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A time-invariant visco-elastic windkessel model relating blood flow and blood volume

Zheng, Y. and Mayhew, J. (2009) A time-invariant visco-elastic windkessel model relating blood flow and blood volume. Neuroimage, 47 (4). pp. 1371-1380. ISSN 1053-8119

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Abstract

The difference between the rate of change of cerebral blood volume (CBV) and cerebral blood flow (CBF) following stimulation is thought to be due to circumferential stress relaxation in veins (Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679-689). In this paper we explore the visco-elastic properties of blood vessels, and present a dynamic model relating changes in CBF to changes in CBV. We refer to this model as the visco-elastic windkessel (VW) model. A novel feature of this model is that the parameter characterising the pressure-volume relationship of blood vessels is treated as a state variable dependent oil the rate of change of CBV, producing hysteresis in the pressure-volume space during vessel dilation and contraction. The VW model is nonlinear time-invariant, and is able to predict the observed differences between the time series of CBV and that of CBF measurements following changes in neural activity. Like the windkessel model derived by Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679-689, the VW model is primarily a model of haemodynamic changes in the venous compartment. The VW model is demonstrated to have the following characteristics typical of visco-elastic materials: (1) hysteresis, (2) creep, and (3) stress relaxation, hence it provides a unified model of the visco-elastic properties of the vasculature. The model will not only contribute to the interpretation of the Blood Oxygen Level Dependent (BOLD) signals from functional Magnetic Resonance Imaging (fMRI) experiments, but also find applications in the study and modelling of the brain vasculature and the haemodynamics of circulatory and cardiovascular systems. (C) 2009 Elsevier Inc. All rights reserved.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009 Elsevier. This is an author produced version of a paper subsequently published in Neuroimage. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: POSITRON-EMISSION-TOMOGRAPHY; RODENT BARREL CORTEX; MEAN TRANSIT TIME; HEMODYNAMIC-RESPONSE; BRAIN ACTIVATION; NEURAL ACTIVITY; BOLD FMRI; DELAYED COMPLIANCE; OXYGEN DELIVERY; BALLOON MODEL
Academic Units: The University of Sheffield > University of Sheffield Research Centres and Institutes > Centre for Signal Processing in NeuroImaging and Systems Neuroscience (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 09 Sep 2009 09:20
Last Modified: 08 Feb 2013 16:59
Published Version: http://dx.doi.org/10.1016/j.neuroimage.2009.04.022
Status: Published
Publisher: Elsevier
Refereed: Yes
Identification Number: 10.1016/j.neuroimage.2009.04.022
URI: http://eprints.whiterose.ac.uk/id/eprint/9291

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