Background Perivascular spaces (PVSs) are annular channels that surround blood vessels and carry cerebrospinal fluid through the brain, sweeping away metabolic waste. In vivo observations reveal that they are not concentric, circular annuli, however: the outer boundaries are often oblate, and the blood vessels that form the inner boundaries are often offset from the central axis.Methods We model PVS cross-sections as circles surrounded by ellipses and vary the radii of the circles, major and minor axes of the ellipses, and two-dimensional eccentricities of the circles with respect to the ellipses. For each shape, we solve the governing Navier-Stokes equation to determine the velocity profile for steady laminar flow and then compute the corresponding hydraulic resistance.Results We find that the observed shapes of PVSs have lower hydraulic resistance than concentric, circular annuli of the same size, and therefore allow faster, more efficient flow of cerebrospinal fluid. We find that the minimum hydraulic resistance (and therefore maximum flow rate) for a given PVS cross-sectional area occurs when the ellipse is elongated and intersects the circle, dividing the PVS into two lobes, as is common around pial arteries. We also find that if both the inner and outer boundaries are nearly circular, the minimum hydraulic resistance occurs when the eccentricity is large, as is common around penetrating arteries.Conclusions The concentric circular annulus assumed in recent studies is not a good model of the shape of actual PVSs observed in vivo , and it greatly overestimates the hydraulic resistance of the PVS. Our parameterization can be used to incorporate more realistic resistances into hydraulic network models of flow of cerebrospinal fluid in the brain. Our results demonstrate that actual shapes observed in vivo are nearly optimal, in the sense of offering the least hydraulic resistance. This optimization may well represent an evolutionary adaptation that maximizes clearance of metabolic waste from the brain.*   CSF    :   cerebrospinal fluid    PVS    :   perivascular space

Hydraulic resistance of perivascular spaces in the brain