Fluid-structure interactions in non-axisymmetric perivascular spaces

The brain’s perivascular spaces (PVSs) are annular channels bound by the cerebral blood vessel (as the inner wall) and the astrocyte endfeet layer (as the outer wall). The cerebrospinal fluid (CSF) flow in these PVSs drives the metabolic waste clearance in the brain. In vivo studies have shown the deformation of the brain tissue induced by CSF flow, emphasizing the need to consider fluid-structure interaction in modeling these flows. Here, we extend the work of Coenen et al. (JFM, 2021, doi:10.1017/jfm.2021.525) to incorporate two-way coupled fluid-structure interaction with the astrocyte endfeet, in addition to the pumping produced by arterial wall motion, under the lubrication approximation. Importantly, the relevant idealized geometries of the PVS consider its eccentricity and outer wall shape. This reduced-order model leads to a single nonlinear unsteady partial differential equation for the axial pressure variation. The parameters investigated are the blood vessel eccentricity, the imposed arterial wall motion (cardiac pulsation/functional hyperemia), and the stiffness of the endfeet layer. Specifically, we analyze their effect on flow quantities such as pressure, flow rate, mean flow rate, PVS resistance, and endfeet displacement. For flows driven by cardiac pulsation, we found that a rigid wall assumption can overestimate the mean flow rate by ≈ 547% and ≈ 17% compared to endfeet walls with compliance numbers of 3.44 × 10⁻⁴ and 3.44 × 10⁻⁵, respectively.