Zhu L, Lemons D E, Weinbaum S
Department of Mechanical Engineering, City College of The City University of New York, NY 10031, USA.
Ann Biomed Eng. 1996 Jan-Feb;24(1):109-123. doi: 10.1007/BF02771000.
A new experimental approach was developed to obtain the first direct measurements of the axial countercurrent thermal equilibration in a microvascular tissue preparation using high resolution infrared thermography. Detailed surface temperature measurements were obtained for an exteriorized rat cremaster muscle in which pharmacological vasoactive agents were used to change the local blood flow Peclet number from 1 to 14 in the feeding artery. Under normal conditions, only the 1A arteries (> 70 microns diameter) showed thermal nonequilibration with the surrounding tissue. The theoretical model developed by Zhu and Weinbaum (28) for a two-dimensional tissue preparation with arbitrarily embedded countercurrent vessels was modified to include axial conduction and the presence of the supporting glass slide. This modified model was used to interpret the experimental results and to relate the surface temperature profiles to the bulk temperature profiles in the countercurrent artery and vein and the local average tissue temperature in the cross-sectional plane. Surface temperature profiles transverse to the vessel axis are shown to depend significantly on the tissue inlet temperature. The eigenfunction for the axial thermal equilibration depends primarily on the blood flow Peclet number and the environmental convective coefficient. The theoretical results predict that when rho(ar)*Pe is less than 1 mm (the range in our experiments), axial conduction is the dominant mode of axial thermal equilibration. For 1 < rho(ar)*PE < 3 mm, countercurrent blood flow becomes comparable to axial conduction, whereas, when rho(ar)*Pe > 3 mm, countercurrent blood flow is the dominant mode of axial thermal equilibration. Therefore, for rho(ar)*Pe > 3 mm the axial equilibration length is proportional to the blood flow Peclet number, as predicted previously by Zhu and Weinbaum in a study in which axial conduction was neglected. It also is shown that the axial decay of the tissue temperature at low perfusion rates can be described by a simple one-dimensional Weinbaum-Jiji equation with a newly derived conduction shape factor.
一种新的实验方法被开发出来，用于在微血管组织制备中使用高分辨率红外热成像技术首次直接测量轴向逆流热平衡。对一只大鼠的离体提睾肌进行了详细的表面温度测量，在该肌肉中使用药理血管活性剂将供血动脉中的局部血流佩克莱数从1改变到14。在正常情况下，只有直径大于70微米的1A动脉与周围组织表现出热不平衡。由Zhu和Weinbaum（28）为具有任意嵌入逆流血管的二维组织制备所开发的理论模型被修改，以纳入轴向传导和支撑载玻片的存在。这个修改后的模型被用来解释实验结果，并将表面温度分布与逆流动脉和静脉中的体温度分布以及横截面中的局部平均组织温度联系起来。垂直于血管轴的表面温度分布被证明显著依赖于组织入口温度。轴向热平衡的特征函数主要取决于血流佩克莱数和环境对流系数。理论结果预测，当ρ(ar)*Pe小于1毫米（我们实验中的范围）时，轴向传导是轴向热平衡的主导模式。对于1 < ρ(ar)*PE < 3毫米，逆流血流与轴向传导相当，而当ρ(ar)*Pe > 3毫米时，逆流血流是轴向热平衡的主导模式。因此，对于ρ(ar)*Pe > 3毫米，轴向平衡长度与血流佩克莱数成正比，正如Zhu和Weinbaum之前在一项忽略轴向传导的研究中所预测的那样。还表明，在低灌注率下组织温度的轴向衰减可以用一个简单的一维Weinbaum-Jiji方程来描述，该方程具有一个新推导的传导形状因子。
