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research-article

A computational model for the dynamics of cerebrospinal fluid in the spinal subarachnoid space

[+] Author and Article Information
Eleuterio Toro

Laboratory of Applied Mathematics, University of Trento, via Mesiano 77, 38123 Mesiano (Trento), Italy
eleuterio.toro@unitn.it

Ben Thornber

School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, Australia
ben.thornber@sydney.edu.au

Qinghui Zhang

Laboratory of Applied Mathematics, University of Trento, via Mesiano 77, 38123 Mesiano (Trento), Italy
qinghui.zhang@kuleuven.be

Alessia Scoz

Department of Mathematics, University of Trento, via Sommarive 14, 38123 Povo (Trento), Italy
alessia.scoz@studenti.unitn.it

Christian Contarino

Department of Mathematics, University of Trento, via Sommarive 14, 38123 Povo (Trento), Italy
christian.contarino@unitn.it

1Corresponding author.

ASME doi:10.1115/1.4041551 History: Received October 24, 2017; Revised September 18, 2018

Abstract

Global models for the dynamics of coupled fluid compartments of the Central Nervous System (CNS) require simplified representations of the individual components which are both accurate and computationally efficient. This paper presents a one-dimensional model for computing the flow of cerebrospinal fluid (CSF) within the spinal sub-arachnoid space under the simplifying assumption that it consists of two coaxial tubes representing the spinal cord and the spinal subarachnoid space. A rigorous analysis of the first-order non-linear system demonstrates that the system is elliptic-hyperbolic, and hence ill-posed, for some values of parameters, being hyperbolic otherwise. In addition, the system cannot be written in conservation-law form and thus an appropriate numerical approach is required, namely the path conservative approach. The designed computational algorithm is shown to be second-order accurate in both space and time, capable of handling strongly nonlinear discontinuities, and a method of coupling it with an unsteady inflow condition is presented. Such an approach is sufficiently rapid to be integrated into a global, closed-loop model for computing the dynamics of coupled fluid compartments of the central nervous system.

Copyright (c) 2018 by ASME
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