For citation:
Zhorina L. V., Tolstoy E. A. Mathematical modeling of the lower limbs varicose veins thermographic image. Izvestiya of Saratov University. Physics , 2024, vol. 24, iss. 4, pp. 348-360. DOI: 10.18500/1817-3020-2024-24-4-348-360, EDN: BHNYOS
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.
- Studennikova V. V., Severgina L. O., Korovin I. A., Rapoport L. M., Krupinov G. E., Novikov I. A. Ultrastructural characteristics of the mechanisms of varicose transformation of veins of different localization. Arkhiv patologii [Russian Journal of Archive of Patology], 2020, vol. 82, no. 6, pp. 16–23 (in Russian). https://doi.org/org/10.17116/patol20208206116
- Chernyago T. Yu., Fomina V. S., Fedyk O. V., Yashkin M. N. Assessment methods of the functional state of the endothelium in patients with varicose veins of the lower extremities: Perspectives of treatment. Vestnik Natsional’nogo mediko-khirurgicheskogo Tsentra im. N. I. Pirogova [Bulletin of Pirogov National Medical & Surgical Center], 2021, vol. 16, no. 1, pp. 145–150 (in Russian). https://doi.org/10.25881/BPNMSC.2021.17.48.028
- Vodovotz L., Zamora R., Barclay D. A., Vodovotz Y., Yin J., Bitner J., Florida J., Avgerinos E. D., Sachdev U. Inflammatory signals and network connections implicate cell-mediated immunity in chronic venous insufficiency. Ann. Transl. Med., 2021, vol. 9, no. 22, pp. 1643. https://doi.org/10.21037/atm-21-688
- Zhorina L. V., Tolstoy E. A. Mathematical Modeling of the Thermographic Image of the Lower Limbs Varicose Disease in Humans. 2023 IEEE 16th International Scientific and Technical Conference Actual Problems of Electronic Instrument Engineering, APEIE Proceedings, 2023, pp. 1150–1154. https://doi.org/10.1109/APEIE59731.2023.10347608
- Zhorina L. V., Tolstoy E. A., Shishkin Yu. V. Thermography of Lower Limbs Varicose Veins: Mathematical Modeling. 2023 IEEE Ural-Siberian Conference on Computational Technologies in Cognitive Science, Genomics and Biomedicine, CSGB Proceedings, 2023, pp. 79–84. https://doi.org/10.1109/CSGB60362.2023.10329626
- Zamechnik T. V., Ovcharenko N. S., Larin S. I., Losev A. G. Reliability assessment of combined thermography as a method for the characteristic of the lower limb venous system. Flebologiya [Journal of Venous Disorders], 2010, vol. 4, no. 3, pp. 23–26 (in Russian).
- Sergeev A. N., Morozov A. M., Charyev Yu. O., Belyak M. A. On the possibility of using medical thermography in clinical practice. Profilakticheskaya meditsina [Russian Journal of Preventive Medicine], 2022, vol. 25, no. 4, pp. 82–88 (in Russian). https://doi.org/10.17116/profmed20222504182
- Dahlmanns S., Reich-Schupke S., Schollemann F., Stücker M., Leonhardt S., Teichmann D. Classification of chronic venous diseases based on skin temperature patterns. Physiol. Meas., 2021, vol. 42, no. 4. https://doi.org/10.1088/1361-6579/abf020
- Bosque J. J., Calvo G. F., Pérez-García V. M., Navarro M. C. The interplay of blood flow and temperature in regional hyperthermia: A mathematical approach. R. Soc. Open Sci., 2021, vol. 8, article no. 201234. https://doi.org/10.1098/rsos.201234
- Hristov J. Bio-Heat Models Revisited: Concepts, Derivations, Nondimensalization and Fractionalization Approaches. Front. Phys., Sec. Statistical and Computational Physics, 2019, vol. 7, article no. 189. https://doi.org/10.3389/fphy.2019.00189
- Sedankin M. K., Leushin V. Y., Gudkov A. G., Vesnin S. G., Sidorov I. A., Agasieva S. V., Markin A. V. Mathematical Simulation of Heat Transfer Processes in a Breast with a Malignant Tumor. Biomed. Eng., 2018, vol. 52, рр.190–194. https://doi.org/10.1007/s10527-018-9811-2
- Zhorina L. V., Manucharyan F. V., Tolstoy E. A., Plokhikh A. I., Shishkin Y. V. Development of a Breast Mock-up for Thermographic Diagnostics. 2023 IEEE 16th International Scientific and Technical Conference Actual Problems of Electronic Instrument Engineering, APEIE Proceedings, 2023, рр. 1260–1264. https://doi.org/10.1109/APEIE59731.2023.10347819
- Zherebtsova A. I. An analytical review of mathematical models of relationship between blood perfusion and skin temperature parameters. Fundamental’nye i prikladnye problemy tekhniki i tekhnologii [Fundamental and Applied Problems of Technics and Technology], 2015, no. 5, pp. 104–113 (in Russian).
- Ivanitsky G. R., Deev A. A., Kresteva I. B., Khizhnyak E. P., Khizhnyak L. N. Development of methods for determining the stages of obliterating vascular atherosclerosis and early diagnosis of varicose veins using modern matrix infrared systems. Materialy konferentsii “Fundamental’nye nauki – meditsine”. RAN [Proceedings of the Conference “Basic Sciences – Medicine”. RAS]. Moscow, Slovo, 2007, pp. 69–70 (in Russian).
- Company LLC “IRTIS”. Website. Available at: http://m.irtis.ru/oblasti-primeneniya/ (accessed April 29, 2024).
- Volovik M. G., Dolgov I. M., Muravina N. L. Teplovizionnaya skrining-diagnostika. Bolezni sistemy krovoobrashcheniya. Varikoznoe rasshirenie ven nizhnikh konechnostey. Flebit. Tromboflebit: atlas termogramm [Thermal imaging screening diagnostics. Diseases of the circulatory system. Varicose veins of lower extremities. Phlebitis. Thrombophlebitis. Atlas of thermograms]. Moscow, INFRA-М, 2020. 91 p. (in Russian). https://doi.org/10.12737/1159602
- Zamechnik T. V., Larin S. I., Stern N. A., Ovcharenko N. S., Andriianov A. Iu. Results of lower leg thermography in patients with primary varicosis depending on ambient temperature. Flebologiya [Journal of Venous Disorders], 2008, vol. 2, no. 1, pp. 10–13 (in Russian).
- Luchakov Yu. I., Kamyshev N. G., Shabanov P. D. Heat transfer in blood vessels: Comparison experimental and mathematical data. Obzory po klinicheskoy farmakologii i lekarstvennoy terapii [Reviews on clinical pharmacology and drug therapy], 2009, vol. 7, no. 4, pp. 3–20 (in Russian).
- Dixon A. K., Bowden D. J., Ellis H., Logan B. M. Human Sectional Anatomy: Atlas of body sections, CT and MRI images. 4th ed. Boca Raton, CRC Press, 2015. 288 p.
- Xu F., Lu T. J., Seffen K. A. Biothermomechanical behavior of skin tissue. Acta Mech. Sinica, 2008, vol. 24, pp. 1–23.
- Ivanitsky G. R., Khizhnyak E. P., Deev A. A., Khizhnyak L. N. Thermal imaging in medicine: A comparative study of infrared systems operating in wavelength ranges of 3–5 and 8–12 µm as applied to diagnosis. Doklady Biochemistry and Biophysics, 2006, vol. 407, March–April, pp. 59–63. https://doi.org/10.1134/S1607672906020049
- 110 reads