Biomedical Simulation Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, ON, Canada.
Physiol Meas. 2017 Nov 1;38(11):2044-2057. doi: 10.1088/1361-6579/aa92bf.
Vessel lumen calibres and flow rates are thought to be related by mathematical power laws, reflecting the optimization of cardiac versus metabolic work. While these laws have been confirmed indirectly via measurement of branch calibres, there is little data confirming power law relationships of flow distribution to branch calibres at individual bifurcations.
Flow rates and diameters of parent and daughter vessels of the internal carotid artery terminal bifurcation were determined, via robust and automated methods, from 4D phase-contrast magnetic resonance imaging and 3D rotational angiography of 31 patients.
Junction exponents were 2.06 ± 0.44 for relating parent to daughter branch diameters (geometrical exponent), and 2.45 ± 0.75 for relating daughter branch diameters to their flow division (flow split exponent). These exponents were not significantly different, but showed large inter- and intra-individual variations, and with confidence intervals excluding the theoretical optimum of 3. Power law fits of flow split versus diameter ratio and pooled flow rates versus diameters showed exponents of 2.17 and 1.96, respectively. A significant negative correlation was found between age and the geometrical exponent (r = -0.55, p = 0.003) but not the flow split exponent. We also found a dependence of our results on how lumen diameter is measured, possibly explaining some of the variability in the literature.
Our study confirms that, on average, division of flow to the middle and anterior cerebral arteries is related to these vessels' relative calibres via a power law, but it is closer to a square law than a cube law as commonly assumed.
血管腔直径和流量率被认为通过数学幂律相关，反映了心脏与代谢工作的优化。虽然这些定律已经通过分支直径的间接测量得到了证实，但很少有数据证实分支流量分布与个体分支直径的幂律关系。
通过稳健和自动化的方法，从 31 名患者的 4D 相位对比磁共振成像和 3D 旋转血管造影中确定颈内动脉终末分叉处的母血管和子血管的流量率和直径。
母-子分支直径关系的交界处指数为 2.06±0.44（几何指数），子分支直径与其流量分配关系的交界处指数为 2.45±0.75（流量分配指数）。这些指数没有显著差异，但表现出较大的个体间和个体内变异，置信区间排除了理论上的最优值 3。流量分配与直径比和汇总流量率与直径的幂律拟合的指数分别为 2.17 和 1.96。发现年龄与几何指数之间存在显著负相关（r=-0.55，p=0.003），但与流量分配指数无关。我们还发现，我们的结果取决于如何测量管腔直径，这可能解释了文献中一些变异性的原因。
我们的研究证实，平均而言，血流分配到大脑中动脉和大脑前动脉与这些血管的相对直径通过幂律相关，但与通常假设的立方律相比，更接近平方律。
