Research Papers

Ventricle Equilibrium Position in Healthy and Normal Pressure Hydrocephalus Brains Using an Analytical Model

[+] Author and Article Information
K. Shahim1

J.-M. Drezet

 LSMX,Ecole Polytechnique,Fédérale de Lausanne, Station 12, CH-1015, Lausanne, Switzerland

Bryn A. Martin

 LHTC,Ecole Polytechnique,Fédérale de Lausanne, Station 17, CH-1015, Lausanne, Switzerland

S. Momjian

 University Hospitals of Geneva, University of Geneva, Rue Gabrielle-Perret-Gentil 41211 Genève 14, Switzerland


Corresponding author.

J Biomech Eng 134(4), 041007 (Apr 27, 2012) (10 pages) doi:10.1115/1.4006466 History: Received May 09, 2011; Revised March 25, 2012; Posted March 29, 2012; Published April 27, 2012; Online April 27, 2012

The driving force that causes enlargement of the ventricles remains unclear in case of normal pressure hydrocephalus (NPH). Both healthy and NPH brain conditions are characterized by a low transparenchymal pressure drop, typically 1 mm Hg. The present paper proposes an analytical model for normal and NPH brains using Darcy’s and Biot’s equations and simplifying the brain geometry to a hollow sphere with an internal and external radius. Self-consistent solutions for the large deformation problem that is associated with large ventricle dilation are presented and the notion of equilibrium or stable ventricle position is highlighted for both healthy and NPH conditions. The influence of different biomechanical parameters on the stable ventricle geometry is assessed and it is shown that both CSF seepage through the ependyma and parenchymal permeability play a key role. Although very simple, the present model is able to predict the onset and development of NPH conditions as a deviation from healthy conditions.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 3

(a) Radial displacement (μm) and (b) ISF pressure relative to the venous pressure (mm Hg) for a healthy brain with CSF seepage is 5% of total CSF production

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Figure 4

(a) Cumulated radial displacement (m) versus initial radial position (initial configuration) and (b) fluid pressure (mm Hg) versus final radial position (deformed configuration) leading to a different stable position. The net ventricle wall dilation is sought to have the dilation of 1 cm.

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Figure 5

(a) Radial strain ɛr and tangential strain ɛθ ; (b) trace of strain tensor representing local volume change

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Figure 6

Resulting cumulated radial displacement and fluid pressure in the parenchyma for two values of kabs in m2 /Ns

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Figure 7

Radial ventricle equilibrium position versus CSF seepage expressed in percentage of ψmax for two absorption coefficients

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Figure 8

(a) Rate of ventricular enlargement in an experimental study of hydrocephalus induced by surgical obstruction of the fourth ventricle and caudal aqueduct [42] and (b) ventricle dilation versus seepage predicted by the simulation

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Figure 2

Pressure drop in mm Hg when the absorption coefficient (a), internal radius (b) and permeability of parenchyma change

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Figure 1

Simplified spherical model of brain showing the parenchyma, ependyma and pia layer and associated biomechanical parameters




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