AN EVALUATION OF THE WEINBAUM-JIJI BIOHEAT EQUATION FOR NORMAL AND HYPERTHERMIC CONDITIONS
AN EVALUATION OF THE WEINBAUM-JIJI BIOHEAT EQUATION FOR NORMAL AND HYPERTHERMIC CONDITIONS
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DOI：
10.1115/1.2891130
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发表时间：
1990-02-01
影响因子：
1.7
通讯作者：
LEVIN, RL
中科院分区：
文献类型：
--
作者：
CHARNY, CK;WEINBAUM, S;LEVIN, RL
将一维简化 Weinbaum-Jiji (WJ) 生物传热方程的预测与代表 WJ 方程推导起点的完整一维三方程模型的预测以及使用 Pennes 传统生物传热方程获得的结果进行比较 [6]。 WJ方程与第2代至第9代血管的三方程模型非常吻合，这些血管位于肌肉层的外半部，在基础血流条件下，成对的血管直径小于500μm。同时，Pennes 方程更好地描述了第一代中的传热，其中容器的直径大于 500 μm，并且容器的归一化热平衡长度 ε 大于 0.3。这些结果是在常温和高温条件下获得的。从这些结果中得出了 Pennes 方程中血液源项的新概念视图。该源术语最初旨在表示毛细血管中的各向同性热源，但显示为描述由于小血管泄放而从最大逆流微血管到组织的热传递。 WJ 方程包括这种效应，但在 ε 时显着高估了第二种类型的组织热传递，即逆流对流热传递。 > 0.3。迹象表明，在第一代（正常体温）和前两到三代（出现高热后）中应用 Pennes 方程以及在后续几代中应用 Weinbaum-Jiji 方程的“混合”模型将最适合模拟灌注组织中的生物传热。
The predictions of the simplified Weinbaum-Jiji (WJ) bioheat transfer equation in one dimension are compared to those of the complete one-dimensional three-equation model that represented the starting point for the derivation of the WJ equation, as well as results obtained using the traditional bioheat transfer equation of Pennes [6]. The WJ equation provides very good agreement with the three-equation model for vascular generations 2 to 9, which are located in the outer half of the muscle layer, where the paired vessel diameters are less than 500 .mu.m, under basal blood flow conditions. At the same time, the Pennes equation yields a better description of heat transfer in the first generation, where the vessels'' diameters are greater than 500 .mu.m and .epsilon., the vessels'' normalized thermal equilibration length, is greater than 0.3. These results were obtained under both normothermic and hyperthermic conditions. A new conceptual view of the blood source term in the Pennes equation has emerged from these results. This source term, which was originally intended to represent an isotropic heat source in the capillaries, is shown to describe instead the heat transfer from the largest countercurrent microvessels to the tissue due to small vessel bleed-off. The WJ equation includes this effect, but significantly overestimates the second type of tissue heat transfer, countercurrent convective heat transfer, when .epsilon. > 0.3. Indications are that a "hybrid" model that applies the Pennes equation in the first generation (normothermic) and first two to three generations (after onset of hyperthermia) and the Weinbaum-Jiji equation in the subsequent generations would be most appropriate for simulations of bioheat transfer in perfused tissue.