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

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.

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.

A mechanistic pharmacokinetic model for intrathecal administration of antisense oligonucleotides

Intrathecal administration is an important mode for delivering biological agents targeting central nervous system (CNS) diseases. However, current clinical practices lack a sound theorical basis for a quantitative understanding of the variables and conditions that govern the delivery efficiency and specific tissue targeting especially in the brain. This work presents a distributed mechanistic pharmacokinetic model (DMPK) for predictive analysis of intrathecal drug delivery to CNS. The proposed DMPK model captures the spatiotemporal dispersion of antisense oligonucleotides (ASO) along the neuraxis over clinically relevant time scales of days and weeks as a function of infusion, physiological and molecular properties. We demonstrate its prediction capability using biodistribution data of antisense oligonucleotide (ASO) administration in non-human primates. The results are in close agreement with the observed ASO pharmacokinetics in all key compartments of the central nervous system. The model enables determination of optimal injection parameters such as intrathecal infusion volume and duration for maximum ASO delivery to the brain. Our quantitative model-guided analysis is suitable for identifying optimal parameter settings to target specific brain regions with therapeutic drugs such as ASOs.

Oscillating viscous flow past a streamwise linear array of circular cylinders

This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.

Buoyancy-modulated Lagrangian drift in wavy-walled vertical channels as a model problem to understand drug dispersion in the spinal canal

This paper investigates flow and transport in a slender wavy-walled vertical channel subject to a prescribed oscillatory pressure difference between its ends. When the ratio of the stroke length of the pulsatile flow to the channel wavelength is small, the resulting flow velocity is known to include a slow steady-streaming component resulting from the effect of the convective acceleration. Our study considers the additional effect of gravitational forces in configurations with a non-uniform density distribution. Specific attention is given to the slowly evolving buoyancy-modulated flow emerging after the deposition of a finite amount of solute whose density is different from that of the fluid contained in the channel, a relevant problem in connection with drug dispersion in intrathecal drug delivery (ITDD) processes, involving the injection of the drug into the cerebrospinal fluid that fills the spinal canal. It is shown that when the Richardson number is of order unity, the relevant limit in ITDD applications, the resulting buoyancy-induced velocities are comparable to those of steady streaming. As a consequence, the slow time-averaged Lagrangian motion of the fluid, involving the sum of the Stokes drift and the time-averaged Eulerian velocity, is intimately coupled with the transport of the solute, resulting in a slowly evolving problem that can be treated with two-time-scale methods. The asymptotic development leads to a time-averaged, nonlinear integro-differential transport equation that describes the slow dispersion of the solute, thereby circumventing the need to describe the small concentration fluctuations associated with the fast oscillatory motion. The ideas presented here can find application in developing reduced models for future quantitative analyses of drug dispersion in the spinal canal.

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.

Intrathecal Drug Delivery: Advances and Applications in the Management of Chronic Pain Patient

Advances in our understanding of the biology of spinal systems in organizing and defining the content of exteroceptive information upon which higher centers define the state of the organism and its role in the regulation of somatic and automatic output, defining the motor response of the organism, along with the unique biology and spatial organization of this space, have resulted in an increased focus on therapeutics targeted at this extracranial neuraxial space. Intrathecal (IT) drug delivery systems (IDDS) are well-established as an effective therapeutic approach to patients with chronic non-malignant or malignant pain and as a tool for management of patients with severe spasticity and to deliver therapeutics that address a myriad of spinal pathologies. The risk to benefit ratio of IDD makes it a useful interventional approach. While not without risks, this approach has a significant therapeutic safety margin when employed using drugs with a validated safety profile and by skilled practioners. The present review addresses current advances in our understanding of the biology and dynamics of the intrathecal space, therapeutic platforms, novel therapeutics, delivery technology, issues of safety and rational implementation of its therapy, with a particular emphasis upon the management of pain.

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.

Assessing Cerebrospinal Fluid Flow Dynamics in Pediatric Patients with Central Nervous System Tumors Treated with Intraventricular Radioimmunotherapy

The incidence of abnormal cerebrospinal fluid (CSF) flow dynamics in children with central nervous system (CNS) tumors before intraventricular therapy has not been described. Methods: We performed a single-institution, retrospective review of patients with primary or metastatic CNS tumors treated between 2003 and 2018 (15 y). Patients underwent ¹¹¹In-diethylenetriaminepentaacetic acid injection into the CSF intraventricular space followed by nuclear medicine imaging at 90 min, 4 h, 24 h, and 48 h (if required). CSF flow was classified as normal, delayed, asymmetric, or obstructed. Results: In total, 278 CSF flow studies were performed on 224 patients, 202 of whom (90%) were less than 18 y old. Of these, 116 patients (52%) had metastatic CNS neuroblastoma, 57 (25%) had medulloblastoma, and 51 (23%) had other histologic types of CNS tumors. Of the 278 studies, 237 (85%) were normal, 9 (3%) required neurosurgical intervention, 25 (9%) were delayed, and 7 (3%) were asymmetric. Conclusion: Abnormal CSF flow and the necessity for neurosurgical intervention must be considered when attempting to ensure appropriate intraventricular therapy in the pediatric population.