Impact of decentralised control in cerebral blood flow auto-regulation using 1D and 3D models

Abstract

The Circle of Willis is a ring-like structure of blood vessels at the base of the brain that distributes oxygen-rich arterial blood to the cerebral mass at a specific rate. One dimensional (1D) and three-dimensional (3D) Computational Fluid Dynamics (CFD) models of the Circle of Willis have been created to simulate clinical scenarios, such as stenoses and occlusions in afferent arteries. Both models capture cerebral haemodynamic auto-regulation using a Proportional-Integral (PI) controller to modify efferent artery resistances to maintain optimal efferent flow rates for a given circle geometry and afferent blood pressure. Auto-regulatory control is decentralised so that each individual territory of the cerebral mass regulates flow to satisfy its requirements independent of the remaining territories. Results show that if a sudden occlusion is imposed in an afferent artery, efferent flux profiles fluctuate as an equilibrium is found that best satisfies the independent requirements of each territory of the cerebral mass. Clinically, this unique insight into the transient dynamics of cerebral blood flow and auto-regulation will enable pre-surgical scenario testing using simple models to minimise stroke risk.