Author(s)

Emmanuel Kengne, Fathi Ben Hamouda, Ahmed Lakhssassi

Department of Computer Science and Engineering, University of Quebec at Outaouais, Gatineau, Canada.

Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended generalized Riccati equation mapping method, we find analytical traveling wave solutions of the considered BHT equation. All the travelling wave solutions obtained have been used to explicitly investigate the effect of linear and quadratic coefficients of temperature dependence on temperature distribution in tissues. We found that the parameter of the nonlinear superposition formula for Riccati can be used to control the temperature of living tissues. Our results prove that the extended generalized Riccati equation mapping method is a powerful tool for investigating thermal traveling-wave distribution in biological tissues.

Bio-Heat Transfer; Pennes Bio-Heat Model; Temperature-Dependent Blood Perfusion; Thermal Therapy; Extended Generalized Riccati Equation Mapping Method

Kengne, E. , Hamouda, F. and Lakhssassi, A. (2013) Extended Generalized Riccati Equation Mapping for Thermal Traveling-Wave Distribution in Biological Tissues through a Bio-Heat Transfer Model with Linear/Quadratic Temperature-Dependent Blood Perfusion. Applied Mathematics, 4, 1471-1484. doi: 10.4236/am.2013.410199.