Meshfree implementation of the cardiac monodomain model through the Fragile Points Method

TL;DR

This paper applies the Fragile Points Method, a meshfree numerical technique, to simulate cardiac electrophysiology, demonstrating comparable or better accuracy and efficiency than traditional FEM without requiring a mesh.

Contribution

It introduces the FPM for cardiac monodomain modeling, showing improved convergence and meshless simulation capabilities over FEM.

Findings

FPM achieves similar accuracy to FEM in benchmarks.

FPM demonstrates better convergence than FEM.

Meshless FPM reduces complexity in cardiac simulations.

Abstract

Meshfree methods for in silico modelling and simulation of cardiac electrophysiology are gaining more and more popularity. These methods do not require a mesh and are more suitable than the Finite Element Method (FEM) to simulate the activity of complex geometrical structures like the human heart. However, challenges such as numerical integration accuracy and time efficiency remain and limit their applicability. Recently, the Fragile Points Method (FPM) has been introduced in the meshfree methods family. It uses local, simple, polynomial, discontinuous functions to construct trial and test functions in the Galerkin weak form. This allows for accurate integration and improved efficiency while enabling the imposition of essential and natural boundary conditions as in the FEM. In this work, we consider the application of FPM for cardiac electrophysiology simulation. We derive the cardiac monodomain model using the FPM formulation and we solve several benchmark problems in 2D and 3D. We show that FPM leads to solutions of similar accuracy and efficiency with FEM while alleviating the need for a mesh. Additionally, FPM demonstrates better convergence than FEM in the considered benchmarks.