Three-phase-lag bioheat transfer model and its validation with experimental data

Abstract

In this study, we introduce a three-phase-lag (TPL) bioheat transfer model for living biological tissue by considering the heat conduction law that includes heat flux, temperature gradient and thermal displacement gradient, among the constitutive relation. The formulated TPL bioheat model is an extension of bioheat transfer models proposed by Pennes, Cattaneo-Vernotte and Tzou. The semi-analytical method has been used for the solution of TPL bioheat transfer model and this model is validated with experimental data [Stolwijk, J. A. J., and J. D. Hardy. 1966. Temperature regulation in man: a theoretical study. Pflugers Archiv Fur Die Gesamte Physiologie Des Menschen Und Der Tiere 291(2):129–62]. The phase lag times due to heat flux, temperature gradient and thermal displacement gradient is semi analytically investigated and it is found that phase-lag due to thermal displacement gradient affects significantly on temperature distribution in tissue. The semi-analytical solution has been verified with a numerical solution. The effect of parameters, such as lagging times, blood perfusion rate, metabolic heat source term and TPL parameter on tissue temperature is also discussed in detail.

Highlights

• Three-phase-lag bioheat transfer model has been introduced for the study of heat transfer in living biological tissue.

• The semi analytical method has been used for the solution of the TPL model.

• Proposed model is validated with experimental data.

• The formulated TPL model is more accurate than other existing models.

Keywords:

• Three-phase-lag
• skin tissue
• heat transfer
• Laplace transform technique

Acknowledgments

The authors express their sincere thanks to the editor and anonymous reviewers for their valuable suggestions for the improvement of manuscript. Authors are thankful to DST-center for Interdisciplinary Mathematical Sciences, Banaras Hindu University Varanasi, India, for providing necessary facilities during preparation of the manuscript. First author is also thankful to Govt. Polytechnic Nawada, Bihar, India for providing necessary facilities of the revision of the manuscript.