Turbulent-like Dynamics in the Human Brain

Individualized epidemic spreading models predict epilepsy surgery outcomes: A pseudo-prospective study

Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but up to 50% of patients continue to have seizures one year after the resection. In order to aid presurgical planning and predict postsurgical outcome on a patient-by-patient basis, we developed a framework of individualized computational models that combines epidemic spreading with patient-specific connectivity and epileptogeneity maps: the Epidemic Spreading Seizure and Epilepsy Surgery framework (ESSES). ESSES parameters were fitted in a retrospective study (N = 15) to reproduce invasive electroencephalography (iEEG)-recorded seizures. ESSES reproduced the iEEG-recorded seizures, and significantly better so for patients with good (seizure-free, SF) than bad (nonseizure-free, NSF) outcome. We illustrate here the clinical applicability of ESSES with a pseudo-prospective study (N = 34) with a blind setting (to the resection strategy and surgical outcome) that emulated presurgical conditions. By setting the model parameters in the retrospective study, ESSES could be applied also to patients without iEEG data. ESSES could predict the chances of good outcome after any resection by finding patient-specific model-based optimal resection strategies, which we found to be smaller for SF than NSF patients, suggesting an intrinsic difference in the network organization or presurgical evaluation results of NSF patients. The actual surgical plan overlapped more with the model-based optimal resection, and had a larger effect in decreasing modeled seizure propagation, for SF patients than for NSF patients. Overall, ESSES could correctly predict 75% of NSF and 80.8% of SF cases pseudo-prospectively. Our results show that individualised computational models may inform surgical planning by suggesting alternative resections and providing information on the likelihood of a good outcome after a proposed resection. This is the first time that such a model is validated with a fully independent cohort and without the need for iEEG recordings.

The Thermodynamics of Mind

To not only survive, but also thrive, the brain must efficiently orchestrate distributed computation across space and time. This requires hierarchical organisation facilitating fast information transfer and processing at the lowest possible metabolic cost. Quantifying brain hierarchy is difficult but can be estimated from the asymmetry of information flow. Thermodynamics has successfully characterised hierarchy in many other complex systems. Here, we propose the 'Thermodynamics of Mind' framework as a natural way to quantify hierarchical brain orchestration and its underlying mechanisms. This has already provided novel insights into the orchestration of hierarchy in brain states including movie watching, where the hierarchy of the brain is flatter than during rest. Overall, this framework holds great promise for revealing the orchestration of cognition.

Gaming expertise induces meso‑scale brain plasticity and efficiency mechanisms as revealed by whole-brain modeling

Video games are a valuable tool for studying the effects of training and neural plasticity on the brain. However, the underlying mechanisms related to plasticity-associated brain structural changes and their impact on brain dynamics are unknown. Here, we used a semi-empirical whole-brain model to study structural neural plasticity mechanisms linked to video game expertise. We hypothesized that video game expertise is associated with neural plasticity-mediated changes in structural connectivity that manifest at the meso‑scale level, resulting in a more segregated functional network topology. To test this hypothesis, we combined structural connectivity data of StarCraft II video game players (VGPs, n = 31) and non-players (NVGPs, n = 31), with generic fMRI data from the Human Connectome Project and computational models, to generate simulated fMRI recordings. Graph theory analysis on simulated data was performed during both resting-state conditions and external stimulation. VGPs' simulated functional connectivity was characterized by a meso‑scale integration, with increased local connectivity in frontal, parietal, and occipital brain regions. The same analyses at the level of structural connectivity showed no differences between VGPs and NVGPs. Regions that increased their connectivity strength in VGPs are known to be involved in cognitive processes crucial for task performance such as attention, reasoning, and inference. In-silico stimulation suggested that differences in FC between VGPs and NVGPs emerge in noisy contexts, specifically when the noisy level of stimulation is increased. This indicates that the connectomes of VGPs may facilitate the filtering of noise from stimuli. These structural alterations drive the meso‑scale functional changes observed in individuals with gaming expertise. Overall, our work sheds light on the mechanisms underlying structural neural plasticity triggered by video game experiences.

Cholinergic-related pupil activity reflects level of emotionality during motor performance

Pupil size covaries with the diffusion rate of the cholinergic and noradrenergic neurons throughout the brain, which are essential to arousal. Recent findings suggest that slow pupil fluctuations during locomotion are an index of sustained activity in cholinergic axons, whereas phasic dilations are related to the activity of noradrenergic axons. Here, we investigated movement induced arousal (i.e., by singing and swaying to music), hypothesising that actively engaging in musical behaviour will provoke stronger emotional engagement in participants and lead to different qualitative patterns of tonic and phasic pupil activity. A challenge in the analysis of pupil data is the turbulent behaviour of pupil diameter due to exogenous ocular activity commonly encountered during motor tasks and the high variability typically found between individuals. To address this, we developed an algorithm that adaptively estimates and removes pupil responses to ocular events, as well as a functional data methodology, derived from Pfaffs' generalised arousal, that provides a new statistical dimension on how pupil data can be interpreted according to putative neuromodulatory signalling. We found that actively engaging in singing enhanced slow cholinergic-related pupil dilations and having the opportunity to move your body while performing amplified the effect of singing on pupil activity. Phasic pupil oscillations during motor execution attenuated in time, which is often interpreted as a measure of sense of agency over movement.

Re-awakening the brain: Forcing transitions in disorders of consciousness by external in silico perturbation

A fundamental challenge in neuroscience is accurately defining brain states and predicting how and where to perturb the brain to force a transition. Here, we investigated resting-state fMRI data of patients suffering from disorders of consciousness (DoC) after coma (minimally conscious and unresponsive wakefulness states) and healthy controls. We applied model-free and model-based approaches to help elucidate the underlying brain mechanisms of patients with DoC. The model-free approach allowed us to characterize brain states in DoC and healthy controls as a probabilistic metastable substate (PMS) space. The PMS of each group was defined by a repertoire of unique patterns (i.e., metastable substates) with different probabilities of occurrence. In the model-based approach, we adjusted the PMS of each DoC group to a causal whole-brain model. This allowed us to explore optimal strategies for promoting transitions by applying off-line in silico probing. Furthermore, this approach enabled us to evaluate the impact of local perturbations in terms of their global effects and sensitivity to stimulation, which is a model-based biomarker providing a deeper understanding of the mechanisms underlying DoC. Our results show that transitions were obtained in a synchronous protocol, in which the somatomotor network, thalamus, precuneus and insula were the most sensitive areas to perturbation. This motivates further work to continue understanding brain function and treatments of disorders of consciousness.

Turbulence hierarchy in foreign exchange markets

We present a multiscale stochastic analysis of foreign exchange rates using the H-theory formalism, which provides a hierarchical intermittency model for the information cascade in the currency market. We examine the distributions of returns and volatilities for the three most traded currency pairs: euro-U.S. dollar, U.S. dollar-Japanese yen, and British pound-U.S. dollar. We find that these markets have a hierarchy of timescales, with larger markets exhibiting more hierarchy levels. We provide a theoretical framework for understanding why the number of levels in the information cascade increases with market size, in analogy with similar behavior for the energy cascade in turbulence as a function of Reynolds number. We briefly argue that using turbulence-like models for financial markets can also provide valuable insights for developing efficient algorithmic trading strategies.

The evolution of whole-brain turbulent dynamics during recovery from traumatic brain injury

It has been previously shown that traumatic brain injury (TBI) is associated with reductions in metastability in large-scale networks in resting-state fMRI (rsfMRI). However, little is known about how TBI affects the local level of synchronization and how this evolves during the recovery trajectory. Here, we applied a novel turbulent dynamics framework to investigate whole-brain dynamics using an rsfMRI dataset from a cohort of moderate to severe TBI patients and healthy controls (HCs). We first examined how several measures related to turbulent dynamics differ between HCs and TBI patients at 3, 6, and 12 months post-injury. We found a significant reduction in these empirical measures after TBI, with the largest change at 6 months post-injury. Next, we built a Hopf whole-brain model with coupled oscillators and conducted in silico perturbations to investigate the mechanistic principles underlying the reduced turbulent dynamics found in the empirical data. A simulated attack was used to account for the effect of focal lesions. This revealed a shift to lower coupling parameters in the TBI dataset and, critically, decreased susceptibility and information-encoding capability. These findings confirm the potential of the turbulent framework to characterize longitudinal changes in whole-brain dynamics and in the reactivity to external perturbations after TBI.

Turbulent dynamics and whole-brain modeling: toward new clinical applications for traumatic brain injury

Traumatic Brain Injury (TBI) is a prevalent disorder mostly characterized by persistent impairments in cognitive function that poses a substantial burden on caregivers and the healthcare system worldwide. Crucially, severity classification is primarily based on clinical evaluations, which are non-specific and poorly predictive of long-term disability. In this Mini Review, we first provide a description of our model-free and model-based approaches within the turbulent dynamics framework as well as our vision on how they can potentially contribute to provide new neuroimaging biomarkers for TBI. In addition, we report the main findings of our recent study examining longitudinal changes in moderate-severe TBI (msTBI) patients during a one year spontaneous recovery by applying the turbulent dynamics framework (model-free approach) and the Hopf whole-brain computational model (model-based approach) combined with in silico perturbations. Given the neuroinflammatory response and heightened risk for neurodegeneration after TBI, we also offer future directions to explore the association with genomic information. Moreover, we discuss how whole-brain computational modeling may advance our understanding of the impact of structural disconnection on whole-brain dynamics after msTBI in light of our recent findings. Lastly, we suggest future avenues whereby whole-brain computational modeling may assist the identification of optimal brain targets for deep brain stimulation to promote TBI recovery.

Psychedelia: The interplay of music and psychedelics

Music and psychedelics have been intertwined throughout the existence of Homo sapiens, from the early shamanic rituals of the Americas and Africa to the modern use of psychedelic-assisted therapy for a variety of mental health conditions. Across such settings, music has been highly prized for its ability to guide the psychedelic experience. Here, we examine the interplay between music and psychedelics, starting by describing their association with the brain's functional hierarchy that is relied upon for music perception and its psychedelic-induced manipulation, as well as an exploration of the limited research on their mechanistic neural overlap. We explore music's role in Western psychedelic therapy and the use of music in indigenous psychedelic rituals, with a specific focus on ayahuasca and the Santo Daime Church. Furthermore, we explore work relating to the evolution and onset of music and psychedelic use. Finally, we consider music's potential to lead to altered states of consciousness in the absence of psychedelics as well as the development of psychedelic music. Here, we provide an overview of several perspectives on the interaction between psychedelic use and music-a topic with growing interest given increasing excitement relating to the therapeutic efficacy of psychedelic interventions.

Subcortical influences on the topology of cortical networks align with functional processing hierarchies

fMRI of the human brain reveals spatiotemporal patterns of functional connectivity (FC), forming distinct cortical networks. Lately, subcortical contributions to these configurations are receiving renewed interest, but investigations rarely focus explicitly on their effects on cortico-cortical FC. Here, we employ a straightforward multivariable approach and graph-theoretic tools to assess subcortical impact on topological features of cortical networks. Given recent evidence showing that structures like the thalamus and basal ganglia integrate input from multiple networks, we expect increased segregation between cortical networks after removal of subcortical effects on their FC patterns. We analyze resting state data of young and healthy participants (male and female; N = 100) from the human connectome project. We find that overall, the cortical network architecture becomes less segregated, and more integrated, when subcortical influences are accounted for. Underlying these global effects are the following trends: 'Transmodal' systems become more integrated with the rest of the network, while 'unimodal' networks show the opposite effect. For single nodes this hierarchical organization is reflected by a close correspondence with the spatial layout of the principal gradient of FC (Margulies et al., 2016). Lastly, we show that the limbic system is significantly less coherent with subcortical influences removed. The findings are validated in a (split-sample) replication dataset. Our results provide new insight regarding the interplay between subcortex and cortical networks, by putting the integrative impact of subcortex in the context of macroscale patterns of cortical organization.

Violations of the fluctuation-dissipation theorem reveal distinct nonequilibrium dynamics of brain states

The brain is a nonequilibrium system whose dynamics change in different brain states, such as wakefulness and deep sleep. Thermodynamics provides the tools for revealing these nonequilibrium dynamics. We used violations of the fluctuation-dissipation theorem to describe the hierarchy of nonequilibrium dynamics associated with different brain states. Together with a whole-brain model fitted to empirical human neuroimaging data, and deriving the appropriate analytical expressions, we were able to capture the deviation from equilibrium in different brain states that arises from asymmetric interactions and hierarchical organization.

Gaming expertise induces meso-scale brain plasticity and efficiency mechanisms as revealed by whole-brain modeling Gaming expertise, neuroplasticity and functional dynamics

Video games are a valuable tool for studying the effects of training and neural plasticity on the brain. However, the underlaying mechanisms related to plasticity-induced brain structural changes and their impact in brain dynamics are unknown. Here, we used a semi-empirical whole-brain model to study structural neural plasticity mechanisms linked to video game expertise. We hypothesized that video game expertise is associated with neural plasticity-mediated changes in structural connectivity that manifest at the meso-scale level, resulting in a more segregated functional network topology. To test this hypothesis, we combined structural connectivity data of StarCraft II video game players (VGPs, n = 31) and non-players (NVGPs, n = 31), with generic fMRI data from the Human Connectome Project and computational models, with the aim of generating simulated fMRI recordings. Graph theory analysis on simulated data was performed during both resting-state conditions and external stimulation. VGPs' simulated functional connectivity was characterized by a meso-scale integration, with increased local connectivity in frontal, parietal and occipital brain regions. The same analyses at the level of structural connectivity showed no differences between VGPs and NVGPs. Regions that increased their connectivity strength in VGPs are known to be involved in cognitive processes crucial for task performance such as attention, reasoning, and inference. In-silico stimulation suggested that differences in FC between VGPs and NVGPs emerge in noisy contexts, specifically when the noisy level of stimulation is increased. This indicates that the connectomes of VGPs may facilitate the filtering of noise from stimuli. These structural alterations drive the meso-scale functional changes observed in individuals with gaming expertise. Overall, our work sheds light into the mechanisms underlying structural neural plasticity triggered by video game experiences.

Tau protein spreads through functionally connected neurons in Alzheimer's disease: a combined MEG/PET study

Recent studies on Alzheimer's disease (AD) suggest that tau proteins spread through the brain following neuronal connections. Several mechanisms could be involved in this process: spreading between brain regions that interact strongly (functional connectivity); through the pattern of anatomical connections (structural connectivity); or simple diffusion. Using magnetoencephalography (MEG), we investigated which spreading pathways influence tau protein spreading by modelling the tau propagation process using an epidemic spreading model. We compared the modelled tau depositions with 18F-flortaucipir PET binding potentials at several stages of the AD continuum. In this cross-sectional study, we analysed source-reconstructed MEG data and dynamic 100-min 18F-flortaucipir PET from 57 subjects positive for amyloid-β pathology [preclinical AD (n = 16), mild cognitive impairment (MCI) due to AD (n = 16) and AD dementia (n = 25)]. Cognitively healthy subjects without amyloid-β pathology were included as controls (n = 25). Tau propagation was modelled as an epidemic process (susceptible-infected model) on MEG-based functional networks [in alpha (8-13 Hz) and beta (13-30 Hz) bands], a structural or diffusion network, starting from the middle and inferior temporal lobe. The group-level network of the control group was used as input for the model to predict tau deposition in three stages of the AD continuum. To assess performance, model output was compared to the group-specific tau deposition patterns as measured with 18F-flortaucipir PET. We repeated the analysis by using networks of the preceding disease stage and/or using regions with most observed tau deposition during the preceding stage as seeds. In the preclinical AD stage, the functional networks predicted most of the modelled tau-PET binding potential, with best correlations between model and tau-PET [corrected amplitude envelope correlation (AEC-c) alpha C = 0.584; AEC-c beta C = 0.569], followed by the structural network (C = 0.451) and simple diffusion (C = 0.451). Prediction accuracy declined for the MCI and AD dementia stages, although the correlation between modelled tau and tau-PET binding remained highest for the functional networks (C = 0.384; C = 0.376). Replacing the control-network with the network from the preceding disease stage and/or alternative seeds improved prediction accuracy in MCI but not in the dementia stage. These results suggest that in addition to structural connections, functional connections play an important role in tau spread, and highlight that neuronal dynamics play a key role in promoting this pathological process. Aberrant neuronal communication patterns should be taken into account when identifying targets for future therapy. Our results also suggest that this process is more important in earlier disease stages (preclinical AD/MCI); possibly, in later stages, other processes may be influential.

The arrow of time of brain signals in cognition: Potential intriguing role of parts of the default mode network

A promising idea in human cognitive neuroscience is that the default mode network (DMN) is responsible for coordinating the recruitment and scheduling of networks for computing and solving task-specific cognitive problems. This is supported by evidence showing that the physical and functional distance of DMN regions is maximally removed from sensorimotor regions containing environment-driven neural activity directly linked to perception and action, which would allow the DMN to orchestrate complex cognition from the top of the hierarchy. However, discovering the functional hierarchy of brain dynamics requires finding the best way to measure interactions between brain regions. In contrast to previous methods measuring the hierarchical flow of information using, for example, transfer entropy, here we used a thermodynamics-inspired, deep learning based Temporal Evolution NETwork (TENET) framework to assess the asymmetry in the flow of events, 'arrow of time', in human brain signals. This provides an alternative way of quantifying hierarchy, given that the arrow of time measures the directionality of information flow that leads to a breaking of the balance of the underlying hierarchy. In turn, the arrow of time is a measure of nonreversibility and thus nonequilibrium in brain dynamics. When applied to large-scale Human Connectome Project (HCP) neuroimaging data from close to a thousand participants, the TENET framework suggests that the DMN plays a significant role in orchestrating the hierarchy, that is, levels of nonreversibility, which changes between the resting state and when performing seven different cognitive tasks. Furthermore, this quantification of the hierarchy of the resting state is significantly different in health compared to neuropsychiatric disorders. Overall, the present thermodynamics-based machine-learning framework provides vital new insights into the fundamental tenets of brain dynamics for orchestrating the interactions between cognition and brain in complex environments.

Non-reversibility outperforms functional connectivity in characterisation of brain states in MEG data

Characterising brain states during tasks is common practice for many neuroscientific experiments using electrophysiological modalities such as electroencephalography (EEG) and magnetoencephalography (MEG). Brain states are often described in terms of oscillatory power and correlated brain activity, i.e. functional connectivity. It is, however, not unusual to observe weak task induced functional connectivity alterations in the presence of strong task induced power modulations using classical time-frequency representation of the data. Here, we propose that non-reversibility, or the temporal asymmetry in functional interactions, may be more sensitive to characterise task induced brain states than functional connectivity. As a second step, we explore causal mechanisms of non-reversibility in MEG data using whole brain computational models. We include working memory, motor, language tasks and resting-state data from participants of the Human Connectome Project (HCP). Non-reversibility is derived from the lagged amplitude envelope correlation (LAEC), and is based on asymmetry of the forward and reversed cross-correlations of the amplitude envelopes. Using random forests, we find that non-reversibility outperforms functional connectivity in the identification of task induced brain states. Non-reversibility shows especially better sensitivity to capture bottom-up gamma induced brain states across all tasks, but also alpha band associated brain states. Using whole brain computational models we find that asymmetry in the effective connectivity and axonal conduction delays play a major role in shaping non-reversibility across the brain. Our work paves the way for better sensitivity in characterising brain states during both bottom-up as well as top-down modulation in future neuroscientific experiments.

The impact of regional heterogeneity in whole-brain dynamics in the presence of oscillations

Large variability exists across brain regions in health and disease, considering their cellular and molecular composition, connectivity, and function. Large-scale whole-brain models comprising coupled brain regions provide insights into the underlying dynamics that shape complex patterns of spontaneous brain activity. In particular, biophysically grounded mean-field whole-brain models in the asynchronous regime were used to demonstrate the dynamical consequences of including regional variability. Nevertheless, the role of heterogeneities when brain dynamics are supported by synchronous oscillating state, which is a ubiquitous phenomenon in brain, remains poorly understood. Here, we implemented two models capable of presenting oscillatory behavior with different levels of abstraction: a phenomenological Stuart-Landau model and an exact mean-field model. The fit of these models informed by structural- to functional-weighted MRI signal (T1w/T2w) allowed us to explore the implication of the inclusion of heterogeneities for modeling resting-state fMRI recordings from healthy participants. We found that disease-specific regional functional heterogeneity imposed dynamical consequences within the oscillatory regime in fMRI recordings from neurodegeneration with specific impacts on brain atrophy/structure (Alzheimer's patients). Overall, we found that models with oscillations perform better when structural and functional regional heterogeneities are considered, showing that phenomenological and biophysical models behave similarly at the brink of the Hopf bifurcation.

Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing

The large-scale activity of the human brain exhibits rich and complex patterns, but the spatiotemporal dynamics of these patterns and their functional roles in cognition remain unclear. Here by characterizing moment-by-moment fluctuations of human cortical functional magnetic resonance imaging signals, we show that spiral-like, rotational wave patterns (brain spirals) are widespread during both resting and cognitive task states. These brain spirals propagate across the cortex while rotating around their phase singularity centres, giving rise to spatiotemporal activity dynamics with non-stationary features. The properties of these brain spirals, such as their rotational directions and locations, are task relevant and can be used to classify different cognitive tasks. We also demonstrate that multiple, interacting brain spirals are involved in coordinating the correlated activations and de-activations of distributed functional regions; this mechanism enables flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing. Our findings suggest that brain spirals organize complex spatiotemporal dynamics of the human brain and have functional correlates to cognitive processing.

Reduced emergent character of neural dynamics in patients with a disrupted connectome

High-level brain functions are widely believed to emerge from the orchestrated activity of multiple neural systems. However, lacking a formal definition and practical quantification of emergence for experimental data, neuroscientists have been unable to empirically test this long-standing conjecture. Here we investigate this fundamental question by leveraging a recently proposed framework known as "Integrated Information Decomposition," which establishes a principled information-theoretic approach to operationalise and quantify emergence in dynamical systems - including the human brain. By analysing functional MRI data, our results show that the emergent and hierarchical character of neural dynamics is significantly diminished in chronically unresponsive patients suffering from severe brain injury. At a functional level, we demonstrate that emergence capacity is positively correlated with the extent of hierarchical organisation in brain activity. Furthermore, by combining computational approaches from network control theory and whole-brain biophysical modelling, we show that the reduced capacity for emergent and hierarchical dynamics in severely brain-injured patients can be mechanistically explained by disruptions in the patients' structural connectome. Overall, our results suggest that chronic unresponsiveness resulting from severe brain injury may be related to structural impairment of the fundamental neural infrastructures required for brain dynamics to support emergence.

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.

Nonlinear Theta-Gamma Coupling between the Anterior Thalamus and Hippocampus Increases as a Function of Running Speed

The hippocampal theta rhythm strongly correlates to awake behavior leading to theories that it represents a cognitive state of the brain. As theta has been observed in other regions of the Papez circuit, it has been theorized that activity propagates in a reentrant manner. These observations complement the energy cascade hypothesis in which large-amplitude, slow-frequency oscillations reflect activity propagating across a large population of neurons. Higher frequency oscillations, such as gamma, are related to the speed with which inhibitory and excitatory neurons interact and distribute activity on the local level. The energy cascade hypothesis suggests that the larger anatomic loops, maintaining theta, drive the smaller loops. As hippocampal theta increases in power with running speed, so does the power and frequency of the gamma rhythm. If theta is propagated through the circuit, it stands to reason that the local field potential (LFP) recorded in other regions would be coupled to the hippocampal theta, with the coupling increasing with running speed. We explored this hypothesis using open-source simultaneous recorded data from the CA1 region of the hippocampus and the anterior dorsal and anterior ventral thalamus. Cross-regional theta coupling increased with running speed. Although the power of the gamma rhythm was lower in the anterior thalamus, there was an increase in the coupling of hippocampal theta to anterior thalamic gamma. Broadly, the data support models of how activity moves across the nervous system, suggesting that the brain uses large-scale volleys of activity to support higher cognitive processes.

Toward naturalistic neuroscience: Mechanisms underlying the flattening of brain hierarchy in movie-watching compared to rest and task

Identifying the functional specialization of the brain has moved from using cognitive tasks and resting state to using ecological relevant, naturalistic movies. We leveraged a large-scale neuroimaging dataset to directly investigate the hierarchical reorganization of functional brain activity when watching naturalistic films compared to performing seven cognitive tasks and resting. A thermodynamics-inspired whole-brain model paradigm revealed the generative underlying mechanisms for changing the balance in causal interactions between brain regions in different conditions. Paradoxically, the hierarchy is flatter for movie-watching, and the level of nonreversibility is significantly smaller in comparison to both rest and tasks, where the latter in turn have the highest levels of hierarchy and nonreversibility. The underlying mechanisms were revealed by the model-based generative effective connectivity (GEC). Naturalistic films could therefore provide a fast and convenient way to measure important changes in GEC (integrating functional and anatomical connectivity) found in, for example, neuropsychiatric disorders. Overall, this study demonstrates the benefits of moving toward a more naturalistic neuroscience.

Dynamic sensitivity analysis: Defining personalised strategies to drive brain state transitions via whole brain modelling

Traditionally, in neuroimaging, model-free analyses are used to find significant differences between brain states via signal detection theory. Depending on the a priori assumptions about the underlying data, different spatio-temporal features can be analysed. Alternatively, model-based techniques infer features from the data and compare significance from model parameters. However, to assess transitions from one brain state to another remains a challenge in current paradigms. Here, we introduce a "Dynamic Sensitivity Analysis" framework that quantifies transitions between brain states in terms of stimulation ability to rebalance spatio-temporal brain activity towards a target state such as healthy brain dynamics. In practice, it means building a whole-brain model fitted to the spatio-temporal description of brain dynamics, and applying systematic stimulations in-silico to assess the optimal strategy to drive brain dynamics towards a target state. Further, we show how Dynamic Sensitivity Analysis extends to various brain stimulation paradigms, ultimately contributing to improving the efficacy of personalised clinical interventions.

Strength-dependent perturbation of whole-brain model working in different regimes reveals the role of fluctuations in brain dynamics

Despite decades of research, there is still a lack of understanding of the role and generating mechanisms of the ubiquitous fluctuations and oscillations found in recordings of brain dynamics. Here, we used whole-brain computational models capable of presenting different dynamical regimes to reproduce empirical data's turbulence level. We showed that the model's fluctuations regime fitted to turbulence more faithfully reproduces the empirical functional connectivity compared to oscillatory and noise regimes. By applying global and local strength-dependent perturbations and subsequently measuring the responsiveness of the model, we revealed each regime's computational capacity demonstrating that brain dynamics is shifted towards fluctuations to provide much-needed flexibility. Importantly, fluctuation regime stimulation in a brain region within a given resting state network modulates that network, aligned with previous empirical and computational studies. Furthermore, this framework generates specific, testable empirical predictions for human stimulation studies using strength-dependent rather than constant perturbation. Overall, the whole-brain models fitted to the level of empirical turbulence together with functional connectivity unveil that the fluctuation regime best captures empirical data, and the strength-dependent perturbative framework demonstrates how this regime provides maximal flexibility to the human brain.

Effects of classic psychedelic drugs on turbulent signatures in brain dynamics

Psychedelic drugs show promise as safe and effective treatments for neuropsychiatric disorders, yet their mechanisms of action are not fully understood. A fundamental hypothesis is that psychedelics work by dose-dependently changing the functional hierarchy of brain dynamics, but it is unclear whether different psychedelics act similarly. Here, we investigated the changes in the brain's functional hierarchy associated with two different psychedelics (LSD and psilocybin). Using a novel turbulence framework, we were able to determine the vorticity, that is, the local level of synchronization, that allowed us to extend the standard global time-based measure of metastability to become a local-based measure of both space and time. This framework produced detailed signatures of turbulence-based hierarchical change for each psychedelic drug, revealing consistent and discriminate effects on a higher level network, that is, the default mode network. Overall, our findings directly support a prior hypothesis that psychedelics modulate (i.e., "compress") the functional hierarchy and provide a quantification of these changes for two different psychedelics. Implications for therapeutic applications of psychedelics are discussed.

Hormone-based models for comparing menstrual cycle and hormonal contraceptive effects on human resting-state functional connectivity

Oral contraceptives (OCs) are widely used yet understudied given their potential for public health consequences. Emerging investigations scaling from single-subject, dense-sampling neuroimaging studies to population-level metrics have linked OCs to altered brain structure and function. Modeling the hypogonadal, hypergonadal, or mixed state effects of OCs in terms of their impact on hormone action in the brain is a valuable approach to synthesizing results across neuroimaging studies and comparing OC effects to companion findings from research on menstrual cycle phase effects on brain anatomy and function. Resting-state functional connectivity studies provide a powerful tool to evaluate the role of OCs on the intrinsic network connectivity that underlies multiple behavioral domains. The preponderance (but not consensus) of the current literature indicates that (1) as the menstrual cycle proceeds from a low to high progesterone state, prefrontal connectivity increases and parietal connectivity decreases; (2) OCs tend to mimic this connectivity pattern; therefore (3) OCs may produce a hyperprogestogenic state in the brain, in spite of overall reductions in endogenous steroid hormone levels. Alternative models are also considered.

Cognitive efficacy and neural mechanisms of music-based neurological rehabilitation for traumatic brain injury

Traumatic brain injury (TBI) causes lifelong cognitive deficits, most often in executive function (EF). Both musical training and music-based rehabilitation have been shown to enhance EF and neuroplasticity. Thus far, however, there is little evidence for the potential rehabilitative effects of music for TBI. Here, we review the core findings from our recent cross-over randomized controlled trial in which a 10-week music-based neurological rehabilitation (MBNR) protocol was administered to 40 patients with moderate-to-severe TBI. Neuropsychological testing and structural/functional magnetic resonance imaging were collected at three time points (baseline, 3 months, and 6 months); one group received the MBNR between time points 1 and 2, while a second group received it between time points 2 and 3. We found that both general EF and set shifting improved after the intervention, and this effect was maintained long term. Morphometric analyses revealed therapy-induced gray matter volume changes most consistently in the right inferior frontal gyrus, changes that correlated with better outcomes in set shifting. Finally, we found changes in the between- and within-network functional connectivity of large-scale resting-state networks after MBNR, which also correlated with measures of EF. Taken together, the data provide evidence for concluding that MBNR improves EF in TBI; also, the data show that morphometric and resting-state functional connectivity are sensitive markers with which to monitor the neuroplasticity induced by the MBNR intervention.

On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI

Measuring the temporal complexity of functional MRI (fMRI) time series is one approach to assess how brain activity changes over time. In fact, hemodynamic response of the brain is known to exhibit critical behaviour at the edge between order and disorder. In this study, we aimed to revisit the spatial distribution of temporal complexity in resting state and task fMRI of 100 unrelated subjects from the Human Connectome Project (HCP). First, we compared two common choices of complexity measures, i.e., Hurst exponent and multiscale entropy, and observed a high spatial similarity between them. Second, we considered four tasks in the HCP dataset (Language, Motor, Social, and Working Memory) and found high task-specific complexity, even when the task design was regressed out. For the significance thresholding of brain complexity maps, we used a statistical framework based on graph signal processing that incorporates the structural connectome to develop the null distributions of fMRI complexity. The results suggest that the frontoparietal, dorsal attention, visual, and default mode networks represent stronger complex behaviour than the rest of the brain, irrespective of the task engagement. In sum, the findings support the hypothesis of fMRI temporal complexity as a marker of cognition.

Replay, the default mode network and the cascaded memory systems model

The spontaneous replay of patterns of activity related to past experiences and memories is a striking feature of brain activity, as is the coherent activation of sets of brain areas - particularly those comprising the default mode network (DMN) - during rest. We propose that these two phenomena are strongly intertwined and that their potential functions overlap. In the 'cascaded memory systems model' that we outline here, we hypothesize that the DMN forms the backbone for the propagation of replay, mediating interactions between the hippocampus and the neocortex that enable the consolidation of new memories. The DMN may also independently ignite replay cascades, which support reactivation of older memories or high-level semantic representations. We suggest that transient cortical activations, inducing long-range correlations across the neocortex, are a key mechanism supporting a hierarchy of representations that progresses from simple percepts to semantic representations of causes and, finally, to whole episodes.

Metastable oscillatory modes emerge from synchronization in the brain spacetime connectome

A rich repertoire of oscillatory signals is detected from human brains with electro- and magnetoencephalography (EEG/MEG). However, the principles underwriting coherent oscillations and their link with neural activity remain under debate. Here, we revisit the mechanistic hypothesis that transient brain rhythms are a signature of metastable synchronization, occurring at reduced collective frequencies due to delays between brain areas. We consider a system of damped oscillators in the presence of background noise - approximating the short-lived gamma-frequency oscillations generated within neuronal circuits - coupled according to the diffusion weighted tractography between brain areas. Varying the global coupling strength and conduction speed, we identify a critical regime where spatially and spectrally resolved metastable oscillatory modes (MOMs) emerge at sub-gamma frequencies, approximating the MEG power spectra from 89 healthy individuals at rest. Further, we demonstrate that the frequency, duration, and scale of MOMs - as well as the frequency-specific envelope functional connectivity - can be controlled by global parameters, while the connectome structure remains unchanged. Grounded in the physics of delay-coupled oscillators, these numerical analyses demonstrate how interactions between locally generated fast oscillations in the connectome spacetime structure can lead to the emergence of collective brain rhythms organized in space and time.

Understanding brain states across spacetime informed by whole-brain modelling

In order to survive in a complex environment, the human brain relies on the ability to flexibly adapt ongoing behaviour according to intrinsic and extrinsic signals. This capability has been linked to specific whole-brain activity patterns whose relative stability (order) allows for consistent functioning, supported by sufficient intrinsic instability needed for optimal adaptability. The emergent, spontaneous balance between order and disorder in brain activity over spacetime underpins distinct brain states. For example, depression is characterized by excessively rigid, highly ordered states, while psychedelics can bring about more disordered, sometimes overly flexible states. Recent developments in systems, computational and theoretical neuroscience have started to make inroads into the characterization of such complex dynamics over space and time. Here, we review recent insights drawn from neuroimaging and whole-brain modelling motivating using mechanistic principles from dynamical system theory to study and characterize brain states. We show how different healthy and altered brain states are associated to characteristic spacetime dynamics which in turn may offer insights that in time can inspire new treatments for rebalancing brain states in disease. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Normalizing the brain connectome for communication through synchronization

Networks in neuroscience determine how brain function unfolds, and their perturbations lead to psychiatric disorders and brain disease. Brain networks are characterized by their connectomes, which comprise the totality of all connections, and are commonly described by graph theory. This approach is deeply rooted in a particle view of information processing, based on the quantification of informational bits such as firing rates. Oscillations and brain rhythms demand, however, a wave perspective of information processing based on synchronization. We extend traditional graph theory to a dual, particle-wave, perspective, integrate time delays due to finite transmission speeds, and derive a normalization of the connectome. When applied to the database of the Human Connectome Project, it explains the emergence of frequency-specific network cores including the visual and default mode networks. These findings are robust across human subjects (N = 100) and are a fundamental network property within the wave picture. The normalized connectome comprises the particle view in the limit of infinite transmission speeds and opens the applicability of graph theory to a wide range of novel network phenomena, including physiological and pathological brain rhythms. These two perspectives are orthogonal, but not incommensurable, when understood within the novel, here-proposed, generalized framework of structural connectivity.

Unifying turbulent dynamics framework distinguishes different brain states

Significant advances have been made by identifying the levels of synchrony of the underlying dynamics of a given brain state. This research has demonstrated that non-conscious dynamics tend to be more synchronous than in conscious states, which are more asynchronous. Here we go beyond this dichotomy to demonstrate that different brain states are underpinned by dissociable spatiotemporal dynamics. We investigated human neuroimaging data from different brain states (resting state, meditation, deep sleep and disorders of consciousness after coma). The model-free approach was based on Kuramoto’s turbulence framework using coupled oscillators. This was extended by a measure of the information cascade across spatial scales. Complementarily, the model-based approach used exhaustive in silico perturbations of whole-brain models fitted to these measures. This allowed studying of the information encoding capabilities in given brain states. Overall, this framework demonstrates that elements from turbulence theory provide excellent tools for describing and differentiating between brain states.

A unifying turbulent dynamics framework using both model-free and modelbased measures of whole-brain information provides insights into brain states.

The INSIDEOUT framework provides precise signatures of the balance of intrinsic and extrinsic dynamics in brain states

Finding precise signatures of different brain states is a central, unsolved question in neuroscience. We reformulated the problem to quantify the 'inside out' balance of intrinsic and extrinsic brain dynamics in brain states. The difference in brain state can be described as differences in the detailed causal interactions found in the underlying intrinsic brain dynamics. We used a thermodynamics framework to quantify the breaking of the detailed balance captured by the level of asymmetry in temporal processing, i.e. the arrow of time. Specifically, the temporal asymmetry was computed by the time-shifted correlation matrices for the forward and reversed time series, reflecting the level of non-reversibility/non-equilibrium. We found precise, distinguishing signatures in terms of the reversibility and hierarchy of large-scale dynamics in three radically different brain states (awake, deep sleep and anaesthesia) in electrocorticography data from non-human primates. Significantly lower levels of reversibility were found in deep sleep and anaesthesia compared to wakefulness. Non-wakeful states also showed a flatter hierarchy, reflecting the diversity of the reversibility across the brain. Overall, this provides signatures of the breaking of detailed balance in different brain states, perhaps reflecting levels of conscious awareness.

Epidemic models characterize seizure propagation and the effects of epilepsy surgery in individualized brain networks based on MEG and invasive EEG recordings

Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients. However, seizure-freedom is currently achieved in only 2/3 of the patients after surgery. In this study we have developed an individualized computational model based on MEG brain networks to explore seizure propagation and the efficacy of different virtual resections. Eventually, the goal is to obtain individualized models to optimize resection strategy and outcome. We have modelled seizure propagation as an epidemic process using the susceptible-infected (SI) model on individual brain networks derived from presurgical MEG. We included 10 patients who had received epilepsy surgery and for whom the surgery outcome at least one year after surgery was known. The model parameters were tuned in in order to reproduce the patient-specific seizure propagation patterns as recorded with invasive EEG. We defined a personalized search algorithm that combined structural and dynamical information to find resections that maximally decreased seizure propagation for a given resection size. The optimal resection for each patient was defined as the smallest resection leading to at least a 90% reduction in seizure propagation. The individualized model reproduced the basic aspects of seizure propagation for 9 out of 10 patients when using the resection area as the origin of epidemic spreading, and for 10 out of 10 patients with an alternative definition of the seed region. We found that, for 7 patients, the optimal resection was smaller than the resection area, and for 4 patients we also found that a resection smaller than the resection area could lead to a 100% decrease in propagation. Moreover, for two cases these alternative resections included nodes outside the resection area. Epidemic spreading models fitted with patient specific data can capture the fundamental aspects of clinically observed seizure propagation, and can be used to test virtual resections in silico. Combined with optimization algorithms, smaller or alternative resection strategies, that are individually targeted for each patient, can be determined with the ultimate goal to improve surgery outcome. MEG-based networks can provide a good approximation of structural connectivity for computational models of seizure propagation, and facilitate their clinical use.

Unique spatiotemporal fMRI dynamics in the awake mouse brain

Human imaging studies have shown that spontaneous brain activity exhibits stereotypic spatiotemporal reorganization in awake, conscious conditions with respect to minimally conscious states. However, whether and how this phenomenon can be generalized to lower mammalian species remains unclear. Leveraging a robust protocol for resting-state fMRI (rsfMRI) mapping in non-anesthetized, head-fixed mice, we investigated functional network topography and dynamic structure of spontaneous brain activity in wakeful animals. We found that rsfMRI networks in the awake state, while anatomically comparable to those observed under anesthesia, are topologically configured to maximize interregional communication, departing from the underlying community structure of the mouse axonal connectome. We further report that rsfMRI activity in wakeful animals exhibits unique spatiotemporal dynamics characterized by a state-dependent, dominant occurrence of coactivation patterns encompassing a prominent participation of arousal-related forebrain nuclei and functional anti-coordination between visual-auditory and polymodal cortical areas. We finally show that rsfMRI dynamics in awake mice exhibits a stereotypical temporal structure, in which state-dominant coactivation patterns are configured as network attractors. These findings suggest that spontaneous brain activity in awake mice is critically shaped by state-specific involvement of basal forebrain arousal systems and document that its dynamic structure recapitulates distinctive, evolutionarily relevant principles that are predictive of conscious states in higher mammalian species.

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fMRI networks in awake mice depart from underlying anatomical structure

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fMRI dynamics in wakeful mice is critically shaped by arousal-related nuclei

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Occurrence and topography of rsfMRI coactivation patterns define conscious states

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fMRI coactivation dynamics defines a signature of consciousness in the mouse brain

Dynamic primitives of brain network interaction Special Issue "Advances in Mapping the Connectome"

What dynamic processes underly functional brain networks? Functional connectivity (FC) and functional connectivity dynamics (FCD) are used to represent the patterns and dynamics of functional brain networks. FC(D) is related to the synchrony of brain activity: when brain areas oscillate in a coordinated manner this yields a high correlation between their signal time series. To explain the processes underlying FC(D) we review how synchronized oscillations emerge from coupled neural populations in brain network models (BNMs). From detailed spiking networks to more abstract population models, there is strong support for the idea that the brain operates near critical instabilities that give rise to multistable or metastable dynamics that in turn lead to the intermittently synchronized slow oscillations underlying FC(D). We explore further consequences from these fundamental mechanisms and how they fit with reality. We conclude by highlighting the need for integrative brain models that connect separate mechanisms across levels of description and spatiotemporal scales and link them with cognitive function.

The Menstrual Cycle Modulates Whole-Brain Turbulent Dynamics

Brain dynamics have recently been shown to be modulated by rhythmic changes in female sex hormone concentrations across an entire menstrual cycle. However, many questions remain regarding the specific differences in information processing across spacetime between the two main follicular and luteal phases in the menstrual cycle. Using a novel turbulent dynamic framework, we studied whole-brain information processing across spacetime scales (i.e., across long and short distances in the brain) in two open-source, dense-sampled resting-state datasets. A healthy naturally cycling woman in her early twenties was scanned over 30 consecutive days during a naturally occurring menstrual cycle and under a hormonal contraceptive regime. Our results indicated that the luteal phase is characterized by significantly higher information transmission across spatial scales than the follicular phase. Furthermore, we found significant differences in turbulence levels between the two phases in brain regions belonging to the default mode, salience/ventral attention, somatomotor, control, and dorsal attention networks. Finally, we found that changes in estradiol and progesterone concentrations modulate whole-brain turbulent dynamics in long distances. In contrast, we reported no significant differences in information processing measures between the active and placebo phases in the hormonal contraceptive study. Overall, the results demonstrate that the turbulence framework is able to capture differences in whole-brain turbulent dynamics related to ovarian hormones and menstrual cycle stages.

Broken detailed balance and entropy production in the human brain

To perform biological functions, living systems must break detailed balance by consuming energy and producing entropy. At microscopic scales, broken detailed balance enables a suite of molecular and cellular functions, including computations, kinetic proofreading, sensing, adaptation, and transportation. But do macroscopic violations of detailed balance enable higher-order biological functions, such as cognition and movement? To answer this question, we adapt tools from nonequilibrium statistical mechanics to quantify broken detailed balance in complex living systems. Analyzing neural recordings from hundreds of human subjects, we find that the brain violates detailed balance at large scales and that these violations increase with physical and cognitive exertion. Generally, we provide a flexible framework for investigating broken detailed balance at large scales in complex systems.

Living systems break detailed balance at small scales, consuming energy and producing entropy in the environment to perform molecular and cellular functions. However, it remains unclear how broken detailed balance manifests at macroscopic scales and how such dynamics support higher-order biological functions. Here we present a framework to quantify broken detailed balance by measuring entropy production in macroscopic systems. We apply our method to the human brain, an organ whose immense metabolic consumption drives a diverse range of cognitive functions. Using whole-brain imaging data, we demonstrate that the brain nearly obeys detailed balance when at rest, but strongly breaks detailed balance when performing physically and cognitively demanding tasks. Using a dynamic Ising model, we show that these large-scale violations of detailed balance can emerge from fine-scale asymmetries in the interactions between elements, a known feature of neural systems. Together, these results suggest that violations of detailed balance are vital for cognition and provide a general tool for quantifying entropy production in macroscopic systems.

Brain connectivity dynamics in cisgender and transmen people with gender incongruence before gender affirmative hormone treatment

Large-scale brain network interactions have been described between trans- and cis-gender binary identities. However, a temporal perspective of the brain's spontaneous fluctuations is missing. We investigated the functional connectivity dynamics in transmen with gender incongruence and its relationship with interoceptive awareness. We describe four states in native and meta-state spaces: (i) one state highly prevalent with sparse overall connections; (ii) a second with strong couplings mainly involving components of the salience, default, and executive control networks. Two states with global sparse connectivity but positive couplings (iii) within the sensorimotor network, and (iv) between salience network regions. Transmen had more dynamical fluidity than cismen, while cismen presented less meta-state fluidity and range dynamism than transmen and ciswomen. A positive association between attention regulation and fluidity and meta-state range dynamism was found in transmen. There exist gender differences in the temporal brain dynamism, characterized by distinct interrelations of the salience network as catalyst interacting with other networks. We offer a functional explanation from the neurodevelopmental cortical hypothesis of a gendered-self.

Neuroscience: Turbulent times for brain information processing

A recent study shows that rare long-range connections between brain areas may considerably improve transmission of information between areas. The study suggests that information may propagate better through long-range connections when neural activity exhibits turbulent dynamics.

Rare long-range cortical connections enhance human information processing

What are the key topological features of connectivity critically relevant for generating the dynamics underlying efficient cortical function? A candidate feature that has recently emerged is that the connectivity of the mammalian cortex follows an exponential distance rule, which includes a small proportion of long-range high-weight anatomical exceptions to this rule. Whole-brain modeling of large-scale human neuroimaging data in 1,003 participants offers the unique opportunity to create two models, with and without long-range exceptions, and explicitly study their functional consequences. We found that rare long-range exceptions are crucial for significantly improving information processing. Furthermore, modeling in a simplified ring architecture shows that this improvement is greatly enhanced by the turbulent regime found in empirical neuroimaging data. Overall, the results provide strong empirical evidence for the immense functional benefits of long-range exceptions combined with turbulence for information processing.

Leonardo da Vinci and the search for order in neuroscience

Finding order in disorder is a hallmark of science and art. In the time of Leonardo da Vinci, the schism between science and art had yet to arise. In fact, Leonardo freely used scientific methods for his art and vice versa; for example, when he used his observations of turbulent, whirling water to guide his artistic imagination. Half a millennium later, a cornerstone of modern biology is the continuing search for order in dynamic processes. In neuroscience, the search has focussed on understanding complex spacetime brain dynamics. Recently, turbulence has been shown to be a guiding principle underlying the necessary information processing, supporting Leonardo's search for order in disorder. Here, we argue that Leonardo's seminal insights have ongoing relevance for modern neuroscience.

Spectrum Degradation of Hippocampal LFP During Euthanasia

The hippocampal local field potential (LFP) exhibits a strong correlation with behavior. During rest, the theta rhythm is not prominent, but during active behavior, there are strong rhythms in the theta, theta harmonics, and gamma ranges. With increasing running velocity, theta, theta harmonics and gamma increase in power and in cross-frequency coupling, suggesting that neural entrainment is a direct consequence of the total excitatory input. While it is common to study the parametric range between the LFP and its complementing power spectra between deep rest and epochs of high running velocity, it is also possible to explore how the spectra degrades as the energy is completely quenched from the system. Specifically, it is unknown whether the 1/f slope is preserved as synaptic activity becomes diminished, as low frequencies are generated by large pools of neurons while higher frequencies comprise the activity of more local neuronal populations. To test this hypothesis, we examined rat LFPs recorded from the hippocampus and entorhinal cortex during barbiturate overdose euthanasia. Within the hippocampus, the initial stage entailed a quasi-stationary LFP state with a power-law feature in the power spectral density. In the second stage, there was a successive erosion of power from high- to low-frequencies in the second stage that continued until the only dominant remaining power was <20 Hz. This stage was followed by a rapid collapse of power spectrum toward the absolute electrothermal noise background. As the collapse of activity occurred later in hippocampus compared with medial entorhinal cortex, it suggests that the ability of a neural network to maintain the 1/f slope with decreasing energy is a function of general connectivity. Broadly, these data support the energy cascade theory where there is a cascade of energy from large cortical populations into smaller loops, such as those that supports the higher frequency gamma rhythm. As energy is pulled from the system, neural entrainment at gamma frequency (and higher) decline first. The larger loops, comprising a larger population, are fault-tolerant to a point capable of maintaining their activity before a final collapse.