Kolios M C, Sherar M D, Hunt J W
Division of Experimental Therapeutics, Ontario Cancer Institute, University of Toronto, Canada.
Phys Med Biol. 1995 Apr;40(4):477-94. doi: 10.1088/0031-9155/40/4/001.
Large blood vessels can produce steep temperature gradients in heated tissues leading to inadequate tissue temperatures during hyperthermia. This paper utilizes a finite difference scheme to solve the basic equations of heat transfer and fluid flow to model blood vessel cooling. Unlike previous formulations, heat transfer coefficients were not used to calculate heat transfer to large blood vessels. Instead, the conservation form of the finite difference equations implicitly modelled this process. Temperature profiles of heated tissues near thermally significant vessels were calculated. Microvascular heat transfer was modelled either as an effective conductivity or a heat sink. An increase in perfusion in both microvascular models results in a reduction of the cooling effects of large vessels. For equivalent perfusion values, the effective conductivity model predicted more effective heating of the blood and adjacent tissue. Furthermore, it was found that optimal vessel heating strategies depend on the microvascular heat transfer model adopted; localized deposition of heat near vessels could produce higher temperature profiles when microvascular heat transfer was modelled according to the bioheat transfer equation (BHTE) but not the effective thermal conductivity equation (ETCE). Reduction of the blood flow through thermally significant vessels was found to be the most effective way of reducing localized cooling.
大血管可在受热组织中产生陡峭的温度梯度，导致热疗期间组织温度不足。本文采用有限差分格式求解传热和流体流动的基本方程，以模拟血管冷却。与先前的公式不同，传热系数未用于计算向大血管的传热。相反，有限差分方程的守恒形式隐含地模拟了这一过程。计算了热显著血管附近受热组织的温度分布。微血管传热被建模为有效热导率或热汇。两种微血管模型中灌注的增加都会导致大血管冷却效应的降低。对于等效的灌注值，有效热导率模型预测血液和相邻组织的加热更有效。此外，发现最佳的血管加热策略取决于所采用的微血管传热模型；当根据生物传热方程（BHTE）而非有效热导率方程（ETCE）对微血管传热进行建模时，在血管附近局部沉积热量可产生更高的温度分布。发现减少通过热显著血管的血流是减少局部冷却的最有效方法。
