Abstract
BackgroundPeriarterial 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 brain’s 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.MethodsWe 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 Navier–Stokes equation to determine the velocity profile for steady laminar flow and then compute the corresponding hydraulic resistance.ResultsWe 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.ConclusionsThe 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. 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.
Highlights
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 brain’s system for clearing metabolic wastes
The eccentric circular annulus The eccentric circular annulus is a good model for the PASs around some penetrating arteries, so it is useful to show how the volume flow rate and hydraulic resistance vary for this model
In order to understand the glymphatic system, and various effects on its operation, it will be very helpful to develop a predictive hydraulic model of CSF flow in the PASs. Such a model must take into account two important recent findings: (i) the PASs, as measured in vivo, are generally much larger than the size determined from post-fixation data [7, 8, 36] and offer much lower hydraulic resistance; and (ii) the concentric circular annulus model is not a good geometric representation of an actual PAS, as it overestimates the hydraulic resistance
Summary
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 brain’s system for clearing metabolic wastes. The in vivo experimental methods of Mestre et al [8] enable measurements of the size and shape of the perivascular spaces, the motions of the arterial wall, and the flow velocity field in great detail With these in vivo measurements, direct simulations can in principle predict the observed fluid flow by solving the Navier–Stokes (momentum) equation. Development of a fully-resolved fluid-dynamic model that captures CSF transport through the entire brain is beyond current capabilities for two reasons: (i) the very large computational cost of such a simulation, and (ii) the lack of detailed knowledge of the configuration and mechanical properties of the various flow channels throughout the glymphatic pathway, especially deep within the brain. We note that these limitations and the modest number of publications modeling CSF transport through the brain are in contrast with the much more extensive body of research modeling CSF flow in the spinal canal, which has pursued modeling based on idealized [21,22,23], patient-specific [24, 25], and in vitro [26] geometries (see the recent review articles [27,28,29])
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