Ion and transmitter movements during spreading cortical depression.

A reaction--diffusion system of equations whose components are the extracellular concentrations of K+, Ca++, Na+, Cl-, an excitatory neurotransmitter and an inhibitory neurotransmitter, is developed in order to model the movements of these substances through various kinds of membrane in brain structures. Expressions are derived from probabilistic arguments for the conductances induced in subsynaptic membrane by transmitter substances at various concentrations, for one-way active transport rates and for an exchange pump rate. These expressions are employed in the reaction terms of the system. The meaning of the many constants is explained and, with appropriate choices for their values, the model predicts subthreshold responses to small enough local elevations of KCl or glutamate and stable propagating SD waves if the local elevations of these chemicals is sufficient. The SD waves consist of elevated K+ and transmitter substances and diminished Ca++, Na+ and Cl-, the velocity of propagation in cortex being about 0.6 mm/min. This is in the experimental range, the K+-amplitude being 17 mM relative to a baseline of 3 mM, as the model developed ignores the effects of action potentials. There is no SD response to either NaCl or GABA. The effects of no K+ and no glutamate diffusion are investigated, both being manifest as a failure in propagation of the stable SD waves. The wave solutions are analysed in terms of phase portraits. The roles of various amino acid uptake and release processes by neurons and glia are discussed, as are the complications with regard to their incorporation in a model for SD. The roles of neurons and glia are analysed and the six basic fluxes of K+ are outlined. It is postulated that under some circumstances, in cortex treated with TTX, there may be practically no transmitter release, but SD may propagate if TTX does not completely abolish gNa for nonsynaptic membrane, a corresponding system of model equations being developed. The data and ideas of K+-based and glutamate-based SD of Van Harreveld are discussed and interpreted in terms of which reaction terms are operative in the K+ equation. An appendix contains the values of the parameters used in the numerical calculations.