Modeling Wound Healing Dynamics Using the Fisher–Kolmogorov Equation

Abstract Wound healing is a meticulously regulated biological process involving the coordination of cell migration, proliferation, and tissue remodeling. Experimental investigations are often constrained by ethical and practical limitations, rendering computational approaches a valuable complementary tool. In this study, we utilized the Fisher–Kolmogorov reaction–diffusion equation, implemented in COMSOL Multiphysics, to simulate the proliferation phase of wound repair on a three-dimensional forearm model. A semi-cylindrical partial-thickness wound with dimensions of 20 × 20 × 8 mm was introduced, and parameters for cell diffusivity, proliferation rate, and carrying capacity in three cases (normal, diabetic and older) were derived from published experimental data. Simulation results reveal a biphasic healing trajectory: initial closure is driven by diffusion-mediated migration of cells from intact tissue (days 1–5), followed by proliferation that accelerates recovery (days 6–13). The wound approaches complete closure within approximately 15 days, a timeline consistent with clinically reported healing rates for injuries of comparable size. Quantitative indicators, including wound healing percentage and wound area percentage, confirmed the complementary roles of migration and proliferation throughout the process. While the model simplifies biological complexity by neglecting inflammation, angiogenesis, and matrix remodeling, it provides physiologically relevant predictions and establishes a computational foundation for more advanced, patient-specific simulations. These findings underscore the potential of mathematical modeling to support predictive wound assessment and guide clinical decision-making in wound management.