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.

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.

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.

A Framework for Image-Based Modeling of Acute Myocardial Ischemia Using Intramurally Recorded Extracellular Potentials.

The biophysical basis for electrocardiographic evaluation of myocardial ischemia stems from the notion that ischemic tissues develop, with relative uniformity, along the endocardial aspects of the heart. These injured regions of subendocardial tissue give rise to intramural currents that lead to ST segment deflections within electrocardiogram (ECG) recordings. The concept of subendocardial ischemic regions is often used in clinical practice, providing a simple and intuitive description of ischemic injury; however, such a model grossly oversimplifies the presentation of ischemic disease-inadvertently leading to errors in ECG-based diagnoses. Furthermore, recent experimental studies have brought into question the subendocardial ischemia paradigm suggesting instead a more distributed pattern of tissue injury. These findings come from experiments and so have both the impact and the limitations of measurements from living organisms. Computer models have often been employed to overcome the constraints of experimental approaches and have a robust history in cardiac simulation. To this end, we have developed a computational simulation framework aimed at elucidating the effects of ischemia on measurable cardiac potentials. To validate our framework, we simulated, visualized, and analyzed 226 experimentally derived acute myocardial ischemic events. Simulation outcomes agreed both qualitatively (feature comparison) and quantitatively (correlation, average error, and significance) with experimentally obtained epicardial measurements, particularly under conditions of elevated ischemic stress. Our simulation framework introduces a novel approach to incorporating subject-specific, geometric models and experimental results that are highly resolved in space and time into computational models. We propose this framework as a means to advance the understanding of the underlying mechanisms of ischemic disease while simultaneously putting in place the computational infrastructure necessary to study and improve ischemia models aimed at reducing diagnostic errors in the clinic.

Electrocardiographic Comparison of Dobutamine and BRUCE Cardiac Stress Testing With High Resolution Mapping in Experimental Models.

Clinical tests to detect acute myocardial ischemia induce transient cardiac stress by means of exercise or pharmaceutical stimulation and measure electrical changes of the heart on the body surface via an electrocardiogram (ECG). Such tests assume that both stress mechanisms induce identical-or at least similar-forms of ischemia. To improve electrocardiographic detection of myocardial ischemia, we must study how varied stressing agents (pharmacological or paced stressors) change electrocardiographic signatures. We simultaneously measured electrical recordings within the myocardium, on the epicardial surface, and on the body surface. We then induced acute, controlled ischemia and monitored the electrical response. To create the hemodynamic substrate for ischemia, we applied a hydraulic occlusion to the left anterior descending coronary artery. We varied the ischemic stress with two clinical protocols, the BRUCE and dobutamine stress tests. Our results suggest significant differences in the recorded electrical signal between stress mechanisms. Differences include the location, volume, and temporal development of ischemia throughout a stress episode. These results, and the experimental means used to obtain them, are a significant breakthrough in the field with simultaneous, high density electrical recordings within the myocardium and on the heart and torso surfaces.

Effect of Segmentation Variation on ECG Imaging.

ECG imaging (ECGI) is the process of calculating electrical cardiac activity from body surface recordings from the geometry and conductivity of the torso volume. A key first step to create geometric models for ECGI and a possible source of considerable variability is to segment the surface of the heart. We hypothesize that this variation in cardiac segmentation will produce variation in the computed ventricular surface potentials from ECGI. To evaluate this hypothesis, we leveraged the resources of the Consortium for ECG Imaging (CEI) to carry out a comparison of ECGI results from the same body surface potentials and multiple ventricular segmentations. We found that using the different segmentations produced variability in the computed ventricular surface potentials. Not surprisingly, locations of greater variance in the computed potential correlated to locations of greater variance in the segmentations, for example near the pulmonary artery and basal anterior left ventricular wall. Our results indicate that ECGI may be more sensitive to segmentation errors on the anterior epicardial surface than on other areas of the heart.

Overcoming Barriers to Quantification and Comparison of Electrocardiographic Imaging Methods: A Community-Based Approach.

There has been a recent upsurge in the development of electrocardiographic imaging (ECGI) methods, along with a significant increase in clinical application. To better assess the state-of-the-art, enable reliable progress, and facilitate clinical adoption, it is important to be able to compare results in a comprehensive manner, scientifically and clinically. However, studies vary in modeling choices, computational methods, validation mechanisms and metrics, and clinical applications, making unified evaluation and comparison of ECGI a critical challenge. This paper describes initial results of a project to address this challenge via a community-based approach organized by the Consortium for Electrocardiographic Imaging (CEI). We detail different aspects of this collective effort including a data sharing repository, a platform for comparison of different algorithms and modeling approaches on the same datasets, several active workgroups and progress made along these directions. We also summarize the results from groups participating in this collaboration and contributing solutions by applying their methods to the same dataset for comparison.

The Role of Reduced Left Ventricular, Systolic Blood Volumes in ST Segment Potentials Overlying Diseased Tissue of the Ischemic Heart.

Myocardial ischemia is the response of the heart to reduced coronary blood flow, leading to changes in ST segment potentials. ST segment depression is regarded as an indicator of nontransmural myocardial ischemia; however, not all nontransmural ischemia results in ST depression. This apparent discrepancy may be the result of many complex factors in cardiac response mechanisms to reduced blood flow. As a result, sophisticated computer models have emerged that have provided key insights into this complex phenomenon and the circumstances surrounding ST depression. Though these models have been able to produce ST depressions, many have neglected the effect of intracavitary blood volume, associated with different phases of the cardiac cycle. To explore the influence of the cardiac blood volume variability on epicardial potentials during nontransmural ischemia, we incorporated a thin, subendocardial ischemic zone geometry into an anatomically realistic, image-based ventricular model, and generated a finite element, static bidomain solution to determine the resulting epicardial surface potentials. It was first determined that, under baseline conditions (i.e., expanded left ventricular volumes corresponding to diastole), a predictable ST depression developed over the ischemic region. Left ventricular volume was then incrementally reduced, while maintaining the size and general shape of the ischemic region, in order to reflect the systolic phase of the cardiac cycle. As blood volume geometries decreased, epicardial ST depression overlying the ischemic region first increased in surface area as blood volume was reduced and before dramatically reducing near 30% blood volume reduction - accentuating the role and importance of blood volume variation in computational models of ischemia.

The Consortium for Electrocardiographic Imaging.

Electrocardiographic imaging (ECGI) has recently gained attention as a viable diagnostic tool for reconstructing cardiac electrical activity in normal hearts as well as in cardiac arrhythmias. However, progress has been limited by the lack of both standards and unbiased comparisons of approaches and techniques across the community, as well as the consequent difficulty of effective collaboration across research groups.. To address these limitations, we created the Consortium for Electrocardiographic Imaging (CEI), with the objective of facilitating collaboration across the research community in ECGI and creating standards for comparisons and reproducibility. Here we introduce CEI and describe its two main efforts, the creation of EDGAR, a public data repository, and the organization of three collaborative workgroups that address key components and applications in ECGI. Both EDGAR and the workgroups will facilitate the sharing of ideas, data and methods across the ECGI community and thus address the current lack of reproducibility, broad collaboration, and unbiased comparisons.

New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment.

Cardiac electrical imaging often requires the examination of different forward and inverse problem formulations based on mathematical and numerical approximations of the underlying source and the intervening volume conductor that can generate the associated voltages on the surface of the body. If the goal is to recover the source on the heart from body surface potentials, the solution strategy must include numerical techniques that can incorporate appropriate constraints and recover useful solutions, even though the problem is badly posed. Creating complete software solutions to such problems is a daunting undertaking. In order to make such tools more accessible to a broad array of researchers, the Center for Integrative Biomedical Computing (CIBC) has made an ECG forward/inverse toolkit available within the open source SCIRun system. Here we report on three new methods added to the inverse suite of the toolkit. These new algorithms, namely a Total Variation method, a non-decreasing TMP inverse and a spline-based inverse, consist of two inverse methods that take advantage of the temporal structure of the heart potentials and one that leverages the spatial characteristics of the transmembrane potentials. These three methods further expand the possibilities of researchers in cardiology to explore and compare solutions to their particular imaging problem.

A toolkit for forward/inverse problems in electrocardiography within the SCIRun problem solving environment.

Computational modeling in electrocardiography often requires the examination of cardiac forward and inverse problems in order to non-invasively analyze physiological events that are otherwise inaccessible or unethical to explore. The study of these models can be performed in the open-source SCIRun problem solving environment developed at the Center for Integrative Biomedical Computing (CIBC). A new toolkit within SCIRun provides researchers with essential frameworks for constructing and manipulating electrocardiographic forward and inverse models in a highly efficient and interactive way. The toolkit contains sample networks, tutorials and documentation which direct users through SCIRun-specific approaches in the assembly and execution of these specific problems.

Measurement of Defibrillator Surface Potentials for Simulation Verification.

Despite the growing use of implantable cardioverter defibrillators (ICDs) in adults and children, there has been little progress in optimizing device and electrode placement. To facilitate effective placement of ICDs, especially in pediatric cases, we have developed a predictive model that evaluates the efficacy of a delivered shock. Most recently, we have also developed an experimental validation approach based on measurements from clinical cases. The approach involves obtaining body surface potential maps of ICD discharges during implantation surgery and comparing these measured potentials with simulated surface potentials to determine simulation accuracy. Comparison of the simulated and measured potentials yielded very similar patterns and a typical correlation greater than 0.9, suggesting that the predictive simulation generates realistic potential values. Ongoing sensitivity studies will determine the robustness of the results and pave the way for use of this approach for assisting optimization of ICD use.