Development of Mathematical Model for Understanding Microcirculation in Diabetic Foot Ulcers Based on Ankle-Brachial...

Area of Science:

• Biomedical Engineering
• Cardiovascular Physiology
• Mathematical Modeling

Background:

• Diabetic foot ulcers are associated with microcirculatory dysfunction.
• Assessing microcirculation in these patients is crucial for effective treatment.
• Conventional methods may not detect subtle hemodynamic changes.

Purpose of the Study:

• To develop and validate an innovative mathematical model for assessing microcirculation in diabetic ulcer patients.
• To correlate microcirculatory parameters with ulcer severity using the ankle-brachial index (ABI).
• To identify key indicators of vascular impairment in the microvasculature.

Main Methods:

• Utilized Bond Graph (BG) modeling combined with Particle Swarm Optimization (PSO).
• Analyzed hemodynamic patterns in a pilot sample of three patients.
• Employed PSO to optimize parameters of an equivalent capillary circuit.

Main Results:

• A correlation was found between diabetic ulcer size and reduced ABI values.
• All patients demonstrated high capillary resistance, indicating impaired microcirculatory blood flow.
• PSO-optimized parameters (R1=89.784Ω, R2=426.55Ω, L=27.506H, C=0.00040675F) confirmed high vascular resistance and low compliance.

Conclusions:

• The mathematical model effectively quantifies microcirculatory dynamics in diabetic ulcer patients.
• Increased capillary resistance is a potential indicator of vascular impairment and ulcer severity.
• The model offers a valuable tool for early detection and intervention in diabetic foot care, pending further validation.