Metabolism plays a central role in the cortical spreading depression: Evidence from a mathematical model. (7th February 2020) - Capo-Rangel, G; Gerardo-Giorda, L; Somersalo, E; Calvetti, D
Highlights: A novel mathematical model coupling metabolic activity of neurons and astrocytes with electrophysiology to study cortical spreading depolarization (SD) is developed. The model predictions clearly demonstrate that changes in electrophysiology uncoupled with the underlying metabolism cannot trigger the repeated depolarization events observed experimentally. Coupled with metabolism, the model is able to produce spontaneous repetitions of spreading depolarization events, thus confirm the key role of the metabolism in SD. There is mathematical evidence that increased astrocytic density lowers the spontaneous SD repetition frequency, supporting the hypothesized role of extracellular potassium concentration in SD events, as well as astrocytes' role in potassium clearance. Abstract: The slow propagating waves of strong depolarization of neural cells characterizing cortical spreading depression, or depolarization, (SD) are known to break cerebral homeostasis and induce significant hemodynamic and electro-metabolic alterations. Mathematical models of cortical spreading depression found in the literature tend to focus on the changes occurring at the electrophysiological level rather than on the ensuing metabolic changes. In this paper, we propose a novel mathematical model which is able to simulate the coupled electrophysiology and metabolism dynamics of SD events, including the swelling of neurons and astrocytes and the concomitant shrinkage of extracellular space. The simulations show that the metabolic coupling leads to spontaneous repetitions of the SD events, which the electrophysiological model alone is not capable to produce. The model predictions, which corroborate experimental findings from the literature, show a strong disruption in metabolism accompanying each wave of spreading depression in the form of a sharp decrease of glucose and oxygen concentrations, with a simultaneous increase in lactate concentration which, in turn, delays the clearing of excess potassium in extracellular space. Our model suggests that the depletion of glucose and oxygen concentration is more pronounced in astrocyte than neuron, in line with the partitioning of the energetic cost of potassium clearing. The model suggests that the repeated SD events are electro-metabolic oscillations that cannot be explained by the electrophysiology alone. The model highlights the crucial role of astrocytes in cleaning the excess potassium flooding extracellular space during a spreading depression event: further, if the ratio of glial/neuron density increases, the frequency of cortical SD events decreases, and the peak potassium concentration in extracellular space is lower than with equal volume fractions.