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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: als@ucsd.edu
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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

REFERENCES

Bardan, G., Plouraboué, F., Zagzoule, M. & Baledent, O. 2012 Simple patient-based transmantle pressure and shear estimate from cine phase-contrast MRI in cerebral aqueduct. IEEE Trans. Biomed. Engng 59 (10), 2874–2883.CrossRefGoogle ScholarPubMed
Chen, L., Beckett, A., Verma, A. & Feinberg, D. A. 2015 Dynamics of respiratory and cardiac CSF motion revealed with real-time simultaneous multi-slice EPI velocity phase contrast imaging. Neuroimage 122, 281–287.CrossRefGoogle ScholarPubMed
Dreha-Kulaczewski, S., Joseph, A. A., Merboldt, K.-D., Ludwig, H.-C., Gärtner, J. & Frahm, J. 2015 Inspiration is the major regulator of human CSF flow. J. Neurosci. 35 (6), 2485–2491.CrossRefGoogle ScholarPubMed
Eide, P. K. & Sæhle, T. 2010 Is ventriculomegaly in idiopathic normal pressure hydrocephalus associated with a transmantle gradient in pulsatile intracranial pressure? Acta Neurochir. (Wien) 152 (6), 989–995.CrossRefGoogle ScholarPubMed
Feinberg, D. A. & Mark, A. S. 1987 Human brain motion and cerebrospinal fluid circulation demonstrated with mr velocity imaging. Radiology 163 (3), 793–799.CrossRefGoogle ScholarPubMed
Fin, L. & Grebe, R. 2003 Three dimensional modeling of the cerebrospinal fluid dynamics and brain interactions in the aqueduct of sylvius. Comput. Methods Biomech. Biomed. Engng 6 (3), 163–170.CrossRefGoogle ScholarPubMed
Friese, S., Hamhaber, U., Erb, M., Kueker, W. & Klose, U. 2004 The influence of pulse and respiration on spinal cerebrospinal fluid pulsation. Invest. Radiol. 39 (2), 120–130.CrossRefGoogle ScholarPubMed
Gupta, S., Soellinger, M., Boesiger, P., Poulikakos, D. & Kurtcuoglu, V. 2009 Three-dimensional computational modeling of subject-specific cerebrospinal fluid flow in the subarachnoid space. Trans. ASME J. Biomech. Engng 131 (2), 021010.CrossRefGoogle ScholarPubMed
Jacobson, E. E., Fletcher, D. F., Morgan, M. K. & Johnston, I. H. 1996 Fluid dynamics of the cerebral aqueduct. Pediatr. Neurosurg. 24 (5), 229–236.CrossRefGoogle ScholarPubMed
Jacobson, E. E., Fletcher, D. F., Morgan, M. K. & Johnston, I. H. 1999 Computer modelling of the cerebrospinal fluid flow dynamics of aqueduct stenosis. Med. Biol. Engng Comput. 37 (1), 59–63.CrossRefGoogle ScholarPubMed
Kurtcuoglu, V., Soellinger, M., Summers, P., Boomsma, K., Poulikakos, D., Boesiger, P. & Ventikos, Y. 2007 Computational investigation of subject-specific cerebrospinal fluid flow in the third ventricle and aqueduct of sylvius. J. Biomech. 40 (6), 1235–1245.CrossRefGoogle ScholarPubMed
Lawrence, J. J., Coenen, W., Sánchez, A. L., Pawlak, G., Martínez-Bazán, C., Haughton, V. & Lasheras, J. C. 2019 On the dispersion of a drug delivered intrathecally in the spinal canal. J. Fluid Mech. 861, 679–720.CrossRefGoogle Scholar
Linninger, A. A., Tangen, K., Hsu, C.-Y. & Frim, D. 2016 Cerebrospinal fluid mechanics and its coupling to cerebrovascular dynamics. Annu. Rev. Fluid Mech. 48, 219–257.CrossRefGoogle Scholar
Longatti, P., Fiorindi, A., Peruzzo, P., Basaldella, L. & Susin, F. M. 2019 Form follows function: estimation of CSF flow in the third ventricle–aqueduct–fourth ventricle complex modeled as a diffuser/nozzle pump. J. Neurosurg. 1 (aop), 1–8.CrossRefGoogle Scholar
Markenroth Bloch, K., Töger, J. & Ståhlberg, F. 2018 Investigation of cerebrospinal fluid flow in the cerebral aqueduct using high-resolution phase contrast measurements at 7T MRI. Acta Radiol. 59 (8), 988–996.CrossRefGoogle ScholarPubMed
Penn, R. D., Lee, M. C., Linninger, A. A., Miesel, K., Lu, S. N. & Stylos, L. 2005 Pressure gradients in the brain in an experimental model of hydrocephalus. J. Neurosurg. 102 (6), 1069–1075.CrossRefGoogle Scholar
Ringstad, G., Emblem, K. E., Geier, O., Alperin, N. & Eide, P. K. 2015 Aqueductal stroke volume: comparisons with intracranial pressure scores in idiopathic normal pressure hydrocephalus. Am. J. Neuroradiol. 36 (9), 1623–1630.CrossRefGoogle ScholarPubMed
Sánchez, A. L., Martínez-Bazan, C., Gutiérrez-Montes, C., Criado-Hidalgo, E., Pawlak, G., Bradley, W., Haughton, V. & Lasheras, J. C. 2018 On the bulk motion of the cerebrospinal fluid in the spinal canal. J. Fluid Mech. 841, 203–227.CrossRefGoogle Scholar
Shanks, J., Markenroth Bloch, K., Laurell, K., Cesarini, K. G., Fahlström, M., Larsson, E.-M. & Virhammar, J. 2019 Aqueductal CSF stroke volume is increased in patients with idiopathic normal pressure hydrocephalus and decreases after shunt surgery. Am. J. Neuroradiol. 40 (3), 453–459.Google ScholarPubMed
Stephensen, H., Tisell, M. & Wikkelsö, C. 2002 There is no transmantle pressure gradient in communicating or noncommunicating hydrocephalus. Neurosurgery 50 (4), 763–773.CrossRefGoogle ScholarPubMed
Sweetman, B., Xenos, M., Zitella, L. & Linninger, A. A. 2011 Three-dimensional computational prediction of cerebrospinal fluid flow in the human brain. Med. Biol. Engng Comput. 41 (2), 67–75.CrossRefGoogle ScholarPubMed
Takizawa, K., Matsumae, M., Sunohara, S., Yatsushiro, S. & Kuroda, K. 2017 Characterization of cardiac-and respiratory-driven cerebrospinal fluid motion based on asynchronous phase-contrast magnetic resonance imaging in volunteers. Fluids Barriers CNS 14 (1), 25.CrossRefGoogle Scholar
Tannehill, J. C., Anderson, D. A. & Pletcher, R. H. 1997 Computational Fluid Mechanics and Heat Transfer, 2nd edn. Taylor and Francis.Google Scholar
Vinje, V., Ringstad, G., Lindstrøm, E. K., Valnes, L. M., Rognes, M. E., Eide, P. K. & Mardal, K.-A. 2019 Respiratory influence on cerebrospinal fluid flow – a computational study based on long-term intracranial pressure measurements. Sci. Rep. 9 (1), 1–13.CrossRefGoogle ScholarPubMed
Yamada, S., Miyazaki, M., Yamashita, Y., Ouyang, C., Yui, M., Nakahashi, M., Shimizu, S., Aoki, I., Morohoshi, Y. & McComb, J. G. 2013 Influence of respiration on cerebrospinal fluid movement using magnetic resonance spin labeling. Fluids Barries CNS 10 (1), 36.CrossRefGoogle ScholarPubMed
Yatsushiro, S., Sunohara, S., Atsumi, H., Matsumae, M. & Kuroda, K. 2018 Visualization and characterization of cerebrospinal fluid motion based on magnetic resonance imaging. In Hydrocephalus: Water on the Brain (ed. B. Gürer), p. 9. IntechOpen.CrossRefGoogle Scholar
Yildiz, S., Thyagaraj, S., Jin, N., Zhong, X. S., Heidari, P., Martin, B. A., Loth, F., Oshinski, J. & Sabra, K. G. 2017 Quantifying the influence of respiration and cardiac pulsations on cerebrospinal fluid dynamics using real-time phase-contrast MRI. J. Magn. Reson. Imag. 46 (2), 431–439.CrossRefGoogle ScholarPubMed