Kassab G S, Fung Y C
Institute for Biomedical Engineering, University of California, San Diego, La Jolla 92093-0412, USA.
Ann Biomed Eng. 1995 Jan-Feb;23(1):13-20. doi: 10.1007/BF02368296.
By minimizing the cost function, which is the sum of the friction power loss and the metabolic energy proportional to blood volume, Murray derived an optimal condition for a vascular bifurcation. Murray's law states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughters. We tested Murray's law against our data of pig's maximally vasodilated coronary arteriolar blood vessels at bifurcation points in control and hypertensive ventricles. Data were obtained from 7 farm pigs, 4 normal controls and 3 with right ventricular hypertrophy induced by stenosis of a pulmonary artery. Data on coronary arteriolar bifurcations were obtained from histological specimens by optical sectioning. The experimental results show excellent agreement with Murray's law in control and hypertensive hearts. Theoretically, we show that Murray's law can be derived alternatively as a consequence of the uniform vessel-wall shear strain rate hypothesis and a fluid mechanics equation based on conservation of mass and momentum. Conversely, the fluid mechanical equation, together with Murray's law, established as an empirical equation of actual measurements implies the uniformity of the shear strain rate of the blood at the vessel wall throughout the arterioles. The validity of these statements is discussed.
通过最小化成本函数（即摩擦功率损失与与血容量成正比的代谢能量之和），默里推导出了血管分支的最优条件。默里定律指出，母血管半径的立方等于子血管半径立方之和。我们根据猪的最大血管舒张冠状动脉小动脉在对照和高血压心室分叉点的数据对默里定律进行了检验。数据取自7头农场猪，4头正常对照猪和3头因肺动脉狭窄诱发右心室肥大的猪。冠状动脉小动脉分叉的数据通过光学切片从组织学标本中获取。实验结果表明，在对照心脏和高血压心脏中，实验结果与默里定律高度吻合。从理论上讲，我们表明默里定律可以作为血管壁剪切应变率均匀性假设以及基于质量和动量守恒的流体力学方程的结果而推导得出。相反，流体力学方程与作为实际测量经验方程建立的默里定律一起，意味着整个小动脉血管壁处血液的剪切应变率是均匀的。讨论了这些陈述的有效性。
