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

Tensile properties of human spinal dura mater and pericranium

Autologous pericranium is a promising dural graft material. An optimal graft should exhibit similar mechanical properties to the native dura, but the mechanical properties of human pericranium have not been characterized, and studies of the biomechanical performance of human spinal dura are limited. The primary aim of this study was to measure the tensile structural and material properties of the pericranium, in the longitudinal and circumferential directions, and of the dura in each spinal region (cervical, thoracic and lumbar) and in three directions (longitudinal anterior and posterior, and circumferential). The secondary aim was to determine corresponding constitutive stress-strain equations using a one-term Ogden model. A total of 146 specimens were tested from 7 cadavers. Linear regression models assessed the effect of tissue type, region, and orientation on the structural and material properties. Pericranium was isotropic, while spinal dura was anisotropic with higher stiffness and strength in the longitudinal than the circumferential direction. Pericranium had lower strength and modulus than spinal dura across all regions in the longitudinal direction but was stronger and stiffer than dura in the circumferential direction. Spinal dura and pericranium had similar strain at peak force, toe, and yield, across all regions and directions. Human pericranium exhibits isotropic mechanical behavior that lies between that of the longitudinal and circumferential spinal dura. Further studies are required to determine if pericranium grafts behave like native dura under in vivo loading conditions. The Ogden parameters reported may be used for computational modeling of the central nervous system. Graphical abstract.

A one-dimensional model for the pulsating flow of cerebrospinal fluid in the spinal canal

The monitoring of intracranial pressure (ICP) fluctuations, which is needed in the context of a number of neurological diseases, requires the insertion of pressure sensors, an invasive procedure with considerable risk factors. Intracranial pressure fluctuations drive the wave-like pulsatile motion of cerebrospinal fluid (CSF) along the compliant spinal canal. Systematically derived simplified models relating the ICP fluctuations with the resulting CSF flow rate can be useful in enabling indirect evaluations of the former from non-invasive magnetic resonance imaging (MRI) measurements of the latter. As a preliminary step in enabling these predictive efforts, a model is developed here for the pulsating viscous motion of CSF in the spinal canal, assumed to be a linearly elastic compliant tube of slowly varying section, with a Darcy pressure-loss term included to model the fluid resistance introduced by the trabeculae, which are thin collagen-reinforced columns that form a web-like structure stretching across the spinal canal. Use of Fourier-series expansions enables predictions of CSF flow rate for realistic anharmonic ICP fluctuations. The flow rate predicted using a representative ICP waveform together with a realistic canal anatomy is seen to compare favourably with in vivo phase-contrast MRI measurements at multiple sections along the spinal canal. The results indicate that the proposed model, involving a limited number of parameters, can serve as a basis for future quantitative analyses targeting predictions of ICP temporal fluctuations based on MRI measurements of spinal-canal anatomy and CSF flow rate.

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.

Characterization of intrathecal cerebrospinal fluid geometry and dynamics in cynomolgus monkeys (macaca fascicularis) by magnetic resonance imaging

Recent advancements have been made toward understanding the diagnostic and therapeutic potential of cerebrospinal fluid (CSF) and related hydrodynamics. Increased understanding of CSF dynamics may lead to improved detection of central nervous system (CNS) diseases and optimized delivery of CSF based CNS therapeutics, with many proposed therapeutics hoping to successfully treat or cure debilitating neurological conditions. Before significant strides can be made toward the research and development of interventions designed for human use, additional research must be carried out with representative subjects such as non-human primates (NHP). This study presents a geometric and hydrodynamic characterization of CSF in eight cynomolgus monkeys (Macaca fascicularis) at baseline and two-week follow-up.

Results showed that CSF flow along the entire spine was laminar with a Reynolds number ranging up to 80 and average Womersley number ranging from 4.1–7.7. Maximum CSF flow rate occurred ~25 mm caudal to the foramen magnum. Peak CSF flow rate ranged from 0.3–0.6 ml/s at the C3-C4 level. Geometric analysis indicated that average intrathecal CSF volume below the foramen magnum was 7.4 ml. The average surface area of the spinal cord and dura was 44.7 and 66.7 cm² respectively. Subarachnoid space cross-sectional area and hydraulic diameter ranged from 7–75 mm² and 2–3.7 mm, respectively. Stroke volume had the greatest value of 0.14 ml at an axial location corresponding to C3-C4.

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.

Nonuniform Moving Boundary Method for Computational Fluid Dynamics Simulation of Intrathecal Cerebrospinal Flow Distribution in a Cynomolgus Monkey

A detailed quantification and understanding of cerebrospinal fluid (CSF) dynamics may improve detection and treatment of central nervous system (CNS) diseases and help optimize CSF system-based delivery of CNS therapeutics. This study presents a computational fluid dynamics (CFD) model that utilizes a nonuniform moving boundary approach to accurately reproduce the nonuniform distribution of CSF flow along the spinal subarachnoid space (SAS) of a single cynomolgus monkey. A magnetic resonance imaging (MRI) protocol was developed and applied to quantify subject-specific CSF space geometry and flow and define the CFD domain and boundary conditions. An algorithm was implemented to reproduce the axial distribution of unsteady CSF flow by nonuniform deformation of the dura surface. Results showed that maximum difference between the MRI measurements and CFD simulation of CSF flow rates was <3.6%. CSF flow along the entire spine was laminar with a peak Reynolds number of ∼150 and average Womersley number of ∼5.4. Maximum CSF flow rate was present at the C4-C5 vertebral level. Deformation of the dura ranged up to a maximum of 134 μm. Geometric analysis indicated that total spinal CSF space volume was ∼8.7 ml. Average hydraulic diameter, wetted perimeter, and SAS area were 2.9 mm, 37.3 mm and 27.24 mm2, respectively. CSF pulse wave velocity (PWV) along the spine was quantified to be 1.2 m/s.

Microgravity-induced fluid shift and ophthalmic changes

Although changes to visual acuity in spaceflight have been observed in some astronauts since the early days of the space program, the impact to the crew was considered minor. Since that time, missions to the International Space Station have extended the typical duration of time spent in microgravity from a few days or weeks to many months. This has been accompanied by the emergence of a variety of ophthalmic pathologies in a significant proportion of long-duration crewmembers, including globe flattening, choroidal folding, optic disc edema, and optic nerve kinking, among others. The clinical findings of affected astronauts are reminiscent of terrestrial pathologies such as idiopathic intracranial hypertension that are characterized by high intracranial pressure. As a result, NASA has placed an emphasis on determining the relevant factors and their interactions that are responsible for detrimental ophthalmic response to space. This article will describe the Visual Impairment and Intracranial Pressure syndrome, link it to key factors in physiological adaptation to the microgravity environment, particularly a cephalad shifting of bodily fluids, and discuss the implications for ocular biomechanics and physiological function in long-duration spaceflight.

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.