Purpose

In the present paper, the new concept of “memory dependent derivative” in the Pennes’ bioheat transfer and heat-induced mechanical response in human living tissue with variable thermal conductivity and rheological properties of the volume is considered.

Design/methodology/approach

A problem of cancerous layered with arbitrary thickness is considered and solved analytically by Kirchhoff and Laplace transformation. The analytical expressions for temperature, displacement and stress are obtained in the Laplace transform domain. The inversion technique for Laplace transforms is carried out using a numerical technique based on Fourier series expansions.

Findings

Comparisons are made with the results anticipated through the coupled and generalized theories. The influence of variable thermal, volume materials properties and time-delay parameters for all the regarded fields for different forms of kernel functions is examined.

Originality/value

The results indicate that the thermal conductivity and volume relaxation parameters and MDD parameter play a major role in all considered distributions. This dissertation is an attempt to provide a theoretical thermo-viscoelastic structure to help researchers understand the complex thermo-mechanical processes present in thermal therapies.

中文翻译：

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具有可变热材料特性的生物粘弹性组织的热机械记忆响应

目的

在本文中，考虑了具有可变的热导率和流变特性的人体生物组织中Pennes生物传热和热诱导的机械响应中的“记忆相关导数”新概念。

设计/方法/方法

考虑并通过基尔霍夫（Kirchhoff）和拉普拉斯（Laplace）变换解析地解决了具有任意厚度的癌变问题。在拉普拉斯变换域中获得了温度，位移和应力的解析表达式。使用基于傅立叶级数展开的数值技术执行Laplace变换的反演技术。

发现

与通过耦合和广义理论预期的结果进行比较。对于不同形式的核函数，研究了所有所考虑领域的可变热，体积材料特性和时延参数的影响。

创意/价值

结果表明，热导率和体积弛豫参数以及MDD参数在所有考虑的分布中均起主要作用。本论文试图提供一种理论上的热粘弹性结构，以帮助研究人员了解热疗法中存在的复杂的热机械过程。