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Research Papers

Syrinx Fluid Transport: Modeling Pressure-Wave-Induced Flux Across the Spinal Pial Membrane

[+] Author and Article Information
N. S. J. Elliott1 n2

Fluid Dynamics Research Group,Department of Mechanical Engineering,  Curtin University, GPO Box U1987, Perth WA 6845, Australian.s.j.elliott@curtin.edu.au

Similar fenestrations were found in dogs by Cloyd and Low [40] but scant details were given beyond a single scanning electron microscopy image (Fig. 16 therein).

1

Author to whom correspondence should be addressed.

2

The author’s official university e-mail address is: n.s.j.elliott@curtin.edu.au. During the period 28 December 2011-12 March 2012 the author is on leave and is checking e-mail for the account at: nsje.out.of.office@gmail.com, which is the e-mail address registered with ASME during this period.

J Biomech Eng 134(3), 031006 (Mar 23, 2012) (9 pages) doi:10.1115/1.4005849 History: Received June 13, 2011; Revised January 12, 2012; Posted February 01, 2012; Published March 22, 2012; Online March 23, 2012

Syrinxes are fluid-filled cavities of the spinal cord that characterize syringomyelia, a disease involving neurological damage. Their formation and expansion is poorly understood, which has hindered successful treatment. Syrinx cavities are hydraulically connected with the spinal subarachnoid space (SSS) enveloping the spinal cord via the cord interstitium and the network of perivascular spaces (PVSs), which surround blood vessels penetrating the pial membrane that is adherent to the cord surface. Since the spinal canal supports pressure wave propagation, it has been hypothesized that wave-induced fluid exchange across the pial membrane may play a role in syrinx filling. To investigate this conjecture a pair of one-dimensional (1-d) analytical models were developed from classical elastic tube theory coupled with Darcy’s law for either perivascular or interstitial flow. The results show that transpial flux serves as a mechanism for damping pressure waves by alleviating hoop stress in the pial membrane. The timescale ratio over which viscous and inertial forces compete was explicitly determined, which predicts that dilated PVS, SSS flow obstructions, and a stiffer and thicker pial membrane—all associated with syringomyelia—will increase transpial flux and retard wave travel. It was also revealed that the propagation of a pressure wave is aided by a less-permeable pial membrane and, in contrast, by a more-permeable spinal cord. This is the first modeling of the spinal canal to include both pressure-wave propagation along the spinal axis and a pathway for fluid to enter and leave the cord, which provides an analytical foundation from which to approach the full poroelastic problem.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagrams of the coaxial tubes representation of the spinal canal. In both models space A is filled with inviscid fluid representing CSF. In model I space B is filled with inviscid fluid representing a syrinx and the flexible tube is permeable, allowing transpial flux (qAB ); in model II space B represents the permeable spinal cord parenchyma, allowing interstitial flux, and the flexible tube is impermeable. (a) The tube constriction moving at speed c corresponds to a pressure wave with Δp = (pB  − pA ) < 0. (b) In model I the perivascular space extends inward from the pial surface with a length lPVS , becoming maximal if the cord center is reached.

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Figure 2

Space-time plots of normalized pressure as the pulse wave travels a distance of one spinal cord length for various values of β, expressed with reference to βI (Table 1; model I).

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Figure 5

(a) Acceleration, and (b) velocity of the syrinx fluid when the pressure impulse has almost traveled a distance of one spinal cord length (t = 0.07 s) for various values of β, expressed with reference to βI (Table 1; model I).

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Figure 4

The normalized pressure at x = 0 plotted over the time taken for the pulse wave to travel a distance of one spinal cord length for various values of β, expressed with reference to βI (Table 1; model I).

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Figure 3

Tracking the normalized pressure of the wave crest with position over the distance of one spinal cord length for various values of β, expressed with reference to βI (Table 1; model I).

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