Research Papers

A Poroelastic Fluid/Structure-Interaction Model of Cerebrospinal Fluid Dynamics in the Cord With Syringomyelia and Adjacent Subarachnoid-Space Stenosis

[+] Author and Article Information
C. D. Bertram

School of Mathematics and Statistics,
University of Sydney,
New South Wales 2006, Australia

M. Heil

School of Mathematics,
University of Manchester,
Manchester M13 9PL, UK

Manuscript received March 16, 2016; final manuscript received August 21, 2016; published online November 4, 2016. Assoc. Editor: C. Alberto Figueroa.

J Biomech Eng 139(1), 011001 (Nov 04, 2016) (10 pages) Paper No: BIO-16-1102; doi: 10.1115/1.4034657 History: Received March 16, 2016; Revised August 21, 2016

An existing axisymmetric fluid/structure-interaction (FSI) model of the spinal cord, pia mater, subarachnoid space, and dura mater in the presence of syringomyelia and subarachnoid-space stenosis was modified to include porous solids. This allowed investigation of a hypothesis for syrinx fluid ingress from cerebrospinal fluid (CSF). Gross model deformation was unchanged by the addition of porosity, but pressure oscillated more in the syrinx and the subarachnoid space below the stenosis. The poroelastic model still exhibited elevated mean pressure in the subarachnoid space below the stenosis and in the syrinx. With realistic cord permeability, there was slight oscillatory shunt flow bypassing the stenosis via the porous tissue over the syrinx. Weak steady streaming flow occurred in a circuit involving craniocaudal flow through the stenosis and back via the syrinx. Mean syrinx volume was scarcely altered when the adjacent stenosis bisected the syrinx, but increased slightly when the syrinx was predominantly located caudal to the stenosis. The fluid content of the tissues over the syrinx oscillated, absorbing most of the radial flow seeping from the subarachnoid space so that it did not reach the syrinx. To a lesser extent, this cyclic swelling in a boundary layer of cord tissue just below the pia occurred all along the cord, representing a mechanism for exchange of interstitial fluid (ISF) and cerebrospinal fluid which could explain recent tracer findings without invoking perivascular conduits. The model demonstrates that syrinx volume increase is possible when there is subarachnoid-space stenosis and the cord and pia are permeable.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Levine, D. N. , 2004, “ The Pathogenesis of Syringomyelia Associated With Lesions at the Foramen Magnum: A Critical Review of Existing Theories and Proposal of a New Hypothesis,” J. Neurol. Sci., 220, pp. 3–21. [CrossRef] [PubMed]
Elliott, N. S. J. , Bertram, C. D. , Martin, B. A. , and Brodbelt, A. , 2013, “ Syringomyelia: A Review of the Biomechanics,” J. Fluids Struct., 40, pp. 1–24. [CrossRef]
Bertram, C. D. , 2010, “ Evaluation by Fluid/Structure-Interaction Spinal-Cord Simulation of the Effects of Subarachnoid-Space Stenosis on an Adjacent Syrinx,” ASME J. Biomech. Eng., 132(6), p. 061009. [CrossRef]
Bertram, C. D. , 2009, “ A Numerical Investigation of Waves Propagating in the Spinal Cord and Subarachnoid Space in the Presence of a Syrinx,” J. Fluids Struct., 25(7), pp. 1189–1205. [CrossRef]
Brugières, P. , Idy-Peretti, I. , Iffenecker, C. , Parker, F. , Jolivet, O. , Hurth, M. , Gaston, A. , and Bittoun, J. , 2000, “ CSF Flow Measurement in Syringomyelia,” Am. J. Neuroradiol., 21(10), pp. 1785–1792. http://www.ajnr.org/content/21/10/1785.short
Williams, B. , 1980, “ On the Pathogenesis of Syringomyelia: A Review,” J. R. Soc. Med., 73(11), pp. 798–806. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1437943/ [PubMed]
Martin, B. A. , Labuda, R. , Royston, T. J. , Oshinski, J. N. , Iskandar, B. , and Loth, F. , 2010, “ Spinal Canal Pressure Measurements in an In Vitro Spinal Stenosis Model: Implications on Syringomyelia Theories,” ASME J. Biomech. Eng., 132(11), p. 111007. [CrossRef]
Heil, M. , and Bertram, C. D. , “ A Poroelastic Fluid-Structure Interaction Model of Syringomyelia,” J. Fluid Mech. (in press).
Bertram, C. D. , Brodbelt, A. R. , and Stoodley, M. A. , 2005, “ The Origins of Syringomyelia: Numerical Models of Fluid/Structure Interactions in the Spinal Cord,” ASME J. Biomech. Eng., 127(7), pp. 1099–1109. [CrossRef]
Simon, B. R. , 1992, “ Multiphase Poroelastic Finite Element Models for Soft Tissue Structures,” ASME Appl. Mech. Rev., 45(6), pp. 191–218. [CrossRef]
Jäger, W. , and Mikelić, A. , 2000, “ On the Interface Boundary Condition of Beavers, Joseph, and Saffman,” SIAM J. Appl. Math., 60(4), pp. 1111–1127. [CrossRef]
Ozawa, H. , Matsumoto, T. , Ohashi, T. , Sato, M. , and Kokubun, S. , 2004, “ Mechanical Properties and Function of the Spinal Pia Mater,” J. Neurosurg. (Spine), 1(1), pp. 122–127. [CrossRef] [PubMed]
Bertram, C. D. , 2012, “ Benchmarking of Fluid/Structure Interaction Models of Wave Propagation (Poster),” ECI Conference on Computational Fluid Dynamics in Medicine and Biology, and Seventh International Biofluid Mechanics Symposium, Ein Bokek, Dead Sea, Israel, Mar. 25–30.
Smillie, A. , Sobey, I. , and Molnar, Z. , 2005, “ A Hydroelastic Model of Hydrocephalus,” J. Fluid Mech., 539, pp. 417–443. [CrossRef]
Cloyd, M. W. , and Low, F. N. , 1974, “ Scanning Electron Microscopy of the Subarachnoid Space in the Dog. I. Spinal Cord Levels,” J. Comp. Neurol., 153(4), pp. 325–367. [CrossRef] [PubMed]
Heil, M. , and Hazel, A. L. , 2006, “ oomph-lib—An Object-Oriented Multi-Physics Finite-Element Library,” Fluid-Structure Interaction (Lecture Notes on Computational Science and Engineering), M. Schafer , and H.-J. Bungartz , eds., Springer-Verlag, Berlin, pp. 19–49.
Detournay, E. , and Cheng, A. H.-D. , 1993, “ Fundamentals of Poroelasticity,” Comprehensive Rock Engineering: Principles, Practice and Projects (Analysis and Design Method, Vol. II), C. Fairhurst , ed., Pergamon Press, Oxford, UK, pp. 113–171.
Brodbelt, A. R. , and Stoodley, M. A. , 2003, “ Post-Traumatic Syringomyelia: A Review,” J. Clin. Neurosci., 10(4), pp. 401–408. [CrossRef] [PubMed]
Klekamp, J. , 2009, “ Syringomyelia,” Practical Handbook of Neurosurgery—From Leading Neurosurgeons, M. Sindou, ed., Springer-Verlag, Wien, Germany, Vol. 3, pp. 145–161.
Samii, M. , and Klekamp, J. , 1994, “ Surgical Results of 100 Intramedullary Tumors in Relation to Accompanying Syringomyelia,” Neurosurgery, 35(5), pp. 865–873. [CrossRef] [PubMed]
Oldfield, E. H. , Muraszko, K. , Shawker, T. H. , and Patronas, N. J. , 1994, “ Pathophysiology of Syringomyelia Associated With Chiari I Malformation of the Cerebellar Tonsils,” J. Neurosurg., 80(1), pp. 3–15. [CrossRef] [PubMed]
Davis, C. H. G. , and Symon, L. , 1989, “ Mechanisms and Treatment in Post-Traumatic Syringomyelia,” Br. J. Neurosurg., 3(6), pp. 669–674. [CrossRef] [PubMed]
Ellertsson, A. B. , and Greitz, T. , 1970, “ The Distending Force in the Production of Communicating Syringomyelia,” Lancet, 295(7658), p. 1234. [CrossRef]
Hall, P. , Turner, M. , Aichinger, S. , Bendick, P. , and Campbell, R. , 1980, “ Experimental Syringomyelia: The Relationship Between Intraventricular and Intrasyrinx Pressures,” J. Neurosurg., 52(6), pp. 812–817. [CrossRef] [PubMed]
Milhorat, T. H. , Capocelli, A. L. , Kotzen, R. M. , Bolognese, P. , Heger, I . M. , and Cottrell, J. E. , 1997, “ Intramedullary Pressure in Syringomyelia: Clinical and Pathophysiological Correlates of Syrinx Distension,” Neurosurgery, 41(5), pp. 1102–1110. [CrossRef] [PubMed]
Bilston, L. E. , Stoodley, M. A. , and Fletcher, D. F. , 2010, “ The Influence of the Relative Timing of Arterial and Subarachnoid Space Pulse Waves on Spinal Perivascular Cerebrospinal Fluid Flow as a Possible Factor in Syrinx Developments,” J. Neurosurg., 112(4), pp. 808–813. [CrossRef] [PubMed]
Sansur, C. A. , Heiss, J. D. , DeVroom, H. L. , Eskioglu, E. , Ennis, R. , and Oldfield, E. H. , 2003, “ Pathophysiology of Headache Associated With Cough in Patients With Chiari I Malformation,” J. Neurosurg., 98(3), pp. 453–458. [CrossRef] [PubMed]
Williams, B. , 1976, “ Cerebrospinal Fluid Pressure Changes in Response to Coughing,” Brain, 99(2), pp. 331–346. [CrossRef] [PubMed]
Klekamp, J. , 2002, “ The Pathophysiology of Syringomyelia—Historical Overview and Current Concept,” Acta Neurochir., 144(7), pp. 649–664. [CrossRef]
Iliff, J. J. , Lee, H. , Yu, M. , Feng, T. , Logan, J. , Nedergaard, M. , and Benveniste, H. , 2013, “ Brain-Wide Pathway for Waste Clearance Captured by Contrast-Enhanced MRI,” J. Clin. Invest., 123(3), pp. 1299–1309. [CrossRef] [PubMed]
Iliff, J. J. , Wang, M. , Zeppenfeld, D. M. , Venkataraman, A. , Plog, B. A. , Liao, Y. , Deane, R. , and Nedergaard, M. , 2013, “ Cerebral Arterial Pulsation Drives Paravascular CSF–Interstitial Fluid Exchange in the Murine Brain,” J. Neurosci., 33(46), pp. 18190–18199. [CrossRef] [PubMed]
Carare, R. O. , Bernardes-Silva, M. , Newman, T. A. , Page, A. M. , Nicoll, J. A. R. , Perry, V . H. , and Weller, R. O. , 2008, “ Solutes, but Not Cells, Drain From the Brain Parenchyma Along Basement Membranes of Capillaries and Arteries: Significance for Cerebral Amyloid Angiopathy and Neuroimmunology,” Neuropathol. Appl. Neurobiol., 34(2), pp. 131–144. [CrossRef] [PubMed]
Rossi, C. , Boss, A. , Steidle, G. , Martirosian, P. , Klose, U. , Capuani, S. , Maraviglia, B. , Claussen, C. D. , and Schick, F. , 2008, “ Water Diffusion Anisotropy in White and Gray Matter of the Human Spinal Cord,” J. Magn. Reson. Imaging, 27(3), pp. 476–482. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

The model geometry, at 1:1 scale on the left and radially exaggerated 20× on the right. Aqueous fluid in syrinx and SSS (blue). Three solids having different stiffnesses are shown (in differing colors); chequering (with blue) denotes a porous medium, uniform shading an impermeable solid.

Grahic Jump Location
Fig. 4

Upper panels compare the flow-rate through the stenosis gap (blue, “thru gap”) with that arriving in the caudal SSS via the syrinx and overlying porous media (green, “crossing iSSS caudally”—iSSS denotes the inner boundary of the SSS). Lower panels compare the same flow-rate entering the caudal SSS (green, “thru SSS”) with that leaving the caudal half of the syrinx (red). Start-up transients are visible over the first three cycles (1.2 s).

Grahic Jump Location
Fig. 3

Profiles of cycle-average pressure versus axial position at the inner (solid lines) and outer (dotted) edges of the SSS, and at the syrinx center-line (dashed). Only the axial region 70 < z < 230 mm, which spans the syrinx, is shown. Results are shown for the nonporous cord and pia (blue), with cord and pia porous only over the syrinx (green, “cover porous”), and with the whole cord and pia porous (red, “all porous”).

Grahic Jump Location
Fig. 2

The deflection (a) and (b) of the FSI boundaries of the model, magnified 5×, and the pressure along the inner boundary of the SSS (solid line) and (broken line) on the syrinx center-line (c) and (d), both shown at the peak (a) and (c) and the trough (b) and (d) of the forcing cycle. The permeable model outline (red) almost entirely overlaps that of the impermeable model (blue). The real change in gap width is much smaller than depicted in the exaggerated views (a, b) shown here.

Grahic Jump Location
Fig. 5

Steady streaming flow

Grahic Jump Location
Fig. 9

Traces as in Fig. 8, but for a radial cut through the cord cranial to the syrinx, and with k increased to 10−13 m2

Grahic Jump Location
Fig. 7

The solids outline and the fluid pressure at four equispaced times during an excitation cycle, with the syrinx displaced 30 mm caudally. Color key shows pressure in Pa. Radial scale 10× axial scale, displacements exaggerated 20×.

Grahic Jump Location
Fig. 8

Instantaneous profiles of (a) radial displacement, (b) seepage velocity, (c) pore pressure, and (d) the divergence of seepage velocity, for eight equispaced times through the cycle, versus radial position within a cut through the cord and pia overlying the syrinx as indicated in the sketch on the left. In each panel, the syrinx is to the left, and the SSS to the right.

Grahic Jump Location
Fig. 6

(a) and (c) Instantaneous changes in syrinx volume at k = 10−13 m2, with (b) and (d) the corresponding running averages over a cycle. Panels (a) and (b) compare (red) the result when the whole cord and pia are fully poroelastic (α = 1) to (green) that when the cord and pia are poroelastic only over the syrinx, and (blue) Darcy flow only occurs over the syrinx. Panels (c) and (d) compare (red) the same whole-cord-poroelastic result with that when the syrinx is displaced axially (“shift”) by (beige) +30 mm or (black) −30 mm relative to the stenosis. Monoexponentials are fitted to the curves in (d) and extrapolated to find the asymptotic values (dashed lines).



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In