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. 3]. Experiments have shown that tracers injected into the subarachnoid space are 6 transported preferentially into the brain through periarterial spaces at rates much 7 faster than can be explained by diffusion alone [4, 5, 6]. Recent experimental results 8 [7, 8] now show unequivocally that there is pulsatile flow in the perivascular spaces 9 around pial arteries in the mouse brain, with net (bulk) flow in the same direction 10 as the blood flow. These in vivo measurements support the hypothesis that this flow 11 is driven primarily by "perivascular pumping" due to motions of the arterial wall 12 synchronized with the cardiac cycle [8]. From the continuity equation (expressing 13 conservation of mass), we know that this net flow must continue in some form 14 through other parts of the system (e.g., along PVSs around penetrating arteries, 15 arterioles, capillaries, venules). The in vivo experimental methods of Mestre et al.
16[8] now enable measurements of the size and shape of the perivascular spaces, the 17...