Biomorphoelasticity alone: limitations in modeling post-burn contraction and hypertrophy without finite strains

Abstract

We present a continuum hypothesis-based two-dimensional biomorphoelastic model describing post-burn scar hypertrophy and contraction. The model is based on morphoelasticity for permanent deformations and combined with a chemical-biological model that incorporates cellular densities, collagen density, and the concentration of chemoattractants. We perform a sensitivity analysis for the independent parameters of the model and focus on the effects on the features of the post-burn dermal thickness given a low myofibroblast apoptosis rate. We conclude that the most sensitive parameters are the equilibrium collagen concentration, the signaling molecule secretion rate and the cell force constant, and link these results to stability constraints. Next, we observe a relationship between the simulated contraction and hypertrophy and show the effects for significant variations in the myofibroblast apoptosis rate (high/low). Our ultimate goal is to optimize post-burn treatments, by developing models that predict with a high degree of certainty. We consider the presented model and sensitivity analysis to be a step toward their construction.