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.

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

2005 ◽  
Vol 127 (7) ◽  
pp. 1099-1109 ◽  
Author(s):  
C. D. Bertram ◽  
A. R. Brodbelt ◽  
M. A. Stoodley
Keyword(s):  
Spinal Cord ◽  
Cerebrospinal Fluid ◽  
Wave Propagation ◽  
Numerical Models ◽  
Scar Tissue ◽  
Central Canal ◽  
Radial Wave ◽  
Wave Speeds ◽  
Arterial Pulsation ◽  
Elastic Cord

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.

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.

Spinal Level

2017 ◽  
pp. 523-558
Author(s):  
Eduardo E. Benarroch ◽  
Jeremy K. Cutsforth-Gregory ◽  
Kelly D. Flemming
Keyword(s):  
Spinal Cord ◽  
Cerebrospinal Fluid ◽  
Spinal Canal ◽  
Vertebral Column ◽  
Spinal Column ◽  
Foramen Magnum ◽  
Vascular Supply ◽  
Spinal Level ◽  
Spinal Nerves ◽  
Fluid Systems

The spinal level includes the vertebral column and its contents. The spinal canal within the vertebral column is the passage formed by the vertebrae. It extends from the foramen magnum of the skull through the sacrum of the spinal column and contains the spinal cord, nerve roots, spinal nerves, meninges, and vascular supply of the spinal cord. Five of the major systems are represented in the spinal canal: the sensory, motor, autonomic, vascular, and cerebrospinal fluid systems. The vascular and cerebrospinal fluid structures are the support systems of the spinal cord. Diseases of the spinal canal involve 1 or more of these systems and produce patterns of disease distinctive to this level. The anatomical and physiologic characteristics of the spinal cord and spinal nerves that permit the identification and localization of diseases in the spinal canal are presented in this chapter.

A Fluid Structure Interaction Simulation of the Cerebrospinal Fluid, Spinal Cord, and Spinal Stenosis Present in Syringomyelia

2010 ◽  
Author(s):  
Yifei Liu ◽  
Bryn A. Martin ◽  
Thomas J. Royston ◽  
Francis Loth
Keyword(s):  
Spinal Cord ◽  
Cerebrospinal Fluid ◽  
Wave Propagation ◽  
In Silico ◽  
Fluid Structure Interaction ◽  
Csf Flow ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Csf Pressure

Syringomyelia (SM) is a neurological disease in which a fluid-filled cystic cavity, or syrinx, forms in the spinal cord (SC) resulting in progressive loss of sensory, motor functions, and/or pain in the patient. It has been hypothesized that abnormal cerebrospinal fluid (CSF) pressure distribution and absorption in the subarachnoid space (SAS), resulting from a CSF flow blockage (stenosis), could be a key etiological factor for syrinx pathogenesis. In particular, the magnitude of the abrupt SAS pressure waves produced during coughing has been correlated with headache and pain in the patient. To better understand the influence of coughing on the spinal SAS, four axisymmetric fluid-structure interaction (FSI) in silico models representative of various conditions associated with SM were constructed. Each of the models was subjected to a cough-like CSF pressure pulse. The CSF flow stenosis was shown to attenuate and decelerate the CSF wave propagation in the SAS. The spinal SAS distensibility was also shown to have significant influence on the wave propagation. The in silico pressure results were found to be in agreement with a set of similar in vitro experiments [1].

Effect of altering cerebrospinal fluid pressure on spinal cord blood flow

1994 ◽  
Vol 58 (1) ◽  
pp. 112-115 ◽  
Author(s):  
Shigeru Kazama ◽  
Yoshihiko Masaki ◽  
Shigeyoshi Maruyama ◽  
Akira Ishihara
Keyword(s):  
Spinal Cord ◽  
Blood Flow ◽  
Cerebrospinal Fluid ◽  
Cord Blood ◽  
Fluid Pressure ◽  
Cerebrospinal Fluid Pressure ◽  
Spinal Cord Blood Flow

Thermoelastic Small-Amplitude Wave Propagation in Nonlinear Elastic Multilayers

2004 ◽  
Vol 9 (5) ◽  
pp. 555-568 ◽  
Author(s):  
Massimiliano Gei ◽  
Davide Bigoni ◽  
Giulia Franceschni
Keyword(s):  
Wave Propagation ◽  
Small Amplitude ◽  
Amplitude Wave ◽  
Nonlinear Elastic
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