VASCULAR DIMENSIONS OF THE CEREBRAL-ARTERIES FOLLOW THE PRINCIPLE OF MINIMUM WORK
VASCULAR DIMENSIONS OF THE CEREBRAL-ARTERIES FOLLOW THE PRINCIPLE OF MINIMUM WORK
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DOI：
10.1161/01.str.24.3.371
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发表时间：
1993-03-01
期刊：
影响因子：
8.3
通讯作者：
LOFGREN, J
中科院分区：
文献类型：
--
作者：
ROSSITTI, S;LOFGREN, J
背景和目的：最小功原理是动脉树生长和适应的参数优化模型。它在层流摩擦阻力（剪切应力）引起的能量耗散与血管系统的最小体积之间建立了平衡，这意味着血管半径被调整为体积流量的立方根。本研究的目的是验证颈内动脉系统是否遵守最小功原理。方法：在模拟血管造影片上测量颈内动脉、大脑前动脉和大脑中动脉的母动脉和分支段的半径，这些血管造影片是从被归类为正常的一组中随机选择的。分支角由大脑前动脉分叉处的侧向投影测量。结果：174例动脉分支的面积比为1.2 ± 0.4（mean ± SD）。求解方程（r 0）n=（r1）n+（r2）n，得到n=2.9+/-0.7（平均值+/-SD，N=157）。根据理论方程r 0（3）r1（3）+r2（3）（r=0.989，N=174），在4代分支血管造影中验证了颈内动脉系统中母血管（r 0）和分支血管（r1和r2）半径之间的最佳比例。没有明确的相关性被发现之间的测量分支角度，相对分支横截面积，和理论上的最佳angles.Conclusions：这项研究表明，颈内动脉系统的分支的过程中遵守最小功的原则，直径指数接近3。最小功原理建立了体积流量、流速和血管半径之间的严格函数关系。该模型被扩展到分支角度的参数优化，这已被证明是无关的功能优化。我们的结果证实了这一发现。剪切应力诱导的内皮调解似乎是维持这种最佳血管设计的调节机制。在遵循最小功原理的血管网络中的每一点处，壁剪切应力的大小是相同的，因为剪切速率与血管半径的三次方成比例地影响剪切应力。这一观察结果对于了解动静脉畸形时脑血管网的重塑和囊状动脉瘤的发病机制具有重要意义。
Background and Purpose: The principle of minimum work is a parametric optimization model for the growth and adaptation of arterial trees. It establishes a balance between energy dissipation due to frictional resistance of laminar flow (shear stress) and the minimum volume of the vascular system, implying that the radius of the vessel is adjusted to the cube root of the volumetric flow. The purpose of this study is to verify whether the internal carotid artery system obeys the principle of minimum work.Methods: Measurements of the radius of parent and branch segments of the internal carotid, anterior, and middle cerebral arteries were performed on analog angiographs chosen at random from a set classified as normal. The branch angles were measured from lateral projections in bifurcations of the anterior cerebral artery. The relation of the calibers of parent and branch vessels was analyzed.Results: The area ratio of the bifurcations (N=174) was 1.2+/-0.4 (mean+/-SD). The equation (r0)n=(r1)n+(r2)n was solved for n, resulting in n=2.9+/-0.7 (mean+/-SD, N=157). Optimum proportions between the radii of parent (r0) and branch (r1 and r2) vessels in the internal carotid artery system were verified in normal carotid angiographs up to four branch generations, according to the theoretical equation r0(3)r1(3)+r2(3) (r=0.989, N=174). No clear correlation was found between the measured branch angles, the relative branch cross-sectional area, and the theoretical optimum angles.Conclusions: This study demonstrates that the process of branching of the internal carotid artery system obeys the principle of minimum work, as the diameter exponent approximates 3. The principle of minimum work establishes strict functional relations between volumetric flow, flow velocity, and vessel radius. This model was extended to parametric optimization of branch angles, which has proved irrelevant in terms of functional optimization. Our results corroborate this finding. Shear stress-induced endothelial mediation seems to be the regulating mechanism for the maintenance of this optimum vessel design. The magnitude of wall shear stress is the same at every point in a vascular network obeying the principle of minimum work, because the How rate influences the shear stress proportionally to the third power of the vessel radius. This observation has implications for understanding the remodeling of the cerebral vascular network in the presence of arteriovenous malformations and for the pathogenesis of saccular aneurysms.