Analytical studies of heat transport in the peripheral region of a human limb undergoing healing after surgery

Regular Article
  • 7 Downloads

Abstract.

In the present study, an axisymmetric one-dimensional Pennes bioheat transfer model is used to investigate analytically the heat transport in the peripheral region of a human limb undergoing healing after surgery. The analytical exact solution to the model is presented in terms of modified Bessel functions. Through the found analytical solution, the time-dependent temperature distribution of normal and abnormal tissues is investigated. Effects of different biological parameters like metabolic heat generation, rate of sweat evaporation, variable physiological parameters in dermal layer of peripheral region, and ambient temperature on temperature distribution are also studied.

References

  1. 1.
    K.R. Diller, Adv. Heat Transf. 22, 157 (1992)CrossRefGoogle Scholar
  2. 2.
    H.H. Pennes, J. Appl. Physiol. 1, 93 (1948)ADSCrossRefGoogle Scholar
  3. 3.
    H. Arkin, L.X. Xu, K.R. Holmes, IEEE Trans. Biomed. Eng. 41, 97 (1994)CrossRefGoogle Scholar
  4. 4.
    L. Zhu, C. Diao, Med. Biol. Eng. Comput. 39, 681 (2001)CrossRefGoogle Scholar
  5. 5.
    H.S. Kou, T.C. Shih, W.L. Lin, Phys. Med. Biol. 48, 1577 (2003)CrossRefGoogle Scholar
  6. 6.
    D.A. Torvi, J.D. Dale, ASME J. Biomech. Eng. 116, 250 (1994)CrossRefGoogle Scholar
  7. 7.
    M.M. Chen, K.R. Holmes, V. Rupinskas, ASME J. Biomech. Eng. 103, 253 (1981)CrossRefGoogle Scholar
  8. 8.
    E. Kengne, A. Lakhssassi, R. Vaillancourt, W.-M. Liu, Eur. Phys. J. Plus 127, 15 (2012)CrossRefGoogle Scholar
  9. 9.
    M.M. Chen, K.R. Holmes, Ann. NY Acad. Sci. 335, 137 (1980)ADSCrossRefGoogle Scholar
  10. 10.
    W. Wulff, IEEE Trans. Biomed. Eng. 21, 494 (1974)CrossRefGoogle Scholar
  11. 11.
    E. Kengne, M. Saydé, A. Lakhssassi, Eur. Phys. J. Plus 128, 10 (2013)CrossRefGoogle Scholar
  12. 12.
    C.W. Song, A. Lokshina, J.C. Rhee, M. Patten, S.H. Levitt, IEEE Trans. Biomed. Eng. 31, 9 (1984)CrossRefGoogle Scholar
  13. 13.
    D.T. Tompkins, R. Vanderby, S.A. Klein, W.A. Beckman, R.A. Steeves, D.M. Frey, B.R. Palival, Int. J. Hyperth. 10, 517 (1994)CrossRefGoogle Scholar
  14. 14.
    K.H. Keller, L. Seiler, J. Appl. Physiol. 30, 779 (1971)CrossRefGoogle Scholar
  15. 15.
    H.G. Klinger, Bull. Math. Biol. 36, 403 (1974)MathSciNetGoogle Scholar
  16. 16.
    R.A. Gordon. R.B. Roemer, S.M. Horvath, IEEE Trans. Biomed. Eng. BME 23, 43 (1976)Google Scholar
  17. 17.
    J. Erdmann, B. Lang, M. Seebass, IEEE Trans. Biomed. Eng. 46, 1129 (1999)CrossRefGoogle Scholar
  18. 18.
    T.R. Gowrishankar, D.A. Stewart, G.T. Martin, J.C. Weaver, BioMed. Eng. On-Line 3, 1 (2004)Google Scholar
  19. 19.
    W. Perl, J. Theor. Biol. 2, 201 (1962)CrossRefGoogle Scholar
  20. 20.
    Zh.-S. Deng, J. Liu, J. Biomech. Eng. 124, 638 (2002)CrossRefGoogle Scholar
  21. 21.
    N. Gupta, M. Shakya, IOSR J. Math. 10, 66 (2014)CrossRefGoogle Scholar
  22. 22.
    Z. Minhua, C. Qian, Study of the surface temperature distribution of the tissue affected by the point heat source (IEEE, 2007)Google Scholar
  23. 23.
    M. Zhou, Q. Chen, in 2nd International Conference on Biomedical Engineering and Informatics, BMEI, IEEE, Nanjing, China (2009)Google Scholar
  24. 24.
    R. Vyas, M.L. Rustgi, Med. Phys. 19, 1319 (1992)CrossRefGoogle Scholar
  25. 25.
    S. Hossain, F. Mohammadi, in The 6th International Multi-Conference on Engineering and Technological Innovation: IMETI 2013Google Scholar
  26. 26.
    M. Jain, M. Shakya, Appl. Math. Sci. 3, 2651 (2009)MathSciNetGoogle Scholar
  27. 27.
    J. Baish, Microvascular heat transfer, in The Biomedical Engineering Handbook, vol. 2, edited by Joseph D. Bronzino, (CRC Press LLC, Boca Raton, 2000) pp. 98--11Google Scholar
  28. 28.
    K. Pardasani, M. Shakya, J. Math. Stat. 1, 184 (2005)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Emmanuel Kengne, Ahmed Lakhssassi, Math. Biosci. 269, 1 (2015)MathSciNetCrossRefGoogle Scholar
  30. 30.
    D. Fiala, K.J. Lomas, M. Stohrer, J. Appl. Physiol. 87, 1957 (1999)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Département d’informatique et d’ingénierieUniversité du Québec en OutaouaisGatineauCanada

Personalised recommendations