Uncertainty quantification of the effect of cardiac position variability in the inverse problem of electrocardiographic imaging.

Objective.Electrocardiographic imaging (ECGI) is a functional imaging modality that consists of two related problems, the forward problem of reconstructing body surface electrical signals given cardiac bioelectric activity, and the inverse problem of reconstructing cardiac bioelectric activity given measured body surface signals. ECGI relies on a model for how the heart generates bioelectric signals which is subject to variability in inputs. The study of how uncertainty in model inputs affects the model output is known as uncertainty quantification (UQ). This study establishes develops, and characterizes the application of UQ to ECGI.Approach.We establish two formulations for applying UQ to ECGI: a polynomial chaos expansion (PCE) based parametric UQ formulation (PCE-UQ formulation), and a novel UQ-aware inverse formulation which leverages our previously established 'joint-inverse' formulation (UQ joint-inverse formulation). We apply these to evaluate the effect of uncertainty in the heart position on the ECGI solutions across a range of ECGI datasets.Main results.We demonstrated the ability of our UQ-ECGI formulations to characterize the effect of parameter uncertainty on the ECGI inverse problem. We found that while the PCE-UQ inverse solution provided more complex outputs such as sensitivities and standard deviation, the UQ joint-inverse solution provided a more interpretable output in the form of a single ECGI solution. We find that between these two methods we are able to assess a wide range of effects that heart position variability has on the ECGI solution.Significance.This study, for the first time, characterizes in detail the application of UQ to the ECGI inverse problem. We demonstrated how UQ can provide insight into the behavior of ECGI using variability in cardiac position as a test case. This study lays the groundwork for future development of UQ-ECGI studies, as well as future development of ECGI formulations which are robust to input parameter variability.

UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering.

BACKGROUND: Computational biomedical simulations frequently contain parameters that model physical features, material coefficients, and physiological effects, whose values are typically assumed known a priori. Understanding the effect of variability in those assumed values is currently a topic of great interest. A general-purpose software tool that quantifies how variation in these parameters affects model outputs is not broadly available in biomedicine. For this reason, we developed the 'UncertainSCI' uncertainty quantification software suite to facilitate analysis of uncertainty due to parametric variability. METHODS: We developed and distributed a new open-source Python-based software tool, UncertainSCI, which employs advanced parameter sampling techniques to build polynomial chaos (PC) emulators that can be used to predict model outputs for general parameter values. Uncertainty of model outputs is studied by modeling parameters as random variables, and model output statistics and sensitivities are then easily computed from the emulator. Our approaches utilize modern, near-optimal techniques for sampling and PC construction based on weighted Fekete points constructed by subsampling from a suitably randomized candidate set. RESULTS: Concentrating on two test cases-modeling bioelectric potentials in the heart and electric stimulation in the brain-we illustrate the use of UncertainSCI to estimate variability, statistics, and sensitivities associated with multiple parameters in these models. CONCLUSION: UncertainSCI is a powerful yet lightweight tool enabling sophisticated probing of parametric variability and uncertainty in biomedical simulations. Its non-intrusive pipeline allows users to leverage existing software libraries and suites to accurately ascertain parametric uncertainty in a variety of applications.

Treatment Planning for Atrial Fibrillation Using Patient-Specific Models Showing the Importance of Fibrillatory-Areas.

Computational models have made it possible to study the effect of fibrosis and scar on atrial fibrillation (AF) and plan future personalized treatments. Here, we study the effect of area available for fibrillatory waves to sustain AF. Then we use it to plan for AF ablation to improve procedural outcomes. CARPentry was used to create patient-specific models to determine the association between the size of residual contiguous areas available for AF wavefronts to propagate and sustain AF [fibrillatory area (FA)] after ablation with procedural outcomes. The FA was quantified in a novel manner accounting for gaps in ablation lines. We selected 30 persistent AF patients with known ablation outcomes. We divided the atrial surface into five areas based on ablation scar pattern and anatomical landmarks and calculated the FAs. We validated the models based on clinical outcomes and suggested future ablation lines that minimize the FAs and terminate rotor activities in simulations. We also simulated the effects of three common antiarrhythmic drugs. In the patient-specific models, the predicted arrhythmias matched the clinical outcomes in 25 of 30 patients (accuracy 83.33%). The average largest FA (FAmax) in the recurrence group was 8517 ± 1444 vs. 6772 ± 1531 mm2 in the no recurrence group (p < 0.004). The final FAs after adding the suggested ablation lines in the AF recurrence group reduced the average FAmax from 8517 ± 1444 to 6168 ± 1358 mm2 (p < 0.001) and stopped the sustained rotor activity. Simulations also correctly anticipated the effect of antiarrhythmic drugs in 5 out of 6 patients who used drug therapy post unsuccessful ablation (accuracy 83.33%). Sizes of FAs available for AF wavefronts to propagate are important determinants for ablation outcomes. FA size in combination with computational simulations can be used to direct ablation in persistent AF to minimize the critical mass required to sustain recurrent AF.

Effect of Segmentation Uncertainty on the ECGI Inverse Problem Solution and Source Localization.

Electrocardiographic Imaging (ECGI) is a promising tool to non-invasively map the electrical activity of the heart using body surface potentials (BSPs) and the patient specific anatomical data. One of the first steps of ECGI is the segmentation of the heart and torso geometries. In the clinical practice, the segmentation procedure is not fully-automated yet and is in consequence operator-dependent. We expect that the inter-operator variation in cardiac segmentation would influence the ECGI solution. This effect remains however non quantified. In the present work, we study the effect of segmentation variability on the ECGI estimation of the cardiac activity with 262 shape models generated from fifteen different segmentations. Therefore, we designed two test cases: with and without shape model uncertainty. Moreover, we used four cases for ectopic ventricular excitation and compared the ECGI results in terms of reconstructed activation times and excitation origins. The preliminary results indicate that a small variation of the activation maps can be observed with a model uncertainty but no significant effect on the source localization is observed.

The Effect of Segmentation Variability in Forward ECG Simulation.

Segmentation of patient-specific anatomical models is one of the first steps in Electrocardiographic imaging (ECGI). However, the effect of segmentation variability on ECGI remains unexplored. In this study, we assess the effect of heart segmentation variability on ECG simulation. We generated a statistical shape model from segmentations of the same patient and generated 262 cardiac geometries to run in an ECG forward computation of body surface potentials (BSPs) using an equivalent dipole layer cardiac source model and 5 ventricular stimulation protocols. Variability between simulated BSPs for all models and protocols was assessed using Pearson's correlation coefficient (CC). Compared to the BSPs of the mean cardiac shape model, the lowest variability (average CC = 0.98 ± 0.03) was found for apical pacing whereas the highest variability (average CC = 0.90 ± 0.23) was found for right ventricular free wall pacing. Furthermore, low amplitude BSPs show a larger variation in QRS morphology compared to high amplitude signals. The results indicate that the uncertainty in cardiac shape has a significant impact on ECGI.

The electrocardiographic forward problem: A benchmark study.

BACKGROUND: Electrocardiographic forward problems are crucial components for noninvasive electrocardiographic imaging (ECGI) that compute torso potentials from cardiac source measurements. Forward problems have few sources of error as they are physically well posed and supported by mature numerical and computational techniques. However, the residual errors reported from experimental validation studies between forward computed and measured torso signals remain surprisingly high. OBJECTIVE: To test the hypothesis that incomplete cardiac source sampling, especially above the atrioventricular (AV) plane is a major contributor to forward solution errors. METHODS: We used a modified Langendorff preparation suspended in a human-shaped electrolytic torso-tank and a novel pericardiac-cage recording array to thoroughly sample the cardiac potentials. With this carefully controlled experimental preparation, we minimized possible sources of error, including geometric error and torso inhomogeneities. We progressively removed recorded signals from above the atrioventricular plane to determine how the forward-computed torso-tank potentials were affected by incomplete source sampling. RESULTS: We studied 240 beats total recorded from three different activation sequence types (sinus, and posterior and anterior left-ventricular free-wall pacing) in each of two experiments. With complete sampling by the cage electrodes, all correlation metrics between computed and measured torso-tank potentials were above 0.93 (maximum 0.99). The mean root-mean-squared error across all beat types was also low, less than or equal to 0.10 mV. A precipitous drop in forward solution accuracy was observed when we included only cage measurements below the AV plane. CONCLUSION: First, our forward computed potentials using complete cardiac source measurements set a benchmark for similar studies. Second, this study validates the importance of complete cardiac source sampling above the AV plane to produce accurate forward computed torso potentials. Testing ECGI systems and techniques with these more complete and highly accurate datasets will improve inverse techniques and noninvasive detection of cardiac electrical abnormalities.

Estimation and Validation of Cardiac Conduction Velocity and Wavefront Reconstruction Using Epicardial and Volumetric Data.

OBJECTIVE: In this study, we have used whole heart simulations parameterized with large animal experiments to validate three techniques (two from the literature and one novel) for estimating epicardial and volumetric conduction velocity (CV). METHODS: We used an eikonal-based simulation model to generate ground truth activation sequences with prescribed CVs. Using the sampling density achieved experimentally we examined the accuracy with which we could reconstruct the wavefront, and then examined the robustness of three CV estimation techniques to reconstruction related error. We examined a triangulation-based, inverse-gradient-based, and streamline-based techniques for estimating CV cross the surface and within the volume of the heart. RESULTS: The reconstructed activation times agreed closely with simulated values, with 50-70% of the volumetric nodes and 97-99% of the epicardial nodes were within 1 ms of the ground truth. We found close agreement between the CVs calculated using reconstructed versus ground truth activation times, with differences in the median estimated CV on the order of 3-5% volumetrically and 1-2% superficially, regardless of what technique was used. CONCLUSION: Our results indicate that the wavefront reconstruction and CV estimation techniques are accurate, allowing us to examine changes in propagation induced by experimental interventions such as acute ischemia, ectopic pacing, or drugs. SIGNIFICANCE: We implemented, validated, and compared the performance of a number of CV estimation techniques. The CV estimation techniques implemented in this study produce accurate, high-resolution CV fields that can be used to study propagation in the heart experimentally and clinically.

Advances in the electron diffraction characterization of atomic clusters and nanoparticles.

Nanoparticles and metallic clusters continue to make a remarkable impact on novel and emerging technologies. In recent years, there have been impressive advances in the controlled synthesis of clusters and their advanced characterization. One of the most common ways to determine the structures of nanoparticles and clusters is by means of X-ray diffraction methods. However, this requires the clusters to crystallize in a similar way to those used in protein studies, which is not possible in many cases. Novel methods based on electron diffraction have been used to efficiently study individual nanoparticles and clusters and these can overcome the obstacles commonly encountered during X-ray diffraction methods without the need for large crystals. These novel methodologies have improved with advances in electron microscopy instrumentation and electron detection. Here, we review advanced methodologies for characterizing metallic nanoparticles and clusters using a variety of electron diffraction procedures. These include selected area electron diffraction, nanobeam diffraction, coherent electron diffraction, precession electron diffraction, scanning transmission electron microcopy diffraction, and high throughput data analytics, which leverage deep learning to reduce the propensity for data errors and translate nanometer and atomic scale measurements into material data.

Uncertainty Quantification in Simulations of Myocardial Ischemia.

Computational models of myocardial ischemia are parameterized using assumptions of tissue properties and physiological values such as conductivity ratios in cardiac tissue and conductivity changes between healthy and ischemic tissues. Understanding the effect of uncertainty in these parameter selections would provide useful insight into the performance and variability of the modeling outputs. Recently developed uncertainty quantification tools allow for the application of polynomial chaos expansion uncertainty quantification to such bioelectric models in order to parsimoniously examine model response to input uncertainty. We applied uncertainty quantification to examine reconstructed extracellular potentials from the cardiac passive bidomain based on variation in the conductivity values for the ischemic tissue. We investigated the model response in both a synthetic dataset with simulated ischemic regions and a dataset with ischemic regions derived from experimental recordings. We found that extracellular longitudinal and intracellular longitudinal conductivities predominately affected simulation output, with the highest standard deviations in regions of extracellular potential elevations. We found that transverse conductivity had almost no effect on model output.

The Role of Myocardial Fiber Direction in Epicardial Activation Patterns via Uncertainty Quantification.

Fiber structure governs the spread of excitation in the heart; however, little is known about the effects of physiological variability in fiber orientation on epicardial activation. To investigate these effects, we implemented ventricular simulations of activation using rule-based fiber orientations, and robust uncertainty quantification algorithms to capture detailed maps of model sensitivity. Specifically, we implemented polynomial chaos expansion, which allows for robust exploration with reduced computational demand through an emulator function to approximate the underlying forward model. We applied these techniques to examine the activation sequence of the heart in response to both epicardial and endocardial stimuli within the left ventricular free wall and variations in fiber orientation. Our results showed that physiological variation in fiber orientation does not significantly impact the location of activation features, but it does impact the overall spread of activation. Future studies will investigate under which circumstances physiological changes in fiber orientation might alter electrical propagation such that the resulting simulations produce misleading outcomes.

Uncertainty Quantification of the Effects of Segmentation Variability in ECGI.

Despite advances in many of the techniques used in Electrocardiographic Imaging (ECGI), uncertainty remains insufficiently quantified for many aspects of the pipeline. The effect of geometric uncertainty, particularly due to segmentation variability, may be the least explored to date. We use statistical shape modeling and uncertainty quantification (UQ) to compute the effect of segmentation variability on ECGI solutions. The shape model was made with Shapeworks from nine segmentations of the same patient and incorporated into an ECGI pipeline. We computed uncertainty of the pericardial potentials and local activation times (LATs) using polynomial chaos expansion (PCE) implemented in UncertainSCI. Uncertainty in pericardial potentials from segmentation variation mirrored areas of high variability in the shape model, near the base of the heart and the right ventricular outflow tract, and that ECGI was less sensitive to uncertainty in the posterior region of the heart. Subsequently LAT calculations could vary dramatically due to segmentation variability, with a standard deviation as high as 126ms, yet mainly in regions with low conduction velocity. Our shape modeling and UQ pipeline presented possible uncertainty in ECGI due to segmentation variability and can be used by researchers to reduce said uncertainty or mitigate its effects. The demonstrated use of statistical shape modeling and UQ can also be extended to other types of modeling pipelines.

A Cardiac Shape Model for Segmentation Uncertainty Quantification.

Segmentation of cardiac images is a variable component of many patient specific computational pipelines, yet its impact on simulated results are still not fully understood. A hurdle to to exploring the impact of the segmentation variability is the technical challenge of building a statistical shape model of the ventricles. In this study, we improved open our previous shape analysis by creating a unified shape model including both the epicardium and endocardium. We tested four techniques within ShapeWorks to generate a ventricular shape model: standard, multidomain, hybrid multidomain, and geodesic distance. The multidomain and hybrid multidomain generated a shape model using all eleven segmentations, and the geodesic distance method generated a shape model using a subset of four segmentations. Each of the shape models captured spatially dependent characteristics of the segmentation variability, including wall thickness, annular diameter, and basal truncation. While each of the three methods have benefits, the hybrid multidomain approach provided the most accurate shape model with fewest points and may be most useful in a majority of applications.

Using UncertainSCI to Quantify Uncertainty in Cardiac Simulations.

Cardiac simulations have become increasingly accurate at representing physiological processes. However, simulations often fail to capture the impact of parameter uncertainty in predictions. Uncertainty quantification (UQ) is a set of techniques that captures variability in simulation output based on model assumptions. Although many UQ methods exist, practical implementation can be challenging. We created UncertainSCI, a UQ framework that uses polynomial chaos (PC) expansion to model the forward stochastic error in simulations parameterized with random variables. UncertainSCI uses non-intrusive methods that parsimoniously explores parameter space. The result is an efficient, stable, and accurate PC emulator that can be analyzed to compute output statistics. We created a Python API to run UncertainSCI, minimizing user inputs needed to guide the UQ process. We have implemented UncertainSCI to: (1) quantify the sensitivity of computed torso potentials using the boundary element method to uncertainty in the heart position, and (2) quantify the sensitivity of computed torso potentials using the finite element method to uncertainty in the conductivities of biological tissues. With UncertainSCI, it is possible to evaluate the robustness of simulations to parameter uncertainty and establish realistic expectations on the accuracy of the model results and the clinical guidance they can provide.

Validating defibrillation simulation in a human-shaped phantom.

BACKGROUND: We previously developed a computational model to aid clinicians in positioning implantable cardioverter-defibrillators (ICDs), especially in the case of abnormal anatomies that commonly arise in pediatric cases. We have validated the model clinically on the body surface; however, validation within the volume of the heart is required to establish complete confidence in the model and improve its use in clinical settings. OBJECTIVE: The goal of this study was to use an animal model and thoracic phantom to record the ICD potential field within the heart and on the torso to validate our defibrillation simulation system. METHODS: We recorded defibrillator shock potentials from an ICD suspended together with an animal heart in a human-shaped torso tank and compared them with simulated values. We also compared the scaled distribution threshold, an analog to the defibrillation threshold, calculated from the measured and simulated electric fields within the myocardium. RESULTS: ICD potentials recorded on the tank and cardiac surface and within the myocardium agreed well with those predicted by the simulation. A quantitative comparison of the recorded and simulated potentials yielded a mean correlation of 0.94 and a relative error of 19.1%. The simulation can also predict scaled distribution thresholds similar to those calculated from the measured potential fields. CONCLUSION: We found that our simulation could predict potential fields with high correlation with the measured values within the heart and on the torso surface. These results support the use of this model for the optimization of ICD placements.

Novel experimental model for studying the spatiotemporal electrical signature of acute myocardial ischemia: a translational platform.

Myocardial ischemia is one of the most common cardiovascular pathologies and can indicate many severe and life threatening diseases. Despite these risks, current electrocardiographic detection techniques for ischemia are mediocre at best, with reported sensitivity and specificity ranging from 50%-70% and 70%-90%, respectively. OBJECTIVE: To improve this performance, we set out to develop an experimental preparation to induce, detect, and analyze bioelectric sources of myocardial ischemia and determine how these sources reflect changes in body-surface potential measurements. APPROACH: We designed the experimental preparation with three important characteristics: (1) enable comprehensive and simultaneous high-resolution electrical recordings within the myocardial wall, on the heart surface, and on the torso surface; (2) develop techniques to visualize these recorded electrical signals in time and space; and (3) accurately and controllably simulate ischemic stress within the heart by modulating the supply of blood, the demand for perfusion, or a combination of both. MAIN RESULTS: To achieve these goals we designed comprehensive system that includes (1) custom electrode arrays (2) signal acquisition and multiplexing units, (3) a surgical technique to place electrical recording and myocardial ischemic control equipment, and (4) an image based modeling pipeline to acquire, process, and visualize the results. With this setup, we are uniquely able to capture simultaneously and continuously the electrical signatures of acute myocardial ischemia within the heart, on the heart surface, and on the body surface. SIGNIFICANCE: This novel experimental preparation enables investigation of the complex and dynamic nature of acute myocardial ischemia that should lead to new, clinically translatable results.

GRÖMeR: A Pipeline for Geodesic Refinement of Mesh Registration.

The electrical signals produced by the heart can be used to assess cardiac health and diagnose adverse pathologies. Experiments on large mammals provide essential sources of these signals through measurements of up to 1000 simultaneous, distributed locations throughout the heart and torso. To perform accurate spatial analysis of the resulting electrical recordings, researchers must register the locations of each electrode, typically by defining correspondence points from post-experiment, three-dimensional imaging, and directly measured surface electrodes. Often, due to the practical limitations of the experimental situation, only a subset of the electrode locations can be measured, from which the rest must be estimated. We have developed a pipeline, GRÖMeR, that can perform registration of cardiac surface electrode arrays given a limited correspondence point set. This pipeline accounts for global deformations and uses a modified iterative closest points algorithm followed by a geodesically constrained radial basis deformation to calculate a smooth, correspondence-driven registration. To assess the performance of this pipeline, we generated a series of target geometries and limited correspondence patterns based on experimental scenarios. We found that the best performing correspondence pattern required only 20, approximately uniformly distributed points over the epicardial surface of the heart. This study demonstrated the GRÖMeR pipeline to be an accurate and effective way to register cardiac sock electrode arrays from limited correspondence points.

Correcting Undersampled Cardiac Sources in Equivalent Double Layer Forward Simulations.

Electrocardiographic Imaging (ECGI) requires robust ECG forward simulations to accurately calculate cardiac activity. However, many questions remain regarding ECG forward simulations, for instance: there are not common guidelines for the required cardiac source sampling. In this study we test equivalent double layer (EDL) forward simulations with differing cardiac source resolutions and different spatial interpolation techniques. The goal is to reduce error caused by undersampling of cardiac sources and provide guidelines to reduce said source undersampling in ECG forward simulations. Using a simulated dataset sampled at 5 spatial resolutions, we computed body surface potentials using an EDL forward simulation pipeline. We tested two spatial interpolation methods to reduce error due to undersampling triangle weighting and triangle splitting. This forward modeling pipeline showed high frequency artifacts in the predicted ECG time signals when the cardiac source resolution was too low. These low resolutions could also cause shifts in extrema location on the body surface maps. However, these errors in predicted potentials can be mitigated by using a spatial interpolation method. Using spatial interpolation can reduce the number of nodes required for accurate body surface potentials from 9,218 to 2,306. Spatial interpolation in this forward model could also help improve accuracy and reduce computational cost in subsequent ECGI applications.

Validation of Intramural Wavefront Reconstruction and Estimation of 3D Conduction Velocity.

INTRODUCTION: Changes in conduction velocity are indicative of a wide variety of cardiac abnormalities yet measuring conduction velocity is challenging, especially within the myocardial volume. In this study we investigated a novel technique to reconstruct activation fronts and estimate three-dimensional (3D) conduction velocity (CV) from experimental intramural recordings. METHODS: From the intermittently sampled electrograms we both reconstruct the activation profile and compute the reciprocal of the gradient of activation times and a series of streamlines that allows for the CV estimation. RESULTS: The reconstructed activation times agreed closely with simulated values, with 50% to 70% of the nodes ≤ 1ms of absolute error. We found close agreement between the CVs calculated using reconstructed versus simulated activation times. Across the reconstructed stimulation sites we saw that the reconstructed CV was on average 3.8% different than the ground truth CV. DISCUSSION: This study used simulated datasets to validate our methods for reconstructing 3D activation fronts and estimating conduction velocities. Our results indicate that our method allows accurate reconstructions from sparse measurements, thus allowing us to examine changes in activation induced by experimental interventions such as acute ischemia, ectopic pacing, or drugs.

Optimizing the Reconstruction of Cardiac Potentials Using a Novel High Resolution Pericardiac Cage.

INTRODUCTION: Experimental preparations in which cardiac and torso recordings are made simultaneously typically do not have uniform sampling around the entire surface of the heart. To fill in the resulting gaps in coverage, signals captured from the sampled region are extended to the unsampled region of the heart before being utilized in computational models. The resulting errors have never been evaluated systematically. We explored this relationship using a novel experimental preparation, and compared the resulting measurements against a set of interpolation and optimization methods. METHODS: Measurements came from a modified Langenorff preparation in which we placed a rigid, heart shaped pericardiac cage electrode array around an isolated canine heart within an electrolytic torso-tank. Using the measured cage potentials we optimized a reconstruction from the subset of the cage below the base of the heart (ventricular) to the subset above it (atrial). This optimization minimized the difference between the reconstructed and measured signals. We then compared the reconstruction to a spatial Laplacian interpolation of the same potentials. RESULTS: Qualitative results show a high degree of agreement between optimized reconstructed potentials and measured potentials whereas the Laplacian interpolation resulted in poorer reconstructions in most cases. Calculated mean and maximum error were lower for optimization based approaches than spatial Laplacian interpolation. DISCUSSION: In this study we aimed to utilize novel pericardiac cage recordings to investigate interpolation strategies from sampled signals to unsampled signals. We demonstrate that the sampled ventricular subset of signals is sufficient to reconstruct the atrial subset but that Laplacian interpolation does not achieve the level of accuracy that is possible.

Experimental Validation of Image-Based Modeling of Torso Surface Potentials During Acute Myocardial Ischemia.

INTRODUCTION: Myocardial ischemia is an early clinical indicator of several underlying cardiac pathologies, including coronary artery disease, Takatsobu cardiomyopathy, and coronary artery dissection. Significant progress has been made in computing body-surface potentials from cardiac sources by solving the forward problem of electrocardiography. However, the lack of in vivo studies to validate such computations from ischemic sources has limited the translational potential of such models. METHODS: To resolve this need, we have developed a large-animal experimental model that includes simultaneous recordings within the myocardium, on the epicardial surface, and on the torso surface during episodes of acute, controlled ischemia. Following each experiment, magnetic resonance images were obtained of the anatomy and electrode locations to create a subject-specific model for each animal. From the electrical recordings of the heart, we identified ischemic sources and used the finite element method to solve a static bidomain equation on a geometric model to compute torso surface potentials. RESULTS: Across 33 individual heartbeats, the forward computed torso potentials showed only moderate agreement in both pattern and amplitude with the measured values on the torso surface. Qualitative analysis showed a more encouraging pattern of elevations and depressions shared by computed and measured torso potentials. Pearson's correlation coefficient, root mean squared error, and absolute error varied significantly by heartbeat (0.1642 ± 0.223, 0.10 ± 0.03mV, and 0.08 ± 0.03mV, respectively). DISCUSSION: We speculate several sources of error in our computation including noise within torso surface recordings, registration of electrode and anatomical locations, assuming a homogeneous torso conductivities, and imposing a uniform "transition zone" between ischemic and non-ischemic tissues. Further studies will focus on characterizing these sources of error and understanding how they effect the study results.