In this talk presented at the Mathematical Neuroscience Subgroup Minisymposium I will discuss a numerical analysis of the steady-state solutions of a neural field model of the corticothalamic system. The independent synaptic connections of the corticothalamic model define an eight-dimensional parameter space, while specific combinations of these connections parameterize intracortical, corticothalamic, and intrathalamic loops.
The first part of the analysis consists of a systematic identification of multistable regions for physiological parameter ranges representing normal arousal waking states in adult humans. Parameter values have been derived from human electroencephalographic recordings (EEG). The key results are the confirmation of the existence of up to five steady-state solutions, up to three of which are linearly stable. The presence of multiple stable steady-state solutions implies that the system has enough degrees of freedom to capture multiple operating points (e.g., mutiple global brain states). Indeed, two out of the three linearly stable steady-state equilibria represent two waking modes for adult human physiology while resting with the eyes closed. These two modes are termed the low- and high- waking modes.
While the low-waking mode has been previously identified with normal brain activity during quiet wakefulness, the high-waking mode has not been fully characterized. The second part of the analysis focus on (i) the spectral features of high-waking mode states; (ii) the nonlinear attractors between the two waking modes; and, (iii) the switching dynamics between the low- and high-waking modes using small amplitude and bandlimited random perturbations.
We argue that the high-waking mode may represent hyperarousal waking states. This result opens up the possibility to predict and identify subtypes of primary insomnia in which cortical hyperarousal is the main hallmark from human neuroimaging data.