Peristaltic flow in the glymphatic system

Abstract

Introduction: The glymphatic system refers to the pathway for the transport of cerebrospinal fluid (CSF) from the subarachnoid space through brain tissue. CSF flows through annular paravascular spaces driven by arterial pulsation and enters brain tissue across the permeable outer boundary lined by glial cells. CSF convection in brain tissue is crucial for enhancing the diffusion-limited transport of extracellular solutes and waste products in brain tissue. Here we model CSF transport in the glymphatic system as flow through an annular space with a porous outer (glial) boundary driven by peristaltic motion of the inner (arterial) boundary and study its dependence on the permeability and elastic properties of the boundaries.

Materials and Methods: The paravascular space is modeled as a straight cylindrical annulus whose length is long compared to the radius of the artery. The outer (glial) boundary is elastic and porous while the inner (arterial) boundary is elastic and impermeable. The pressure gradient in the arterial blood is prescribed as a travelling wave and tube laws are prescribed linking the radius of the inner and outer boundaries to the pressure difference across them. The governing equations are solved using the lubrication approximation as a perturbation series in the pulsation amplitude δ and analytical solutions are obtained.

Results and Discussion: At leading order (O(δ)), the solution is periodic and in phase with the arterial pulsation for typical values of porosity and permeability parameters. There is no net influx or efflux of CSF across the porous boundary at this order. Steady streaming is found at O(δ2) with net efflux of CSF from the paravascular space into brain tissue. The efflux velocity is on the order of 0.1 mm/s and scales linearly with the permeability of the glial boundary. The mean axial flow parallel to the axis of the annulus is on the order of 1 mm/s and scales as the square root of the glial permeability. It is found to reverse close to the inner and outer boundaries, but the magnitude of the reversal is small (about 10-3 times the mean flow). Both velocity components depend linearly on the elasticity of the arterial boundary. The efflux rate, axial flow and annulus gap are predicted to decrease exponentially with axial distance.

Conclusions: The model predicts that the CSF transport in the glymphatic system is tightly coupled to the mechanical and permeability characteristics of the boundaries and provides quantitative estimates of transport rates. This provides an initial model of the flow that can be coupled to models of solute transport through the brain tissue to provide a fuller understanding of the nature and significance of glymphatic transport.

Acknowledgements: (Optional) The University of Auckland Vice Chancellor’s Distinguished Visitor Award supported JB Grotberg’s visit to Auckland that led to this collaboration.