Interstitial solute transport in 3D reconstructed neuropil occurs by diffusion rather than bulk flow

Abstract

The brain lacks lymph vessels and must rely on other mechanisms for clearance of waste products, including amyloid [Formula: see text] that may form pathological aggregates if not effectively cleared. It has been proposed that flow of interstitial fluid through the brain's interstitial space provides a mechanism for waste clearance. Here we compute the permeability and simulate pressure-mediated bulk flow through 3D electron microscope (EM) reconstructions of interstitial space. The space was divided into sheets (i.e., space between two parallel membranes) and tunnels (where three or more membranes meet). Simulation results indicate that even for larger extracellular volume fractions than what is reported for sleep and for geometries with a high tunnel volume fraction, the permeability was too low to allow for any substantial bulk flow at physiological hydrostatic pressure gradients. For two different geometries with the same extracellular volume fraction the geometry with the most tunnel volume had [Formula: see text] higher permeability, but the bulk flow was still insignificant. These simulation results suggest that even large molecule solutes would be more easily cleared from the brain interstitium by diffusion than by bulk flow. Thus, diffusion within the interstitial space combined with advection along vessels is likely to substitute for the lymphatic drainage system in other organs.

Keywords: AQP4; extracellular space; glymphatic; interstitial fluid; simulation.

Fig. 1.

Model systems and microscopic structure of the extracellular volume. (A) Schematic illustration of the EM reconstruction. Tunnels are in cyan and sheets in red. (B) Submicrometer partition of the EM reconstruction showing typical sizes of the 84 million tetrahedrons used in the simulation. (C and D) EM reconstruction from Kinney et al. (18) with a small tunnel volume fraction (C) and with a larger tunnel volume fraction (D). Both C and D have extracellular volume fractions of about $20\%$ ($20.1\%$ and $20.7\%$, respectively). (E) Schematic illustration showing the cylinder model of the paravascular space and solutes (solid circles) in the surrounding interstitial space. (F) Schematic illustration showing the pial surface model.

Fig. 2.

Bulk flow velocity through the EM reconstruction from Kinney et al. (18). A pressure gradient of 1 mmHg/mm is applied in the vertical ($z$) direction. (A) The geometry with a low tunnel volume fraction. The cross-sections are at depth $z=\mathrm{\hspace{0.17em}1.5}\mu \text{m}$ and $z=\mathrm{\hspace{0.17em}3.5}\mu \text{m}$. For clarity only streamlines originating from a small circle with radius $0.1\mu \text{m}$ at $z=\mathrm{\hspace{0.17em}0}$ are shown. (B) Distribution of the $z$ component of flow velocities through different cross-sectional extracellular areas of the geometry in A, with the corresponding depth of the plane expressed in the key. All traces are normalized to the mean extracellular cross-sectional area. The mean distribution is shown in black. (C) The percentage of water which has reached $100\mu \text{m}$ as a function of time (Inset), assuming each streamline to be straight, along the $z$ axis and with a constant velocity given by the velocity distribution in B. (D–F) Same as A–C for the EM reconstruction with a higher tunnel volume fraction, but approximately the same extracellular volume fraction.

Fig. 3.

Color plot showing velocity for the bulk flow from arteriole (red, solid circle) to venule (blue, solid circle) for the highest permeability $\kappa =14.69{\text{nm}}^2$, assumed viscosity $\mu =0.8\text{mPa}\cdot \text{s}$, and extracellular volume fraction of 20%. Diameter is 30 $\mu \text{m}$ for both arteriole and venule, and their center-to-center distance is 280 $\mu \text{m}$ (6, 28). The line plots in red/pink and black/gray correspond to the absolute value of the velocity profiles along the red ($x$ axis) and black ($y$ axis) lines in the color plot, and the two colors correspond to the two different permeabilities derived from the geometries with high tunnel volume fraction and low tunnel fraction. The pressure difference between the two vessel surfaces facing each other is 1 mmHg/mm. Lower Left Inset illustrates the cylindrical geometry of the vessels.

Fig. 4.

(A–D) Diffusion from neuropil toward (A and C) a cylindrical vessel (C, Inset) and toward (B and D) the cortical surface (D, Inset). At time $t=\mathrm{\hspace{0.17em}0}$ the solute is assumed to be evenly spread throughout the interstitial space, and the cortical surface/cylinder is assumed to have zero concentration of the solute. The different colors correspond to effective diffusion coefficients for potassium ions (green), 3 kDa Texas Red Dextran (red), and 70 kDa dextran (blue). (A) Concentration profile around a vessel for three time instances. (B) Concentration profile below the cortical surface for three time instances. (C) Concentration of the three solutes as a function of time at a distance 100 $\mu \text{m}$ from the cylinder center. (D) Concentration of the three solutes as a function of time 100 $\mu \text{m}$ below the cortical surface.

Fig. 5.

Péclet numbers. Shown are effective diffusion coefficients ($D^{\ast }$) from Syková and Nicholson (19).