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Research Papers

Evaluation by Fluid/Structure-Interaction Spinal-Cord Simulation of the Effects of Subarachnoid-Space Stenosis on an Adjacent Syrinx

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

Biofluid Mechanics Laboratory, Faculty of Engineering, University of New South Wales, Sydney 2052, Australia

The specifications of this material were as previously specified for the homogeneous pialess cord (10).

Wherever peak response pressures or stresses are reported in this paper, they should be compared with the peak value of the corresponding excitatory pressure pulse. Collectively they build the conclusion that responses near the syrinx did not reach the magnitude of the excitation.

In fact, the events here, controlled by the time-course of the excitation, are slow enough that the system is behaving largely as though lumped. The pressures illustrated set up the SSS pressure gradient that propels the bulk flow. The apparent delay provides a favorable pressure gradient for craniocaudal fluid acceleration up to the time of peak cranial-end pressure and an adverse one subsequently, with gradual changeover.

Technically, this is equivalent to a high Womersley number. The Womersley number based on the frequency of the slow cyclic excitation was 17.1. Values over 10 correspond to increasingly flat profiles.

The model of Martin et al. (28) lacked a separate stiff pial membrane; consequently, the radial excursions of the thinned cord overlying the syrinx in their model in response to SSS pressure changes will have been exaggerated relative to what would occur in vivo. Nevertheless, the principle still holds that cord elasticity suffices in the absence of dural flexibility to create the necessary dynamically varying stenosis.

In general, venous pulsations arise mainly from retrograde venous wave propagation following the right atrial contraction, there being no valve to prevent backflow at the atrial entrance.

J Biomech Eng 132(6), 061009 (Apr 23, 2010) (15 pages) doi:10.1115/1.4001165 History: Received August 26, 2009; Revised January 27, 2010; Posted February 03, 2010; Published April 23, 2010; Online April 23, 2010

A finite-element numerical model was constructed of the spinal cord, pia mater, filum terminale, cerebrospinal fluid in the spinal subarachnoid space (SSS), and dura mater. The cord was hollowed out by a thoracic syrinx of length 140 mm, and the SSS included a stenosis of length 30 mm opposite this syrinx. The stenosis severity was varied from 0% to 90% by area. Pressure pulse excitation was applied to the model either at the cranial end of the SSS, simulating the effect of cranial arterial pulsation, or externally to the abdominal dura mater, simulating the effect of cough. A very short pulse was used to examine wave propagation; a pulse emulating cardiac systole was used to examine the effects of fluid displacement. Additionally, repetitive sinusoidal excitation was applied cranially. Bulk fluid flow past the stenosis gave rise to prominent longitudinal pressure dissociation (“suck”) in the SSS adjacent to the syrinx. However, this did not proportionally increase the longitudinal motion of fluid in the syrinx. The inertia of the fluid in the SSS, together with the compliance of this space, gave a resonance capable of being excited constructively or destructively by cardiac or coughing impulses. The main effect of mild stenosis was to lower the frequency of this resonance; severe stenosis damped out to-and-fro motions after the end of the applied excitation. Syrinx fluid motion indicated the fluid momentum and thus the pressure developed when the fluid was stopped by the end of the syrinx; however, the tearing stress in the local cord material depended also on the instantaneous local SSS pressure and was therefore not well predicted by syrinx fluid motion. Stenosis was also shown to give rise to a one-way valve effect causing raised SSS pressure caudally and slight average cord displacement cranially. The investigation showed that previous qualitative predictions of the effects of suck neglected factors that reduced the extent of the resulting syrinx fluid motion and of the cord tearing stress, which ultimately determines whether the syrinx lengthens.

FIGURES IN THIS ARTICLE
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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Diagram of the solid model. The axis of 2D axisymmetry is the vertical dot-dashed line on the left. The parentheses show y,z-coordinates in millimeters, where y is radial and z is axial. The model is here shown scaled up 20× radially relative to axial distance. Three different material specifications are used in parts of the model, as indicated online by the colors. The diagram shows the version of the model where the stenosis of the SSS locally constricted the SSS by 50% by radius; in other versions, the constriction was increased to 75% and 87.5%. The accompanying fluid model occupied the white spaces of the SSS and syrinx.

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Figure 2

The two waveforms of periodic excitation applied to the cranial end of the fluid model. Results presented are from the last (bold) cycle in each case, when the effects of the start-up transient had died away.

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Figure 3

Pressure as a function of time and position in the SSS of the nonstenosed model during and after (a) brief and (b) slow transient abdominal excitations. The pressures created in the model with 75% stenosis in response to brief excitation were virtually identical to (a) and are not shown, whereas (c) this degree of stenosis had significant effects on pressures associated with slow excitation. Note the different time scale and color-contour pressure scale in (a).

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Figure 4

Pressure in the part of the SSS adjacent to the syrinx (top panel) is here compared with the pressure in the syrinx itself (middle panel), both as functions of time and position, for the 75% stenosed model subjected to slow cranial transient excitation. Superficially, the pressure in the syrinx appears approximately uniform at almost all instants, but the extent of axial syrinx pressure gradients is shown in the bottom panel (the positive values indicate higher pressure cranially, i.e., a pressure gradient to accelerate fluid caudally).

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Figure 5

Comparison of fluid pressures in the SSS and in the syrinx at (a) 40 ms and (b) 160 ms, during the application of the 400 ms, 1000 Pa cranial transient excitation to the nonstenosed (upper outline in both (a) and (b)) and 75% stenosed (lower outline) models. High pressure is denoted online by colors tending to red, and low pressure by colors tending to blue. Within each panel ((a) or (b)), the same scale is applied to the color contours. As in Fig. 1, radial dimensions of each outline are exaggerated relative to axial dimensions, here by a factor of 14. The cranial end is on the left.

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Figure 6

Comparison of slosh in the syrinx in (a) the nonstenosed and (b) the 75% stenosed models following excitation of the cranial end of the fluid model with a 400 ms, 1000 Pa transient. Slosh is defined as the net difference between the axial velocity of the on-axis fluid (in the center of the syrinx cross section) and of that at the syrinx wall (broken curve), halfway along the syrinx. Positive values are directed caudocranially.

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Figure 7

Radial stress on the cord axis in response to the 400 ms pressure transient applied to the cranial end of the SSS, as a function of both time and position. Positive stress, as indicated online by colors at the red end of the spectrum, is tensile, i.e., a potential tearing stress to dissect cord tissue. (a) Data from the model with syrinx (location indicated by the absence of solid model stress) but no stenosis; (b) data from the equivalent model with 75% stenosis.

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Figure 8

The outline of the solid model during the response to periodic cranial excitation with nonzero mean, at two instants corresponding to the peak (t=1.0 s) and trough (t=1.2 s) of pressure applied to the cranial end of the fluid model. Radial dimensions are here scaled up relative to axial dimensions by a factor of 14. All deflections are exaggerated by a factor of 20.

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Figure 9

Time averages over a cycle, of SSS (broken curve) and syrinx pressure ((a) and (b)), cord axial displacement ((c) and (d)), cord-axis radial stress ((e) and (f)), and subpial radial displacement ((g) and (h)), all as functions of axial position. The left-hand panels ((a), (c), (e), and (g)) show the result of sine-squared (nonzero mean) excitation; the right-hand panels ((b), (d), (f), and (h) the result of sinusoidal excitation.

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Figure 10

The velocity profile of the syrinx fluid motions across the line (in 2D—representative of a plane in 3D) cutting the syrinx into a cranial and a caudal half at its original position, in response to the cyclic cranial forcing with nonzero mean. The syrinx itself executed axial motions, as indicated by the nonzero fluid velocity where it was in contact with the wall at the maximum radial position.

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