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TECHNICAL PAPERS: Fluids/Heat/Transport

The Origins of Syringomyelia: Numerical Models of Fluid/Structure Interactions in the Spinal Cord

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

Graduate School of Biomedical Engineering, University of New South Wales, Sydney, Australia

A. R. Brodbelt, M. A. Stoodley

 Prince of Wales Medical Research Institute, Randwick, New South Wales, Australia

The original interpretation was restored in debating the likelihood of one of the previously proposed mechanisms of transient pressure peaking.

J Biomech Eng 127(7), 1099-1109 (May 20, 2005) (11 pages) doi:10.1115/1.2073607 History: Received October 18, 2004; Revised May 20, 2005

A two-dimensional axi-symmetric numerical model is constructed of the spinal cord, consisting of elastic cord tissue surrounded by aqueous cerebrospinal fluid, in turn surrounded by elastic dura. The geometric and elastic parameters are simplified but of realistic order, compared with existing measurements. A distal reflecting site models scar tissue formed by earlier trauma to the cord, which is commonly associated with syrinx formation. Transients equivalent to both arterial pulsation and percussive coughing are used to excite wave propagation. Propagation is investigated in this model and one with a central canal down the middle of the cord tissue, and in further idealized versions of it, including a model with no cord, one with a rigid cord, one with a rigid dura, and a double-length untapered variant of the rigid-dura model. Analytical predictions for axial and radial wave-speeds in these different situations are compared with, and used to explain, the numerical outcomes. We find that the anatomic circumstances of the spinal cerebrospinal fluid cavity probably do not allow for significant wave steepening phenomena. The results indicate that wave propagation in the real cord is set by the elastic properties of both the cord tissue and the confining dura mater, fat, and bone. The central canal does not influence the wave propagation significantly.

FIGURES IN THIS ARTICLE
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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

The cord model is shown both with fluid and structural elements in their correct relative positions (left) and exploded (right). Note that the horizontal scale is greatly exaggerated relative to the vertical scale (cranial end at the top). The exploded version indicates diagrammatically how the model is solved numerically, as three separate domains linked at fluid-structure interaction boundaries. The fluid was ascribed the properties of water; the stiffness moduli for the two elastic solids are shown.

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Figure 2

The dimensions of the cord model are compared with the corresponding radii calculated for circular cross-sections of area corresponding to the irregular spinal cord outlines measured by MRI for the Visible Human project

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Figure 3

Pressure vs time at the cranial (excited) end of the model (broken line) and at the caudal end where reflection occurs (solid line), in response to a solitary smooth sinusoidal excitation transient of duration 400ms (a) and 200ms (b)

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Figure 4

The pressures generated in the SAS fluid at the cord boundary in response to a solitary triangular excitation transient of duration 50ms. (a) Pressure vs time at the excited end of the model (broken line) and at the end where reflection occurs (solid line). (b) Pressure vs position at t=10,20,…100ms, identified as curves 1, 2, … 10.

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Figure 5

As Fig. 4, but for a triangular transient of duration 5ms. (a) Pressure vs time at the excited end (broken line) and at the reflecting end (solid line). (b) Pressure vs position at t=5,10,…50ms, identified as curves 1, 2, …10.

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Figure 6

Pressure vs time, at the excited (broken line) and reflecting (solid line) ends, for (a) the model with no cord (replaced by extra CSF), and (b) the model with the cord made rigid, both in response to a triangular transient of duration 5ms

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Figure 7

Pressures and displacements generated in the model with the dura made rigid, in response to a 5ms triangular transient. (a) Pressure vs time, at the excited (broken line) and reflecting (solid line) ends. In view of the disparity in magnitude, different scales are used for the cranial and caudal pressures. (b) Pressure along the SAS-cord boundary is displayed as a function of position and time by means of gray level (dark=high, light=low pressure). (c) The radial displacement of the SAS-cord boundary is similarly displayed. To match p(t,x), where the initial excitation results in a high pressure (dark gray), the displacement scale is inverted.

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Figure 8

Pressures and displacements in the double-length untapered model with rigid dura. (a) Pressure along the SAS-cord boundary as a gray-scale image of p(t,x). (b) Radial displacement of the SAS-cord boundary (inverted), as δr(t,x). (c) The radial displacements when the caudal end was fixed.

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Figure 9

(a) The gray-scale image of p(t,x) for the original model as in Fig. 1. (b) The corresponding image when a central fluid canal of radius 1mm was incorporated in the model. Pressure along the SAS-cord boundary is essentially unchanged.

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