Fluid flow reconstruction

Abstract

Methods and devices to reconstruct a flow of a fluid are described. The disclosed embodiments include techniques to extract flow information from computed tomography (CT) data. Some disclosed embodiments use machine learning to obtain a reconstruction of the flow of the fluid. Some disclosed techniques relate to eliminating motion artifacts from the reconstruction. Among other applications, the disclosed technology can be used to estimate fluid flow through cardiovascular vessels to enable an evaluation of cardiac health.

Description

FLUID FLOW RECONSTRUCTIONCROSS-REFERENCE TO RELATED APPLICATION

[0001] This patent document claims priority to and benefits of U.S. Provisional Application 63 / 677,231 , entitled “FLUID FLOW RECONSTRUCTION,” and filed on July 30, 2024. The entire content of the above noted patent application is incorporated by reference as part of the disclosure of this patent document.TECHNICAL FIELD

[0002] The present patent document relates to methods, devices and systems for estimating fluid flow through cardiovascular vessels that can be used for evaluating cardiac health.BRIEF DESCRIPTION OF THE DRAWINGS

[0003] FIG. 1 A shows an example embodiment of an in-silico pipeline based on the disclosed technology.

[0004] FIG. 1 B shows example data obtained using the in-silico pipeline of FIG. 1 A.

[0005] FIG. 2A shows example data, obtained in a study performed in accordance with an embodiment of the disclosed technology, illustrating the effect of a computed tomography (CT) scanning process on ground truth computational fluid dynamics (CFD) data.

[0006] FIG. 2B shows example data, obtained in the study of FIG. 2A, illustrating the mean square error calculated from CFD simulated and CT scanned flow data at different gantry rotation speeds.

[0007] FIG. 3A shows example flow velocity profiles predicted by a PINN based on the disclosed technology.

[0008] FIG. 3B shows examples of velocity percentage error under different CT gantry rotation speeds and reconstruction frame rates as predicted by a PINN based on the disclosed technology.

[0009] FIG. 4 shows a diagram depicting differences between ImageFlow and an example embodiment of SinoFlow.

[0010] FIG. 5A shows an example visualization of an inlet and outlet of a vessel which was used in a study performed in accordance with disclosed techniques.

[0011] FIG. 5B shows example color plots obtained in a study performed in accordance with disclosed techniques.

[0012] FIG. 6A shows plots, obtained in a study performed in accordance with disclosed techniques, of example concentration and flow losses versus the number of steps elapsed in training for ImageFlow and SinoFlow.

[0013] FIG. 6B shows a comparison of example fluid speeds predicted by ImageFlow and SinoFlow in the study of FIG. 6A.

[0014] FIG. 7 shows a flowchart of an example method according to an embodiment of the disclosed technology.

[0015] FIG. 8 shows a flowchart of another example method according to an embodiment of the disclosed technology.DETAILED DESCRIPTION

[0016] Section headings are used in the present document only for ease of understanding and do not limit scope of the embodiments to the section in which they are described.

[0017] The disclosed technology relates to fluid flow reconstruction techniques.

[0018] In one aspect, a method for estimating a flow of a fluid through a conduit is disclosed. The method comprises: obtaining computed tomography (CT) data representing the flow of the fluid through the conduit at multiple times, wherein the fluid comprises a contrast agent, wherein the CT data comprises timing data representing evolution of a concentration of the contrast agent within the conduit at the multiple times; receiving, by a machine learning (ML) engine as input, spatiotemporal coordinates associated with the CT data, wherein each of the spatiotemporal coordinates comprises a time coordinate associated with a respective time in the timing data and spatial coordinates associated with a location of the fluid within the conduit at the respective time, wherein the ML engine is trained by the CT data; obtaining, as output by the MLengine and for each of the spatiotemporal coordinates, a set of initial values, wherein each of the initial values represents a property of the fluid, the contrast agent, or the flow; and performing by the ML engine multiple iterations on the set of initial values to obtain a refined set of values that enables the property to be quantitatively estimated at the multiple times and at multiple locations within the conduit

[0019] In another aspect, a method for reconstructing a flow of a fluid through a conduit is disclosed. The method comprises: obtaining time-series data associated with the flow of the fluid through the conduit; processing a set of spatiotemporal coordinates representing the time-series data using an analytical model; obtaining, based on results of the processing, a dataset that enables quantification of one or more properties associated with the flow of the fluid through the conduit at multiple times and at multiple locations; and using the dataset to obtain a reconstruction of the flow of the fluid through the conduit.

[0020] In yet another aspect, the present patent document discloses a device, comprising a processor and a memory including instructions stored thereon, wherein the instructions upon execution by the processor cause the processor to perform any of the methods recited in this document.

[0021] Blood flow is routinely measured using echocardiography and magnetic resonance imaging (MRI). However, in the existing state of the art, there are no techniques to extract flow information from computed tomography (CT) data. The present patent document discloses techniques which use a physics-informed approach to estimate flow fields from CT data.

[0022] One aspect of the present patent disclosure relates to X-ray computed tomography imaging.

[0023] X-ray CT imaging is widely used clinically to evaluate cardiovascular anatomy and function. CT can provide time-resolved volumetric assessment of the patient's heart and blood vessels. The combination of fast, volumetric high-resolution acquisition and the ability to evaluate patients with implanted metal devices makes X- ray imaging a promising imaging technique to evaluate blood flow irregularities.

[0024] However, a CT-based quantitative approach for blood flow measurement (similar to Doppler echocardiography or phase contrast encoding of MRI signals) is notavailable. Instead, flow estimation relies on building computational fluid dynamics (CFD) models in patient-specific anatomies. However, the results of CFD simulations depend on user-defined parameters such as boundary conditions and model assumptions. For example, a Y-shaped vessel will have a flow distribution which depends on the downstream vascular resistance; a parameter set by the user in the CFD model which cannot be directly measured from CT. Therefore, the potential for X- ray based methods to quantitatively evaluate blood flow fields over space and time remains underutilized.

[0025] Recently, a Physics-Informed Neural Networks (PINNs) framework was introduced to estimate fluid flow and pressure fields from images of spatiotemporally evolving contrast. It does so by penalizing deviations from the observed contrast movie (Xoata) as well as adherence to the Navier-Stoke equations (£FIOW) via loss functions shown below:where n is the spatiotemporal coordinate (x, y, z, t), Re is the Reynolds number, Pe is the Peclet number and p is a parameter that specifies the level of regularization, c, u and p are estimates of contrast concentration, flow velocity and pressure and c are the ground truth contrast concentration. £;,L1penalizes the discrepancy between measured and predicted contrast evolution, c (x, y, z, t) and c (x, y, z, t). £HOWis a combination of Navier- Stokes and Advection-diffusion Transport equations. The total loss is the sum of the two equations weighted by p and the equations are weighted equally in this study (^=1). Automated differentiation and gradient descent enable minimization of this loss function.

[0026] However, the extent to which this PINN framework can be used to estimate flow from CT images is unknown. Specifically, CT images suffer artifacts due to having a finite temporal resolution (determined by the CT gantry rotation speed) and a limited frame rate. The impact of these limitations on the accuracy of flow estimated using this PINN has not been assessed.

[0027] Contrast-enhanced computed tomography (CT) is a fast and robust imaging modality which acquires 3D high-resolution spatial acquisitions over time. Currently, estimation of 4D flow from CT relies on using anatomical segmentations to prescribe patient-specific boundary conditions for computational fluid dynamics (CFD) simulations. Unfortunately, CFD simulations can be highly sensitive to modeling choices and boundary conditions. Physics-Informed Neural Networks (PINNs) can recover 4D flow fields from movies visualizing the dynamics of a contrast agent, are less sensitive than CFD to model parameters, and do not require boundary conditions. This could enable estimation of blood flow directly from 4D CT contrast dynamics, but it remains unknown how CT data acquisition and reconstruction parameters affect PINN flow estimation.

[0028] An example embodiment of the disclosed technology relates to an in-silico pipeline to assess the performance of the Neural Network-based flow estimation in CT.

[0029] Another aspect of the present patent disclosure relates to fluid flow estimation from sinograms using a PINN.

[0030] Computed Tomography (CT) is clinically used to evaluate cardiovascular vessels' anatomy and size. CT has high spatial resolution and the ability to obtain volumetric data which makes it an appropriate choice for this task. Moreover, it is quite robust and can be done across a range of patient conditions. In terms of cardiovascular diseases, measuring accurate flow information is of great importance. However, this information is not typically obtained from CT images. This is because there does not exist a quantitative analysis tool to evaluate flow directly from images. As a result, flow estimation using CT relies on modeling approaches such as computational fluid dynamics (CFD). However, the results obtained using CFD can be sensitive to modeling choices (e.g., blood rheology) and boundary conditions (e.g., upstream / downstream vascular impedances).

[0031] Physics-Informed Neural Networks (PINNs) can reconstruct flow fields from sequences of images depicting the dynamics of transported scalars like CT contrast agents. However, the potential of PINNs for CT imaging remains underexplored. One challenge associated with this reconstruction is that the scalar field changes during the interval of time involved in acquiring each CT image. Thus, an accurate flow reconstruction requires disentangling the fluid motion within each frame from the motion between different frames. It has been shown elsewhere that these flow motion artifacts limit the capability of PINNs to evaluate flows imaged with CT.

[0032] Blood flow in heart vessels and chambers is an important indicator of cardiac health. Imaging modalities such as echocardiography and magnetic resonance imaging (MRI) are clinically used to measure flow since fluid velocity can be encoded in the imaging signal. However, no equivalent modalities exist to assess flow in vessels directly using CT. As a result, clinical evaluation of CT images indirectly assess flow by evaluating changes in the size of vessels, looking to detect changes in vessel caliber or obstructions, or evaluation downstream consequences (lack of iodine enhancement in the parenchymal tissue).

[0033] CT has volumetric spatial coverage and high spatial resolution. Therefore, a method to evaluate flow using CT could have significant impacts. However, a key limitation of CT in the setting of imaging cardiovascular flow is the presence of motion artifacts which can arise due to voluntary and involuntary movements.

[0034] Contemporary work on flow field reconstruction makes use of Physics Informed Neural Networks (PINNs). In one approach (referred to hereinafter as “ImageFlow”), movies of the flowing concentration field are used as the supervision to train a neural network that predicts the flow field. Although this approach has shown promise to infer flow metrics associated with adverse events (e.g., atrial blood stasis and stroke), its application to full flow reconstruction from CT imaging critically depends on image reconstruction accuracy. In particular, the quality of ImageFlow is limited when the flow significantly deforms the contrast agent over a timescale comparable to the interval required to acquire an image.

[0035] Another example embodiment of the disclosed technology relates to SinoFlow, a novel PINN that incorporates fluid motion into the image rendering, thus accurately reconstructing flow velocities and eliminating motion artifacts. In SinoFlow,the acquired sinogram data is used to learn an implicit representation of the contrast evolution movie and its CT acquisition process. To this end, SinoFlow optimizes losses from equations modeling contrast transport, fluid mass conservation, and fluid momentum balance, to learn the flow field in vessels. SinoFlow is trained using the raw sinogram data instead of FBP reconstructed data, leading to more precise contrast and flow field reconstructions. In some embodiments of SinoFlow, SinoFlow includes a model of the scalar transport during CT image acquisition to bypass image reconstruction and use the raw sinogram data directly for flow prediction.

[0036] FIG. 1 A shows an in-silico pipeline according to an embodiment of the disclosed technology. The in-silico pipeline was used in an example study to assess the performance of a Neural Network-based flow estimation in CT. FIG. 1 B shows example data that was obtained using the in-silico pipeline of FIG. 1 A in the example study.

[0037] In the study, we used CFD to simulate contrast passing through a 2D Y- shaped vessel with pulsatile flow. Then, we simulated CT scanning with different gantry rotation speeds (2-20 Hz) and used filtered backprojection with different number of frames for image reconstruction. The resulting time series of 2D images were used as inputs to train a PINN constrained by the equations of fluid motion and contrast transport. By comparing the flow fields recovered by the PINN to the ground truth CFD data, we evaluated how artifacts in the simulated image acquisition process and changes in frame rate impacted the accuracy of flow reconstruction. We observed that a PINN's ability to estimate flow velocity increases with CT gantry rotation speed and with frame rate used to reconstruct contrast CT images.CFD Simulation

[0038] A 2D Y-shaped vessel of 1 cm in diameter and 7 cm in length was designed and used for pulsatile flow simulation (1 cycle per second, mimicking a heart rate of 60 beats per minute with average forward flow of 20 cm / s) using CFD. Contrast injections were applied at the inlet and the concentration (normalized from 0 - 100 %) across the whole vessel is shown in FIG. 1 A. Laminar flow was simulated with pulsatile contrast injection and flow velocity shown in FIG. 1 B. This results in movies of contrast evolving over space and time CCFD(X, y, z, t) and velocity fields on x and y direction, [UCFD(X, y, z, t), VCFD(X, y, Z, r)].

[0039] FIG. 1 A shows the three data processing steps and corresponding sample contrast / velocity fields at time frame 50. FIG. 1 B shows the normalized (from 0 to 1 ) pulsatile flow velocity and contrast concentration value as a function of frame numbers at the vessel inlet.CT Scanning

[0040] The CT scanning process was simulated in Python. The movie of contrast evolution was scanned with a user-defined gantry rotation speed. We simulated imaging of CCFD(X, y, z, t) at 2, 4, 10 and 20 Hz gantry rotation speed. These values were chosen to mimic a slow rotation of a current scanner CT, high speed CT, dual-source CT scanning speed and evaluate the value of a next generation CT. This process generates CT scanned movies of the contrast cCT(x, y, z, t) at different gantry rotation speeds.

[0041] FIGS. 2A-2B show the effect of CT scanning process on ground truth CFD data. Specifically, FIG. 2A shows 2, 4, 10 and 20 Hz CT scanned contrast flow and their absolute difference from ground truth. FIG. 2B shows the mean square error calculated from CFD simulated and CT scanned flow data at different gantry rotation speed.

[0042] Each data point in FIG. 2A is the mean percent error averaged over all time frames and the shaded areas include one standard deviation up and below the means. As the gantry rotation speed decreases, there are more motion artifacts in the images. The images obtained with gantry speeds of 2 and 4 Hz exhibit noticeable motion artifacts, significantly compromising data fidelity and potentially transmitting these distortions to the final flow field estimation.

[0043] Reconstruction was performed via view-sharing with frame rates of 40, 20 and 10 frames per second to investigate the impact of frame rate on PINN-derived flow accuracy.Physics Informed Neural Network Flow Estimation

[0044] A neural network was used to estimate flow from CT scanned flow data CCT(X, y, z, t) and to generate predicted flow velocity fields [u(x, y, z, t), v(x, y, z, t)J. CFD simulated and PINN predicted U, V velocity fields are shown in FIGS. 1 A-1 B.

[0045] This pipeline facilitates a direct comparison between the flow velocity fields produced by CFD and those estimated by the neural network. CFD flow simulationconducted in a Y-shaped vessel serves as the ground truth data in two experiments, Experiment 1 and 2. PINN prediction using CT scanned movies generate flow velocity fields [u(x, y, z, t), v(x, y, z, r)]. The flow velocity was assessed at three distinct checkpoints: one at the inlet and two at each of the outlets. The location of the three checkpoints and sample flow velocity profiles predicted by PINN are shown in FIGS. 3A-3B. Specifically, FIGS. 3A-3B show PINN predicted flow velocity field and percentage error from ground truth. FIG. 3A shows sample flow velocity profiles predicted by PINN at the three checkpoints of the Y-shaped vessel. FIG. 3B shows PINN predicted velocity percentage error under different CT gantry rotation speed and reconstruction frame rates. Flow accuracy was assessed using the mean value of the predicted velocity at the checkpoints and the percentage error (PE) with respect the ground truth velocity:PE = (v -v) / v where V is PINN predicted mean velocity at a checkpoint, calculated from [tifx, y, z, t), v(x, y, z„ ] and V is ground truth mean velocity from CFD at the same checkpoint calculated from [UCFD(X, y, z, t), VCFD(X, y, z, r ]. Percentage errors exceeding the threshold of 10% were regarded as inaccurate predictions by PINN.

[0046] In Experiment 2, the effect of varying the frame rate of the contrast evolution movie was evaluated. This corresponds to the information richness and is determined by the reconstruction rate of the CT-scanned flow data. The experiment conducted in Experiment 1 is replicated at varying CT reconstruction frame rates, including 40, 20, and 10 frames per second (FPS), and the PINN predicted velocity PE at three checkpoints under different frame rates is assessed. Calculated percentage errors exceeding the threshold of 10% are regarded as inaccurate predictions by PINN.Example Results

[0047] CT scanning and reconstruction result in images CCT that differ from the ground truth contrast movies, CCFD. FIG. 2 shows the impact of 2, 4, 10 and 20 Hz gantry rotations speed on the CT scanned data CCT and the mean squared error (MSE) between ccr and C FD- The MSE is low for CT scanning at 10 and 20 Hz. However, when the gantry rotation speed drops below 10 Hz, the MSE increases much faster.

[0048] The errors in ccrdue to the CT imaging process lead to errors in PINN flow field prediction. The percentage error at three checkpoints is reported in FIG. 3A. Percentage error below 10% was achieved by the PINN at all three checkpoints when the CT gantry rotation was 10 or 20 Hz. However, accuracy declined at slower gantry rotation speed. For 4 Hz, the percentage errors exceeded 20% (PE in the inlet, outlet 1 , and outlet 2: 25.5%, 22.9%, and 24.1 %). For 2Hz, values surpassed 40% (PE in the inlet, outlet 1 , and outlet 2: 42.8%, 53.1 %, and 61 .5%).

[0049] The perfect error seen in flow estimates agrees with the error in CCT as measured by MSE. Notably, the error in PI NN's predictions escalates as the CT gantry rotation speed decreases, resulting in flow velocity percentage errors beyond the acceptable 10% threshold for 4 and 2 Hz CT scans.

[0050] The accuracy of PINN flow prediction also varied based on the reconstruction frame rate. The velocity percent error at three distinct checkpoints are presented in FIG. 3B. For 10 and 20 Hz gantry rotation, imaging with 20 or 40 FPS achieved <10% error. However, if the frame rate dropped to 10 FPS, then the error increased significantly (-80%). For 2 and 4 Hz gantry rotation, reduction in the reconstructed frame rate led to stepwise losses in performance.

[0051] In addition to GRS and frame rate, other factors likely influence the accuracy of PINN flow that were not accounted for in this study. For example, the size of the vessel, the complexity of the flow pattern, and the shape and duration of the contrast bolus could all be optimized to improve PINN-based flow estimation.

[0052] Results of the example study demonstrate that PINNs based on the disclosed technology offer a powerful alternative method for estimating blood flow velocity fields from 4D CT scans.

[0053] Another example embodiment of the disclosed technology, as previously discussd, relates to SinoFlow, a PINN that incorporates fluid motion into image rendering to accurately reconstruct flow velocities and eliminate motion artifacts.

[0054] In the description that follows, a study comparing an existing technology (ImageFlow) to an example embodiment of SinoFlow is disclosed.

[0055] For both ImageFlow and SinoFlow, a multi-layer perceptron network was used to generate an implicit representation of the concentration field in the contrastevolution movie as well as to learn velocity and pressure fields by optimizing over partial differential equations modeling the contrast transport, fluid mass conservation, fluid momentum balance (i.e., the Navier-Stokes equations). FIG. 4 shows differences between the initial and proposed approaches (ImageFlow, left and SinoFlow, right). In both cases, the same neural network (NN) is used to predict concentration and flow field movies. However, as will be explained in further detail below, SinoFlow uses sinogram for supervision, while ImageFlow uses FBP concentration values for supervision. The input to the network is of the form (t, x, y) where t represents the time elapsed in contrast evolution movie, and x, y are the spatial locations of a point in space. The network outputs a quadruplet of values (c, u, v, p) which represent the concentration, magnitude of velocity along x direction, magnitude of velocity along y direction and the pressure value at the specified spatiotemporal position.

[0056] For SinoFlow, the sinogram of the contrast evolution movie was used for supervision instead of the artifact-prone, reconstructed concentration field, with the model jointly optimizing over the mean squared error of sinogram and the flow model equations losses.Network Architecture

[0057] A Multi Layer Perceptron network with 10 hidden layers and 200 neurons in each layer was used for both approaches. For the activation function, we use the Sigmoid Linear Unit (SiLU). This model was implemented in Python using the PyTorch library.Loss Function

[0058] The loss function is a combination of loss over sinogram and physics-based terms. Mathematically,where Ai and / .2are hyperparameters. In our experiments, we set 2 = — , where n„ isthe number of spatial points used for calculating sinogram value at a particular location, and / .2 = 1. In our experiments npwas equal to 1600. These values were experimentally tuned to ensure that both sinogram and flow information are given adequate weight in model supervision.

[0059] Mathematically,^4 =llx+ Vy where [x(l, 0), y(l, 0)] represents the projection ray for gantry angle 0, which varies along time as d0+ cot, with co being the gantry rotation speed. In the flow equations, Re is the Reynolds number, which indicates the ratio of inertial forces vs. viscous forces. In this work, we used a fixed value Re = 900 to match our ground-truth CFD simulations, although this parameter is also trainable. This Reynolds number is representative of mid-size arteries like the coronary or cerebral arteries.Data Generation and Training

[0060] Flow was simulated for a 2D Y-shaped vessel with pulsatile flow (with a simulated heartrate of 60 bpm). The vessel was 1 cm in diameter and 7 cm in length. Contrast was injected sinusoidally into the vessel to generate a gradient of contrast. The Y-shaped vessel can be seen in FIG. 5A with the location of inlet and outlet measurements shown using vertical lines. FIG. 5B shows visualizations of the concentration field in ImageFlow and SinoFlow (top) and the error with respect to ground truth (bottom).

[0061] We simulated CT imaging by creating a sinogram using a parallel beam geometry and gantry rotation speed of 2Hz.

[0062] SinoFlow was trained on the generated data for 600k iterations. In each iteration we sampled 256 locations on the sinogram. Corresponding to each location, a set of 1600 spatiotemporal points, i.e., ( y), were generated, such that the summation of concentration across these points represents the sinogram value.

[0063] The model was trained using the Adam optimizer with a learning rate of 0.001 . The training was done using an Nvidia RTX 3090 GPU, and it took approximately 48 hours to complete. Since SinoFlow and ImageFlow use the same underlying architecture, the per iteration training time of both approaches is similar. However, SinoFlow takes significantly more time for convergence.

[0064] This is expected, since SinoFlow relies on indirect supervision and significantly smaller training data (i.e., line integral of concentration values) whereas ImageFlow makes use of direct supervision (i.e., full concentration value images).Data Sampling

[0065] As shown in FIG. 5B, most of the image comprises zeros. Therefore, if the whole domain was sampled uniformly, most of the components of the line integral would have zero concentration and flow. This would lead to highly inefficient training.

[0066] To correct this situation, we filtered the input to the network, to ensure that only the points that fall inside the vessel are used for model training. This improved the training.Example Experiments and Results

[0067] We compared ImageFlow and SinoFlow at three different levels. First, we evaluated differences during training in terms of losses. Second, we compared the concentration fields relative to the ground truth. Third, we evaluated differences in the resulting flow estimates at the inlet and outlet locations. Our overall hypothesis is that SinoFlow will improve flow estimation accuracy at the 3 locations of interest (relative to ImageFlow) by creating a better estimate of the concentration field which in turn, leads to a better estimate of the flow fields.Experiment 1: Comparison of Training

[0068] FIG. 6A shows loss plots obtained while training SinoFlow and ImageFlow. More specifically, FIG. 6A shows a plot of concentration and flow loss terms over thenumber of steps elapsed in training for ImageFlow and SinoFlow. ImageFlow is extremely quick in achieving convergence on all losses. In less than 100k iterations, the values of the training losses converges.

[0069] The training plot for SinoFlow shows that the model begins with a low error in the flow field. Presumably, the network starts by predicting a zero flow field which is incorrect but consistent with the Navier-Stokes terms. After approximately 150k iterations, the flow errors increase and then start to decrease again. Our interpretation is that when the model begins training, it has a large error in terms of concentration. Reducing the concentration error introduces errors in the flow field in terms of deviations from Navier-Stokes terms. However, once the concentration error decreases, then the network aims to lower its loss by improving its estimate of the flow errors.

[0070] The delayed learning of SinoFlow is justified, since the supervision using sinogram is an indirect supervision, compared to ImageFlow, where the model has a simpler objective function to match a given concentration field.Experiment 2: Comparison of Concentration Images Generated with SinoFlow and ImageFlow

[0071] ImageFlow aims to learn or represent the concentration field obtained usingFiltered Back Projection (FBP). However, in SinoFlow, the sinogram is used directly as the supervision, and the optimization generates a prediction of the concentration field along with the flow fields.

[0072] FIG. 5B shows a visual comparison of the concentration field predicted by ImageFlow and SinoFlow. SinoFlow is able to learn a much better representation of the concentration field than ImageFlow.Experiment 3: Impact of Reconstruction Accuracy on Flow Field

[0073] The flow fields generated by SinoFlow and ImageFlow were evaluated at three locations in the vessel: the inlet, the outlet 1 and the outlet 2. FIG. 6B shows a comparison of fluid speeds predicted by SinoFlow and ImageFlow over time. SinoFlow performs considerably better than ImageFlow at the outlets. At the inlet, SinoFlow performs better than ImageFlow for the most part, except for a small section towards the end.

[0074] These results indicate that SinoFlow can be useful in a variety of applications, e.g., in scenarios where CT scanning is done using low frequency.

[0075] Among other features and benefits, the disclosed embodiments are robust to noise. For example, the present patent document discloses techniques to remove one or more artifacts from a dataset. The one or more artifacts can include motion- induced artifacts or artifacts arising from noise such as noise induced by equipment used to acquire the dataset.

[0076] Some disclosed embodiments utilize machine learning techniques to reconstruct or estimate datapoints. In an example embodiment, a machine learning algorithm is used to estimate a value of an empty or null datapoint in CT data, where the empty or null datapoint is associated with a time delay (e.g., a pause or break) in acquisition of the CT data. One advantage provided this technique is that it can be used to reduce a radiation dose to a patient by requiring fewer datapoints to be taken during the acquisition of the data, thereby minimizing patient exposure to potentially harmful radiation.

[0077] FIG. 7 shows a flow chart of an example method 700 for estimating a flow of a fluid through a conduit according to an embodiment of the disclosed technology. At step 710, the method 700 comprises: obtaining computed tomography (CT) data representing the flow of the fluid through the conduit at multiple times, wherein the fluid comprises a contrast agent, wherein the CT data comprises timing data representing evolution of a concentration of the contrast agent within the conduit at the multiple times. At step 720, the method 700 comprises: receiving, by a machine learning (ML) engine as input, spatiotemporal coordinates associated with the CT data, wherein each of the spatiotemporal coordinates comprises a time coordinate associated with a respective time in the timing data and spatial coordinates associated with a location of the fluid within the conduit at the respective time, wherein the ML engine is trained by the CT data. At step 730, the method 700 comprises: obtaining, as output by the ML engine and for each of the spatiotemporal coordinates, a set of initial values, wherein each of the initial values represents a property of the fluid, the contrast agent, or the flow. At step 740, the method 700 comprises: performing by the ML engine multiple iterations on the set of initial values to obtain a refined set of values that enables the property tobe quantitatively estimated at the multiple times and at multiple locations within the conduit.

[0078] FIG. 8 shows a flow chart of an example method 800 for reconstructing a flow of a fluid through a conduit. At step 810, the method 800 comprises: obtaining timeseries data associated with the flow of the fluid through the conduit. At step 820, the method 800 comprises: processing a set of spatiotemporal coordinates representing the time-series data using an analytical model. At step 830, the method 800 comprises: obtaining, based on results of the processing, a dataset that enables quantification of one or more properties associated with the flow of the fluid through the conduit at multiple times and at multiple locations. At step 840, the method 800 comprises: using the dataset to obtain a reconstruction of the flow of the fluid through the conduit.

[0079] Various implementations of features of the disclosed technology can be made based on the above disclosure, including the examples listed below.

[0080] Example 1 . A method for estimating a flow of a fluid through a conduit, comprising: obtaining computed tomography (CT) data representing the flow of the fluid through the conduit at multiple times, wherein the fluid comprises a contrast agent, wherein the CT data comprises timing data representing evolution of a concentration of the contrast agent within the conduit at the multiple times; receiving, by a machine learning (ML) engine as input, spatiotemporal coordinates associated with the CT data, wherein each of the spatiotemporal coordinates comprises a time coordinate associated with a respective time in the timing data and spatial coordinates associated with a location of the fluid within the conduit at the respective time, wherein the ML engine is trained by the CT data; obtaining, as output by the ML engine and for each of the spatiotemporal coordinates, a set of initial values, wherein each of the initial values represents a property of the fluid, the contrast agent, or the flow; and performing by the ML engine multiple iterations on the set of initial values to obtain a refined set of values that enables the property to be quantitatively estimated at the multiple times and at multiple locations within the conduit.

[0081] Example 2. The method of example 1 , wherein the CT data comprises one or more artifacts and the method comprises: using the refined set of values to obtain a graphical representation of the flow of the fluid or the contrast agent at at least one ofthe multiple times with the one or more artifacts removed from the graphical representation.

[0082] Example 3. The method of example 2, wherein the graphical representation is substantially free of motion artifacts.

[0083] Example 4. The method of example 2, wherein the graphical representation is substantially free of noise artifacts induced by equipment used to acquire the CT data.

[0084] Example 5. The method of example 1 , wherein the property corresponds to: (i) the concentration of the contrast agent at the respective time, (ii) a velocity of the flow at the location at the respective time, or (iii) a pressure of the flow at the location at the respective time.

[0085] Example 6. The method of example 5, comprising using the refined set of values to obtain a graphical representation of the property at at least one of the multiple times.

[0086] Example 7. The method of example 1 , wherein the machine learning engine comprises a Physics Informed Neural Network (PINN).

[0087] Example 8. The method of example 1 , wherein the fluid is blood.

[0088] Example 9. The method of example 1 , wherein the conduit is or is part of an anatomical object.

[0089] Example 10. The method of example 1 , wherein the CT data is acquired at one or more gantry angles of a CT scanner.

[0090] Example 11. The method of example 10, wherein the ML algorithm comprises a loss function to describe losses associated with the one or more gantry angles.

[0091] Example 12. The method of example 1 , comprising: estimating, by the ML algorithm, a value of an empty or null datapoint in the CT data, wherein the empty or null datapoint is associated with a time delay in acquisition of the CT data.

[0092] Example 13. The method of example 1 , wherein the CT data is a sinogram.

[0093] Example 14. A method for reconstructing a flow of a fluid through a conduit, comprising: obtaining time-series data associated with the flow of the fluid through theconduit; processing a set of spatiotemporal coordinates representing the time-series data using an analytical model; obtaining, based on results of the processing, a dataset that enables quantification of one or more properties associated with the flow of the fluid through the conduit at multiple times and at multiple locations; and using the dataset to obtain a reconstruction of the flow of the fluid through the conduit.

[0094] Example 15. The method of example 14, wherein the time-series data is used to supervise the analytical model during the processing.

[0095] Example 16. The method of example 14, wherein each of the one or more properties is associated with a respective spatiotemporal coordinate, wherein the one or more properties correspond to one or more of: a concentration of an additive transported through the conduit by the flow of the fluid, a velocity of the flow, or a pressure of the flow.

[0096] Example 17. The method of example 16, wherein one or more of the concentration of the additive, the velocity, or the pressure are visualized within the reconstruction.

[0097] Example 18. The method of example 14, wherein the time-series data is obtained from a sinogram.

[0098] Example 19. The method of example 14, wherein the conduit is or is part of an anatomical object.

[0099] Example 20. A device, comprising a processor and a memory including instructions stored thereon, wherein the instructions upon execution by the processor cause the processor to perform any of the methods in examples 1 -19.

[0100] Example 21. A method for estimating fluid flow through a conduit, comprising: acquisition of the graphical representations of raw imagery files of fluid motion including scalar transport data; processing acquired data through an analytical model with predicted fluid concentration and flow properties; and using the resulting data to directly supervise the raw imagery data.

[0101] Example 22. The method of example 21 , wherein the conduit is a blood vessel.

[0102] Example 23. The method of example 21 , wherein the analytical model uses Physics-Informed Neural Networks (PINNs).

[0103] Example 24. The method of example 21 , wherein supervision of the raw imagery data includes modification of the data.

[0104] Example 25. The method of example 21 , wherein the resulting data includes a prediction of the fluid flow parameters.

[0105] Example 26. The method of example 21 , wherein supervision of the raw imagery data includes reconstruction of the flow velocity.

[0106] Example 27. The method of example 21 , wherein supervision of the raw imagery data includes partial or complete elimination of motion artifacts.

[0107] Example 28. The method of example 21 , wherein multiple iterations of the data processing is performed through the analytical model to further improve results.

[0108] Example 29. The method of example 21 , wherein the image data is sourced from CT scans.

[0109] Example 30. A method for estimating fluid flow through a conduit, comprising: acquisition of the CT sinogram raw imagery files of fluid motion including scalar transport data; processing acquired sinogram through an analytical model with predicted fluid concentration and flow properties; and using the resulting sinogram to directly supervise the raw sinogram data.

[0110] Example 31 . The method of example 30, wherein the analytical model uses Physics-Informed Neural Networks (PINNs).

[0111] Example 32. The method of example 30, wherein supervision of the raw imagery data includes modification of the data.

[0112] Example 33. The method of example 30, wherein the resulting data includes a prediction of the fluid flow parameters.

[0113] Example 34. The method of example 30, wherein supervision of the raw imagery data includes reconstruction of the flow velocity.

[0114] Example 35. The method of example 30, wherein supervision of the raw imagery data includes partial or complete elimination of motion artifacts.

[0115] Example 36. The method of example 30, wherein multiple iterations of the data processing is performed through the analytical model to further improve results.

[0116] Example 37. A device, comprising a processor and a memory including instructions stored thereon, wherein the instructions upon execution by the processor cause the processor to perform any of the methods in examples 1 -36.

[0117] From the foregoing, it will be appreciated that specific embodiments of the invention have been described herein for purposes of illustration, but that various modifications may be made without deviating from the scope of the invention. Accordingly, the invention is not limited except as by the appended claims.

[0118] Implementations of the subject matter and the functional operations described in this patent document can be implemented in various systems, digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Implementations of the subject matter described in this specification can be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a tangible and non-transitory computer readable medium for execution by, or to control the operation of, data processing apparatus. The computer readable medium can be a machine- readable storage device, a machine-readable storage substrate, a memory device, a composition of matter effecting a machine-readable propagated signal, or a combination of one or more of them. The term "data processing unit" or "data processing apparatus" encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0119] A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markuplanguage document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

[0120] The processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0121] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of nonvolatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0122] While this patent document contains many specifics, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this patent document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in anysuitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

[0123] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. Moreover, the separation of various system components in the embodiments described in this patent document should not be understood as requiring such separation in all embodiments.

[0124] Only a few implementations and examples are described and other implementations, enhancements and variations can be made based on what is described and illustrated in this patent document.

Claims

CLAIMSWhat is claimed is:1 . A method for reconstructing a flow of a fluid through a conduit, comprising: obtaining computed tomography (CT) data representing the flow of the fluid through the conduit at multiple times, wherein the fluid comprises a contrast agent, wherein the CT data comprises timing data representing evolution of a concentration of the contrast agent within the conduit at the multiple times; receiving, by a machine learning (ML) engine as input, spatiotemporal coordinates associated with the CT data, wherein each of the spatiotemporal coordinates comprises a time coordinate associated with a respective time in the timing data and spatial coordinates associated with a location of the fluid within the conduit at the respective time, wherein the ML engine is trained by the CT data; obtaining, as output by the ML engine and for each of the spatiotemporal coordinates, a set of initial values, wherein each of the initial values represents a property of the fluid, the contrast agent, or the flow; and performing by the ML engine multiple iterations on the set of initial values to obtain a refined set of values that enables the property to be quantitatively estimated at the multiple times and at multiple locations within the conduit.

2. The method of claim 1 , wherein the method comprises: using the refined set of values to obtain a graphical representation of the flow of the fluid or the contrast agent at at least one of the multiple times.

3. The method of claim 2, wherein the graphical representation is substantially free of motion artifacts.

4. The method of claim 2, wherein the graphical representation is substantially free of noise artifacts induced by equipment used to acquire the CT data.

5. The method of claim 1 , wherein the property corresponds to: (i) the concentration of the contrast agent at the respective time, (ii) a velocity of the flow at the location at the respective time, or (iii) a pressure of the flow at the location at the respective time.

6. The method of claim 5, comprising using the refined set of values to obtain a graphical representation of the property at at least one of the multiple times.

7. The method of claim 1 , wherein the machine learning engine comprises a Physics Informed Neural Network (PINN).

8. The method of claim 1 , wherein the fluid is blood.

9. The method of claim 1 , wherein the conduit is or is part of an anatomical object.

10. The method of claim 1 , wherein the CT data is acquired at one or more gantry angles of a CT scanner.

11. The method of claim 10, wherein the ML engine comprises a loss function to describe losses associated with the one or more gantry angles.

12. The method of claim 1 , comprising: estimating, by the ML engine, a value of an empty or null datapoint in the CT data, wherein the empty or null datapoint is associated with a time delay in acquisition of the CT data.

13. The method of claim 1 , wherein the CT data is a sinogram.

14. A method for reconstructing a flow of a fluid through a conduit, comprising: obtaining time-series data associated with the flow of the fluid through the conduit; processing a set of spatiotemporal coordinates representing the time-series data using an analytical model;obtaining, based on results of the processing, a dataset that enables quantification of one or more properties associated with the flow of the fluid through the conduit at multiple times and at multiple locations; and using the dataset to obtain a reconstruction of the flow of the fluid through the conduit.

15. The method of claim 14, wherein the time-series data is used to supervise the analytical model during the processing.

16. The method of claim 14, wherein each of the one or more properties is associated with a respective spatiotemporal coordinate, wherein the one or more properties correspond to one or more of: a concentration of an additive transported through the conduit by the flow of the fluid, a velocity of the flow, or a pressure of the flow.

17. The method of claim 16, wherein one or more of the concentration of the additive, the velocity, or the pressure are visualized within the reconstruction.

18. The method of claim 14, wherein the time-series data is obtained from a sinogram.

19. The method of claim 14, wherein the conduit is or is part of an anatomical object.

20. A device, comprising a processor and a memory including instructions stored thereon, wherein the instructions upon execution by the processor cause the processor to perform any of the methods in claims 1 -19.

Images