Computational 3D Modelling of Hemodynamics in the Circle of Willis

Abstract

The Circle of Willis (CoW) is a ring-like arterial structure forming the major anastomotic connection between arterial supply systems in the brain, and is responsible for the distribution of oxygenated blood throughout the cerebral mass. Among the general population, only approximately 50% have a complete CoW, where absent or hypoplastic vessels are common among a multitude of possible anatomical variations, reducing the degree to which blood may be rerouted. While an individual with one of these variations may under normal circumstances suffer no ill effects, there are certain pathological conditions which can present a risk to the person's health and increase the possibility of suffering an ischaemic stroke when compounded with an anatomical variation. This body of work presents techniques for generating 3D models of the cerebral vasculature using magnetic resonance imaging (MRI) and performing computational fluid dynamics (CFD) simulations in order to simulate the flow patterns throughout a circle of Willis. Incorporated with the simulations is a mathematical model of the cerebral autoregulation mechanism, simulating the ability of the smaller arteries and arterioles in the brain to either constrict or dilate in response to alterations in cerebral blood flow, thereby altering the cerebrovascular resistance of each major brain territory and regulating the amount of blood flow within a physiological range of cerebral perfusion pressure. The CFD simulations have the ability to predict the amount of collateral flow rerouted via the communicating arteries in response to a stenosis or occlusion, and the major objective of this study has been the investigation of how anatomical variations of the circle of Willis affect the capacity to provide this collateral flow. Initial work began with the development of three idealized models of common anatomical variations, created using computer aided design software (CAD) and based on the results of MRI scans. The research then shifted to developing a technique whereby patient specific models of the circle of Willis could be directly segmented from the MRI data. As a result of this shift, an interactive GUI-based tool was developed for the processing of the MRI datasets, allowing for rapid data enhancement and creation of a surface topology representing the arterial wall of the circle of Willis, suitable for a CFD simulation. The results of both sets of simulations illustrate that there exist a number of variables associated with a patients circle of Willis geometry, such as cerebral blood flow and combinations and degrees of stenosis, implying that the initial goal of drawing generalized conclusions was perhaps flawed. Instead, a crucial outcome of this body of work is that the future research should be directed toward extending the physiological complexity of both the geometry and the autoregulation model, with the intention of a patient specific application rather than producing large datasets with which to make broad generalizations.