Hillen B, Drinkenburg B A, Hoogstraten H W, Post L
Department of Anatomy and Embryology, University of Groningen, The Netherlands.
J Biomech. 1988;21(10):807-14. doi: 10.1016/0021-9290(88)90013-9.
A very simple model of the flow in the circle of Willis is described in this paper. Disregarding pulsatility and vessel wall elasticity, fluxes in all segments of the circle of Willis and its afferent and efferent vessels are calculated by applying the Poiseuille-Hagen formula. Comparison with the fluxes calculated numerically from a more sophisticated mathematical model, including pulsatility, vessel wall elasticity and nonlinear effects, revealed only very slight differences. In short, fluxes in the afferent vessels and the segments of the circle of Willis are influenced by any change of resistance within the network, whereas the fluxes in the efferent segments are dominated by the efferent resistance distribution. However, a great advantage of the present simple model is that it offers the possibility of an analytical approach which yields both an easy sensitivity analysis of parameters and an insight into the mechanisms that govern the flow in a network like the circle of Willis. It can be concluded that these mechanisms are similar to the principles of the Wheatstone bridge, known from electrical circuit theory.
本文描述了一种非常简单的 Willis 环血流模型。忽略脉动性和血管壁弹性，通过应用泊肃叶 - 哈根公式计算 Willis 环及其传入和传出血管所有段的流量。与从更复杂的数学模型（包括脉动性、血管壁弹性和非线性效应）数值计算得到的流量进行比较，发现差异非常小。简而言之，传入血管和 Willis 环各段的流量受网络内任何阻力变化的影响，而传出段的流量则由传出阻力分布主导。然而，当前简单模型的一个很大优点是它提供了一种分析方法的可能性，这种方法既能对参数进行简单的敏感性分析，又能深入了解像 Willis 环这样的网络中血流的控制机制。可以得出结论，这些机制类似于电路理论中已知的惠斯通电桥原理。
