Upscaling between an Agent-Based Model (Smoothed Particle Approach) and a Continuum-Based Model for Skin Contractions

TL;DR

This paper explores the connection between microscale agent-based models and macroscale continuum models for skin contraction, providing rigorous links in 1D and computational evidence in multidimensional cases.

Contribution

It establishes a rigorous mathematical link between agent-based and continuum models for skin contraction in 1D and offers computational evidence for multidimensional cases.

Findings

Rigorous connection in 1D models for closed-form and finite-element solutions.

Computational evidence supporting the link in multidimensional models.

Abstract

Skin contraction is an important biophysical process that takes place during and after the recovery of deep tissue injury. This process 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. In this manuscript, we present some results from our study of the connection between these scales. For the one-dimensional case, we managed to rigorously establish the link between the two modelling approaches for both closed-form solutions and finite-element approximations. For the multidimensional case, we computationally evidence the connection between the agent-based and continuum-based modelling approaches.