PDE and agent based simulation approaches to Ischemic Dermal Wound Closure

Abstract

Ischemic dermal wounds present a significant medical challenge, especially in the case where the wound does not close in an expected time, typically 30 days. We developed two very different mathematical models of symmetric flat wounds, one by Partial Differential Equations (PDE) and another by Agent-based Simulation (ABS) with some parameters taken from the PDE model. The models include the important role of keratinocytes who make 90% of the cells in the epidermis. We used both models to assess the effectiveness of oxygen therapy in wound closure for different levels α of ischemia; ischemia increases as α increases from 0 to 1. We found that (i) the decreasing profiles of the radius R ( t ) of the open wound derived by the two models are in a high degree of agreement, and (ii) standard hyperbaric and topical oxygen therapies effec t ively achieve complete closure of the wound in expected time in cases where the ischemic level is not too high, i.e., α ≤ 0.3 under standard hyperbaric therapy and α ≤ 0.5 under continuous topical oxygen therapy. These findings provide a quantitative framework for evaluating ischemic wound healing and therapeutic interventions.