Mathematical Model of Unsteady Flow of Cerebrospinal Fluid in the Perivascular Region

Cerebrospinal fluid (CSF) transport through the perivascular
space (PVS) plays an impotent role in the glymphatic system of the
brain, supporting nutrient delivery and metabolic waste clearance.
Here we describe the unsteady flow of CSF in the perivascular region.
The governing equations are derived from the Navier Stokes
equations coupled with a solute transport equation. The model Darcy
is the permeability parameter, and chemical reaction parameter. The
governing equations are non-dimensionalized and solved using the
Laplace transform technique. Analytical expressions for velocity and
concentration fields are derived and discussed. The results
demonstrate that wall motion significantly enhances the CSF
transport while buoyancy and porous medium resistance affect the
velocity distribution. The proposed model provides deeper insight into
fluid dynamics in the glymphatic pathway and can contribute to
improved understanding of neurological diseases associated with
impaired CSF circulation.