Analysis of Cortical Spreading Depression in Brain with Multiscale Mathematical Models

The present study aims at modeling the cortical spreading depression (CSD) propagation in brain considering two different approaches available in the literature: (a) a simplified model consisting of six coupled equations of the reaction-diffusion type in two space dimensions and (b) a one-dimensional, more complex neuronal model comprising of ionic currents and ionic pumps. A study has been conducted to quantify the effects of varying extracellular potassium concentrations on the propagation of CSD in the multiscale reaction-diffusion model by monitoring the respective changes in the extracellular and intracellular concentrations of sodium, chlorine and calcium ions, in addition to evaluating the changes in the generated membrane potentials. In the multiscale neuronal model, the influence of gated conductance on the intracellular and extracellular potassium concentrations of the sodium and potassium and the membrane potential has been reported. The study revealed that the variation in gated conductance results in an increase of the pump currents that leads to the spatio-temporal variations of extracellular potassium.