A numerical scheme for modeling wavefront propagation on a monolayer of arbitrary geometry

Area of Science:

• Computational Biology
• Cardiac Electrophysiology
• Numerical Methods

Background:

• Existing cardiac wavefront propagation models often use simplified geometries.
• Simulating complex 3D cardiac tissue is computationally intensive and faces challenges in flux conservation.
• Accurate modeling of cardiac electrophysiology is crucial for understanding arrhythmias.

Purpose of the Study:

• To develop a computationally efficient method for simulating cardiac wavefront propagation in arbitrary 3D cardiac tissue shapes.
• To ensure local flux conservation in the simulation of reaction-diffusion systems.
• To provide a unified matrix formulation for calculating wavefront conduction and local electrograms.

Main Methods:

• Development of a generalized finite difference scheme (GDFS), a vertex-centered finite-volume method.
• Application of GDFS to simulate the reaction-diffusion system on 3D monolayers of arbitrary geometry.
• Utilizing a matrix formulation for computing wavefront conduction and local electrograms.

Main Results:

• GDFS successfully simulates wavefront propagation in 3D cardiac tissue with arbitrary shapes.
• The method ensures local flux conservation, a key requirement for accurate simulations.
• Reduced computational time compared to full 3D models at equivalent spatial resolution.
• Simulations were performed on simple and complex monolayers, including human atria models.

Conclusions:

• The generalized finite difference scheme (GDFS) offers an efficient and accurate approach for 3D cardiac electrophysiology simulations.
• GDFS overcomes computational challenges associated with complex geometries and flux conservation.
• The method's ability to model complex structures like human atria has significant implications for cardiac research.