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Three-dimensional hemodynamics analysis of the circle of Willis in the patient-specific nonintegral arterial structures

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The hemodynamic alteration in the cerebral circulation caused by the geometric variations in the cerebral circulation arterial network of the circle of Wills (CoW) can lead to fatal ischemic attacks in the brain. The geometric variations due to impairment in the arterial network result in incomplete cerebral arterial structure of CoW and inadequate blood supply to the brain. Therefore, it is of great importance to understand the hemodynamics of the CoW, for efficiently and precisely evaluating the status of blood supply to the brain. In this paper, three-dimensional computational fluid dynamics of the main CoW vasculature coupled with zero-dimensional lumped parameter model boundary condition for the CoW outflow boundaries is developed for analysis of the blood flow distribution in the incomplete CoW cerebral arterial structures. The geometric models in our study cover the arterial segments from the aorta to the cerebral arteries, which can allow us to take into account the innate patient-specific resistance of the arterial trees. Numerical simulations of the governing fluid mechanics are performed to determine the CoW arterial structural hemodynamics, for illustrating the redistribution of the blood flow in CoW due to the structural variations. We have evaluated our coupling methodology in five patient-specific cases that were diagnosed with the absence of efferent vessels or impairment in the connective arteries in their CoWs. The velocity profiles calculated by our approach in the segments of the patient-specific arterial structures are found to be very close to the Doppler ultrasound measurements. The accuracy and consistency of our hemodynamic results have been improved (to \(16.1 \pm 18.5\) %) compared to that of the pure-resistance boundary conditions (of 43.5 \(\pm \) 28 %). Based on our grouping of the five cases according to the occurrence of unilateral occlusion in vertebral arteries, the inter-comparison has shown that (i) the flow reduction in posterior cerebral arteries is the consequence of the unilateral vertebral arterial occlusion, and (ii) the flow rate in the anterior cerebral arteries is correlated with the posterior structural variations. This study shows that our coupling approach is capable of providing comprehensive information of the hemodynamic alterations in the pathological CoW arterial structures. The information generated by our methodology can enable evaluation of both the functional and structural status of the clinically significant symptoms, for assisting the treatment decision-making.

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Anterior cerebral artery


Middle cerebral artery


Posterior cerebral artery


Posterior communication artery


Anterior communication artery


Internal carotid artery


External carotid artery


Common carotid artery


Vertebral artery






Peak systolic velocity


Lump parameter model


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This work was supported in part by Guangdong Image-guided Therapy Innovation Team (2011S013), the science technology, Shenzhen innovation funding of Government (CXZZ20140909004122087, SGLH20150213143207911, SGLH20150216172854731) and Innovation committee of Shenzhen (JCYJ20140414170821190, JCYJ20140901003939025, JCYJ20140414170821323, JCYJ20151030151431727).

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Correspondence to Heye Zhang.

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Liu, X., Gao, Z., Xiong, H. et al. Three-dimensional hemodynamics analysis of the circle of Willis in the patient-specific nonintegral arterial structures. Biomech Model Mechanobiol 15, 1439–1456 (2016).

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