This paper presents mathematical responses for the dual-phase-lag (DPL) hypothesis, which accounts for nonequilibrium heat transfer during magnetic nanoparticle hyperthermia in tumor. To get this precision, volume averaging is used for the local instantaneous energy formulation for tissues and blood. This study proposes a hybrid numerical strategy to solve this problem by combining change of variables, improved discretization techniques, and Laplace transforms. Using the Arrhenius formulas, the range of denatured proteins is used to assess the degree of heat damages to the tumor and healthy tissues. The impacts of porosity, the blood perfusion and metabolism on the temperature and the thermal injuries are studied. The numerical estimations of temperature and the resulting of thermal injuries are shown on a graph, and a comparison with earlier research establishes the results’ validity.

中文翻译：

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磁性纳米颗粒热疗过程中肿瘤非平衡生物热传递的分析解决方案


本文提出了双相滞后（DPL）假说的数学响应，该假说解释了肿瘤中磁性纳米颗粒热疗过程中的非平衡传热。为了获得这种精度，体积平均用于组织和血液的局部瞬时能量公式。本研究提出了一种混合数值策略，通过结合变量的变化、改进的离散化技术和拉普拉斯变换来解决这个问题。使用阿伦尼乌斯公式，变性蛋白质的范围用于评估热损伤对肿瘤和健康组织的程度。研究了孔隙率、血液灌注和代谢对温度和热损伤的影响。温度的数值估计和热损伤的结果显示在图表上，与早期研究的比较确定了结果的有效性。