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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.

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Figures

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. 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. 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. 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. 5

Steady streaming flow

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).

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. 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

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