Measurement of excitation-inhibition ratio in autism spectrum disorder using critical brain dynamics.

Balance between excitation (E) and inhibition (I) is a key principle for neuronal network organization and information processing. Consistent with this notion, excitation-inhibition imbalances are considered a pathophysiological mechanism in many brain disorders including autism spectrum disorder (ASD). However, methods to measure E/I ratios in human brain networks are lacking. Here, we present a method to quantify a functional E/I ratio (fE/I) from neuronal oscillations, and validate it in healthy subjects and children with ASD. We define structural E/I ratio in an in silico neuronal network, investigate how it relates to power and long-range temporal correlations (LRTC) of the network's activity, and use these relationships to design the fE/I algorithm. Application of this algorithm to the EEGs of healthy adults showed that fE/I is balanced at the population level and is decreased through GABAergic enforcement. In children with ASD, we observed larger fE/I variability and stronger LRTC compared to typically developing children (TDC). Interestingly, visual grading for EEG abnormalities that are thought to reflect E/I imbalances revealed elevated fE/I and LRTC in ASD children with normal EEG compared to TDC or ASD with abnormal EEG. We speculate that our approach will help understand physiological heterogeneity also in other brain disorders.

An EEG nicotinic acetylcholine index to assess the efficacy of pro-cognitive compounds.

OBJECTIVES: Cognitive impairment models are used in clinical studies aimed at proving pharmacology of drugs being developed for Alzheimer's disease and other cognitive disorders. Due to rising interest in nicotinic agonists, we aimed to establish a method to monitor neurophysiological effects of modulating the nicotinic cholinergic system. METHODS: In a four-way cross-over study, eyes-closed rest EEG was recorded in 28 healthy subjects receiving mecamylamine-a nicotinic acetylcholine receptor (nAChR) antagonist, which induces temporary cognitive dysfunction in healthy subjects-with co-administration of placebo, nicotine or galantamine. RESULTS: Using machine learning to optimally contrast the effects of 30 mg of mecamylamine and placebo on the brain, we developed a nAChR index that consists of 10 EEG biomarkers and shows high classification accuracy (∼95% non-cross-validated, ∼70% cross-validated). Importantly, using the nAChR index, we demonstrate reversal of mecamylamine-induced neurophysiological effects due to 16 mg of galantamine as well as administering 21 mg of nicotine transdermally. CONCLUSIONS: Our findings indicate that the mecamylamine challenge model jointly with the nAChR index-a measure of the nicotinic EEG profile-could aid future proof-of-pharmacology studies to demonstrate effects of nicotinic cholinergic compounds. SIGNIFICANCE: This novel measure for quantifying nicotinic cholinergic effects on the EEG could serve as a useful tool in drug development of pro-cognitive compounds.

Long-Range Temporal Correlations in Alpha Oscillations Stabilize Perception of Ambiguous Visual Stimuli.

Ongoing brain dynamics have been proposed as a type of "neuronal noise" that can trigger perceptual switches when viewing an ambiguous, bistable stimulus. However, no prior study has directly quantified how such neuronal noise relates to the rate of percept reversals. Specifically, it has remained unknown whether individual differences in complexity of resting-state oscillations-as reflected in long-range temporal correlations (LRTC)-are associated with perceptual stability. We hypothesized that participants with stronger resting-state LRTC in the alpha band experience more stable percepts, and thereby fewer perceptual switches. Furthermore, we expected that participants who report less discontinuous thoughts during rest, experience less switches. To test this, we recorded electroencephalography (EEG) in 65 healthy volunteers during 5 min Eyes-Closed Rest (ECR), after which they filled in the Amsterdam Resting-State Questionnaire (ARSQ). This was followed by three conditions where participants attended an ambiguous structure-from-motion stimulus-Neutral (passively observe the stimulus), Hold (the percept for as long as possible), and Switch (as often as possible). LRTC of resting-state alpha oscillations predicted the number of switches only in the Hold condition, with stronger LRTC associated with less switches. Contrary to our expectations, there was no association between resting-state Discontinuity of Mind and percept stability. Participants were capable of controlling switching according to task goals, and this was accompanied by increased alpha power during Hold and decreased power during Switch. Fewer switches were associated with stronger task-related alpha LRTC in all conditions. Together, our data suggest that bistable visual perception is to some extent under voluntary control and influenced by LRTC of alpha oscillations.

Strong long-range temporal correlations of beta/gamma oscillations are associated with poor sustained visual attention performance.

Neuronal oscillations exhibit complex amplitude fluctuations with autocorrelations that persist over thousands of oscillatory cycles. Such long-range temporal correlations (LRTC) are thought to reflect neuronal systems poised near a critical state, which would render them capable of quick reorganization and responsive to changing processing demands. When we concentrate, however, the influence of internal and external sources of distraction is better reduced, suggesting that neuronal systems involved with sustained attention could benefit from a shift toward the less volatile sub-critical state. To test these ideas, we recorded electroencephalography (EEG) from healthy volunteers during eyes-closed rest and during a sustained attention task requiring a speeded response to images deviating in their presentation duration. We show that for oscillations recorded during rest, high levels of alpha-band LRTC in the sensorimotor region predicted good reaction-time performance in the attention task. During task execution, however, fast reaction times were associated with high-amplitude beta and gamma oscillations with low LRTC. Finally, we show that reduced LRTC during the attention task compared to the rest condition correlates with better performance, while increased LRTC of oscillations from rest to attention is associated with reduced performance. To our knowledge, this is the first empirical evidence that 'resting-state criticality' of neuronal networks predicts swift behavioral responses in a sensorimotor task, and that steady attentive processing of visual stimuli requires brain dynamics with suppressed temporal complexity.

Bumetanide As a Candidate Treatment for Behavioral Problems in Tuberous Sclerosis Complex.

BACKGROUND: Recent studies indicate excitatory GABA action in and around tubers in patients with tuberous sclerosis complex (TSC). This may contribute to recurrent seizures and behavioral problems that may be treated by agents that enhance GABAergic transmission by influencing chloride regulation. CASE PRESENTATION: Here, we used the chloride transporter antagonist bumetanide to treat a female adolescent TSC patient with refractory seizures, sensory hyper-reactivity, and a variety of repetitive and compulsive behaviors. METHODS: To evaluate the effect of bumetanide on behavior, auditory sensory processing, and hyperexcitability, we obtained questionnaire data, event-related potentials (ERP), and resting state EEG at baseline, after 3 and 6 months of treatment and after 1 month washout period. DISCUSSION: Six months of treatment resulted in a marked improvement in all relevant behavioral domains, as was substantiated by the parent questionnaires. In addition, resting-state electroencephalography and ERP suggested a favorable effect of bumetanide on hyperexcitability and sensory processing. These findings encourage further studies of bumetanide on neuropsychiatric outcome in TSC.

EEG machine learning for accurate detection of cholinergic intervention and Alzheimer's disease.

Monitoring effects of disease or therapeutic intervention on brain function is increasingly important for clinical trials, albeit hampered by inter-individual variability and subtle effects. Here, we apply complementary biomarker algorithms to electroencephalography (EEG) recordings to capture the brain's multi-faceted signature of disease or pharmacological intervention and use machine learning to improve classification performance. Using data from healthy subjects receiving scopolamine we developed an index of the muscarinic acetylcholine receptor antagonist (mAChR) consisting of 14 EEG biomarkers. This mAChR index yielded higher classification performance than any single EEG biomarker with cross-validated accuracy, sensitivity, specificity and precision ranging from 88-92%. The mAChR index also discriminated healthy elderly from patients with Alzheimer's disease (AD); however, an index optimized for AD pathophysiology provided a better classification. We conclude that integrating multiple EEG biomarkers can enhance the accuracy of identifying disease or drug interventions, which is essential for clinical trials.

Age-dependent and -independent changes in attention-deficit/hyperactivity disorder (ADHD) during spatial working memory performance.

OBJECTIVES: Attention-deficit/hyperactivity disorder (ADHD) has been associated with spatial working memory as well as frontostriatal core deficits. However, it is still unclear how the link between these frontostriatal deficits and working memory function in ADHD differs in children and adults. This study examined spatial working memory in adults and children with ADHD, focussing on identifying regions demonstrating age-invariant or age-dependent abnormalities. METHODS: We used functional magnetic resonance imaging to examine a group of 26 children and 35 adults to study load manipulated spatial working memory in patients and controls. RESULTS: In comparison to healthy controls, patients demonstrated reduced positive parietal and frontostriatal load effects, i.e., less increase in brain activity from low to high load, despite similar task performance. In addition, younger patients showed negative load effects, i.e., a decrease in brain activity from low to high load, in medial prefrontal regions. Load effect differences between ADHD and controls that differed between age groups were found predominantly in prefrontal regions. Age-invariant load effect differences occurred predominantly in frontostriatal regions. CONCLUSIONS: The age-dependent deviations support the role of prefrontal maturation and compensation in ADHD, while the age-invariant alterations observed in frontostriatal regions provide further evidence that these regions reflect a core pathophysiology in ADHD.

Effects of Steroid Hormones on Sex Differences in Cerebral Perfusion.

Sex differences in the brain appear to play an important role in the prevalence and progression of various neuropsychiatric disorders, but to date little is known about the cerebral mechanisms underlying these differences. One widely reported finding is that women demonstrate higher cerebral perfusion than men, but the underlying cause of this difference in perfusion is not known. This study investigated the putative role of steroid hormones such as oestradiol, testosterone, and dehydroepiandrosterone sulphate (DHEAS) as underlying factors influencing cerebral perfusion. We acquired arterial spin labelling perfusion images of 36 healthy adult subjects (16 men, 20 women). Analyses on average whole brain perfusion levels included a multiple regression analysis to test for the relative impact of each hormone on the global perfusion. Additionally, voxel-based analyses were performed to investigate the sex difference in regional perfusion as well as the correlations between local perfusion and serum oestradiol, testosterone, and DHEAS concentrations. Our results replicated the known sex difference in perfusion, with women showing significantly higher global and regional perfusion. For the global perfusion, DHEAS was the only significant predictor amongst the steroid hormones, showing a strong negative correlation with cerebral perfusion. The voxel-based analyses revealed modest sex-dependent correlations between local perfusion and testosterone, in addition to a strong modulatory effect of DHEAS in cortical, subcortical, and cerebellar regions. We conclude that DHEAS in particular may play an important role as an underlying factor driving the difference in cerebral perfusion between men and women.

Paradoxical Benzodiazepine Response: A Rationale for Bumetanide in Neurodevelopmental Disorders?

The diuretic agent bumetanide has recently been put forward as a novel, promising treatment of behavioral symptoms in autism spectrum disorder (ASD) and related conditions. Bumetanide can decrease neuronal chloride concentrations and may thereby reinstate γ-aminobutyric acid (GABA)-ergic inhibition in patients with neurodevelopmental disorders. However, strategies to select appropriate candidates for bumetanide treatment are lacking. We hypothesized that a paradoxical response to GABA-enforcing agents such as benzodiazepines may predict the efficacy of bumetanide treatment in neurodevelopmental disorders. We describe a case of a 10-year-old girl with ASD, epilepsy, cortical dysplasia, and a 15q11.2 duplication who had exhibited marked behavioral arousal after previous treatment with clobazam, a benzodiazepine. We hypothesized that this response indicated the presence of depolarizing excitatory GABA and started bumetanide treatment with monitoring of behavior, cognition, and EEG. The treatment resulted in a marked clinical improvement in sensory behaviors, rigidity, and memory performance, which was substantiated by questionnaires and cognitive assessments. At baseline, the girl's EEG showed a depression in absolute α power, an electrographic sign previously related to ASD, which was normalized with bumetanide treatment. The effects of bumetanide on cognition and EEG seemed to mirror the "nonparadoxical" responses to benzodiazepines in healthy subjects. In addition, temporal lobe epilepsy and cortical dysplasia have both been linked to disturbed chloride homeostasis and seem to support our assumption that the observed paradoxical response was due to GABA-mediated excitation. This case highlights that a paradoxical behavioral response to GABA-enforcing drugs may constitute a framework for targeted treatment with bumetanide.

Subcortical glutamate mediates the reduction of short-range functional connectivity with age in a developmental cohort.

Marked changes in brain physiology and structure take place between childhood and adulthood, including changes in functional connectivity and changes in the balance between main excitatory and inhibitory neurotransmitters glutamate (Glu) and GABA. The balance of these neurotransmitters is thought to underlie neural activity in general and functional connectivity networks in particular, but so far no studies have investigated the relationship between human development related differences in these neurotransmitters and concomitant changes in functional connectivity. GABA+/H2O and Glu/H2O levels were acquired in a group of healthy children, adolescents, and adults in a subcortical (basal ganglia) region, as well as in a frontal region in adolescents and adults. Our results showed higher GABA+/Glu with age in both the subcortical and the frontal voxel, which were differentially associated with significantly lower Glu/H2O with age in the subcortical voxel and by significantly higher GABA+/H2O with age in the frontal voxel. Using a seed-to-voxel analysis, we were further able to show that functional connectivity between the putamen (seed) and other subcortical structures was lower with age. Lower subcortical Glu/H2O with age mediated the lower connectivity in the dorsal putamen. Based on these results, and the potential role of Glu in synaptic pruning, we suggest that lower Glu mediates a reduction of local connectivity during human development.

Integrative EEG biomarkers predict progression to Alzheimer's disease at the MCI stage.

Alzheimer's disease (AD) is a devastating disorder of increasing prevalence in modern society. Mild cognitive impairment (MCI) is considered a transitional stage between normal aging and AD; however, not all subjects with MCI progress to AD. Prediction of conversion to AD at an early stage would enable an earlier, and potentially more effective, treatment of AD. Electroencephalography (EEG) biomarkers would provide a non-invasive and relatively cheap screening tool to predict conversion to AD; however, traditional EEG biomarkers have not been considered accurate enough to be useful in clinical practice. Here, we aim to combine the information from multiple EEG biomarkers into a diagnostic classification index in order to improve the accuracy of predicting conversion from MCI to AD within a 2-year period. We followed 86 patients initially diagnosed with MCI for 2 years during which 25 patients converted to AD. We show that multiple EEG biomarkers mainly related to activity in the beta-frequency range (13-30 Hz) can predict conversion from MCI to AD. Importantly, by integrating six EEG biomarkers into a diagnostic index using logistic regression the prediction improved compared with the classification using the individual biomarkers, with a sensitivity of 88% and specificity of 82%, compared with a sensitivity of 64% and specificity of 62% of the best individual biomarker in this index. In order to identify this diagnostic index we developed a data mining approach implemented in the Neurophysiological Biomarker Toolbox (http://www.nbtwiki.net/). We suggest that this approach can be used to identify optimal combinations of biomarkers (integrative biomarkers) also in other modalities. Potentially, these integrative biomarkers could be more sensitive to disease progression and response to therapeutic intervention.

The Amsterdam Resting-State Questionnaire reveals multiple phenotypes of resting-state cognition.

Resting-state neuroimaging is a dominant paradigm for studying brain function in health and disease. It is attractive for clinical research because of its simplicity for patients, straightforward standardization, and sensitivity to brain disorders. Importantly, non-sensory experiences like mind wandering may arise from ongoing brain activity. However, little is known about the link between ongoing brain activity and cognition, as phenotypes of resting-state cognition-and tools to quantify them-have been lacking. To facilitate rapid and structured measurements of resting-state cognition we developed a 50-item self-report survey, the Amsterdam Resting-State Questionnaire (ARSQ). Based on ARSQ data from 813 participants assessed after 5 min eyes-closed rest in their home, we identified seven dimensions of resting-state cognition using factor analysis: Discontinuity of Mind, Theory of Mind, Self, Planning, Sleepiness, Comfort, and Somatic Awareness. Further, we showed that the structure of cognition was similar during resting-state fMRI and EEG, and that the test-retest correlations were remarkably high for all dimensions. To explore whether inter-individual variation of resting-state cognition is related to health status, we correlated ARSQ-derived factor scores with psychometric scales measuring depression, anxiety, and sleep quality. Mental health correlated positively with Comfort and negatively with Discontinuity of Mind. Finally, we show that sleepiness may partially explain a resting-state EEG profile previously associated with Alzheimer's disease. These findings indicate that the ARSQ readily provides information about cognitive phenotypes and that it is a promising tool for research on the neural correlates of resting-state cognition in health and disease.

Individual differences in white matter diffusion affect sleep oscillations.

The characteristic oscillations of the sleeping brain, spindles and slow waves, show trait-like, within-subject stability and a remarkable interindividual variability that correlates with functionally relevant measures such as memory performance and intelligence. Yet, the mechanisms underlying these interindividual differences are largely unknown. Spindles and slow waves are affected by the recent history of learning and neuronal activation, indicating sensitivity to changes in synaptic strength and thus to the connectivity of the neuronal network. Because the structural backbone of this network is formed by white matter tracts, we hypothesized that individual differences in spindles and slow waves depend on the white matter microstructure across a distributed network. We recorded both diffusion-weighted magnetic resonance images and whole-night, high-density electroencephalography and investigated whether individual differences in sleep spindle and slow wave parameters were associated with diffusion tensor imaging metrics; white matter fractional anisotropy and axial diffusivity were quantified using tract-based spatial statistics. Individuals with higher spindle power had higher axial diffusivity in the forceps minor, the anterior corpus callosum, fascicles in the temporal lobe, and the tracts within and surrounding the thalamus. Individuals with a steeper rising slope of the slow wave had higher axial diffusivity in the temporal fascicle and frontally located white matter tracts (forceps minor, anterior corpus callosum). These results indicate that the profiles of sleep oscillations reflect not only the dynamics of the neuronal network at the synaptic level, but also the localized microstructural properties of its structural backbone, the white matter tracts.

Detrended fluctuation analysis: a scale-free view on neuronal oscillations.

Recent years of research have shown that the complex temporal structure of ongoing oscillations is scale-free and characterized by long-range temporal correlations. Detrended fluctuation analysis (DFA) has proven particularly useful, revealing that genetic variation, normal development, or disease can lead to differences in the scale-free amplitude modulation of oscillations. Furthermore, amplitude dynamics is remarkably independent of the time-averaged oscillation power, indicating that the DFA provides unique insights into the functional organization of neuronal systems. To facilitate understanding and encourage wider use of scaling analysis of neuronal oscillations, we provide a pedagogical explanation of the DFA algorithm and its underlying theory. Practical advice on applying DFA to oscillations is supported by MATLAB scripts from the Neurophysiological Biomarker Toolbox (NBT) and links to the NBT tutorial website http://www.nbtwiki.net/. Finally, we provide a brief overview of insights derived from the application of DFA to ongoing oscillations in health and disease, and discuss the putative relevance of criticality for understanding the mechanism underlying scale-free modulation of oscillations.

External drive to inhibitory cells induces alternating episodes of high- and low-amplitude oscillations.

Electrical oscillations in neuronal network activity are ubiquitous in the brain and have been associated with cognition and behavior. Intriguingly, the amplitude of ongoing oscillations, such as measured in EEG recordings, fluctuates irregularly, with episodes of high amplitude alternating with episodes of low amplitude. Despite the widespread occurrence of amplitude fluctuations in many frequency bands and brain regions, the mechanisms by which they are generated are poorly understood. Here, we show that irregular transitions between sub-second episodes of high- and low-amplitude oscillations in the alpha/beta frequency band occur in a generic neuronal network model consisting of interconnected inhibitory and excitatory cells that are externally driven by sustained cholinergic input and trains of action potentials that activate excitatory synapses. In the model, we identify the action potential drive onto inhibitory cells, which represents input from other brain areas and is shown to desynchronize network activity, to be crucial for the emergence of amplitude fluctuations. We show that the duration distributions of high-amplitude episodes in the model match those observed in rat prefrontal cortex for oscillations induced by the cholinergic agonist carbachol. Furthermore, the mean duration of high-amplitude episodes varies in a bell-shaped manner with carbachol concentration, just as in mouse hippocampus. Our results suggest that amplitude fluctuations are a general property of oscillatory neuronal networks that can arise through background input from areas external to the network.

Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks.

Criticality has gained widespread interest in neuroscience as an attractive framework for understanding the character and functional implications of variability in brain activity. The metastability of critical systems maximizes their dynamic range, storage capacity, and computational power. Power-law scaling-a hallmark of criticality-has been observed on different levels, e.g., in the distribution of neuronal avalanches in vitro and in vivo, but also in the decay of temporal correlations in behavioral performance and ongoing oscillations in humans. An unresolved issue is whether power-law scaling on different organizational levels in the brain-and possibly in other hierarchically organized systems-can be related. Here, we show that critical-state dynamics of avalanches and oscillations jointly emerge in a neuronal network model when excitation and inhibition is balanced. The oscillatory activity of the model was qualitatively similar to what is typically observed in recordings of human resting-state MEG. We propose that homeostatic plasticity mechanisms tune this balance in healthy brain networks, and that it is essential for critical behavior on multiple levels of neuronal organization with ensuing functional benefits. Based on our network model, we introduce a concept of multi-level criticality in which power-law scaling can emerge on multiple time scales in oscillating networks.

Fast network oscillations in vitro exhibit a slow decay of temporal auto-correlations.

Ongoing neuronal oscillations in vivo exhibit non-random amplitude fluctuations as reflected in a slow decay of temporal auto-correlations that persist for tens of seconds. Interestingly, the decay of auto-correlations is altered in several brain-related disorders, including epilepsy, depression and Alzheimer's disease, suggesting that the temporal structure of oscillations depends on intact neuronal networks in the brain. Whether structured amplitude modulation occurs only in the intact brain or whether isolated neuronal networks can also give rise to amplitude modulation with a slow decay is not known. Here, we examined the temporal structure of cholinergic fast network oscillations in acute hippocampal slices. For the first time, we show that a slow decay of temporal correlations can emerge from synchronized activity in isolated hippocampal networks from mice, and is maximal at intermediate concentrations of the cholinergic agonist carbachol. Using zolpidem, a positive allosteric modulator of GABA(A) receptor function, we found that increased inhibition leads to longer oscillation bursts and more persistent temporal correlations. In addition, we asked if these findings were unique for mouse hippocampus, and we therefore analysed cholinergic fast network oscillations in rat prefrontal cortex slices. We observed significant temporal correlations, which were similar in strength to those found in mouse hippocampus and human cortex. Taken together, our data indicate that fast network oscillations with temporal correlations can be induced in isolated networks in vitro in different species and brain areas, and therefore may serve as model systems to investigate how altered temporal correlations in disease may be rescued with pharmacology.

Altered temporal correlations in parietal alpha and prefrontal theta oscillations in early-stage Alzheimer disease.

Encoding and retention of information in memory are associated with a sustained increase in the amplitude of neuronal oscillations for up to several seconds. We reasoned that coordination of oscillatory activity over time might be important for memory and, therefore, that the amplitude modulation of oscillations may be abnormal in Alzheimer disease (AD). To test this hypothesis, we measured magnetoencephalography (MEG) during eyes-closed rest in 19 patients diagnosed with early-stage AD and 16 age-matched control subjects and characterized the autocorrelation structure of ongoing oscillations using detrended fluctuation analysis and an analysis of the life- and waiting-time statistics of oscillation bursts. We found that Alzheimer's patients had a strongly reduced incidence of alpha-band oscillation bursts with long life- or waiting-times (< 1 s) over temporo-parietal regions and markedly weaker autocorrelations on long time scales (1-25 seconds). Interestingly, the life- and waiting-times of theta oscillations over medial prefrontal regions were greatly increased. Whereas both temporo-parietal alpha and medial prefrontal theta oscillations are associated with retrieval and retention of information, metabolic and structural deficits in early-stage AD are observed primarily in temporo-parietal areas, suggesting that the enhanced oscillations in medial prefrontal cortex reflect a compensatory mechanism. Together, our results suggest that amplitude modulation of neuronal oscillations is important for cognition and that indices of amplitude dynamics of oscillations may prove useful as neuroimaging biomarkers of early-stage AD.

Avalanche dynamics of human brain oscillations: relation to critical branching processes and temporal correlations.

Human brain oscillations fluctuate erratically in amplitude during rest and exhibit power-law decay of temporal correlations. It has been suggested that this dynamics reflects self-organized activity near a critical state. In this framework, oscillation bursts may be interpreted as neuronal avalanches propagating in a network with a critical branching ratio. However, a direct comparison of the temporal structure of ongoing oscillations with that of activity propagation in a model network with critical connectivity has never been made. Here, we simulate branching processes and characterize the activity propagation in terms of avalanche life-time distributions and temporal correlations. An equivalent analysis is introduced for characterizing ongoing oscillations in the alpha-frequency band recorded with magnetoencephalography (MEG) during rest. We found that models with a branching ratio near the critical value of one exhibited power-law scaling in life-time distributions with similar scaling exponents as observed in the MEG data. The models reproduced qualitatively the power-law decay of temporal correlations in the human data; however, the correlations in the model appeared on time scales only up to the longest avalanche, whereas human data indicate persistence of correlations on time scales corresponding to several burst events. Our results support the idea that neuronal networks generating ongoing alpha oscillations during rest operate near a critical state, but also suggest that factors not included in the simple classical branching process are needed to account for the complex temporal structure of ongoing oscillations during rest on time scales longer than the duration of individual oscillation bursts.