Metabifurcation analysis of a mean field model of the cortex

Abstract

Mean field models (MFMs) of cortical tissue incorporate salient features of neural masses to model activity at the population level. One of the common aspects of MFM descriptions is the presence of a high dimensional parameter space capturing neurobiological attributes relevant to brain dynamics. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two families. After investigating and characterizing these, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli, distribution of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs significantly between families, we are able to show how metamorphoses between the families can be brought about by exogenous stimuli. We unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods. They emerge when the parameter space is partitioned according to bifurcation responses. This partitioning cannot be achieved by the investigation of only a small number of parameter sets, but is the result of an automated bifurcation analysis of a representative sample of 73,454 physiologically admissible sets. Our approach generalizes straightforwardly and is well suited to probing the dynamics of other models with large and complex parameter spaces.