Hydraulic resistance of perivascular spaces in the brain

Abstract

Perivascular spaces (PVSs) are annular channels that surround arteries and carry cerebrospinal fluid into 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 arteries that form the inner boundaries are often offset from the central axis. Here we show 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. To calculate hydraulic resistance, we parameterize PVS cross-sections as circles surrounded by ellipses, varying 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 the corresponding hydraulic resistance. 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 circular, the minimum hydraulic resistance occurs when the eccentricity is large, as is common around penetrating arteries. The circular, concentric annuli assumed in recent studies maximize hydraulic resistance and therefore minimize flow. Our parameterization can incorporate more realistic resistances into hydraulic network models of flow of cerebrospinal fluid in the brain.\n\nSignificance StatementRecent experiments show that there is bulk flow of cerebrospinal fluid in brain perivascular spaces (PVSs) in the direction of the blood flow, driven by pulsations of arterial walls due to the heartbeat. Published hydraulic network models have argued against such a flow due to the purported high hydraulic resistance of the system. Here we show that these high resistances are due to misrepresentations of the size and shape of PVSs. We present an adjustable model PVS that can match closely the actual shapes observed in vivo and show that these shapes are often 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.