Fluid dynamics of cerebrospinal fluid flow in perivascular spaces

Abstract

The flow of cerebrospinal fluid along perivascular spaces (PVSs) is an important part of the brain's system for delivering nutrients and eliminating metabolic waste products (such as amyloid-β); it also offers a pathway for the delivery of therapeutic drugs to the brain parenchyma. Recent experimental results have resolved several important questions about this flow, setting the stage for advances in our understanding of its fluid dynamics. This review summarizes the new experimental evidence and provides a critical evaluation of previous fluid-dynamic models of flows in PVSs. The review also discusses some basic fluid-dynamic concepts relevant to these flows, including the combined effects of diffusion and advection in clearing solutes from the brain.

Keywords: cerebrospinal fluid; diffusion; fluid dynamics; glymphatic system; peristaltic pumping; perivascular spaces.

Figure 1.

Schematic diagram of the PVSs around a pial artery and a penetrating artery in the brain. (Online version in colour.)

Figure 2.

Periarterial flow in mouse pial arteries, as revealed by particle tracking (from Mestre et al. [21]). (a) Superimposed trajectories of tracked microspheres. (b) Time-averaged velocity field (green arrows), showing net flow in the direction of the blood flow. (c) Time-averaged flow speed. (d) Representative traces of the ECG and the root-mean-square flow velocity V_rms, showing synchrony with the heartbeat. (e) Representative traces of the ECG and the artery diameter, showing the shape of the wall wave driving the perivascular pumping. (Online version in colour.)

Figure 3.

Examples of the cross-sections of PVSs (green) around arteries (red), observed in vivo. (a) Pial artery (from [21]). (b) Penetrating artery (adapted from [40]). The white lines show fits to a simple, adjustable geometric model of the cross-section of the PVS, consisting of an elliptical outer wall and a circular artery (from Tithof et al. [25]). (Online version in colour.)

Figure 4.

(a) Taylor dispersion of a solute (blue) in steady, laminar pipe flow (Poiseuille flow, with velocity profile indicated by the arrows). The solute is spread by the velocity shear, while diffusion in the radial direction (red arrows) establishes a uniform radial distribution. The velocity shear continues to spread out the solute further downstream. (b) For comparison, the effect of diffusion alone in a (non-physical) uniform flow (without shear). (c) Taylor dispersion in a purely oscillatory flow: the velocity shear spreads out the solute, but only to an extent limited by the fluid particle paths, and there is no downstream transport. (Online version in colour.)

Figure 5.

Diffusion into a perivascular flow channel. Advection of the solute downstream by the mean flow of CSF in the PVS maintains the gradient $\mathbf{\nabla }C$ that drives diffusion of the solute into the PVS. (Online version in colour.)