Relating epicardial to body surface potential distributions by means of transfer coefficients based on geometry measurements

A transferable in-silico augmented ischemic model for virtual myocardial perfusion imaging and myocardial infarction detection

This paper proposes an innovative approach to generate a generalized myocardial ischemia database by modeling the virtual electrophysiology of the heart and the 12-lead electrocardiography projected by the in-silico model can serve as a ready-to-use database for automatic myocardial infarction/ischemia (MI) localization and classification. Although the virtual heart can be created by an established technique combining the cell model with personalized heart geometry to observe the spatial propagation of depolarization and repolarization waves, we developed a strategy based on the clinical pathophysiology of MI to generate a heterogeneous database with a generic heart while maintaining clinical relevance and reduced computational complexity. First, the virtual heart is simplified into 11 regions that match the types and locations, which can be diagnosed by 12-lead ECG; the major arteries were divided into 3-5 segments from the upstream to the downstream based on the general anatomy. Second, the stenosis or infarction of the major or minor coronary artery branches can cause different perfusion drops and infarct sizes. We simulated the ischemic sites in different branches of the arteries by meandering the infarction location to elaborate on possible ECG representations, which alters the infraction's size and changes the transmembrane potential (TMP) of the myocytes associated with different levels of perfusion drop. A total of 8190 different case combinations of cardiac potentials with ischemia and MI were simulated, and the corresponding ECGs were generated by forward calculations. Finally, we trained and validated our in-silico database with a sparse representation classification (SRC) and tested the transferability of the model on the real-world Physikalisch Technische Bundesanstalt (PTB) database. The overall accuracies for localizing the MI region on the PTB data achieved 0.86, which is only 2% drop compared to that derived from the simulated database (0.88). In summary, we have shown a proof-of-concept for transferring an in-silico model to real-world database to compensate for insufficient data.

Non-invasive estimation of atrial fibrillation driver position using long-short term memory neural networks and body surface potentials

BACKGROUND AND OBJECTIVE

Atrial Fibrillation (AF) is a supraventricular tachyarrhythmia that can lead to thromboembolism, hearlt failure, ischemic stroke, and a decreased quality of life. Characterizing the locations where the mechanisms of AF are initialized and maintained is key to accomplishing an effective ablation of the targets, hence restoring sinus rhythm. Many methods have been investigated to locate such targets in a non-invasive way, such as Electrocardiographic Imaging, which enables an on-invasive and panoramic characterization of cardiac electrical activity using recording Body Surface Potentials (BSP) and a torso model of the patient. Nonetheless, this technique entails some major issues stemming from solving the inverse problem, which is known to be severely ill-posed. In this context, many machine learning and deep learning approaches aim to tackle the characterization and classification of AF targets to improve AF diagnosis and treatment.

METHODS

In this work, we propose a method to locate AF drivers as a supervised classification problem. We employed a hybrid form of the convolutional-recurrent network which enables feature extraction and sequential data modeling utilizing labeled realistic computerized AF models. Thus, we used 16 AF electrograms, 1 atrium, and 10 torso geometries to compute the forward problem. Previously, the AF models were labeled by assigning each sample of the signals a region from the atria from 0 (no driver) to 7, according to the spatial location of the AF driver. The resulting 160 BSP signals, which resemble a 64-lead vest recording, are preprocessed and then introduced into the network following a 4-fold cross-validation in batches of 50 samples.

RESULTS

The results show a mean accuracy of 74.75% among the 4 folds, with a better performance in detecting sinus rhythm, and drivers near the left superior pulmonary vein (R1), and right superior pulmonary vein (R3) whose mean sensitivity bounds around 84%-87%. Significantly good results are obtained in mean sensitivity (87%) and specificity (83%) in R1.

CONCLUSIONS

Good results in R1 are highly convenient since AF drivers are commonly found in this area: the left atrial appendage, as suggested in some previous studies. These promising results indicate that using CNN-LSTM networks could lead to new strategies exploiting temporal correlations to address this challenge effectively.

Basis and applicability of noninvasive inverse electrocardiography: a comparison between cardiac source models

The body surface electrocardiogram (ECG) is a direct result of electrical activity generated by the myocardium. Using the body surface ECGs to reconstruct cardiac electrical activity is called the inverse problem of electrocardiography. The method to solve the inverse problem depends on the chosen cardiac source model to describe cardiac electrical activity. In this paper, we describe the theoretical basis of two inverse methods based on the most commonly used cardiac source models: the epicardial potential model and the equivalent dipole layer model. We discuss similarities and differences in applicability, strengths and weaknesses and sketch a road towards improved inverse solutions by targeted use, sequential application or a combination of the two methods.

An expert review of the inverse problem in electrocardiographic imaging for the non-invasive identification of atrial fibrillation drivers

BACKGROUND AND OBJECTIVE

Electrocardiographic imaging (ECGI) has emerged as a non-invasive approach to identify atrial fibrillation (AF) driver sources. This paper aims to collect and review the current research literature on the ECGI inverse problem, summarize the research progress, and propose potential research directions for the future.

METHODS AND RESULTS

The effectiveness and feasibility of using ECGI to map AF driver sources may be influenced by several factors, such as inaccuracies in the atrial model due to heart movement or deformation, noise interference in high-density body surface potential (BSP), inconvenient and time-consuming BSP acquisition, errors in solving the inverse problem, and incomplete interpretation of the AF driving source information derived from the reconstructed epicardial potential. We review the current research progress on these factors and discuss possible improvement directions. Additionally, we highlight the limitations of ECGI itself, including the lack of a gold standard to validate the accuracy of ECGI technology in locating AF drivers and the challenges associated with guiding AF ablation based on post-processed epicardial potentials due to the intrinsic difference between epicardial and endocardial potentials.

CONCLUSIONS

Before performing ablation, ECGI can provide operators with predictive information about the underlying locations of AF driver by non-invasively and globally mapping the biatrial electrical activity. In the future, endocardial catheter mapping technology may benefit from the use of ECGI to enhance the diagnosis and ablation of AF.

Comparison of dipole-based and potential-based ECGI methods for premature ventricular contraction beat localization with clinical data

Introduction: Localization of premature ventricular contraction (PVC) origin to guide the radiofrequency ablation (RFA) procedure is one of the prominent clinical goals of non-invasive electrocardiographic imaging. However, the results reported in the literature vary significantly depending on the source model and the level of complexity in the forward model. This study aims to compare the paced and spontaneous PVC localization performances of dipole-based and potential-based source models and corresponding inverse methods using the same clinical data and to evaluate the effects of torso inhomogeneities on these performances. Methods: The publicly available EP solution data from the EDGAR data repository (BSPs from a maximum of 240 electrodes) with known pacing locations and the Bratislava data (BSPs in 128 leads) with spontaneous PVCs from patients who underwent successful RFA procedures were used. Homogeneous and inhomogeneous torso models and corresponding forward problem solutions were used to relate sources on the closed epicardial and epicardial-endocardial surfaces. The localization error (LE) between the true and estimated pacing site/PVC origin was evaluated. Results: For paced data, the median LE values were 25.2 and 13.9 mm for the dipole-based and potential-based models, respectively. These median LE values were higher for the spontaneous PVC data: 30.2-33.0 mm for the dipole-based model and 28.9-39.2 mm for the potential-based model. The assumption of inhomogeneities in the torso model did not change the dipole-based solutions much, but using an inhomogeneous model improved the potential-based solutions on the epicardial-endocardial ventricular surface. Conclusion: For the specific task of localization of pacing site/PVC origin, the dipole-based source model is more stable and robust than the potential-based source model. The torso inhomogeneities affect the performances of PVC origin localization in each source model differently. Hence, care must be taken in generating patient-specific geometric and forward models depending on the source model representation used in electrocardiographic imaging (ECGI).

Investigation into the importance of using natural PVCs and pathological models for potential-based ECGI validation

Introduction: Premature ventricular contractions (PVCs) are one of the most commonly targeted pathologies for ECGI validation, often through ventricular stimulation to mimic the ectopic beat. However, it remains unclear if such stimulated beats faithfully reproduce spontaneously occurring PVCs, particularly in the case of the R-on-T phenomenon. The objective of this study was to determine the differences in ECGI accuracy when reconstructing spontaneous PVCs as compared to ventricular-stimulated beats and to explore the impact of pathophysiological perturbation on this reconstruction accuracy. Methods: Langendorff-perfused pig hearts (n = 3) were suspended in a human torso-shaped tank, and local hyperkalemia was induced through perfusion of a high-K⁺ solution (8 mM) into the LAD. Recordings were taken simultaneously from the heart and tank surfaces during ventricular pacing and during spontaneous PVCs (including R-on-T), both at baseline and high K⁺. Epicardial potentials were reconstructed from torso potentials using ECGI. Results: Spontaneously occurring PVCs were better reconstructed than stimulated beats at baseline in terms of electrogram morphology [correlation coefficient (CC) = 0.74 ± 0.05 vs. CC = 0.60 ± 0.10], potential maps (CC = 0.61 ± 0.06 vs. CC = 0.51 ± 0.12), and activation time maps (CC = 0.86 ± 0.07 vs. 0.76 ± 0.10), though there was no difference in the localization error (LE) of epicardial origin (LE = 14 ± 6 vs. 15 ± 11 mm). High K⁺ perfusion reduced the accuracy of ECGI reconstructions in terms of electrogram morphology (CC = 0.68 ± 0.10) and AT maps (CC = 0.70 ± 0.12 and 0.59 ± 0.23) for isolated PVCs and paced beats, respectively. LE trended worse, but the change was not significant (LE = 17 ± 9 and 20 ± 12 mm). Spontaneous PVCs were less well when the R-on-T phenomenon occurred and the activation wavefronts encountered a line of block. Conclusion: This study demonstrates the differences in ECGI accuracy between spontaneous PVCs and ventricular-paced beats. We also observed a reduction in this accuracy near regions of electrically inactive tissue. These results highlight the need for more physiologically realistic experimental models when evaluating the accuracy of ECGI methods. In particular, reconstruction accuracy needs to be further evaluated in the presence of R-on-T or isolated PVCs, particularly when encountering obstacles (functional or anatomical) which cause line of block and re-entry.

Electrocardiographic imaging in the atria

The inverse problem of electrocardiography or electrocardiographic imaging (ECGI) is a technique for reconstructing electrical information about cardiac surfaces from noninvasive or non-contact recordings. ECGI has been used to characterize atrial and ventricular arrhythmias. Although it is a technology with years of progress, its development to characterize atrial arrhythmias is challenging. Complications can arise when trying to describe the atrial mechanisms that lead to abnormal propagation patterns, premature or tachycardic beats, and reentrant arrhythmias. This review addresses the various ECGI methodologies, regularization methods, and post-processing techniques used in the atria, as well as the context in which they are used. The current advantages and limitations of ECGI in the fields of research and clinical diagnosis of atrial arrhythmias are outlined. In addition, areas where ECGI efforts should be concentrated to address the associated unsatisfied needs from the atrial perspective are discussed.

Improving Generalization by Learning Geometry-Dependent and Physics-Based Reconstruction of Image Sequences

Deep neural networks have shown promise in image reconstruction tasks, although often on the premise of large amounts of training data. In this paper, we present a new approach to exploit the geometry and physics underlying electrocardiographic imaging (ECGI) to learn efficiently with a relatively small dataset. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables over their respective geometrical domains. We then explicitly model the geometry-dependent physics in between the two domains via a bipartite graph over their graphical embeddings. We applied the resulting network to reconstruct electrical activity on the heart surface from body-surface potentials. In a series of generalization tasks with increasing difficulty, we demonstrated the improved ability of the network to generalize across geometrical changes underlying the data using less than 10% of training data and fewer variations of training geometry in comparison to its Euclidean alternatives. In both simulation and real-data experiments, we further demonstrated its ability to be quickly fine-tuned to new geometry using a modest amount of data.

Non-Contact Intracardiac Potential Mapping Using Mesh-Based and Meshless Inverse Solvers

Atrial fibrillation (AF) is the most common cardiac dysrhythmia and percutaneous catheter ablation is widely used to treat it. Panoramic mapping with multi-electrode catheters has been used to identify ablation targets in persistent AF but is limited by poor contact and inadequate coverage of the left atrial cavity. In this paper, we investigate the accuracy with which atrial endocardial surface potentials can be reconstructed from electrograms recorded with non-contact catheters. An in-silico approach was employed in which “ground-truth” surface potentials from experimental contact mapping studies and computer models were compared with inverse potential maps constructed by sampling the corresponding intracardiac field using virtual basket catheters. We demonstrate that it is possible to 1) specify the mixed boundary conditions required for mesh-based formulations of the potential inverse problem fully, and 2) reconstruct accurate inverse potential maps from recordings made with appropriately designed catheters. Accuracy improved when catheter dimensions were increased but was relatively stable when the catheter occupied >30% of atrial cavity volume. Independent of this, the capacity of non-contact catheters to resolve the complex atrial potential fields seen in reentrant atrial arrhythmia depended on the spatial distribution of electrodes on the surface bounding the catheter. Finally, we have shown that reliable inverse potential mapping is possible in near real-time with meshless methods that use the Method of Fundamental Solutions.

MUSIC: Cardiac Imaging, Modelling and Visualisation Software for Diagnosis and Therapy

The tremendous advancement of cardiac imaging methods, the substantial progress in predictive modelling, along with the amount of new investigative multimodalities, challenge the current technologies in the cardiology field. Innovative, robust and multimodal tools need to be created in order to fuse imaging data (e.g., MR, CT) with mapped electrical activity and to integrate those into 3D biophysical models. In the past years, several cross-platform toolkits have been developed to provide image analysis tools to help build such software. The aim of this study is to introduce a novel multimodality software platform dedicated to cardiovascular diagnosis and therapy guidance: MUSIC. This platform was created to improve the image-guided cardiovascular interventional procedures and is a robust platform for AI/Deep Learning, image analysis and modelling in a newly created consortium with international hospitals. It also helps our researchers develop new techniques and have a better understanding of the cardiac tissue properties and physiological signals. Thus, this extraction of quantitative information from medical data leads to more repeatable and reliable medical diagnoses.

Ex vivo Validation of Noninvasive Epicardial and Endocardial Repolarization Mapping

Background: The detection and localization of electrophysiological substrates currently involve invasive cardiac mapping. Electrocardiographic imaging (ECGI) using the equivalent dipole layer (EDL) method allows the noninvasive estimation of endocardial and epicardial activation and repolarization times (AT and RT), but the RT validation is limited to in silico studies. We aimed to assess the temporal and spatial accuracy of the EDL method in reconstructing the RTs from the surface ECG under physiological circumstances and situations with artificially induced increased repolarization heterogeneity.

Methods: In four Langendorff-perfused pig hearts, we simultaneously recorded unipolar electrograms from plunge needles and pseudo-ECGs from a volume-conducting container equipped with 61 electrodes. The RTs were computed from the ECGs during atrial and ventricular pacing and compared with those measured from the local unipolar electrograms. Regional RT prolongation (cooling) or shortening (pinacidil) was achieved by selective perfusion of the left anterior descending artery (LAD) region.

Results: The differences between the computed and measured RTs were 19.0 ± 17.8 and 18.6 ± 13.7 ms for atrial and ventricular paced beats, respectively. The region of artificially delayed or shortened repolarization was correctly identified, with minimum/maximum RT roughly in the center of the region in three hearts. In one heart, the reconstructed region was shifted by ~2.5 cm. The total absolute difference between the measured and calculated RTs for all analyzed patterns in selectively perfused hearts (n = 5) was 39.6 ± 27.1 ms.

Conclusion: The noninvasive ECG repolarization imaging using the EDL method of atrial and ventricular paced beats allows adequate quantitative reconstruction of regions of altered repolarization.

Non-invasive Estimation of Atrial Fibrillation Driver Position With Convolutional Neural Networks and Body Surface Potentials

Atrial fibrillation (AF) is characterized by complex and irregular propagation patterns, and AF onset locations and drivers responsible for its perpetuation are the main targets for ablation procedures. ECG imaging (ECGI) has been demonstrated as a promising tool to identify AF drivers and guide ablation procedures, being able to reconstruct the electrophysiological activity on the heart surface by using a non-invasive recording of body surface potentials (BSP). However, the inverse problem of ECGI is ill-posed, and it requires accurate mathematical modeling of both atria and torso, mainly from CT or MR images. Several deep learning-based methods have been proposed to detect AF, but most of the AF-based studies do not include the estimation of ablation targets. In this study, we propose to model the location of AF drivers from BSP as a supervised classification problem using convolutional neural networks (CNN). Accuracy in the test set ranged between 0.75 (SNR = 5 dB) and 0.93 (SNR = 20 dB upward) when assuming time independence, but it worsened to 0.52 or lower when dividing AF models into blocks. Therefore, CNN could be a robust method that could help to non-invasively identify target regions for ablation in AF by using body surface potential mapping, avoiding the use of ECGI.

Space-time shape uncertainties in the forward and inverse problem of electrocardiography

In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be perpetuated in the inverse reconstruction. The purpose of this work is to study the effect of shape uncertainty on the forward and the inverse problem of electrocardiography. To this aim, the problem is first recast into a boundary integral formulation and then discretised with a collocation method to achieve high convergence rates and a fast time to solution. The shape uncertainty of the domain is represented by a random deformation field defined on a reference configuration. We propose a periodic-in-time covariance kernel for the random field and approximate the Karhunen-Loève expansion using low-rank techniques for fast sampling. The space-time uncertainty in the expected potential and its variance is evaluated with an anisotropic sparse quadrature approach and validated by a quasi-Monte Carlo method. We present several numerical experiments on a simplified but physiologically grounded two-dimensional geometry to illustrate the validity of the approach. The tested parametric dimension ranged from 100 up to 600. For the forward problem, the sparse quadrature is very effective. In the inverse problem, the sparse quadrature and the quasi-Monte Carlo method perform as expected, except for the total variation regularisation, where convergence is limited by lack of regularity. We finally investigate an H1/2 regularisation, which naturally stems from the boundary integral formulation, and compare it to more classical approaches.

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.

Deep learning formulation of electrocardiographic imaging integrating image and signal information with data-driven regularization

AIMS

Electrocardiographic imaging (ECGI) is a promising tool to map the electrical activity of the heart non-invasively using body surface potentials (BSP). However, it is still challenging due to the mathematically ill-posed nature of the inverse problem to solve. Novel approaches leveraging progress in artificial intelligence could alleviate these difficulties.

METHODS AND RESULTS

We propose a deep learning (DL) formulation of ECGI in order to learn the statistical relation between BSP and cardiac activation. The presented method is based on Conditional Variational AutoEncoders using deep generative neural networks. To quantify the accuracy of this method, we simulated activation maps and BSP data on six cardiac anatomies.We evaluated our model by training it on five different cardiac anatomies (5000 activation maps) and by testing it on a new patient anatomy over 200 activation maps. Due to the probabilistic property of our method, we predicted 10 distinct activation maps for each BSP data. The proposed method is able to generate volumetric activation maps with a good accuracy on the simulated data: the mean absolute error is 9.40 ms with 2.16 ms standard deviation on this testing set.

CONCLUSION

The proposed formulation of ECGI enables to naturally include imaging information in the estimation of cardiac electrical activity from BSP. It naturally takes into account all the spatio-temporal correlations present in the data. We believe these features can help improve ECGI results.

The effect of interpolating low amplitude leads on the inverse reconstruction of cardiac electrical activity

Electrocardiographic imaging is an imaging modality that has been introduced recently to help in visualizing the electrical activity of the heart and consequently guide the ablation therapy for ventricular arrhythmias. One of the main challenges of this modality is that the electrocardiographic signals recorded at the torso surface are contaminated with noise from different sources. Low amplitude leads are more affected by noise due to their low peak-to-peak amplitude. In this paper, we have studied 6 datasets from two torso tank experiments (Bordeaux and Utah experiments) to investigate the impact of removing or interpolating these low amplitude leads on the inverse reconstruction of cardiac electrical activity. Body surface potential maps used were calculated by using the full set of recorded leads, removing 1, 6, 11, 16, or 21 low amplitude leads, or interpolating 1, 6, 11, 16, or 21 low amplitude leads using one of the three interpolation methods - Laplacian interpolation, hybrid interpolation, or the inverse-forward interpolation. The epicardial potential maps and activation time maps were computed from these body surface potential maps and compared with those recorded directly from the heart surface in the torso tank experiments. There was no significant change in the potential maps and activation time maps after the removal of up to 11 low amplitude leads. Laplacian interpolation and hybrid interpolation improved the inverse reconstruction in some datasets and worsened it in the rest. The inverse forward interpolation of low amplitude leads improved it in two out of 6 datasets and at least remained the same in the other datasets. It was noticed that after doing the inverse-forward interpolation, the selected lambda value was closer to the optimum lambda value that gives the inverse solution best correlated with the recorded one.

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.

Electrocardiographic Imaging: A Comparison of Iterative Solvers

Cardiac disease is a leading cause of morbidity and mortality in developed countries. Currently, non-invasive techniques that can identify patients at risk and provide accurate diagnosis and ablation guidance therapy are under development. One of these is electrocardiographic imaging (ECGI). In ECGI, the first step is to formulate a forward problem that relates the unknown potential sources on the cardiac surface to the measured body surface potentials. Then, the unknown potential sources on the cardiac surface are reconstructed through the solution of an inverse problem. Unfortunately, ECGI still lacks accuracy due to the underlying inverse problem being ill-posed, and this consequently imposes limitations on the understanding and treatment of many cardiac diseases. Therefore, it is necessary to improve the solution of the inverse problem. In this work, we transfer and adapt four inverse problem methods to the ECGI setting: algebraic reconstruction technique (ART), random ART, ART Split Bregman (ART-SB) and range restricted generalized minimal residual (RRGMRES) method. We test all these methods with data from the Experimental Data and Geometric Analysis Repository (EDGAR) and compare their solution with the recorded epicardial potentials provided by EDGAR and a generalized minimal residual (GMRES) iterative method computed solution. Activation maps are also computed and compared. The results show that ART achieved the most stable solutions and, for some datasets, returned the best reconstruction. Differences between the solutions derived from ART and random ART are almost negligible, and the accuracy of their solutions is followed by RRGMRES, ART-SB and finally the GMRES (which returned the worst reconstructions). The RRGMRES method provided the best reconstruction for some datasets but appeared to be less stable than ART when comparing different datasets. In conclusion, we show that the proposed methods (ART, random ART, and RRGMRES) improve the GMRES solution, which has been suggested as inverse problem solution for ECGI.

IRN-MLSQR: An improved iterative reweight norm approach to the inverse problem of electrocardiography incorporating factorization-free preconditioned LSQR

The inverse problem of electrocardiography (ECG) of computing epicardial potentials from body surface potentials, is an ill-posed problem and needs to be solved by regularization techniques. The L2-norm regularization can cause considerable smoothing of the solution, while the L1-norm scheme promotes a solution with sharp boundaries/gradients between piecewise smooth regions, so L1-norm is widely used in the ECG inverse problem. However, large amount of computation and long computation time are needed in the L1-norm scheme. In this paper, by combining iterative reweight norm (IRN) with a factorization-free preconditioned LSQR algorithm (MLSQR), a new IRN-MLSQR method was proposed to accelerate the convergence speed of the L1-norm scheme. We validated the IRN-MLSQR method using experimental data from isolated canine hearts and clinical procedures in the electrophysiology laboratory. The results showed that the IRN-MLSQR method can significantly reduce the number of iterations and operation time while ensuring the calculation accuracy. The number of iterations of the IRN-MLSQR method is about 60%-70% that of the conventional IRN method, and at the same time, the accuracy of the solution is almost the same as that of the conventional IRN method. The proposed IRN-MLSQR method may be used as a new approach to the inverse problem of ECG.

The Arrhythmic Substrate for Atrial Fibrillation in Patients with Mitral Regurgitation

Objective

Patients with severe mitral regurgitation commonly develop atrial fibrillation. The precise mechanisms of this relationship remain unknown. The objective of this study was to apply noninvasive electrocardiographic imaging of the atria during sinus rhythm to identify changes in atrial electrophysiology that may contribute to development of atrial fibrillation in patients with severe mitral regurgitation referred for mitral valve surgery.

Methods

Twenty subjects (9 atrial fibrillation and mitral regurgitation, 11 mitral regurgitation alone) underwent electrocardiographic imaging. Biatrial electrophysiology was imaged with activation maps in sinus rhythm. The reconstructed unipolar electrograms were analyzed for voltage amplitude, number of deflections and conduction heterogeneity. In subjects with mitral regurgitation, left atrial biopsies were obtained at the time of surgery. Results: Subjects with history of atrial fibrillation demonstrated prolonged left atrial conduction times (110±25 ms vs. mitral regurgitation alone (85±21), p=0.025); right atrial conduction times were unaffected. Variable patterns of conduction slowing were imaged in the left atria of most subjects, but those with prior history of atrial fibrillation had more complex patterns of conduction slowing or unidirectional block. The presence of atrial fibrillation was not associated with the extent of fibrosis in atrial biopsies.

Conclusions

Detailed changes in sinus rhythm atrial electrophysiology can be imaged noninvasively and can be used to assess the impact and evolution of atrial fibrillation on atrial conduction properties in patients with mitral regurgitation. If replicated in larger studies, electrocardiographic imaging may identify patients with mitral regurgitation at risk for atrial fibrillation and could be used to guide treatment strategies.

Electrocardiographic imaging for cardiac arrhythmias and resynchronization therapy

Use of the 12-lead electrocardiogram (ECG) is fundamental for the assessment of heart disease, including arrhythmias, but cannot always reveal the underlying mechanism or the location of the arrhythmia origin. Electrocardiographic imaging (ECGi) is a non-invasive multi-lead ECG-type imaging tool that enhances conventional 12-lead ECG. Although it is an established technology, its continuous development has been shown to assist in arrhythmic activation mapping and provide insights into the mechanism of cardiac resynchronization therapy (CRT). This review addresses the validity, reliability, and overall feasibility of ECGi for use in a diverse range of arrhythmias. A systematic search limited to full-text human studies published in peer-reviewed journals was performed through Medline via PubMed, using various combinations of three key concepts: ECGi, arrhythmia, and CRT. A total of 456 studies were screened through titles and abstracts. Ultimately, 42 studies were included for literature review. Evidence to date suggests that ECGi can be used to provide diagnostic insights regarding the mechanistic basis of arrhythmias and the location of arrhythmia origin. Furthermore, ECGi can yield valuable information to guide therapeutic decision-making, including during CRT. Several studies have used ECGi as a diagnostic tool for atrial and ventricular arrhythmias. More recently, studies have tested the value of this technique in predicting outcomes of CRT. As a non-invasive method for assessing cardiovascular disease, particularly arrhythmias, ECGi represents a significant advancement over standard procedures in contemporary cardiology. Its full potential has yet to be fully explored.

In silico validation of electrocardiographic imaging to reconstruct the endocardial and epicardial repolarization pattern using the equivalent dipole layer source model

The solution of the inverse problem of electrocardiology allows the reconstruction of the spatial distribution of the electrical activity of the heart from the body surface electrocardiogram (electrocardiographic imaging, ECGI). ECGI using the equivalent dipole layer (EDL) model has shown to be accurate for cardiac activation times. However, validation of this method to determine repolarization times is lacking. In the present study, we determined the accuracy of the EDL model in reconstructing cardiac repolarization times, and assessed the robustness of the method under less ideal conditions (addition of noise and errors in tissue conductivity). A monodomain model was used to determine the transmembrane potentials in three different excitation-repolarization patterns (sinus beat and ventricular ectopic beats) as the gold standard. These were used to calculate the body surface ECGs using a finite element model. The resulting body surface electrograms (ECGs) were used as input for the EDL-based inverse reconstruction of repolarization times. The reconstructed repolarization times correlated well (COR > 0.85) with the gold standard, with almost no decrease in correlation after adding errors in tissue conductivity of the model or noise to the body surface ECG. Therefore, ECGI using the EDL model allows adequate reconstruction of cardiac repolarization times. Graphical abstract Validation of electrocardiographic imaging for repolarization using forward calculated body surface ECGs from simulated activation-repolarization sequences.

Spatial-dependent regularization to solve the inverse problem in electromyometrial imaging

Recently, electromyometrial imaging (EMMI) was developed to non-invasively image uterine contractions in three dimensions. EMMI collects body surface electromyography (EMG) measurements and uses patient-specific body-uterus geometry generated from magnetic resonance images to reconstruct uterine electrical activity. Currently, EMMI uses the zero-order Tikhonov method with mean composite residual and smoothing operator (CRESO) to stabilize the underlying ill-posed inverse computation. However, this method is empirical and implements a global regularization parameter over all uterine sites, which is sub-optimal for EMMI given the severe eccentricity of body-uterus geometry. To address this limitation, we developed a spatial-dependent (SP) regularization method that considers both body-uterus eccentricity and EMG noise. We used electrical signals simulated with spherical and realistic geometry models to compare the reconstruction accuracy of the SP method to those of the CRESO and the L-Curve methods. The SP method reconstructed electrograms and potential maps more accurately than the other methods, especially in cases of high eccentricity and noise contamination. Thus, the SP method should facilitate clinical use of EMMI and can be used to improve the accuracy of other electrical imaging modalities, such as Electrocardiographic Imaging. Graphical abstract The spatial-dependent regularization (SP) technique was designed to improve the accuracy of Electromyometrial Imaging (EMMI). The top panel shows the eccentricity of body-uterus geometry and four representative body surface electrograms. The bottom panel shows boxplots of correlation coefficients and relative errors for the electrograms reconstructed with SP and two conventional methods, the L-Curve and mean CRESO methods.

How personalized heart modeling can help treatment of lethal arrhythmias: A focus on ventricular tachycardia ablation strategies in post-infarction patients

Precision Cardiology is a targeted strategy for cardiovascular disease prevention and treatment that accounts for individual variability. Computational heart modeling is one of the novel approaches that have been developed under the umbrella of Precision Cardiology. Personalized computational modeling of patient hearts has made strides in the development of models that incorporate the individual geometry and structure of the heart as well as other patient-specific information. Of these developments, one of the potentially most impactful is the research aimed at noninvasively predicting the targets of ablation of lethal arrhythmia, ventricular tachycardia (VT), using patient-specific models. The approach has been successfully applied to patients with ischemic cardiomyopathy in proof-of-concept studies. The goal of this paper is to review the strategies for computational VT ablation guidance in ischemic cardiomyopathy patients, from model developments to the intricacies of the actual clinical application. To provide context in describing the road these computational modeling applications have undertaken, we first review the state of the art in VT ablation in the clinic, emphasizing the benefits that personalized computational prediction of ablation targets could bring to the clinical electrophysiology practice. This article is characterized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Translational, Genomic, and Systems Medicine > Translational Medicine.

Noninvasive Mapping and Electrocardiographic Imaging in Atrial and Ventricular Arrhythmias (CardioInsight)

Electrocardiographic imaging is a mapping technique aiming to noninvasively characterize cardiac electrical activity using signals collected from the torso to reconstruct epicardial potentials. Its efficacy has been demonstrated clinically, from mapping premature ventricular complexes and accessory pathways to of complex arrhythmias. Electrocardiographic imaging uses a standardized workflow. Signals should be checked manually to avoid automatic processing errors. Reentry is confirmed in the presence of local activation covering the arrhythmia cycle length. Focal breakthroughs demonstrate a QS pattern associated with centrifugal activation. Electrocardiographic imaging offers a unique opportunity to better understand the mechanism of cardiac arrhythmias and guide ablation.

Advantages and pitfalls of noninvasive electrocardiographic imaging

BACKGROUND

With increasing clinical use of Electrocardiographic Imaging (ECGI), it is imperative to understand the limits of this technique. The objective of this study is to evaluate a potential-based ECGI approach for activation and repolarization mapping in sinus rhythm.

METHOD

Langendorff-perfused pig hearts were suspended in a human-shaped torso tank. Electrograms were recorded with a 108-electrode sock and ECGs with 256 electrodes embedded in the tank surface. Left bundle branch block (LBBB) was developed in 4 hearts through ablation, and repolarization abnormalities in another 4 hearts through regional perfusion of dofetilide and pinacidil. Electrograms were noninvasively reconstructed and reconstructed activation and repolarization features were compared to those recorded.

RESULTS

Visual consistency between ECGI and recorded activation and repolarization maps was high. While reconstructed repolarization times showed significantly more error than activation times quantitatively, patterns were reconstructed with a similar level of accuracy. The number of epicardial breakthrough sites was underestimated by ECGI and these were misplaced (>20 mm) in location. Likewise, ECGI reconstructed activation maps demonstrated artificial lines of block resulting from a W-shaped QRS waveform that were not present in recorded maps. Nevertheless, ECGI allowed identification of regions of abnormal repolarization reasonably accurately in terms of size, location and timing.

CONCLUSIONS

This study validates a potential-based ECGI approach to noninvasively image activation and recovery in sinus rhythm. Despite inaccuracies in epicardial breakthroughs and lines of conduction block, other important clinical features such as regions of abnormal repolarization can be accurately derived making ECGI a valuable clinical tool.

Effects of Heart Rate and Ventricular Wall Thickness on Non-invasive Mapping: An in silico Study

Background: Non-invasive cardiac mapping—also known as Electrocardiographic imaging (ECGi)—is a novel, painless and relatively economic method to map the electrical activation and repolarization patterns of the heart, providing a valuable tool for early identification and diagnosis of conduction abnormalities and arrhythmias. Moreover, the ability to obtain information on cardiac electrical activity non-invasively using ECGi provides the potential for a priori information to guide invasive surgical procedures, improving success rates, and reducing procedure time.

Previous studies have shown the influence of clinical variables, such as heart rate, heart size, endocardial wall, and body composition on surface electrocardiogram (ECG) measurements. The influence of clinical variables on the ECG variability has provided information on cardiovascular control and its abnormalities in various pathologies. However, the effects of such clinical variables on the Body Surface Potential (BSP) and ECGi maps have yet to be systematically investigated.

Methods: In this study we investigated the effects of heart size, intracardiac thickness, and heart rate on BSP and ECGi maps using a previously-developed 3D electrophysiologically-detailed ventricles-torso model. The inverse solution was solved using the three different Tikhonov regularization methods.

Results: Through comparison of multiple measures of error/accuracy on the ECGi reconstructions, our results showed that using different heart geometries to solve the forward and inverse problems produced a larger estimated focal excitation location. An increase of ~2 mm in the Euclidean distance error was observed for an increase in the heart size. However, the estimation of the location of focal activity was still able to be obtained. Similarly, a Euclidean distance increase was observed when the order of regularization was reduced.

For the case of activation maps reconstructed at the same ectopic focus location but different heart rates, an increase in the errors and Euclidean distance was observed when the heart rate was increased.

Conclusions: Non-invasive cardiac mapping can still provide useful information about cardiac activation patterns for the cases when a different geometry is used for the inverse problem compared to the one used for the forward solution; rapid pacing rates can induce order-dependent errors in the accuracy of reconstruction.

ECG Imaging to Detect the Site of Ventricular Ischemia Using Torso Electrodes: A Computational Study

Electrocardiography provides some information useful for ischemic diagnosis. However, more recently there has been substantial growth in the area of ECG imaging, which by solving the inverse problem of electrocardiography aims to produce high-resolution mapping of the electrical and magnetic dynamics of the heart. Most inverse studies use the full resolution of the body surface potential (BSP) to reconstruct the epicardial potentials, however using a limited number of torso electrodes to interpolate the BSP is more clinically relevant and has an important effect on the reconstruction which must be quantified. A circular ischemic lesion on the right ventricle lateral wall 27 mm in radius is reconstructed using three Tikhonov methods along with 6 different electrode configurations ranging from 32 leads to 1,024 leads. The 2nd order Tikhonov solution performed the most accurately (~80% lesion identified) followed by the 1st (~50% lesion identified) and then the 0 order Tikhonov solution performed the worst with a maximum of ~30% lesion identified regardless of how many leads were used. With an increasing number of leads the solution produces less error, and the error becomes more localised around the lesion for all three regularisation methods. In noisy conditions, the relative performance gap of the 1st and 2nd order Tikhonov solutions was reduced, and determining an accurate regularisation parameter became relatively more difficult. Lesions located on the left ventricle walls were also able to be identified but comparatively to the right ventricle lateral wall performed marginally worse with lesions located on the interventricular septum being able to be indicated by the reconstructions but not successfully identified against the error. The quality of reconstruction was found to decrease as the lesion radius decreased, with a lesion radius of <20 mm becoming difficult to correctly identify against the error even when using >512 torso electrodes.

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.

Localization of Activation Origin on Patient-Specific Endocardial Surface by the Equivalent Double Layer (EDL) Source Model With Sparse Bayesian Learning

OBJECTIVE

Ablation treatment of ventricular arrhythmias can be facilitated by pre-procedure planning aided by electrocardiographic inverse solution, which can help to localize the origin of arrhythmia. Our aim was to improve localization accuracy of the inverse solution for activation originating on the left-ventricular endocardial surface, by using a sparse Bayesian learning (SBL).

METHODS

The inverse problem of electrocardiography was solved by reconstructing endocardial potentials from time integrals of body-surface electrocardiograms and from patient-specific geometry of the heart and torso for three patients with structurally normal ventricular myocardium, who underwent endocardial catheter mapping that included pace mapping. Complementary simulations using dipole sources in patient-specific geometry were also performed. The proposed method is using sparse property of the equivalent-double-layer (EDL) model of cardiac sources; it employs the SBL and makes use of the spatio-temporal features of the cardiac action potentials.

RESULTS

The mean localization error of the proposed method for pooled pacing sites ( n=52) was significantly smaller ( p=0.0039) than that achieved for the same patients in the study of Erem et al. Simulation experiments localized the source dipoles ( n=48) from forward-simulated potentials with the error of 9.4 ± 4.5 mm (mean ± SD).

CONCLUSION

The results of our clinical and simulation experiments demonstrate that localization of left-ventricular endocardial activation by means of the Bayesian approach, based on sparse representation of sources by EDL, is feasible and accurate.

SIGNIFICANCE

The proposed approach to localizing endocardial sources may have important applications in pre-procedure assessment of arrhythmias and in guiding their ablation treatment.

Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data

The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization.

Retrieving hidden atrial repolarization waves from standard surface ECGs

BACKGROUND

This study estimates atrial repolarization activities (Ta waves), which are typically hidden most of the time from body surface electrocardiography when diagnosing cardiovascular diseases. The morphology of Ta waves has been proven to be an important marker for the early sign of inferior injury, such as acute atrial infarction, or arrhythmia, such as atrial fibrillation. However, Ta waves are usually unseen except during conduction system malfunction, such as long QT interval or atrioventricular block. Therefore, justifying heart diseases based on atrial repolarization becomes impossible in sinus rhythm.

METHODS

We obtain TMPs in the atrial part of the myocardium which reflects the correct excitation sequence starting from the atrium to the end of the apex.

RESULTS

The resulting TMP shows the hidden atrial part of ECG waves.

CONCLUSIONS

This extraction makes many diseases, such as acute atrial infarction or arrhythmia, become easily diagnosed.

Localization of Activation Origin on Patient-Specific Epicardial Surface by Empirical Bayesian Method

OBJECTIVE

Ablation treatment of ventricular arrhythmias can be facilitated by pre-procedure planning aided by electrocardiographic inverse solution, which can help to localize the origin of arrhythmia. Our aim was to improve localization accuracy of the inverse solution by using a novel Bayesian approach.

METHODS

The inverse problem of electrocardiography was solved by reconstructing epicardial potentials from 120 body-surface electrocardiograms and from patient-specific geometry of the heart and torso for four patients suffering from scar-related ventricular tachycardia who underwent epicardial catheter mapping, which included pace-mapping. Simulations using dipole sources in patient-specific geometry were also performed. The proposed method, using dynamic spatio-temporal a priori constraints of the solution, was compared with classical Tikhonov methods based on fixed constraints.

RESULTS

The mean localization error of the proposed method for all available pacing sites (n=78) was significantly smaller than that achieved by Tikhonov methods; specifically, the localization accuracy for pacing in the normal tissue (n=17) was [Formula: see text] mm (mean ± SD) versus [Formula: see text] mm reported in the previous study using the same clinical data and Tikhonov regularization. Simulation experiments further supported these clinical findings.

CONCLUSION

The promising results of in vivo and in silico experiments presented in this study provide a strong incentive to pursuing further investigation of data-driven Bayesian methods in solving the electrocardiographic inverse problem.

SIGNIFICANCE

The proposed approach to localizing origin of ventricular activation sequence may have important applications in pre-procedure assessment of arrhythmias and in guiding their ablation treatment.

Reducing Error in ECG Forward Simulations With Improved Source Sampling

A continuing challenge in validating electrocardiographic imaging (ECGI) is the persistent error in the associated forward problem observed in experimental studies. One possible cause of this error is insufficient representation of the cardiac sources; cardiac source measurements often sample only the ventricular epicardium, ignoring the endocardium and the atria. We hypothesize that measurements that completely cover the pericardial surface are required for accurate forward solutions. In this study, we used simulated and measured cardiac potentials to test the effect of different levels of spatial source sampling on the forward simulation. Not surprisingly, increasing the source sampling over the atria reduced the average error of the forward simulations, but some sampling strategies were more effective than others. Uniform and random distributions of samples across the atrial surface were the most efficient strategies in terms of lowest error with the fewest sampling locations, whereas “single direction” strategies, i.e., adding to the atrioventricular (AV) plane or atrial roof only, were the least efficient. Complete sampling of the atria is needed to eliminate errors from missing cardiac sources, but while high density sampling that covers the entire atria yields the best results, adding as few as 11 electrodes on the atria can significantly reduce these errors. Future validation studies of the ECG forward simulations should use a cardiac source sampling that takes these considerations into account, which will, in turn, improve validation and understanding of ECGI.

Analyzing Source Sampling to Reduce Error in ECG Forward Simulations

A continuing challenge in validating ECG Imaging is the persistent error in the associated forward problem observed in experimental studies. One possible cause of error is insufficient representation of the cardiac sources, which is often measured from only the ventricular epicardium, ignoring the endocardium and the atria. We hypothesize that measurements that completely cover the heart are required for accurate forward solutions. In this study, we used simulated and measured cardiac potentials to test the effect of different levels of sampling on the forward simulation. We found that omitting source samples on the atria increases the peak RMS error by a mean of 464 μV when compared the the fully sampled cardiac surface. Increasing the sampling on the atria in stages reduced the average error of the forward simulation proportionally to the number of additional samples and revealed some strategies may reduce error with fewer samples, such as adding samples to the AV plane and the atrial roof. Based on these results, we can design a sampling strategy to use in future validation studies.

Rapid 12-lead automated localization method: Comparison to electrocardiographic imaging (ECGI) in patient-specific geometry

BACKGROUND

Rapid accurate localization of the site of ventricular activation origin during catheter ablation for ventricular arrhythmias could facilitate the procedure. Electrocardiographic imaging (ECGI) using large lead sets can localize the origin of ventricular activation. We have developed an automated method to identify sites of early ventricular activation in real time using the 12-lead ECG. We aim to compare the localization accuracy of ECGI and the automated method, identifying pacing sites/VT exit based on a patient-specific model.

METHODS

A patient undergoing ablation of VT on the left-ventricular endocardium and epicardium had 120-lead body-surface potential mapping (BSPM) recorded during the procedure. (1) ECGI methodology: The L1-norm regularization was employed to reconstruct epicardial potentials based on patient-specific geometry for localizing endocardial ventricular activation origin. We used the BSPM data corresponding to known endocardial pacing sites and a VT exit site identified by 3D contact mapping to analyze them offline. (2) The automatedmethod: location coordinates of pacing sites together with the time integral of the first 120 ms of the QRS complex of 3 ECG predictors (leads III, V2 and V6) were used to calculate patient-specific regression coefficients to predict the location of unknown sites of ventricular activation origin ("target" sites). Localization error was quantified over all pacing sites in millimeters by comparing the calculated location and the known reference location.

RESULTS

Localization was tested for 14 endocardial pacing sites and 1 epicardial VT exit site. For 14 endocardial pacing sites the mean localization error of the automated method was significantly lower than that of the ECGI (8.9 vs. 24.9 mm, p < 0.01), when 10 training pacing sites are used. Emulation of a clinical procedure demonstrated that the automated method achieved localization error of <5 mm for the VT-exit site; while the ECGI approach approximately correlates with the site of VT exit from the scar within a distance of 18.4 mm.

CONCLUSIONS

The automated method using only 3 ECGs shows promise to localize the origin of ventricular activation as tested by pacing, and the VT-exit site and compares favourably to inverse solution calculation, avoiding cumbersome lead sets. As 12-lead ECG data is acquired by current 3D mapping systems, it is conceivable that the algorithm could be directly incorporated into a mapping system. Further validation in a prospective cohort study is needed to confirm and extend observations reported in this study.

Characterizing the Location and Extent of Myocardial Infarctions With Inverse ECG Modeling and Spatiotemporal Regularization

Myocardial infarction (MI) is among the leading causes of death in the United States. It is imperative to identify and characterize MIs for timely delivery of life-saving medical interventions. Cardiac electrical activity propagates in space and evolves over time. Traditional works focus on the analysis of time-domain ECG (e.g., 12-lead ECG) on the body surface for the detection of MIs, but tend to overlook spatiotemporal dynamics in the heart. Body surface potential mappings (BSPMs) provide high-resolution distribution of electric potentials over the entire torso, and therefore provide richer information than 12-lead ECG. However, BSPM are available on the body surface. Clinicians are in need of a closer look of the electric potentials in the heart to investigate cardiac pathology and optimize treatment strategies. In this paper, we applied the method of spatiotemporal inverse ECG (ST-iECG) modeling to map electrical potentials from the body surface to the heart, and then characterize the location and extent of MIs by investigating the reconstructed heart-surface electrograms. First, we investigate the impact of mesh resolution on the inverse ECG modeling. Second, we solve the inverse ECG problem and reconstruct heart-surface electrograms using the ST-iECG model. Finally, we propose a wavelet-clustering method to investigate the pathological behaviors of heart-surface electrograms, and thereby characterize the extent and location of MIs. The proposed methodology is evaluated and validated with real data of MIs from human subjects. Experimental results show that negative QRS waves in heart-surface electrograms indicate potential regions of MI, and the proposed ST-iECG model yields superior characterization results of MIs on the heart surface over existing methods.

Three-Dimensional Noninvasive Imaging of Ventricular Arrhythmias in Patients With Premature Ventricular Contractions

OBJECTIVE

Noninvasive imaging of cardiac electrical activity promises to provide important information regarding the underlying arrhythmic substrates for successful ablation intervention and further understanding of the mechanism of such lethal disease. The aim of this study is to evaluate the performance of a novel 3-D cardiac activation imaging technique to noninvasively localize and image origins of focal ventricular arrhythmias in patients undergoing radio frequency ablation.

METHODS

Preprocedural ECG gated contrast enhanced cardiac CT images and body surface potential maps were collected from 13 patients within a week prior to the ablation. The electrical activation images were estimated over the 3-D myocardium using a cardiac electric sparse imaging technique, and compared with CARTO activation maps and the ablation sites in the same patients.

RESULTS

Noninvasively-imaged activation sequences were consistent with the CARTO mapping results with an average correlation coefficient of 0.79, average relative error of 0.19, and average relative resolution error of 0.017. The imaged initiation sites of premature ventricular contractions (PVCs) were, on average, within 8 mm of the last successful ablation site and within 3 mm of the nearest ablation site.

CONCLUSION

The present results demonstrate the excellent performance of the 3-D cardiac activation imaging technique in imaging the activation sequence associated with PVC, and localizing the initial sites of focal ventricular arrhythmias in patients. These promising results suggest that the 3-D cardiac activation imaging technique may become a useful tool for aiding clinical diagnosis and management of ventricular arrhythmias.

Activation recovery interval imaging of premature ventricular contraction

Dispersion of ventricular repolarization due to abnormal activation contributes to the susceptibility to cardiac arrhythmias. However, the global pattern of repolarization is difficult to assess clinically. Activation recovery interval (ARI) has been used to understand the properties of ventricular repolarization. In this study, we developed an ARI imaging technique to noninvasively reconstruct three-dimensional (3D) ARI maps in 10 premature ventricular contraction (PVC) patients and evaluated the results with the endocardial ARI maps recorded by a clinical navigation system (CARTO). From the analysis results of a total of 100 PVC beats in 10 patients, the average correlation coefficient is 0.86±0.05 and the average relative error is 0.06±0.03. The average localization error is 4.5±2.3 mm between the longest ARI sites in 3D ARI maps and those in CARTO endocardial ARI maps. The present results suggest that ARI imaging could serve as an alternative of evaluating global pattern of ventricular repolarization noninvasively and could assist in the future investigation of the relationship between global repolarization dispersion and the susceptibility to cardiac arrhythmias.

Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart

Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.

Localization of ventricular activation origin using patient-specific geometry: Preliminary results

BACKGROUND AND OBJECTIVES

Catheter ablation of ventricular tachycardia (VT) may include induction of VT and localization of VT-exit site. Our aim was to assess localization performance of a novel statistical pace-mapping method and compare it with performance of an electrocardiographic inverse solution.

METHODS

Seven patients undergoing ablation of VT (4 with epicardial, 3 with endocardial exit) aided by electroanatomic mapping underwent intraprocedural 120-lead body-surface potential mapping (BSPM). Two approaches to localization of activation origin were tested: (1) A statistical method, based on multiple linear regression (MLR), which required only the conventional 12-lead ECG for a sufficient number of pacing sites with known origin together with patient-specific geometry of the endocardial/epicardial surface obtained by electroanatomic mapping; and (2) a classical deterministic inverse solution for recovering heart-surface potentials, which required BSPM and patient-specific geometry of the heart and torso obtained via computed tomography (CT).

RESULTS

For the MLR method, at least 10-15 pacing sites with known coordinates, together with their corresponding 12-lead ECGs, were required to derive reliable patient-specific regression equations, which then enabled accurate localization of ventricular activation with unknown origin. For 4 patients who underwent epicardial mapping, the median of localization error for the MLR was significantly lower than that for the inverse solution (10.6 vs. 27.3 mm, P  =  0.034); a similar result held for 3 patients who underwent endocardial mapping (7.7 vs. 17.1 mm, P  =  0.017). The pooled localization error for all epicardial and endocardial sites was also significantly smaller for the MLR compared with the inverse solution (P  =  0.005).

CONCLUSIONS

The novel pace-mapping approach to localizing the origin of ventricular activation offers an easily implementable supplement and/or alternative to the preprocedure inverse solution; its simplicity makes it suitable for real-time applications during clinical catheter-ablation procedures.

Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart

Realistic electrocardiogram (ECG) simulation with numerical models is important for research linking cellular and molecular physiology to clinically observable signals, and crucial for patient tailoring of numerical heart models. However, ECG simulation with a realistic torso model is computationally much harder than simulation of cardiac activity itself, so that many studies with sophisticated heart models have resorted to crude approximations of the ECG. This paper shows how the classical concept of electrocardiographic lead fields can be used for an ECG simulation method that matches the realism of modern heart models. The accuracy and resource requirements were compared to those of a full-torso solution for the potential and scaling was tested up to 14,336 cores with a heart model consisting of 11 million nodes. Reference ECGs were computed on a 3.3 billion-node heart-torso mesh at 0.2 mm resolution. The results show that the lead-field method is more efficient than a full-torso solution when the number of simulated samples is larger than the number of computed ECG leads. While the initial computation of the lead fields remains a hard and poorly scalable problem, the ECG computation itself scales almost perfectly and, even for several hundreds of ECG leads, takes much less time than the underlying simulation of cardiac activity.

Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart

Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.

Mesh resolution impacts the accuracy of inverse and forward ECG problems

Electrocardiographic imaging (ECGI) has become an important medical diagnosis tool that assists scientists to noninvasively investigate cardiac electric activity. Many previous works have studied the inverse and forward ECG problems to understand how to reconstruct the cardiac electric activity from the body potential distribution. However, the inverse ECG problem is highly ill-conditioned and very sensitive to errors and noises. Thus, there is a need to study the sensitivity of inverse and forward ECG problems. In this paper, we investigated effects of mesh resolution on the accuracy of inverse and forward ECG problems. First, we employed the boundary element method to calculate the relationship between potential distributions on the body and heart surfaces and developed an algorithm to solve inverse and forward ECG problems. Second, we implemented the algorithm to solve the ECG problems in both a concentric spherical geometry and a realistic torso-heart geometry. Third, we evaluated the relative error between our solution and the analytical solution under the condition of different mesh resolutions. Experimental results explicitly show that the relative error in the inverse solution decreased from 30% to 17% when the mesh elements triangulating the two spheres increased from 24 to 400 in the concentric spherical geometry, and that decreased from 26% to 16% when the mesh elements triangulating the heart surface increased from 136 to 546 in the realistic torso-heart geometry.

Physics-driven Spatiotemporal Regularization for High-dimensional Predictive Modeling: A Novel Approach to Solve the Inverse ECG Problem

This paper presents a novel physics-driven spatiotemporal regularization (STRE) method for high-dimensional predictive modeling in complex healthcare systems. This model not only captures the physics-based interrelationship between time-varying explanatory and response variables that are distributed in the space, but also addresses the spatial and temporal regularizations to improve the prediction performance. The STRE model is implemented to predict the time-varying distribution of electric potentials on the heart surface based on the electrocardiogram (ECG) data from the distributed sensor network placed on the body surface. The model performance is evaluated and validated in both a simulated two-sphere geometry and a realistic torso-heart geometry. Experimental results show that the STRE model significantly outperforms other regularization models that are widely used in current practice such as Tikhonov zero-order, Tikhonov first-order and L1 first-order regularization methods.

Regularization Techniques for ECG Imaging during Atrial Fibrillation: A Computational Study

The inverse problem of electrocardiography is usually analyzed during stationary rhythms. However, the performance of the regularization methods under fibrillatory conditions has not been fully studied. In this work, we assessed different regularization techniques during atrial fibrillation (AF) for estimating four target parameters, namely, epicardial potentials, dominant frequency (DF), phase maps, and singularity point (SP) location. We use a realistic mathematical model of atria and torso anatomy with three different electrical activity patterns (i.e., sinus rhythm, simple AF, and complex AF). Body surface potentials (BSP) were simulated using Boundary Element Method and corrupted with white Gaussian noise of different powers. Noisy BSPs were used to obtain the epicardial potentials on the atrial surface, using 14 different regularization techniques. DF, phase maps, and SP location were computed from estimated epicardial potentials. Inverse solutions were evaluated using a set of performance metrics adapted to each clinical target. For the case of SP location, an assessment methodology based on the spatial mass function of the SP location, and four spatial error metrics was proposed. The role of the regularization parameter for Tikhonov-based methods, and the effect of noise level and imperfections in the knowledge of the transfer matrix were also addressed. Results showed that the Bayes maximum-a-posteriori method clearly outperforms the rest of the techniques but requires a priori information about the epicardial potentials. Among the purely non-invasive techniques, Tikhonov-based methods performed as well as more complex techniques in realistic fibrillatory conditions, with a slight gain between 0.02 and 0.2 in terms of the correlation coefficient. Also, the use of a constant regularization parameter may be advisable since the performance was similar to that obtained with a variable parameter (indeed there was no difference for the zero-order Tikhonov method in complex fibrillatory conditions). Regarding the different targets, DF and SP location estimation were more robust with respect to pattern complexity and noise, and most algorithms provided a reasonable estimation of these parameters, even when the epicardial potentials estimation was inaccurate. Finally, the proposed evaluation procedure and metrics represent a suitable framework for techniques benchmarking and provide useful insights for the clinical practice.

Noninvasive Imaging of Human Atrial Activation during Atrial Flutter and Normal Rhythm from Body Surface Potential Maps

Background

Knowledge of atrial electrophysiological properties is crucial for clinical intervention of atrial arrhythmias and the investigation of the underlying mechanism. This study aims to evaluate the feasibility of a novel noninvasive cardiac electrical imaging technique in imaging bi-atrial activation sequences from body surface potential maps (BSPMs).

Methods

The study includes 7 subjects, with 3 atrial flutter patients, and 4 healthy subjects with normal atrial activations. The subject-specific heart-torso geometries were obtained from MRI/CT images. The equivalent current densities were reconstructed from 208-channel BSPMs by solving the inverse problem using individual heart-torso geometry models. The activation times were estimated from the time instant corresponding to the highest peak in the time course of the equivalent current densities. To evaluate the performance, a total of 32 cycles of atrial flutter were analyzed. The imaged activation maps obtained from single beats were compared with the average maps and the activation maps measured from CARTO, by using correlation coefficient (CC) and relative error (RE).

Results

The cardiac electrical imaging technique is capable of imaging both focal and reentrant activations. The imaged activation maps for normal atrial activations are consistent with findings from isolated human hearts. Activation maps for isthmus-dependent counterclockwise reentry were reconstructed on three patients with typical atrial flutter. The method was capable of imaging macro counterclockwise reentrant loop in the right atrium and showed inter-atria electrical conduction through coronary sinus. The imaged activation sequences obtained from single beats showed good correlation with both the average activation maps (CC = 0.91±0.03, RE = 0.29±0.05) and the clinical endocardial findings using CARTO (CC = 0.70±0.04, RE = 0.42±0.05).

Conclusions

The noninvasive cardiac electrical imaging technique is able to reconstruct complex atrial reentrant activations and focal activation patterns in good consistency with clinical electrophysiological mapping. It offers the potential to assist in radio-frequency ablation of atrial arrhythmia and help defining the underlying arrhythmic mechanism.

Non-invasive imaging of ventricular activation during pacing and arrhythmia: Methods and validation

Cardiovascular disease continued to be a leading killer world widely. Each year, about 400,000 cases of sudden cardiac arrest are reported in the U.S. alone. Clinically, radio-frequency ablative procedure has become widely applied in the treatment of ventricular arrhythmia. Non-invasive approaches have been demonstrated to be able to provide important information on the arrhythmogenesis and potentially assist in the clinical practice. In this work, we develop and validate a novel temporal sparse based imaging method, Cardiac Electrical Sparse Imaging (CESI). Computer simulation and animal validation results demonstrate that the CESI approach is capable of imaging with improved accuracy and robustness by exploiting the temporal sparse property underlying cellular electrophysiology. Overall, a CC of 0.8, RE of 0.2 and LE (localization error) of 7 mm has been achieved on human realistic simulation and good accuracy has been observed in canine simultaneous mapping studies. Also, the technique maintains full temporal resolution (RRE <; 0.04) in terms of the activation sequence under various disturbances and in various pathologies such as premature ventricular complex and ventricular tachycardia. Our promising results indicate the excellent performance of noninvasive imaging of cardiac activation under various arrhythmias, and its potential for aiding clinical management of lethal ventricular arrhythmia.