Article citationsMore>>

E. Erdmann, J. Lang and M. Seebass, “Optimization of Temperature Distributions for Regional Hyperthermia Based on a Nonlinear Heat Equation,” In: K. Diller, Ed., Biotransport: Heat and Mass Transfer in Living Systems, 1998, pp. 36-46.

has been cited by the following article:

• TITLE: 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

  AUTHORS: Emmanuel Kengne, Fathi Ben Hamouda, Ahmed Lakhssassi

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

  JOURNAL NAME: Applied Mathematics, Vol.4 No.10, October 29, 2013

  ABSTRACT: 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.