Abstract

In this study, we introduce a three-phase-lag (TPL) bioheat transfer model for living biological tissue by considering the heat conduction law that includes heat flux, temperature gradient and thermal displacement gradient, among the constitutive relation. The formulated TPL bioheat model is an extension of bioheat transfer models proposed by Pennes, Cattaneo-Vernotte and Tzou. The semi-analytical method has been used for the solution of TPL bioheat transfer model and this model is validated with experimental data [Stolwijk, J. A. J., and J. D. Hardy. 1966. Temperature regulation in man: a theoretical study. Pflugers Archiv Fur Die Gesamte Physiologie Des Menschen Und Der Tiere 291(2):129–62]. The phase lag times due to heat flux, temperature gradient and thermal displacement gradient is semi analytically investigated and it is found that phase-lag due to thermal displacement gradient affects significantly on temperature distribution in tissue. The semi-analytical solution has been verified with a numerical solution. The effect of parameters, such as lagging times, blood perfusion rate, metabolic heat source term and TPL parameter on tissue temperature is also discussed in detail.

• Highlights

• Three-phase-lag bioheat transfer model has been introduced for the study of heat transfer in living biological tissue.

• The semi analytical method has been used for the solution of the TPL model.

• Proposed model is validated with experimental data.

• The formulated TPL model is more accurate than other existing models.

摘要

在这项研究中，我们通过考虑本构关系中包括热通量、温度梯度和热位移梯度的热传导规律，引入了活体组织的三相滞后（TPL）生物传热模型。公式化的 TPL 生物热模型是 Pennes、Cattaneo-Vernotte 和 Tzou 提出的生物热传递模型的扩展。半解析法已用于求解 TPL 生物传热模型，并用实验数据验证了该模型 [Stolwijk, JAJ, 和 JD Hardy。1966. 人体温度调节：一项理论研究。Pflugers Archiv Fur Die Gesamte Physiologie Des Menschen Und Der Tiere 291(2):129-62]。由于热通量导致的相位滞后时间，对温度梯度和热位移梯度进行了半解析研究，发现热位移梯度引起的相位滞后对组织中的温度分布有显着影响。半解析解已经用数值解进行了验证。还详细讨论了滞后时间、血液灌注率、代谢热源项和 TPL 参数等参数对组织温度的影响。

• 强调

• 引入了三相滞后生物传热模型来研究活体组织中的传热。

• TPL模型的求解采用了半解析法。

• 用实验数据验证了所提出的模型。

• 制定的 TPL 模型比其他现有模型更准确。