Hydraulic resistance of perivascular spaces in the brain

Abstract

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...

Fluid dynamics in syringomyelia cavities: Effects of heart rate, CSF velocity, CSF velocity waveform and craniovertebral decompression

“…In their view, PVS are simply regions in the SAS where resistance to flow is lower. More puzzling, in recent papers including researchers behind the glymphatic theory and paravascular inflow, Mestre et al [55], Tithof et al [79] and Ray et al [63] have used the term perivascular space to describe these channels.…”

Intracranial pressure elevation alters CSF clearance pathways

“…However, up to this point, experimental studies able to measure paravascular flow velocities have been limited to rodents, and as such are not directly comparable to our model. According to Tithof et al [66], 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 [66], and thus likely to increase PVS velocities by a similar factor in our model.…”

“…According to Tithof et al [66], 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 [66], and thus likely to increase PVS velocities by a similar factor in our model. In addition, peak velocity in a concentric cylinder is double that of the mean velocity, which possibly may increase our velocity estimates of up to 5.66 µm/s in the models by another factor of approximately two.…”

Peristaltic pumping in thin non-axisymmetric annular tubes

“…Tithof et al. (2019) have shown that the various shapes of the cross-sections of perivascular spaces around surface and penetrating arteries in the mouse brain, observed in vivo , can be fit quite well with a simple geometric model, consisting of a circular inner boundary (the artery) and an elliptical outer boundary (the outer wall of the PVS), allowing the circle to be eccentric with respect to the ellipse. We adopt the same adjustable geometric model in our present study of peristaltic pumping (see figure 1).…”

“…Tithof et al. (2019) computed the hydraulic resistance for annular channels with this model cross-section, varying the ellipticity and eccentricity. We also compute the velocity profile and hydraulic resistances for steady Poiseuille flow for several cases and compare them with the results of Tithof et al.…”