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Publication# Bio Simulation of Brain Ventricle Dilation in Normal Pressure Hydrocephalus

Résumé

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).

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High-head steel lined pressure tunnels and shafts may be considered as critical infrastructures especially when rock overburden is small. In the case of lining failure, catastrophic damages can occur when a large amount of water can reach the steep valley slopes and induce dangerous mud and debris flow. In the last decades, high-strength steel has been used more frequently for such high-head pressure tunnels and shafts mainly for economic and construction reasons. Under the more and more rough operation conditions of storage hydropower plants, high-strength steels, which are generally thinner than lower grade steels, are more prone to fail by fatigue. Design guidelines for the application of high-strength steel for steel liners are still missing. With his research project, Dr Alexandre Pachoud made an important and novel contribution for the design of pressure tunnels and shafts considering the influence of anisotropic behavior of rock as well as the geometrical imperfections and flaws at welds on the fatigue resistance of the steel liners. For the first time, Dr Pachoud studied systematically the influence of rock anisotropy on the deformation of the lining system comprising steel liner, backfill concrete and near as well as far field rock mass. He performed an extensive parametric study with the finite element method (FEM) over a wide range of geometrical and material parameters. Normalized stresses and displacements were analyzed in the steel liner and the far-field rock mass and correction factors to be included in the analytical solution for isotropic rock conditions could be derived. For transversely anisotropic rock mass the analytical solution allows a simple and fast estimation of the maximum stresses in the steel liner by a correction applied to the isotropic analytical solution with a high accuracy. Based on extensive FEM simulations Dr Pachoud derived in a further step parametric correction factors, which allow estimating stress concentrations and structural stresses in steel liners considering geometrical imperfections. Dr Pachoud obtained also Stress Intensity Factors (SIF) for axial cracks in the weld material of the longitudinal joints by means of computational Linear Elastic Fracture Mechanics (LEFM) and could propose new parametric equations for the weld shape correction. For fatigue assessment, a probabilistic model for steel liner crack growth and fracture was developed by using the above mentioned new parametric equations for considering geometrical imperfections. Finally, Dr Pachoud illustrated the implementation of all the developed parametric equations in a probabilistic model for crack growth in the steel liner under dynamic loading with a case study for a high-head power plant. The probabilistic model allows determining the acceptable undetected initial crack sizes in the steel liner depending on the choice of the steel grade, which is crucial for engineering practice using high-strength steels for pressure tunnels and shafts.

The effect of wood fiber anisotropy and their geometrical features on wood fiber composite stiffness is analyzed. An analytical model for an N-phase composite with orthotropic properties of constituents is developed and used. This model is a straightforward generalization of Hashin’s concentric cylinder assembly model and Christensen’s generalized self-consistent approach. It was found that most macro-properties are governed by only one property of the cell wall which is very important in attempts to back-calculate the fiber properties. The role of lumen (whether it filled by resin or not) has a very large effect on the composite shear properties. It is shown that several of the unknown anisotropic constants characterizing wood fiber are not affecting the stiffness significantly and rough assumptions regarding their value would suffice. The errors introduced by application of the Hashin’s model and neglecting the orthotropic nature of the material behavior in cylindrical axes are evaluated. The effect of geometrical deviations from circular cross-section, representing, for example, collapsed fibers, is analyzed using the finite element method (FEM) and the observed trends are discussed.

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