A Mathematical Model of Wound Healing Incorporating Strain-Induced MSC Differentiation

Wound healing is a complex physiological process involving numerous cell types and biological factors aimed at repairing damaged tissue. Mathematical models provide insights into physiologic and pathophysiologic processes, which can improve the understanding of wound healing by eliminating biological variability seen in vivo. This work developed a non-spatial, deterministic mathematical model of adult dermal wound healing by incorporating cellular components and biochemical pathways common to prior models and adding additional biochemical regulation, mesenchymal stem/stromal cell (MSC) differentiation, extrinsic mechanical strain, and a new constitutive relationship to predict wound healing strength. The expanded model replicated results of prior models with respect to fibroblast levels, collagen production, and responses to applying transforming growth factor-β isoforms. Applying macroscopic strain accelerated cell responses and collagen production at early timepoints and slightly increased the steady-state collagen I:III ratio. Predicted healed tissue strength matched experimental healed dermal tissue strength results. Finally, the model incorporates user-controlled features, including exogenous MSC injection and depressed oxygen levels, to mimic alternative wound conditions. MSC injection did not alter the healing dynamics, but the model exhibited robust sensitivity to tissue oxygen level.