Mathematical modeling of the lower limbs varicose veins thermographic image

Background and Objectives: The high prevalence of varicose veins of the lower limbs (VVLL) emphasizes the importance of accurate and timely diagnosis of this pathology. Methods for diagnosing VVLL include, among others, infrared thermography (IRT), which is the safest method. It allows surface temperature mapping with a high spatial resolution. The purpose of this work is to mathematically model the distribution of heat along the back surface of the human shin in the presence of VVLL, compare the obtained distribution with the results of IRT, as well as study the effect of model parameters on the simulation results and assess the possibility of detecting varicose veins using IRT. Methods: А differential equation of thermal conductivity was used to simulate heat transfer processes taking into account blood flow in biological tissues. Biological tissues were defined in layers, the boundaries of which were determined based on the results of X-ray computed tomography. Inclusions reflecting the anatomical structure of the superficial and main veins, which are located directly in the main tissue layers, are considered as venous vessels. Numerical modeling of the process of heat propagation in the shin was carried out in order to investigate the dependence of the temperature change caused by VVLL on the posterior surface of the shin on the maximum depth of varicose veins, their diameters, their surface temperature, perfusion rate, and ambient temperature. The analysis of the possibility of recording such temperature changes with a modern IR thermograph is made. Results: Computational experiments to assess the influence of model parameters on the thermal picture of the surface of the back of the shin have shown that the created mathematical model provides sufficient agreement with the results of real thermographic studies. Most of the temperature dependences obtained in the calculations are consistent or do not contradict real studies. Conclusion: A comparison with experimental results available in the literature has shown that the performed mathematical modeling simulates the initial stages of VVLL.