Modelling and direct numerical simulation of flow and solute dispersion in the spinal subarachnoid space

Gutiérrez-Montes, C.; Coenen, Wilfried; Lawrence, Jenna; Martı́nez-Bazán, C.; Sánchez, Antonio L.; Lasheras, Juan C.

doi:10.1016/j.apm.2021.01.037

Cited by 11 publications

(16 citation statements)

References 43 publications

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“…An important outcome of the asymptotic analysis is a time-averaged transport equation that has been recently validated by means of comparisons with results of direct numerical simulations (DNS) spanning hundreds of oscillation cycles (Gutiérrez-Montes et al. 2021), as needed to generate significant dispersion of the solute. The comparisons demonstrate the accuracy of the reduced description, which is seen to provide excellent fidelity at a fraction of the computational cost involved in the DNS.…”

Section: Introductionmentioning

confidence: 99%

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

Alaminos-Quesada

Coenen²,

Gutiérrez-Montes³

et al. 2022

J. Fluid Mech.

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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.

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Section: Introductionmentioning

confidence: 99%

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

Alaminos-Quesada

Coenen²,

Gutiérrez-Montes³

et al. 2022

J. Fluid Mech.

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“…Consequently, the respiratory cycle may be a factor in the movement of drugs and anesthetics administered intrathecally. Modeling of CSF movement and drug transport 32,33 must take into consideration the effect of respiration.…”

Section: Discussionmentioning

confidence: 99%

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

Gutiérrez-Montes

Coenen

Vidorreta

et al. 2022

AJNR Am J Neuroradiol

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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.

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“…When comparing extradural versus subdural implantations, the conductivity of the CSF [39] and dura [40] should be modelled prior to in vivo studies as this will affect the quality and selectivity of neural recordings. This is especially pertinent when designing spinal cord devices as the relative volume of the CSF is greater [41] and is subject to dynamic changes from vascular pulsations [42] as well as eccentric positioning of the spinal cord in the subarachnoid space [43].…”

Section: Epidural and Subdural Electrodes (Invasive Non-penetrating)mentioning

confidence: 99%

Spinal cord bioelectronic interfaces: opportunities in neural recording and clinical challenges

et al. 2022

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Bioelectronic stimulation of the spinal cord has demonstrated significant progress in restoration of motor function in spinal cord injury (SCI). The proximal, uninjured spinal cord presents a viable target for the recording and generation of control signals to drive targeted stimulation. Signals have been directly recorded from the spinal cord in behaving animals and correlated with limb kinematics. Advances in flexible materials, electrode impedance and signal analysis will allow SCR to be used in next-generation neuroprosthetics. In this review, we summarize the technological advances enabling progress in SCR and describe systematically the clinical challenges facing spinal cord bioelectronic interfaces and potential solutions, from device manufacture, surgical implantation to chronic effects of foreign body reaction and stress-strain mismatches between electrodes and neural tissue. Finally, we establish our vision of bi-directional closed-loop spinal cord bioelectronic bypass interfaces that enable the communication of disrupted sensory signals and restoration of motor function in SCI.

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Modelling and direct numerical simulation of flow and solute dispersion in the spinal subarachnoid space

Cited by 11 publications

References 43 publications

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

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

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

Spinal cord bioelectronic interfaces: opportunities in neural recording and clinical challenges

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