Authors: Mohamed M. Sulman; David F. Miller; Gregory Kozlowski
Addresses: Department of Mathematics and Statistics, Wright State University, Dayton, OH, 45435, USA ' Department of Mathematics and Statistics, Wright State University, Dayton, OH, 45435, USA ' Department of Physics, Wright State University, Dayton, OH, 45435, USA
Abstract: In this work, we use Pennes' nonlinear model to estimate the temperature distribution generated by electromagnetically excited nanoparticles and metabolic processes within a spherical tumour surrounded by a sphere of healthy tissue. We describe an efficient numerical approach to analyse the proposed nonlinear model for the heat transfer. Numerical results for the nonlinear bio-heat transfer model with the temperature dependent blood perfusion are presented, and compared with those of the traditional Pennes linear model with constant perfusion rate. We also investigate the dependence of tissue temperature and nanoparticle heat production on the volume fraction of nanoparticles.
Keywords: Pennes; nonlinear modelling; spherical tumours; hyperthermia; magnetic nanoparticles; MNPs; nonlinear perfusion; nanotechnology; temperature distribution; heat transfer; blood perfusion; tissue temperature; nanoparticle heat production; volume fraction.
International Journal of Mathematical Modelling and Numerical Optimisation, 2015 Vol.6 No.3, pp.223 - 234
Received: 03 Mar 2015
Accepted: 16 May 2015
Published online: 21 Sep 2015 *