Eur. Phys. J. Plus (2012) 127: 89
https://doi.org/10.1140/epjp/i2012-12089-7

Regular Article

Monitoring of temperature distribution in living biological tissues via blood perfusion

¹ National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China
² Département d’informatique et d’ingénierie, Université du Québec en Outaouais, 101 St-Jean-Bosco, J8Y 3G5, Gatineau, QC, Canada
³ Department of Mathematics and Statistics, Faculty of Science, University of Ottawa, 585 King Edward Ave., K1N 6N5, Ottawa, ON, Canada

^* e-mail: ekengne@uottawa.ca

Received: 13 June 2012
Revised: 13 July 2012
Accepted: 3 August 2012
Published online: 27 August 2012

Abstract

Several investigators have argued that Pennes’ interpretation of the vascular contribution to heat transfer in perfused tissues fails to account for the actual thermal equilibration process between the flowing blood and the surrounding tissue and proposed new models, presumably based on a more realistic anatomy of the perfused tissue. In this same direction, we introduce an exponential imprint into the thermal order parameter governing the bioheat transfer described by the Pennes model equation and then engineer the imprinted exponent suitably to generate the modified Pennes bioheat transfer model with time-variable coefficients that takes into account the dependence of blood perfusion on both time and temperature. This mathematical model uses blood perfusion to monitor and control temperature distribution in living biological tissues. We observe that all monitoring parameters interact to contribute to the control and monitoring of temperature distribution in tissues. Employing similarity and F-expansion approaches, we propose an algorithm for finding thermal traveling wave-like solutions of the model.