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.

Effect of Normal Breathing on the Movement of CSF in the Spinal Subarachnoid Space.

BACKGROUND AND PURPOSE: Forced respirations reportedly have an effect on CSF movement in the spinal canal. We studied respiratory-related CSF motion during normal respiration. MATERIALS AND METHODS: Six healthy subjects breathed at their normal rate with a visual guide to ensure an unchanging rhythm. Respiratory-gated phase-contrast MR flow images were acquired at 5 selected axial planes along the spine. At each spinal level, we computed the flow rate voxelwise in the spinal canal, together with the associated stroke volume. From these data, we computed the periodic volume changes of spinal segments. A phantom was used to quantify the effect of respiration-related magnetic susceptibility changes on the velocity data measured. RESULTS: At each level, CSF moved cephalad during inhalation and caudad during expiration. While the general pattern of fluid movement was the same in the 6 subjects, the flow rates, stroke volumes, and spine segment volume changes varied among subjects. Peak flow rates ranged from 0.60 to 1.59 mL/s in the cervical region, 0.46 to 3.17 mL/s in the thoracic region, and 0.75 to 3.64 mL/s in the lumbar region. The differences in flow rates along the canal yielded cyclic volume variations of spine segments that were largest in the lumbar spine, ranging from 0.76 to 3.07 mL among subjects. In the phantom study, flow velocities oscillated periodically during the respiratory cycle by up to 0.02 cm/s or 0.5%. CONCLUSIONS: Respiratory-gated measurements of the CSF motion in the spinal canal showed cyclic oscillatory movements of spinal fluid correlated to the breathing pattern.

Drag reduction of three-dimensional bodies by base blowing with various gas densities.

This study reveals that injecting a light fluid of density ρ_{b} in the recirculating bubble of a bluff body at Re≈6.4×10^{4} has a greater drag reduction potential than blowing fluid of a density greater than or equal to that of the free stream ρ. It is found that the maximum drag reduction scales as (ρ_{b}/ρ)^{-1/6}. This power law combines the ability of the recirculating bubble to diffuse the injected momentum and the effectiveness of the injection to increase the recirculating bubble length.

Subject-Specific Studies of CSF Bulk Flow Patterns in the Spinal Canal: Implications for the Dispersion of Solute Particles in Intrathecal Drug Delivery.

BACKGROUND AND PURPOSE: Recent flow dynamics studies have shown that the eccentricity of the spinal cord affects the magnitude and characteristics of the slow bulk motion of CSF in the spinal subarachnoid space, which is an important variable in solute transport along the spinal canal. The goal of this study was to investigate how anatomic differences among subjects affect this bulk flow. MATERIALS AND METHODS: T2-weighted spinal images were obtained in 4 subjects and repeated in 1 subject after repositioning. CSF velocity was calculated from phase-contrast MR images for 7 equally spaced levels along the length of the spine. This information was input into a 2-time-scale asymptotic analysis of the Navier-Stokes and concentration equations to calculate the short- and long-term CSF flow in the spinal subarachnoid space. Bulk flow streamlines were shown for each subject and position and inspected for differences in patterns. RESULTS: The 4 subjects had variable degrees of lordosis and kyphosis. Repositioning in 1 subject changed the degree of cervical lordosis and thoracic kyphosis. The streamlines of bulk flow show the existence of distinct regions where the fluid particles flow in circular patterns. The location and interconnectivity of these recirculating regions varied among individuals and different positions. CONCLUSIONS: Lordosis, kyphosis, and spinal cord eccentricity in the healthy human spine result in subject-specific patterns of bulk flow recirculating regions. The extent of the interconnectivity of the streamlines among these recirculating regions is fundamental in determining the long-term transport of solute particles along the spinal canal.

Axisymmetric bubble pinch-off at high Reynolds numbers.

Analytical considerations and potential-flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, rn, decreases as tau proportional to r2n sqrt[1lnr2n], where tau is the time to break up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a rn proportional to tau1/3 power law. These findings are verified experimentally.