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

Abstract

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.

Fluid–structure interaction for highly complex, statistically defined, biological media: Homogenisation and a 3D multi-compartmental poroelastic model for brain biomechanics

“…In the literature, several works have utilised a poroelastic approach in modelling parenchymal tissue within the realm of hydrocephalus and oedema formation in the brain and small intestine (Tully and Ventikos, 2011;Vardakis et al, 2013b;Guo et al, 2018;Vardakis et al, 2017Vardakis et al, , 2016Chou et al, 2016;Chou, 2016;Vardakis et al, 2013a;Kaczmarek et al, 1997;Levine, 1999Levine, , 2000Smillie et al, 2005;Sobey and Wirth, 2006;Shahim et al, 2012;Aldea et al, 2019;Thompson et al, 2019). The poroelastic modelling of parenchymal tissue for the purpose of investigating AD yields a narrower selection of relevant work (Guo et al, 2018;Thompson et al, 2019).…”

Mechanics of the brain: perspectives, challenges, and opportunities

“… 2005 ; Levine 1999 ; Wirth and Sobey 2006 ; Shahim et al. 2012 ; Tully and Ventikos 2011 ; Wilkie et al. 2012 ; Wirth and Sobey 2009 ; Stoverud et al.…”

Constitutive Modeling of Brain Tissue: Current Perspectives

“…Biphasic and triphasic models are used when the effects of the other phases are non-negligible. These models have been used for the brain tissue to study hydrocephalus, an accumulation of cerebrospinal fluid in the ventricles of the brain [60,61]. Biphasic constitutive models are also used to explore mass-or drug-transport throughout the brain [62,63].…”

“…The stress in the main elastic network r A is determined by a freely jointed eightchain model, see Eqs. (59) and (60). The short-and long-term responses of the tissue are determined by other elastic networks, as r C and r E , respectively.…”

“…5.4. In most reported multiphase models for the brain tissue in the literature, the constitutive model for the solid phase is timeindependent and relatively simple, e.g., compressible Ogden [62], Neo-Hookean [66], or even linear elastic [60,61,63]. As a general rule of thumb, to model the time-dependent behavior in a multiphase problem, the constitutive model for the solid phase should have a limited number of time scales, arguably at most one.…”