da Silva Ana Karoline Almeida, Nunes Gustavo Adolfo Marcelino de Almeida, Faria Rafael Mendes, Fleury Rosa Mário Fabrício, Costa Lindemberg Barreto Mota da, de Faria Newton, da Rocha Adson Ferreira, Tatmatsu-Rocha José Carlos, Fleury Rosa Suelia de Siqueira Rodrigues
Postgraduate Programme in Mechatronic Systems, Mechanical Engineering Department, Campus Darcy Ribeiro, University of Brasilia, Brasilia 70910-900, DF, Brazil.
Department of Electrical Engineering, Federal Institute of Education, Science and Technology of Triângulo Mineiro, Campus Paracatu, Paracatu 38603-402, MG, Brazil.
Bioengineering (Basel). 2025 Feb 19;12(2):206. doi: 10.3390/bioengineering12020206.
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 R1=89.784Ω, R2=426.55Ω, L=27.506H, and C=0.00040675F, 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.
本研究提出了一种创新的数学模型，用于使用踝臂指数（ABI）评估糖尿病溃疡患者的微循环。该方法结合了键合图（BG）建模和粒子群优化（PSO），能够对三名患者的试点样本中的血流动力学模式进行详细分析。结果显示溃疡大小与ABI值降低之间存在相关性，表明微循环缺陷直接影响病变的严重程度。此外，尽管ABI值和动脉压存在差异，但所有患者均表现出高毛细血管阻力，表明微循环血流存在困难。发现毛细管等效电路的PSO优化参数为R1 = 89.784Ω，R2 = 426.55Ω，L = 27.506H，C = 0.00040675F，这证实了糖尿病足溃疡患者微血管系统中存在高血管阻力和降低的顺应性。通过数学建模实现的这种定量分析对于检测微循环动力学中的细微变化至关重要，而这些变化仅通过传统压力测量可能不容易识别。观察到的增加的毛细血管阻力可能是血管损伤的关键指标，有可能指导早期干预策略并优化糖尿病溃疡治疗。我们承认三名患者的样本量是本研究的一个局限性，但有意选择这个数量以便对所涉及的变量进行详细和可控的分析。尽管研究结果很有前景，但仍需要额外的实验验证来确认该模型在更大患者样本中的临床适用性，从而巩固其在临床实践中的相关性。
