The circle of Willis (CoW) is a set of arteries located in the basis of the brain. Prediction of perfusion rates and hemodynamics in the CoW is necessary to understand the relevant vascular diseases and to prescribe effective treatments. In this paper, the effect of ischemic stroke in the CoW is studied, taking into consideration the anatomical variations of the CoW. Moreover, an analysis on the effect of applied boundary conditions is carried out. To do so, a patient-specific model of the CoW is reconstructed from CT (computed tomography) images. Six different cases of boundary conditions are applied to complete and healthy CoW, and the flow rates are investigated. The proper pressure boundary conditions are then imposed to three other variations of the CoW, and the flow rates are compared. The results reveal that the overall inlet flow rate varies from 1.75% to 7.5% in three variations of healthy CoW. Moreover, the changes in flow rates of outlet and inlet branches are indicated in ischemic stroke by considering a spherical clot in the right middle cerebral artery (RMCA). In this case, the RMCA flow reduced by 88.4%, and the internal carotid artery flow decreased by 53.6%. These changes lead to increased flow rates of other inlets to support the brain; however, the overall inlet flow rate falls by 21.5%.

中文翻译：

---

不同解剖变化和缺血性卒中Willis环内灌注率的数值研究

威利斯圆（CoW）是位于大脑基础上的一组动脉。为了了解相关的血管疾病和开出有效的治疗方法，有必要对CoW中的灌注率和血液动力学进行预测。在本文中，研究了缺血性卒中对CoW的影响，同时考虑了CoW的解剖学变化。此外，对施加的边界条件的影响进行了分析。为此，需要从CT（计算机断层扫描）图像重建CoW的患者特定模型。将六种不同的边界条件案例应用于完整健康的CoW，并研究流量。然后将适当的压力边界条件施加到CoW的其他三个变化量上，并比较流速。结果显示，在健康CoW的三种变化中，总入口流速在1.75％至7.5％之间变化。此外，在缺血性卒中中，通过考虑右脑中动脉（RMCA）的球形血凝块可以指示出口和入口分支流速的变化。在这种情况下，RMCA流量减少了88.4％，颈内动脉流量减少了53.6％。这些变化导致其他进气口支持大脑的流量增加。但是，总进口流量下降了21.5％。这些变化导致其他进气口支持大脑的流量增加。但是，总进口流量下降了21.5％。这些变化导致其他进气口支持大脑的流量增加。但是，总进口流量下降了21.5％。