Blood osmolytes such as sugar can drive brain fluid flows in a poroelastic model.

The glymphatic system of fluid flow through brain tissue may clear amyloid-β during sleep and as such underlie the need for sleep. Dysfunctional glymphatic transport has been implicated in pathological conditions ranging from stroke and dementia to psychiatric illnesses. To date, the fastest observed in-vivo brain flows have been reported after the manipulation of blood osmotic pressures. Surprisingly, the brain seems to shrink while receiving more influx. Though influx of an incompressible fluid might expand the tissue, no physical theory for these observations has been proposed. We here present a minimal mathematical model of brain pressure, deformation, and fluid flows due to vascular osmotic pressures. The model is based on Darcy flow, linear poroelasticity theory and conservation of mass. We propose that a screened Poisson equation holds for interstitial pressure because vascular filtration corresponds to fluid divergence. The model resolves the apparent paradox of combined fluid influx with tissue shrinkage by showing that fluid absorption into the blood can drive both. In this model, small glucose concentration differences between plasma and brain can drive brain flow velocities observed in recent in-vivo assays. Osmosis may therefore drive brain fluid flow under physiological conditions and provide an explanation for the known correlations between diabetes and dementia.