A time-dependent, brain-wide model of solute transport in the glymphatic system

The flow of cerebrospinal fluid (CSF) through the perivascular spaces (PVSs) and interstitial fluid (ISF) in the extracellular space (ECS) is important for brain waste removal and drug delivery. The circulation of this flow is often called the glymphatic system. We build on an existing hydraulic network model of steady flow in this system to enable the study of time-dependent flows, allowing the modelling of the processes of tracer injection and drug delivery in the glymphatic network. Using flow rates from the steady-state model and the method of Laplace transforms, we solve this time-dependent advection-diffusion equation for the network semi-analytically and show that the solution closely matches numerical simulations. We find that a particular value of the endfoot gap cavity fraction maximizes solute perfusion. Furthermore, we find that a smaller gap fraction around PVS segments at the brain surface and a larger gap fraction around deeper PVS segments produce more uniform perfusion, which is consistent with a previous study (Wang et al. 2021 Glia69, 715-728 (doi:10.1002/glia.23923)). We also observe that greater permeability of the ECS improves perfusion, and that tracers with lower diffusivity exhibit enhanced perfusion.