Baish J W
Department of Mechanical Engineering, Bucknell University, Lewisburg, PA 17837.
J Biomech Eng. 1990 May;112(2):207-11. doi: 10.1115/1.2891173.
This paper presents a three-dimensional analysis of the temperature field around a pair of countercurrent arteries and veins embedded in an infinite tissue that has an arbitrary temperature gradient along the axes of the vessels. Asymptotic methods are used to show that such vessels are thermally similar to a highly conductive fiber in the same tissue. Expressions are developed for the effective radius and thermal conductivity of the fiber so that it conducts heat at the same rate that the artery and vein together convect heat and so that its local temperature equals the mean temperature of the vessels. This result allows vascular tissue to be viewed as a composite of conductive materials with highly conductive fibers replacing the convective effects of the vasculature. By characterizing the size and thermal conductivity of these fibers, well-established methods from the study of composites may be applied to determine when an effective conductive model is appropriate for the tissue and vasculature as a whole.
本文对嵌入无限大组织中的一对逆流动脉和静脉周围的温度场进行了三维分析，该组织沿血管轴具有任意温度梯度。采用渐近方法表明，此类血管在热学上类似于同一组织中的高导热纤维。推导了纤维的有效半径和热导率的表达式，使得纤维传导热量的速率与动脉和静脉共同对流热量的速率相同，并且其局部温度等于血管的平均温度。这一结果使血管组织可被视为由导电材料组成的复合材料，其中高导热纤维取代了脉管系统的对流效应。通过表征这些纤维的尺寸和热导率，可以应用复合材料研究中成熟的方法来确定何时有效的导电模型适用于整个组织和脉管系统。
