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In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.
The neurophysiological changes associated with Alzheimer's Disease (AD) and Mild Cognitive Impairment (MCI) include an increase in low frequency activity, as measured with electroencephalography or magnetoencephalography (MEG). A relevant property of spectral measures is the alpha peak, which corresponds to the dominant alpha rhythm. Here we studied the spatial distribution of MEG resting state alpha peak frequency and amplitude values in a sample of 27 MCI patients and 24 age-matched healthy controls. Power spectra were reconstructed in source space with linearly constrained minimum variance beamformer. Then, 88 Regions of Interest (ROIs) were defined and an alpha peak per ROI and subject was identified. Statistical analyses were performed at every ROI, accounting for age, sex and educational level. Peak frequency was significantly decreased (p < 0.05) in MCIs in many posterior ROIs. The average peak frequency over all ROIs was 9.68 ± 0.71 Hz for controls and 9.05 ± 0.90 Hz for MCIs and the average normalized amplitude was (2.57 ± 0.59)·10(-2) for controls and (2.70 ± 0.49)·10(-2) for MCIs. Age and gender were also found to play a role in the alpha peak, since its frequency was higher in females than in males in posterior ROIs and correlated negatively with age in frontal ROIs. Furthermore, we examined the dependence of peak parameters with hippocampal volume, which is a commonly used marker of early structural AD-related damage. Peak frequency was positively correlated with hippocampal volume in many posterior ROIs. Overall, these findings indicate a pathological alpha slowing in MCI.
Neuronal activity differs between wakefulness and sleep states. In contrast, an attractor state, called self-organized critical (SOC), was proposed to govern brain dynamics because it allows for optimal information coding. But is the human brain SOC for each vigilance state despite the variations in neuronal dynamics? We characterized neuronal avalanches – spatiotemporal waves of enhanced activity - from dense intracranial depth recordings in humans. We showed that avalanche distributions closely follow a power law – the hallmark feature of SOC - for each vigilance state. However, avalanches clearly differ with vigilance states: slow wave sleep (SWS) shows large avalanches, wakefulness intermediate, and rapid eye movement (REM) sleep small ones. Our SOC model, together with the data, suggested first that the differences are mediated by global but tiny changes in synaptic strength, and second, that the changes with vigilance states reflect small deviations from criticality to the subcritical regime, implying that the human brain does not operate at criticality proper but close to SOC. Independent of criticality, the analysis confirms that SWS shows increased correlations between cortical areas, and reveals that REM sleep shows more fragmented cortical dynamics.
Current theories of the pathophysiology of schizophrenia have focused on abnormal temporal coordination of neural activity. Oscillations in the gamma-band range (>25 Hz) are of particular interest as they establish synchronization with great precision in local cortical networks. However, the contribution of high gamma (>60 Hz) oscillations toward the pathophysiology is less established. To address this issue, we recorded magnetoencephalographic (MEG) data from 16 medicated patients with chronic schizophrenia and 16 controls during the perception of Mooney faces. MEG data were analysed in the 25–150 Hz frequency range. Patients showed elevated reaction times and reduced detection rates during the perception of upright Mooney faces while responses to inverted stimuli were intact. Impaired processing of Mooney faces in schizophrenia patients was accompanied by a pronounced reduction in spectral power between 60–120 Hz (effect size: d = 1.26) which was correlated with disorganized symptoms (r = −0.72). Our findings demonstrate that deficits in high gamma-band oscillations as measured by MEG are a sensitive marker for aberrant cortical functioning in schizophrenia, suggesting an important aspect of the pathophysiology of the disorder.