A reduced‐order model for fluid flow and mass transport in the interstitial space of the brain

The morphology of the brain interstitial space is characterized by sheets between adjacent cells and tunnels where more than two cells meet. Three disparate length scales exist, namely, the sheet thickness, the tunnel diameter, and their extent. Exploiting the differences in these length scales, we develop a reduced‐order model for flow in this particular type of porous media, starting with an asymptotic approach where the small parameter is the ratio of sheet thickness to tunnel diameter. The third length scale introduces a second dimensionless parameter delineating the extremes of tunnel flow and sheet flow dominance in the overall interstitial flow rates. The model can cover the entire domain between these extremes and gives reasonable flow predictions compared to literature results, yet at a much lower computational cost. Simplified models of species mass transport are also presented, indicating that transport of slow‐diffusing species is aided by convection induced by the flow.