Fluid-structure interactions and flow rectification in elliptical gaps in the walls of brain perivascular spaces

The driving mechanism of cerebrospinal fluid (CSF) flow through annular perivascular spaces (PVSs) in the brain may partly be explained by a valve mechanism. PVSs are bounded by an outer wall formed by astrocyte endfeet, with gaps between. Pressure oscillation in the PVS causes deformation of the gap, which would act like a valve, rectifying fluid through it.

To understand and quantify how the aspect ratio and the orientation of the endfoot gaps affect the rectification, we here model the gaps as elliptical holes on a two-dimensional shell with

arbitrary eccentricity. We analytically solve the deformation field of the elliptical gap under pressure oscillation using the method of perturbation. We calculate the resistance per unit length

for flow through straight channels with cross sections corresponding to the deformed gap geometry. We perform three-dimensional simulations to validate the analytical model.