Functional connectivity (FC) sheds light on the interactions between different brain regions. Besides basic research, it is clinically relevant for applications in Alzheimer's disease, schizophrenia, presurgical planning, epilepsy, and traumatic brain injury. Simulations of whole-brain mean-field computational models with realistic connectivity determined by tractography studies enable us to reproduce with accuracy aspects of average FC in the resting state. Most computational studies, however, did not address the prominent non-stationarity in resting state FC, which may result in large intra- and inter-subject variability and thus preclude an accurate individual predictability. Here we show that this non-stationarity reveals a rich structure, characterized by rapid transitions switching between a few discrete FC states. We also show that computational models optimized to fit time-averaged FC do not reproduce these spontaneous state transitions and, thus, are not qualitatively superior to simplified linear stochastic models, which account for the effects of structure alone. We then demonstrate that a slight enhancement of the non-linearity of the network nodes is sufficient to broaden the repertoire of possible network behaviors, leading to modes of fluctuations, reminiscent of some of the most frequently observed Resting State Networks. Because of the noise-driven exploration of this repertoire, the dynamics of FC qualitatively change now and display non-stationary switching similar to empirical resting state recordings (Functional Connectivity Dynamics (FCD)). Thus FCD bear promise to serve as a better biomarker of resting state neural activity and of its pathologic alterations.

In this article, we describe the mathematical framework of the computational model at the core of the tool The Virtual Brain (TVB), designed to simulate collective whole brain dynamics by virtualizing brain structure and function, allowing simultaneous outputs of a number of experimental modalities such as electro- and magnetoencephalography (EEG, MEG) and functional Magnetic Resonance Imaging (fMRI). The implementation allows for a systematic exploration and manipulation of every underlying component of a large-scale brain network model (BNM), such as the neural mass model governing the local dynamics or the structural connectivity constraining the space time structure of the network couplings. Here, a consistent notation for the generalized BNM is given, so that in this form the equations represent a direct link between the mathematical description of BNMs and the components of the numerical implementation in TVB. Finally, we made a summary of the forward models implemented for mapping simulated neural activity (EEG, MEG, sterotactic electroencephalogram (sEEG), fMRI), identifying their advantages and limitations.

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Transcranial direct current stimulation (tDCS) is a noninvasive technique for affecting brain dynamics with promising application in the clinical therapy of neurological and psychiatric disorders such as Parkinson's disease, Alzheimer's disease, depression, and schizophrenia. Resting state dynamics increasingly play a role in the assessment of connectivity-based pathologies such as Alzheimer's and schizophrenia. We systematically applied tDCS in a large-scale network model of 74 cerebral areas, investigating the spatiotemporal changes in dynamic states as a function of structural connectivity changes. Structural connectivity was defined by the human connectome. The main findings of this study are fourfold: Firstly, we found a tDCS-induced increase in functional connectivity among cerebral areas and among EEG sensors, where the latter reproduced empirical findings of other researchers. Secondly, the analysis of the network dynamics suggested synchronization to be the main mechanism of the observed effects. Thirdly, we found that tDCS sharpens and shifts the frequency distribution of scalp EEG sensors slightly towards higher frequencies. Fourthly, new dynamic states emerged through interacting areas in the network compared to the dynamics of an isolated area. The findings propose synchronization as a key mechanism underlying the changes in the spatiotemporal pattern formation due to tDCS. Our work supports the notion that noninvasive brain stimulation is able to bias brain dynamics by affecting the competitive interplay of functional subnetworks.

When the brain is stimulated, for example, by sensory inputs or goal-oriented tasks, the brain initially responds with activities in specific areas. The subsequent pattern formation of functional networks is constrained by the structural connectivity (SC) of the brain. The extent to which information is processed over short- or long-range SC is unclear. Whole-brain models based on long-range axonal connections, for example, can partly describe measured functional connectivity dynamics at rest. Here, we study the effect of SC on the network response to stimulation. We use a human whole-brain network model comprising long- and short-range connections. We systematically activate each cortical or thalamic area, and investigate the network response as a function of its short- and long-range SC. We show that when the brain is operating at the edge of criticality, stimulation causes a cascade of network recruitments, collapsing onto a smaller space that is partly constrained by SC. We found both short- and long-range SC essential to reproduce experimental results. In particular, the stimulation of specific areas results in the activation of one or more resting-state networks. We suggest that the stimulus-induced brain activity, which may indicate information and cognitive processing, follows specific routes imposed by structural networks explaining the emergence of functional networks. We provide a lookup table linking stimulation targets and functional network activations, which potentially can be useful in diagnostics and treatments with brain stimulation.

Bursting is a phenomenon found in a variety of physical and biological systems. For example, in neuroscience, bursting is believed to play a key role in the way information is transferred in the nervous system. In this work, we propose a model that, appropriately tuned, can display several types of bursting behaviors. The model contains two subsystems acting at different time scales. For the fast subsystem we use the planar unfolding of a high codimension singularity. In its bifurcation diagram, we locate paths that underlie the right sequence of bifurcations necessary for bursting. The slow subsystem steers the fast one back and forth along these paths leading to bursting behavior. The model is able to produce almost all the classes of bursting predicted for systems with a planar fast subsystem. Transitions between classes can be obtained through an ultra-slow modulation of the model’s parameters. A detailed exploration of the parameter space allows predicting possible transitions. This provides a single framework to understand the coexistence of diverse bursting patterns in physical and biological systems or in models.

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect.

Introduction: While the prevalence of neurodegenerative diseases associated with dementia such as Alzheimer's disease (AD) increases, our knowledge on the underlying mechanisms, outcome predictors, or therapeutic targets is limited. In this work, we demonstrate how computational multi-scale brain modeling links phenomena of different scales and therefore identifies potential disease mechanisms leading the way to improved diagnostics and treatment. Methods: The Virtual Brain (TVB; thevirtualbrain.org ) neuroinformatics platform allows standardized large-scale structural connectivity-based simulations of whole brain dynamics. We provide proof of concept for a novel approach that quantitatively links the effects of altered molecular pathways onto neuronal population dynamics. As a novelty, we connect chemical compounds measured with positron emission tomography (PET) with neural function in TVB addressing the phenomenon of hyperexcitability in AD related to the protein amyloid beta (Abeta). We construct personalized virtual brains based on an averaged healthy connectome and individual PET derived distributions of Abeta in patients with mild cognitive impairment (MCI, N = 8) and Alzheimer's Disease (AD, N = 10) and in age-matched healthy controls (HC, N = 15) using data from ADNI-3 data base ( http://adni.loni.usc.edu ). In the personalized virtual brains, individual Abeta burden modulates regional Excitation-Inhibition balance, leading to local hyperexcitation with high Abeta loads. We analyze simulated regional neural activity and electroencephalograms (EEG). Results: Known empirical alterations of EEG in patients with AD compared to HCs were reproduced by simulations. The virtual AD group showed slower frequencies in simulated local field potentials and EEG compared to MCI and HC groups. The heterogeneity of the Abeta load is crucial for the virtual EEG slowing which is absent for control models with homogeneous Abeta distributions. Slowing phenomena primarily affect the network hubs, independent of the spatial distribution of Abeta. Modeling the N-methyl-D-aspartate (NMDA) receptor antagonism of memantine in local population models, reveals potential functional reversibility of the observed large-scale alterations (reflected by EEG slowing) in virtual AD brains. Discussion: We demonstrate how TVB enables the simulation of systems effects caused by pathogenetic molecular candidate mechanisms in human virtual brains.