Finite Element Modelling for Biophysical Models of Nervous System Stimulation: Best Practices for Multiscale Adaptive Meshing

This paper presents methods for FEM modelling the peripheral and central nervous systems with considerations for meshing and computational constraints. FEM models in this context are convenient for testing hypothesises about the effects of different stimulation parameters and exploring different electrode designs before moving to in vitro and in vivo experiments. The methods presented in this paper are motivated by assessing differentiation errors from different mesh sizes and the transitions between different materials in the model. We aim to support the development of transparent and reproducible modelling experiments. Accurate and reproducible models are essential, given the importance of the applications in which these models are used. However, a dearth of literature is devoted to promoting best practices in finite element modelling for biophysical models. We evaluate the impact of differentiation errors on calculating the Activating Function and predicting action potentials in a Hodgkin-Huxley (H-H) axon model. We found that poor spatial discretisation facilitates the generation of double-derivative noise. However, it does not generate false predictions of action potentials on the H-H model. Activation thresholds were higher (57.5 mA) for coarser meshes than Fine and Extremely Fine (55 mA). Implementing Multiscale meshes with the finest refined sizes reduced material transition discontinuities reflected in the activating function calculation. Our findings support using the finest spatial discretisations possible within computational constraints, which may rely on adaptive meshing techniques. We advocate coupling the extracellular field to H-H-based axons to further limit potential error sources.