Scaling laws of vascular trees: of form and function
Scaling laws of vascular trees: of form and function
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DOI：
10.1152/ajpheart.00579.2005
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发表时间：
2006-02-01
影响因子：
4.8
通讯作者：
Kassab, GS
中科院分区：
文献类型：
--
作者：
Kassab, GS
血管树的尺度律：形式与功能。美国生理学杂志心脏循环生理学290：H894-H903，2006年。首次发表于2005年9月2日; doi：10.1152/ajpheart.00579.2005。生物树结构的分枝模式和维管几何形状是复杂的。在这里，我们表明，所有的血管树的设计，其中存在的形态学数据在文献中（e。例如，在一个实施例中，冠状动脉、肺动脉;各种骨骼肌、肠系膜、网膜和结膜的血管）服从一组比例定律，该比例定律基于树结构的构造和流体传导的操作的成本被最小化的假设。这些规律包括1）树的长度和血管体积、2）每个分支中的管腔直径和血流速率以及3）血管分支的直径和长度之间的标度关系。直径-流速关系的指数不一定等于默里定律所要求的3.0，而是取决于感兴趣的树的代谢与粘性功率耗散的比率。本文分析的主要意义在于表明，不同器官和物种的各种维管树的设计可以根据最小能量假设和稳态条件下的能量守恒来推导。本研究揭示了自然界的比例法则的相似性，这些法则决定了各种血管树的设计以及潜在的物理和生理原理。
Scaling laws of vascular trees: of form and function. Am J Physiol Heart Circ Physiol 290: H894-H903, 2006. First published September 2, 2005; doi:10.1152/ajpheart.00579.2005.-The branching pattern and vascular geometry of biological tree structure are complex. Here we show that the design of all vascular trees for which there exist morphometric data in the literature (e. g., coronary, pulmonary; vessels of various skeletal muscles, mesentery, omentum, and conjunctiva) obeys a set of scaling laws that are based on the hypothesis that the cost of construction of the tree structure and operation of fluid conduction is minimized. The laws consist of scaling relationships between 1) length and vascular volume of the tree, 2) lumen diameter and blood flow rate in each branch, and 3) diameter and length of vessel branches. The exponent of the diameter-flow rate relation is not necessarily equal to 3.0 as required by Murray's law but depends on the ratio of metabolic to viscous power dissipation of the tree of interest. The major significance of the present analysis is to show that the design of various vascular trees of different organs and species can be deduced on the basis of the minimum energy hypothesis and conservation of energy under steadystate conditions. The present study reveals the similarity of nature's scaling laws that dictate the design of various vascular trees and the underlying physical and physiological principles.