Variational Bayesian electrophysiological imaging of myocardial infarction

Solving the Inverse Problem of Electrocardiography for Cardiac Digital Twins: A Survey

Cardiac digital twins (CDTs) are personalized virtual representations used to understand complex cardiac mechanisms. A critical component of CDT development is solving the ECG inverse problem, which enables the reconstruction of cardiac sources and the estimation of patient-specific electrophysiology (EP) parameters from surface ECG data. Despite challenges from complex cardiac anatomy, noisy ECG data, and the ill-posed nature of the inverse problem, recent advances in computational methods have greatly improved the accuracy and efficiency of ECG inverse inference, strengthening the fidelity of CDTs. This paper aims to provide a comprehensive review of the methods for solving ECG inverse problems, their validation strategies, their clinical applications, and their future perspectives. For the methodologies, we broadly classify state-of-the-art approaches into two categories: deterministic and probabilistic methods, including both conventional and deep learning-based techniques. Integrating physics laws with deep learning models holds promise, but challenges such as capturing dynamic electrophysiology accurately, accessing accurate domain knowledge, and quantifying prediction uncertainty persist. Integrating models into clinical workflows while ensuring interpretability and usability for healthcare professionals is essential. Overcoming these challenges will drive further research in CDTs.

Toward Enabling Cardiac Digital Twins of Myocardial Infarction Using Deep Computational Models for Inverse Inference

Cardiac digital twins (CDTs) have the potential to offer individualized evaluation of cardiac function in a non-invasive manner, making them a promising approach for personalized diagnosis and treatment planning of myocardial infarction (MI). The inference of accurate myocardial tissue properties is crucial in creating a reliable CDT of MI. In this work, we investigate the feasibility of inferring myocardial tissue properties from the electrocardiogram (ECG) within a CDT platform. The platform integrates multi-modal data, such as cardiac MRI and ECG, to enhance the accuracy and reliability of the inferred tissue properties. We perform a sensitivity analysis based on computer simulations, systematically exploring the effects of infarct location, size, degree of transmurality, and electrical activity alteration on the simulated QRS complex of ECG, to establish the limits of the approach. We subsequently present a novel deep computational model, comprising a dual-branch variational autoencoder and an inference model, to infer infarct location and distribution from the simulated QRS. The proposed model achieves mean Dice scores of 0.457 ±0.317 and 0.302 ±0.273 for the inference of left ventricle scars and border zone, respectively. The sensitivity analysis enhances our understanding of the complex relationship between infarct characteristics and electrophysiological features. The in silico experimental results show that the model can effectively capture the relationship for the inverse inference, with promising potential for clinical application in the future. The code is available at https://github.com/lileitech/MI_inverse_inference.

Noninvasive Reconstruction of Transmural Transmembrane Potential With Simultaneous Estimation of Prior Model Error

To reconstruct electrical activity in the heart from body-surface electrocardiograms (ECGs) is an ill-posed inverse problem. Electrophysiological models have been found effective in regularizing these inverse problems by incorporating a priori knowledge about how the electrical potential in the heart propagates over time. However, these models suffer from model errors arising from, for example, parameters associated with tissue properties and the earliest sites of excitation. We present a Bayesian approach to simultaneously estimate transmembrane potential (TMP) signals and prior model errors, exploiting sparsity of the error in the gradient domain in the form of a novel sparse prior based on variational lower bound of the generalized Gaussian distribution. In synthetic and real-data experiments, we demonstrate the improvement of accuracy in TMP reconstruction brought by simultaneous model error estimation. We further provide theoretical and empirical justifications for the change of performances in the presented method at the presence of different model errors.

Examining the Impact of Prior Models in Transmural Electrophysiological Imaging: A Hierarchical Multiple-Model Bayesian Approach

Noninvasive cardiac electrophysiological (EP) imaging aims to mathematically reconstruct the spatiotemporal dynamics of cardiac sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, a fixed-model approach enforces the source distribution to follow a pre-assumed structure that does not always match the varying spatiotemporal distribution of actual sources. To understand the model-data relation and examine the impact of prior models, we present a multiple-model approach for volumetric cardiac EP imaging where multiple prior models are included and automatically picked by the available ECG data. Multiple models are incorporated as an Lp-norm prior for sources, where p is an unknown hyperparameter with a prior uniform distribution. To examine how different combinations of models may be favored by different measurement data, the posterior distribution of cardiac sources and hyperparameter p is calculated using a Markov Chain Monte Carlo (MCMC) technique. The importance of multiple-model prior was assessed in two sets of synthetic and real-data experiments, compared to fixed-model priors (using Laplace and Gaussian priors). The results showed that the posterior combination of models (the posterior distribution of p) as determined by the ECG data differed substantially when reconstructing sources with different sizes and structures. While the use of fixed models is best suited in situations where the prior assumption fits the actual source structures, the use of an automatically adaptive set of models may have the ability to better address model-data mismatch and to provide consistent performance in reconstructing sources with different properties.

Noninvasive electrocardiographic imaging of chronic myocardial infarct scar

BACKGROUND

Myocardial infarction (MI) scar constitutes a substrate for ventricular tachycardia (VT), and an accurate delineation of infarct scar may help to identify reentrant circuits and thus facilitate catheter ablation. One of the recent advancements in characterization of a VT substrate is its volumetric delineation within the ventricular wall by noninvasive electrocardiographic imaging. This paper compares, in four specific cases, epicardial and volumetric inverse solutions, using magnetic resonance imaging (MRI) with late gadolinium enhancement as a gold standard.

METHODS

For patients with chronic MI, who presented at Glasgow Western Infirmary, delayed-enhancement MRI and 120-lead body surface potential mapping (BSPM) data were acquired and 4 selected cases were later made available to a wider community as part of the 2007 PhysioNet/Computers in Cardiology Challenge. These data were used to perform patient-specific inverse solutions for epicardial electrograms and morphology-based criteria were applied to delineate infarct scar on the epicardial surface. Later, the Rochester group analyzed the same data by means of a novel inverse solution for reconstructing intramural transmembrane potentials, to delineate infarct scar in three dimensions. Comparison of the performance of three specific inverse-solution algorithms is presented here, using scores based on the 17-segment ventricular division scheme recommended by the American Heart Association.

RESULTS

The noninvasive methods delineating infarct scar as three-dimensional (3D) intramural distribution of transmembrane action potentials outperform estimates providing scar delineation on the epicardial surface in all scores used for comparison. In particular, the extent of infarct scar (its percentage mass relative to the total ventricular mass) is rendered more accurately by the 3D estimate. Moreover, the volumetric rendition of scar border provides better clues to potential targets for catheter ablation.

CONCLUSIONS

Electrocardiographic inverse solution providing transmural distribution of ventricular action potentials is a promising tool for noninvasively delineating the extent and location of chronic MI scar. Further validation on a larger data set with detailed gold-standard data is needed to confirm observations reported in this study.