Coupled Lattice Boltzmann Modeling of Bidomain Type Models in Cardiac Electrophysiology

Abstract

In this work, a modified coupling Lattice Boltzmann Model (LBM) in simulation of cardiac electrophysiology is developed in order to capture the detailed activities of macro- to micro-scale transport processes. The propagation of electrical activity in the human heart is mathematically modelled by bidomain type systems. As transmembrane potential evolves, we take into account domain anisotropical properties using intracellular and extracellular conductivity, such as in a pacemaker or an electrocardiogram, in both parallel and perpendicular directions to the fibers. The bidomain system represents multi-scale, stiff and strongly nonlinear coupled reaction-diffusion models that consists of a set of ordinary differential equations coupled with a set of partial differential equations. Due to dynamic and geometry complexity, numerical simulation and implementation of bidomain type systems are extremely challenging conceptual and computational problems but are very important in many real-life and biomedical applications. This paper suggests a modified LBM scheme, reliable, efficient, stable and easy to implement in the context of such bidomain systems. The numerical results demonstrate the effectiveness and accuracy of our approach using general methods for bidomain type systems and show good agreement with analytical solutions and numerical results reported in the literature.