Numerical Simulations for Cardiac Electrophysiology Problems

The systems of monodomain and bidomain equations are widely used in modeling of cardiac electrophysiology. The bidomain problem may be extended with an addition of electrically conductive bath to simulate the conductance of the human body. Recently, there has been a growing interest in developing numerical methods for these systems. They can be used in various clinical applications. The numerical solution of monodomain and bidomain equations on high-resolution meshes is computationally expensive in 3D. Thereby the corresponding computational frameworks should take advantage of High Performance Computing (HPC) architectures. Another challenge is to verify that a given code provides the correct numerical solution of the governing equations. In this work we present our approach for the solution of monodomain and bidomain equations based on Ani3D (Advanced Numerical Instruments) framework (Advanced Numerical Instruments 3D. https://sourceforge.net/p/ani3d ). We use finite element method on unstructured tetrahedral meshes for solving PDEs of the diffusion type. To calculate the ionic current density from a system of ODEs, we use CVODE software (Hindmarsh et al., ACM Trans Math Softw 31:363–396, 2005) and CellML repository (Yu et al., Bioinformatics 27:743–744, 2011). Verification of the computational model is conducted by several benchmarks. In order to parallelize the computation of the ionic currents in each node of the computational grid, we use the OpenMP technology. One of the advantages of the Ani3D framework is that it provides tools for usage of anisotropic grids and tensors, which are crucial in real heart modeling due to the essential anisotropic features of the myocardial tissue.