0000 0.00

[0327] TTS- 0.2022 ± 0.0589 ± 42.38 ± 0.613 ± 0.000 Transformer 0.0000 0.0000 0.00

[0328] RNN + FT 0.2051 ± 0.0586 ± 43.00 ± 0.605 ± 0.002

[0329] 0.0001 0.0000 0.01

[0330] Bi-RNN + FT 0.1766 ± 0.0476 ± 37.03 ± 0.609 ± 0.002

[0331] 0.0007 0.0003 0.13

[0332] TTS- 0.1992 ± 0.0626 ± 41.71 ± 0.573 ± 0.008 Transformer 0.0019 0.0013 0.39

[0333] + FT

[0334] FibMap 0.0828 ± 0.0142 ± 17.41 ± 0.795 ±

[0335] 0.0004 0.0002 0.07 0.046

[0336]

[0337] FibMap achieved an MAE of 0.0828 ± 0.0004, representing a 53% improvement over the next best baseline (Bi-RNN + FT: 0.1766 ± 0.0007). For PS detection at standard precision (~1.8 mm, 45 ms), FibMap achieved an F1-score of 0.795 ±0.046, a 23% improvement over the next-best method (Bi-RNN: 0.645 ± 0.000). Performance remained superior across all precision thresholds, from high (~0.6 mm, 15 ms: Fl = 0.461 ± 0.019) to lenient (~2.4 mm, 60 ms: Fl = 0.843 ± 0.053). In contrast, the next best baseline method (Bi-RNN + FT) failed to capture the complex spatiotemporal VF dynamics, producing phase maps with substantial errors (Figure 11A) and poor signal reconstruction (Figure 11B).

[0338] Human AF validation with non-contact data

[0339] Test set evaluation demonstrated accurate reconstruction of complete atrial activity from simulated sparse sequential observations, with rapid convergence during fine-tuning. Figure 12 shows representative reconstructions for three test patients. From 10% surface coverage via simulated catheter patches, FibMap reconstructed full atrial activity, capturing multiple wavefronts and rotational activity invisible in partial observations. Reconstructed phase maps (Figure 12A) revealed the characteristic chaotic dynamics of AF, with FibMap preserving both spatial propagation patterns and temporal dynamics across the entire chamber. FibMap's signal reconstructions at individual tissue regions demonstrated high fidelity to ground truth (Figure 12B), maintaining accurate amplitude and phase even in unobserved regions. Prediction intervals (shaded regions, 10th-90th quantiles) widened when amplitude variations occurred (circled region in Figure 12B), demonstrating the model's ability to quantify reconstruction confidence.

[0340] Referring to Figure 12, a qualitative reconstruction of human atrial fibrillation from simulated sparse sequential contact mapping is shown. A) Representative phase map reconstructions for three test patients (i-iii) showing partial observations (left, ~10% atrial surface coverage), ground truth AcQMap recordings (centre-left), FibMap reconstructions (centre-right), and next-best baseline Matrix Factorisation (MF, right). FibMap accurately reconstructs complete spatiotemporal AF dynamics from sparse observations, capturing complex fibrillation features including multiple wavefronts (yellow arrows) and rotational activity (green arrows) that remain invisible in partial observations. The next-best baseline fails to capture these dynamics, producing overly smooth phase maps that miss critical spatiotemporal features. Simulated catheter parameters: ~10% atrial surface area, no spatial overlap, 1 second dwell time. B) Node-level signal reconstructions at representative atrial locations for the three test patients, showing FibMap predictions (red lines), ground truth (black lines), prediction intervals (pink shaded regions, 10th-90th quantiles), and observed time periods (shaded blue regions). FibMap maintains highsignal fidelity in unobserved regions, with prediction intervals appropriately widening during amplitude variations (circled in patient i), demonstrating effective uncertainty quantification. The next-best baseline (MF, right panels) shows poor reconstruction fidelity with loss of temporal dynamics and phase relationships during unobserved periods.

[0341] Quantitatively, FibMap significantly outperformed all baseline imputation methods (Table 5).

[0342] Table 5: Quantitative reconstruction performance on human AF AcQMap test set. Models evaluated using simulated sequential contact mapping (patches covering ~10% atrial surface area, 1 s dwell time, no spatial overlap). Reconstruction metrics: Mean Absolute Error (MAE), Mean Squared Error (MSE), and Mean Relative Error (MRE). Phase singularity (PS) detection evaluated using Fl-score at standard precision threshold (~1.5 cm, 0.3 s). Models include transductive baselines (Trans.), pre-trained inductive baselines, and fine-tuned variants (FT). Best performing method in bold, second best underlined. Results reported as mean ± standard deviation across 5 random seeds.

[0343] Model MAE 1 MSE 1 MRE (%) 1 PS Fl f Mean 0.1851 ± 0.0569 ± 37.38 ± 0.11 0.000 ± 0.0006 0.0004 0.000

[0344] MF 0.1321 _ ± 0.0318 ± 26.68 ± 0.16 0.441 ± 0.0008 0.0004 0.100 RNN 0.1477 ± 0.0329 ± 29.83 ± 0.03 0.008 ± 0.0001 0.0000 0.007

[0345] Bi-RNN 0.1470 ± 0.0326 ± 29.69 ± 0.03 0.035 ± 0.0001 0.0000 0.018 TTS- 0.1473 ± 0.0328 ± 29.74 ± 0.03 0.074 ± Transformer 0.0001 0.0000 0.038 RNN + FT 0.1469 ± 0.0327 ± 29.68 ± 0.03 0.000 ± 0.0001 0.0000 0.000

[0346] Bi-RNN + FT 0.1464 ± 0.0325 ± 29.57 ± 0.05 0.004 ± 0.0002 0.0000 0.004

[0347]

[0348] TTS- 0.1469 ± 0.0330 ± 29.68 ± 0.05 0.032 ± Transformer 0.0002 0.0001 0.014 + FT

[0349] FibMap 0.0706 ± 0.0104 ± 14.24 ± 0.922 ±

[0350] 0.0007 0.0003 0.15 0.016

[0351]

[0352] FibMap achieved an MAE of 0.0706 ± 0.0007, representing a 47% improvement over the next best baseline (MF: 0.1321 ± 0.0008). For PS detection at standard precision (~1.5 cm, 0.3 s), FibMap achieved an Fl-score of 0.922 ± 0.016, a 109% improvement over the next-best method (MF: 0.441 ± 0.100). Performance remained superior across all precision thresholds, from high (~0.5 cm, 0.1 s: Fl = 0.487 ± 0.059) to lenient (~2.0 cm, 0.4 s: Fl = 0.977 ± 0.008) (Table S4). In contrast, the next best baseline method (MF) failed to capture the complex spatiotemporal AF dynamics, producing phase maps with substantial errors (Figure 12A) and poor signal reconstruction (Figure 12B).

[0353] Performance across mapping parameters and AF organisation

[0354] Sensitivity analysis evaluated performance across catheter parameters and AF organisation levels (quantified by Shannon entropy; patients divided at median into low / high entropy groups). Figure 6A shows reconstruction MAE across catheter areas (5-20% surface coverage) and dwell times (0.5-4.0 s) with no spatial overlap. The low entropy group consistently achieved lower MAE (0.0728 average) compared to high entropy (0.0740 average). Both groups demonstrated improved performance with increased catheter area and reduced dwell time, achieving minimal MAE of 0.066 (low entropy, 20% area, 0.5 s dwell). Shorter dwell times enabled faster atrial sampling, allowing multiple complete coverage cycles within recording durations. Combinations with incomplete atrial coverage within the recording duration (low area, high dwell time) are not shown.

[0355] Referring again to Figure 6, a sensitivity analysis of FibMap reconstruction performance is shown. A) Mean absolute error (MAE) as a function of catheter surface area and dwell time, stratified by AF organisation (low vs. high entropy). Cells not shown indicate incomplete atrial coverage within recording durations. B) MAE (left) and prediction interval width (Pl-Width, right) versus imputation horizon (spatiotemporal distance in graph hops from nearest observation). Shaded regions indicate the standard deviation across test patients.Performance was further assessed by imputation horizon, the spatiotemporal distance (in graph hops) from the nearest observed measurement. Figure 6B demonstrates that MAE increased with imputation horizon, with the high entropy group showing a sharper rise before plateauing, possibly reflecting loss of phase coherence at longer distances. Concurrently, prediction interval width (10th-90th quantiles) increased with imputation horizon (Figure 6B), with wider intervals indicating greater uncertainty at longer spatiotemporal distances. This uncertainty quantification is crucial for reliably interpreting whole-atrial imputation maps and making informed clinical assessments.

[0356] Clinical case study: Real-world contact mapping with HD Grid

[0357] The human AF model was transferred to HD Grid recordings from three patients. Phase signals were compared using sliding windows (0.5-4.0 s duration, 0.1 s stride), yielding 354,600-1,285,218 cross-correlation values per patient-pair at 0.5 s window duration.

[0358] Cross-correlation distributions for 0.5 s window duration revealed consistently higher intra-patient correlations (same patient; 99th percentiles: 0.16-0.17) versus inter-patient comparisons (different patients; 0.13-0.14) for patients i-ii, demonstrating successful patient-specific pattern capture. In contrast, patient iii showed identical 99th percentiles (0.13) for both intra- and inter-patient comparisons. These patterns remained consistent across all sliding window durations: intra-patient correlations consistently exceeded inter-patient correlations for patients i-ii, while for patient iii, inter-patient correlations were slightly higher. This lack of patient-specific discrimination in patient iii may reflect geometric registration uncertainty during this comparison, more disorganised dynamics, its shorter recording duration (13 vs. 18-20 minutes), or higher imputation error. Critically, all correlations (both intra- and inter-patient) substantially exceeded shuffled baselines (99th percentiles: ~0.01) by an order of magnitude across all three patients, confirming FibMap captured genuine AF dynamics rather than spurious correlations.

[0359] These findings show FibMap can reconstruct personalised whole-atrial AF dynamics from routine clinical contact mapping with fidelity comparable to AcQMap.Modifications

[0360] It will be appreciated that various modifications may be made to the embodiments hereinbefore described. Such modifications may involve equivalent and other features which are already known in the design and use of constructing maps of dynamical variables on a cardiac surface and which may be used instead of or in addition to features already described herein. Features of one embodiment may be replaced or supplemented by features of another embodiment.

[0361] Although claims have been formulated in this application to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel features or any novel combination of features disclosed herein either explicitly or implicitly or any generalization thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention. The applicants hereby give notice that new claims may be formulated to such features and / or combinations of such features during the prosecution of the present application or of any further application derived therefrom.

Claims

Claims1. A computer implemented method of training a model for constructing maps of cardiac dynamical variables, the method comprising:receiving a training dataset comprising:dynamical variables from a first region of a cardiac surface; dynamical variables from a plurality of points, the plurality of points located within a subregion of the first region;calculating a predicted dynamical variable at a point on the cardiac surface using the dynamical variables from the plurality of points located within the subregion;calculating a reconstruction error by comparing the calculated predicted dynamical variable with the received dynamical variable from the cardiac surface at the same point;using the reconstruction error to update the model; andstoring the trained model.

2. The computer implemented method of claim 1, further comprising:iteratively:using the updated model to calculate the predicted dynamical variable;calculating an updated reconstruction error by comparing the calculated dynamical variable with the received dynamical variable; and using the updated reconstruction error to update the updated model.

3. The computer implemented method of claim 1 or 2, wherein the dynamical variables from the first region of the cardiac surface are obtained from one or more of:cardiac activity measured from direct contact with the cardiac surface; cardiac activity measured while not in direct contact with the cardiac surface; orsimulated cardiac activity measurements directly or indirectly from the cardiac surface.

4. The computer implemented method of claim 3, wherein the dynamical variables from the whole cardiac surface are used as ground truth measurements to train the model.

5. The computer implemented method of any of claims 1 to 4, wherein at least one of the dynamical variables from the whole cardiac surface are unipolar voltage electrograms.

6. The computer implemented method of any of claims 1 to 5, wherein at least one of the dynamical variables from the whole cardiac surface are directly measured from the cardiac surface using an electrode.

7. The computer implemented method of any of claims 1 to 6, wherein the model is a non-linear state-space and / or a spatio-temporal model for propagating information from the plurality of points located within the area of the cardiac surface to points outside of the area of the cardiac surface.

8. The computer implemented method of any of claims 1 to 7, wherein the plurality of points located within the subregion of the cardiac surface are determined by sampling over at of least part of the cardiac surface.

9. The computer implemented method of any of claims 1 to 8, wherein the plurality of points located within the subregion of the cardiac surface are representative of the electrode arrangement on a grid catheter.

10. The computer implemented method of any of claims 1 to 9, wherein the cardiac surface is an atrial surface and / or a ventricular surface.

11. The computer implemented method of any of claims 1 to 10, wherein the dynamical variables from the first region of the cardiac surface comprise a dynamical variable which has been measured from a subject.

12. The computer implemented method of claim 11, wherein the dynamical variable measured from a subject is acquired from an electrode catheter.

13. The computer implemented method of claim 11 or 12, wherein the dynamical variable measured from a subject is used to train part of the model.

14. The computer implemented method of any of claims 11 to 13, further comprising:calculating a second reconstruction error by comparing the calculated dynamical variable with the measured dynamical variable; andusing the second reconstruction error to update the model.

15. The computer implemented method of any of claims 1 to 14 wherein at least one of the dynamical variables from the whole cardiac surface are dynamical variables from discrete points on the cardiac surface.

16. The computer implemented method of any of claims 1 to 15 wherein the dynamical variables from the first region are associated with a graph.

17. The computer implemented method of any of claims 1 to 16 wherein the dynamical variables from the first region comprise dynamical variables from a plurality of subjects.

18. The computer implemented method of any of claims 1 to 17 wherein the dynamical variables span a time period.

19. A computer implemented method of imputing a dynamical variable at a point on a cardiac surface, the method comprising:receiving a measurement of a dynamical variable at a first point on the cardiac surface;using the trained model of any one of claims 1 to 18 and the received measurement to impute a dynamical variable at a second point on the cardiac surface.

20. The computer implemented method of claim 19, wherein the dynamical variable has a time component and / or a duration component.

21. The computer implemented method of claim 19 or 20 wherein the received measurement of a dynamical variable is used to update subject-specific parameters of the model.

22. The computer implemented method of any of claims 19 to 21, further comprising:using the imputed dynamical variable to phenotype a or the subject.

23. The computer implemented method of any of claims 19 to 22, further comprising:using the imputed dynamical variable to diagnose and / or treat a condition or disease for a or the subject.

24. A system comprising:an electrode for measuring dynamical variables from a cardiac surface; and a processor for receiving the dynamical variables and processing received and / or measured dynamical variables from the electrode, using the trained model of any of claims 1 to 21.

25. The system of claim 24 further comprising:a controller comprising:the processor;system memory; andan interface.

26. A computing device performing the method steps of any of claims 1 to 23.

27. A computer readable medium having program instructions for performing the method of any of claims 1 to 23.

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