Metabolic Model of Autoregulation in the Circle of Willis

[+] Author and Article Information
K. T. Moorhead, J. G. Chase, T. David, J. Arnold

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

J Biomech Eng 128(3), 462-466 (Dec 12, 2005) (5 pages) doi:10.1115/1.2187048 History: Received February 06, 2005; Revised December 12, 2005

The Circle of Willis (CoW) is a ringlike structure of blood vessels found at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. In a previous study, a one-dimensional (1D) model of the CoW was created to simulate a series of possible clinical scenarios such as occlusions in afferent arteries, absent or stringlike circulus vessels, or arterial infarctions (Moorhead, 2004, Comput. Methods Biomech. Biomed. Eng., 7(3), pp. 121–130). The model captured cerebral haemodynamic autoregulation by using a proportional-integral-derivative (PID) controller to modify efferent artery resistances. Although some good results and correlations were achieved, the model was too simple to capture all the transient dynamics of autoregulation. Hence a more physiologically accurate model has been created that additionally includes the oxygen dynamics that drive the autoregulatory response. Results very closely match accepted physiological response and limited clinical data. In addition, a set of boundary conditions and geometry is presented for which the autoregulated system cannot provide sufficient perfusion, representing a condition with increased risk of stroke and highlighting the importance of modeling the haemodynamics of the CoW. The system model created is computationally simple so it can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic representation of the Circle of Willis

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Figure 2

Flowrate as a function of arterial pressure

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Figure 3

Interstitial oxygen partial pressure as a function of flowrate

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Figure 4

Comparison of metabolic model and Newell flux profile

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Figure 5

Efferent arterial response to 80% carotid stenosis with an absent RPCoA




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