Upscaling between an agent-based model (smoothed particle approach) and a continuum-based model for skin contractions in one dimension

Abstract

Skin contraction during wound healing is mainly caused by fibroblasts (skin cells) and myofibroblasts (differentiated fibroblasts) that exert pulling forces on the surrounding extracellular matrix (ECM). Modelling is done in multiple scales: agent-based modelling on the microscale and continuum-based modelling on the macroscale. The momentum equilibrium equation is used to simulate this phenomenon in both models, with different expression of the cellular forces. In this manuscript, we managed to rigorously establish the link between the two modelling approaches for both closed-form solutions and finite-element approximations in one dimension.