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.

Sensitivity of Noninvasive Cardiac Electrophysiological Imaging to Variations in Personalized Anatomical Modeling.

OBJECTIVE: Noninvasive cardiac electrophysiological (EP) imaging techniques rely on anatomically-detailed heart-torso models derived from high-quality tomographic images of individual subjects. However, anatomical modeling involves variations that lead to unresolved uncertainties in the outcome of EP imaging, bringing questions to the robustness of these methods in clinical practice. In this study, we design a systematic statistical approach to assess the sensitivity of EP imaging methods to the variations in personalized anatomical modeling. METHODS: We first quantify the variations in personalized anatomical models by a novel application of statistical shape modeling. Given the statistical distribution of the variation in personalized anatomical models, we then employ unscented transform to determine the sensitivity of EP imaging outputs to the variation in input personalized anatomical modeling. RESULTS: We test the feasibility of our proposed approach using two of the existing EP imaging methods: epicardial-based electrocardiographic imaging and transmural electrophysiological imaging. Both phantom and real-data experiments show that variations in personalized anatomical models have negligible impact on the outcome of EP imaging. CONCLUSION: This study verifies the robustness of EP imaging methods to the errors in personalized anatomical modeling and suggests the possibility to simplify the process of anatomical modeling in future clinical practice. SIGNIFICANCE: This study proposes a systematic statistical approach to quantify anatomical modeling variations and assess their impact on EP imaging, which can be extended to find a balance between the quality of personalized anatomical models and the accuracy of EP imaging that may improve the clinical feasibility of EP imaging.

Hierarchical multiple-model Bayesian approach to transmural electrophysiological imaging.

Noninvasive electrophysiological (EP) imaging of the heart aims to mathematically reconstruct the spatiotemporal dynamics of cardiac current sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, this approach enforces the source distribution to follow a preassumed spatial structure that does not always match the varying spatiotemporal distribution of current sources. We propose a hierarchical Bayesian approach to transmural EP imaging that employs a continuous combination of multiple models, each reflecting a specific spatial property for current sources. Multiple models are incorporated as an Lp-norm prior for current sources, where p is an unknown hyperparameter with a prior probabilistic distribution. The current source estimation is obtained as an optimally weighted combination of solutions across all models, the weight being determined from the posterior distribution of p inferred from ECG data. The accuracy of our approach is assessed in a set of synthetic and real-data experiments on human heart-torso models. While the use of fixed models (L1- and L2-norm) only properly recovers sources with specific structures, our method delivers consistent performance in reconstructing sources with various extents and structures.

Lp-norm regularization in volumetric imaging of cardiac current sources.

Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart. In comparison, our ability to observe and analyze cardiac electrical activities is much limited. The progress to computationally reconstruct cardiac current sources from noninvasive voltage data sensed on the body surface has been hindered by the ill-posedness and the lack of a unique solution of the reconstruction problem. Common L2- and L1-norm regularizations tend to produce a solution that is either too diffused or too scattered to reflect the complex spatial structure of current source distribution in the heart. In this work, we propose a general regularization with Lp-norm (1 < p < 2) constraint to bridge the gap and balance between an overly smeared and overly focal solution in cardiac source reconstruction. In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents. Through computer-simulated and real-data experiments, we further demonstrate the feasibility of the proposed method in imaging the complex structure of excitation wavefront, as well as current sources distributed along the postinfarction scar border. This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.