Abstract
Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarizations, CSD also involves significant changes in perfusion and metabolism—aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD. In our model, the sodium-potassium–ATPase, mainly responsible for ionic homeostasis and active during CSD, operates at a rate that is dependent on the supply of oxygen. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree with an effective local vessel radius that is controlled by the extracellular potassium concentration. We show that during CSD, the metabolic demands of the cortex exceed the physiological limits placed on oxygen delivery, regardless of vascular constriction or dilation. However, vasoconstriction and vasodilation play important roles in the propagation of CSD and its recovery. Our model replicates 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 the contribution of the vasculature. Our results also help explain some of the variability of CSD between species and even within the same animal. These results have clinical and translational implications, as they allow for more precise in vitro, in vivo, and in silico exploration of a phenomenon broadly relevant to neurological disease.
Highlights
Cortical spreading depression (CSD) is a self-propagated depolarization that occurs in the gray matter of many species [1]
There is strong evidence that CSD is responsible for migraine aura [3,4,5], a sensory hallucination associated with migraine attack
We used a minimal amount of potassium to induce CSD, finding that for injections of Gaussian boluses with 120 micron width, a Kz concentration of 15 mM was sufficient to induce CSD
Summary
Cortical spreading depression (CSD) is a self-propagated depolarization that occurs in the gray matter of many species [1]. There is strong evidence that CSD is responsible for migraine aura [3,4,5], a sensory hallucination associated with migraine attack. CSD has been associated with massive changes in cortical perfusion. The magnitudes of these changes vary by animal species, but significant decreases and increases in blood flow volume occur in all species tested [7,8,9]. Common to all species tested is a mismatch in the delivery of substrates to meet metabolic demands, resulting in a derangement of neurovascular coupling [10,11]
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