Article Figures & Data
Figures
- Figure 1.
Multiscale model expanded. Tissue scale: a few of the 36 ⋅ 103 neurons (pink circles) embedded in the ECS of a brain slice submerged in a bath solution where ion and O2 concentrations were held constant. Glia are not explicitly modeled, but instead were represented as a field of sinks in every ECS voxel. Cell scale: each neuron had ion channels, 2 coexchangers; Na+/K+ pump (asterisk indicates ATP/O2 dependence). Ions were well mixed within each neuron (no intracellular diffusion). Protein scale: table (right) indicates species that control the activity of the intrinsic mechanisms in neurons and in glial field. Ion scale: ions diffused between ECS voxels by Fick’s law using diffusion coefficients in Table 1.
- Figure 2.
A small bolus of applied K+ initiates spreading K+ and depolarization waves in perfused slice. A, [K+]ECS averaged across slice depth (400 μm) at 4 time points during SD. B, Spike raster plot of 250 randomly selected neurons (of 36 ⋅103) during SD. Cells are ordered on y-axis by their radial distance from the center of the K+ bolus. Blank area under spikes represents region of spreading depression. Baseline values: [O2] = 0.1 mm; αECS = 0.2; λECS = 1.6; [Cl–]ECS = 130.0 mm; [Cl–]i = 6.0 mm.
- Figure 3.
Diameter (bottom, x-axis) and concentration (top, x-axis) of the K+ bolus had minor effects on K+ wave speed. Mean and SDs (n = 5) for K+ wave speed versus bolus diameter (solid line; bolus [K+]ECS = 70 mm; 5 random cell position initializations) and versus bolus concentration (dashed line; diameter, 200 μm).
- Figure 4.
Concentrations at 7 radial locations measured during SD in perfused 400 μm slice. A, Cell within the K+ bolus (37.5 μm) produced a single spike; cells farther out fired a burst. Cells remained in depolarization block for the remainder of the simulation (10 s). B–D, Intracellular ion concentrations. E–H, Extracellular O2 and ion concentrations in neighboring ECS voxels. Movie 1 shows extracellular ion and O2 concentrations across the slice, as well as neuronal spiking (white dots) from 250 neurons during the course of SD (most easily seen with slowed playback).
- Figure 5.
Hypoxia, propionate, and dynamic ECS increased SD speed principally through αECS reduction. A, Radial K+ wave position over time during SD in perfused (Movie 1), hypoxic, HSD (Movie 2), propionate conditions, and with dynamic changes in
- Figure 6.
K+ wave propagation speed proportional to total neuronal surface area in slice. SD initiated in perfused and hypoxic slices (no reperfusion) by introducing a 100-μm-radius central 70 mm spherical K+ bolus. A–E, Effects of varying S/V of each cell while maintaining a constant βnrn (A); varying βnrn while keeping S/V constant, thus allowing Snrn to vary (B); varying cell density while keeping constant Snrn and volnrn, thus allowing βnrn to vary (C); and varying cell density while keeping βnrn and S/V constant, thus allowing Snrn and volnrn to vary (D). E, Pooled results: K+ wave speed increased linearly with total neuronal surface area in both perfused and hypoxic slices. Hypoxia increased wave speed across conditions (0 speed indicates no SD).
- Figure 7.
Slice thickness effects on SD propagation. K+ wave speed during SD in perfused and hypoxic slices of various thicknesses. SD could not be initiated in very thin (100 μm) slices when perfused but could in hypoxic slices. For perfused slices, K+ wave speed increased with slice thickness between 200 and 400 μm then saturated for slices of greater thickness. A similar pattern was observed in the hypoxic slices with consistently faster K+ wave speeds compared with in perfused slices.
- Figure 8.
Depth dependence of SD propagation in 400-μm-thick perfused slice. A, Spread of K+ wave through slice core (±50 μm from center). B, Wave of mildly elevated K+ reached the periphery (within 50 μm of bath) from the central bolus. C, Spread of SD through the slice core. Voltages in slice core (color map) with spike rasters for 120-cell subset overlaid in white. Neurons in the core showed typical SD voltage dynamics (bursting followed by depolarization block). D, Voltages and raster at periphery; cells show regular spiking patterns at 10–70 Hz (Vmemb averaged across all cells in 25 × 25 × 100 μm voxels at center or periphery).
Tables
- Table 1
Diffusion coefficients and baseline concentrations for ions and O2 in perfused slice (Samson et al., 2003; Haynes, 2014; Wei et al., 2014)
Species D
(⋅10–5 cm2/s)Intracellular
concentration (mm)ECS
concentration (mm)K+ 2.62 140.0 3.5 Na+ 1.78 18.0 144.0 Cl– 2.10 6.0 130.0 O2 3.30 0.1 0.1
Movies
- Movie 1.
Extracellular ion and O2 concentrations across the slice averaged over depth, as well as neuronal spiking (white dots) from 250 neurons during the course of SD in a perfused slice. The spread of spiking and the K+ wave can be seen in real time. We recommend downloading the file and using slower playback to visualize the spread of hypoxia.
- Movie 2.
Extracellular ion and O2 concentrations across the slice averaged over depth, as well as neuronal spiking (white dots) from 250 neurons during the course of hypoxic SD-like depolarization. The spread of spiking and the K+ wave can be seen in real time. We recommend downloading the file and using slower playback to visualize the delay between initiating the simulation and the spread of the K+ wave.
Extended Data 1
Simulation code: our tissue-scale model of SD in brain slices is available on GitHub. We used the NEURON simulator reaction-diffusion framework to implement embed thousands of neurons (based on the model from Wei et al., 2014) in the extracellular space of a brain slice, which is itself embedded in an bath solution. We initiated SD in the slice by elevating extracellular K+ in a spherical region at the center of the slice. The effects of hypoxia and propionate on the slice were modeled by appropriate changes to the volume fraction and tortuosity of the extracellular space and oxygen/chloride concentrations. Users need to install NEURON, and we recommend using MPI to parallelize simulations. Download Extended Data 1, ZIP file.
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