PDE and agent based simulation approaches to Ischemic Dermal Wound Closure.

Area of Science:

• Biomedical Engineering
• Mathematical Modeling
• Wound Healing Research

Background:

• Ischemic dermal wounds pose a significant clinical challenge, often failing to heal within the expected 30-day timeframe.
• Keratinocytes, crucial epidermal cells, play a vital role in the wound healing process.

Purpose of the Study:

• To develop and compare two distinct mathematical models (Partial Differential Equations and Agent-based Simulation) for symmetric flat ischemic wounds.
• To evaluate the efficacy of oxygen therapy in promoting wound closure across varying levels of ischemia.

Main Methods:

• Development of a Partial Differential Equations (PDE) model and an Agent-based Simulation (ABS) model for ischemic wound dynamics.
• Incorporation of keratinocyte cell behavior into both mathematical models.
• Simulation of oxygen therapy's impact on wound closure at different ischemia levels ([Formula: see text]).

Main Results:

• High agreement observed between the wound radius reduction profiles predicted by the PDE and ABS models.
• Oxygen therapies (hyperbaric and topical) demonstrated effectiveness in achieving complete wound closure for mild to moderate ischemia levels.
• Specific ischemia thresholds ([Formula: see text] for hyperbaric, [Formula: see text] for topical oxygen) were identified for successful closure.

Conclusions:

• The developed mathematical models provide a reliable quantitative framework for studying ischemic wound healing.
• Oxygen therapy is a viable intervention for ischemic wounds, with efficacy dependent on the severity of ischemia.
• These findings support evidence-based therapeutic strategies for managing challenging dermal wounds.