Effective Spatio-Temporal Regimes for Wound Treatment by Way of Macrophage Polarization: A Mathematical Model

Abstract

Wound healing consists of a sequence of biological processes often grouped into different stages. Interventions applied to accelerate normal wound healing must take into consideration timing with respect to wound healing stages in order to maximize treatment effectiveness. Macrophage polarization from M1 to M2 represents a transition from the inflammatory to the proliferative stage of wound healing. Accelerating this transition may be an effective way to accelerate wound healing; however, it must be induced at the appropriate time. We search for an optimal spatio-temporal regime to apply wound healing treatment in a mathematical model of wound healing. In this work we show that to maximize effectiveness, treatment must not be applied too early or too late with respect to peak inflammation. We also show that the effective spatial distribution of treatment depends on the heterogeneity of the wound surface. In conclusion, this research provides a possible optimal regime of therapy that focuses on macrophage activity and a hypothesis of treatment outcome to be tested in future experiments. Finding optimal regimes for treatment application is a first step toward the development of intelligent algorithms for wound treatment that minimize healing time.