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Cortical spreading depression (CSD) is a slow-moving ionic and metabolicdisturbance that propagates in cortical brain tissue. In addition to massivecellular depolarization, CSD also involves significant changes in perfusion andmetabolism -- aspects of CSD that had not been modeled and are important totraumatic brain injury, subarachnoid hemorrhage, stroke, and migraine.  In this study, we develop a mathematical model for CSD where we focus onmodeling the features essential to understanding the implications ofneurovascular coupling during CSD. In our model, the sodium-potassium--ATPase,mainly responsible for ionic homeostasis and active during CSD, operates at arate that is dependent on the supply of oxygen. The supply of oxygen isdetermined by modeling blood flow through a lumped vascular tree with aneffective local vessel radius that is controlled by the extracellular potassiumconcentration. We show that during CSD, the metabolic demands of the cortexexceed the physiological limits placed on oxygen delivery, regardless ofvascular constriction or dilation. However, vasoconstriction and vasodilationplay important roles in the propagation of CSD and its recovery. Our modelreplicates the qualitative and quantitative behavior of CSD --vasoconstriction, oxygen depletion, extracellular potassium elevation,prolonged depolarization -- found in experimental studies.  We predict faster, longer duration CSD in vivo than in vitro due to thecontribution of the vasculature. Our results also help explain some of thevariability of CSD between species and even within the same animal. Theseresults have clinical and translational implications, as they allow for moreprecise in vitro, in vivo, and in silico exploration of a phenomenon broadlyrelevant to neurological disease.

A mathematical model of the metabolic and perfusion effects on cortical spreading depression