Metabolic Model of Autoregulation in the Circle of Willis
The Circle of Willis (CoW) is a ring-like structure of blood vessels found at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. In a previous study, a one dimensional model of the CoW was created to simulate a series of possible clinical scenarios such as occlusions in afferent arteries, absent or string-like circulus vessels, or arterial infarctions. The model captured cerebral haemodynamic autoregulation by using a Proportional-Integral-Derivative (PID) controller to modify arterial resistances. Although some good results and correlations were achieved, the model was too simple to capture all the transient dynamics of autoregulation. Hence, a more physiologically accurate model has been created that additionally includes the oxygen dynamics that drive the autoregulatory response. Results very closely match accepted physiological response and limited clinical data. In addition, a se4t of boundary conditions and geometry is presented for which the autoregulated system cannot provide sufficient perfusion, representing a condition with increased risk of stroke and highlighting the importance of modelling the haemodynamics of the CoW. The system model created is computationally simple so it can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures.