Transcranial direct current stimulation changes resting state functional connectivity: A large-scale brain network modeling study.

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.

How do parcellation size and short-range connectivity affect dynamics in large-scale brain network models?

Recent efforts to model human brain activity on the scale of the whole brain rest on connectivity estimates of large-scale networks derived from diffusion magnetic resonance imaging (dMRI). This type of connectivity describes white matter fiber tracts. The number of short-range cortico-cortical white-matter connections is, however, underrepresented in such large-scale brain models. It is still unclear on the one hand, which scale of representation of white matter fibers is optimal to describe brain activity on a large-scale such as recorded with magneto- or electroencephalography (M/EEG) or functional magnetic resonance imaging (fMRI), and on the other hand, to which extent short-range connections that are typically local should be taken into account. In this article we quantified the effect of connectivity upon large-scale brain network dynamics by (i) systematically varying the number of brain regions before computing the connectivity matrix, and by (ii) adding generic short-range connections. We used dMRI data from the Human Connectome Project. We developed a suite of preprocessing modules called SCRIPTS to prepare these imaging data for The Virtual Brain, a neuroinformatics platform for large-scale brain modeling and simulations. We performed simulations under different connectivity conditions and quantified the spatiotemporal dynamics in terms of Shannon Entropy, dwell time and Principal Component Analysis. For the reconstructed connectivity, our results show that the major white matter fiber bundles play an important role in shaping slow dynamics in large-scale brain networks (e.g. in fMRI). Faster dynamics such as gamma oscillations (around 40 Hz) are sensitive to the short-range connectivity if transmission delays are considered.

Functional connectivity dynamics: modeling the switching behavior of the resting state.

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.

Mathematical framework for large-scale brain network modeling in The Virtual Brain.

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.

Bottom up modeling of the connectome: linking structure and function in the resting brain and their changes in aging.

With the increasing availability of advanced imaging technologies, we are entering a new era of neuroscience. Detailed descriptions of the complex brain network enable us to map out a structural connectome, characterize it with graph theoretical methods, and compare it to the functional networks with increasing detail. To link these two aspects and understand how dynamics and structure interact to form functional brain networks in task and in the resting state, we use theoretical models. The advantage of using theoretical models is that by recreating functional connectivity and time series explicitly from structure and pre-defined dynamics, we can extract critical mechanisms by linking structure and function in ways not directly accessible in the real brain. Recently, resting-state models with varying local dynamics have reproduced empirical functional connectivity patterns, and given support to the view that the brain works at a critical point at the edge of a bifurcation of the system. Here, we present an overview of a modeling approach of the resting brain network and give an application of a neural mass model in the study of complexity changes in aging.

Modeling brain resonance phenomena using a neural mass model.

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.

Brain simulation augments machine-learning-based classification of dementia.

Introduction: Computational brain network modeling using The Virtual Brain (TVB) simulation platform acts synergistically with machine learning (ML) and multi-modal neuroimaging to reveal mechanisms and improve diagnostics in Alzheimer's disease (AD). Methods: We enhance large-scale whole-brain simulation in TVB with a cause-and-effect model linking local amyloid beta (Aß) positron emission tomography (PET) with altered excitability. We use PET and magnetic resonance imaging (MRI) data from 33 participants of the Alzheimer's Disease Neuroimaging Initiative (ADNI3) combined with frequency compositions of TVB-simulated local field potentials (LFP) for ML classification. Results: The combination of empirical neuroimaging features and simulated LFPs significantly outperformed the classification accuracy of empirical data alone by about 10% (weighted F1-score empirical 64.34% vs. combined 74.28%). Informative features showed high biological plausibility regarding the AD-typical spatial distribution. Discussion: The cause-and-effect implementation of local hyperexcitation caused by Aß can improve the ML-driven classification of AD and demonstrates TVB's ability to decode information in empirical data using connectivity-based brain simulation.

Bifurcation analysis of neural mass models: Impact of extrinsic inputs and dendritic time constants.

Neural mass models (NMMs) explain dynamics of neuronal populations and were designed to strike a balance between mathematical simplicity and biological plausibility. They are currently widely used as generative models for noninvasive electrophysiological brain measurements; that is, magneto- and electroencephalography (M/EEG). Here, we systematically describe the oscillatory regimes which a NMM of a single cortical source with extrinsic input from other cortical and subcortical areas to each subpopulation can explain. For this purpose, we used bifurcation analysis to describe qualitative changes in system behavior in response to quantitative input changes. This approach allowed us to describe sequences of oscillatory regimes, given some specific input trajectory. We systematically classified these sequential phenomena and mapped them into parameter space. Our analysis suggests a principled scheme of how complex M/EEG phenomena can be modeled parsimoniously on two time scales: While the system displays fast oscillations, it slowly traverses phase space to another qualitatively different oscillatory regime, depending on the input dynamics. The resulting scheme is useful for applications where one needs to model an ordered sequence of switching between qualitatively different oscillatory regimes, for example, in pharmacological interventions, epilepsy, sleep, or context-induced state changes.

In silico exploration of mouse brain dynamics by focal stimulation reflects the organization of functional networks and sensory processing.

Resting-state functional networks such as the default mode network (DMN) dominate spontaneous brain dynamics. To date, the mechanisms linking brain structure and brain dynamics and functions in cognition, perception, and action remain unknown, mainly due to the uncontrolled and erratic nature of the resting state. Here we used a stimulation paradigm to probe the brain's resting behavior, providing insights on state-space stability and multiplicity of network trajectories after stimulation. We performed explorations on a mouse model to map spatiotemporal brain dynamics as a function of the stimulation site. We demonstrated the emergence of known functional networks in brain responses. Several responses heavily relied on the DMN and were suggestive of the DMN playing a mechanistic role between functional networks. We probed the simulated brain responses to the stimulation of regions along the information processing chains of sensory systems from periphery up to primary sensory cortices. Moreover, we compared simulated dynamics against in vivo brain responses to optogenetic stimulation. Our results underwrite the importance of anatomical connectivity in the functional organization of brain networks and demonstrate how functionally differentiated information processing chains arise from the same system.

Linking Molecular Pathways and Large-Scale Computational Modeling to Assess Candidate Disease Mechanisms and Pharmacodynamics in Alzheimer's Disease.

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.

Fast-Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-slow Transitions of Classes.

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.

Ebbinghaus figures that deceive the eye do not necessarily deceive the hand.

In support of the visual stream dissociation hypothesis, which states that distinct visual streams serve vision-for-perception and vision-for-action, visual size illusions were reported over 20 years ago to 'deceive the eye but not the hand'. Ever since, inconclusive results and contradictory interpretations have accumulated. Therefore, we investigated the effects of the Ebbinghaus figure on repetitive aiming movements with distinct dynamics. Participants performed a Fitts' task in which Ebbinghaus figures served as targets. We systematically varied the three parameters which have been shown to influence the perceived size of the Ebbinghaus figure's target circle, namely the size of the target, its distance to the context circles and the size of the context circles. This paper shows that movement is significantly affected by the context size, but, in contrast to perception, not by the other two parameters. This is especially prominent in the approach phase of the movement towards the target, regardless of the dynamics. To reconcile the findings, we argue that different informational variables are used for size perception and the visual control of movements irrespective of whether certain variables induce (perceptual) illusions.

Selective Activation of Resting-State Networks following Focal Stimulation in a Connectome-Based Network Model of the Human Brain.

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.

Heterogeneity of time delays determines synchronization of coupled oscillators.

Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.

Phase coupling between different motor areas during tongue-movement imagery.

Motor imagery can be accompanied by an enhancement of brain oscillations (event-related synchronization, ERS) within specific frequency bands. To characterize the neuronal couplings involved during these prominent power changes, we have chosen a certain coupling measure that bears directly on the issue of transient cortical connections. Specifically, we applied for the first time the phase-locking value to investigate the phase coupling of sensorimotor rhythms in different motor areas during tongue-movement imagery. Most interesting, we showed that robust neuronal couplings within the alpha frequency range are established between the midcentral position and bilateral central electrode positions, overlying the supplementary motor area (SMA) and the right and left primary sensorimotor area, respectively. In contrast, no direct linkage was present between sensorimotor rhythms in both hemispheres. We suggest that the coupling results point at a separate interplay between neural networks within the SMA and lateralized networks in primary sensorimotor areas of each hemisphere during motor imagery.