The brain is a complex system with a diverse hierarchy of spatial and temporal scales. Single neurons at a spatial scale of tens of micrometers interact with each other building a mesoscopic self-organised entity at a spatial scale of few millimetres. This entity is called neuronal patch, neural column in the cortex or just neural population. Moreover, single neurons evolve at various temporal scales, ranging from few milliseconds to hundreds of milliseconds and the mesoscopic neural population evolves on a slower range of time scale between 20 milliseconds and 1 second.
The diverse temporal scales of mesoscopic population activity can be observed experimentally in electroencephalographic data (EEG) measured as voltages on the scalp. Their corresponding power spectrum reflects well the different neural time scales and reveals the neural state of the cortex. In general anaesthesia, the EEG power spectrum accompanies the state of consciousness (i.e. the ability to respond to external stimuli) of the subject during surgery. For instance, in human surgery, increasing the concentration of the anaesthetic drug propofol changes the power spectrum characteristically and allows to detect the concentration at which the subject loses consciousness (i.e. the subject is not able to respond to external commands anymore).
The presented talk shows, in the first part, a system a of stochastic delayed ordinary differential equations, that describes the neural activity of the network of cortex and the thalamus in mammalian brain[1]. The system is driven by external white noise that represents input from brainstem structures. Numerical simulations show that decreasing the noise level describes well experimental EEG data observed during surgery and the decreasing noise level induces a breakdown of functional connectivity in the model. The results indicate that loss of consciousness is strongly correlated to denoising the brain and its functional fragmentation. In a second part of the talk, analytical results are shown that describe how additive noise induces system changes in networks [2].
[1] A. Hutt, J. Lefebvre, D. Hight and J. Sleigh,
Suppression of underlying neuronal fluctuations mediates EEG slowing during general anaesthesia,
Neuroimage 179: 414-428 (2018)
[2] A. Hutt, J. Lefebvre, D. Hight and H. Kaiser, Phase coherence induced by additive Gaussian and non-Gaussian noise in excitable networks with application to burst suppression-like brain signals, Frontiers in Applied Mathematics and Statistics 5:69 (2020)