Background Periarterial spaces PASs are annular channels that surround arteries in the brain and contain cerebrospinal fluid CSF a flow of CSF in these channels is thought to be an important part of the brains system for clearing metabolic wastes. 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. Methods We model PAS 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 NavierStokes 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 PASs 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 PAS cross-sectional area occurs when the ellipse is elongated and intersects the circle, dividing the PAS 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 PASs observed in vivo, and it greatly overestimates the hydraulic resistance of the PAS. Our parameterization can be used to incorporate more realistic resistances into hydraulic network models of flow of cerebrospinal fluid in the brain.
Journal Article - Open Access
Fluids and Barriers of the CNS , 16, 19, 01 Jan 0001, 01 Jan 0001, This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons .org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.