Peristaltic pumping in sub-wavelength channels

TL;DR

This study uses the lubrication approximation to analyze how sub-wavelength channel lengths affect peristaltic flow, revealing significant modulation of flow characteristics that challenge the physiological relevance of simplified models.

Contribution

It provides a comprehensive solution for peristaltic flow in finite channels of arbitrary length, highlighting limitations of sub-wavelength models in replicating in vivo cerebrospinal fluid flow.

Findings

Sub-wavelength channels significantly alter flow rate amplitude and phase.

Flow rate varies along the channel length due to boundary-induced pressure gradients.

Short channels do not replicate in vivo flow distributions in perivascular spaces.

Abstract

We apply the lubrication approximation to solve for the flow generated by a peristaltic traveling wave in a finite, planar channel, and examine the effect of channel length. Cerebrospinal fluid (CSF) is hypothesized to be peristaltically transported by arterial pulsations through the perivascular spaces in the brain. Previous studies of peristaltic perivascular models have chosen model lengths ranging from sub-wavelength, which is more physiologically realistic, to full wavelength. Here, we solve for peristaltic flow rates for arbitrary lengths, and find that sub-wavelength channels significantly modulate the mean value, phase, and amplitude of flow rate for sinusoidal and general peristaltic waveforms. The boundary conditions create an internal pressure gradient such that the instantaneous flow rate varies along the length of the channel, and the difference between the ends and the middle of the channel is more pronounced for very short channels. This longitudinal distribution in flow rate is not observed \emph{in vivo} in perivascular spaces at the surface of the brain, and hence sub-wavelength peristaltic models whose boundary conditions are isolated from the larger perivascular network are limited in their ability to reproduce perivascular flows.