Literature Review on Methods of Modeling the Cerebral Network and the Circle of Willis

Abstract

The Circle of Willis is a network of internal carotid arteries, basilar arteries, and vertebral arteries all coming together to perfuse the brain with blood. In the event that stenosis occludes part of the circle, the communicating arteries located at the posterior and anterior of the circle can compensate for the blood flow. However, if the communicating arteries themselves are occluded or entirely missing, the risk of ischemic stroke and subsequent death is possible. The literature surrounding the Circle of Willis is robust; the following review establishes historical context surrounding the development of mathematical models around the cerebral network and those specific to the circle of Willis, while also highlighting the applications and future for modelling.