The brain relies heavily on cerebral circulation due to its high metabolic rate and sensitivity to ischaemia (insufficient blood supply). Blood flow is maintained by a network of collateral vessels, primarily the circle of Willis (CoW), a ring-like arterial structure at the brain's base, with auto-regulation through vasodilatation and vasoconstriction. Sudden flow obstructions, especially during procedures like carotid endarterectomy (plaque removal by incision), angioplasty (balloon expansion), and stenting (inserting a mesh to keep the lumen open), increase the risk of cerebral ischemia.

We studied the effects of CoW anatomical variations and neck artery occlusions on cerebral flow using a new model of pulsatile cerebral blood flow that accounts for auto-regulation (Int J Numer Meth Fluids, 2008), verified qualitatively by comparison to in vivo Doppler ultrasound measurements (J Biomech, 2007).

The model has enabled us to:

1. Identify haemodynamic factors that increase ischeamic risk during afferent artery surgeries. It highlighted the CoW anatomical variation that least supports cerebral flow restoration after a sudden carotid occlusion: a circle lacking the first segment of the contralateral anterior cerebral artery (Int J Numer Meth Fluids, 2008). It also identified the anterior communicating artery (ACoA) as a critical collateral pathway to compensate for carotid occlusions (J Biomech, 2007);

2. Link frequent CoW anatomical variations with specific cerebral blood flow patterns detectable by transcranial colour-coded duplex ultrasonography, providing a basis for infering CoW anatomy from pulse wave analysis (J Biomech, 2007);

3. Demonstrate machine learning's potential for noninvasive CoW topology detection using Doppler ultrasound, achieving 98% classification accuracy with a convolutional neural network. Under 20% noise, a multi-layer perceptron achieved 79% accuracy, with mean and peak systolic velocities as key predictive features. Models performed best for topologies without posterior communication arteries (Biomed Signal Process Control, 2024);


4. Show that the collateral pathways of a complete CoW can support localised increases in regional brain demands without reducing blood flow to other brain areas (J Biomech Eng, 2015).

In a related project (Comput Methods Biomech Biomed Engin, 2006), the modified Allen’s test was modelled to account for anatomical variations in hand arteries and was found to risk false positives if the palmar arch is narrow or if radial artery compression is insufficient. Measuring the drop in digital systolic pressure during compression may offer a more reliable assessment of ulnar collateral flow.