Spatiotemporal analysis of electrophysiological data
An important theme of computational neuroscience is to develop analysis techniques for complex electrophysiological signals. In my PhD thesis work with Agnessa Babloyantz and Grégoire Nicolis (University of Brussels, Belgium), methods from nonlinear dynamics were designed and applied to analyze human electroencephalogram (EEG) data. We showed that the complex dynamics of EEG oscillations have similar statistical and dynamical properties as low-dimensional chaotic systems [1,2]. The design of methods based on symbolic dynamics  suggested that patterns of oscillations are not random but exhibit temporal correlations. These results were modeled by simple networks where the thalamus was represented by a pacemaker  (see Section 3.2). An explanation for the presence of chaotic states in neural systems was proposed based on the maximization of information transport , similar to the onset of turbulent states which maximize transport properties in fluids.
We also investigated the spatiotemporal dynamics of oscillations in cat cerebral cortex and thalamus based on multi-electrode recordings (in collaboration with Diego Contreras and Mircea Steriade). We combined multisite recordings in vivo with computer analyses to investigate the role of corticothalamic feedback connections on the synchrony and spatiotemporal coherence of thalamic oscillations [6,7,8]. Here, relatively simple analysis techniques such as spatiotemporal maps, local Fourier analysis and spatial correlations, were used to characterize the spatiotemporal coherence. These methods helped to establish that the spatiotemporal coherence of thalamic oscillations is destroyed by removal of the cortex . These experimental measurements of spatiotemporal properties were successfully modeled by thalamocortical networks [9,10] (see Section 3.2).
Still in collaboration with Diego Contreras and Mircea Steriade, we characterized the spatiotemporal distribution of oscillatory activity from multisite field potential recordings in cat cerebral cortex during natural wake and sleep states . The spatiotemporal pattern of activity was markedly different for slow-wave events and fast oscillations: slow waves were characterized by a generalized silence in all cell types and were of remarkable spatiotemporal coherence, whereas during fast oscillations the activity was less coherent and correlations were local within a millimeter range . Although fast oscillations are present during wake and REM sleep, brief periods of fast oscillations with identical spatiotemporal characteristics were also present during slow-wave sleep. These results suggest that slow-wave sleep in cats consists in brief periods of activity ("up states") with low spatiotemporal coherence, similar to wakefulness, interleaved with slow-wave complexes coherent over large cortical territories. We recently wrote a review article that summarizes the evidence that these "up" states represents fragments of wakefulness that are replayed during sleep .
In a more recent study , we compared the above evidence for stochastic dynamics of single neurons with the earlier evidence for low-dimensional dynamics in the EEG (see above). To attempt reconcile these results, we investigated models of randomly-connected networks of integrate-and-fire neurons, and also contrast global (averaged) variables, with neuronal activity. The network displays different states, such as "synchronous regular" (SR) or "asynchronous irregular" (AI) states. In SR states, the global variables display coherent behavior with low dimensionality, while in AI states, the global activity is high-dimensionally chaotic with exponentially distributed neuronal discharges, similar to awake cats. Scale-dependent Lyapunov exponents and epsilon-entropies show that the seemingly stochastic nature at small scales (neurons) can coexist with more coherent behavior at larger scales (averages). Thus, we suggest that brain activity obeys similar scheme, with seemingly stochastic dynamics at small scales (neurons), while large scales (EEG) display more coherent behavior or high-dimensional chaos .
As detailed in Section 4.5, an important aspect of the spatiotemporal properties of brain activity is the occurrence of self-organized states and long-range correlations, which can appear through specific properties of power-law or frequency scaling. For example the LFP scales as 1/f, but simultaneously recorded units do not show signs of organized activity and rather behave as stochastic processes [13,17]. Further investigations show that an 1/f filtering of the neuronal signals by extracellular space is possible and could be explained by ionic diffusion  (see details in Section 1.3). It was also shown that other models than SOC can account for unit activity, for example Ising type models can predict the occurrence of population patterns in distributed spiking activity based on pairwise correlations . Such correlations in the activity can appear in the frequency scaling of the Vm recorded in vivo . This relation between intracellular scaling and network correlations could be reproduced by dynamic-clamp experiments . Chaotic dynamics can also provide possible models for macroscopic variables . These power-law analyses were detailed in Section 4.5.
These conclusions were later confirmed by an avalanche analysis from cat, monkey and human cerebral cortex, in wake and sleep states . This analysis made use of recently acquired unit and LFP recordings in humans where a spatiotemporal correlation analysis was performed . The avalanche analysis of such data, as well as from similar high-density recordings in cat and monkey (from 96 to 160 electrodes), all pointed to the absence of power-law distributions, in both units, and LFP recordings . Recently it was found that the excitatory and inhibitory cells are perfectly balanced, at different scales . These data and analyses suggest that the awake and sleeping brain displays complex dynamical states different than SOC (see details in Section 4.5).
We also investigated another spatiotemporal aspect of neural dynamics: the occurrence of propagating waves. We reviewed experiments on propagating activity in thalamus and neocortex across various levels of anesthesia and stimulation conditions, as well as computational models . Some discrepancies between experiments can be explained by the "network state", which differs vastly between anesthetized and awake conditions. This hypothesis was investigated in a network model displaying different states and investigate their effect on the spatial structure of self-sustained and externally driven activity. Indeed, the models showed that the occurence of propagation very sensitively depends on network state .
The presence of propagating waves in the awake and aroused brain was further investigated in collaboration with Frederic Chavane (INT, Marseille) . By combining voltage-sensitive dye (VSD) recordings of neuronal activity in awake monkey visual cortex, with a novel detection method based on the phase latency maps, we could show that not only propagating waves are present in the visual cortex, but nearly all visual stimuli evoke a propagating wave. There are also waves occurring spontaneously, and the interaction between these noisy spontaneous waves with those evoked by sensory stimuli constitute a fascinating perspective for future research, as we reviewed recently .
We also investigated the spatiotemporal distribution of unit and local field potentials in parallel in human and monkey, by using Utah-array recordings [23, 24]. We found that the excitatory and inhibitory cells are perfectly balanced, at different scales, in both wake and sleep states . We also investigated how fast oscillations (beta and gamma frequencies) are organized in space and time . We found that mostly inhibitory neurons are active during these oscillations, in wake and sleep states. Surprisingly, the largest spatiotemporal coherence was found in slow-wave sleep, and among inhibitory cells. These results suggest that inhibitory cells are dominantly involved in the genesis of beta and gmma oscillations, as well as in the organization of their large-scale coherence in the awake and sleeping brain.
The relation between units and LFP also concerns many spatial and temporal scales. We studied this relation  and found that it extends to scales of several millimetes in cortex, which can be explained by the effect of on-going network dynamics. Removing this network dynamics by spatial whitening, allowed us to reveal the ``private'' and local-scale relation between units and LFPs . This also revealed that inhibitory neurons have the largest influence on LFPs. We are presently building models of LFP that take into account these findings.
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 El Boustani, S., Marre, O., Behuret, S., Baudot, P., Yger, P., Bal, T., Destexhe, A. and Frégnac, Y. Network-state modulation of power-law frequency-scaling in visual cortical neurons. PLoS Computational Biology 5: e1000519, 2009 (see abstract).
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 Peyrache, A., Dehghani, N., Eskandar, E.N., Madsen, J.R., Anderson, W.S., Donoghue, J.S., Hochberg, L.R., Halgren, E., Cash, S.S., and Destexhe, A. Spatiotemporal dynamics of neocortical excitation and inhibition during human sleep. Proc. Natl. Acad. Sci. USA 109: 1731-1736, 2012 (see abstract)
 Dehghani, N., Hatsopoulos, N.G., Haga, Z.D., Parker, R.A., Greger, B., Halgren, E., Cash, S.S., and Destexhe, A. Avalanche analysis from multi-electrode ensemble recordings in cat, monkey and human cerebral cortex during wakefulness and sleep. Frontiers Physiol. 3: 302, 2012 (see abstract).
 Muller, L.E. and Destexhe, A. Propagating waves in thalamus, cortex and the thalamocortical system: experiments and models. J. Physiol. Paris 106: 222-238, 2012 (see abstract)
 Muller, L.E., Reynaud, A., Chavane, F. and Destexhe, A. The stimulus-evoked population response in visual cortex of awake monkey is a propagating wave. Nature Communications 5: 3675, 2014 (see abstract)
 Dehghani, N., Peyrache, A., Telenczuk, B., Le Van Quyen, M., Halgren, E., Cash, S.S., Hatsopoulos, N.G. and Destexhe, A. Dynamic balance of excitation and inhibition in human and monkey neocortex. Nature Scientific Reports 6: 23176, 2016 see abstract)
 Le Van Quyen, M., Muller, L., Telenczuk, B., Cash, S.S., Halgren, E., Hatsopoulos, N.G., Dehghani, N. and Destexhe, A. High-frequency oscillations in human and monkey neocortex during the wake-sleep cycle. Proc. Natl. Acad. Sci. USA 113: 9363-9368, 2016 (see abstract)
 Chemla, S., Muller, L., Reynaud, A., Takerkart, S., Destexhe, A. and Chavane, F. Improving voltage-sensitive dye imaging: with a little help from computational approaches. Neurophotonics 4: 031215, 2017 (see abstract)
 Telenczuk, B., Dehghani, N., Le Van Quyen, M., Cash, S., Halgren, E., Hatsopoulos, N.G. and Destexhe, A. Local field potentials primarily reflect inhibitory neuron activity in human and monkey cortex. Nature Scientific Reports 7: 40211, 2017 (see abstract)
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