Kengne, E., Hamouda, F.B. 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.
http://dx.doi.org/10.4236/am.2013.410199

has been cited by the following article:

• TITLE: A Mathematical Model to Solve Bio-Heat Transfer Problems through a Bio-Heat Transfer Equation with Quadratic Temperature-Dependent Blood Perfusion under a Constant Spatial Heating on Skin Surface

  AUTHORS: Emmanuel Kengne, Idir Mellal, Mariem Ben Hamouda, Ahmed Lakhssassi

  KEYWORDS: Bio-Heat Transfer Problems, Pennes Bio-Heat Model, Temperature-Dependent Blood Perfusion, Thermal Therapy, Extended Mapping Method

  JOURNAL NAME: Journal of Biomedical Science and Engineering, Vol.7 No.9, July 28, 2014

  ABSTRACT: We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method with symbolic computation, we obtain the exact analytical thermal traveling wave solution, which describes the non-uniform temperature distribution inside the bodies. The found exact solution is used to investigate the temperature distribution in the tissues. It is found that the surrounding medium with higher temperature does not necessarily imply that the tissue will quickly (after a short duration of heating process) reach the desired temperature. It is also found that increased perfusion causes a decline in local temperature.