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Journal of Atomic, Molecular, and Optical Physics
Volume 2012 (2012), Article ID 135708, 22 pages
Research Article

An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle

1Department of Electrical Engineering, Faculty of Engineering, Tel-Aviv University, 69978 Tel-Aviv, Israel
2Department of Biomedical Engineering, Faculty of Engineering, Tel-Aviv University, 69978 Tel-Aviv, Israel

Received 10 February 2012; Revised 1 June 2012; Accepted 4 June 2012

Academic Editor: Yuval Garini

Copyright © 2012 Brenda Dana and Israel Gannot. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study analytically analyzes the changes in the temperature profile of a homogenous and isotropic medium having the same thermal parameters as a muscular tissue, due to the heat released by a single magnetic nanoparticle (MNP) to its surroundings when subject to different magnetic field profiles. Exploring the temperature behavior of a heated MNP can be very useful predicting the temperature increment of it immediate surroundings. Therefore, selecting the most effective magnetic field profile (MFP) in order to reach the necessary temperature for cancer therapy is crucial in hyperthermia treatments. In order to find the temperature profile caused by the heated MNP immobilized inside a homogenous medium, the 3D diffusive-heat-flow equation (DHFE) was solved for three different types of boundary conditions (BCs). The change in the BC is caused by the different MF profiles (MFP), which are analyzed in this article. The analytic expressions are suitable for describing the transient temperature response of the medium for each case. The analysis showed that the maximum temperature increment surrounding the MNP can be achieved by radiating periodic magnetic pulses (PMPs) on it, making this MFP more effective than the conventional cosine profile.