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

A computational fluid dynamics study to assess the impact of coughing on cerebrospinal fluid dynamics in Chiari type 1 malformation

Chiari type 1 malformation is a neurological disorder characterized by an obstruction of the cerebrospinal fluid (CSF) circulation between the brain (intracranial) and spinal cord (spinal) compartments. Actions such as coughing might evoke spinal cord complications in patients with Chiari type 1 malformation, but the underlying mechanisms are not well understood. More insight into the impact of the obstruction on local and overall CSF dynamics can help reveal these mechanisms. Therefore, our previously developed computational fluid dynamics framework was used to establish a subject-specific model of the intracranial and upper spinal CSF space of a healthy control. In this model, we emulated a single cough and introduced porous zones to model a posterior (OBS-1), mild (OBS-2), and severe posterior-anterior (OBS-3) obstruction. OBS-1 and OBS-2 induced minor changes to the overall CSF pressures, while OBS-3 caused significantly larger changes with a decoupling between the intracranial and spinal compartment. Coughing led to a peak in overall CSF pressure. During this peak, pressure differences between the lateral ventricles and the spinal compartment were locally amplified for all degrees of obstruction. These results emphasize the effects of coughing and indicate that severe levels of obstruction lead to distinct changes in intracranial pressure.

An analytic model for the flow induced in syringomyelia cavities

A simple two-dimensional fluid-structure-interaction problem, involving viscous oscillatory flow in a channel separated by an elastic membrane from a fluid-filled slender cavity, is analyzed to shed light on the flow dynamics pertaining to syringomyelia, a neurological disorder characterized by the appearance of a large tubular cavity (syrinx) within the spinal cord. The focus is on configurations in which the velocity induced in the cavity, representing the syrinx, is comparable to that found in the channel, representing the subarachnoid space surrounding the spinal cord, both flows being coupled through a linear elastic equation describing the membrane deformation. An asymptotic analysis for small stroke lengths leads to closed-form expressions for the leading-order oscillatory flow, and also for the stationary flow associated with the first-order corrections, the latter involving a steady distribution of transmembrane pressure. The magnitude of the induced flow is found to depend strongly on the frequency, with the result that for channel flow rates of non-sinusoidal waveform, as those found in the spinal canal, higher harmonics can dominate the sloshing motion in the cavity, in agreement with previous in vivo observations. Under some conditions, the cycle-averaged transmembrane pressure, also showing a marked dependence on the frequency, changes sign on increasing the cavity transverse dimension (i.e. orthogonal to the cord axis), underscoring the importance of cavity size in connection with the underlying hydrodynamics. The analytic results presented here can be instrumental in guiding future numerical investigations, needed to clarify the pathogenesis of syringomyelia cavities.

The mechanical behavior of bovine spinal cord white matter under various strain rate conditions: tensile testing and visco-hyperelastic constitutive modeling

The mechanical behavior of the white matter is important for estimating the damage of the spinal cord during accidents. In this study, we conducted uniaxial tension testing in vitro of bovine spinal cord white matter under extremely high strain rate conditions (up to 100 s^-1). A visco-hyperelastic constitutive law for modeling the strain rate-dependent behavior of the bovine spinal cord white matter was developed. A set of material constants was obtained using a Levenberg-Marquardt fitting algorithm to match the uniaxial tension experimental data with various strain rates. Our experimental data confirmed that the modulus and tensile strength increased when the strain rate is higher. For the extremely high strain rate condition (100 s^-1), we found that both the modulus and failure stress significantly increased compared with the low strain rate case. These new data in terms of mechanical response at high strain rate provide insight into the spine injury mechanism caused by high-speed impact. Moreover, the developed constitutive model will allow researchers to perform more realistic finite element modeling and simulation of spinal cord injury damage under various complicated conditions.

Characterising spinal cerebrospinal fluid flow in the pig with phase-contrast magnetic resonance imaging

BACKGROUND

Detecting changes in pulsatile cerebrospinal fluid (CSF) flow may assist clinical management decisions, but spinal CSF flow is relatively understudied. Traumatic spinal cord injuries (SCI) often cause spinal cord swelling and subarachnoid space (SAS) obstruction, potentially causing pulsatile CSF flow changes. Pigs are emerging as a favoured large animal SCI model; therefore, the aim of this study was to characterise CSF flow along the healthy pig spine.

METHODS

Phase-contrast magnetic resonance images (PC-MRI), retrospectively cardiac gated, were acquired for fourteen laterally recumbent, anaesthetised and ventilated, female domestic pigs (22-29 kg). Axial images were obtained at C2/C3, T8/T9, T11/T12 and L1/L2. Dorsal and ventral SAS regions of interest (ROI) were manually segmented. CSF flow and velocity were determined throughout a cardiac cycle. Linear mixed-effects models, with post-hoc comparisons, were used to identify differences in peak systolic/diastolic flow, and maximum velocity (cranial/caudal), across spinal levels and dorsal/ventral SAS. Velocity wave speed from C2/C3 to L1/L2 was calculated.

RESULTS

PC-MRI data were obtained for 11/14 animals. Pulsatile CSF flow was observed at all spinal levels. Peak systolic flow was greater at C2/C3 (dorsal: - 0.32 ± 0.14 mL/s, ventral: - 0.15 ± 0.13 mL/s) than T8/T9 dorsally (- 0.04 ± 0.03 mL/s; p < 0.001), but not different ventrally (- 0.08 ± 0.08 mL/s; p = 0.275), and no difference between thoracolumbar levels (p > 0.05). Peak diastolic flow was greater at C2/C3 (0.29 ± 0.08 mL/s) compared to T8/T9 (0.03 ± 0.03 mL/s, p < 0.001) dorsally, but not different ventrally (p = 1.000). Cranial and caudal maximum velocity at C2/C3 were greater than thoracolumbar levels dorsally (p < 0.001), and T8/T9 and L1/L2 ventrally (p = 0.022). Diastolic velocity wave speed was 1.41 ± 0.39 m/s dorsally and 1.22 ± 0.21 m/s ventrally, and systolic velocity wave speed was 1.02 ± 0.25 m/s dorsally and 0.91 ± 0.22 m/s ventrally.

CONCLUSIONS

In anaesthetised and ventilated domestic pigs, spinal CSF has lower pulsatile flow and slower velocity wave propagation, compared to humans. This study provides baseline CSF flow at spinal levels relevant for future SCI research in this animal model.

Fluid transport in the brain

The brain harbors a unique ability to, figuratively speaking, shift its gears. During wakefulness, the brain is geared fully toward processing information and behaving, while homeostatic functions predominate during sleep. The blood-brain barrier establishes a stable environment that is optimal for neuronal function, yet the barrier imposes a physiological problem; transcapillary filtration that forms extracellular fluid in other organs is reduced to a minimum in brain. Consequently, the brain depends on a special fluid [the cerebrospinal fluid (CSF)] that is flushed into brain along the unique perivascular spaces created by astrocytic vascular endfeet. We describe this pathway, coined the term glymphatic system, based on its dependency on astrocytic vascular endfeet and their adluminal expression of aquaporin-4 water channels facing toward CSF-filled perivascular spaces. Glymphatic clearance of potentially harmful metabolic or protein waste products, such as amyloid-β, is primarily active during sleep, when its physiological drivers, the cardiac cycle, respiration, and slow vasomotion, together efficiently propel CSF inflow along periarterial spaces. The brain's extracellular space contains an abundance of proteoglycans and hyaluronan, which provide a low-resistance hydraulic conduit that rapidly can expand and shrink during the sleep-wake cycle. We describe this unique fluid system of the brain, which meets the brain's requisites to maintain homeostasis similar to peripheral organs, considering the blood-brain-barrier and the paths for formation and egress of the CSF.

Slosh Simulation in a Computer Model of Canine Syringomyelia

The exact pathogenesis of syringomyelia is unknown. Epidural venous distention during raised intrathoracic pressure (Valsalva) may cause impulsive movement of fluid ("slosh") within the syrinx. Such a slosh mechanism is a proposed cause of syrinx dissection into spinal cord parenchyma resulting in craniocaudal propagation of the cavity. We sought to test the "slosh" hypothesis by epidural excitation of CSF pulse in a computer model of canine syringomyelia. Our previously developed canine syringomyelia computer model was modified to include an epidural pressure pulse. Simulations were run for: cord free of cavities; cord with small syringes at different locations; and cord with a syrinx that was progressively expanding caudally. If small syringes are present, there are peaks of stress at those locations. This effect is most pronounced at the locations at which syringes initially form. When a syrinx is expanding caudally, the peak stress is typically at the caudal end of the syrinx. However, when the syrinx reaches the lumbar region; the stress becomes moderate. The findings support the "slosh" hypothesis, suggesting that small cervical syringes may propagate caudally. However, when the syrinx is large, there is less focal stress, which may explain why a syrinx can rapidly expand but then remain unchanged in shape over years.

Elucidating the Pivotal Neuroimmunomodulation of Stem Cells in Spinal Cord Injury Repair

Spinal cord injury (SCI) is a distressing incident with abrupt onset of the motor as well as sensory dysfunction, and most often, the injury occurs as result of high-energy or velocity accidents as well as contact sports and falls in the elderly. The key challenges associated with nerve repair are the lack of self-repair as well as neurotrophic factors and primary and secondary neuronal apoptosis, as well as factors that prevent the regeneration of axons locally. Neurons that survive the initial traumatic damage may be lost due to pathogenic activities like neuroinflammation and apoptosis. Implanted stem cells are capable of differentiating into neural cells that replace injured cells as well as offer local neurotrophic factors that aid neuroprotection, immunomodulation, axonal sprouting, axonal regeneration, and remyelination. At the microenvironment of SCI, stem cells are capable of producing growth factors like brain-derived neurotrophic factor and nerve growth factor which triggers neuronal survival as well as axonal regrowth. Although stem cells have proven to be of therapeutic value in SCI, the major disadvantage of some of the cell types is the risk for tumorigenicity due to the contamination of undifferentiated cells prior to transplantation. Local administration of stem cells via either direct cellular injection into the spinal cord parenchyma or intrathecal administration into the subarachnoid space is currently the best transplantation modality for stem cells during SCI.

Correlating Tissue Mechanics and Spinal Cord Injury: Patient-Specific Finite Element Models of Unilateral Cervical Contusion Spinal Cord Injury in Non-Human Primates

Non-human primate (NHP) models are the closest approximation of human spinal cord injury (SCI) available for pre-clinical trials. The NHP models, however, include broader morphological variability that can confound experimental outcomes. We developed subject-specific finite element (FE) models to quantify the relationship between impact mechanics and SCI, including the correlations between FE outcomes and tissue damage. Subject-specific models of cervical unilateral contusion SCI were generated from pre-injury MRIs of six NHPs. Stress and strain outcomes were compared with lesion histology using logit analysis. A parallel generic model was constructed to compare the outcomes of subject-specific and generic models. The FE outcomes were correlated more strongly with gray matter damage (0.29 < R² < 0.76) than white matter (0.18 < R² < 0.58). Maximum/minimum principal strain, Von-Mises and Tresca stresses showed the strongest correlations (0.31 < R² < 0.76) with tissue damage in the gray matter while minimum principal strain, Von-Mises stress, and Tresca stress best predicted white matter damage (0.23 < R² < 0.58). Tissue damage thresholds varied for each subject. The generic FE model captured the impact biomechanics in two of the four models; however, the correlations between FE outcomes and tissue damage were weaker than the subject-specific models (gray matter [0.25 < R² < 0.69] and white matter [R² < 0.06] except for one subject [0.26 < R² < 0.48]). The FE mechanical outputs correlated with tissue damage in spinal cord white and gray matters, and the subject-specific models accurately mimicked the biomechanics of NHP cervical contusion impacts.

Nonreflecting Boundary Conditions for a CSF Model of Fourth Ventricle: Spinal SAS Dynamics

In this paper, we introduce a one-dimensional model for analyzing the cerebrospinal fluid dynamics within the fourth ventricle and the spinal subarachnoid space (SSAS). The model has been derived starting from an original model of Linninger et al. and from the detailed mathematical analysis of two different reformulations. We show the steps of the modelization and the rigorous analysis of the first-order nonlinear hyperbolic system of equations which rules the new CSF model, whose conservative-law form and characteristic form are required for the boundary conditions treatment. By assuming sub-critical flows, for the particular dynamics we are dealing with, the most desirable option is to employ the nonreflecting boundary conditions, that allow the simple wave associated with the outgoing characteristic to exit the computational domain with no reflections. Finally, we carry out some numerical simulations related to different cerebral physiological conditions.

Anthropomorphic Model of Intrathecal Cerebrospinal Fluid Dynamics Within the Spinal Subarachnoid Space: Spinal Cord Nerve Roots Increase Steady-Streaming

Cerebrospinal fluid (CSF) dynamics are thought to play a vital role in central nervous system (CNS) physiology. The objective of this study was to investigate the impact of spinal cord (SC) nerve roots (NR) on CSF dynamics. A subject-specific computational fluid dynamics (CFD) model of the complete spinal subarachnoid space (SSS) with and without anatomically realistic NR and nonuniform moving dura wall deformation was constructed. This CFD model allowed detailed investigation of the impact of NR on CSF velocities that is not possible in vivo using magnetic resonance imaging (MRI) or other noninvasive imaging methods. Results showed that NR altered CSF dynamics in terms of velocity field, steady-streaming, and vortical structures. Vortices occurred in the cervical spine around NR during CSF flow reversal. The magnitude of steady-streaming CSF flow increased with NR, in particular within the cervical spine. This increase was located axially upstream and downstream of NR due to the interface of adjacent vortices that formed around NR.

A Computational Model for the Dynamics of Cerebrospinal Fluid in the Spinal Subarachnoid Space

Global models for the dynamics of coupled fluid compartments of the central nervous system (CNS) require simplified representations of the individual components which are both accurate and computationally efficient. This paper presents a one-dimensional model for computing the flow of cerebrospinal fluid (CSF) within the spinal subarachnoid space (SSAS) under the simplifying assumption that it consists of two coaxial tubes representing the spinal cord and the dura. A rigorous analysis of the first-order nonlinear system demonstrates that the system is elliptic-hyperbolic, and hence ill-posed, for some values of parameters, being hyperbolic otherwise. In addition, the system cannot be written in conservation-law form, and thus, an appropriate numerical approach is required, namely the path conservative approach. The designed computational algorithm is shown to be second-order accurate in both space and time, capable of handling strongly nonlinear discontinuities, and a method of coupling it with an unsteady inflow condition is presented. Such an approach is sufficiently rapid to be integrated into a global, closed-loop model for computing the dynamics of coupled fluid compartments of the CNS.

Computer simulation of syringomyelia in dogs

Background

Syringomyelia is a pathological condition in which fluid-filled cavities (syringes) form and expand in the spinal cord. Syringomyelia is often linked with obstruction of the craniocervical junction and a Chiari malformation, which is similar in both humans and animals. Some brachycephalic toy breed dogs such as Cavalier King Charles Spaniels (CKCS) are particularly predisposed. The exact mechanism of the formation of syringomyelia is undetermined and consequently with the lack of clinical explanation, engineers and mathematicians have resorted to computer models to identify possible physical mechanisms that can lead to syringes. We developed a computer model of the spinal cavity of a CKCS suffering from a large syrinx. The model was excited at the cranial end to simulate the movement of the cerebrospinal fluid (CSF) and the spinal cord due to the shift of blood volume in the cranium related to the cardiac cycle. To simulate the normal condition, the movement was prescribed to the CSF. To simulate the pathological condition, the movement of CSF was blocked.

Results

For normal conditions the pressure in the SAS was approximately 400 Pa and the same applied to all stress components in the spinal cord. The stress was uniformly distributed along the length of the spinal cord. When the blockage between the cranial and spinal CSF spaces forced the cord to move with the cardiac cycle, shear and axial normal stresses in the cord increased significantly. The sites where the elevated stress was most pronounced coincided with the axial locations where the syringes typically form, but they were at the perimeter rather than in the central portion of the cord. This elevated stress originated from the bending of the cord at the locations where its curvature was high.

Conclusions

The results suggest that it is possible that repetitive stressing of the spinal cord caused by its exaggerated movement could be a cause for the formation of initial syringes. Further consideration of factors such as cord tethering and the difference in mechanical properties of white and grey matter is needed to fully explore this possibility.

Electronic supplementary material

The online version of this article (10.1186/s12917-018-1410-7) contains supplementary material, which is available to authorized users.

A Poroelastic Fluid/Structure-Interaction Model of Cerebrospinal Fluid Dynamics in the Cord With Syringomyelia and Adjacent Subarachnoid-Space Stenosis

An existing axisymmetric fluid/structure-interaction (FSI) model of the spinal cord, pia mater, subarachnoid space, and dura mater in the presence of syringomyelia and subarachnoid-space stenosis was modified to include porous solids. This allowed investigation of a hypothesis for syrinx fluid ingress from cerebrospinal fluid (CSF). Gross model deformation was unchanged by the addition of porosity, but pressure oscillated more in the syrinx and the subarachnoid space below the stenosis. The poroelastic model still exhibited elevated mean pressure in the subarachnoid space below the stenosis and in the syrinx. With realistic cord permeability, there was slight oscillatory shunt flow bypassing the stenosis via the porous tissue over the syrinx. Weak steady streaming flow occurred in a circuit involving craniocaudal flow through the stenosis and back via the syrinx. Mean syrinx volume was scarcely altered when the adjacent stenosis bisected the syrinx, but increased slightly when the syrinx was predominantly located caudal to the stenosis. The fluid content of the tissues over the syrinx oscillated, absorbing most of the radial flow seeping from the subarachnoid space so that it did not reach the syrinx. To a lesser extent, this cyclic swelling in a boundary layer of cord tissue just below the pia occurred all along the cord, representing a mechanism for exchange of interstitial fluid (ISF) and cerebrospinal fluid which could explain recent tracer findings without invoking perivascular conduits. The model demonstrates that syrinx volume increase is possible when there is subarachnoid-space stenosis and the cord and pia are permeable.

Direct-trauma model of posttraumatic syringomyelia with a computer-controlled motorized spinal cord impactor

OBJECTIVE The pathogenesis of posttraumatic syringomyelia remains enigmatic and is not adequately explained by current theories. Experimental investigations require a reproducible animal model that replicates the human condition. Current animal models are imperfect because of their low reliability, severe neurological deficits, or dissimilar mechanism of injury. The objective of this study was to develop a reproducible rodent model of posttraumatic syringomyelia using a spinal cord impactor that produces an injury that more closely mimics the human condition and does not produce severe neurological deficits. METHODS The study consisted of 2 parts. Seventy animals were studied overall: 20 in Experiment 1 and 48 in Experiment 2 after two rats with severe deficits were killed early. Experiment 1 aimed to determine the optimal force setting for inducing a cystic cavity without neurological deficits using a computer-controlled motorized spinal cord impactor. Twenty animals received an impact that ranged from 50 to 150 kDyn. Using the optimal force for producing an initial cyst determined from Experiment 1, Experiment 2 aimed to compare the progression of cavities in animals with and those without arachnoiditis induced by kaolin. Forty-eight animals were killed at 1, 3, 6, or 12 weeks after syrinx induction. Measurements of cavity size and maximum anteroposterior and lateral diameters were evaluated using light microscopy. RESULTS In Experiment 1, cavities were present in 95% of the animals. The duration of limb weakness and spinal cord cavity size correlated with the delivered force. The optimal force chosen for Experiment 2 was 75 kDyn. In Experiment 2, cavities occurred in 92% of the animals. Animals in the kaolin groups developed larger cavities and more vacuolations and enlarged perivascular spaces than those in the nonkaolin groups. CONCLUSIONS This impact model reliably produces cavities that resemble human posttraumatic syringomyelia and is suitable for further study of posttraumatic syringomyelia pathophysiology.

Inter-operator Reliability of Magnetic Resonance Image-Based Computational Fluid Dynamics Prediction of Cerebrospinal Fluid Motion in the Cervical Spine

For the first time, inter-operator dependence of MRI based computational fluid dynamics (CFD) modeling of cerebrospinal fluid (CSF) in the cervical spinal subarachnoid space (SSS) is evaluated. In vivo MRI flow measurements and anatomy MRI images were obtained at the cervico-medullary junction of a healthy subject and a Chiari I malformation patient. 3D anatomies of the SSS were reconstructed by manual segmentation by four independent operators for both cases. CFD results were compared at nine axial locations along the SSS in terms of hydrodynamic and geometric parameters. Intraclass correlation (ICC) assessed the inter-operator agreement for each parameter over the axial locations and coefficient of variance (CV) compared the percentage of variance for each parameter between the operators. Greater operator dependence was found for the patient (0.19 < ICC < 0.99) near the craniovertebral junction compared to the healthy subject (ICC > 0.78). For the healthy subject, hydraulic diameter and Womersley number had the least variance (CV = ~2%). For the patient, peak diastolic velocity and Reynolds number had the smallest variance (CV = ~3%). These results show a high degree of inter-operator reliability for MRI-based CFD simulations of CSF flow in the cervical spine for healthy subjects and a lower degree of reliability for patients with Type I Chiari malformation.

Volume change theory for syringomyelia: A new perspective

Background:

The etiopathogenesis of syringomyelia is still an enigma. The authors present a novel theory based on fluid dynamics at the craniovertebral (CV) junction to explain the genesis of syringomyelia (SM). The changes in volume of spinal canal, spinal cord, central canal and spinal subarachnoid space (SSS) in relation to the posterior fossa have been analysed, specifically during postural movements of flexion and extension. The effect of fluctuations in volume of spinal canal and its contents associated with cerebrospinal fluid (CSF) flow dynamics at the CV junction have been postulated to cause the origin and propagation of the syringomyelia. The relevant literature on the subject has been reviewed and the author's theory has been discussed.

Conclusion:

Volume of spinal canal in flexion is always greater than that in extension. Flexion of spine causes narrowing of the ventral subarachnoid space (SAS) and widening of dorsal SAS while extension causes reverse changes leading to fluid movement in dorsal spinal SAS in flexion and ventral spinal SAS in extension. Cervical and lumbar spinal region with maximum bulk hence maximum area and volume undergo maximum deformation during postural changes. SSS CSF is the difference between the volume of spinal canal and spinal cord, varies in flexion and extension which is compensated by changes in posterior fossa (CSF) volume in normal circumstances. Blocked SAS at foramen magnum donot permit spinal SAS CSF exchange which during postural changes is compensated by cavitatory/cystic (syrinx) change at locations in cervical and lumbar spine with propensity for maximum deformation. Augmentation of posterior fossa volume by decompression helps by normalization of this CSF exchange dynamics but immobilizing the spinal movement theoretically will cease any dynamic volume changes thereby minimizing the destructive influence of the fluid exchange on the cord. Thus, this theory strengthens the rational of treating patients by either methodology.

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.

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.

Nonlinear viscoelastic characterization of the porcine spinal cord

Although quasi-static and quasi-linear viscoelastic properties of the spinal cord have been reported previously, there are no published studies that have investigated the fully (strain-dependent) nonlinear viscoelastic properties of the spinal cord. In this study, stress relaxation experiments and dynamic cycling were performed on six fresh porcine lumbar cord specimens to examine their viscoelastic mechanical properties. The stress relaxation data were fitted to a modified superposition formulation and a novel finite ramp time correction technique was applied. The parameters obtained from this fitting methodology were used to predict the average dynamic cyclic viscoelastic behavior of the porcine cord. The data indicate that the porcine spinal cord exhibited fully nonlinear viscoelastic behavior. The average weighted root mean squared error for a Heaviside ramp fit was 2.8 kPa, which was significantly greater (p<0.001) than that of the nonlinear (comprehensive viscoelastic characterization method) fit (0.365 kPa). Further, the nonlinear mechanical parameters obtained were able to accurately predict the dynamic behavior, thus exemplifying the reliability of the obtained nonlinear parameters. These parameters will be important for future studies investigating various damage mechanisms of the spinal cord and studies developing high-resolution finite elements models of the spine.

Effect of the central canal in the spinal cord on fluid movement within the cord

Computational studies are used to demonstrate the effect of oscillating CSF flow on pressures within the spinal cord. We tested the hypothesis that the central canal in the spinal cord affects spinal cord pressure gradients resulting from oscillatory CSF flow. Two computational models of the spinal cord were created with the same dimensions. Model 1 had a homogeneous porous structure. Model 2 had the same structure with the addition of a central fluid filled space, representing the central canal of the cord. We simulated oscillatory flow in the fluid space using standard computational fluid dynamics tools. For all phases of the CSF flow cycle and for specific projections through the model we calculated pressure gradients and fluid movement in the cord models. Pressures in the models varied through the flow cycle. Model 1 had linearly varying pressure along its long axis that varied with the cycle and had no pressure gradients across the cord. Model 2 had nonlinear varying pressure along its long axis varying with the time in the cycle and had transient centrifugal and centripetal pressure gradients with a central fluid space. The radial pressures varied linearly with distance from the fluid space. Centrifugal and centripetal pressure gradients resulted in radially directed fluid flow in the cord. The central canal within the spinal cord alters the pressure fields occurring during oscillatory CSF flow and creates centrifugal and centripetal fluid flux in the cord.

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.

Syrinx fluid transport: modeling pressure-wave-induced flux across the spinal pial membrane

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.

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.

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.

Cerebrospinal fluid hydrodynamics in type I Chiari malformation

PURPOSE

The objective of this study was to review past studies that have used engineering analysis to examine cerebrospinal fluid hydrodynamics in cranial and spinal subarachnoid spaces in both healthy humans and those affected by type I Chiari malformation.

METHODS

A PubMed search of literature pertaining to cerebrospinal fluid hydrodynamics was performed with a particular focus on those that utilized methods such as computational fluid dynamics or experimental flow modeling.

DISCUSSION

From the engineer's perspective, type I Chiari malformation is an abnormal geometry of the cerebellum that causes increased resistance to cerebrospinal fluid flow between the intracranial and spinal subarachnoid space. As such, understanding the hydrodynamics of cerebrospinal fluid in the craniospinal subarachnoid space has long been thought to be important in the diagnosis and management of type I Chiari malformation. Hydrodynamic quantification of cerebrospinal fluid motion in the subarachnoid space may better reflect the pathophysiology of the disorder and serve as a prognostic indicator in conjunction with geometric magnetic resonance measurements that are currently used clinically. This review discusses the results of studies that have sought to quantify the hydrodynamics of cerebrospinal fluid motion using computational and experimental modeling and critiques the methods by which the results were obtained.

CONCLUSION

Researchers have found differences in cerebrospinal fluid velocities and pressures in type I Chiari malformation patients compared to healthy subjects. However, further research is necessary to determine the causal relationship between changes to hydrodynamic parameters such as cerebrospinal fluid velocity, pressure, resistance to flow, and craniospinal compliance and clinical aspects such as neurological symptoms, radiological evidence of severity, and surgical success.

Spinal subarachnoid space pressure measurements in an in vitro spinal stenosis model: implications on syringomyelia theories

Full explanation for the pathogenesis of syringomyelia (SM), a neuropathology characterized by the formation of a cystic cavity (syrinx) in the spinal cord (SC), has not yet been provided. It has been hypothesized that abnormal cerebrospinal fluid (CSF) pressure, caused by subarachnoid space (SAS) flow blockage (stenosis), is an underlying cause of syrinx formation and subsequent pain in the patient. However, paucity in detailed in vivo pressure data has made theoretical explanations for the syrinx difficult to reconcile. In order to understand the complex pressure environment, four simplified in vitro models were constructed to have anatomical similarities with post-traumatic SM and Chiari malformation related SM. Experimental geometry and properties were based on in vivo data and incorporated pertinent elements such as a realistic CSF flow waveform, spinal stenosis, syrinx, flexible SC, and flexible spinal column. The presence of a spinal stenosis in the SAS caused peak-to-peak cerebrospinal fluid CSF pressure fluctuations to increase rostral to the stenosis. Pressure with both stenosis and syrinx present was complex. Overall, the interaction of the syrinx and stenosis resulted in a diastolic valve mechanism and rostral tensioning of the SC. In all experiments, the blockage was shown to increase and dissociate SAS pressure, while the axial pressure distribution in the syrinx remained uniform. These results highlight the importance of the properties of the SC and spinal SAS, such as compliance and permeability, and provide data for comparison with computational models. Further research examining the influence of stenosis size and location, and the importance of tissue properties, is warranted.

A lumped-parameter model of the cerebrospinal system for investigating arterial-driven flow in posttraumatic syringomyelia

Fluid transport in syringomyelia has remained enigmatic ever since the disease was first identified some three centuries ago. However, accumulating evidence in the last decade from animal studies implicates arterial pulsations in syrinx formation. In particular, it has been suggested that a phase difference between the pressure pulse in the spinal subarachnoid space and the perivascular spaces, due to a pathologically disturbed cerebrospinal fluid (CSF) or blood supply, could result in a net influx of CSF into the spinal cord (SC). A lumped-parameter model is developed of the cerebrospinal system to investigate this conjecture. It is found that although this phase-lag mechanism may operate, it requires the SC to have an intrinsic storage capacity due to the collapsibility of the contained venous reservoir. This net flux is associated with a higher mean pressure in the SC than the SSS which is maintained in the periodic steady state. According to our simulations the mechanical perturbations of arachnoiditis exacerbate the phase-lag effect, which may be partially alleviated by the presence of a posttraumatic syrinx and more completely by a syringo-subarachnoid shunt.

Characterization of cyclic CSF flow in the foramen magnum and upper cervical spinal canal with MR flow imaging and computational fluid dynamics

CSF flow has been shown to exhibit complex patterns in MR images in both healthy subjects and in patients with Chiari I. Abnormal CSF flow oscillations, according to prevailing opinion, cause syringomyelia and other clinical manifestations that affect some patients with the Chiari I malformation. For this article, we reviewed the literature on PC MR of CSF flow, collected the published CFD studies relevant to CSF flow, and performed flow simulations. PC MR creates cine and still images of CSF flow and measurements of flow velocities. CFD, a technique used to compute flow and pressure in liquid systems, simulates the CSF flow patterns that occur in a specific geometry or anatomy of the SAS and a specific volume of flow. Published PC MR studies show greater peak CSF velocities and more complex flow patterns in patients with Chiari I than in healthy subjects, with synchronous bidirectional flow one of the characteristic markers of pathologic flow. In mathematic models of the SAS created from high-resolution MR images, CFD displays complex CSF flow patterns similar to those shown in PC MR in patients. CFD shows that the pressure and flow patterns vary from level to level in the upper spinal canal and differ between patients with Chiari and healthy volunteers. In models in which elasticity and motion are incorporated, CFD displays CSF pressure waves in the SAS. PC MR and CFD studies to date demonstrate significant alterations of CSF flow and pressure patterns in patients with Chiari I. CSF flow has nonlaminar complex spatial and temporal variations and associated pressure waves and pressure gradients. Additional simulations of CSF flow supplemented by PC MR will lead to better measures for distinguishing pathologic flow abnormalities that cause syringomyelia, headaches, and other clinical manifestations in Chiari I malformations.

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.

The influence of coughing on cerebrospinal fluid pressure in an in vitro syringomyelia model with spinal subarachnoid space stenosis

Background

The influence of coughing, on the biomechanical environment in the spinal subarachnoid space (SAS) in the presence of a cerebrospinal fluid flow stenosis, is thought to be an important etiological factor in craniospinal disorders, including syringomyelia (SM), Chiari I malformation, and hydrocephalus. The aim of this study was to investigate SAS and syrinx pressures during simulated coughing using in vitro models and to provide information for the understanding of the craniospinal fluid system dynamics to help develop better computational models.

Methods

Four in vitro models were constructed to be simplified representations of: 1) non-communicating SM with spinal SAS stenosis; 2) non-communicating SM due to spinal SAS stenosis with a distensible spinal column; 3) non-communicating SM post surgical removal of a spinal SAS stenosis; and 4) a spinal SAS stenosis due to spinal trauma. All of the models had a flexible spinal cord. To simulate coughing conditions, an abrupt CSF pressure pulse (~ 5 ms) was imposed at the caudal end of the spinal SAS by a computer-controlled pump. Pressure measurements were obtained at 4 cm intervals along the spinal SAS and syrinx using catheter tip transducers.

Results

Pressure measurements during a simulated cough, showed that removal of the stenosis was a key factor in reducing pressure gradients in the spinal SAS. The presence of a stenosis resulted in a caudocranial pressure drop in the SAS, whereas pressure within the syrinx cavity varied little caudocranially. A stenosis in the SAS caused the syrinx to balloon outward at the rostral end and be compressed at the caudal end. A >90% SAS stenosis did not result in a significant Venturi effect. Increasing compliance of the spinal column reduced forces acting on the spinal cord. The presence of a syrinx in the cord when there was a stenosis in the SAS, reduced pressure forces in the SAS. Longitudinal pressure dissociation acted to suck fluid and tissue caudocranially in the SAS with a stenosis.

Conclusions

Pressures in the spinal SAS during a simulated cough in vitro had similar peak, transmural, and longitudinal pressures to in vivo measurements reported in the literature. The pressure wave velocities and pressure gradients during coughing (longitudinal pressure dissociation and transmural pressure) were impacted by alterations in geometry, compliance, and the presence of a syrinx and/or stenosis.

CSF flow dynamics at the craniovertebral junction studied with an idealized model of the subarachnoid space and computational flow analysis

BACKGROUND AND PURPOSE

How CSF flow varies with the anatomy of the subarachnoid space has not been sufficiently well studied. The goal of this study was to develop an idealized 3D computational model of the subarachnoid space and then to use this model to study the detailed spatiotemporal effects of anatomic variations on CSF pressures and velocities.

MATERIALS AND METHODS

We created a geometric model with a computer-assisted design program. The model contained a central structure for the brain and spinal cord axis and a second surrounding structure for the peripheral borders of the subarachnoid space. Model dimensions were adjusted to capture the main characteristics of the normal human posterior fossa and cervical spinal anatomy. CSF flow was modeled as water with a sinusoidal flow pattern in time. Velocities and pressures during craniocaudal and caudocranial flow were calculated with computational fluid dynamics (CFD) software. Simulated flow was compared with published phase-contrast MR imaging measurements of CSF flow in healthy human subjects.

RESULTS

The model contained geometric characteristics of the posterior fossa and spinal canal. Flow velocities varied with the time in the cycle and location in space. Flow velocities had spatial variations that resembled those in healthy human subjects. Reynolds numbers were moderate, showing a laminar flow regime. Pressure varied uniformly along the long axis of the model during craniocaudal and caudocranial flow.

CONCLUSIONS

In an idealized geometric approximation of the human subarachnoid space, CSF velocities and pressures can be studied in spatiotemporal detail with mathematic models.

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

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.

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

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.