An inverse model for localization of low-diffusivity regions in the heart using ECG/MCG sensor arrays

Cardiac activation and consequently performance of the heart can be severely affected by certain electrophysiological anomalies such as irregular patterns in the activation of the heart. Since the wavefront propagation occurs through the diffusion of ions (Na⁺, K⁺, etc.) the reduced mobility of ions can be equivalently represented as a reduction of ionic diffusivity causing irregularities in heartbeats. In this paper we propose models for the cardiac activation using inhomogeneous reaction-diffusion equations in the presence of diffusivity disorders. We also derive corresponding statistical signal processing algorithms for estimating (localizing) parameters describing these anomalies. We illustrate applicability of our techniques and demonstrate the identifiability of the parameters through numerical examples using a realistic geometry.