Prediction of electroencephalographic spectra from neurophysiology

A comprehensive investigation of intracortical and corticothalamic models of the alpha rhythm

The electroencephalographic alpha rhythm is one of the most robustly observed and widely studied empirical phenomena in all of neuroscience. However, despite its extensive implication in a wide range of cognitive processes and clinical pathologies, the mechanisms underlying alpha generation in neural circuits remain poorly understood. In this paper we offer a renewed foundation for research on this question, by undertaking a systematic comparison and synthesis of the most prominent theoretical models of alpha rhythmogenesis in the published literature. We focus on four models, each studied intensively by multiple authors over the past three decades: (i) Jansen-Rit, (ii) Moran-David-Friston, (iii) Robinson-Rennie-Wright, and (iv) Liley-Wright. Several common elements are identified, such as the use of second-order differential equations and sigmoidal potential-to-rate operators to represent population-level neural activity. Major differences are seen in other features such as wiring topologies and conduction delays. Through a series of mathematical analyses and numerical simulations, we nevertheless demonstrate that the selected models can be meaningfully compared, by associating parameters and circuit motifs of analogous biological significance. With this established, we conduct explorations of rate constant and synaptic connectivity parameter spaces, with the aim of identifying common patterns in key behaviours, such as the role of excitatory-inhibitory interactions in the generation of oscillations. Finally, using linear stability analysis we identify two qualitatively different alpha-generating dynamical regimes across the models: (i) noise-driven fluctuations and (ii) self-sustained limit-cycle oscillations, emerging due to an Andronov-Hopf bifurcation. The comprehensive survey and synthesis developed here can, we suggest, be used to help guide future theoretical and experimental work aimed at disambiguating these and other candidate theories of alpha rhythmogenesis.

The Neural Correlates of Consciousness: A Spectral Exponent Approach to Diagnosing Disorders of Consciousness

BACKGROUND/OBJECTIVES

Disorder of consciousness (DoC) poses diagnostic challenges due to behavioral assessment limitations. This study evaluates the spectral exponent (SE)-a neurophysiological biomarker quantifying the decay slope of electroencephalography (EEG) aperiodic activity-as an objective tool for consciousness stratification and clinical behavior scores correlation.

METHODS

The study involved 15 DoC patients, nine conscious brain-injured controls (BI), and 23 healthy controls (HC). Resting-state 32-channel EEG data were analyzed to compute SE across broadband (1-40 Hz) and narrowband (1-20 Hz, 20-40 Hz). Statistical frameworks included Bonferroni-corrected Kruskal-Wallis H tests, Bayesian ANOVA, and correlation analyses with CRS-R behavioral scores.

RESULTS

Narrowband SE (1-20 Hz) showed superior diagnostic sensitivity, differentiating DoC from controls (HC vs. DoC: p < 0.0001; BI vs. DoC: p = 0.0006) and MCS from VS/UWS (p = 0.0014). SE correlated positively with CRS-R index (1-20 Hz: r = 0.590, p = 0.021) and visual subscale (1-20 Hz: r = 0.684, p = 0.005). High-frequency (20-40 Hz) SE exhibited inconsistent results. Longitudinal tracking in an individual revealed a reduction in SE negativity, a flattening of the 1/f slope, and behavioral recovery occurring in parallel.

CONCLUSIONS

Narrowband SE (1-20 Hz) is a robust biomarker for consciousness quantification, overcoming behavioral assessment subjectivity. Its correlation with visual function highlights potential clinical utility. Future studies should validate SE in larger cohorts and integrate multimodal neuroimaging.

A Novel Multi-Dynamic Coupled Neural Mass Model of SSVEP

Steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs) leverage high-speed neural synchronization to visual flicker stimuli for efficient device control. While SSVEP-BCIs minimize user training requirements, their dependence on physical EEG recordings introduces challenges, such as inter-subject variability, signal instability, and experimental complexity. To overcome these limitations, this study proposes a novel neural mass model for SSVEP simulation by integrating frequency response characteristics with dual-region coupling mechanisms. Specific parallel linear transformation functions were designed based on SSVEP frequency responses, and weight coefficient matrices were determined according to the frequency band energy distribution under different visual stimulation frequencies in the pre-recorded SSVEP signals. A coupled neural mass model was constructed by establishing connections between occipital and parietal regions, with parameters optimized through particle swarm optimization to accommodate individual differences and neuronal density variations. Experimental results demonstrate that the model achieved a high-precision simulation of real SSVEP signals across multiple stimulation frequencies (10 Hz, 11 Hz, and 12 Hz), with maximum errors decreasing from 2.2861 to 0.8430 as frequency increased. The effectiveness of the model was further validated through the real-time control of an Arduino car, where simulated SSVEP signals were successfully classified by the advanced FPF-net model and mapped to control commands. This research not only advances our understanding of SSVEP neural mechanisms but also releases the user from the brain-controlled coupling system, thus providing a practical framework for developing more efficient and reliable BCI-based systems.

Sleep and circadian rhythms modeling: From hypothalamic regulatory networks to cortical dynamics and behavior

Sleep and circadian rhythms are regulated by dynamic physiologic processes that operate across multiple spatial and temporal scales. These include, but are not limited to, genetic oscillators, clearance of waste products from the brain, dynamic interplay among brain regions, and propagation of local dynamics across the cortex. The combination of these processes, modulated by environmental cues, such as light-dark cycles and work schedules, represents a complex multiscale system that regulates sleep-wake cycles and brain dynamics. Physiology-based mathematical models have successfully explained the mechanisms underpinning dynamics at specific scales and are a useful tool to investigate interactions across multiple scales. They can help answer questions such as how do electroencephalographic (EEG) features relate to subthalamic neuron activity? Or how are local cortical dynamics regulated by the homeostatic and circadian mechanisms? In this chapter, we review two types of models that are well-positioned to consider such interactions. Part I of the chapter focuses on the subthalamic sleep regulatory networks and a model of arousal dynamics capable of predicting sleep, circadian rhythms, and cognitive outputs. Part II presents a model of corticothalamic circuits, capable of predicting spatial and temporal EEG features. We then discuss existing approaches and unsolved challenges in developing unified multiscale models.

Secondary thalamic dysfunction underlies abnormal large-scale neural dynamics in chronic stroke

Stroke causes pronounced and widespread slowing of neural activity. Despite decades of work exploring these abnormal neural dynamics and their associated functional impairments, their causes remain largely unclear. To close this gap in understanding, we applied a neurophysiological corticothalamic circuit model to simulate magnetoencephalography (MEG) power spectra recorded from chronic stroke patients. Comparing model-estimated physiological parameters to those of controls, patients demonstrated significantly lower intrathalamic inhibition in the lesioned hemisphere, despite the absence of direct damage to the thalamus itself. We hypothesized that this disinhibition could instead be related to secondary degeneration of the thalamus, for which growing evidence exists in the literature. Further analyses confirmed that spectral slowing correlated significantly with overall secondary degeneration of the ipsilesional thalamus, encompassing decreased thalamic volume, altered tissue microstructure, and decreased blood flow. Crucially, this relationship was mediated by model-estimated thalamic disinhibition, suggesting a causal link between secondary thalamic degeneration and abnormal brain dynamics via thalamic disinhibition. Finally, thalamic degeneration was correlated significantly with poorer cognitive and language outcomes, but not lesion volume, reinforcing that thalamus damage may account for additional individual variability in poststroke disability. Overall, our findings indicate that the frequently observed poststroke slowing reflects a disruption of corticothalamic circuit dynamics due to secondary thalamic dysfunction, and highlights the thalamus as an important target for understanding and potentially treating poststroke brain dysfunction.

Multiple Intrinsic Timescales Govern Distinct Brain States in Human Sleep

Human sleep exhibits multiple, recurrent temporal regularities, ranging from circadian rhythms to sleep stage cycles and neuronal oscillations during nonrapid eye movement sleep. Moreover, recent evidence revealed a functional role of aperiodic activity, which reliably discriminates different sleep stages. Aperiodic activity is commonly defined as the spectral slope χ of the 1/frequency (1/fχ) decay function of the electrophysiological power spectrum. However, several lines of inquiry now indicate that the aperiodic component of the power spectrum might be better characterized by a superposition of several decay processes with associated timescales. Here, we determined multiple timescales, which jointly shape aperiodic activity using human intracranial electroencephalography. Across three independent studies (47 participants, 23 female), our results reveal that aperiodic activity reliably dissociated sleep stage-dependent dynamics in a regionally specific manner. A principled approach to parametrize aperiodic activity delineated several, spatially and state-specific timescales. Lastly, we employed pharmacological modulation by means of propofol anesthesia to disentangle state-invariant timescales that may reflect physical properties of the underlying neural population from state-specific timescales that likely constitute functional interactions. Collectively, these results establish the presence of multiple intrinsic timescales that define the electrophysiological power spectrum during distinct brain states.

Imbalance in positive and negative acceleration ratio of alpha oscillation in patients with complex regional pain syndrome

Objectives

To elucidate the functional characteristics of the brain in the presence of chronic pain using electroencephalography (EEG), with a focus on the dynamics of neural excitation and inhibition.

Methods

Resting-state EEG was performed in: 17 patients with complex regional pain syndrome (CRPS) who exhibited chronic pain higher than 20 on the visual analogue scale (VAS), 6 patients with reduced CRPS symptoms and chronic pain less than 20 on VAS, and healthy age-matched controls. For the analysis, 50 s of electroencephalogram (EEG) signals were extracted from EEG recordings during wakefulness and rest with eyes closed. The envelope of the alpha frequency band was calculated by examining the positive and negative accelerations of the envelope oscillation, ratio of positive (Ap) to negative (An) accelerations (Ap-An ratio), and mean amplitude of the envelope. Comparisons were made between patients and controls, and correlations between these EEG measures and the subjective pain VAS were evaluated.Significant differences in the value of Ap, An and Ap-An ratio were observed at temporal and central electrodes between patients with pain symptoms and controls. Those with reduced CRPS symptoms exhibited a distinct Ap-An ratio at the majority of electrodes when compared with those exhibiting chronic pain.

Conclusions

Distinct patterns in alpha wave envelope dynamics, reflecting excitatory and inhibitory activities, were associated with chronic pain in patients with CRPS. The pain-relieved state of CRPS suggested that a new balance of activities was established. This relationship indicated a potential association between altered alpha oscillation characteristics and the subjective experience of pain.

Significance

This study introduces a novel method for analyzing alpha oscillation envelopes, providing new insights into the neural pathophysiology of chronic pain in CRPS patients. This approach has the potential to enhance our understanding of the alterations in brain function that occur under chronic pain conditions.

Analysis of the alpha activity envelope in electroencephalography in relation to the ratio of excitatory to inhibitory neural activity

Alpha waves, one of the major components of resting and awake cortical activity in human electroencephalography (EEG), are known to show waxing and waning, but this phenomenon has rarely been analyzed. In the present study, we analyzed this phenomenon from the viewpoint of excitation and inhibition. The alpha wave envelope was subjected to secondary differentiation. This gave the positive (acceleration positive, Ap) and negative (acceleration negative, An) values of acceleration and their ratio (Ap-An ratio) at each sampling point of the envelope signals for 60 seconds. This analysis was performed on 36 participants with Alzheimer's disease (AD), 23 with frontotemporal dementia (FTD) and 29 age-matched healthy participants (NC) whose data were provided as open datasets. The mean values of the Ap-An ratio for 60 seconds at each EEG electrode were compared between the NC and AD/FTD groups. The AD (1.41 ±0.01 (SD)) and FTD (1.40 ±0.02) groups showed a larger Ap-An ratio than the NC group (1.38 ±0.02, p<0.05). A significant correlation between the envelope amplitude of alpha activity and the Ap-An ratio was observed at most electrodes in the NC group (Pearson's correlation coefficient, r = -0.92 ±0.15, mean for all electrodes), whereas the correlation was disrupted in AD (-0.09 ±0.21, p<0.05) and disrupted in the frontal region in the FTD group. The present method analyzed the envelope of alpha waves from a new perspective, that of excitation and inhibition, and it could detect properties of the EEG, Ap-An ratio, that have not been revealed by existing methods. The present study proposed a new method to analyze the alpha activity envelope in electroencephalography, which could be related to excitatory and inhibitory neural activity.

Recruiting neural field theory for data augmentation in a motor imagery brain-computer interface

We introduce a novel approach to training data augmentation in brain-computer interfaces (BCIs) using neural field theory (NFT) applied to EEG data from motor imagery tasks. BCIs often suffer from limited accuracy due to a limited amount of training data. To address this, we leveraged a corticothalamic NFT model to generate artificial EEG time series as supplemental training data. We employed the BCI competition IV '2a' dataset to evaluate this augmentation technique. For each individual, we fitted the model to common spatial patterns of each motor imagery class, jittered the fitted parameters, and generated time series for data augmentation. Our method led to significant accuracy improvements of over 2% in classifying the "total power" feature, but not in the case of the "Higuchi fractal dimension" feature. This suggests that the fit NFT model may more favorably represent one feature than the other. These findings pave the way for further exploration of NFT-based data augmentation, highlighting the benefits of biophysically accurate artificial data.

Neural complexity and the spectral slope characterise auditory processing in wakefulness and sleep

Auditory processing and the complexity of neural activity can both indicate residual consciousness levels and differentiate states of arousal. However, how measures of neural signal complexity manifest in neural activity following environmental stimulation and, more generally, how the electrophysiological characteristics of auditory responses change in states of reduced consciousness remain under-explored. Here, we tested the hypothesis that measures of neural complexity and the spectral slope would discriminate stages of sleep and wakefulness not only in baseline electroencephalography (EEG) activity but also in EEG signals following auditory stimulation. High-density EEG was recorded in 21 participants to determine the spatial relationship between these measures and between EEG recorded pre- and post-auditory stimulation. Results showed that the complexity and the spectral slope in the 2-20 Hz range discriminated between sleep stages and had a high correlation in sleep. In wakefulness, complexity was strongly correlated to the 20-40 Hz spectral slope. Auditory stimulation resulted in reduced complexity in sleep compared to the pre-stimulation EEG activity and modulated the spectral slope in wakefulness. These findings confirm our hypothesis that electrophysiological markers of arousal are sensitive to sleep/wake states in EEG activity during baseline and following auditory stimulation. Our results have direct applications to studies using auditory stimulation to probe neural functions in states of reduced consciousness.

Modelling cortical network dynamics

We have investigated the theoretical constraints of the interactions between coupled cortical columns. Each cortical column consists of a set of neural populations where each population is modelled as a neural mass. The existence of semi-stable states within a cortical column is dependent on the type of interaction between the neuronal populations, i.e., the form of the synaptic kernels. Current-to-current coupling has been shown, in contrast to potential-to-current coupling, to create semi-stable states within a cortical column. The interaction between semi-stable states of the cortical columns is studied where we derive the dynamics for the collected activity. For small excitations the dynamics follow the Kuramoto model; however, in contrast to previous work we derive coupled equations between phase and amplitude dynamics with the possibility of defining connectivity as a stationary and dynamic variable. The turbulent flow of phase dynamics which occurs in networks of Kuramoto oscillators would indicate turbulent changes in dynamic connectivity for coupled cortical columns which is something that has been recorded in epileptic seizures. We used the results we derived to estimate a seizure propagation model which allowed for inversions using the Laplace assumption (Dynamic Causal Modelling). The seizure propagation model was trialed on simulated data, and future work will investigate the estimation of the connectivity matrix from empirical data. This model can be used to predict changes in seizure evolution after virtual changes in the connectivity network, something that could be of clinical use when applied to epilepsy surgical cases.

The non-specific matrix thalamus facilitates the cortical information processing modes relevant for conscious awareness

The neurobiological mechanisms of arousal and anesthesia remain poorly understood. Recent evidence highlights the key role of interactions between the cerebral cortex and the diffusely projecting matrix thalamic nuclei. Here, we interrogate these processes in a whole-brain corticothalamic neural mass model endowed with targeted and diffusely projecting thalamocortical nuclei inferred from empirical data. This model captures key features seen in propofol anesthesia, including diminished network integration, lowered state diversity, impaired susceptibility to perturbation, and decreased corticocortical coherence. Collectively, these signatures reflect a suppression of information transfer across the cerebral cortex. We recover these signatures of conscious arousal by selectively stimulating the matrix thalamus, recapitulating empirical results in macaque, as well as wake-like information processing states that reflect the thalamic modulation of large-scale cortical attractor dynamics. Our results highlight the role of matrix thalamocortical projections in shaping many features of complex cortical dynamics to facilitate the unique communication states supporting conscious awareness.

Comparative analysis of multifaceted neural effects associated with varying endogenous cognitive load

Contemporary neuroscience has firmly established that mental state variation concurs with changes in neural dynamic activity in a complex way that a one-to-one mapping cannot describe. To explore the scenario of the multifaceted changes in neural dynamics associated with simple mental state variation, we took cognitive load - a common cognitive manipulation in psychology - as a venue to characterize how multiple neural dynamic features are simultaneously altered by the manipulation and how their sensitivity differs. Electroencephalogram was collected from 152 participants performing stimulus-free tasks with different demands. The results show that task demand alters wide-ranging neural dynamic features, including band-specific oscillations across broad frequency bands, scale-free dynamics, and cross-frequency phase-amplitude coupling. The scale-free dynamics outperformed others in indexing cognitive load variation. This study demonstrates a complex relationship between cognitive dynamics and neural dynamics, which points to a necessity to integrate multifaceted neural dynamic features when studying mind-brain relationship in the future.

Geometric constraints on human brain function

The anatomy of the brain necessarily constrains its function, but precisely how remains unclear. The classical and dominant paradigm in neuroscience is that neuronal dynamics are driven by interactions between discrete, functionally specialized cell populations connected by a complex array of axonal fibres1-3. However, predictions from neural field theory, an established mathematical framework for modelling large-scale brain activity4-6, suggest that the geometry of the brain may represent a more fundamental constraint on dynamics than complex interregional connectivity7,8. Here, we confirm these theoretical predictions by analysing human magnetic resonance imaging data acquired under spontaneous and diverse task-evoked conditions. Specifically, we show that cortical and subcortical activity can be parsimoniously understood as resulting from excitations of fundamental, resonant modes of the brain's geometry (that is, its shape) rather than from modes of complex interregional connectivity, as classically assumed. We then use these geometric modes to show that task-evoked activations across over 10,000 brain maps are not confined to focal areas, as widely believed, but instead excite brain-wide modes with wavelengths spanning over 60 mm. Finally, we confirm predictions that the close link between geometry and function is explained by a dominant role for wave-like activity, showing that wave dynamics can reproduce numerous canonical spatiotemporal properties of spontaneous and evoked recordings. Our findings challenge prevailing views and identify a previously underappreciated role of geometry in shaping function, as predicted by a unifying and physically principled model of brain-wide dynamics.

The mesoanatomy of the cortex, minimization of free energy, and generative cognition

Capacity for generativity and unlimited association is the defining characteristic of sentience, and this capacity somehow arises from neuronal self-organization in the cortex. We have previously argued that, consistent with the free energy principle, cortical development is driven by synaptic and cellular selection maximizing synchrony, with effects manifesting in a wide range of features of mesoscopic cortical anatomy. Here, we further argue that in the postnatal stage, as more structured inputs reach the cortex, the same principles of self-organization continue to operate at multitudes of local cortical sites. The unitary ultra-small world structures that emerged antenatally can represent sequences of spatiotemporal images. Local shifts of presynapses from excitatory to inhibitory cells result in the local coupling of spatial eigenmodes and the development of Markov blankets, minimizing prediction errors in each unit's interactions with surrounding neurons. In response to the superposition of inputs exchanged between cortical areas, more complicated, potentially cognitive structures are competitively selected by the merging of units and the elimination of redundant connections that result from the minimization of variational free energy and the elimination of redundant degrees of freedom. The trajectory along which free energy is minimized is shaped by interaction with sensorimotor, limbic, and brainstem mechanisms, providing a basis for creative and unlimited associative learning.

Preservation of thalamocortical circuitry is essential for good recovery after cardiac arrest

Continuous electroencephalographam (EEG) monitoring contributes to prediction of neurological outcome in comatose cardiac arrest survivors. While the phenomenology of EEG abnormalities in postanoxic encephalopathy is well known, the pathophysiology, especially the presumed role of selective synaptic failure, is less understood. To further this understanding, we estimate biophysical model parameters from the EEG power spectra from individual patients with a good or poor recovery from a postanoxic encephalopathy. This biophysical model includes intracortical, intrathalamic, and corticothalamic synaptic strengths, as well as synaptic time constants and axonal conduction delays. We used continuous EEG measurements from hundred comatose patients recorded during the first 48 h postcardiac arrest, 50 with a poor neurological outcome [cerebral performance category ( CPC = 5 ) ] and 50 with a good neurological outcome ( CPC = 1 ). We only included patients that developed (dis-)continuous EEG activity within 48 h postcardiac arrest. For patients with a good outcome, we observed an initial relative excitation in the corticothalamic loop and corticothalamic propagation that subsequently evolved towards values observed in healthy controls. For patients with a poor outcome, we observed an initial increase in the cortical excitation-inhibition ratio, increased relative inhibition in the corticothalamic loop, delayed corticothalamic propagation of neuronal activity, and severely prolonged synaptic time constants that did not return to physiological values. We conclude that the abnormal EEG evolution in patients with a poor neurological recovery after cardiac arrest may result from persistent and selective synaptic failure that includes corticothalamic circuitry and also delayed corticothalamic propagation.

Dissociation between phase and power correlation networks in the human brain is driven by co-occurrent bursts

Well-known haemodynamic resting-state networks are better mirrored in power correlation networks than phase coupling networks in electrophysiological data. However, what do these power correlation networks reflect? We address this long-outstanding question in neuroscience using rigorous mathematical analysis, biophysical simulations with ground truth and application of these mathematical concepts to empirical magnetoencephalography (MEG) data. Our mathematical derivations show that for two non-Gaussian electrophysiological signals, their power correlation depends on their coherence, cokurtosis and conjugate-coherence. Only coherence and cokurtosis contribute to power correlation networks in MEG data, but cokurtosis is less affected by artefactual signal leakage and better mirrors haemodynamic resting-state networks. Simulations and MEG data show that cokurtosis may reflect co-occurrent bursting events. Our findings shed light on the origin of the complementary nature of power correlation networks to phase coupling networks and suggests that the origin of resting-state networks is partly reflected in co-occurent bursts in neuronal activity.

Unification of free energy minimization, spatiotemporal energy, and dimension reduction models of V1 organization: Postnatal learning on an antenatal scaffold

Developmental selection of neurons and synapses so as to maximize pulse synchrony has recently been used to explain antenatal cortical development. Consequences of the same selection process—an application of the Free Energy Principle—are here followed into the postnatal phase in V1, and the implications for cognitive function are considered. Structured inputs transformed via lag relay in superficial patch connections lead to the generation of circumferential synaptic connectivity superimposed upon the antenatal, radial, “like-to-like” connectivity surrounding each singularity. The spatiotemporal energy and dimension reduction models of cortical feature preferences are accounted for and unified within the expanded model, and relationships of orientation preference (OP), space frequency preference (SFP), and temporal frequency preference (TFP) are resolved. The emergent anatomy provides a basis for “active inference” that includes interpolative modification of synapses so as to anticipate future inputs, as well as learn directly from present stimuli. Neurodynamic properties are those of heteroclinic networks with coupled spatial eigenmodes.

Globally elevated excitation-inhibition ratio in children with autism spectrum disorder and below-average intelligence

Background

Altered neuronal excitation–inhibition (E–I) balance is strongly implicated in ASD. However, it is not known whether the direction and degree of changes in the E–I ratio in individuals with ASD correlates with intellectual disability often associated with this developmental disorder. The spectral slope of the aperiodic 1/f activity reflects the E–I balance at the scale of large neuronal populations and may uncover its putative alternations in individuals with ASD with and without intellectual disability.

Methods

Herein, we used magnetoencephalography (MEG) to test whether the 1/f slope would differentiate ASD children with average and below–average (< 85) IQ. MEG was recorded at rest with eyes open/closed in 49 boys with ASD aged 6–15 years with IQ ranging from 54 to 128, and in 49 age-matched typically developing (TD) boys. The cortical source activity was estimated using the beamformer approach and individual brain models. We then extracted the 1/f slope by fitting a linear function to the log–log-scale power spectra in the high-frequency range.

Results

The global 1/f slope averaged over all cortical sources demonstrated high rank-order stability between the two conditions. Consistent with previous research, it was steeper in the eyes-closed than in the eyes-open condition and flattened with age. Regardless of condition, children with ASD and below-average IQ had flatter slopes than either TD or ASD children with average or above-average IQ. These group differences could not be explained by differences in signal-to-noise ratio or periodic (alpha and beta) activity.

Limitations

Further research is needed to find out whether the observed changes in E–I ratios are characteristic of children with below-average IQ of other diagnostic groups.

Conclusions

The atypically flattened spectral slope of aperiodic activity in children with ASD and below-average IQ suggests a shift of the global E–I balance toward hyper-excitation. The spectral slope can provide an accessible noninvasive biomarker of the E–I ratio for making objective judgments about treatment effectiveness in people with ASD and comorbid intellectual disability.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13229-022-00498-2.

Alpha blocking and 1/fβ spectral scaling in resting EEG can be accounted for by a sum of damped alpha band oscillatory processes

The dynamical and physiological basis of alpha band activity and 1/f^β noise in the EEG are the subject of continued speculation. Here we conjecture, on the basis of empirical data analysis, that both of these features may be economically accounted for through a single process if the resting EEG is conceived of being the sum of multiple stochastically perturbed alpha band damped linear oscillators with a distribution of dampings (relaxation rates). The modulation of alpha-band and 1/f^β noise activity by changes in damping is explored in eyes closed (EC) and eyes open (EO) resting state EEG. We aim to estimate the distribution of dampings by solving an inverse problem applied to EEG power spectra. The characteristics of the damping distribution are examined across subjects, sensors and recording condition (EC/EO). We find that there are robust changes in the damping distribution between EC and EO recording conditions across participants. The estimated damping distributions are found to be predominantly bimodal, with the number and position of the modes related to the sharpness of the alpha resonance and the scaling (β) of the power spectrum (1/f^β). The results suggest that there exists an intimate relationship between resting state alpha activity and 1/f^β noise with changes in both governed by changes to the damping of the underlying alpha oscillatory processes. In particular, alpha-blocking is observed to be the result of the most weakly damped distribution mode becoming more heavily damped. The results suggest a novel way of characterizing resting EEG power spectra and provides new insight into the central role that damped alpha-band activity may play in characterising the spatio-temporal features of resting state EEG.

The resting human electroencephalogram (EEG) exhibits two dominant spectral features: the alpha rhythm (8–13 Hz) and its associated attenuation between eyes-closed and eyes-open resting state (alpha blocking), and the 1/f^β scaling of the power spectrum. While these phenomena are well studied a thorough understanding of their respective generative processes remains elusive. By employing a theoretical approach that follows from neural population models of EEG we demonstrate that it is possible to economically account for both of these phenomena using a singular mechanistic framework: resting EEG is assumed to arise from the summed activity of multiple uncorrelated, stochastically driven, damped alpha band linear oscillatory processes having a distribution of relaxation rates or dampings. By numerically estimating these damping distributions from eyes-closed and eyes-open EEG data, in a total of 136 participants, it is found that such damping distributions are predominantly bimodal in shape. The most weakly damped mode is found to account for alpha band power, with alpha blocking being driven by an increase in the damping of this weakly damped mode, whereas the second, and more heavily damped mode, is able to explain 1/f^β scaling present in the resting state EEG spectra.

Functional and structural brain network correlates of visual hallucinations in Lewy body dementia

Visual hallucinations are a common feature of Lewy body dementia. Previous studies have shown that visual hallucinations are highly specific in differentiating Lewy body dementia from Alzheimer’s disease dementia and Alzheimer–Lewy body mixed pathology cases. Computational models propose that impairment of visual and attentional networks is aetiologically key to the manifestation of visual hallucinations symptomatology. However, there is still a lack of experimental evidence on functional and structural brain network abnormalities associated with visual hallucinations in Lewy body dementia.

We used EEG source localization and network based statistics to assess differential topographical patterns in Lewy body dementia between 25 participants with visual hallucinations and 17 participants without hallucinations. Diffusion tensor imaging was used to assess structural connectivity between thalamus, basal forebrain and cortical regions belonging to the functionally affected network component in the hallucinating group, as assessed with network based statistics. The number of white matter streamlines within the cortex and between subcortical and cortical regions was compared between hallucinating and not hallucinating groups and correlated with average EEG source connectivity of the affected subnetwork. Moreover, modular organization of the EEG source network was obtained, compared between groups and tested for correlation with structural connectivity.

Network analysis showed that compared to non-hallucinating patients, those with hallucinations feature consistent weakened connectivity within the visual ventral network, and between this network and default mode and ventral attentional networks, but not between or within attentional networks. The occipital lobe was the most functionally disconnected region. Structural analysis yielded significantly affected white matter streamlines connecting the cortical regions to the nucleus basalis of Meynert and the thalamus in hallucinating compared to not hallucinating patients. The number of streamlines in the tract between the basal forebrain and the cortex correlated with cortical functional connectivity in non-hallucinating patients, while a correlation emerged for the white matter streamlines connecting the functionally affected cortical regions in the hallucinating group.

This study proposes, for the first time, differential functional networks between hallucinating and not hallucinating Lewy body dementia patients, and provides empirical evidence for existing models of visual hallucinations. Specifically, the outcome of the present study shows that the hallucinating condition is associated with functional network segregation in Lewy body dementia and supports the involvement of the cholinergic system as proposed in the current literature.

Complementary roles of neural synchrony and complexity for indexing consciousness and chances of surviving in acute coma

An open challenge in consciousness research is understanding how neural functions are altered by pathological loss of consciousness. To maintain consciousness, the brain needs synchronized communication of information across brain regions, and sufficient complexity in neural activity. Coordination of brain activity, typically indexed through measures of neural synchrony, has been shown to decrease when consciousness is lost and to reflect the clinical state of patients with disorders of consciousness. Moreover, when consciousness is lost, neural activity loses complexity, while the levels of neural noise, indexed by the slope of the electroencephalography (EEG) spectral exponent decrease. Although these properties have been well investigated in resting state activity, it remains unknown whether the sensory processing network, which has been shown to be preserved in coma, suffers from a loss of synchronization or information content. Here, we focused on acute coma and hypothesized that neural synchrony in response to auditory stimuli would reflect coma severity, while complexity, or neural noise, would reflect the presence or loss of consciousness. Results showed that neural synchrony of EEG signals was stronger for survivors than non-survivors and predictive of patients' outcome, but indistinguishable between survivors and healthy controls. Measures of neural complexity and neural noise were not informative of patients' outcome and had high or low values for patients compared to controls. Our results suggest different roles for neural synchrony and complexity in acute coma. Synchrony represents a precondition for consciousness, while complexity needs an equilibrium between high or low values to support conscious cognition.

Inference of brain networks with approximate Bayesian computation - assessing face validity with an example application in Parkinsonism

This paper describes and validates a novel framework using the Approximate Bayesian Computation (ABC) algorithm for parameter estimation and model selection in models of mesoscale brain network activity. We provide a proof of principle, first pass validation of this framework using a set of neural mass models of the cortico-basal ganglia thalamic circuit inverted upon spectral features from experimental, in vivo recordings. This optimization scheme relaxes an assumption of fixed-form posteriors (i.e. the Laplace approximation) taken in previous approaches to inverse modelling of spectral features. This enables the exploration of model dynamics beyond that approximated from local linearity assumptions and so fit to explicit, numerical solutions of the underlying non-linear system of equations. In this first paper, we establish a face validation of the optimization procedures in terms of: (i) the ability to approximate posterior densities over parameters that are plausible given the known causes of the data; (ii) the ability of the model comparison procedures to yield posterior model probabilities that can identify the model structure known to generate the data; and (iii) the robustness of these procedures to local minima in the face of different starting conditions. Finally, as an illustrative application we show (iv) that model comparison can yield plausible conclusions given the known neurobiology of the cortico-basal ganglia-thalamic circuit in Parkinsonism. These results lay the groundwork for future studies utilizing highly nonlinear or brittle models that can explain time dependant dynamics, such as oscillatory bursts, in terms of the underlying neural circuits.

Computational Models in Electroencephalography

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by “computational model” is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Characterizing pink and white noise in the human electroencephalogram

OBJECTIVE

The power spectrum of the human electroencephalogram (EEG) as a function of frequency is a mix of brain oscillations (e.g. alpha activity around 10 Hz) and non-oscillations or noise of uncertain origin. "White noise" is uniformly distributed over frequency, while "pink noise" has an inverse power-frequency relation (power ∝ 1/f). Interest in EEG pink noise has been growing, but previous human estimates appear methodologically flawed. We propose a new approach to extract separate valid estimates of pink and white noise from an EEG power spectrum.

APPROACH

We use simulated data to demonstrate its effectiveness compared with established procedures, and provide an illustrative example from a new resting eyes-open (EO) and eyes-closed (EC) dataset. The topographic characteristics of the obtained pink and white noise estimates are examined, as is the alpha power in this sample.

MAIN RESULTS

Valid pink and white noise estimates were successfully obtained for each of our 5400 individual spectra (60 participants × 30 electrodes × 3 conditions/blocks [EO1, EC, EO2]). The 1/f noise had a distinct central scalp topography, and white noise was occipital in distribution, both differing from the parietal topography of the alpha oscillation. These differences point to their separate neural origins. EC pink and white noise powers were globally greater than in EO.

SIGNIFICANCE

This valid estimation of pink and white noise in the human EEG holds promise for more accurate assessment of oscillatory neural activity in both typical and clinical groups, such as those with attention deficits. Further, outside the human EEG, the new methodology can be generalized to remove noise from spectra in many fields of science and technology.

Noise induced quiescence of epileptic spike generation in patients with epilepsy

Clinical scalp electroencephalographic recordings from patients with epilepsy are distinguished by the presence of epileptic discharges i.e. spikes or sharp waves. These often occur randomly on a background of fluctuating potentials. The spike rate varies between different brain states (sleep and awake) and patients. Epileptogenic tissue and regions near these often show increased spike rates in comparison to other cortical regions. Several studies have shown a relation between spike rate and background activity although the underlying reason for this is still poorly understood. Both these processes, spike occurrence and background activity show evidence of being at least partly stochastic processes. In this study we show that epileptic discharges seen on scalp electroencephalographic recordings and background activity are driven at least partly by a common biological noise. Furthermore, our results indicate noise induced quiescence of spike generation which, in analogy with computational models of spiking, indicate spikes to be generated by transitions between semi-stable states of the brain, similar to the generation of epileptic seizure activity. The deepened physiological understanding of spike generation in epilepsy that this study provides could be useful in the electrophysiological assessment of different therapies for epilepsy including the effect of different drugs or electrical stimulation.

A Connectome-Based, Corticothalamic Model of State- and Stimulation-Dependent Modulation of Rhythmic Neural Activity and Connectivity

Rhythmic activity in the brain fluctuates with behaviour and cognitive state, through a combination of coexisting and interacting frequencies. At large spatial scales such as those studied in human M/EEG, measured oscillatory dynamics are believed to arise primarily from a combination of cortical (intracolumnar) and corticothalamic rhythmogenic mechanisms. Whilst considerable progress has been made in characterizing these two types of neural circuit separately, relatively little work has been done that attempts to unify them into a single consistent picture. This is the aim of the present paper. We present and examine a whole-brain, connectome-based neural mass model with detailed long-range cortico-cortical connectivity and strong, recurrent corticothalamic circuitry. This system reproduces a variety of known features of human M/EEG recordings, including spectral peaks at canonical frequencies, and functional connectivity structure that is shaped by the underlying anatomical connectivity. Importantly, our model is able to capture state- (e.g., idling/active) dependent fluctuations in oscillatory activity and the coexistence of multiple oscillatory phenomena, as well as frequency-specific modulation of functional connectivity. We find that increasing the level of sensory drive to the thalamus triggers a suppression of the dominant low frequency rhythms generated by corticothalamic loops, and subsequent disinhibition of higher frequency endogenous rhythmic behaviour of intracolumnar microcircuits. These combine to yield simultaneous decreases in lower frequency and increases in higher frequency components of the M/EEG power spectrum during states of high sensory or cognitive drive. Building on this, we also explored the effect of pulsatile brain stimulation on ongoing oscillatory activity, and evaluated the impact of coexistent frequencies and state-dependent fluctuations on the response of cortical networks. Our results provide new insight into the role played by cortical and corticothalamic circuits in shaping intrinsic brain rhythms, and suggest new directions for brain stimulation therapies aimed at state-and frequency-specific control of oscillatory brain activity.

Diffuse neural coupling mediates complex network dynamics through the formation of quasi-critical brain states

The biological mechanisms that allow the brain to balance flexibility and integration remain poorly understood. A potential solution may lie in a unique aspect of neurobiology, which is that numerous brain systems contain diffuse synaptic connectivity. Here, we demonstrate that increasing diffuse cortical coupling within a validated biophysical corticothalamic model traverses the system through a quasi-critical regime in which spatial heterogeneities in input noise support transient critical dynamics in distributed subregions. The presence of quasi-critical states coincides with known signatures of complex, adaptive brain network dynamics. Finally, we demonstrate the presence of similar dynamic signatures in empirical whole-brain human neuroimaging data. Together, our results establish that modulating the balance between local and diffuse synaptic coupling in a thalamocortical model subtends the emergence of quasi-critical brain states that act to flexibly transition the brain between unique modes of information processing.

Relationships Between Neuronal Oscillatory Amplitude and Dynamic Functional Connectivity

Event-related fluctuations of neural oscillatory amplitude are reported widely in the context of cognitive processing and are typically interpreted as a marker of brain "activity". However, the precise nature of these effects remains unclear; in particular, whether such fluctuations reflect local dynamics, integration between regions, or both, is unknown. Here, using magnetoencephalography, we show that movement induced oscillatory modulation is associated with transient connectivity between sensorimotor regions. Further, in resting-state data, we demonstrate a significant association between oscillatory modulation and dynamic connectivity. A confound with such empirical measurements is that increased amplitude necessarily means increased signal-to-noise ratio (SNR): this means that the question of whether amplitude and connectivity are genuinely coupled, or whether increased connectivity is observed purely due to increased SNR is unanswered. Here, we counter this problem by analogy with computational models which show that, in the presence of global network coupling and local multistability, the link between oscillatory modulation and long-range connectivity is a natural consequence of neural networks. Our results provide evidence for the notion that connectivity is mediated by neural oscillations, and suggest that time-frequency spectrograms are not merely a description of local synchrony but also reflect fluctuations in long-range connectivity.

A Critical Analysis on Characterizing the Meditation Experience Through the Electroencephalogram

Meditation practices, originated from ancient traditions, have increasingly received attention due to their potential benefits to mental and physical health. The scientific community invests efforts into scrutinizing and quantifying the effects of these practices, especially on the brain. There are methodological challenges in describing the neural correlates of the subjective experience of meditation. We noticed, however, that technical considerations on signal processing also don't follow standardized approaches, which may hinder generalizations. Therefore, in this article, we discuss the usage of the electroencephalogram (EEG) as a tool to study meditation experiences in healthy individuals. We describe the main EEG signal processing techniques and how they have been translated to the meditation field until April 2020. Moreover, we examine in detail the limitations/assumptions of these techniques and highlight some good practices, further discussing how technical specifications may impact the interpretation of the outcomes. By shedding light on technical features, this article contributes to more rigorous approaches to evaluate the construct of meditation.

An electrophysiological marker of arousal level in humans

Deep non-rapid eye movement sleep (NREM) and general anesthesia with propofol are prominent states of reduced arousal linked to the occurrence of synchronized oscillations in the electroencephalogram (EEG). Although rapid eye movement (REM) sleep is also associated with diminished arousal levels, it is characterized by a desynchronized, 'wake-like' EEG. This observation implies that reduced arousal states are not necessarily only defined by synchronous oscillatory activity. Using intracranial and surface EEG recordings in four independent data sets, we demonstrate that the 1/f spectral slope of the electrophysiological power spectrum, which reflects the non-oscillatory, scale-free component of neural activity, delineates wakefulness from propofol anesthesia, NREM and REM sleep. Critically, the spectral slope discriminates wakefulness from REM sleep solely based on the neurophysiological brain state. Taken together, our findings describe a common electrophysiological marker that tracks states of reduced arousal, including different sleep stages as well as anesthesia in humans.

The growth of cognition: Free energy minimization and the embryogenesis of cortical computation

The assumption that during cortical embryogenesis neurons and synaptic connections are selected to form an ensemble maximising synchronous oscillation explains mesoscopic cortical development, and a mechanism for cortical information processing is implied by consistency with the Free Energy Principle and Dynamic Logic. A heteroclinic network emerges, with stable and unstable fixed points of oscillation corresponding to activity in symmetrically connected, versus asymmetrically connected, sets of neurons. Simulations of growth explain a wide range of anatomical observations for columnar and non-columnar cortex, superficial patch connections, and the organization and dynamic interactions of neurone response properties. An antenatal scaffold is created, upon which postnatal learning can establish continuously ordered neuronal representations, permitting matching of co-synchronous fields in multiple cortical areas to solve optimization problems as in Dynamic Logic. Fast synaptic competition partitions equilibria, minimizing "the curse of dimensionality", while perturbations between imperfectly partitioned synchronous fields, under internal reinforcement, enable the cortex to become adaptively self-directed. As learning progresses variational free energy is minimized and entropy bounded.

Power spectrum of resting-state blood-oxygen-level-dependent signal

Hemodynamic modeling is used to explore the origin, predict, and analyze the power spectrum of the resting-state blood-oxygen-level-dependent (BOLD) signal measured by functional magnetic resonance imaging (fMRI), which has been reported to have a power-law form, i.e., P(f)∝f^{-s}, where P(f) is the power, f is the frequency, and s>0 is the power-law exponent. However, current fMRI experimental paradigms have limited acquisition durations, affecting the spectral resolution of fMRI data at the low-frequency regime. Here, the claimed power-law spectrum is investigated by using a recent hemodynamic model to analytically derive the BOLD power spectrum, with parameters that are related to neurophysiology. The theoretical results show that, for all realistic parameter combinations, the BOLD power spectrum is flat at f≲0.01Hz, has a weak resonance originating from intrinsic oscillations of vasodilatory response, and becomes a power law for high frequencies, all of which is in agreement with an empirical data set that describes the spectrum of one subject and brain region. However, the results are contrary to studies reporting a pure power-law spectrum at f≲0.2Hz. The discrepancy is attributed largely to data averaging employed by current approaches that averages together important properties of the BOLD power spectrum, such as its resonance, that biases the spectrum to only show a power law. Data averaging also reduces the high-frequency power-law exponent relative to individual cases. Overall, this work demonstrates how the model can reproduce BOLD dynamics and further analyze its low-frequency behavior. Moreover, it also uses the model to explain the impact of procedures, such as data averaging, on the reported features of the BOLD power spectrum.

On the Hierarchical Organization of Oscillatory Assemblies: Layered Superimposition and a Global Bioelectric Framework

Bioelectric oscillations occur throughout the nervous system of nearly all animals, revealed to play an important role in various aspects of cognitive activity such as information processing and feature binding. Modern research into this dynamic and intrinsic bioelectric activity of neural cells continues to raise questions regarding their role in consciousness and cognition. In this theoretical article, we assert a novel interpretation of the hierarchical nature of "brain waves" by identifying that the superposition of multiple oscillations varying in frequency corresponds to the superimposing of the contents of consciousness and cognition. In order to describe this isomorphism, we present a layered model of the global functional oscillations of various frequencies which act as a part of a unified metastable continuum described by the Operational Architectonics theory and suggested to be responsible for the emergence of the phenomenal mind. We detail the purposes, functions, and origins of each layer while proposing our main theory that the superimposition of these oscillatory layers mirrors the superimposition of the components of the integrated phenomenal experience as well as of cognition. In contrast to the traditional view that localizations of high and low-frequency activity are spatially distinct, many authors have suggested a hierarchical nature to oscillations. Our theoretical interpretation is founded in four layers which correlate not only in frequency but in evolutionary development. As other authors have done, we explore how these layers correlate to the phenomenology of human experience. Special importance is placed on the most basal layer of slow oscillations in coordinating and grouping all of the other layers. By detailing the isomorphism between the phenomenal and physiologic aspects of how lower frequency layers provide a foundation for higher frequency layers to be organized upon, we provide a further means to elucidate physiological and cognitive mechanisms of mind and for the well-researched outcomes of certain voluntary breathing patterns and meditative practices which modulate the mind and have therapeutic effects for psychiatric and other disorders.

Unified dynamics of interictal events and absence seizures

The dynamics of interictal events between absence seizures and their relationship to seizures themselves are investigated by employing a neural field model of the corticothalamic system. Interictal events are modeled as being due to transient parameter excursions beyond the seizure threshold, in the present case by sufficiently temporally varying the connection strength between the cerebral cortex and the thalamus. Increasing connection strength drives the system into ∼3-Hz seizure oscillations via a supercritical Hopf bifurcation once the linear instability threshold is passed. Depending on the time course of the excursion above threshold, different interictal activity event dynamics are seen in the time series of corticothalamic fields. These resemble experimental interictal time series observed via electroencephalography. It is found that the morphology of these events depends on the magnitude and duration of the excursion above threshold. For a large-amplitude excursion of short duration, events resemble interictal spikes, where one large spike is seen, followed by small damped oscillations. For a short excursion with long duration, events like observed interictal periodic sharp waves are seen. When both amplitude and duration above threshold are large, seizure oscillations are seen. Using these outcomes, proximity to seizure can be estimated and tracked.

Large-scale brain modes reorganize between infant sleep states and carry prognostic information for preterms

Sleep architecture carries vital information about brain health across the lifespan. In particular, the ability to express distinct vigilance states is a key physiological marker of neurological wellbeing in the newborn infant although systems-level mechanisms remain elusive. Here, we demonstrate that the transition from quiet to active sleep in newborn infants is marked by a substantial reorganization of large-scale cortical activity and functional brain networks. This reorganization is attenuated in preterm infants and predicts visual performance at two years. We find a striking match between these empirical effects and a computational model of large-scale brain states which uncovers fundamental biophysical mechanisms not evident from inspection of the data. Active sleep is defined by reduced energy in a uniform mode of neural activity and increased energy in two more complex anteroposterior modes. Preterm-born infants show a deficit in this sleep-related reorganization of modal energy that carries novel prognostic information.

Optimal Model Parameter Estimation from EEG Power Spectrum Features Observed during General Anesthesia

Mathematical modeling is a powerful tool that enables researchers to describe the experimentally observed dynamics of complex systems. Starting with a robust model including model parameters, it is necessary to choose an appropriate set of model parameters to reproduce experimental data. However, estimating an optimal solution of the inverse problem, i.e., finding a set of model parameters that yields the best possible fit to the experimental data, is a very challenging problem. In the present work, we use different optimization algorithms based on a frequentist approach, as well as Monte Carlo Markov Chain methods based on Bayesian inference techniques to solve the considered inverse problems. We first probe two case studies with synthetic data and study models described by a stochastic non-delayed linear second-order differential equation and a stochastic linear delay differential equation. In a third case study, a thalamo-cortical neural mass model is fitted to the EEG spectral power measured during general anesthesia induced by anesthetics propofol and desflurane. We show that the proposed neural mass model fits very well to the observed EEG power spectra, particularly to the power spectral peaks within δ - (0 - 4 Hz) and α - (8 - 13 Hz) frequency ranges. Furthermore, for each case study, we perform a practical identifiability analysis by estimating the confidence regions of the parameter estimates and interpret the corresponding correlation and sensitivity matrices. Our results indicate that estimating the model parameters from analytically computed spectral power, we are able to accurately estimate the unknown parameters while avoiding the computational costs due to numerical integration of the model equations.

Suppression of Parkinsonian Beta Oscillations by Deep Brain Stimulation: Determination of Effective Protocols

A neural field model of the corticothalamic-basal ganglia system is developed that describes enhanced beta activity within subthalamic and pallidal circuits in Parkinson's disease (PD) via system resonances. A model of deep brain stimulation (DBS) of typical clinical targets, the subthalamic nucleus (STN) and globus pallidus internus (GPi), is added and studied for several distinct stimulation protocols that are used for treatment of the motor symptoms of PD and that reduce pathological beta band activity (13-30 Hz) in the corticothalamic-basal ganglia network. The resulting impact of DBS on enhanced beta activity in the STN and GPi, as well as cortico-subthalamic and cortico-pallidal coherence, are studied. Both STN-DBS and GPi-DBS are found to be effective for suppressing peak STN and GPi power in the beta band, with GPi-DBS being slightly more effective in both the STN and the GPi for all stimulus protocols tested. The largest decrease in cortico-STN coherence is observed during STN-DBS, whereas GPi-DBS is most effective for reducing cortico-GPi coherence. A reduction of the pathologically large STN connection strengths that define the parkinsonian state results in enhanced 6 Hz activity and could thus represent a compensatory mechanism that has the side effect of driving parkinsonian tremor-like oscillations. This model provides a method for systematically testing effective DBS protocols that agrees with experimental and clinical findings. Furthermore, the model suggests GPi-DBS and STN-DBS have distinct impacts on elevated synchronization between the basal ganglia and motor cortex in PD.

Dynamics of large-scale electrophysiological networks: A technical review

For several years it has been argued that neural synchronisation is crucial for cognition. The idea that synchronised temporal patterns between different neural groups carries information above and beyond the isolated activity of these groups has inspired a shift in focus in the field of functional neuroimaging. Specifically, investigation into the activation elicited within certain regions by some stimulus or task has, in part, given way to analysis of patterns of co-activation or functional connectivity between distal regions. Recently, the functional connectivity community has been looking beyond the assumptions of stationarity that earlier work was based on, and has introduced methods to incorporate temporal dynamics into the analysis of connectivity. In particular, non-invasive electrophysiological data (magnetoencephalography/electroencephalography (MEG/EEG)), which provides direct measurement of whole-brain activity and rich temporal information, offers an exceptional window into such (potentially fast) brain dynamics. In this review, we discuss challenges, solutions, and a collection of analysis tools that have been developed in recent years to facilitate the investigation of dynamic functional connectivity using these imaging modalities. Further, we discuss the applications of these approaches in the study of cognition and neuropsychiatric disorders. Finally, we review some existing developments that, by using realistic computational models, pursue a deeper understanding of the underlying causes of non-stationary connectivity.

Biophysical Modeling of Large-Scale Brain Dynamics and Applications for Computational Psychiatry

Noninvasive neuroimaging has revolutionized the study of the organization of the human brain and how its structure and function are altered in psychiatric disorders. A critical explanatory gap lies in our mechanistic understanding of how systems-level neuroimaging biomarkers emerge from underlying synaptic-level perturbations associated with a disease state. We describe an emerging computational psychiatry approach leveraging biophysically based computational models of large-scale brain dynamics and their potential integration with clinical and pharmacological neuroimaging. In particular, we focus on neural circuit models, which describe how patterns of functional connectivity observed in resting-state functional magnetic resonance imaging emerge from neural dynamics shaped by inter-areal interactions through underlying structural connectivity defining long-range projections. We highlight the importance of local circuit physiological dynamics, in combination with structural connectivity, in shaping the emergent functional connectivity. Furthermore, heterogeneity of local circuit properties across brain areas, which impacts large-scale dynamics, may be critical for modeling whole-brain phenomena and alterations in psychiatric disorders and pharmacological manipulation. Finally, we discuss important directions for future model development and biophysical extensions, which will expand their utility to link clinical neuroimaging to neurobiological mechanisms.

Effect of Stimulation Waveform on the Non-linear Entrainment of Cortical Alpha Oscillations

In the past decade, there has been a surge of interest in using patterned brain stimulation to manipulate cortical oscillations, in both experimental and clinical settings. But the relationship between stimulation waveform and its impact on ongoing oscillations remains poorly understood and severely restrains the development of new paradigms. To address some aspects of this intricate problem, we combine computational and mathematical approaches, providing new insights into the influence of waveform of both low and high-frequency stimuli on synchronous neural activity. Using a cellular-based cortical microcircuit network model, we performed numerical simulations to test the influence of different waveforms on ongoing alpha oscillations, and derived a mean-field description of stimulation-driven dynamics to better understand the observed responses. Our analysis shows that high-frequency periodic stimulation translates into an effective transformation of the neurons' response function, leading to waveform-dependent changes in oscillatory dynamics and resting state activity. Moreover, we found that randomly fluctuating stimulation linearizes the neuron response function while constant input moves its activation threshold. Taken together, our findings establish a new theoretical framework in which stimulation waveforms impact neural systems at the population-scale through non-linear interactions.

Cortical Statistical Correlation Tomography of EEG Resting State Networks

Resting state networks (RSNs) have been found in human brains during awake resting states. RSNs are composed of spatially distributed regions in which spontaneous activity fluctuations are temporally and dynamically correlated. A new computational framework for reconstructing RSNs with human EEG data has been developed in the present study. The proposed framework utilizes independent component analysis (ICA) on short-time Fourier transformed inverse source maps imaged from EEG data and statistical correlation analysis to generate cortical tomography of electrophysiological RSNs. The proposed framework was evaluated on three sets of resting-state EEG data obtained in the comparison of two conditions: (1) healthy controls with eyes closed and eyes open; (2) healthy controls and individuals with a balance disorder; (3) individuals with a balance disorder before and after receiving repetitive transcranial magnetic stimulation (rTMS) treatment. In these analyses, the same group of five RSNs with similar spatial and spectral patterns were successfully reconstructed by the proposed framework from each individual EEG dataset. These EEG RSN tomographic maps showed significant similarity with RSN templates derived from functional magnetic resonance imaging (fMRI). Furthermore, significant spatial and spectral differences of RSNs among compared conditions were observed in tomographic maps as well as their spectra, which were consistent with findings reported in the literature. Beyond the success of reconstructing EEG RSNs spatially on the cortical surface as in fMRI studies, this novel approach defines RSNs further with spectra, providing a new dimension in understanding and probing basic neural mechanisms of RSNs. The findings in patients' data further demonstrate its potential in identifying biomarkers for the diagnosis and treatment evaluation of neuropsychiatric disorders.

Dependence of absence seizure dynamics on physiological parameter evolution

A neural field model of the corticothalamic system is applied to investigate the temporal and spectral characteristics of absence seizures in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into an absence seizure-like state once a threshold is passed and a supercritical Hopf bifurcation occurs. The dynamics and spectral characteristics of the resulting model seizures are explored as functions of maximum connection strength, time above threshold, and the rate at which the connection strength increases (ramp rate). Our results enable spectral and temporal characteristics of seizures to be related to changes in the underlying physiological evolution of connections via nonlinear dynamics and neural field theory. Spectral analysis reveals that the power of the harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. It is also found that the time to reach the stable limit-cycle seizure oscillation from the instability threshold decreases with the square root of the ramp rate.

Quantitative theory of deep brain stimulation of the subthalamic nucleus for the suppression of pathological rhythms in Parkinson's disease

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is modeled to explore the mechanisms of this effective, but poorly understood, treatment for motor symptoms of drug-refractory Parkinson's disease and dystonia. First, a neural field model of the corticothalamic-basal ganglia (CTBG) system is developed that reproduces key clinical features of Parkinson's disease, including its characteristic 4-8 Hz and 13-30 Hz electrophysiological signatures. Deep brain stimulation of the STN is then modeled and shown to suppress the pathological 13-30 Hz (beta) activity for physiologically realistic and optimized stimulus parameters. This supports the idea that suppression of abnormally coherent activity in the CTBG system is a major factor in DBS therapy for Parkinson's disease, by permitting normal dynamics to resume. At high stimulus intensities, nonlinear effects in the target population mediate wave-wave interactions between resonant beta activity and the stimulus pulse train, leading to complex spectral structure that shows remarkable similarity to that seen in steady-state evoked potential experiments.