Mathematical model for wound healing caused by exogeneous mechanical forces

Abstract

Motivated by the experimental study showing that exogeneous mechanical forces promote wound healing, we introduce a mathematical model for wound healing caused by exogeneous mechanical stimuli. For the dynamics of cells such as movement, growth, and division, we use the Cellular Pots Model (CPM), which is a popular discretized model on a lattice, where the movement of a ”cell” is determined by Monte Carlo procedure. In the experiment, the mechanosensitive ATP release from the leading cells facing the wound edge and the subsequent intracellular Ca2+ influx were observed. To model these phenomena, the Reaction-Diffusion (RD) equations for ATP and Ca2+ concentrations are introduced and combined with CPM. From the numerical simulations using this hybrid model, we discuss effects of the collective cell movement due to the ATP release and the Ca2+ influx caused by the mechanical forces and the consequent promotion of wound healing.