A spatial healing metric for wound healing modeling

We propose a new healing metric for improved tracking of the wound healing process across arbitrary wound geometries. A Fickian diffusion equation with a logistic nonlinear term is solved using the open-source finite element framework FEniCSx. The model is verified and calibrated by comparing finite element simulation results with experimental data from the literature, focused on the circular rabbit ear wound. To address the limitations of fixed-threshold metrics, we introduce a spatial healing metric, β, which captures the average cell density across the wound domain. This metric reflects healing differences arising from geometry and variations in diffusion and mitotic parameters. Parametric sweeps over the diffusion coefficient–mitotic generation (D–s) space reveal that different parameter combinations can yield the same healing time but with quite different spatial profiles. We also study multiple wound geometries to validate the applicability of the proposed metric. Our results demonstrate that the proposed β metric exposes limitations of the classical threshold-based approach, particularly under conditions of high diffusion and low mitotic generation, where traditional metrics suggest full healing despite spatial discrepancies in cell density.