Modelling the Impact of Cellular Diffusion on the Wound–Slough Healing Dynamics

This study investigates an ordinary differential equation model with lumped parameters that describesthe interaction between wound tissue and slough tissue. We extend this model to a partial differential equation framework to better represent cellular level characteristics and examine how varying tissue diffusivities affect the healing process. We analyze the well-posedness of the system, including the existence, uniqueness, and positivity of solutions, under homogeneous Neumann boundary conditions and given initial distributions. Furthermore, we provide numerical simulations for various wound healing scenarios. The results indicate that acute wounds tend to heal quickly, while chronic wounds suffer from disruptions that inhibit successful healing. We also explore the impact of diffusion on the stability of equilibrium points in the earlier model and demonstrate that the system does not exhibit Turing instability. Additionally, we analyze how various cellular properties, particularly differences in diffusion rates, affect the healing process.