Flow in a highly porous annular conduit: Coupling wall compliance, eccentricity and peristalsis

The perivascular spaces (PVSs) are low-resistance annular pathways that allow the entry of the cerebrospinal fluid (CSF) into the brain tissue. In vivo imaging suggests that the arteries are often located eccentrically within the PVSs, and that the pressure fluctuations within the PVSs deforms the brain tissue by ≈ 1.5 μm. Further, flow tracer studies suggest that the penetrating PVSs form a highly porous pathway. Here we extend the work of Coenen et al. (JFM, 2021, doi:10.1017/jfm.2021.525) to incorporate a two-way coupled fluid-structure interaction between the CSF flow and the brain tissue in a highly porous eccentric annular pathway, with flow driven by artery wall pulsations under the lubrication approximation. The Darcy-Brinkman term in the axial momentum equation accounts for the drag due to flow through a highly porous domain. This reduced-order model leads to a single nonlinear unsteady partial differential equation for the axial pressure variation. We apply the model to study the effect of eccentricity, brain tissue stiffness, and Darcy number on flow quantities such as pressure, flow rate, and channel resistance. This reduced-order model captures important elements of PVS flows such as the pulsation-driven driving mechanism, in vivo PVS geometry, and tissue properties, enabling parametric studies, and further extension to understand the basic mechanisms (and their interactions) involved in CSF flows in the PVS.