Development of Mathematical Model for Understanding Microcirculation in Diabetic Foot Ulcers Based on Ankle–Brachial Index

Abstract

This study proposes an innovative mathematical model for assessing microcirculation in patients with diabetic ulcers, using the ankle–brachial index (ABI). The methodology combines Bond Graph (BG) modeling and Particle Swarm Optimization (PSO), enabling a detailed analysis of hemodynamic patterns in a pilot sample of three patients. The results revealed a correlation between ulcer size and reduced ABI values, suggesting that deficits in microcirculation directly impact the severity of lesions. Furthermore, despite variations in ABI values and arterial pressures, all patients exhibited high capillary resistance, indicating difficulties in microcirculatory blood flow. The PSO-optimized parameters for the capillary equivalent circuit were found to be (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.), which confirms the presence of high vascular resistance and reduced compliance in the microvascular system of patients with diabetic foot ulcers. This quantitative analysis, made possible through mathematical modeling, is crucial for detecting subtle changes in microcirculatory dynamics, which may not be easily identified through conventional pressure measurements alone. The increased capillary resistance observed may serve as a key indicator of vascular impairment, potentially guiding early intervention strategies and optimizing diabetic ulcer treatment. We acknowledge that the sample size of three patients represents a limitation of the study, but this number was intentionally chosen to allow for a detailed and controlled analysis of the variables involved. Although the findings are promising, additional experimental validations are necessary to confirm the clinical applicability of the model in a larger patient sample, thus solidifying its relevance in clinical practice.