A flexible idealized model for investigating extracellular solute transport in the brain

The exchange between the cerebrospinal fluid (CSF) flowing through the perivascular spaces (PVSs; annular channels lining the brain vasculature) and interstitial fluid in the brain parenchyma is hypothesized to play a key role in clearing metabolic waste from the brain tissue. Impaired waste clearance has been linked to neurodegenerative diseases like Alzheimer's. We analytically formulate an axisymmetric model of fluid flow exchange between the PVS of a penetrating arteriole and the surrounding brain parenchyma modeled as a porous medium. We then numerically solve an advection-diffusion equation to model the solute transport in the domain. We find that the solute clearance leads to a gradient of concentration along the boundary between the PVS and the parenchyma and that a zero concentration boundary condition at the PVSs often used in parenchymal clearance models may not always be accurate. The model's simplicity offers flexibility in varying key parameters like PVS width, parenchyma thickness, permeability, inlet boundary conditions, and CSF flow velocity in the PVS to probe solute clearance conditions in both healthy conditions and in neurodegenerative disorders.