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

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
N. S. J. Elliott
Keyword(s):  
Spinal Cord ◽  
Wave Propagation ◽  
Spinal Canal ◽  
Pressure Wave ◽  
Elastic Tube ◽  
Analytical Models ◽  
Perivascular Spaces ◽  
Interstitial Flow ◽  
Fluid Exchange ◽  
Wave Induced

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.

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

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
N. S. J. Elliott ◽  
D. A. Lockerby ◽  
A. R. Brodbelt
Keyword(s):  
Spinal Cord ◽  
Wave Propagation ◽  
Subarachnoid Space ◽  
Pressure Wave ◽  
Fluid Accumulation ◽  
Elastic Tubes ◽  
Spinal Subarachnoid Space ◽  
Poor Treatment ◽  
Relative Rarity ◽  
Set Up

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.

Towards Non-Invasive Assessment of the Elastic Properties of the Spinal Aqueduct

2009 ◽  
Author(s):  
Bryn A. Martin ◽  
Thomas J. Royston ◽  
John N. Oshinski ◽  
Francis Loth
Keyword(s):  
Mechanical Properties ◽  
Wave Propagation ◽  
Elastic Properties ◽  
Pressure Wave ◽  
Wave Speed ◽  
Experimental Studies ◽  
Propagation Speed ◽  
Analytical Models

Analytical models are developed for cerebrospinal fluid (CSF) pressure wave propagation speed based on viscoelastic properties and geometry of the subarachnoid space (SAS). The models were compared to experimental tests on various compliant coaxial tube phantom models of the spinal SAS having different thicknesses and mechanical properties, with the ultimate goal of developing a noninvasive in vivo technique for determining the elastic properties of the spinal aqueduct. The in vitro models were constructed based on a healthy persons’ spinal geometry and properties, and the generation of pressure waves in it mimics the in vivo mechanism. Results suggest that pressure wave propagation is a weighted combination of two types of wave motion inherent to the coupled fluid-structure system. Additionally, theoretical and experimental studies indicate that the spinal cord (SC) mechanical properties do not play a significant role in wave speed propagation through the system, whereas mechanical properties of the encasing structures of the spinal aqueduct (SA) do influence wave speed.

A Study for Theoretical Modeling of Cavitation Inducement From the Solid-Fluid Interface With Fluid-Structure Interaction

2018 ◽  
Author(s):  
Tomohisa Kojima ◽  
Kazuaki Inaba ◽  
Yuto Takada
Keyword(s):  
Wave Propagation ◽  
Fracture Mechanics ◽  
Pressure Wave ◽  
Fluid Structure Interaction ◽  
Initial Crack ◽  
Elastic Tube ◽  
Fluid Interface ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Cavitation Intensity

A theoretical model was explored for predicting cavitation generation from a solid-fluid interface with fluid-structure interaction. Predicting cavitation generation is crucial to evaluate the lifetime of fluid machines. Cavitation has been generated from a solid-fluid interface with tensile stress (pressure) wave propagation across the interface. It was revealed that cavitation generation was suppressed when the surface wettability of the solid in a solid-fluid interface was improved (hydrophilized). It means that a condition exists in which cavitation is not generated despite the existence of bubble nuclei in water. This phenomenon cannot be explained by the conventional theory of fluid mechanics. In this study, an analogy between the theory of crack propagation in fracture mechanics and cavitation generation and propagation from a solid-fluid interface with fluid-structure interactions is developed and applied. An impact experiment was conducted with a free-falling projectile that hit a cylindrical solid buffer placed on top of a water surface within an elastic tube standing on the ground. The projectile impact created a stress wave propagating through the buffer and across the interface of the buffer and water. During the experiments, cavitation bubbles were generated from the interface of the buffer and water due to tensile wave propagation across the interface. Cavitation intensity was controlled by adding a surfactant to water. A bubble was set on the solid-fluid interface beforehand, then its growth with stress (or pressure) wave propagation was observed. The formularization of cavitation occurrence was tested by using initial crack length and stress in fracture mechanics as an analogy for the diameter of pre-set bubble and pressure wave amplitude.

A Coaxial Tube Model of the Cerebrospinal Fluid Pulse Propagation in the Spinal Column

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Srdjan Cirovic
Keyword(s):  
Spinal Cord ◽  
Cerebrospinal Fluid ◽  
Wave Propagation ◽  
Small Amplitude ◽  
Pulse Propagation ◽  
Finite Thickness ◽  
Spinal Column ◽  
Analytical Models ◽  
Amplitude Analysis ◽  
Wave Limit

The dynamics of the movement of the cerebrospinal fluid (CSF) may play an important role in the genesis of pathological neurological conditions such as syringomyelia, which is characterized by the presence of a cyst (syrinx) in the spinal cord. In order to provide sound theoretical grounds for the hypotheses that attribute the formation and growth of the syrinx to impediments to the normal movement of the CSF, it is necessary to understand various modes through which CSF pulse in the spinal column propagates. Analytical models of small-amplitude wave propagation in fluid-filled coaxial tubes, where the outer tube represents dura, the inner tube represents the spinal cord, and the fluid is the CSF, have been used to that end. However, so far, the tendency was to model one of the two tubes as rigid and to neglect the effect of finite thickness of the tube walls. The aim of this study is to extend the analysis in order to address these two potentially important issues. To that end, classical linear small-amplitude analysis of wave propagation was applied to a system consisting of coaxial tubes of finite thickness filled with inviscid incompressible fluid. General solutions to the governing equations for the case of harmonic waves in the long wave limit were replaced with the boundary conditions to yield the characteristic (dispersion) equation for the system. The four roots of the characteristic equation correspond to four modes of wave propagation, of which the first three are associated with significant motion of the CSF. For the normal range of parameters the speeds of the four modes are c1=13m∕s, c2=14.7m∕s, c3=30.3m∕s, and c4=124.5m∕s, which are well within the range of values previously reported in experimental and theoretical studies. The modes with the highest and the lowest speeds of propagation can be attributed to the dura and the spinal cord, respectively, whereas the remaining two modes involve some degree of coupling between the two. When the thickness of the spinal cord, is reduced below its normal value, the first mode becomes dominant in terms of the movement of the CSF, and its speed drops significantly. This suggests that the syrinx may be characterized by an abnormally low speed of the CSF pulse.

scholarly journals Pressure wave propagation in a granular bed

2005 ◽  
Vol 72 (3) ◽  
Author(s):  
Stephen R. Hostler ◽  
Christopher E. Brennen
Keyword(s):  
Wave Propagation ◽  
Pressure Wave ◽  
Granular Bed
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