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. 2023 Jul 21;19(7):e1010996.
doi: 10.1371/journal.pcbi.1010996. eCollection 2023 Jul.

Neural activity induces strongly coupled electro-chemo-mechanical interactions and fluid flow in astrocyte networks and extracellular space-A computational study

Marte J Sætra  1 , Ada J Ellingsrud  1 , Marie E Rognes  1
Affiliations

Neural activity induces strongly coupled electro-chemo-mechanical interactions and fluid flow in astrocyte networks and extracellular space-A computational study

Marte J Sætra et al. PLoS Comput Biol. .

Abstract

The complex interplay between chemical, electrical, and mechanical factors is fundamental to the function and homeostasis of the brain, but the effect of electrochemical gradients on brain interstitial fluid flow, solute transport, and clearance remains poorly quantified. Here, via in-silico experiments based on biophysical modeling, we estimate water movement across astrocyte cell membranes, within astrocyte networks, and within the extracellular space (ECS) induced by neuronal activity, and quantify the relative role of different forces (osmotic, hydrostatic, and electrical) on transport and fluid flow under such conditions. We find that neuronal activity alone may induce intracellular fluid velocities in astrocyte networks of up to 14μm/min, and fluid velocities in the ECS of similar magnitude. These velocities are dominated by an osmotic contribution in the intracellular compartment; without it, the estimated fluid velocities drop by a factor of ×34-45. Further, the compartmental fluid flow has a pronounced effect on transport: advection accelerates ionic transport within astrocytic networks by a factor of ×1-5 compared to diffusion alone.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Model schematics.
Illustration of brain tissue between two blood vessels with astrocytes (purple), neurons (grey), and ECS with neural activity in the center (A). The tissue is represented as a 1D domain of length 300 μm including ICS (astrocytes) and the ECS (B). Within each compartment, the model describes the dynamics of the volume fraction (α), the Na+, K+, and Cl− concentrations ([Na+], [K+], [Cl−]), the electrical potential (ϕ), and the hydrostatic pressure (p). Neuronal activity is implicitly represented by K+ and Na+ input currents (jinputK and jinputNa) in the input zone (of length 30 μm) and decay currents (jdecayK and jdecayNa) across the whole domain. Transmembrane currents include an inward rectifying K+ current (jKir), Na+ and Cl− leak currents (jleakK and jleakCl), and a Na+/K+ pump current (jpump). Intra- and extracellular currents (jik and jek) are driven by electrodiffusion and advection. Fluid can travel across the membrane (wm) and compartmentally in the intra- and extracellular space (ui and ue).
Fig 2
Fig 2. Electrical, chemical, and mechanical dynamics in the input zone during local neuronal activity.
The panels display the time evolution of the K+-injection current (A) and K+-decay current (B), changes in the ECS (C) and ICS (D) ion concentrations, changes in the ECS (E) and ICS (F) volume fractions, changes in the transmembrane hydrostatic pressure difference (G), and membrane potential (H) at x = 150 μm (center of the input zone). All changes are calculated from baseline values, which are listed in Methods. Panel I and J display a schematic overview of ionic dynamics and swelling at respectively t = 0 s and t = 200 s at x = 150 μm.
Fig 3
Fig 3. Interplay between transmembrane- and compartmental pressures and fluid velocities (M1).
The panels display a snapshot (at t = 200 s) of the spatial distribution of the changes in intra- and extracellular osmolarities (A), osmotic and hydrostatic pressure gradients across the glial membrane (B), transmembrane fluid velocity (C), changes in the intra- and extracellular hydrostatic pressures (D), intra- and extracellular superficial fluid velocities (E), and illustration of the flow pattern (F). All changes are calculated from baseline values, which are listed in Methods.
Fig 4
Fig 4. Comparison of osmotic pressures and ECS water potentials predicted by model scenarios M0, M1, and M2.
The upper panels display a snapshot of ICS osmolarities (A), ECS osmolarities (B), and osmotic pressures across the membrane (C). The lower panels display a snapshot of ECS solute potentials (D), ECS hydrostatic pressures (E), and ECS water potentials (F). All panels display the deviation from baseline levels at t = 200 s.
Fig 5
Fig 5. Fluid velocities predicted by model scenarios M2 and M3.
Spatial profiles of the total superficial fluid velocities (black dashed lines), together with their hydrostatic (dotted green lines), osmotic (yellow line), and electro-osmotic (solid green line) contributions at t = 200 s. The upper panels show the intra- (A) and extracellular (B) fluid velocities for model scenario M2. The lower panels show the intra- (C) and extracellular (D) fluid velocities for model scenario M3.
Fig 6
Fig 6. Compartmental ionic fluxes.
Spatial profiles of the total compartmental ionic fluxes (grey dashed lines), and their diffusive (dark green lines), electric drift (light green lines), and advective (yellow lines) components at t = 200 s for the different ionic species. Each panel additionally contains the advection/diffusion fraction (Fdiff) and the advection/electric drift fraction (Fdrift) for the associated ion species. Panels A-F display fluxes for modeling scenario M1, and panels G-L display fluxes for modeling scenario M3. All fluxes are multiplied by the volume fraction α.
Fig 7
Fig 7. Electrical, chemical, and mechanical dynamics during slow, ultraslow, and constant stimuli.
The panels display the time evolution of the K+-input current (A,B,C), extracellular potential (D,E,F), changes in the ECS K+ concentration (G,H,I), and changes in the ECS volume fraction (J,K,L), at x = 150 μm (center of the input zone) for input varying at 1 Hz (left column), input varying at 0.05 Hz (middle column), and constant input (right column) (see Methods for details). All simulations correspond to model scenario M3.
Fig 8
Fig 8. Compartmental fluid velocities during slow, ultraslow, and constant stimuli.
The upper panels display spatial profiles of the intracellular superficial fluid velocities at peak (light blue), average (blue), and nadir input (purple) for slow (1 Hz) (A), ultraslow (0.05 Hz) (B), and constant (C) stimuli. The lower panels display the time evolution of the maximum intracellular superficial fluid velocity for the slow (D), ultraslow (E), and constant (F) stimuli, plotted alongside the corresponding K+-input current (gray). The dotted markers in panels D–F correspond to the time points in panels A–C. Note that panels D–F show different time windows on the x-axes. All simulations were run for 250 s and correspond to model scenario M3.
Fig 9
Fig 9. Sensitivity analysis.
The maximum superficial fluid velocity, αiui, for different values of the compartmental permeability κ (A), membrane stiffness Km (B), membrane water permeability ηm (C), and input flux density jinputK (D) at t = 200 s for modeling scenarios M1 (blue dots) and M3 (green dots). The horizontal dashed lines mark the maximum value of αiui corresponding to the default values of the model parameters, marked with vertical dashed lines. The default value of κ was set to be the same in the ICS and ECS, and we changed the two simultaneously by the same amount.
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Grants and funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement #714892 (received by MER) and the Research Council of Norway (RCN) via FRIPRO grant agreement #324239 (EMIx, received by MER). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.