The circle of Willis is a ring-like arterial structure located in the base of the brain, and is responsible for the distribution of oxygenated blood throughout the cerebral mass. Among the general population, approximately 50 per cent have a complete circle of Willis; for the others a multitude of possible anatomical variations are present, with absent or hypoplastic vessels being 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 three-dimensional computer model has been developed based on the results of magnetic resonance imaging data, incorporating a numerical algorithm to simulate the body's autoregulation mechanism, such that oxygen delivery to the cerebral territories can be predicted in response events, leading to a reduction in cerebral blood flow. Sample results are presented for combinations of occlusion and stenosis.