Hydraulic resistance model for interstitial fluid flow in the brain

Flow of interstitial fluid between the perivascular spaces around penetrating blood vessels in the brain tissue called the parenchyma is thought to be an important part of the brain's glymphatic system for waste clearance. Due to the difficulty of making measurements in the parenchyma, fluid-dynamic models are employed to better understand this flow. We used an analytical solution for Darcy flow in a porous medium with line sources (representing arterioles) and line sinks (representing venules) to model the flow and hydraulic resistance for various arrangements of the vessels. Other models use a 1:1 ratio of arterioles to venules, but experimental data suggest that humans have a 2:1 ratio and mice have a 1:3 ratio. We find that the resistances produced by these ratios are significantly different, implying that a simple dipole is not an appropriate model of the flow. We calculated flows and resistances based on experimental measurements of the locations of arterioles and venules in rodent and primate brains. We also created idealized arrangements that maximize intervessel spacing, thus minimizing the resistance and required driving pressure, which can be used to estimate the resistance in the absence of data of the locations of the penetrating vessels.