Modeling The Invers Electrophysiology of the Heart Activation As Anisotropic Volume Source Inside Inhomogeneous Volume Conductor

The electrophysiological modeling of the heart involves two critical challenges: the Forward Problem and the Inverse Problem. While the Forward Problem calculates body surface potentials from known internal cardiac sources, the Inverse Problem seeks to identify the internal bioelectric source distribution from external body surface potential measurements. This study focuses on solving the Inverse Problem using three regularization-based methods: Minimum Norm (MN), Weighted Minimum Norm (WMN), and exact Low Resolution Brain Electromagnetic Tomography (eLORETA). Each method addresses the ill-posed nature of the problem by minimizing error in reconstructing source distributions. The inverse solutions are evaluated using varying electrode configurations and multiple source settings. Results demonstrate that eLORETA provides superior localization accuracy, particularly with single-source scenarios and higher electrode counts. A novel approach to resolve the challenge of boundary point localization is also proposed, enhancing accuracy in problematic regions like the endocardium. Simulations validate the effectiveness of regularization techniques, with eLORETA consistently outperforming MN and WMN methods.