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

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.

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).

Localization of magnetocardiographic sources for myocardial infarction cases using deterministic and Bayesian approaches

In this paper, the inverse problems of cardiac sources using analytical and probabilistic methods are solved and discussed. The standard Tikhonov regularization technique is solved initially to estimate the under-determined heart surface potentials from Magnetocardiographic (MCG) signals. The results of the deterministic method subjected to noise in the measurements are discussed and compared with the probabilistic models. Hierarchical Bayesian modeling with fixed Gaussian prior is employed to quantify the uncertainties in source reconstructions. A novel application of Variational Bayesian inference approach has been presented to estimate the heart sources. The reconstruction results of Variational Bayesian model with non-stationary priors are compared with solutions of simplistic Bayesian approach; and the performances are evaluated using Root Mean Square Error (RMSE) and correlation co-efficient metrics. The Bayesian solutions in the study are also extended to localize the MCG sources for two types of Myocardial infarction cases.

Locally Adaptive Total p-Variation Regularization for Non-Rigid Image Registration With Sliding Motion

Due to the complicated thoracic movements which contain both sliding motion occurring at lung surfaces and smooth motion within individual organs, respiratory estimation is still an intrinsically challenging task. In this paper, we propose a novel regularization term called locally adaptive total p-variation (LaTpV) and embed it into a parametric registration framework to accurately recover lung motion. LaTpV originates from a modified L_p-norm constraint (1 < p < 2), where a prior distribution of p modeled by the Dirac-shaped function is constructed to specifically assign different values to voxels. LaTpV adaptively balances the smoothness and discontinuity of the displacement field to encourage an expected sliding interface. Additionally, we also analytically deduce the gradient of the cost function with respect to transformation parameters. To validate the performance of LaTpV, we not only test it on two mono-modal databases including synthetic images and pulmonary computed tomography (CT) images, but also on a more difficult thoracic CT and positron emission tomography (PET) dataset for the first time. For all experiments, both the quantitative and qualitative results indicate that LaTpV significantly surpasses some existing regularizers such as bending energy and parametric total variation. The proposed LaTpV based registration scheme might be more superior for sliding motion correction and more potential for clinical applications such as the diagnosis of pleural mesothelioma and the adjustment of radiotherapy plans.

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.

ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging

In electrocardiographic imaging (ECGI), one solves the inverse problem of electrocardiography (ECG) to reconstruct equivalent cardiac sources based on the body surface potential measurements and a mathematical model of the torso. Due to attenuation and spatial smoothing within the torso, this inverse problem is ill-posed. Among many regularization approaches used in the ECG literature to overcome this ill-posedness, statistical techniques have received great attention because of their flexibility to represent the data, and ability to provide performance evaluation tools for quantification of uncertainties and errors in the model. However, despite their potential to accurately reconstruct the equivalent cardiac sources, one major challenge in these methods is how to best utilize the prior information available in terms of training data. In this paper, we address the question of how to define the prior probability distributions (pdf) of the sources and the error terms so that we can obtain more accurate and robust inverse solutions. We employ two methods, maximum likelihood (ML) and maximum a posteriori (MAP), for estimating the model parameters such as the prior pdfs, error pdfs, and the state-transition matrix, based on the same training data. These model parameters are then used for the state-space representation and estimation of the epicardial potentials, which constitute the equivalent cardiac sources in this study. The performances of ML- and MAP-based model parameter estimation methods are evaluated qualitatively and quantitatively at various noise levels and geometric disturbances using two different simulated datasets. Bayesian MAP estimation, which is also a well-known statistical inversion technique, and Tikhonov regularization, which can be formulated as a special and simplified version of Bayesian MAP estimation, have been included here for comparison with the Kalman filtering method. Our results show that the state-space approach outperforms Bayesian MAP estimation in all cases; ML yields accurate results when the test and training beats come from the same physiological model, but MAP is superior to ML, especially if the test and training beats are from different physiological models. Graphical Abstract ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging.

Impact of the Endocardium in a Parameter Optimization to Solve the Inverse Problem of Electrocardiography

Electrocardiographic imaging aims at reconstructing cardiac electrical events from electrical signals measured on the body surface. The most common approach relies on the inverse solution of the Laplace equation in the torso to reconstruct epicardial potential maps from body surface potential maps. Here we apply a method based on a parameter identification problem to reconstruct both activation and repolarization times. From an ansatz of action potential, based on the Mitchell-Schaeffer ionic model, we compute body surface potential signals. The inverse problem is reduced to the identification of the parameters of the Mitchell-Schaeffer model. We investigate whether solving the inverse problem with the endocardium improves the results or not. We solved the parameter identification problem on two different meshes: one with only the epicardium, and one with both the epicardium and the endocardium. We compared the results on both the heart (activation and repolarization times) and the torso. The comparison was done on validation data of sinus rhythm and ventricular pacing. We found similar results with both meshes in 6 cases out of 7: the presence of the endocardium slightly improved the activation times. This was the most visible on a sinus beat, leading to the conclusion that inclusion of the endocardium would be useful in situations where endo-epicardial gradients in activation or repolarization times play an important role.

Evaluation of multivariate adaptive non-parametric reduced-order model for solving the inverse electrocardiography problem: a simulation study

In the inverse electrocardiography (ECG) problem, the goal is to reconstruct the heart's electrical activity from multichannel body surface potentials and a mathematical model of the torso. Over the years, researchers have employed various approaches to solve this ill-posed problem including regularization, optimization, and statistical estimation. It is still a topic of interest especially for researchers and clinicians whose goal is to adopt this technique in clinical applications. Among the wide range of mathematical tools available in the fields of operational research, inverse problems, optimization, and parameter estimation, spline-based techniques have been applied to inverse problems in several areas. If proper spline bases are chosen, the complexity of the problem can be significantly reduced while increasing estimation accuracy. However, there are few studies within the context of the inverse ECG problem that take advantage of this property of the spline-based approaches. In this paper, we evaluate the performance of Multivariate Adaptive Regression Splines (MARS)-based method for the solution of the inverse ECG problem using two different collections of simulated data. The results show that the MARS-based method improves the inverse ECG solutions and is "robust" to modeling errors, especially in terms of localizing the arrhythmia sources. Graphical Abstract Multivariate adaptive non-parametric model for inverse ECG problem.

Data assimilation and multisource decision-making in systems biology based on unobtrusive Internet-of-Things devices

Biological and medical diagnoses depend on high-quality measurements. A wearable device based on Internet of Things (IoT) must be unobtrusive to the human body to encourage users to accept continuous monitoring. However, unobtrusive IoT devices are usually of low quality and unreliable because of the limitation of technology progress that has slowed down at high peak. Therefore, advanced inference techniques must be developed to address the limitations of IoT devices. This review proposes that IoT technology in biological and medical applications should be based on a new data assimilation process that fuses multiple data scales from several sources to provide diagnoses. Moreover, the required technologies are ready to support the desired disease diagnosis levels, such as hypothesis test, multiple evidence fusion, machine learning, data assimilation, and systems biology. Furthermore, cross-disciplinary integration has emerged with advancements in IoT. For example, the multiscale modeling of systems biology from proteins and cells to organs integrates current developments in biology, medicine, mathematics, engineering, artificial intelligence, and semiconductor technologies. Based on the monitoring objectives of IoT devices, researchers have gradually developed ambulant, wearable, noninvasive, unobtrusive, low-cost, and pervasive monitoring devices with data assimilation methods that can overcome the limitations of devices in terms of quality measurement. In the future, the novel features of data assimilation in systems biology and ubiquitous sensory development can describe patients' physical conditions based on few but long-term measurements.

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.

Transfer Learning From Simulations on a Reference Anatomy for ECGI in Personalized Cardiac Resynchronization Therapy

GOAL

Noninvasive cardiac electrophysiology (EP) model personalisation has raised interest for instance in the scope of predicting EP cardiac resynchronization therapy (CRT) response. However, the restricted clinical applicability of current methods is due in particular to the limitation to simple situations and the important computational cost.

METHODS

We propose in this manuscript an approach to tackle these two issues. First, we analyze more complex propagation patterns (multiple onsets and scar tissue) using relevance vector regression and shape dimensionality reduction on a large simulated database. Second, this learning is performed offline on a reference anatomy and transferred onto patient-specific anatomies in order to achieve fast personalized predictions online.

RESULTS

We evaluated our method on a dataset composed of 20 dyssynchrony patients with a total of 120 different cardiac cycles. The comparison with a commercially available electrocardiographic imaging (ECGI) method shows a good identification of the cardiac activation pattern. From the cardiac parameters estimated in sinus rhythm, we predicted five different paced patterns for each patient. The comparison with the body surface potential mappings (BSPM) measured during pacing and the ECGI method indicates a good predictive power.

CONCLUSION

We showed that learning offline from a large simulated database on a reference anatomy was able to capture the main cardiac EP characteristics from noninvasive measurements for fast patient-specific predictions.

SIGNIFICANCE

The fast CRT pacing predictions are a step forward to a noninvasive CRT patient selection and therapy optimisation, to help clinicians in these difficult tasks.

Noninvasive Personalization of a Cardiac Electrophysiology Model From Body Surface Potential Mapping

GOAL

We use noninvasive data (body surface potential mapping, BSPM) to personalize the main parameters of a cardiac electrophysiological (EP) model for predicting the response to different pacing conditions.

METHODS

First, an efficient forward model is proposed, coupling the Mitchell-Schaeffer transmembrane potential model with a current dipole formulation. Then, we estimate the main parameters of the cardiac model: activation onset location and tissue conductivity. A large patient-specific database of simulated BSPM is generated, from which specific features are extracted to train a machine learning algorithm. The activation onset location is computed from a Kernel Ridge Regression and a second regression calibrates the global ventricular conductivity.

RESULTS

The evaluation of the results is done both on a benchmark dataset of a patient with premature ventricular contraction (PVC) and on five nonischaemic implanted cardiac resynchonization therapy (CRT) patients with a total of 21 different pacing conditions. Good personalization results were found in terms of the activation onset location for the PVC (mean distance error, MDE = 20.3 mm), for the pacing sites (MDE = 21.7 mm) and for the CRT patients (MDE = 24.6 mm). We tested the predictive power of the personalized model for biventricular pacing and showed that we could predict the new electrical activity patterns with a good accuracy in terms of BSPM signals.

CONCLUSION

We have personalized the cardiac EP model and predicted new patient-specific pacing conditions.

SIGNIFICANCE

This is an encouraging first step towards a noninvasive preoperative prediction of the response to different pacing conditions to assist clinicians for CRT patient selection and therapy planning.