Efficient Generation of Membrane and Solvent Tetrahedral Meshes for Ion Channel Finite Element Calculation

TL;DR

This paper introduces new numerical schemes implemented in Python for efficient generation of high-quality tetrahedral meshes of ion channels, membranes, and solvents, improving mesh quality and computational performance for finite element ion channel simulations.

Contribution

The paper presents novel numerical schemes and a Python-based software package for generating complex tetrahedral meshes for ion channel simulations, enhancing efficiency and mesh quality.

Findings

New schemes significantly improve mesh quality.

Generated meshes enable more accurate ion channel simulations.

Software demonstrates high efficiency across various geometries.

Abstract

A finite element solution of an ion channel dielectric continuum model such as Poisson-Boltzmann equation (PBE) and a system of Poisson-Nernst-Planck equations (PNP) requires tetrahedral meshes for an ion channel protein region, a membrane region, and an ionic solvent region as well as an interface fitted irregular tetrahedral mesh of a simulation box domain. However, generating these meshes is very difficult and highly technical due to the related three regions having very complex geometrical shapes. Currently, an ion channel mesh generation software package developed in Lu's research group is one available in the public domain. To significantly improve its mesh quality and computer performance, in this paper, new numerical schemes for generating membrane and solvent meshes are presented and implemented in Python, resulting in a new ion channel mesh generation software package. Numerical results are then reported to demonstrate the efficiency of the new numerical schemes and the quality of meshes generated by the new package for ion channel proteins with ion channel pores having different geometric complexities.