Multiscale Computer Modeling of Spreading Depolarization in Brain Slices

Spreading depolarization (SD) is a slow-moving wave of neuronal depolarization accompanied by a breakdown of ion concentration homeostasis, followed by long periods of neuronal silence (spreading depression), and is associated with several neurologic conditions. We developed multiscale (ions to tissue slice) computer models of SD in brain slices using the NEURON simulator: 36,000 neurons (two voltage-gated ion channels; three leak channels; three ion exchangers/pumps) in the extracellular space (ECS) of a slice (1 mm sides, varying thicknesses) with ion (K⁺, Cl^-, Na⁺) and O₂ diffusion and equilibration with a surrounding bath. Glia and neurons cleared K⁺ from the ECS via Na⁺/K⁺ pumps. SD propagated through the slices at realistic speeds of 2-4 mm/min, which increased by as much as 50% in models incorporating the effects of hypoxia or propionate. In both cases, the speedup was mediated principally by ECS shrinkage. Our model allows us to make testable predictions, including the following: (1) SD can be inhibited by enlarging ECS volume; (2) SD velocity will be greater in areas with greater neuronal density, total neuronal volume, or larger/more dendrites; (3) SD is all-or-none: initiating K⁺ bolus properties have little impact on SD speed; (4) Slice thickness influences SD because of relative hypoxia in the slice core, exacerbated by SD in a pathologic cycle; and (5) SD and high neuronal spike rates will be observed in the core of the slice. Cells in the periphery of the slice near an oxygenated bath will resist SD.