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Abstract
Human behavior and cognitive function correlate with complex patterns of spatio-temporal brain dynamics, which can be simulated using computational models with different degrees of biophysical realism. We used a data-driven optimization algorithm to determine and classify the types of local dynamics that enable the reproduction of different observables derived from functional magnetic resonance recordings. The phase space analysis of the resulting equations revealed a predominance of stable spiral attractors, which optimized the similarity to the empirical data in terms of the synchronization, metastability, and functional connectivity dynamics. For stable limit cycles, departures from harmonic oscillations improved the fit in terms of functional connectivity dynamics. Eigenvalue analyses showed that proximity to a bifurcation improved the accuracy of the simulation for wakefulness, whereas deep sleep was associated with increased stability. Our results provide testable predictions that constrain the landscape of suitable biophysical models, while supporting noise-driven dynamics close to a bifurcation as a canonical mechanism underlying the complex fluctuations that characterize endogenous brain activity.

A fundamental problem in systems neuroscience is how to force a transition from one brain state to another by external driven stimulation in, for example, wakefulness, sleep, coma, or neuropsychiatric diseases. This requires a quantitative and robust definition of a brain state, which has so far proven elusive. Here, we provide such a definition, which, together with whole-brain modeling, permits the systematic study in silico of how simulated brain stimulation can force transitions between different brain states in humans. Specifically, we use a unique neuroimaging dataset of human sleep to systematically investigate where to stimulate the brain to force an awakening of the human sleeping brain and vice versa. We show where this is possible using a definition of a brain state as an ensemble of "metastable substates," each with a probabilistic stability and occurrence frequency fitted by a generative whole-brain model, fine-tuned on the basis of the effective connectivity. Given the biophysical limitations of direct electrical stimulation (DES) of microcircuits, this opens exciting possibilities for discovering stimulation targets and selecting connectivity patterns that can ensure propagation of DES-induced neural excitation, potentially making it possible to create awakenings from complex cases of brain injury. ; Spanish Research Project PSI2016-75688-P (Agencia Estatal de Investigación/Fondo Europeo de Desarrollo Regional, European Union); by the European Union's Horizon 2020 Re-search and Innovation Programme under Grant Agreements 720270 (Hu-man Brain Project [HBP] SGA1) and 785907 (HBP SGA2); and by the CatalanAgency for Management of University and Research Grants Programme 2017 SGR 1545. J. Cabral is supported by Portuguese Foundation for Sci-ence and Technology CEECIND/03325/2017, Portugal. M.L.K. is supportedby the European Research Council Consolidator Grant: CAREGIVING (615539) and Center for Music in the Brain, funded by the Danish National Research Foundation ...

A fundamental problem in systems neuroscience is how to force a transition from one brain state to another by external driven stimulation in, for example, wakefulness, sleep, coma, or neuropsychiatric diseases. This requires a quantitative and robust definition of a brain state, which has so far proven elusive. Here, we provide such a definition, which, together with whole-brain modeling, permits the systematic study in silico of how simulated brain stimulation can force transitions between different brain states in humans. Specifically, we use a unique neuroimaging dataset of human sleep to systematically investigate where to stimulate the brain to force an awakening of the human sleeping brain and vice versa. We show where this is possible using a definition of a brain state as an ensemble of "metastable substates," each with a probabilistic stability and occurrence frequency fitted by a generative whole-brain model, fine-tuned on the basis of the effective connectivity. Given the biophysical limitations of direct electrical stimulation (DES) of microcircuits, this opens exciting possibilities for discovering stimulation targets and selecting connectivity patterns that can ensure propagation of DES-induced neural excitation, potentially making it possible to create awakenings from complex cases of brain injury. ; G.D. is supported by the Spanish Research Project PSI2016-75688-P (Agencia Estatal de Investigación/Fondo Europeo de Desarrollo Regional, European Union); by the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreements 720270 (Human Brain Project [HBP] SGA1) and 785907 (HBP SGA2); and by the Catalan Agency for Management of University and Research Grants Programme 2017 SGR 1545. J. Cabral is supported by Portuguese Foundation for Science and Technology CEECIND/03325/2017, Portugal. M.L.K. is supported by the European Research Council Consolidator Grant: CAREGIVING (615539) and Center for Music in the Brain, funded by the Danish National Research Foundation (DNRF117).

During the sleep-wake cycle, the brain undergoes profound dynamical changes, which manifest subjectively as transitions between conscious experience and unconsciousness. Yet, neurophysiological signatures that can objectively distinguish different consciousness states based are scarce. Here, we show that differences in the level of brain-wide signals can reliably distinguish different stages of sleep and anesthesia from the awake state in human and monkey fMRI resting state data. Moreover, a whole-brain computational model can faithfully reproduce changes in global synchronization and other metrics such as functional connectivity, structure-function relationship, integration and segregation across vigilance states. We demonstrate that the awake brain is close to a Hopf bifurcation, which naturally coincides with the emergence of globally correlated fMRI signals. Furthermore, simulating lesions of individual brain areas highlights the importance of connectivity hubs in the posterior brain and subcortical nuclei for maintaining the model in the awake state, as predicted by graph-theoretical analyses of structural data. ; G.D. was supported by the Spanish Research Project AWAKENING: using whole-brain models perturbational approaches for predicting external stimulation to force transitions between different brain states, ref. PID2019-105772GB-I00 /AEI/10.13039/501100011033, financed by the Spanish Ministry of Science, Innovation and Universities (MCIU), State Research Agency (AEI), and by the Catalan AGAUR program 2017 SGR 1545. G.D., G.H. and G.Z. received support from the European Union's Horizon 2020 research and innovation program under Grant Agreement No. 720270 (Human Brain Project SGA1), No. 785907 (Human Brain Project SGA2) and No. 945539 (Human Brain Project SGA3). G.H. was funded by the grant CONSCBRAIN (n. 661583) of the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie action. G.D. and G.H. received funding from the German Research Council (DFG, No. KN 588/7 – 1) within the priority program Computational Connectomics (SPP 2041). E.T. and H.L. were supported by the Bundesministerium für Bildung und Forschung (grant number 01 EV 0703) and the LOEWE Neuronale Koordination Forschungsschwerpunkt Frankfurt (NeFF). M.L.K. is supported by the ERC Consolidator Grant: CAREGIVING (n. 615539), Center for Music in the Brain, funded by the Danish National Research Foundation (DNRF117), and centre for Eudaimonia and Human Flourishing funded by the Pettit and Carlsberg Foundations.

Recent research has found that the human sleep cycle is characterised by changes in spatiotemporal patterns of brain activity. Yet, we are still missing a mechanistic explanation of the local neuronal dynamics underlying these changes. We used whole-brain computational modelling to study the differences in global brain functional connectivity and synchrony of fMRI activity in healthy humans during wakefulness and slow-wave sleep. We applied a whole-brain model based on the normal form of a supercritical Hopf bifurcation and studied the dynamical changes when adapting the bifurcation parameter for all brain nodes to best match wakefulness and slow-wave sleep. Furthermore, we analysed differences in effective connectivity between the two states. In addition to significant changes in functional connectivity, synchrony and metastability, this analysis revealed a significant shift of the global dynamic working point of brain dynamics, from the edge of the transition between damped to sustained oscillations during wakefulness, to a stable focus during slow-wave sleep. Moreover, we identified a significant global decrease in effective interactions during slow-wave sleep. These results suggest a mechanism for the empirical functional changes observed during slow-wave sleep, namely a global shift of the brain's dynamic working point leading to increased stability and decreased effective connectivity. ; BMJ, RH, GH, APA and GD were funded by the European Research Council (ERC) Advanced Grant DYSTRUCTURE (n. 295129), European Union's Horizon 2020 research and innovation programme under grant agreement No. 720270 (HBP SGA1) and No. 661583 (CONSBRAIN), by the Programa Estatal de Investigación Cientifica y Tecnica de Excelencia MINECO (PSI2013-42091, PSI2016-75688-P (AEI/FEDER, EU) and PCIN-2013-026), Juan de la Cierva fellowship (IJCI-2014-21066) and by the Catalan Agency for Management of University and Research Grants, AGAUR (2014SGR856). ET and HL were supported by the Bundesministerium für Bildung und Forschung (grantnumber 01 EV 0703) and the LOEWE Neuronale Koordination Forschungsschwerpunkt Frankfurt (NeFF). ET was further funded by a postdoctoral grant of the AXA foundation. MLK was supported by the ERC Consolidator Grant CAREGIVING (n. 615539).

Brain dynamics depicts an extremely complex energy landscape that changes over time, and its characterisation is a central unsolved problem in neuroscience. We approximate the non-stationary landscape sustained by the human brain through a novel mathematical formalism that allows us characterise the attractor structure, i.e. the stationary points and their connections. Due to its time-varying nature, the structure of the global attractor and the corresponding number of energy levels changes over time. We apply this formalism to distinguish quantitatively between the different human brain states of wakefulness and different stages of sleep, as a step towards future clinical applications. ; J.A.G., I.G. and J.A.L have been partially supported by Spanish Ministerio de Economía y Competitividad and FEDER, projects MTM2015-63723-P, PGC2018-096540-B-I00, Proyecto US-1254251 del Fondo Europeo de Desarrollo Regional (FEDER) y la Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía, dentro del Programa Operativo FEDER 2014-2020 and Proyecto PAIDI 2020 P20_00592. S.S.P. is supported by the Research Project PGC2018-096641-B-I00 (Ministerio de Ciencia, Innovación y Universidades / Agencia Estatal de Investigación /FEDER, UE). G.D. is supported by the Spanish Research Project PSI2016-75688-P (Agencia Estatal de Investigacíon/Fondo Europeo de Desarrollo Regional, European Union); by the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreements 720270 (Human Brain Project [HBP] SGA1) and 785907 (HBP SGA2); and by the Catalan Agency for Management of University and Research Grants Programme 2017 SGR 1545. M.L.K. is supported by the European Research Council Consolidator Grant: CAREGIVING (615539) and Center for Music in the Brain, funded by the Danish National Research Foundation (DNRF117). H.L. and data acquisition were supported by the Bundesministerium für Bildung und Forschung (grant no. 01 EV 0703); H.L. and E.T. by the LOEWE Neuronale Koordination ...

The modern understanding of sleep is based on the classification of sleep into stages defined by their electroencephalography (EEG) signatures, but the underlying brain dynamics remain unclear. Here we aimed to move significantly beyond the current state-of-the-art description of sleep, and in particular to characterise the spatiotemporal complexity of whole-brain networks and state transitions during sleep. In order to obtain the most unbiased estimate of how whole-brain network states evolve through the human sleep cycle, we used a Markovian data-driven analysis of continuous neuroimaging data from 57 healthy participants falling asleep during simultaneous functional magnetic resonance imaging (fMRI) and EEG. This Hidden Markov Model (HMM) facilitated discovery of the dynamic choreography between different whole-brain networks across the wake-non-REM sleep cycle. Notably, our results reveal key trajectories to switch within and between EEG-based sleep stages, while highlighting the heterogeneities of stage N1 sleep and wakefulness before and after sleep. ; G.D. was supported by the Spanish Research Project PSI2016-75688-P (AEI/FEDER) and by the European Union's Horizon 2020 research and innovation programme under Grant agreement no. 720270 (HBP SGA1). M.L.K. was supported by the ERC Consolidator Grant CAREGIVING (615539) and the Center for Music in the Brain, funded by the Danish National Research Foundation Grant DNRF117. J.C. was supported under the project NORTE-01-0145-FEDER-000023.