Modelling and investigation of temperature field in the boundary layer of biological bodies

Fìz.-mat. model. ìnf. tehnol. 2017, 26:90-99

Abstract

A problem on finding temperature field in the boundary layer of biological body when blood perfusion coefficient depends on coordinate is solved. Temperature distribution is caused by the temperature differences between the inside and outside of a body and by the outside heat sources and metabolic heat generation. Heat transfer problem is formulated by using generalized Heaviside functions. Applying the variation of constants method this problem is reduced to the Fredholm integral equation of the second kind. Numerical method of Simpson quadratures was used to solve integral equation. Analysis of temperature distribution in the boundary layer for some cases of boundary conditions is performed. Dependence on temperature inside body from metabolic heat generation and outside heat source is analyzed.

References

1. Diller, K. R. (1999). Modeling of Bioheat Transfer Processes at High and Low Temperatures. Adv. Heat Transfer, 22, 157-357.
   DOI https://doi.org/10.1016/S0065-2717(08)70345-9
2. Clegg, S. T., Roemer, R. B. (1993). Reconstruction of Experimental Hyperthermia Temperature Distributions: Application of State and Parameter Estimation. ASME J. Biomech. Eng., 115, 380-388.
   DOI https://doi.org/10.1115/1.2895501
3. Liu, J., Zhu, L., Xu, L. X. (2000). Studies on the Three-Dimensional Temperature Transients in the Canine Prostate During Transurethral Microwave Thermal Therapy. ASME J. Biomech. Eng., 122, 372-379.
   DOI https://doi.org/10.1115/1.1288208
4. Seip, R., Ebbini, E. S. (1995). Noninvasive Estimation of Tissue Temperature Response to eating Fields Using Diagnostic Ultrasound. IEEE Trans. BioMed. Eng., 42, 828-839.
   DOI https://doi.org/10.1109/10.398644
5. Pustovalov, V. K. (1993). Thermal Processes under the Action of Laser Radiation Pulse on Absorbing Granules in Heterogeneous Biotissues. Int. J. Heat Mass Transf., 36, 391-399.
   DOI https://doi.org/10.1016/0017-9310(93)80015-m
6. Vyas, R., Rustgi, M. L. (1992). Green’s Function Solution to the Tissue Bioheat Equation. Med. Phys., 19, 1319-1324.
   DOI https://doi.org/10.1118/1.596767
7. Gao, B., Langer, S., Corry, P. M. (1995). Application of the Time-Dependent Green’s Function and Fourier Transforms to the Solution of the Bioheat Equation. Int. J. Hyperthermia, 11, 267-285.
   DOI https://doi.org/10.3109/02656739509022462
8. Deng, Z. S., Liu, J. (2002). Analytical Study on Bioheat Nransfer Problems with Spatial or Transient Heating on Skin Surface or Inside Biological Bodits. ASME J. Biomech. Eng., 124, 638-649.
   DOI https://doi.org/10.1115/1.1516810
9. Crezee, J., Crezee, J., Mooibroek, J., Lagendijk, J. J. W., Vanleeuwen, G. M. J. (1994). The Theoretical and Experimental Evaluation of the Heat-Balance in Perfused Tissue. Phys. Med. Biol., 39, 813-832.
   DOI https://doi.org/10.1088/0031-9155/39/5/003
10. Kushnir, R. M. (1980). Pro pobudovu rozviazkiv zvychainykh liniinykh dyferentsialnykh rivnian z kuskovo–stalymy koefitsiientamy. Dop. AN URSR. Ser. A., 9, 54–57.
11. Koliano, Yu. M., Popovych. V. S. (1976). Ob odnom effektivnom metode resheniya zadach termouprugosti dlya kusochno–odnorodnyih tel, nagrevaemyih vneshney sredoy. Fiz.–him. mehanika materialov, 2, 108-112.
12. Khapko, B. S. (2006). Pro rozviazok kraiovoi zadachi dlia dyferentsialnykh rivnian u chastynnykh pokhidnykh z impulsnymy koefitsiientamy. Mat. metody i fiz.- mekh. polia, 49(3), 47-55.
13. Liu, J., Xu, L. X. (1999). Estimation of Blood Perfusion Using Phase Shift in Temperature Response to Sinusoidal Heating at the Skin Surface. IEEE Trans. Biomed. Eng., 46, 1037-1043.
    DOI https://doi.org/10.1109/10.784134
14. Pennes, H. H. (1948). Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm. J. Appl. Physiol, 1, 93-122.
15. Verlan, A. F., Sizikov, V. S. (1978). Metody resheniya integralnyh uravnenij s programmami dlya EVM. Kiev: Nauk. dumka.
16. Khapko, B.S., Chyzh, A. I. (2009). Temperaturne pole ta prohyn pivbezmezhnoi plastynky iz zalezhnymy vid koordynaty koefitsiientamy teploviddachi. Fizyko-matematychne modeliuvannia ta informatsiini tekhnolohii, 9, 133-143.