Numerical Analysis of Blood Flow in the Dysplastic Circle of Willis Using One-dimensional Patient-Specific Model

In this work, aiming at studying the impact of anatomical variations in the circle of Willis on the capacity of collateral blood supply, a computational scheme for constructing the patient-specific one-dimensional geometric models has been developed based on computerized tomography images. The lengths and diameters for different structures of circle of Willis (CoW) are extracted. Blood flow in the circle of Willis is modeled by using one dimensional equations derived from axisymmetric Navier-Stokes equations for flow in elastic and compliant vessels.Two frequently observed anatomical variations of the CoW (ACA, A1 aplasia and ACA, A1 hypoplasia) have been simulated. The results are compared with those of the complete and well-balanced CoW. The results show that, in the complete and well balanced CoW, it is almost not required to use collateral pathways through the anterior communicating artery (ACoA) to regulate the blood supply in the brain. However, in the unilateral A1 aplasia (non-visualization of one A1) and A1 hypoplasia (less than 90% in size of dominant A1) structure, the role of ACoA becomes considerably important. Moreover, the result of our patient-specific models show that the ACoA outward hypertrophic remodeling can compensate the blood flow in the contralateral side well, which is different from that obtained by the previous average anatomical geometric models.