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TECHNICAL PAPERS: Fluids/Heat/Transport

One-Dimensional and Three-Dimensional Models of Cerebrovascular Flow

[+] Author and Article Information
S. M. Moore, K. T. Moorhead, J. G. Chase, T. David, J. Fink

Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

J Biomech Eng 127(3), 440-449 (Sep 18, 2004) (10 pages) doi:10.1115/1.1894350 History: Received March 18, 2004; Revised September 18, 2004

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 can potentially be used to identify at-risk cerebral arterial geometries and conditions and replicate clinical scenarios, such as occlusions in afferent arteries and absent circulus vessels. Both models capture cerebral haemodynamic autoregulation 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. 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 the 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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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic representation of the Circle of Willis

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Figure 2

MRA scan of a Circle of Willis

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Figure 3

Schematic representation of the Circle of Willis for a 1D model

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Figure 4

Solid model of the Circle of Willis used in simulations

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Figure 5

Solution flow diagram

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Figure 6

A comparison of the computational result with Newell (16).

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Figure 7

Ipsilateral arterial response to 20 mm Hg pressure drop in RICA—Ideal configuration

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Figure 8

Contralateral arterial response to 20 mm Hg pressure drop in RICA—Ideal configuration

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Figure 9

Ipsilateral resistance for 20 mm Hg pressure drop in RICA—Ideal configuration

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Figure 10

A comparison of flow rates for 1D and 3D models—Ideal configuration after a 20 mmHg pressure drop

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Figure 11

A comparison of flow rates for the 1D model, 3D model, and 1D model with increased ACoA resistance—Ideal configuration after a 20 mm Hg pressure drop

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Figure 12

Ipsilateral arterial response to an absent ACA-A1

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Figure 13

Ipsilateral resistance—Absent ACA-A1

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