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Mathematical Medicine and Biology Advance Access originally published online on February 20, 2009
Mathematical Medicine and Biology 2009 26(3):187-200; doi:10.1093/imammb/dqp002
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Analytical thermal–optic model for laser heating of biological tissue using the hyperbolic heat transfer equation

Macarena Trujillo{dagger}, María J. Rivera{ddagger} and Juan A. López Molina§

Departamento de Matemática Aplicada, Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

Enrique J. Berjano

Institute for Research and Innovation on Bioengineering, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

{dagger} Email: matrugui{at}mat.upv.es

{ddagger} Email: mjrivera{at}mat.upv.es

§ Email: jalopez{at}mat.upv.es

Email: eberjano{at}eln.upv.es

Received on April 7, 2008. Revised on December 5, 2008. Accepted on January 19, 2009.

In this paper, we solve in an analytical way the thermal-optic coupled problem associated with a 1D model of non-perfused homogeneous biological tissue irradiated by a laser beam. We consider a laser pulse duration of 200 µs and study the temperatures of areas very close to the point of laser beam application. We consider that these values of the temporal and spatial variables mean that the problem has to be solved by means of the hyperbolic heat conduction model instead of the classic or parabolic model. We therefore obtain the solution using both models and apply the temperature profiles obtained to a specific biological tissue for comparison. Finally, we theoretically study the effect of the thermal relaxation time on the temperature profiles in the tissue for both heating and cooling phases (i.e. during and after laser application).

Keywords: hyperbolic heat transfer equation; laser heating; thermal wave


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