Point Forces and Their Alternatives in Cell-Based Models for Skin Contraction in Two Dimensions

Abstract

Deep tissue injury is often followed by contraction of the scar tissue. This contraction occurs as a result of pulling forces that are exerted by fibroblasts (skin cells). We consider a cell-based approach to simulate the contraction behavior of the skin. Since the cells are much smaller than the wound region, we model cellular forces by means of Dirac Delta distributions. Since Dirac Delta distributions cause a singularity of the solution in terms of loss of smoothness, we study alternative approaches where smoothed forces are considered. We prove convergence and consistency between the various approaches, and we also show computational consistency between the approaches.