Hydraulic resistance of periarterial spaces in the brain

Abstract

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 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. 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 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 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. 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.

Intracranial pressure elevation alters CSF clearance pathways

“…According to Tithof et al [91], PVS are not concentric cylinders, but rather form ellipses around vessels to minimize resistance. This geometrical change along all vessels may decrease resistance by a factor of 2-3 [91], and thus likely increase PVS velocities by a similar factor in some of our models.…”

“…According to Tithof et al [91], PVS are not concentric cylinders, but rather form ellipses around vessels to minimize resistance. This geometrical change along all vessels may decrease resistance by a factor of 2-3 [91], and thus likely increase PVS velocities by a similar factor in some of our models. In addition, peak velocity in a concentric cylinder is double that of the mean velocity, which possibly may increase our velocity estimates in some of the models by another factor of approximately two.…”

Arterial pulsations drive oscillatory flow of CSF but not directional pumping

“…The phase difference between the arterial wall velocity and the downstream fluid velocity (axial velocity, ) remained the same throughout the length of the domain. Flow resistance ( ) of a tube with an annular cross-section decreases with approximately the fourth power of the internal radius 26 .…”

“…We found that a very small pressure difference, 0.01 mmHg across the length of the PVS (5 mm), was sufficient to drive a mean downstream speed of 24.4µm/sec (Fig 4g), close to the mean flow speed observed in vivo 7 (Fig 4h). The pressure difference value was also found using equations derived in another recent theoretical study that estimated the flow resistance of paravascular spaces 26 . Such a small pressure difference is practically impossible to measure in live animals, due to the lack of instruments sensitive to such small changes 43,44 .…”

“…For the 3D simulations presented in Fig 3 and 4, we created the cross section of the PVS to resemble the geometries observed in vivo 7,26 . The inner wall of the cross section is a circle of radius R1.…”