Cerebral Haemodynamics and Auto-Regulatory Models of the Circle of Willis

Abstract

The Circle of Willis (CoW) is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain distributing blood to the cerebral hemispheres. A one-dimensional computational fluid dynamic [1-D CFD] model is developed to capture the auto-regulation dynamics that maintain blood perfusion pressure with a goal of developing diagnostic tools for stroke prediction.

The afferent and circulus arteries have constant resistances, and the efferent arteries have variable resistors limited to changes in radius of up to 40% to capture auto-regulatory behaviour. Auto-regulation is modelled by feedback control coupled with peripheral resistance dynamics to create a non-linear system. Solutions are obtained far more quickly than higher dimensional CFD models via a unique non-linear solution method. The overall model enables simulation of different CoW geometries for different patient conditions.

The CoW is simulated with a 20mmHg arterial pressure drop in the right internal carotid artery for the balanced configuration and each case where a single circulus vessel is omitted. Results match the 20% drop in flowrate, and 20 second response time from published clinical data and prior research. No single omission leads to failure in reaching the required efferent flowrates, highlighting the overall robustness of this arterial structure. A high stroke risk case, however, fails to achieve the required flowrate in the left posterior communicating artery (LPCA2), representing a potential stroke. All of these results agree well with known clinical results, indicating the potential of this model for pre-determining potential outcomes of surgical or other procedures.