Weinbaum S, Xu L X, Zhu L, Ekpene A
Department of Mechanical Engineering, City College of The City University of New York, NY 10031, USA.
J Biomech Eng. 1997 Aug;119(3):278-88. doi: 10.1115/1.2796092.
A new model for muscle tissue heat transfer has been developed using Myrhage and Eriksson's [23] description of a muscle tissue cylinder surrounding secondary (s) vessels as the basic heat transfer unit. This model provides a rational theory for the venous return temperature for the perfusion source term in a modified Pennes bioheat equation, and greatly simplifies the anatomical description of the microvascular architecture required in the Weinbaum-Jiji bioheat equation. An easy-to-use closed-from analytic expression has been derived for the difference between the inlet artery and venous return temperatures using a model for the countercurrent heat exchange in the individual muscle tissue cylinders. The perfusion source term calculated from this model is found to be similar in form to the Pennes's source term except that there is a correction factor or efficiency coefficient multiplying the Pennes term, which rigorously accounts for the thermal equilibration of the returning vein. This coefficient is a function of the vascular cross-sectional geometry of the muscle tissue cylinder, but independent of the Peclet number in contrast to the recent results in Brinck and Werner [8]. The value of this coefficient varies between 0.6 and 0.7 for most muscle tissues. In part II of this study a theory will be presented for determining the local arterial supply temperature at the inlet to the muscle tissue cylinder.
一种新的肌肉组织热传递模型已经开发出来，该模型以米尔哈格（Myrhage）和埃里克森（Eriksson）[23]对围绕二级（s）血管的肌肉组织圆柱体的描述为基础热传递单元。该模型为修正的彭尼斯（Pennes）生物热方程中灌注源项的静脉回流温度提供了合理的理论，并极大地简化了温鲍姆-吉吉（Weinbaum-Jiji）生物热方程所需的微血管结构的解剖学描述。利用单个肌肉组织圆柱体中的逆流热交换模型，推导出了一个易于使用的封闭形式解析表达式，用于表示动脉入口温度与静脉回流温度之间的差值。从该模型计算出的灌注源项在形式上与彭尼斯源项相似，只是有一个校正因子或效率系数乘以彭尼斯项，该系数严格考虑了回流静脉的热平衡。该系数是肌肉组织圆柱体血管横截面几何形状的函数，但与布林克（Brinck）和维尔纳（Werner）[8]最近的结果不同，它与佩克莱特数无关。对于大多数肌肉组织，该系数的值在0.6到0.7之间变化。在本研究的第二部分，将提出一种理论，用于确定肌肉组织圆柱体入口处的局部动脉供应温度。
