Multiscale Computer Modeling of Spreading Depolarization in Brain Slices

Abstract

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 associated with several neurological conditions. We developed multiscale (ions to tissue slice) computer models of SD in brain slices using the NEURON simulator: 36,000 neurons (2 voltage-gated ion channels; 3 leak channels; 3 ion exchangers/pumps) in the extracellular space (ECS) of a slice (1 mm sides, varying thickness) with ion (K + , Cl − , Na + ) and O 2 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: 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 due to relative hypoxia in the slice core, exacerbated by SD in a pathological cycle; 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. SignificanceSpreading depolarization (SD) is a slow moving wave of electrical and ionic imbalances in brain tissue and is a hallmark of several neurological disorders. We developed a multiscale computer model of brain slices with realistic neuronal densities, ions, and oxygenation. Our model shows that SD is exacerbated by and causes hypoxia, resulting in strong SD dependence on slice thickness. Our model also predicts that the velocity of SD propagation is not dependent on its initiation, but instead on tissue properties, including the amount of extracellular space and the total area of neuronal membrane, suggesting faster SD following ischemic stroke or traumatic brain injury.

An electrodiffusive network model with multicompartmental neurons and synaptic connections

“…With single-cell compartmental models, geometrically explicit models, and domain-type tissue models already in the toolbox, the neuroscience community currently lacks an electrodiffusive network model that allows tracking of individual, compartmentalized cells. Although a few models exist that account for ion concentration dynamics in neuronal networks to some extent, these models take shortcuts that compromise biophysical consistency [32][33][34][35][36][37][38]. These shortcuts are taken by ignoring the combined effect of diffusion and electric drift on ionic transport, or neglecting the transport of ions through the extracellular space altogether.…”

“…Several existing models account for ion concentration dynamics, see e.g. [1, 9–38]. A particular subset of these models, sometimes referred to as electrodiffusive neuron models, consider both diffusion and electric drift in the transport of ions [1, 22–31].…”

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics

“…This assumption is generally justified by the brain's inherent mechanisms, such as pumps and cotransporters, that work to uphold ion concentration levels close to baseline values. However, to investigate scenarios where ion concentrations may change significantly-such as in epilepsy and spreading depression [2,3]-certain models incorporate ion concentration dynamics and consider its influence on neuronal activity (see e.g., [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]).…”