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Hydrocephalus is a brain disease wherein the ventricles dilate and compress the parenchyma towards the skull. It is primarily characterized by the disruption of the cerebrospinal fluid (CSF) flow within the ventricular system. Normal pressure hydrocephalus (NPH) is a form of hydrocephalus for which the enlargement of ventricles occurs although the intracranial pressure (ICP) remains close to normal. The pressure gradient between the source of CSF production in the ventricles and the absorption sites is reported to be very low (∼1 mm Hg), i.e. within the experimental errors. The mechanism of NPH evolution is still obscure and its distinction from the other causes of dementia such as Alzheimer and neurodegenerative diseases is difficult. The present work contributes to a better understanding of the NPH mechanism in terms of CSF disturbances and/or parenchyma defects. To this end, imaging techniques such as Magnetic resonance imaging (MRI), Diffusion tensor imaging (DTI) and Magnetic resonance elastography (MRE) are used together with a finite element (FE) model. As a final step, NPH onset and evolution are clarified via a theoretical model for healthy and NPH brains assuming a spherical geometry. The proposed mechanism is further analyzed in a realistic 3D model of the brain parenchyma. Geometries of ventricular system and skull are obtained from MRI images of a human brain. DTI data are used to establish the fiber tracts direction as well as the local frame of anisotropic elasticity and permeability. The brain parenchyma is considered as a poro-elastic material where the tissue displacement and CSF flow are modeled using the Biot's theory. A link between the CSF diffusion and CSF permeability in brain parenchyma is established and the importance of space dependent CSF content and transverse isotropic (TI) permeability is highlighted in case of low pressure gradient hydrocephalus. Calculations are carried out to simulate the ventricular dilation using FE softwares such as MATLAB® and COMSOL®. The numerical results show that consideration of space dependent CSF content and TI permeability leads to a much more realistic model for NPH in terms of CSF velocity and CSF content. Anisotropic MRE experiment is conducted over selected slices of a healthy human brain. The experimental results are statistically refined and further used to assess the healthy brain stiffness as well as the degree of anisotropy in elasticity. Moreover, the constitutive behavior of the white matter is modeled as a composite material containing fiber tracts surrounded by a matrix; with the assumption of a low fiber-matrix bonding and fiber tract undulation. A non-linear elastic model is proposed in order to take into account the load transfer from white matter matrix to fiber tracts when these are fully stretched. The unknown value of the elastic coefficients in a sick brain is determined by using inverse modeling, i.e. by adjusting these coefficients so that the right ventricle dilation is obtained. It is demonstrated that NPH development can be associated with a degradation of the brain parenchyma elastic stiffness in NPH patients. It is shown that during NPH development, a load transfer from the white matter matrix (cell bodies and interstitial fluid) to fiber tracts takes place, initiating elastic anisotropy in white matter tissues at rather large strains. An analytical approach is developed to seek the underlying NPH mechanism in a simplified model of brain. Without further refinement in the constitutive equation or adding complexity to the material behavior, the Biot's formulation is regarded as the basis. However, an absorption term is added to the Biot's model to consider the possible transparenchymal CSF resorption. The ventricle stability concept is introduced and is further utilized to investigate the equilibrium positions. The influence of different biomechanical parameters on the stable ventricle geometry is assessed and the healthy and NPH equilibrium positions are found to be dependent in particular on the CSF seepage through the ventricle wall and the absorption and permeability coefficients of the brain parenchyma. Although very simple, the proposed analytical model is able to predict the onset and development of NPH conditions as a deviation from healthy conditions. Incorporating the stability concept in a more realistic geometry of brain (3D), the respective equilibrium positions are recaptured using the parameter values provided by the analytical spherical model. The disruption of ventricle surface during the NPH development increases CSF seepage and consequently the medium permeability. A dilation dependent permeability is moreover incorporated in a 3D model of the brain. The results emphasize the importance of strain dependent permeability which favors the ventricle equilibrations in more realistic geometries of brain. Future works might consider the time dependent deformation (creep effects and stress induced remodeling) of ventricles and the incorporation of anisotropic permeability and elasticity in the 3D model. The geometry should be extended to the full ventricular system including the subarachnoid spaces (SAS).

Hydrocephalus is a cerebral disease where brain ventricles enlarge and compress the brain parenchyma towards the skull leading to symptoms like dementia, walking disorder and incontinence. The origin of normal pressure hydrocephalus is still obscure. In order to study this disease, a finite element model is built using the geometries of the ventricles and the skull measured by magnetic resonance imaging. The brain parenchyma is modelled as a porous medium fully saturated with cerebrospinal fluid (CSF) using Biot’s theory of consolidation (1941). Owing to the existence of bundles of axons, the brain parenchyma shows locally anisotropic behaviour. Indeed, permeability is higher along the fibre tracts in the white matter region. In contrast, grey matter is isotropic. Diffusion tensor imaging is used to establish the local CSF content and the fibre tracts direction together with the associated local frame where the permeability coefficients are given by dedicated formulas. The present study shows that both inhomogeneous CSF content and anisotropy in permeability have a great influence on the CSF flow pattern through the parenchyma under an imposed pressure gradient between the ventricles and the subarachnoid spaces.