Analytical modeling of hyperthermia using magnetic nanoparticles

Hyperthermia using magnetic nanoparticles (MNPs) is one of many techniques to treat cancer causing minimal damage to healthy tissues. In the present work we give an analytical resolution of the bio-heat equation (based on Pennes model) providing the temperature rise as a function of the characteristics of the magnetic nanoparticles, the applied magnetic field and the biological properties of the tissue. The temperature inside the tumor was found to be very sensitive to the frequency f of alternating magnetic field, magnetic field amplitude H0 and volume fraction φ. This study optimizes the intensity of magnetic field to reach ideal hyperthermia conditions. When f varies between 50 and 150 KHz, temperature increases from 39 °C until 53 °C; when H0 is ranged from 5 − 15 kA/m, it increases from 39.5 °C until 49 °C, and when volume fraction φ of MNPs is ranged from 2 × 10−4 to 3 × 10−4 it increases from 44 °C until 48 °C.

Analysis of Non-Fourier Thermal Behavior in Layered Tissue with Pulse Train Heating

This paper investigates the thermal behavior in laser-irradiated layered tissue, which was stratified into skin, fat, and muscle. A modified nonFourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase lag model. This equation is a fourth order partial differential equation and can be simplified as the bio-heat transfer equations derived from Pennes model, thermal wave model, and the linearized form of dual-phase lag model. The boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The deviations of the results from the bio-heat transfer equations based on Pennes model, thermal wave model and dual-phase lag model are presented and discussed.

Pennes’ 1948 paper revisited

A paper published by Harry H. Pennes in Volume 1 of the Journal of Applied Physiology defined the theoretical basis for a considerable body of analysis performed by many investigators during the ensuing half century. However, during the past decade, the Pennes’ model of heat transfer in perfused tissue has been criticized for various reasons, one of which is that his own experimental data seemed to be at variance with the model. More specifically, the shape of the mean temperature-depth relationship measured by Pennes was distinctly different from the shape of the theoretical curve. In this paper, I show that Pennes used an inappropriate procedure to analyze his data and that, when the data are analyzed in a more rigorous manner, they support his theory. Additional support for Pennes’ theory is provided by the experimental data of H. Barcroft and O. G. Edholm [ J. Physiol. (Lond.) 102: 5–20, 1942 and 104: 366–376, 1946], who had previously studied cooling of the forearm during immersion in water at various temperatures.

Bioheat Transfer in a Branching Countercurrent Network During Hyperthermia

A bioheat transfer model which computes the spatial variations in the arteriole, venule, and muscle temperatures in a human extremity under both resting and hyperthermic conditions is presented. This model uses the two-parameter model first proposed by Baish et al. [2] to account for the heat exchange between tissue and the paired arterioles and venules that comprise the microcirculation. Thermoregulation of the muscle blood flow during hyperthermia is also incorporated into the model. Results show that even when the paired arteriole and venule are assumed to have equal radii, the mean temperature under both steady and transient conditions is not equal to the mean of the arteriole and venule blood temperatures. Tissue temperature profiles during hyperthermia computed with the three-equation model presented in this study are similar in shape and magnitude to those predicted by the traditional one-equation Pennes bioheat transfer model [1]. This is due primarily to the influence of thermoregulatory mechanism in the heated muscle. The unexpected agreement is significant given the inherent relative simplicity of the traditional Pennes model. An “experimental” thermal conductivity is presented to relate the theoretical results to experimental procedures that are widely used to estimate the enhancement of conductivity by perfusion.