Eur. Phys. J. Plus (2013) 128: 98
https://doi.org/10.1140/epjp/i2013-13098-8

Regular Article

Effect of convective term on temperature distribution in biological tissue

Département d’informatique et d’ingénierie, Université du Québec en Outaouais, 101 St-Jean-Bosco, J8Y 3G5, Gatineau(PQ), Canada

^* e-mail: kengem01@uqo.ca

Received: 2 July 2013
Revised: 19 July 2013
Accepted: 28 July 2013
Published online: 30 August 2013

Abstract

We introduce a phase imprint into the order parameter describing the influence of blood flow on the temperature distribution in the tissue described by the one-dimensional Pennes equation and then engineer the imprinted phase suitably to generate a modified Pennes equation with a gradient term (known in the theory of biological systems as convective term) which is associated with the heat convected by the flowing blood. Using the derived model, we analytically investigate temperature distribution in biological tissues subject to two different spatial heating methods. The applicability of our results is illustrated by one of typical bio-heat transfer problems which is often encountered in therapeutic treatment, cancer hyperthermia, laser surgery, thermal injury evaluation, etc. Analyzing the effect of the convective term on temperature distribution, we found that an optimum heating of a biological system can be obtained through regulating the convective term.