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 subarachnoid space (SSAS) under the simplifying assumption that it consists of two coaxial tubes representing the spinal cord and the dura. A rigorous analysis of the first-order nonlinear 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 CNS.
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January 2019
Research-Article
A Computational Model for the Dynamics of Cerebrospinal Fluid in the Spinal Subarachnoid Space
Eleuterio F. Toro,
Eleuterio F. Toro
Laboratory of Applied Mathematics,
University of Trento,
via Mesiano 77,
Mesiano,
Trento 38123, Italy
University of Trento,
via Mesiano 77,
Mesiano,
Trento 38123, Italy
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Ben Thornber,
Ben Thornber
School of Aerospace, Mechanical and
Mechatronic Engineering,
University of Sydney,
Sydney 2006, Australia
e-mail: ben.thornber@sydney.edu.au
Mechatronic Engineering,
University of Sydney,
Sydney 2006, Australia
e-mail: ben.thornber@sydney.edu.au
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Qinghui Zhang,
Qinghui Zhang
Laboratory of Applied Mathematics,
University of Trento,
via Mesiano 77,
Mesiano,
Trento 38123, Italy
University of Trento,
via Mesiano 77,
Mesiano,
Trento 38123, Italy
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Alessia Scoz,
Alessia Scoz
Department of Mathematics,
University of Trento,
via Sommarive 14,
Povo,
Trento 38123, Italy
University of Trento,
via Sommarive 14,
Povo,
Trento 38123, Italy
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Christian Contarino
Christian Contarino
Department of Mathematics,
University of Trento,
via Sommarive 14,
Povo,
Trento 38123, Italy
University of Trento,
via Sommarive 14,
Povo,
Trento 38123, Italy
Search for other works by this author on:
Eleuterio F. Toro
Laboratory of Applied Mathematics,
University of Trento,
via Mesiano 77,
Mesiano,
Trento 38123, Italy
University of Trento,
via Mesiano 77,
Mesiano,
Trento 38123, Italy
Ben Thornber
School of Aerospace, Mechanical and
Mechatronic Engineering,
University of Sydney,
Sydney 2006, Australia
e-mail: ben.thornber@sydney.edu.au
Mechatronic Engineering,
University of Sydney,
Sydney 2006, Australia
e-mail: ben.thornber@sydney.edu.au
Qinghui Zhang
Laboratory of Applied Mathematics,
University of Trento,
via Mesiano 77,
Mesiano,
Trento 38123, Italy
University of Trento,
via Mesiano 77,
Mesiano,
Trento 38123, Italy
Alessia Scoz
Department of Mathematics,
University of Trento,
via Sommarive 14,
Povo,
Trento 38123, Italy
University of Trento,
via Sommarive 14,
Povo,
Trento 38123, Italy
Christian Contarino
Department of Mathematics,
University of Trento,
via Sommarive 14,
Povo,
Trento 38123, Italy
University of Trento,
via Sommarive 14,
Povo,
Trento 38123, Italy
1Corresponding author.
Manuscript received October 24, 2017; final manuscript received September 18, 2018; published online October 17, 2018. Assoc. Editor: Guy M. Genin.
J Biomech Eng. Jan 2019, 141(1): 011004 (16 pages)
Published Online: October 17, 2018
Article history
Received:
October 24, 2017
Revised:
September 18, 2018
Citation
Toro, E. F., Thornber, B., Zhang, Q., Scoz, A., and Contarino, C. (October 17, 2018). "A Computational Model for the Dynamics of Cerebrospinal Fluid in the Spinal Subarachnoid Space." ASME. J Biomech Eng. January 2019; 141(1): 011004. https://doi.org/10.1115/1.4041551
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