Interconnected Neural, Vascular, and Metabolic Dysfunction during Cortical Spreading Depression: A Mathematical Model

Summary of model components Neuronal behavior determined by conductances, Na + /K + ATPaseATPase behavior governed by availability of oxygenOxygen delivery determined by blood flow and thus arterial diameterArterial diameter driven by extracellular [K + ]Extracellular [K + ] buffered by astrocytes, generated by neurons Effect of vascular parameters on CSD Duration of CSD for different vascular responses. Shown are CSD durations plotted against percent dilation b, constriction parameter a, (this parameter has the units of mM and is a measure of how rapidly the effective radius decreases as [K + ] changes) and oxygen coupling constant γ. Duration is defined by the length of time that potas-sium concentration is elevated to a level greater than 6 mM. Speed of CSD for different vascular responses. Increasing the constriction parameter a makes the vessel less sensitive to potassium, weakening the resulting constriction. The speed decreases as [K + ] increases from 30mM up tp 80mM, but increasing the amount of dilation by inreasing b seems to have a greater effect.