The bio‐heat transfer equation and its applications in hyperthermia treatments

Murat Tunç (Yeditepe University, Istanbul, Turkey)
Ünal Çamdali (Development Bank of Turkey, Ankara, Turkey)
Cem Parmaksizoğlu (Technical University of Istanbul, Istanbul, Turkey)
Sermet Çikrikçi (Technical University of Istanbul, Istanbul, Turkey)

Engineering Computations

ISSN: 0264-4401

Publication date: 1 June 2006



Cancer is the foremost disease that causes death. The objective of hyperthermia in cancer therapy is to raise the temperature of cancerous tissue above a therapeutic value while maintaining the surrounding normal tissue at sublethal temperature values in cases where surgical intervention is dangerous or impossible. The malignant tissue is heated up to 42°C in the treatment. In this method, the unaffected tissues are aimed to have minimum damage, while the affected ones are destroyed. Therefore, it is very important for the optimization of the method to know the temperature profiles in both tissues. Accurately estimating the tissue temperatures has been a very important issue for tumor hyperthermia treatment planning. This paper, proposes to theoretically predict the temperature response of the biological tissues subject to external EM heating by using the space‐dependent blood perfusion term in Pennes bio‐heat equation.


The bio‐heat transfer equation is parabolic partial differential equation. Grid points including independent variables are initially formed in solution of partial differential equation by finite element method. In this study, one dimensional bio‐heat transfer equation is solved by flex‐PDE finite element method.


In this study, the bio‐heat transfer equation is solved for variable blood perfusion values and the temperature field resulting after a hyperthermia treatment is obtained. Homogeneous, non‐homogeneous tissue and constant, variable blood perfusion rates are considered in this study to display the temperature fields in the biological material exposed to externally induced electromagnetic irradiation.


Temperature‐dependent tissue thermophysical properties have been used and the Pennes equation is solved by FEM analysis. Variable blood perfusion and heat generation values have been used in calculations for healthy tissue and tissue with tumor.



Tunç, M., Çamdali, ., Parmaksizoğlu, C. and Çikrikçi, S. (2006), "The bio‐heat transfer equation and its applications in hyperthermia treatments", Engineering Computations, Vol. 23 No. 4, pp. 451-463.

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