During rest, envelopes of band-limited on-going MEG signals co-vary across the brain in consistent patterns, which have been related to resting-state networks measured with fMRI. To investigate the genesis of such envelope correlations, we consider a whole-brain network model assuming two distinct fundamental scenarios: one where each brain area generates oscillations in a single frequency, and a novel one where each brain area can generate oscillations in multiple frequency bands. The models share, as a common generator of damped oscillations, the normal form of a supercritical Hopf bifurcation operating at the critical border between the steady state and the oscillatory regime. The envelopes of the simulated signals are compared with empirical MEG data using new methods to analyse the envelope dynamics in terms of their phase coherence and stability across the spectrum of carrier frequencies.Considering the whole-brain model with a single frequency generator in each brain area, we obtain the best fit with the empirical MEG data when the fundamental frequency is tuned at 12 Hz. However, when multiple frequency generators are placed at each local brain area, we obtain an improved fit of the spatio-temporal structure of on-going MEG data across all frequency bands. Our results indicate that the brain is likely to operate on multiple frequency channels during rest, introducing a novel dimension for future models of large-scale brain activity.

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.

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.

Human neuroimaging research has revealed that wakefulness and sleep involve very different activity patterns. Yet, it is not clear why brain states differ in their dynamical complexity, e.g. in the level of integration and segregation across brain networks over time. Here, we investigate the mechanisms underlying the dynamical stability of brain states using a novel off-line in silico perturbation protocol. We first adjust a whole-brain computational model to the basal dynamics of wakefulness and deep sleep recorded with fMRI in two independent human fMRI datasets. Then, the models of sleep and awake brain states are perturbed using two distinct multifocal protocols either promoting or disrupting synchronization in randomly selected brain areas. Once perturbation is halted, we use a novel measure, the Perturbative Integration Latency Index (PILI), to evaluate the recovery back to baseline. We find a clear distinction between models, consistently showing larger PILI in wakefulness than in deep sleep, corroborating previous experimental findings. In the models, larger recoveries are associated to a critical slowing down induced by a shift in the model's operation point, indicating that the awake brain operates further from a stable equilibrium than deep sleep. This novel approach opens up for a new level of artificial perturbative studies unconstrained by ethical limitations allowing for a deeper investigation of the dynamical properties of different brain states.

To survive in an ever-changing environment, the brain must seamlessly integrate a rich stream of incoming information into coherent internal representations that can then be used to efficiently plan for action. The brain must, however, balance its ability to information from various sources with a complementary capacity to information into modules which perform specialized computations in local circuits. Importantly, evidence suggests that imbalances in the brain's ability to bind together and/or segregate information over both space and time is a common feature of several neuropsychiatric disorders. Most studies have, however, until recently strictly attempted to characterize the principles of integration and segregation in static (i.e. time-invariant) representations of human brain networks, hence disregarding the complex spatio-temporal nature of these processes. In the present Review, we describe how the emerging discipline of may be used to study the causal mechanisms of the integration and segregation of information on behaviourally relevant timescales. We emphasize how novel methods from network science and whole-brain computational modelling can expand beyond traditional neuroimaging paradigms and help to uncover the neurobiological determinants of the abnormal integration and segregation of information in neuropsychiatric disorders.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Deep brain stimulation (DBS) for Parkinson’s disease is a highly effective treatment in controlling otherwise debilitating symptoms. Yet the underlying brain mechanisms are currently not well understood. Whole-brain computational modeling was used to disclose the effects of DBS during resting-state functional Magnetic Resonance Imaging in ten patients with Parkinson’s disease. Specifically, we explored the local and global impact that DBS has in creating asynchronous, stable or critical oscillatory conditions using a supercritical bifurcation model. We found that DBS shifts global brain dynamics of patients towards a Healthy regime. This effect was more pronounced in very specific brain areas such as the thalamus, globus pallidus and orbitofrontal regions of the right hemisphere (with the left hemisphere not analyzed given artifacts arising from the electrode lead). Global aspects of integration and synchronization were also rebalanced. Empirically, we found higher communicability and coherence brain measures during DBS-ON compared to DBS-OFF. Finally, using our model as a framework, artificial in silico DBS was applied to find potential alternative target areas for stimulation and whole-brain rebalancing. These results offer important insights into the underlying large-scale effects of DBS as well as in finding novel stimulation targets, which may offer a route to more efficacious treatments.

In order to promote survival through flexible cognition and goal-directed behaviour, the brain has to optimize segregation and integration of information into coherent, distributed dynamical states. Certain organizational features of the brain have been proposed to be essential to facilitate cognitive flexibility, especially hub regions in the so-called rich club which show dense interconnectivity. These structural hubs have been suggested to be vital for integration and segregation of information. Yet, this has not been evaluated in terms of resulting functional temporal dynamics. A complementary measure covering the temporal aspects of functional connectivity could thus bring new insights into a more complete picture of the integrative nature of brain networks. Here, we use causal whole-brain computational modelling to determine the functional dynamical significance of the rich club and compare this to a new measure of the most functionally relevant brain regions for binding information over time ("dynamical workspace of binding nodes"). We found that removal of the iteratively generated workspace of binding nodes impacts significantly more on measures of integration and encoding of information capability than the removal of the rich club regions. While the rich club procedure produced almost half of the binding nodes, the remaining nodes have low degree yet still play a significant role in the workspace essential for binding information over time and as such goes beyond a description of the structural backbone.

Crying is the most salient vocal signal of distress. The cries of a newborn infant alert adult listeners and often elicit caregiving behavior. For the parent, rapid responding to an infant in distress is an adaptive behavior, functioning to ensure offspring survival. The ability to react rapidly requires quick recognition and evaluation of stimuli followed by a co-ordinated motor response. Previous neuroimaging research has demonstrated early specialized activity in response to infant faces. Using magnetoencephalography, we found similarly early (100–200 ms) differences in neural responses to infant and adult cry vocalizations in auditory, emotional, and motor cortical brain regions. We propose that this early differential activity may help to rapidly identify infant cries and engage affective and motor neural circuitry to promote adaptive behavioral responding, before conscious awareness. These differences were observed in adults who were not parents, perhaps indicative of a universal brain-based “caregiving instinct.”