Bicoherence of intracranial EEG in sleep, wakefulness and seizures

Bullock, T. H.; Achimowicz, Jerzy; Duckrow, Robert B.; Spencer, Susan S.; Iragui-Madoz, Vicente

doi:10.1016/s0013-4694(97)00087-4

Cited by 72 publications

(64 citation statements)

References 18 publications

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“…A simple example of this is frequency doubling when one squares a sinusoid; i.e., exp(jωt) 2 = exp(j2ωt) (see Friston (2001)). Biological evidence speaks to the prevalence of non-linear interactions among cortical areas during cognitive tasks (e.g., Bullock et al, 1997;Schack et al, 2002). We have shown that second-order features of the data (i.e., the spectrum) can be modelled by DCM for induced responses in a way that can disambiguate between linear and non-linear coupling.…”

Section: Discussionmentioning

confidence: 95%

Dynamic causal modelling of induced responses

2008

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This paper describes a dynamic causal model (DCM) for induced or spectral responses as measured with the electroencephalogram (EEG) or the magnetoencephalogram (MEG). We model the time-varying power, over a range of frequencies, as the response of a distributed system of coupled electromagnetic sources to a spectral perturbation. The model parameters encode the frequency response to exogenous input and coupling among sources and different frequencies. The Bayesian inversion of this model, given data enables inferences about the parameters of a particular model and allows us to compare different models, or hypotheses. One key aspect of the model is that it differentiates between linear and non-linear coupling; which correspond to within and betweenfrequency coupling respectively. To establish the face validity of our approach, we generate synthetic data and test the identifiability of various parameters to ensure they can be estimated accurately, under different levels of noise. We then apply our model to EEG data from a faceperception experiment, to ask whether there is evidence for non-linear coupling between early visual cortex and fusiform areas.

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Section: Discussionmentioning

confidence: 95%

Dynamic causal modelling of induced responses

2008

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“…Whereas the stimulus-response coherence (Eq.2) is built upon first-order correlations and thus is a measure of linear relations between various frequency components of a stimulus and response, in contrast, the cross bicoherence involves the cross bispectrum, a two-dimensional Fourier transform of second-order cross-correlations, 54 which thus characterize non-linear relations of components at triplets of frequencies, f 1 , f 2 , and f 1 þ f 2 . Bicoherence and higher order spectra have been utilized successfully to reveal quadratic coupling of phases at various frequency bands in electroencephalographic data 2,11,39 and in multiple microelectrode recordings from visual cortex of cats and monkeys. 68 In certain cases, nonlinearities still allow for optimal linear encoding.…”

Section: B Data Analysesmentioning

confidence: 99%

Sensory coding in oscillatory electroreceptors of paddlefish

Neiman

Russell²

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Coherence and information theoretic analyses were applied to quantitate the response properties and the encoding of time-varying stimuli in paddlefish electroreceptors (ERs), studied in vivo. External electrical stimuli were Gaussian noise waveforms of varied frequency band and strength, including naturalistic waveforms derived from zooplankton prey. Our coherence analyses elucidated the role of internal oscillations and transduction processes in shaping the 0.5-20 Hz best frequency tuning of these electroreceptors, to match the electrical signals emitted by zooplankton prey. Stimulus-response coherence fell off above approximately 20 Hz, apparently due to intrinsic limits of transduction, but was detectable up to 40-50 Hz. Aligned with this upper fall off was a narrow band of intense internal noise at $25 Hz, due to prominent membrane potential oscillations in cells of sensory epithelia, which caused a narrow deadband of external insensitivity. Using coherence analysis, we showed that more than 76% of naturalistic stimuli of weak strength, $1 lV=cm, was linearly encoded into an afferent spike train, which transmitted information at a rate of $30 bits=s. Stimulus transfer to afferent spike timing became essentially nonlinear as the stimulus strength was increased to induce bursting firing. Strong stimuli, as from nearby zooplankton prey, acted to synchronize the bursting responses of afferents, including across populations of electroreceptors, providing a plausible mechanism for reliable information transfer to higher-order neurons through noisy synapses. Rhythmical activity underlies various complex physiological processes in central nervous systems. Peripheral sensory receptors, on the other hand, are often considered as "passive" systems with relatively simple and linear dynamics. Nevertheless, self-sustained oscillations have been observed in several types of peripheral sensory receptors. This paper reports on stimulus encoding in electroreceptors (ERs) of paddlefish, which use passive electrosense to feed on zooplankton. A single peripheral electroreceptor in paddlefish is a complex system comprised of several thousands of sensory epithelial cells innervated by a few primary sensory neurons (afferents). It embeds distinct oscillators: one resides in a population of epithelial cells, synaptically coupled to another oscillator in afferent terminals. In contrast to auditory receptors, which resonate to sound waves of certain frequency, neither epithelial nor afferent rhythms of electroreceptors match the low-frequency bioelectric signals emitted by zooplankton prey. We applied Gaussian noise stimuli to study how oscillators embedded in paddlefish electroreceptors shape the linear and nonlinear responses of electroreceptors, and to characterize quantitatively how external stimuli, including bioelectrical signals from zooplankton prey, are encoded into the timing of afferent firing.

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“…It has been proved that bicoherence spectrum is a powerful tool to detect the phase coupling among series. Bicoherence based on Fourier transform (FT) has been applied to quantify phase coupling between a pair of EEG recordings (Bullock et al, 1997); this is based on the principle that the sum and difference frequencies in the non-linear system are generated with a fixed phase relationship. Calculation of the bicoherence enables us to quantify the amount of phase coupling and number of independent signal sources.…”

Section: Methodsmentioning

confidence: 99%

“…There is increasing interest in the use of wavelet-based techniques in processing non-stationary EEG recordings, not only with respect to oscillatory behaviour (Klein et al, 2006;Bullock et al, 1997;Li et al, 2005a,b), but also for spike detection (Senhadji and Wendling, 2002;Latka et al, 2003;Nenadic and Burdick, 2005), sleep stage identification (Jobert et al, 1994;Kiymik et al, 2004), anesthetics (Kochs et al, 2001) and filtering (Glassman, 2005). In addition to providing spectral statistics similar to those obtained with Fourier analysis, wavelet-based methods are capable of detecting the short lived temporal interactions, which occur in EEG recordings.…”

Section: Introductionmentioning

confidence: 99%

Interaction dynamics of neuronal oscillations analysed using wavelet transforms

Yao

Fox

et al. 2007

Journal of Neuroscience Methods

109

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This paper describes the use of a computational tool based on the Morlet wavelet transform to investigate the interaction dynamics between oscillations generated by two anatomically distinct neuronal populations. The tool uses cross wavelet transform, coherence, bi-spectrum/bicoherence and phase synchronization.Using specimen data recorded from the hippocampus of a rat with experimentally induced focal epilepsy, linear and non-linear correlations between neuronal oscillations in the CA1 and CA3 regions have been computed.The results of this real case study show that the computational tool can successfully analyse and quantify the temporal interactions between neuronal oscillators and could be employed to investigate the mechanisms underlying epilepsy.

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Bicoherence of intracranial EEG in sleep, wakefulness and seizures

Cited by 72 publications

References 18 publications

Dynamic causal modelling of induced responses

Dynamic causal modelling of induced responses

Sensory coding in oscillatory electroreceptors of paddlefish

Interaction dynamics of neuronal oscillations analysed using wavelet transforms

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