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Mathematical Medicine and Biology Advance Access originally published online on December 2, 2008
Mathematical Medicine and Biology 2009 26(1):25-61; doi:10.1093/imammb/dqn021
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Analytic solution during an infusion test of the linear unsteady poroelastic equations in a spherically symmetric model of the brain

Benedikt Wirth

Institute for Numerical Simulation, University of Bonn, Nussallee 15, 53113 Bonn, Germany

Ian Sobey{dagger}

Computing Laboratory, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK

{dagger} Email: ian.sobey{at}comlab.ox.ac.uk

Received on July 9, 2007. Revised on May 14, 2008. Accepted on September 11, 2008.

This work determines the spatial and temporal distribution of cerebrospinal fluid (CSF) pressure and brain displacement during an infusion test in a spherically symmetric model of the brain. The response of CSF pressure and parenchymal displacement to blood pressure pulsations is determined in the solution. We use a spherically symmetric, three-component poroelastic model of the brain, differentiating between the solid elastic matrix, the CSF and the arterial blood compartments. The governing equations are linearized with quasi-constant poroelastic parameters. The solution does reproduce the average intracranial pressure increase during the test as well as the rise in CSF pressure pulsation amplitude due to transmission of blood pressure oscillations. In addition, the CSF flux into and out of the parenchyma is shown over time.

Keywords: multi-poroelasticity; cerebrospinal fluid; infusion test; pressure oscillations; analytic solution


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