Modeling the circle of Willis to assess the effect of anatomical variations on the development of unilateral internal carotid artery stenosis

Circle of Willis (CoW) plays a significant role in maintaining the blood supply for the brain. Specifically, when the stenosis occurs in the internal carotid artery (ICA), abnormal structures of CoW would decrease the compensatory capacity, leading to the local insufficiency of cerebral blood supply. The present paper built a series of lumped parameter models for CoW, and simulated the blood redistribution caused by the unilateral ICA stenosis with different severities in cerebral arteries in the normal and abnormal CoW respectively. The results showed that when unilateral ICA stenosis occurred, the collateral circulation was built through the anterior communicating artery and the ipsilateral posterior communicating artery, maintaining the flow in cerebral arteries. The absence of the two communicating arteries would cause an obvious decrease of flow in local cerebral arteries in the anterior circulation. In conclusion, the two arteries play a significant role in maintaining the balance of cerebral blood supply in the development of ICA stenosis.