<p>We present a novel astro-neural-field population model with application to migraine-related cortical spreading depolarization. The model is composed of four spatio-temporal state variables: excitatory and inhibitory membrane potentials, astrocytic potassium uptake recruitment, and extracellular potassium concentration. Extending a previous neural field model, we incorporate activity-dependent astrocytic potassium clearance via a nonlinear term coupled to astrocyte dynamics. The astrocyte transfer function, like its neural counterpart, exhibits three regimes governed by extracellular potassium, capturing its effect on clearance. This yields a more comprehensive framework, better fits experimental data, and provides new insights into the mechanisms of cortical spreading depolarization.</p>