Evaluation by fluid/structure-interaction spinal-cord simulation of the effects of subarachnoid-space stenosis on an adjacent syrinx

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.     

Poro-elastic modeling of Syringomyelia – a systematic study of the effects of pia mater,central canal,median fissure,white and gray matter on pressure wave propagation and fluid movement within the cervical spinal cord

Syringomyelia, fluid-filled cavities within the spinal cord, occurs frequently in association with a Chiari I malformation and produces some of its most severe neurological symptoms. The exact mechanism causing syringomyelia remains unknown. Since syringomyelia occurs frequently in association with obstructed cerebrospinal fluid (CSF) flow, it has been hypothesized that syrinx formation is mechanically driven. In this study we model the spinal cord tissue either as a poro-elastic medium or as a solid linear elastic medium, and simulate the propagation of pressure waves through an anatomically plausible 3D geometry, with boundary conditions based on in vivo CSF pressure measurements. Then various anatomic and tissue properties are modified, resulting in a total of 11 variations of the model that are compared. The results show that an open segment of the central canal and a stiff pia (relative to the cord) both increase the radial pressure gradients and enhance interstitial fluid flow in the central canal. The anterior median fissure, anisotropic permeability of the white matter, and Poisson ratio play minor roles.     

A coupled hydrodynamic model of the cardiovascular and cerebrospinal fluid system

Coupling of the cardiovascular and cerebrospinal fluid (CSF) system is considered to be important to understand the pathophysiology of cerebrovascular and craniospinal disease and intrathecal drug delivery. A coupled cardiovascular and CSF system model was designed to examine the relation of spinal cord (SC) blood flow (SCBF) and CSF pulsations along the spinal subarachnoid space (SSS). A one-dimensional (1-D) cardiovascular tree model was constructed including a simplified SC arterial network. Connection between the cardiovascular and CSF system was accomplished by a transfer function based on in vivo measurements of CSF and cerebral blood flow. A 1-D tube model of the SSS was constructed based on in vivo measurements in the literature. Pressure and flow throughout the cardiovascular and CSF system were determined for different values of craniospinal compliance. SCBF results indicated that the cervical, thoracic, and lumbar SC each had a signature waveform shape. The cerebral blood flow to CSF transfer function reproduced an in vivo-like CSF flow waveform. The 1-D tube model of the SSS resulted in a distribution of CSF pressure and flow and a wave speed that were similar to those in vivo. The SCBF to CSF pulse delay was found to vary a great degree along the spine depending on craniospinal compliance and vascular anatomy. The properties and anatomy of the SC arterial network and SSS were found to have an important impact on pressure and flow and perivascular fluid movement to the SC. Overall, the coupled model provides predictions about the flow and pressure environment in the SC and SSS. More detailed measurements are needed to fully validate the model.     

Arterial pulsation-driven cerebrospinal fluid flow in the perivascular space: a computational model

This study was conducted to determine whether local arterial pulsations are sufficient to cause cerebrospinal fluid (CSF) flow along perivascular spaces (PVS) within the spinal cord. A theoretical model of the perivascular space surrounding a "typical" small artery was analysed using computational fluid dynamics. Systolic pulsations were modelled as travelling waves on the arterial wall. The effects of wave geometry and variable pressure conditions on fluid flow were investigated. Arterial pulsations induce fluid movement in the PVS in the direction of arterial wave travel. Perivascular flow continues even in the presence of adverse pressure gradients of a few kilopascals. Flow rates are greater with increasing pulse wave velocities and arterial deformation, as both an absolute amplitude and as a proportion of the PVS. The model suggests that arterial pulsations are sufficient to cause fluid flow in the perivascular space even against modest adverse pressure gradients. Local increases in flow in this perivascular pumping mechanism or reduction in outflow may be important in the etiology of syringomyelia.     

Arterial Pulsation-driven Cerebrospinal Fluid Flow in the Perivascular Space: A Computational Model

This study was conducted to determine whether local arterial pulsations are sufficient to cause cerebrospinal fluid (CSF) flow along perivascular spaces (PVS) within the spinal cord. A theoretical model of the perivascular space surrounding a "typical" small artery was analysed using computational fluid dynamics. Systolic pulsations were modelled as travelling waves on the arterial wall. The effects of wave geometry and variable pressure conditions on fluid flow were investigated. Arterial pulsations induce fluid movement in the PVS in the direction of arterial wave travel. Perivascular flow continues even in the presence of adverse pressure gradients of a few kilopascals. Flow rates are greater with increasing pulse wave velocities and arterial deformation, as both an absolute amplitude and as a proportion of the PVS. The model suggests that arterial pulsations are sufficient to cause fluid flow in the perivascular space even against modest adverse pressure gradients. Local increases in flow in this perivascular pumping mechanism or reduction in outflow may be important in the etiology of syringomyelia.     

The origins of syringomyelia: numerical models of fluid/structure interactions in the spinal 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.     

Hydrodynamic modeling of cerebrospinal fluid motion within the spinal cavity

The fluid that resides within cranial and spinal cavities, cerebrospinal fluid (CSF), moves in a pulsatile fashion to and from the cranial cavity. This motion can be measured hy magnetic resonance imaging (MRI) and may he of clinical importance in the diagnosis of several brain and spinal cord disorders such as hydrocephalus, Chiari malformation, and syringomyelia. In the present work, a geometric and hydrodynamic characterization of an anatomically relevant spinal canal model is presented. We found that inertial effects dominate the flow field under normal physiological flow rates. Along the length of the spinal canal, hydraulic diameter was found to vary significantly from 5 to 15 mm. The instantaneous Reynolds number at peak flow rate ranged from 150 to 450, and the Womersle number ranged from 5 to 17. Pulsatile flow calculations are presented for an idealized geometric representation of the spinal cavity. A linearized Navier-Stokes model of the pulsatile CSF flow was constructed based on MRI flow rate measurements taken on a healthy volunteer. The numerical model was employed to investigate effects of cross-sectional geometry and spinal cord motion on unsteady velocity, shear stress, and pressure gradientfields. The velocity field was shown to be blunt, due to the inertial character of the flow, with velocity peaks located near the boundaries of the spinal canal rather than at the midpoint between boundaries. The pressure gradient waveform was found to be almost exclusively dependent on the flow waveform and cross-sectional area. Characterization of the CSF dynamics in normal and diseased states may be important in understanding the pathophysiology of CSF related disorders. Flow models coupled with MRI flow measurements mnay become a noninvasive tool to explain the abnormal dynamics of CSF in related brain disorders as well as to determine concentration and local distribution of drugs delivered into the CSF space.     

Distribution of intraventricularly injected horseradish peroxidase in cerebrospinal fluid compartments of the rat spinal cord

Summary The circulation of the cerebrospinal fluid along the central canal and its access to the parenchyma of the spinal cord of the rat have been analyzed by injection of horseradish peroxidase (HRP) into the lateral ventricle. Peroxidase was found throughout the central canal 13 min after injection, suggesting a rapid circulation of cerebrospinal fluid along the central canal of the rat spinal cord. It was cleared from the central canal within 2 h, in contrast with the situation in the brain tissue, where it remained in the periventricular areas for 4 h. In the central canal, HRP bound to Reissner's fiber and the luminal surface of the ependymal cells; it penetrated through the intercellular space of the ependymal lining, reached the subependymal neuropil, the basement membrane of local capillaries, and appeared in the lumen of endothelial pinocytotic vesicles. Furthermore, it accumulated in the labyrinths of the basement membrane contacting the basolateral aspect of the ependymal cells. In ependymocytes, HRP was found in single pinocytotic vesicles. The blood vessels supplying the spinal cord were classified into two types. Type-A vessels penetrated the spinal cord laterally and dorsally and displayed the tracer along their external wall as far as the gray matter. Type-B vessels intruded into the spinal cord from the medial ventral sulcus and occupied the anterior commissure of the gray matter, approaching the central canal. They represented the only vessels marked by HRP along their course through the gray matter. HRP spread from the wall of type-B vessels, labeling the labyrinths, the intercellular space of the ependymal lining, and the lumen of the central canal. This suggests a communication between the central canal and the outer cerebrospinal fluid space, at the level of the medial ventral sulcus, via the intercellular spaces, the perivascular basement membrane and its labyrinthine extensions.     

Sustained high-pressure in the spinal subarachnoid space while arterial expansion is low may be linked to syrinx development

Syringomyelia (a spinal cord cyst) usually develops as a result of conditions that cause cerebrospinal fluid (CSF) obstruction. The mechanism of syrinx formation and enlargement remains unclear, though previous studies suggest that the fluid enters via the perivascular spaces (PVS) of the penetrating arteries of the spinal cord, and that alterations in the CSF pulse timing and pressure could contribute to enhanced PVS inflow. This study uses an idealised computational model of the PVS to investigate the factors that influence peri-arterial fluid flow. First, we used three sample patient-specific models to explore whether changes in subarachnoid space (SAS) pressures in individuals with and without syringomyelia could influence PVS inflow. Second we conducted a parametric study to determine how features of the CSF pulse altered perivascular fluid, including alterations to timing and magnitude of the peak SAS pressure, the timing of reversal from high to low pressure (diastolic phase), and the area under the pressure–time curve. The model for the patient with syringomyelia had higher net CSF inflow to the PVS than the two subjects without syringomyelia. In the parametric study, only increasing the area under the high pressure region of the SAS pulse substantially increased PVS inflow, when coupled with a temporal shift in arterial and SAS pulses. This suggests that a period of sustained high SAS pressure while arterial diameter is low may increase net CSF pumping into the PVS.     

Pressure wave propagation in fluid-filled co-axial elastic tubes. Part 1: Basic theory

Our work is motivated by ideas about the pathogenesis of syringomyelia. This is a serious disease characterized by the appearance of longitudinal cavities within the spinal cord. Its causes are unknown, but pressure propagation is probably implicated. We have developed an inviscid theory for the propagation of pressure waves in co-axial, fluid-filled, elastic tubes. This is intended as a simple model of the intraspinal cerebrospinal-fluid system. Our approach is based on the classic theory for the propagation of longitudinal waves in single, fluid-filled, elastic tubes. We show that for small-amplitude waves the governing equations reduce to the classic wave equation. The wave speed is found to be a strong function of the ratio of the tubes' cross-sectional areas. It is found that the leading edge of a transmural pressure pulse tends to generate compressive waves with converging wave fronts. Consequently, the leading edge of the pressure pulse steepens to form a shock-like elastic jump. A weakly nonlinear theory is developed for such an elastic jump.     

Numerical simulation of wave propagation in a realistic model of the human external ear

In this study, a numerical investigation is performed to evaluate the effects of high-pressure sinusoidal and blast wave's propagation around and inside of a human external ear. A series of computed tomography images are used to reconstruct a realistic three-dimensional (3D) model of a human ear canal and the auricle. The airflow field is then computed by solving the governing differential equations in the time domain using a computational fluid dynamics software. An unsteady algorithm is used to obtain the high-pressure wave propagation throughout the ear canal which is validated against the available analytical and numerical data in literature. The effects of frequency, wave shape, and the auricle on pressure distribution are then evaluated and discussed. The results clearly indicate that the frequency plays a key role on pressure distribution within the ear canal. At 4 kHz frequency, the pressure magnitude is much more amplified within the ear canal than the frequencies of 2 and 6 kHz, for the incident wave angle of 90° investigated in this study, attributable to the ‘4-kHz notch’ in patients with noise-induced hearing loss. According to the results, the pressure distribution patterns at the ear canal are very similar for both sinusoidal pressure waveform with the frequency of 2 kHz and blast wave. The ratio of the peak pressure value at the eardrum to that at the canal entrance increases from about 8% to 30% as the peak pressure value of the blast wave increases from 5 to 100 kPa for the incident wave angle of 90° investigated in this study. Furthermore, incorporation of the auricle to the ear canal model is associated with centerline pressure magnitudes of about 50% and 7% more than those of the ear canal model without the auricle throughout the ear canal for sinusoidal and blast waves, respectively, without any significant effect on pressure distribution pattern along the ear canal for the incident wave angle of 90° investigated in this study.     

Syringomyelia hydrodynamics: an in vitro study based on in vivo measurements

A simplified in vitro model of the spinal canal, based on in vivo magnetic resonance imaging, was used to examine the hydrodynamics of the human spinal cord and subarachnoid space with syringomyelia. In vivo magnetic resonance imaging (MRI) measurements of subarachnoid (SAS) geometry and cerebrospinal fluid velocity were acquired in a patient with syringomyelia and used to aid in the in vitro model design and experiment. The in vitro model contained a fluid-filled coaxial elastic tube to represent a syrinx. A computer controlled pulsatile pump was used to subject the in vitro model to a CSF flow waveform representative of that measured in vivo. Fluid velocity was measured at three axial locations within the in vitro model using the same MRI scanner as the patient study. Pressure and syrinx wall motion measurements were conducted external to the MR scanner using the same model and flow input. Transducers measured unsteady pressure both in the SAS and intra-syrinx at four axial locations in the model A laser Doppler vibrometer recorded the syrinx wall motion at 18 axial locations and three polar positions. Results indicated that the peak-to-peak amplitude of the SAS flow waveform in vivo was approximately tenfold that of the syrinx and in phase (SAS approximately 5.2 +/- 0.6 ml/s, syrinx approximately 0.5 +/- 0.3 ml/s). The in vitro flow waveform approximated the in vivo peak-to-peak magnitude (SAS approximately 4.6 +/- 0.2 ml/s, syrinx approximately 0.4 +/- 0.3 ml/s). Peak-to-peak in vitro pressure variation in both the SAS and syrinx was approximately 6 mm Hg. Syrinx pressure waveform lead the SAS pressure waveform by approximately 40 ms. Syrinx pressure was found to be less than the SAS for approximately 200 ms during the 860-ms flow cycle. Unsteady pulse wave velocity in the syrinx was computed to be a maximum of approximately 25 m/s. LDV measurements indicated that spinal cord wall motion was nonaxisymmetric with a maximum displacement of approximately 140 microm, which is below the resolution limit of MRI. Agreement between in vivo and in vitro MR measurements demonstrates that the hydrodynamics in the fluid filled coaxial elastic tube system are similar to those present in a single patient with syringomyelia. The presented in vitro study of spinal cord wall motion, and complex unsteady pressure and flow environment within the syrinx and SAS, provides insight into the complex biomechanical forces present in syringomyelia.     

Method of prolonged perfusion of the spinal cord central canal in the adult cat in vivo in neurophysiological studies

A method for in-vivo long-lasting perfusion of the central canal of the cat lumbosacral spinal cord with artificial cerebrospinal fluid is described. The method provides for a stable continuous flow of perfusion fluid for many hours. The perfusion adjustment does not entail any injuries to the inferior lumbar and sacral segments of the spinal cord or their roots.     

新生鼠中枢神经系统内Nestin蛋白免疫阳性的组织分布

为了观察Nestin在新生SD大鼠中枢神经系统中的分布,探讨神经干细胞在新生鼠的分布.采用免疫荧光法,显示含神经干细胞特征性的标志物Nestin的阳性结构在新生SD大鼠中枢神经系统中的分布.结果表明在新生SD大鼠中枢神经系统中,Nestin在前脑、脑干和小脑的各个部位均有表达,阳性结构多为纤细的纤维状突起,分布密集,标记强度多为中等强度,分布相对比较均匀.在脊髓实质的Nestin免疫阳性产物明显减少,分布稀疏,染色也较浅,中央管Nestin免疫染色阳性的室管膜细胞很少,但在脊髓中央管的背侧(延髓见于腹侧和背侧)可见到“喷泉”状免疫强阳性纤维束垂直伸展,直达软膜.由此可得出结论:新生SD大鼠中枢神经系统的广泛脑区均存在大量的神经干细胞,而脊髓的神经干细胞数目较少,提示神经干细胞在生后从神经系统的尾端开始逐渐减少.     

The effects of variation in the arterial pulse waveform on perivascular flow

Cerebrospinal fluid (CSF) enters nervous tissues through perivascular spaces. Flow through these pathways is important for solute transport and to prevent fluid accumulation. Syringomyelia is commonly associated with subarachnoid space obstructions such as Chiari I malformation. However, the mechanism of development of these fluid-filled cavities is unclear. Studies have suggested that changes in the arterial and CSF pressures could alter normal perivascular flow. This study uses an idealised model of the perivascular space to investigate how variation in the arterial pulse influences fluid flow. The model used simulated subarachnoid pressures from healthy controls (N = 9), Chiari patients with (N = 7) and without (N = 8) syringomyelia. A parametric analysis was conducted to determine how features of the arterial pulse altered flow. The features of interest included: the timing and magnitude of the peak displacement, and the area under the curve in the phases of uptake and decline. A secondary aim was to determine if the previously observed differences between subject groups were sensitive to variation in the arterial pulse wave. The study demonstrated that the Chiari patients without a syrinx maintained a significantly higher level of perivascular inflow over a physiologically likely range of pulse wave shapes. The analysis also suggested that age-related changes in the arterial pulse (i.e. increased late systolic pulse amplitude and faster diastolic decay), could increase resistance to perivascular inflow affecting solute transport.     

Comparison of 4D Phase-Contrast MRI Flow Measurements to Computational Fluid Dynamics Simulations of Cerebrospinal Fluid Motion in the Cervical Spine

Cerebrospinal fluid (CSF) dynamics in the cervical spinal subarachnoid space (SSS) have been thought to be important to help diagnose and assess craniospinal disorders such as Chiari I malformation (CM). In this study we obtained time-resolved three directional velocity encoded phase-contrast MRI (4D PC MRI) in three healthy volunteers and four CM patients and compared the 4D PC MRI measurements to subject-specific 3D computational fluid dynamics (CFD) simulations. The CFD simulations considered the geometry to be rigid-walled and did not include small anatomical structures such as nerve roots, denticulate ligaments and arachnoid trabeculae. Results were compared at nine axial planes along the cervical SSS in terms of peak CSF velocities in both the cranial and caudal direction and visual interpretation of thru-plane velocity profiles. 4D PC MRI peak CSF velocities were consistently greater than the CFD peak velocities and these differences were more pronounced in CM patients than in healthy subjects. In the upper cervical SSS of CM patients the 4D PC MRI quantified stronger fluid jets than the CFD. Visual interpretation of the 4D PC MRI thru-plane velocity profiles showed greater pulsatile movement of CSF in the anterior SSS in comparison to the posterior and reduction in local CSF velocities near nerve roots. CFD velocity profiles were relatively uniform around the spinal cord for all subjects. This study represents the first comparison of 4D PC MRI measurements to CFD of CSF flow in the cervical SSS. The results highlight the utility of 4D PC MRI for evaluation of complex CSF dynamics and the need for improvement of CFD methodology. Future studies are needed to investigate whether integration of fine anatomical structures and gross motion of the brain and/or spinal cord into the computational model will lead to a better agreement between the two techniques.     

Effects of fluid structure interaction in a three dimensional model of the spinal subarachnoid space

It is unknown whether spinal cord motion has a significant effect on cerebrospinal fluid (CSF) pressure and therefore the importance of including fluid structure interaction (FSI) in computational fluid dynamics models (CFD) of the spinal subarachnoid space (SAS) is unclear. This study aims to determine the effects of FSI on CSF pressure and spinal cord motion in a normal and in a stenosis model of the SAS. A three-dimensional patient specific model of the SAS and spinal cord were constructed from MR anatomical images and CSF flow rate measurements obtained from a healthy human being. The area of SAS at spinal level T4 was constricted by 20% to represent the stenosis model. FSI simulations in both models were performed by running ANSYS CFX and ANSYS Mechanical in tandem. Results from this study show that the effect of FSI on CSF pressure is only about 1% in both the normal and stenosis models and therefore show that FSI has a negligible effect on CSF pressure.     

The Impact of Spinal Cord Nerve Roots and Denticulate Ligaments on Cerebrospinal Fluid Dynamics in the Cervical Spine

Cerebrospinal fluid (CSF) dynamics in the spinal subarachnoid space (SSS) have been thought to play an important pathophysiological role in syringomyelia, Chiari I malformation (CM), and a role in intrathecal drug delivery. Yet, the impact that fine anatomical structures, including nerve roots and denticulate ligaments (NRDL), have on SSS CSF dynamics is not clear. In the present study we assessed the impact of NRDL on CSF dynamics in the cervical SSS. The 3D geometry of the cervical SSS was reconstructed based on manual segmentation of MRI images of a healthy volunteer and a patient with CM. Idealized NRDL were designed and added to each of the geometries based on in vivo measurments in the literature and confirmation by a neuroanatomist. CFD simulations were performed for the healthy and patient case with and without NRDL included. Our results showed that the NRDL had an important impact on CSF dynamics in terms of velocity field and flow patterns. However, pressure distribution was not altered greatly although the NRDL cases required a larger pressure gradient to maintain the same flow. Also, the NRDL did not alter CSF dynamics to a great degree in the SSS from the foramen magnum to the C1 level for the healthy subject and CM patient with mild tonsillar herniation (∼6 mm). Overall, the NRDL increased fluid mixing phenomena and resulted in a more complex flow field. Comparison of the streamlines of CSF flow revealed that the presence of NRDL lead to the formation of vortical structures and remarkably increased the local mixing of the CSF throughout the SSS.     

Perivascular tethering modulates the geometry and biomechanics of cerebral arterioles

Recent studies have renewed interest in the effects of perivascular tethering on vascular mechanics, particularly growth and remodeling. We quantified effects of axial and circumferential tethering on rabbit pial arterioles from the ventral occipital lobe of the brain. The homeostatic axial pre-stretch, which is influenced by perivascular tethering, was measured in situ to be 1.24±0.04. Using a cannulated microvessel preparation, wall mechanics were then quantified in vitro for isolated arterioles at low (1.10) or normal (1.24) values of axial stretch and for tethered arterioles having perivascular support. Axial stretch did not significantly affect changes in circumferential stretch or stress upon pressurization, but circumferential tethering caused arteriolar geometry to change from a circular cross-section at normal pressure to an elliptical one at pressures above and below normal. Calculations suggested that the observed levels of ellipticity could cause a modest decrease in volumetric blood flow, but also a pronounced variation in shear stress around the circumference of the arteriole. An elliptical cross-section could thus increase vascular resistance or promote luminal remodeling at pressures different from normal. This characterization of effects of perivascular tethering on pial arterioles should prove useful in future studies of roles of perturbed cerebral blood flow on the propensity of the cerebral microcirculation to remodel.     

A one-dimensional model of the spinal cerebrospinal-fluid compartment

Modeling of the cerebrospinal fluid (CSF) system in the spine is strongly motivated by the need to understand the origins of pathological conditions such as the emergence and growth of fluid-filled cysts in the spinal cord. In this study, a one-dimensional (1D) approximation for the flow in elastic conduits was used to formulate a model of the spinal CSF compartment. The modeling was based around a coaxial geometry in which the inner elastic cylinder represented the spinal cord, middle elastic tube represented the dura, and the outermost tube represented the vertebral column. The fluid-filled annuli between the cord and dura, and the dura and vertebral column, represented the subarachnoid and epidural spaces, respectively. The system of governing equations was constructed by applying a 1D form of mass and momentum conservation to all segments of the model. The developed 1D model was used to simulate CSF pulse excited by pressure disturbances in the subarachnoid and epidural spaces. The results were compared to those obtained from an equivalent two-dimensional finite element (FE) model which was implemented using a commercial software package. The analysis of linearized governing equations revealed the existence of three types of waves, of which the two slower waves can be clearly related to the wave modes identified in previous similar studies. The third, much faster, wave emanates directly from the vertebral column and has little effect on the deformation of the spinal cord. The results obtained from the 1D model and its FE counterpart were found to be in good general agreement even when sharp spatial gradients of the spinal cord stiffness were included; both models predicted large radial displacements of the cord at the location of an initial cyst. This study suggests that 1D modeling, which is computationally inexpensive and amenable to coupling with the models of the cranial CSF system, should be a useful approach for the analysis of some aspects of the CSF dynamics in the spine. The simulation of the CSF pulse excited by a pressure disturbance in the epidural space, points to the possibility that regions of the spinal cord with abnormally low stiffness may be prone to experiencing large strains due to coughing and sneezing.