Skip to main content
SpringerLink
Log in

Analytico-numerical study of bio-heat transfer problems with temperature-dependent perfusion

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

We consider the one-dimensional bio-heat transfer problems with linear temperature-dependent blood perfusion and spatially distributed heating which describe heat transport in blood perfused tissues. Analytical methods for solving nonlinear partial differential equations are combined with the Crank-Nicholson scheme to study several selected typical bio-heat transfer processes, which are often encountered in cancer hyperthermia, laser surgery, and thermal comfort analysis. The results mainly show that: i) the larger heating power increases the amplitude of the temperature response of the tissues; ii) a very low frequency of the heating power can be associated to a large frequency of the surrounding medium temperature to make irregular the frequency of the resulted temperature response.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Z.-S. Deng, J. Liu, Comp. Biol. Med. 34, 495 (2004).

    Article  MathSciNet  Google Scholar 

  2. J. Liu, L.S. Xu, Int. J. Heat Mass Transfer 43, 2827 (2000).

    Article  MATH  Google Scholar 

  3. S.B. Field, N.M. Bleehen, Cancer Treat Rev. 6, 63 (1979).

    Article  Google Scholar 

  4. Z.P. Chen, R.B. Roemer, ASME J. Biomech. Eng. 114, 473 (1992).

    Article  Google Scholar 

  5. S.T. Clegg, R.B. Roemer, ASME J. Biomech. Eng. 115, 380 (1993).

    Article  Google Scholar 

  6. J. Liu, L. Zhu, X.L. Xu, ASME J. Biomech. Eng. 122, 372 (2000).

    Article  Google Scholar 

  7. G.T. Martin, H.F. Bowman, W.H. Newman, E.G. Cravalho, Adv Biol Heat Mass Transf, ASME 18, 33 (1991).

    Google Scholar 

  8. R. Seip, E.S. Ebbini, IEEE Trans. Biomed. Eng. 42, 828 (1995).

    Article  Google Scholar 

  9. S. Puccini, N.K. Bär, M. Bublat, T. Kahn, H. Busse, Mag. Res. Med. 49, 351 (2003).

    Article  Google Scholar 

  10. R. Magin, A. Peterson, Int. J. Hyperthermia 5, 467 (1989).

    Article  Google Scholar 

  11. G. Fibich, ASME Heat Transfer Division, HTD 322, 27 (1995).

    Google Scholar 

  12. W.M. Whelan, D.R. Wyman, ASME Heat Transfer Division, HTD 322, 17 (1995).

    Google Scholar 

  13. G.L. Valderrama, L.G. Fredin, M.J. Berry, B.P. Dempsey, G.M. Harpole, Proc. SPIE 1427, 200 (1991).

    Article  ADS  Google Scholar 

  14. V.K. Pustovalov, Int. J. Heat Mass Transfer 36, 391 (1993).

    Article  Google Scholar 

  15. H.H. Pennes, J. Appl. Physiol. 1, 93 (1948).

    ADS  Google Scholar 

  16. E.H. Wissler, J. Appl. Physiol. 85, 35 (1998).

    Google Scholar 

  17. J. Lang, B. Erdmann, M. Seebass, IEEE Tr. Biomed. Eng. 46, 1129 (1999).

    Article  Google Scholar 

  18. C.W. Song, A. Lokshina, J.G. Rhee, M. Patten, S.H. Levitt, IEEE Trans. Biomed. Eng. 31, 9 (1984).

    Article  Google Scholar 

  19. T.E. Dudar, R.K. Jain, Cancer Res. 44, 605 (1984).

    Google Scholar 

  20. C.W. Song, Cancer Res. 44, 4721S (1984).

    Google Scholar 

  21. D.T. Tompkins, R. Vanderby, S.A. Klein, W.A. Beckman, R.A. Steeves, D.M. Frye, B.R. Paliwal, Int. J. Hyperthermia 10, 517 (1994).

    Article  Google Scholar 

  22. B. Erdmann, J. Lang, M. Seebass, Ann. New York Acad. Sci. 858, 36 (1998).

    Article  ADS  Google Scholar 

  23. H.S. Carslaw, J.C. Jaeger, Conduction of heat in solids, second edition (Oxford University Press, Oxford, 1959).

  24. J.H. Lienhard, A heat transfer textbook Englewood Cliffs (Prentice-Hall, 1987).

  25. R. Vyas, M.L. Rustgi, Med. Phys. 19, 1319 (1992).

    Article  Google Scholar 

  26. B. Gao, S. Langer, P.M. Corry, Int. J. Hyperthermia 11, 267 (1995).

    Article  Google Scholar 

  27. W.H. Newman, P.P. Lele, H.F. Bowman, Int. J. Hyperthermia 6, 771 (1990).

    Article  Google Scholar 

  28. E. Kengne, F.B. Hamouda, A. Lakhssassi, Appl. Math. 4, 1471 (2013).

    Article  Google Scholar 

  29. E. Kengne, M. Saydé, A. Lakhssassi, Eur. Phys. J. Plus 128, 98 (2013).

    Article  Google Scholar 

  30. C.R. Davies, G.M. Saidel, H. Harasaki, J. Biomech. Eng. 119, 77 (1997).

    Article  Google Scholar 

  31. E. Kengne, A. Lakhssassi, R. Vaillancourt, Appl. Math. 3, 217 (2012).

    Article  MathSciNet  Google Scholar 

  32. Z.-S. Deng, J. Liu, Med. Eng. Phys. 22, 693 (2000).

    Article  Google Scholar 

  33. T.R. Gowrishankar, A.S. Donald, T.M. Gregory, C.W. James, BioMed. Eng. OnLine 3, 1 (2004).

    Article  Google Scholar 

  34. S. Weinbaum, L.M. Jiji, D.E. Lemons, ASME J. Biomech. Eng. 106, 321 (1984).

    Article  Google Scholar 

  35. J. Liu, L.X. Xu, IEEE Trans. Biomed. Eng. 46, 1037 (1999).

    Article  Google Scholar 

  36. K.R. Holmes, Biological Structures and Heat Transfer, Allerton Workshop on the Future of Biothermal Engineering, 1997.

  37. K.R. Diller, Adv. Heat Transfer 22, 157 (1992).

    Article  Google Scholar 

  38. J.H. Li, H. Liang, Laser Medicine - Applications of Laser in Biology and Medicine (Science Press, Beijing, 1989) (in Chinese).

  39. G.T. Anderson, G. Burnside, Proc. Adv. Meas. Comput. Temp. Biomed. 147, 31 (1990).

    Google Scholar 

  40. A.T. Patera, B.B. Mikic, G. Eden, H.F. Bowman, Prediction of Tissue Perfusion from Measurement of the Phase Shift Between Heat Flux and Temperature, in Winter Annual Meeting of ASME, Advances in Bioengineering (1979) pp. 187--191.

  41. K. Weierstrass, Mathematische, Werke V (New York: Johnson, 1915) pp. 4-16.

  42. E.T. Whittaker, G.N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1927) p. 454.

  43. H.W. Schurmann, Phys. Rev. E 54, 4312 (1996).

    Article  ADS  Google Scholar 

  44. J.H. Li, H. Liang, Laser Medicine - Applications of Laser in Biology and Medicine (Science Press, Beijing, 1989).

Download references

Author information

Authors and Affiliations

  1. Département d’informatique et d’ingénierie, Université du Québec en Outaouais, 101 St-Jean-Bosco, Succursale Hull, J8Y 3G5, Gatineau, PQ, Canada

    Emmanuel Kengne & Ahmed Lakhssassi

Authors
  1. Emmanuel Kengne
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed Lakhssassi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Emmanuel Kengne.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kengne, E., Lakhssassi, A. Analytico-numerical study of bio-heat transfer problems with temperature-dependent perfusion. Eur. Phys. J. Plus 130, 89 (2015). https://doi.org/10.1140/epjp/i2015-15089-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2015-15089-1

Keywords

Search

Navigation