The Circle of Willis (CoW) is a ring-like arterial structure located in the base of the brain, responsible for the distribution of oxygenated blood throughout the cerebral mass. Among the general population, approximately 50% have a complete CoW, and among a multitude of possible anatomical variations, vessels absent from the CoW are common. Certain conditions such as a build up of atherosclerotic plaque on the arterial wall can result in ischaemic damage and stroke-like symptoms. A 3D computer model has been developed based on the results of MRA scans of 3 patients' cerebral-vasculature incorporating a numerical algorithm to simulate the body's autoregulation mechanism. The intention of the present study was to investigate different anatomical states, including different vessels missing from the circle whilst occluding the main afferent arteries such as the Internal Carotid and Basilar Arteries.