1D and 3D models of cerebrovascular flow

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Journal Article
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Publisher
University of Canterbury. Mechanical Engineering.
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Date
2005
Authors
Moore, S.M.
Moorhead, K.T.
Chase, Geoff
David, T.
Fink, J.
Abstract

The Circle of Willis is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. One-dimensional (1D) and three-dimensional (3D) Computational Fluid Dynamics (CFD) models of the Circle of Willis have been created to provide a simulation tool which could be used to replicate clinical scenarios, such as occlusions in afferent arteries and absent circulus vessels. Both models capture cerebral haemodynamic auto-regulation using a Proportional-Integral (PI) controller to modify efferent artery resistances to maintain optimal efferent flowrates for a given circle geometry and afferent blood pressure. The models can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures. The 1D model is particularly relevant in this instance, with its fast solution time suitable for real-time clinical decisions. Results show excellent correlation between models for the transient efferent flux profile. The assumption of strictly Poiseuille flow in the 1D model allows more flow through the geometrically extreme communicating arteries than the 3D model. This discrepancy was overcome by increasing the resistance to flow in the Anterior Communicating Artery in the 1D model to better match the resistance seen in the 3D results.

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Citation
Moore, S.M., Moorhead, K.T., Chase, J.G., David, T., Fink, J. (2005) 1D and 3D models of cerebrovascular flow. Journal of Biomechanical Engineering, 127(3), pp. 440-449.
Keywords
circle of Willis, cerebral haemodynamics, computational model, auto-regulation, PI controller
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