脑Willis环的一维血流动力学及氧输运特性的数值研究

Willis环是大脑侧枝循环的重要组成部分, 研究其血流动力学特性以及氧输运规律对脑缺血疾病的认知和预防有着非常重要的作用. 该文旨在利用一维血流动力学模型模拟整个Willis环的流量变化和压力分布, 并建立动脉内氧输运的一维模型以模拟Willis 环内氧分压的变化规律, 为研究脑组织内血液流动和氧输运打下基础. 首先, 基于弹性圆管内的一维非线性流动方程和状态方程建立血流动力学模型, 在一维对流扩散方程的基础上, 考虑由管腔向壁面的扩散和壁面细胞的新陈代谢消耗推导出氧输运特性方程. 通过 Lax-Wendroff两步法对血流动力学方程进行离散, 而在进行对流扩散方程的离散时, 则运用迎风格式. 通过数值计算得到了正常情况下Willis环各个血管任意位置的流量、压力和氧分压的变化曲线, 正常情况下各个位置的氧分压处于稳定的平衡状态. 最后, 还通过此模型进一步模拟了右侧颈内动脉狭窄对各个血管内流动的影响. 当狭窄程度达到80%时, 中脑动脉的流量和压力会明显下降, 造成其供应区域的血流减少. 同时, Willis环右侧血管内的氧分压会大大降低, 而左侧血管的氧分压会出现上升趋势, 但幅度要小于右侧血管降低的幅度.

A MODELING STUDY OF BLOOD FLOW AND OXYGEN TRANSPORT IN THE CIRCLE OF WILLIS

Sufficient blood supply is of importance in maintaining the normal function of brain.If the brain cells are lack of oxygen for more than a few minutes due to decreased flow and perfusion pressure,they will be irreversibly damaged.In this study,blood flow and oxygen transport in the circle of Willis are modeled using one-dimensional equations derived from the axisymmetric Navier-Stokes equations for flow in elastic and compliant vessels and the convective-diffusive equation with the consideration of the diffusion from the lumen to artery wall and the metabolism produced by the wall cells.The nonlinear equations for hemodynamics were numerically solved using the two-step Lax-Wendroff scheme,and the upwind scheme was used in the discretization of the oxygen transport equations.The computational results were obtained,which were in good agreement with the available physiological data in normal and stenosis condition.It is shown that,when the degree of stenosis existing at the right internal carotid artery is up to 80%,the flow rate of the middle cerebral artery is reduced significantly.Furthermore,the oxygen partial pressure in ipsilateral vessels decreases with the increasing of stenosis degree,while the oxygen partial pressure of the vessel in another side increases.