Analytical Study on Bioheat Transfer Problems with Spatial or Transient Heating on Skin Surface or Inside Biological Bodies

Abstract

Several closed form analytical solutions to the bioheat transfer problems with space or transient heating on skin surface or inside biological bodies were obtained using Green's function method. The solutions were applied to study several selected typical bioheat transfer processes, which are often encountered in cancer hyperthermia, laser surgery, thermal comfort analysis, and tissue thermal parameter estimation. Thus a straightforward way to quantitatively interpret the temperature behavior of living tissues subject to constant, sinusoidal, step, point or stochastic heatings etc. both in volume and on boundary were established. Further solution to the three-dimensional bioheat transfer problems was also given to illustrate the versatility of the present method. Implementations of this study to the practical problems were addressed.

Thermal Therapy, Part IV: Electromagnetic and Thermal Dosimetry

“…[127][128][129][130] Closed-form analytical solutions to the bioheat transport problems with space and transient heating were reported using Green's function method. 131 …”

“…131 Unlike the prediction of the electric fi eld, for which an appropriate continuum physical model may exist, no clear compromise exists for a suitable mathematical model to predict heating patterns in biological objects. 106 Biomedical engineers have attempted to model accurately bioheat transfer in tissues since it is the basis for the human thermotherapy 152 and the human thermoregulation system.…”

“…Zhu and Diao 156 used the Pennes equation to simulate the steady-state temperature distribution within the brain after head injury. Also, Deng and Liu 131 used the equation to study analytically the effect of pulsative blood perfusion on the tissue temperature. Wainwright 157 applied Pennes thermal model and found the fi nal steady-state temperature rise in the brain for a 0.25-W antenna at frequencies of 900 MHz and 1800 MHz to be as high as 0.1 o C. However, other EM devices could produce greater heating and there is the possibility that nonuniform heating could produce local, higher temperature rises.…”

Solution of hyperbolic bioheat transfer problems by numerical green's functions: the ExGA-linear θ method

“…Both analytical and numerical techniques for the solution of heat conduction problems based upon Green's functions are well-documented (Beck, 1992;Wu and Chu, 1999;Wrobel, 2002). However, the solution of bioheat problems using Green's functions is not widely popular (Newman, Bowman, 1990;Chan, 1992;Gao B., Langer and Corry, 1995;Deng and Liu, 2002;Li, Liu and Yue, 2009), with few published papers which concentrate mainly on the parabolic Pennes equation. It is well known that one of the major drawbacks in the solution of partial differential equations by Green's function-based techniques is the lack of analytical Green's functions for complicated geometries and/or variable material properties.…”

Software didático para modelagem do padrão de aquecimento dos tecidos irradiados por ultra-som fisioterapêutico

“…Given this scenario, this paper puts forward an educational software that simulates the ultrasound heating pattern of tissue, based on a simplified mathematical model of the biothermal equation (Bioheat Transfer, BHT) 13 . This equation describes the behavior of temperature in tissues over time, at different depths.…”