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Journal of Biomechanical Engineering | Volume 134 | Issue 4 | Research Paper
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

1

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
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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.
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Figures

Grahic Jump Location
+Simplified spherical model of brain showing the parenchyma, ependyma and pia layer and associated biomechanical parameters
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Simplified spherical model of brain showing the parenchyma, ependyma and pia layer and associated biomechanical parameters
Figure 1

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

Grahic Jump Location
+Pressure drop in mm Hg when the absorption coefficient (a), internal radius (b) and permeability of parenchyma change
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Pressure drop in mm Hg when the absorption coefficient (a), internal radius (b) and permeability of parenchyma change
Figure 2

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

Grahic Jump Location
+(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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(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
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

Grahic Jump Location
+(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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(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
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

Grahic Jump Location
+(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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(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.
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.

Grahic Jump Location
+(a) Radial strain ɛr and tangential strain ɛθ ; (b) trace of strain tensor representing local volume change
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(a) Radial strain ɛr and tangential strain ɛθ ; (b) trace of strain tensor representing local volume change
Figure 5

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

Grahic Jump Location
+Resulting cumulated radial displacement and fluid pressure in the parenchyma for two values of kabs in m2 /Ns
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Resulting cumulated radial displacement and fluid pressure in the parenchyma for two values of kabs in m2 /Ns
Figure 6

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

Grahic Jump Location
+Radial ventricle equilibrium position versus CSF seepage expressed in percentage of ψmax for two absorption coefficients
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Radial ventricle equilibrium position versus CSF seepage expressed in percentage of ψmax for two absorption coefficients
Figure 7

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

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