The Circle of Willis (CoW) is a ring-like structure blood vessels at the base of the brain that distributes arterial blood to the cerebral mass. 1D and 3D CFD models of the Circle of Willis have been created to simulate clinical scenarios such as inclusions in afferent arteries and absent circulus vessels. Both models capture cerebral haemodynamic auto-regulation using proportional-integral controller to modify efferent artery distances to maintain optimal efferent flowrates for a given cycle geometry and afferent blood pressure. The models can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures. The model is particularly relevant in this instance, with its fast execution time suitable for real-time clinical decisions and senario testing, as long as it captures the necessary details as a model would. Results show excellent correlation between models for the transient efferent flux profile with differences more than 5%. The assumption of strictly Poiseulile flow in the model allows more flow through the geometrically extreme communicating arteries than the 3D model. This discrepancy is overcome by increasing the resistance to flow in the ACoA the 1D model to better match the resistance seen in the 3D model, significantly improving correlation of the results.