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A model for the oscillatory flow in the cerebral aqueduct

Published online by Cambridge University Press:  20 July 2020

S. Sincomb Open the ORCID record for S. Sincomb [Opens in a new window] ,
W. Coenen Open the ORCID record for W. Coenen [Opens in a new window] ,
A. L. Sánchez Open the ORCID record for A. L. Sánchez [Opens in a new window]  and
J. C. Lasheras Open the ORCID record for J. C. Lasheras [Opens in a new window]
S. Sincomb
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, USA
W. Coenen
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, USA Grupo de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, Av. Universidad 30, 28911 Leganés, Madrid, Spain
A. L. Sánchez*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, USA
J. C. Lasheras
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, USA Department of Bioengineering, University of California San Diego, La Jolla, USA
*
†Email address for correspondence: [email protected]
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Abstract

This paper addresses the pulsating motion of cerebrospinal fluid in the aqueduct of Sylvius, a slender canal connecting the third and fourth ventricles of the brain. Specific attention is given to the relation between the instantaneous values of the flow rate and the interventricular pressure difference, needed in clinical applications to enable indirect evaluations of the latter from direct magnetic resonance measurements of the former. An order of magnitude analysis accounting for the slenderness of the canal is used in simplifying the flow description. The boundary layer approximation is found to be applicable in the slender canal, where the oscillating flow is characterized by stroke lengths comparable to the canal length and periods comparable to the transverse diffusion time. By way of contrast, the flow in the non-slender opening regions connecting the aqueduct with the two ventricles is found to be inviscid and quasi-steady in the first approximation. The resulting simplified description is validated by comparison with results of direct numerical simulations. The model is used to investigate the relation between the interventricular pressure and the stroke length, in parametric ranges of interest in clinical applications.

JFM classification

Biological Fluid Dynamics: Biomedical flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , R1
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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