A Novel Paradigm for In Silico Simulation of Cardiac Electrophysiology Through the Mixed Collocation Meshless Petrov-Galerkin Method

Multi-scale cardiac electrophysiological modeling involves high computational load due to the inherent complexity as well as to limitations of the employed numerical methods (e.g., Finite Element Method - FEM). This study investigates the use of the Meshless Local Petrov-Galerkin Mixed Collocation (MLPG-MC) method to simulate cardiac electrophysiology. MLPG-MC is a truly meshless method where both the unknown function and its gradient are interpolated using nodal collocation. A 3 cm × 3 cm human ventricular tissue was simulated based on the monodomain reaction-diffusion model using the operator splitting technique. MLPG-MC or FEM were used to solve the diffusion term and the O’Hara-Virág-Varró-Rudy AP model to represent cellular electrophysiology at baseline and under 30% I
Kr
inhibition (IKr30). Mean differences between MLPG-MC and FEM in AP duration at 90% (APD
90
), 50% (APD
50
) and 20% (APD
20
) repolarization levels were 4.47%, 4.16% and 3.29% for baseline conditions and 3.66%, 2.10% and 1.62% for IKr30 conditions. The computational time associated with each of the two methods was comparable. In conclusion, considering that MLPG-MC does not involve any mesh requirements and is well suited for massive parallelization, this study shows that it represents a promising alternative to FEM for cardiac electrophysiology simulations.