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

Effects of buoyancy on the dispersion of drugs released intrathecally in the spinal canal

This paper investigates the transport of drugs delivered by direct injection into the cerebrospinal fluid (CSF) that fills the intrathecal space surrounding the spinal cord. Because of the small drug diffusivity, the dispersion of neutrally buoyant drugs has been shown in previous work to rely mainly on the mean Lagrangian flow associated with the CSF oscillatory motion. Attention is given here to effects of buoyancy, arising when the drug density differs from the CSF density. For the typical density differences found in applications, the associated Richardson number is shown to be of order unity, so that the Lagrangian drift includes a buoyancy-induced component that depends on the spatial distribution of the drug, resulting in a slowly evolving cycle-averaged flow problem that can be analysed with two-time scale methods. The asymptotic analysis leads to a nonlinear integro-differential equation for the spatiotemporal solute evolution that describes accurately drug dispersion at a fraction of the cost involved in direct numerical simulations of the oscillatory flow. The model equation is used to predict drug dispersion of positively and negatively buoyant drugs in an anatomically correct spinal canal, with separate attention given to drug delivery via bolus injection and constant infusion.

Validating the accuracy of real-time phase-contrast MRI and quantifying the effects of free breathing on cerebrospinal fluid dynamics

BACKGROUND

Understanding of the cerebrospinal fluid (CSF) circulation is essential for physiological studies and clinical diagnosis. Real-time phase contrast sequences (RT-PC) can quantify beat-to-beat CSF flow signals. However, the detailed effects of free-breathing on CSF parameters are not fully understood. This study aims to validate RT-PC's accuracy by comparing it with the conventional phase-contrast sequence (CINE-PC) and quantify the effect of free-breathing on CSF parameters at the intracranial and extracranial levels using a time-domain multiparametric analysis method.

METHODS

Thirty-six healthy participants underwent MRI in a 3T scanner for CSF oscillations quantification at the cervical spine (C2-C3) and Sylvian aqueduct, using CINE-PC and RT-PC. CINE-PC uses 32 velocity maps to represent dynamic CSF flow over an average cardiac cycle, while RT-PC continuously quantifies CSF flow over 45-seconds. Free-breathing signals were recorded from 25 participants. RT-PC signal was segmented into independent cardiac cycle flow curves (Qt) and reconstructed into an averaged Qt. To assess RT-PC's accuracy, parameters such as segmented area, flow amplitude, and stroke volume (SV) of the reconstructed Qt from RT-PC were compared with those derived from the averaged Qt generated by CINE-PC. The breathing signal was used to categorize the Qt into expiratory or inspiratory phases, enabling the reconstruction of two Qt for inspiration and expiration. The breathing effects on various CSF parameters can be quantified by comparing these two reconstructed Qt.

RESULTS

RT-PC overestimated CSF area (82.7% at aqueduct, 11.5% at C2-C3) compared to CINE-PC. Stroke volumes for CINE-PC were 615 mm³ (aqueduct) and 43 mm³ (spinal), and 581 mm³ (aqueduct) and 46 mm³ (spinal) for RT-PC. During thoracic pressure increase, spinal CSF net flow, flow amplitude, SV, and cardiac period increased by 6.3%, 6.8%, 14%, and 6%, respectively. Breathing effects on net flow showed a significant phase difference compared to the other parameters. Aqueduct-CSF flows were more affected by breathing than spinal-CSF.

CONCLUSIONS

RT-PC accurately quantifies CSF oscillations in real-time and eliminates the need for cardiac synchronization, enabling the quantification of the cardiac and breathing components of CSF flow. This study quantifies the impact of free-breathing on CSF parameters, offering valuable physiological references for understanding the effects of breathing on CSF dynamics.

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.

Neurofluids and the glymphatic system: anatomy, physiology, and imaging

First described in 2012, the glymphatic system is responsible for maintaining homeostasis within the central nervous system, including nutrient delivery, waste clearance, and consistency of the ionic microenvironment. It is comprised of glial cells and barrier systems that modulate neurofluid production, circulation, and exchange. Experimental interrogation of neurofluid dynamics is restricted to ex vivo and in vitro studies in animals and humans, therefore diagnostic imaging plays an important role in minimally invasive evaluation. This review article will synthesize current knowledge and theories regarding neurofluid circulation and implications for neuroimaging. First, we will discuss the anatomy of the neurogliovascular unit, including paravascular and perivascular pathways of fluid exchange. In addition, we will summarize the structure and function of barrier systems including the blood-brain, blood-cerebrospinal fluid, and brain-cerebrospinal fluid barriers. Next, we will mention physiologic factors that yield normal variations in neurofluid circulation, and how various disease pathologies can disrupt glymphatic drainage pathways. Lastly, we will cover the spectrum of diagnostic imaging and interventional techniques with relevance to glymphatic structure, flow, and function. We conclude by highlighting current barriers and future directions for translational imaging and applications to neurologic disorders.

Stationary flow driven by non-sinusoidal time-periodic pressure gradients in wavy-walled channels

The classical problem of secondary flow driven by a sinusoidally varying pressure gradient is extended here to address periodic pressure gradients of complex waveform, which are present in many oscillatory physiological flows. A slender two-dimensional wavy-walled channel is selected as a canonical model problem. Following standard steady-streaming analyses, valid for small values of the ratio ε of the stroke length of the pulsatile motion to the channel wavelength, the spatially periodic flow is described in terms of power-law expansions of ε , with the Womersley number assumed to be of order unity. The solution found at leading order involves a time-periodic velocity with a zero time-averaged value at any given point. As in the case of a sinusoidal pressure gradient, effects of inertia enter at the following order to induce a steady flow in the form of recirculating vortices with zero net flow rate. An improved two-term asymptotic description of this secondary flow is sought by carrying the analysis to the following order. It is found that, when the pressure gradient has a waveform with multiple harmonics, the resulting velocity corrections display a nonzero flow rate, not present in the single-frequency case, which enables stationary convective transport along the channel. Direct numerical simulations for values of ε of order unity are used to investigate effects of inertia and delineate the range of validity of the asymptotic limit ε ≪ 1 . The comparisons of the time-averaged velocity obtained numerically with the two-term asymptotic description reveals that the latter remains remarkably accurate for values of ε exceeding 0.5. As an illustrative example, the results of the model problem are used to investigate the cerebrospinal-fluid flow driven along the spinal canal by the cardiac and respiratory cycles, characterized by markedly non-sinusoidal waveforms.

Real-time phase contrast MRI versus conventional phase contrast MRI at different spatial resolutions and velocity encodings

PURPOSES

To compare the accuracy of real-time phase-contrast echo-planar MRI (EPI-PC) and conventional cine phase-contrast MRI (Conv-PC) and to assess the influence of spatial resolutions (pixel size) and velocity encoding on flow measurements obtained with the two sequences.

METHODS

Flow quantification was assessed using a pulsatile flow phantom (diameter: 9.5 mm; mean flow rate: 1150 mm³/s; mean flow velocity: 1.6 cm/s). Firstly, the accuracy of the EPI-PC was checked by comparing it with the flow rate in the calibrated phantom and the pulsation index from Conv-PC. Secondly, flow data from the two sequences were compared quantitatively as a function of the pixel size and the velocity encoding.

RESULTS

The mean percentage difference between the EPI-PC flow rate and calibrated phantom flow rate was -2.9 ± 2.1% (Mean ± SD). The pulsatility indices for EPI-PC and Conv-PC were respectively 0.64 and 0.59. In order to keep the flow rate measurement error within 10%, the ROI in Conv-PC had to contain at least 13 pixels, while the ROI in EPI-PC had to contain at least 9 pixels. Furthermore, Conv-PC had a higher velocity-to-noise ratio and could use a higher velocity encoding than EPI-PC (20 cm/s and 15 cm/s, respectively).

CONCLUSIONS

The result of this in vitro study confirmed the accuracy of EPI-PC, and found that EPI-PC can adapt to lower spatial resolutions, but is more sensitive to velocity encoding than Conv-PC.