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Technical Briefs

# The Pathogenesis of Syringomyelia: A Re-Evaluation of the Elastic-Jump Hypothesis

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

Fluid Dynamics Research Centre, University of Warwick, Coventry CV4 7AL, UKn.s.j.elliott@warwick.ac.uk

D. A. Lockerby

Fluid Dynamics Research Centre, University of Warwick, Coventry CV4 7AL, UKduncan.lockerby@warwick.ac.uk

A. R. Brodbelt

Walton Centre for Neuroradiology and Neurosurgery NHS Trust, Liverpool L9 7LJ, UKandrew.brodbelt@thewaltoncentre.nhs.uk

Carpenter et al.  used lowercase notation for the general governing equations but swapped to a mixture of lowercase and uppercase notation when modeling the elastic jump to distinguish the various regions of the pressure wave (1-2); lowercase is used throughout the present analysis for pressure variables $(pA,pB,Δp)$ and their uppercase counterparts denote constant values associated with the initial impulse $(PA,PB,ΔP)$. Negative $ΔP$ will be dealt with in Sec. 2.

For sources that did not list measurements by value the measurements were computed by digitizing an electronic copy of the relevant figure (be it a graph or histological section). The SC segment axis was taken from Fig. 1d in Ref. 13, in which the mean segment length was plotted for C3-S5, and supplemented by Ref. 3, Table 1, for segments C1 and C2. In cases where measurements were assigned to vertebral level (6-7,9,11-12,16), the equivalent SC segment position was calculated from Fig. 2-1 in Ref. 17. The Visible Human data were digitized from Fig. 2 in Ref. 18, and registration on the SC segment axis was achieved with the additional assistance of Fig. 1 in Ref. 19.

By comparison the recent numerical model by Bertram et al. (20), with linearly varying cross section, agrees well with the anatomical data in Fig. 2.

The nondimensional number $T$ used by Berkouk et al. (1) (Eq. (10) in Ref. 1) to describe the ratio of viscous-to-inertial forces is thus related to the Womersley number as $T=π/2/Wo$.

1

Corresponding author.

J Biomech Eng 131(4), 044503 (Feb 02, 2009) (6 pages) doi:10.1115/1.3072894 History: Received June 02, 2008; Revised October 22, 2008; Published February 02, 2009

## Abstract

Syringomyelia is a disease in which fluid-filled cavities, called syrinxes, form in the spinal cord causing progressive loss of sensory and motor functions. Invasive monitoring of pressure waves in the spinal subarachnoid space implicates a hydrodynamic origin. Poor treatment outcomes have led to myriad hypotheses for its pathogenesis, which unfortunately are often based on small numbers of patients due to the relative rarity of the disease. However, only recently have models begun to appear based on the principles of mechanics. One such model is the mathematically rigorous work of Carpenter and colleagues (2003, “Pressure Wave Propagation in Fluid-Filled Co-Axial Elastic Tubes Part 1: Basic Theory,” ASME J. Biomech. Eng., 125(6), pp. 852–856; 2003, “Pressure Wave Propagation in Fluid-Filled Co-Axial Elastic Tubes Part 2: Mechanisms for the Pathogenesis of Syringomyelia,” ASME J. Biomech. Eng., 125(6), pp. 857–863). They suggested that a pressure wave due to a cough or sneeze could form a shocklike elastic jump, which when incident at a stenosis, such as a hindbrain tonsil, would generate a transient region of high pressure within the spinal cord and lead to fluid accumulation. The salient physiological parameters of this model were reviewed from the literature and the assumptions and predictions re-evaluated from a mechanical standpoint. It was found that, while the spinal geometry does allow for elastic jumps to occur, their effects are likely to be weak and subsumed by the small amount of viscous damping present in the subarachnoid space. Furthermore, the polarity of the pressure differential set up by cough-type impulses opposes the tenets of the elastic-jump hypothesis. The analysis presented here does not support the elastic-jump hypothesis or any theory reliant on cough-based pressure impulses as a mechanism for the pathogenesis of syringomyelia.

###### FIGURES IN THIS ARTICLE
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Copyright © 2009 by American Society of Mechanical Engineers
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## Figures

Figure 3

(a) Amplification factor, Δr, —— Δp>0, –.– Δp<0; (b) distance required for an elastic jump to form, sτ

Figure 1

A schematic of the coaxial tubes model used in the elastic-jump hypothesis: (a) end view and (b) side view. The contents of the spinal subarachnoid space and spinal cord are represented by the inviscid fluid.

Figure 2

Variation of transverse dimensions of the SC and SSS with SC segment: (a) SC radius, (b) SSS radius, and (c) cross-sectional area ratio. The bold line is the sample-weighted least-squares regression line and the three dotted lines correspond to theoretical values used in the indicated papers.

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