Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia.
Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt; Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia.
J Therm Biol. 2019 May;82:229-233. doi: 10.1016/j.jtherbio.2019.04.003. Epub 2019 Apr 14.
In the present paper, the bioheat equation under fractional derivatives is used to study the thermal damage within the skin tissue during the thermal therapy. Basically, the analytical solutions in the Laplace domain are easily obtainable. The influences of the fractional derivative and moving heat source velocity on the temperature of skin tissues and the thermal injuries are precisely investigated. The outcomes show that the fractional bioheat model are reduced to the hyperbolic and parabolic bioheat models when the fractional order parameter is equal to one and the relaxation time is close to zero respectively. The thermal injuries to the tissue are assessed by the denatured protein range using the formulation of Arrhenius. The numerical outcomes of thermal injuries and temperatures are graphically introduced. In conclusion, a parametric analysis is devoted to the identification of an appropriate procedure for selecting important design variables to reach effective heating in hyperthermia treatment.
本文采用分数阶导数下的生物传热方程研究热疗过程中皮肤组织内的热损伤。基本上，可以很容易地获得拉普拉斯域中的解析解。精确地研究了分数阶导数和移动热源速度对皮肤组织温度和热损伤的影响。结果表明，当分数阶参数等于 1 且弛豫时间接近 0 时，分数生物传热模型分别简化为双曲型和抛物型生物传热模型。使用阿累尼乌斯公式来评估组织的变性蛋白范围来评估热损伤。热损伤和温度的数值结果以图形方式呈现。总之，进行了参数分析以确定选择重要设计变量以实现高热治疗中有效加热的适当程序。
