Modeling the Slow Wave Shapes of Spreading Depression in a Rat Cortex: A Methodology for Seeking Physiological Parameters

Spreading depression (SD) consists of a transient significant suppression of the spontaneous neural electrical activity that spreads slowly across regions of the gray matter in a wave form. Nowadays, this phenomenon is being studied by means of mathematical and computational models to reproduce the main characteristics of SD. Given the high number of parameters and their unknown ranges of variation, the setting of parameters for current SD models is usually a hard task that must be addressed in order to make such models reproduce real data. In this paper, we present a 1-D model which is able to reproduce the most important characteristics of SD waves observed in laboratory experiments: the slow extracellular potential shift and extracellular ionic concentration variations regarding speed, shape, and amplitude. Such a reproduction is possible due to a methodology that we introduced to set the parameters of the SD models. The methodology allows the impact of each parameter on the results produced by the model and the range of parameters for which the model displays plausible behavior to be determined. The methodology also helps to identify features that the model cannot produce and it gives insights about what parts of the model should be modified to improve its capacities through the identification of parameters involved with each behavior.