This paper is devoted to the development of a mathematical model and its computational analysis targeted at investigating the effects of dual-phase lag on the heating protocol of tumor tissue by the method of electromagnetic hyperthermia. The model comprises two layers, one of them being the vessel layer in which blood flows under the action of a pressure gradient and an external magnetic field, while the other is a tissue layer containing a small rectangular tumor. The tumor tissue is heated by the periodic nature of metabolic and external heat sources. Two phase lags due to the presence of temperature gradient and heat flux are treated to observe the effect of faster heating phenomena. The wave equation representing bioheat transfer in the tissue layer is considered. The problem has been solved directly by employing a suitable finite difference numerical tool. The study shows that the phase lag caused by heat flux is more effective for heating the tumor than the phase lag due to the temperature gradient, and further that transversely applied magnetic field to the blood flow has a limited impact on enhancing the tumor temperature.

本文致力于数学模型的开发及其计算分析，旨在研究电磁热疗方法对双相滞后对肿瘤组织加热方案的影响。该模型包括两层，其中一层是血管层，血液在压力梯度和外部磁场的作用下在其中流动，而另一层是包含小矩形肿瘤的组织层。肿瘤组织被代谢和外部热源的周期性加热。处理由于存在温度梯度和热通量而引起的两个相位滞后，以观察更快的加热现象的影响。考虑表示组织层中生物热传递的波动方程。通过采用合适的有限差分数值工具可以直接解决该问题。研究表明，由于温度梯度，由热通量引起的相位滞后比相位滞后更有效地加热肿瘤，此外，向血流横向施加磁场对提高肿瘤温度的影响有限。