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Mechanics of Hydrocephalus

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Mathematical Modelling and Biomechanics of the Brain

Part of the book series: Fields Institute Monographs ((FIM,volume 37))

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Abstract

Hydrocephalus is a serious neurological disorder which was first described by Hippocrates (460–370 BC) as water on the brain. The disorder is characterized by an abnormal accumulation of cerebrospinal fluid in the brain’s ventricles and in pediatric cases often by an increased intracranial pressure. Currently, the general medical community consensus is that hydrocephalus is a heterogeneous group of disorders, rather than a single disease entity, and therefore the pathophysiology of hydrocephalus is much more complex and obscure than the clinical or radiological presentation of hydrocephalus (going beyond simply ventricular dilatation). Together with gross macroscopic changes, hydrocephalus results in significant changes to the brain tissue, not only of its morphology, but also of its dynamics, biochemistry, metabolism, and maturation. Successful treatment does not always reverse the injuries caused by hydrocephalus—early therapeutic intervention plays a crucial role in determining the reversibility of lesions, and, hence, the overall outcome. Realistic biomechanical models of hydrocephalus could advance our understanding about the pathophysiology of hydrocephalus and play an important role in predicting the evolution of hydrocephalus as well as the outcome of its treatment. In this chapter we will provide some basic facts about brain anatomy and mechanisms involved in the onset and evolution of hydrocephalus, and review some of the mathematical models of hydrocephalus currently in the literature.

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Notes

  1. 1.

    By definition, the Poisson’s ratio is the negative ratio of the transverse and axial strains. The Poisson’s ratio of an incompressible material is 1/2.

  2. 2.

    According to this definition, the spatial point used in mixture theories does not correspond to a material point but rather to a very small region around a material point.

  3. 3.

    The pore fluid pressure introduced by Eq. (3.12) is by definition the product between the fluid pressure and the porosity (the volume fraction of the fluid phase over the constant total volume of the mixure).

  4. 4.

    Magnetic resonance elastography is a noninvasive technique facilitated by a magnetic resonance imaging scanner that is used to estimate viscoelastic properties of human internal organs based on their response to applied stress.

  5. 5.

    The Dirichlet boundary condition equates the pore fluid pressure to a given ventricular CSF pressure, while the Neumann boundary condition the radial variation of the fluid pressure is equal to the radial velocity of CSF entering the brain tissue from the ventricles.

  6. 6.

    The inseparability of length scales as well as the very dynamic nature of numerous components and their assembles could support modeling the brain tissue as a multi-phasic mixture.

  7. 7.

    In [31], the authors propose to use the genetic algorithm (an adaptive search algorithm based on the concepts of natural selection and genetics) to simultaneously fit ramping and relaxation experimental data to Fung’s quasi-linear viscoelastic model to obtain the mechanical parameters. The robustness of the genetic algorithm is shown on experimental data of ligaments. However, a similar set of experimental data for the brain parenchyma that will allow the use of this algorithm to find more accurate parameters for Fung’s quasi-linear viscoelastic model has not been reported to date.

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Authors and Affiliations

  1. College of Engineering, Penn State University, University Park, PA, USA

    Corina Drapaca

  2. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada

    Siv Sivaloganathan

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  1. Corina Drapaca
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Drapaca, C., Sivaloganathan, S. (2019). Mechanics of Hydrocephalus. In: Mathematical Modelling and Biomechanics of the Brain. Fields Institute Monographs, vol 37. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9810-4_3

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