Connecting Local and Global Sensitivities in a Mathematical Model for Wound Healing

The process of wound healing is governed by complex interactions between proteins and the extracellular matrix, involving a range of signaling pathways. This study aimed to formulate, quantify, and analyze a mathematical model describing interactions among matrix metalloproteinases (MMP-1), their inhibitors (TIMP-1), and extracellular matrix in the healing of a diabetic foot ulcer. De-identified patient data for modeling were taken from Muller et al. (Diabet Med 25(4):419-426, 2008), a research outcome that collected average physiological data for two patient subgroups: "good healers" and "poor healers," where classification was based on rate of ulcer healing. Model parameters for the two patient subgroups were estimated using least squares. The model and parameter values were analyzed by conducting a steady-state analysis and both global and local sensitivity analyses. The global sensitivity analysis was performed using Latin hypercube sampling and partial rank correlation analysis, while local analysis was conducted through a classical sensitivity analysis followed by an SVD-QR subset selection. We developed a "local-to-global" analysis to compare the results of the sensitivity analyses. Our results show that the sensitivities of certain parameters are highly dependent on the size of the parameter space, suggesting that identifying physiological bounds may be critical in defining the sensitivities.