Simple models for the heating curve in magnetic hyperthermia experiments

The use of magnetic nanoparticles for magnetic hyperthermia cancer treatment is a rapidly developing field of multidisciplinary research. From the material's standpoint, the main challenge is to optimize the heating properties of the material while maintaining the frequency of the exciting field as low as possible to avoid biological side effects. The figure of merit in this context is the specific absorption rate (SAR), which is usually measured from calorimetric experiments. Such measurements, which we refer to as heating curves, contain a substantial amount of information regarding the energy barrier distribution of the sample. This follows because the SAR itself is a function of temperature, and reflect the underlying magneto-thermal properties of the system. Unfortunately, however, this aspect of the problem is seldom explored and, commonly, only the SAR at ambient temperature is extracted from the heating curve. In this paper we introduce a simple model capable of describing the entire heating curve via a single differential equation. The SAR enters as a forcing term, thus facilitating the use of different models for it. We discuss in detail the heating in the context of Neel relaxation and show that high anisotropy samples may present an inflection point related to the reduction of the energy barrier caused by the increase in temperature. Mono-disperse and poli-disperse systems are discussed in detail and a new alternative to compute the temperature dependence of the SAR from the heating curve is presented. (C) 2012 Elsevier B.V. All rights reserved.