1D analysis of pial perivascular pumping

Arterial pulsations have been hypothesized to be a significant driver of the flow of cerebrospinal fluid (CSF) in perivascular spaces (PVSs). However, models based on perivascular pumping struggle to reproduce in vivo velocities in space and time. By analyzing the 1D lubrication equations, we show that in pial perivascular spaces with fixed, impermeable outer walls, enforcing conservation of mass will necessarily result in unrealistically large instantaneous velocity gradients across the length of the PVS when arterial pulsations are included. We thus conclude that the change in perivascular area with respect to time must be orders of magnitude smaller than the change in arterial area to be consistent with experimentally measured velocities. Thus, changes in perivascular area are not a driver for CSF flow in pial perivascular spaces. Instead, we find that applying a time-varying pressure gradient can reproduce observed mean and oscillatory components of pial PVS flow, which could suggest an alternate physiological driving mechanism.