Fundamental solutions to the bioheat equation and their application to magnetic fluid hyperthermia

Abstract

Methods of predicting temperature profiles during local hyperthermia treatment are very important to avoid damage to healthy tissue. With this aim, fundamental solutions of Pennes' bioheat equation are derived in rectangular, cylindrical, and spherical coordinates. The medium is idealised as isotropic with effective thermal properties. Temperature distributions due to space- and time-dependent heat sources are obtained by the solution method presented. Applications of the fundamental solutions are addressed with emphasis on a particular problem of Magnetic Fluid Hyperthermia (MFH) consisting of a thin shell of magnetic nanoparticles in the outer surface of a spherical solid tumour. It is observed from the solution of this particular problem that the temperature profiles are strongly dependent on the distribution of the magnetic nanoparticles within the tissue. An almost uniform temperature profile is obtained inside the tumour with little penetration of therapeutic temperatures to the outer region of healthy tissue. The fundamental solutions obtained can be used to develop boundary element methods to predict temperature profiles with more complicated geometries.

Temperature distribution in multi-layer skin tissue in presence of a tumor

“…A significant amount of research in bioheat transfer over the past few decades has led to an understanding of the governing dynamics of thermal transport in a tissue [1][2][3]. A number of thermal based therapeutic measures have been developed and adopted in practice, including laser surgery, cryotherapy, magnetic nanoparticle based hyperthermia and radio frequency ablation [4][5][6][7][8][9]. The design and optimization of these procedures has been aided by advancements in the understanding of bioheat transfer.…”

“…An analytical study of an axisymmetric tissue-vascular system is used to analyze the effect due to the radiofrequency ablation treatment due to volumetric heat generation in the tissue region due to a heater probe [9]. The application of Pennes equation to magnetic fluid hyperthermia has been studied, where a theoretical solution is presented for a spherical tumor surrounded by a thin shell of magnetic nanoparticles [7]. An analytical model was proposed to investigate the rate of cell destruction during a freeze-thaw cryosurgical procedure, in order to minimize damage to healthy cells [5].…”

State of Art on Bioimaging by Nanoparticles in Hyperthermia and Thermometry: Visualization of Tissue Protein Targeting

“…The art of nanoparticles in hyperthermia is growing technical development focused on thermal behavior and particle chemical characteristics such as magnetic polymersomes, nickel ferrite [161][162][163][164][165][166][167]. Real time adaptive control algorithms are reported as robust tools of hyperthermia treatment in cancer [168][169][170][171][172][173][174][175][176].…”

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

“…Moreover, (9) is related to the TTF by (3). Sometimes, the derivative of the temperature profile, or the rate of the change in the temperature surrounding the MNP is taken in consideration in order to verify that the treatment is safe for inducing controlled MH [47,52].…”

“…Magnetic Hyperthermia (MH) is one of many approaches currently being tested for cancer therapy [1][2][3]. The goal of this approach is to specifically heat the regions containing the cancerous cells by means of the magnetic losses caused by the physical properties of the magnetic nanoparticles (MNPs) when being exposed to an external magnetic field (MF).…”