Stability, convergence, and sensitivity analysis of the Filament Based Lamellipodium Model and the corresponding FEM

TL;DR

This paper analyzes the numerical stability, convergence, and sensitivity of the Filament Based Lamellipodium Model (FBLM) and its FEM implementation, demonstrating reliable performance and parameter influence in complex biological environments.

Contribution

It provides a detailed numerical analysis of the FBLM and FEM, including stability conditions, adaptive time-stepping, convergence proofs, and sensitivity studies in complex environments.

Findings

FEM satisfies a timestep stability condition.

Adaptive time-stepping improves numerical performance.

FBLM's sensitivity to parameters affects model development.

Abstract

This paper focuses on the study of the Filament Based Lamellipodium Model (FBLM) and the corresponding Finite Element Method (FEM) from a numerical point of view. We study fundamental numerical properties of the FEM and justify the further use of the FBLM. We exhibit that the FEM satisfies a timestep stability condition that is consistent with the nature of the problem. We propose a particular strategy to automatically adapt the time step of the method. We show that the FEM convergences with respect to the (two-dimensional) space discretization in a series of characteristic and representative experiments. We embed and couple the FBLM with a complex extracellular environment comprised of chemical and haptic components and study their combined time evolution. Under this prism, we study the sensitivity of the FBLM on several of its controlling parameters and discuss their influence in the development of the model.