Key role of coupling, delay, and noise in resting brain fluctuations

The longitudinal relationship between BOLD signal variability changes and white matter maturation during early childhood

Intra-individual transient temporal fluctuations in brain signal, as measured by fMRI blood oxygenation level dependent (BOLD) variability, is increasingly considered an important signal rather than measurement noise. Evidence from computational and cognitive neuroscience suggests that signal variability is a good proxy-measure of brain functional integrity and information processing capacity. Here, we sought to explore across-participant and longitudinal relationships between BOLD variability, age, and white matter structure in early childhood. We measured standard deviation of BOLD signal, total white matter volume, global fractional anisotropy (FA) and mean diffusivity (MD) during passive movie viewing in a sample of healthy children (aged 2-8 years; N = 83). We investigated how age and white matter development related to changes in BOLD variability both across- and within-participants. Our across-participant analyses using behavioural partial least squares (bPLS) revealed that the influence of age and white matter maturation on BOLD variability was highly interrelated. BOLD variability increased in widespread frontal, temporal and parietal regions, and decreased in the hippocampus and parahippocampal gyrus with age and white matter development. Our longitudinal analyses using linear mixed effects modelling revealed significant associations between BOLD variability, age and white matter microstructure. Analyses using artificial neural networks demonstrated that BOLD variability and white matter micro and macro-structure at earlier ages were strong predictors of BOLD variability at later ages. By characterizing the across-participant and longitudinal features of the association between BOLD variability and white matter micro- and macrostructure in early childhood, our results provide a novel perspective to understand structure-function relationships in the developing brain.

Inference of brain networks with approximate Bayesian computation - assessing face validity with an example application in Parkinsonism

This paper describes and validates a novel framework using the Approximate Bayesian Computation (ABC) algorithm for parameter estimation and model selection in models of mesoscale brain network activity. We provide a proof of principle, first pass validation of this framework using a set of neural mass models of the cortico-basal ganglia thalamic circuit inverted upon spectral features from experimental, in vivo recordings. This optimization scheme relaxes an assumption of fixed-form posteriors (i.e. the Laplace approximation) taken in previous approaches to inverse modelling of spectral features. This enables the exploration of model dynamics beyond that approximated from local linearity assumptions and so fit to explicit, numerical solutions of the underlying non-linear system of equations. In this first paper, we establish a face validation of the optimization procedures in terms of: (i) the ability to approximate posterior densities over parameters that are plausible given the known causes of the data; (ii) the ability of the model comparison procedures to yield posterior model probabilities that can identify the model structure known to generate the data; and (iii) the robustness of these procedures to local minima in the face of different starting conditions. Finally, as an illustrative application we show (iv) that model comparison can yield plausible conclusions given the known neurobiology of the cortico-basal ganglia-thalamic circuit in Parkinsonism. These results lay the groundwork for future studies utilizing highly nonlinear or brittle models that can explain time dependant dynamics, such as oscillatory bursts, in terms of the underlying neural circuits.

Virtual Connectomic Datasets in Alzheimer's Disease and Aging Using Whole-Brain Network Dynamics Modelling

Large neuroimaging datasets, including information about structural connectivity (SC) and functional connectivity (FC), play an increasingly important role in clinical research, where they guide the design of algorithms for automated stratification, diagnosis or prediction. A major obstacle is, however, the problem of missing features [e.g., lack of concurrent DTI SC and resting-state functional magnetic resonance imaging (rsfMRI) FC measurements for many of the subjects]. We propose here to address the missing connectivity features problem by introducing strategies based on computational whole-brain network modeling. Using two datasets, the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset and a healthy aging dataset, for proof-of-concept, we demonstrate the feasibility of virtual data completion (i.e., inferring “virtual FC” from empirical SC or “virtual SC” from empirical FC), by using self-consistent simulations of linear and nonlinear brain network models. Furthermore, by performing machine learning classification (to separate age classes or control from patient subjects), we show that algorithms trained on virtual connectomes achieve discrimination performance comparable to when trained on actual empirical data; similarly, algorithms trained on virtual connectomes can be used to successfully classify novel empirical connectomes. Completion algorithms can be combined and reiterated to generate realistic surrogate connectivity matrices in arbitrarily large number, opening the way to the generation of virtual connectomic datasets with network connectivity information comparable to the one of the original data.

The Impact of Small Time Delays on the Onset of Oscillations and Synchrony in Brain Networks

The human brain constitutes one of the most advanced networks produced by nature, consisting of billions of neurons communicating with each other. However, this communication is not in real-time, with different communication or time-delays occurring between neurons in different brain areas. Here, we investigate the impacts of these delays by modeling large interacting neural circuits as neural-field systems which model the bulk activity of populations of neurons. By using a Master Stability Function analysis combined with numerical simulations, we find that delays (1) may actually stabilize brain dynamics by temporarily preventing the onset to oscillatory and pathologically synchronized dynamics and (2) may enhance or diminish synchronization depending on the underlying eigenvalue spectrum of the connectivity matrix. Real eigenvalues with large magnitudes result in increased synchronizability while complex eigenvalues with large magnitudes and positive real parts yield a decrease in synchronizability in the delay vs. instantaneously coupled case. This result applies to networks with fixed, constant delays, and was robust to networks with heterogeneous delays. In the case of real brain networks, where the eigenvalues are predominantly real, owing to the nearly symmetric nature of these weight matrices, biologically plausible, small delays, are likely to increase synchronization, rather than decreasing it.

Circuit mechanisms for the chemical modulation of cortex-wide network interactions and behavioral variability

Influential theories postulate distinct roles of catecholamines and acetylcholine in cognition and behavior. However, previous physiological work reported similar effects of these neuromodulators on the response properties (specifically, the gain) of individual cortical neurons. Here, we show a double dissociation between the effects of catecholamines and acetylcholine at the level of large-scale interactions between cortical areas in humans. A pharmacological boost of catecholamine levels increased cortex-wide interactions during a visual task, but not rest. An acetylcholine boost decreased interactions during rest, but not task. Cortical circuit modeling explained this dissociation by differential changes in two circuit properties: the local excitation-inhibition balance (more strongly increased by catecholamines) and intracortical transmission (more strongly reduced by acetylcholine). The inferred catecholaminergic mechanism also predicted noisier decision-making, which we confirmed for both perceptual and value-based choice behavior. Our work highlights specific circuit mechanisms for shaping cortical network interactions and behavioral variability by key neuromodulatory systems.

On the influence of prior information evaluated by fully Bayesian criteria in a personalized whole-brain model of epilepsy spread

Individualized anatomical information has been used as prior knowledge in Bayesian inference paradigms of whole-brain network models. However, the actual sensitivity to such personalized information in priors is still unknown. In this study, we introduce the use of fully Bayesian information criteria and leave-one-out cross-validation technique on the subject-specific information to assess different epileptogenicity hypotheses regarding the location of pathological brain areas based on a priori knowledge from dynamical system properties. The Bayesian Virtual Epileptic Patient (BVEP) model, which relies on the fusion of structural data of individuals, a generative model of epileptiform discharges, and a self-tuning Monte Carlo sampling algorithm, is used to infer the spatial map of epileptogenicity across different brain areas. Our results indicate that measuring the out-of-sample prediction accuracy of the BVEP model with informative priors enables reliable and efficient evaluation of potential hypotheses regarding the degree of epileptogenicity across different brain regions. In contrast, while using uninformative priors, the information criteria are unable to provide strong evidence about the epileptogenicity of brain areas. We also show that the fully Bayesian criteria correctly assess different hypotheses about both structural and functional components of whole-brain models that differ across individuals. The fully Bayesian information-theory based approach used in this study suggests a patient-specific strategy for epileptogenicity hypothesis testing in generative brain network models of epilepsy to improve surgical outcomes.

Dynamical consequences of regional heterogeneity in the brain's transcriptional landscape

Brain regions vary in their molecular and cellular composition, but how this heterogeneity shapes neuronal dynamics is unclear. Here, we investigate the dynamical consequences of regional heterogeneity using a biophysical model of whole-brain functional magnetic resonance imaging (MRI) dynamics in humans. We show that models in which transcriptional variations in excitatory and inhibitory receptor (E:I) gene expression constrain regional heterogeneity more accurately reproduce the spatiotemporal structure of empirical functional connectivity estimates than do models constrained by global gene expression profiles or MRI-derived estimates of myeloarchitecture. We further show that regional transcriptional heterogeneity is essential for yielding both ignition-like dynamics, which are thought to support conscious processing, and a wide variance of regional-activity time scales, which supports a broad dynamical range. We thus identify a key role for E:I heterogeneity in generating complex neuronal dynamics and demonstrate the viability of using transcriptomic data to constrain models of large-scale brain function.

On a Quantitative Approach to Clinical Neuroscience in Psychiatry: Lessons from the Kuramoto Model

The human brain is a complex system comprising subregions that dynamically exchange information between its various parts through synchronization. These dynamic, complex interactions ultimately play a role in perception, emotion, cognition, and behavior, as well as in various maladaptive neurologic and psychiatric processes. It is therefore important to understand how brain dynamics might be implicated in these processes. Over the past few years, network neuroscience and computational neuroscience have highlighted the importance of measures such as metastability (a property whereby members of an oscillating system tend to linger at the edge of synchronicity without permanently becoming synchronized) in quantifying brain dynamics. Altered metastability has been implicated in various psychiatric illnesses, such as traumatic brain injury and Alzheimer's disease. Computational models, which range in complexity, have been used to assess how various parameters affect metastability, synchronization, and functional connectivity. These models, though limited, can act as heuristics in understanding brain dynamics. This article (aimed at the clinical psychiatrist who might not possess an extensive mathematical background) is intended to provide a brief and qualitative summary of studies that have used a specific, highly simplified computational model of coupled oscillators (Kuramoto model) for understanding brain dynamics-which might bear some relevance to clinical psychiatry.

Breakdown of Whole-brain Dynamics in Preterm-born Children

The brain operates at a critical point that is balanced between order and disorder. Even during rest, unstable periods of random behavior are interspersed with stable periods of balanced activity patterns that support optimal information processing. Being born preterm may cause deviations from this normal pattern of development. We compared 33 extremely preterm (EPT) children born at < 27 weeks of gestation and 28 full-term controls. Two approaches were adopted in both groups, when they were 10 years of age, using structural and functional brain magnetic resonance imaging data. The first was using a novel intrinsic ignition analysis to study the ability of the areas of the brain to propagate neural activity. The second was a whole-brain Hopf model, to define the level of stability, desynchronization, or criticality of the brain. EPT-born children exhibited fewer intrinsic ignition events than controls; nodes were related to less sophisticated aspects of cognitive control, and there was a different hierarchy pattern in the propagation of information and suboptimal synchronicity and criticality. The largest differences were found in brain nodes belonging to the rich-club architecture. These results provide important insights into the neural substrates underlying brain reorganization and neurodevelopmental impairments related to prematurity.

Clinical connectome fingerprints of cognitive decline

Brain connectome fingerprinting is rapidly rising as a novel influential field in brain network analysis. Yet, it is still unclear whether connectivity fingerprints could be effectively used for mapping and predicting disease progression from human brain data. We hypothesize that dysregulation of brain activity in disease would reflect in worse subject identification. We propose a novel framework, Clinical Connectome Fingerprinting, to detect individual connectome features from clinical populations. We show that "clinical fingerprints" can map individual variations between elderly healthy subjects and patients with mild cognitive impairment in functional connectomes extracted from magnetoencephalography data. We find that identifiability is reduced in patients as compared to controls, and show that these connectivity features are predictive of the individual Mini-Mental State Examination (MMSE) score in patients. We hope that the proposed methodology can help in bridging the gap between connectivity features and biomarkers of brain dysfunction in large-scale brain networks.

Brain States and Transitions: Insights from Computational Neuroscience

Within the field of computational neuroscience there are great expectations of finding new ways to rebalance the complex dynamic system of the human brain through controlled pharmacological or electromagnetic perturbation. Yet many obstacles remain between the ability to accurately predict how and where best to perturb to force a transition from one brain state to another. The foremost challenge is a commonly agreed definition of a given brain state. Recent progress in computational neuroscience has made it possible to robustly define brain states and force transitions between them. Here, we review the state of the art and propose a framework for determining the functional hierarchical organization describing any given brain state. We describe the latest advances in creating sophisticated whole-brain computational models with interacting neuronal and neurotransmitter systems that can be studied fully in silico to predict and design novel pharmacological and electromagnetic interventions to rebalance them in disease.

Brain Connectivity Studies on Structure-Function Relationships: A Short Survey with an Emphasis on Machine Learning

This short survey reviews the recent literature on the relationship between the brain structure and its functional dynamics. Imaging techniques such as diffusion tensor imaging (DTI) make it possible to reconstruct axonal fiber tracks and describe the structural connectivity (SC) between brain regions. By measuring fluctuations in neuronal activity, functional magnetic resonance imaging (fMRI) provides insights into the dynamics within this structural network. One key for a better understanding of brain mechanisms is to investigate how these fast dynamics emerge on a relatively stable structural backbone. So far, computational simulations and methods from graph theory have been mainly used for modeling this relationship. Machine learning techniques have already been established in neuroimaging for identifying functionally independent brain networks and classifying pathological brain states. This survey focuses on methods from machine learning, which contribute to our understanding of functional interactions between brain regions and their relation to the underlying anatomical substrate.

Emergence of canonical functional networks from the structural connectome

How do functional brain networks emerge from the underlying wiring of the brain? We examine how resting-state functional activation patterns emerge from the underlying connectivity and length of white matter fibers that constitute its “structural connectome”. By introducing realistic signal transmission delays along fiber projections, we obtain a complex-valued graph Laplacian matrix that depends on two parameters: coupling strength and oscillation frequency. This complex Laplacian admits a complex-valued eigen-basis in the frequency domain that is highly tunable and capable of reproducing the spatial patterns of canonical functional networks without requiring any detailed neural activity modeling. Specific canonical functional networks can be predicted using linear superposition of small subsets of complex eigenmodes. Using a novel parameter inference procedure we show that the complex Laplacian outperforms the real-valued Laplacian in predicting functional networks. The complex Laplacian eigenmodes therefore constitute a tunable yet parsimonious substrate on which a rich repertoire of realistic functional patterns can emerge. Although brain activity is governed by highly complex nonlinear processes and dense connections, our work suggests that simple extensions of linear models to the complex domain effectively approximate rich macroscopic spatial patterns observable on BOLD fMRI.

Inter-regional BOLD signal variability is an organizational feature of functional brain networks

Neuronal variability patterns promote the formation and organization of neural circuits. Macroscale similarities in regional variability patterns may therefore be linked to the strength and topography of inter-regional functional connections. To assess this relationship, we used multi-echo resting-state fMRI and investigated macroscale connectivity-variability associations in 154 adult humans (86 women; mean age = 22yrs). We computed inter-regional measures of moment-to-moment BOLD signal variability and related them to inter-regional functional connectivity. Region pairs that showed stronger functional connectivity also showed similar BOLD signal variability patterns, independent of inter-regional distance and structural similarity. Connectivity-variability associations were predominant within all networks and followed a hierarchical spatial organization that separated sensory, motor and attention systems from limbic, default and frontoparietal control association networks. Results were replicated in a second held-out fMRI run. These findings suggest that macroscale BOLD signal variability is an organizational feature of large-scale functional networks, and shared inter-regional BOLD signal variability may underlie macroscale brain network dynamics.

Transmission delays and frequency detuning can regulate information flow between brain regions

Brain networks exhibit very variable and dynamical functional connectivity and flexible configurations of information exchange despite their overall fixed structure. Brain oscillations are hypothesized to underlie time-dependent functional connectivity by periodically changing the excitability of neural populations. In this paper, we investigate the role of the connection delay and the detuning between the natural frequencies of neural populations in the transmission of signals. Based on numerical simulations and analytical arguments, we show that the amount of information transfer between two oscillating neural populations could be determined by their connection delay and the mismatch in their oscillation frequencies. Our results highlight the role of the collective phase response curve of the oscillating neural populations for the efficacy of signal transmission and the quality of the information transfer in brain networks.

Bridging the gap between single receptor type activity and whole-brain dynamics

What is the effect of activating a single modulatory neuronal receptor type on entire brain network dynamics? Can such effect be isolated at all? These are important questions because characterizing elementary neuronal processes that influence network activity across the given anatomical backbone is fundamental to guide theories of brain function. Here, we introduce the concept of the cortical 'receptome' taking into account the distribution and densities of expression of different modulatory receptor types across the brain's anatomical connectivity matrix. By modelling whole-brain dynamics in silico, we suggest a bidirectional coupling between modulatory neurotransmission and neuronal connectivity hardware exemplified by the impact of single serotonergic (5-HT) receptor types on cortical dynamics. As experimental support of this concept, we show how optogenetic tools enable specific activation of a single 5-HT receptor type across the cortex as well as in vivo measurement of its distinct effects on cortical processing. Altogether, we demonstrate how the structural neuronal connectivity backbone and its modulation by a single neurotransmitter system allow access to a rich repertoire of different brain states that are fundamental for flexible behaviour. We further propose that irregular receptor expression patterns-genetically predisposed or acquired during a lifetime-may predispose for neuropsychiatric disorders like addiction, depression and anxiety along with distinct changes in brain state. Our long-term vision is that such diseases could be treated through rationally targeted therapeutic interventions of high specificity to eventually recover natural transitions of brain states.

Computational Models in Electroencephalography

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by “computational model” is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Frequency-Resolved Functional Connectivity: Role of Delay and the Strength of Connections

The brain functional network extracted from the BOLD signals reveals the correlated activity of the different brain regions, which is hypothesized to underlie the integration of the information across functionally specialized areas. Functional networks are not static and change over time and in different brain states, enabling the nervous system to engage and disengage different local areas in specific tasks on demand. Due to the low temporal resolution, however, BOLD signals do not allow the exploration of spectral properties of the brain dynamics over different frequency bands which are known to be important in cognitive processes. Recent studies using imaging tools with a high temporal resolution has made it possible to explore the correlation between the regions at multiple frequency bands. These studies introduce the frequency as a new dimension over which the functional networks change, enabling brain networks to transmit multiplex of information at any time. In this computational study, we explore the functional connectivity at different frequency ranges and highlight the role of the distance between the nodes in their correlation. We run the generalized Kuramoto model with delayed interactions on top of the brain's connectome and show that how the transmission delay and the strength of the connections, affect the correlation between the pair of nodes over different frequency bands.

Antiphase synchronization in multiplex networks with attractive and repulsive interactions

A series of recent publications, within the framework of network science, have focused on the coexistence of mixed attractive and repulsive (excitatory and inhibitory) interactions among the units within the same system, motivated by the analogies with spin glasses as well as to neural networks, or ecological systems. However, most of these investigations have been restricted to single layer networks, requiring further analysis of the complex dynamics and particular equilibrium states that emerge in multilayer configurations. This article investigates the synchronization properties of dynamical systems connected through multiplex architectures in the presence of attractive intralayer and repulsive interlayer connections. This setting enables the emergence of antisynchronization, i.e., intralayer synchronization coexisting with antiphase dynamics between coupled systems of different layers. We demonstrate the existence of a transition from interlayer antisynchronization to antiphase synchrony in any connected bipartite multiplex architecture when the repulsive coupling is introduced through any spanning tree of a single layer. We identify, analytically, the required graph topologies for interlayer antisynchronization and its interplay with intralayer and antiphase synchronization. Next, we analytically derive the invariance of intralayer synchronization manifold and calculate the attractor size of each oscillator exhibiting interlayer antisynchronization together with intralayer synchronization. The necessary conditions for the existence of interlayer antisynchronization along with intralayer synchronization are given and numerically validated by considering Stuart-Landau oscillators. Finally, we also analytically derive the local stability condition of the interlayer antisynchronization state using the master stability function approach.

Noise-driven multistability vs deterministic chaos in phenomenological semi-empirical models of whole-brain activity

An outstanding open problem in neuroscience is to understand how neural systems are capable of producing and sustaining complex spatiotemporal dynamics. Computational models that combine local dynamics with in vivo measurements of anatomical and functional connectivity can be used to test potential mechanisms underlying this complexity. We compared two conceptually different mechanisms: noise-driven switching between equilibrium solutions (modeled by coupled Stuart-Landau oscillators) and deterministic chaos (modeled by coupled Rossler oscillators). We found that both models struggled to simultaneously reproduce multiple observables computed from the empirical data. This issue was especially manifested in the case of noise-driven dynamics close to a bifurcation, which imposed overly strong constraints on the optimal model parameters. In contrast, the chaotic model could produce complex behavior over a range of parameters, thus being capable of capturing multiple observables at the same time with good performance. Our observations support the view of the brain as a non-equilibrium system able to produce endogenous variability. We presented a simple model capable of jointly reproducing functional connectivity computed at different temporal scales. Besides adding to our conceptual understanding of brain complexity, our results inform and constrain the future development of biophysically realistic large-scale models.

Signal Fluctuations and the Information Transmission Rates in Binary Communication Channels

In the nervous system, information is conveyed by sequence of action potentials, called spikes-trains. As MacKay and McCulloch suggested, spike-trains can be represented as bits sequences coming from Information Sources (IS). Previously, we studied relations between spikes’ Information Transmission Rates (ITR) and their correlations, and frequencies. Now, I concentrate on the problem of how spikes fluctuations affect ITR. The IS are typically modeled as stationary stochastic processes, which I consider here as two-state Markov processes. As a spike-trains’ fluctuation measure, I assume the standard deviation σ, which measures the average fluctuation of spikes around the average spike frequency. I found that the character of ITR and signal fluctuations relation strongly depends on the parameter s being a sum of transitions probabilities from a no spike state to spike state. The estimate of the Information Transmission Rate was found by expressions depending on the values of signal fluctuations and parameter s. It turned out that for smaller s<1, the quotient ITRσ has a maximum and can tend to zero depending on transition probabilities, while for 1<s, the ITRσ is separated from 0. Additionally, it was also shown that ITR quotient by variance behaves in a completely different way. Similar behavior was observed when classical Shannon entropy terms in the Markov entropy formula are replaced by their approximation with polynomials. My results suggest that in a noisier environment (1<s), to get appropriate reliability and efficiency of transmission, IS with higher tendency of transition from the no spike to spike state should be applied. Such selection of appropriate parameters plays an important role in designing learning mechanisms to obtain networks with higher performance.

Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome

Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed "connectome harmonics", have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed graph neural fields, in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for Connectome-Harmonic Analysis Of Spatiotemporal Spectra). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.

A Connectome-Based, Corticothalamic Model of State- and Stimulation-Dependent Modulation of Rhythmic Neural Activity and Connectivity

Rhythmic activity in the brain fluctuates with behaviour and cognitive state, through a combination of coexisting and interacting frequencies. At large spatial scales such as those studied in human M/EEG, measured oscillatory dynamics are believed to arise primarily from a combination of cortical (intracolumnar) and corticothalamic rhythmogenic mechanisms. Whilst considerable progress has been made in characterizing these two types of neural circuit separately, relatively little work has been done that attempts to unify them into a single consistent picture. This is the aim of the present paper. We present and examine a whole-brain, connectome-based neural mass model with detailed long-range cortico-cortical connectivity and strong, recurrent corticothalamic circuitry. This system reproduces a variety of known features of human M/EEG recordings, including spectral peaks at canonical frequencies, and functional connectivity structure that is shaped by the underlying anatomical connectivity. Importantly, our model is able to capture state- (e.g., idling/active) dependent fluctuations in oscillatory activity and the coexistence of multiple oscillatory phenomena, as well as frequency-specific modulation of functional connectivity. We find that increasing the level of sensory drive to the thalamus triggers a suppression of the dominant low frequency rhythms generated by corticothalamic loops, and subsequent disinhibition of higher frequency endogenous rhythmic behaviour of intracolumnar microcircuits. These combine to yield simultaneous decreases in lower frequency and increases in higher frequency components of the M/EEG power spectrum during states of high sensory or cognitive drive. Building on this, we also explored the effect of pulsatile brain stimulation on ongoing oscillatory activity, and evaluated the impact of coexistent frequencies and state-dependent fluctuations on the response of cortical networks. Our results provide new insight into the role played by cortical and corticothalamic circuits in shaping intrinsic brain rhythms, and suggest new directions for brain stimulation therapies aimed at state-and frequency-specific control of oscillatory brain activity.

Signal diffusion along connectome gradients and inter-hub routing differentially contribute to dynamic human brain function

Human cognition is dynamic, alternating over time between externally-focused states and more abstract, often self-generated, patterns of thought. Although cognitive neuroscience has documented how networks anchor particular modes of brain function, mechanisms that describe transitions between distinct functional states remain poorly understood. Here, we examined how time-varying changes in brain function emerge within the constraints imposed by macroscale structural network organization. Studying a large cohort of healthy adults (n = 326), we capitalized on manifold learning techniques that identify low dimensional representations of structural connectome organization and we decomposed neurophysiological activity into distinct functional states and their transition patterns using Hidden Markov Models. Structural connectome organization predicted dynamic transitions anchored in sensorimotor systems and those between sensorimotor and transmodal states. Connectome topology analyses revealed that transitions involving sensorimotor states traversed short and intermediary distances and adhered strongly to communication mechanisms of network diffusion. Conversely, transitions between transmodal states involved spatially distributed hubs and increasingly engaged long-range routing. These findings establish that the structure of the cortex is optimized to allow neural states the freedom to vary between distinct modes of processing, and so provides a key insight into the neural mechanisms that give rise to the flexibility of human cognition.

Influence of Delayed Conductance on Neuronal Synchronization

In the brain, the excitation-inhibition balance prevents abnormal synchronous behavior. However, known synaptic conductance intensity can be insufficient to account for the undesired synchronization. Due to this fact, we consider time delay in excitatory and inhibitory conductances and study its effect on the neuronal synchronization. In this work, we build a neuronal network composed of adaptive integrate-and-fire neurons coupled by means of delayed conductances. We observe that the time delay in the excitatory and inhibitory conductivities can alter both the state of the collective behavior (synchronous or desynchronous) and its type (spike or burst). For the weak coupling regime, we find that synchronization appears associated with neurons behaving with extremes highest and lowest mean firing frequency, in contrast to when desynchronization is present when neurons do not exhibit extreme values for the firing frequency. Synchronization can also be characterized by neurons presenting either the highest or the lowest levels in the mean synaptic current. For the strong coupling, synchronous burst activities can occur for delays in the inhibitory conductivity. For approximately equal-length delays in the excitatory and inhibitory conductances, desynchronous spikes activities are identified for both weak and strong coupling regimes. Therefore, our results show that not only the conductance intensity, but also short delays in the inhibitory conductance are relevant to avoid abnormal neuronal synchronization.

Development of Dynamic Functional Architecture during Early Infancy

Uncovering the moment-to-moment dynamics of functional connectivity (FC) in the human brain during early development is crucial for understanding emerging complex cognitive functions and behaviors. To this end, this paper leveraged a longitudinal resting-state functional magnetic resonance imaging dataset from 51 typically developing infants and, for the first time, thoroughly investigated how the temporal variability of the FC architecture develops at the "global" (entire brain), "mesoscale" (functional system), and "local" (brain region) levels in the first 2 years of age. Our results revealed that, in such a pivotal stage, 1) the whole-brain FC dynamic is linearly increased; 2) the high-order functional systems tend to display increased FC dynamics for both within- and between-network connections, while the primary systems show the opposite trajectories; and 3) many frontal regions have increasing FC dynamics despite large heterogeneity in developmental trajectories and velocities. All these findings indicate that the brain is gradually reconfigured toward a more flexible, dynamic, and adaptive system with globally increasing but locally heterogeneous trajectories in the first 2 postnatal years, explaining why infants have rapidly developing high-order cognitive functions and complex behaviors.

Neuronal Oscillations on Evolving Networks: Dynamics, Damage, Degradation, Decline, Dementia, and Death

Neurodegenerative diseases, such as Alzheimer's or Parkinson's disease, show characteristic degradation of structural brain networks. This degradation eventually leads to changes in the network dynamics and degradation of cognitive functions. Here, we model the progression in terms of coupled physical processes: The accumulation of toxic proteins, given by a nonlinear reaction-diffusion transport process, yields an evolving brain connectome characterized by weighted edges on which a neuronal-mass model evolves. The progression of the brain functions can be tested by simulating the resting-state activity on the evolving brain network. We show that while the evolution of edge weights plays a minor role in the overall progression of the disease, dynamic biomarkers predict a transition over a period of 10 years associated with strong cognitive decline.

Relations between large-scale brain connectivity and effects of regional stimulation depend on collective dynamical state

At the macroscale, the brain operates as a network of interconnected neuronal populations, which display coordinated rhythmic dynamics that support interareal communication. Understanding how stimulation of different brain areas impacts such activity is important for gaining basic insights into brain function and for further developing therapeutic neurmodulation. However, the complexity of brain structure and dynamics hinders predictions regarding the downstream effects of focal stimulation. More specifically, little is known about how the collective oscillatory regime of brain network activity—in concert with network structure—affects the outcomes of perturbations. Here, we combine human connectome data and biophysical modeling to begin filling these gaps. By tuning parameters that control collective system dynamics, we identify distinct states of simulated brain activity and investigate how the distributed effects of stimulation manifest at different dynamical working points. When baseline oscillations are weak, the stimulated area exhibits enhanced power and frequency, and due to network interactions, activity in this excited frequency band propagates to nearby regions. Notably, beyond these linear effects, we further find that focal stimulation causes more distributed modifications to interareal coherence in a band containing regions’ baseline oscillation frequencies. Importantly, depending on the dynamical state of the system, these broadband effects can be better predicted by functional rather than structural connectivity, emphasizing a complex interplay between anatomical organization, dynamics, and response to perturbation. In contrast, when the network operates in a regime of strong regional oscillations, stimulation causes only slight shifts in power and frequency, and structural connectivity becomes most predictive of stimulation-induced changes in network activity patterns. In sum, this work builds upon and extends previous computational studies investigating the impacts of stimulation, and underscores the fact that both the stimulation site, and, crucially, the regime of brain network dynamics, can influence the network-wide responses to local perturbations.

Stimulation can be used to alter brain activity and is a therapeutic option for certain neurological conditions. However, predicting the distributed effects of local perturbations is difficult. Previous studies show that responses to stimulation depend on anatomical (or structural) coupling. In addition to structure, here we consider how stimulation effects also depend on the brain’s collective dynamical (or functional) state, arising from the coordination of rhythmic activity across large-scale networks. In a whole-brain computational model, we show that global responses to regional stimulation can indeed be contingent upon and differ across various dynamical working points. Notably, depending on the network’s oscillatory regime, stimulation can accelerate the activity of the stimulated site, and lead to widespread effects at both the new, excited frequency, as well as in a much broader frequency range including areas’ baseline frequencies. While structural connectivity is a good predictor of “excited band” changes, in some states “baseline band” effects can be better predicted by functional connectivity, which depends upon the system’s oscillatory regime. By integrating and extending past efforts, our results thus indicate that dynamical—in additional to structural—brain organization plays a role in governing how focal stimulation modulates interactions between distributed network elements.

The effects of Alzheimer's disease related striatal pathologic changes on the fractional amplitude of low-frequency fluctuations

This paper aims to correlate Alzheimer's disease (AD) related striatal pathologic changes with the fractional amplitude of low-frequency fluctuations (fALLF) in the blood oxygenation level-dependent (BOLD) signal in the resting state functional Magnetic Resonance Imaging (rs-fMRI). A dopamine modulated Izikhevich neuron model based network of striatum region is constructed. Balloon-Windkessel hemodynamic model is used to obtain BOLD signals. fALFF differences between two frequency bands (slow-5:0.01-0.027 Hz; slow-4:0.027-0.073 Hz) are investigated in the case of dopamine depletion, decrease in the synaptic connectivity and the input from cortical and thalamic region, assumed that they are the degenerations occurring in AD.

Non-invasive inference of information flow using diffusion MRI, functional MRI, and MEG

OBJECTIVE

To infer information flow in the white matter of the brain and recover cortical activity using functional MRI, diffusion MRI, and MEG without a manual selection of the white matter connections of interest.

APPROACH

A Bayesian network which encodes the priors knowledge of possible brain states is built from imaging data. Diffusion MRI is used to enumerate all possible connections between cortical regions. Functional MRI is used to prune connections without manual intervention and increase the likelihood of specific regions being active. MEG data is used as evidence into this network to obtain a posterior distribution on cortical regions and connections.

MAIN RESULTS

We show that our proposed method is able to identify connections associated with the a sensory-motor task. This allows us to build the Bayesian network with no manual selection of connections of interest. Using sensory-motor MEG evoked response as evidence into this network, our method identified areas known to be involved in a visuomotor task. In addition, information flow along white matter fiber bundles connecting those regions was also recovered.

SIGNIFICANCE

Current methods to estimate white matter information flow are extremely invasive, therefore limiting our understanding of the interaction between cortical regions. The proposed method makes use of functional MRI, diffusion MRI, and M/EEG to infer communication between cortical regions, therefore opening the door to the non-invasive exploration of information flow in the white matter.

Experimental and Computational Study on Motor Control and Recovery After Stroke: Toward a Constructive Loop Between Experimental and Virtual Embodied Neuroscience

Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.

Multi-timescale hybrid components of the functional brain connectome: A bimodal EEG-fMRI decomposition

Concurrent electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) bridge brain connectivity across timescales. During concurrent EEG-fMRI resting-state recordings, whole-brain functional connectivity (FC) strength is spatially correlated across modalities. However, cross-modal investigations have commonly remained correlational, and joint analysis of EEG-fMRI connectivity is largely unexplored. Here we investigated if there exist (spatially) independent FC networks linked between modalities. We applied the recently proposed hybrid connectivity independent component analysis (connICA) framework to two concurrent EEG-fMRI resting-state datasets (total 40 subjects). Two robust components were found across both datasets. The first component has a uniformly distributed EEG frequency fingerprint linked mainly to intrinsic connectivity networks (ICNs) in both modalities. Conversely, the second component is sensitive to different EEG frequencies and is primarily linked to intra-ICN connectivity in fMRI but to inter-ICN connectivity in EEG. The first hybrid component suggests that connectivity dynamics within well-known ICNs span timescales, from millisecond range in all canonical frequencies of FC_EEG to second range of FC_fMRI. Conversely, the second component additionally exposes linked but spatially divergent neuronal processing at the two timescales. This work reveals the existence of joint spatially independent components, suggesting that parts of resting-state connectivity are co-expressed in a linked manner across EEG and fMRI over individuals.

Functional connectivity is governed by a whole-brain organization measurable over multiple timescales by functional magnetic resonance imaging (fMRI) and electroencephalography (EEG). The relationship across the whole-brain organization captured at the different timescales of EEG and fMRI is largely unknown. Using concurrent EEG-fMRI, we identified spatially independent components consisting of brain connectivity patterns that co-occur in EEG and fMRI over subjects. We observed a component with similar connectivity organization across EEG and fMRI as well as a component with divergent connectivity. The former component governed all EEG frequencies while the latter was modulated by frequency. These findings show that part of functional connectivity organizes in a common spatial layout over several timescales, while a spatially independent part is modulated by frequency-specific information.

Activity-dependent myelination: A glial mechanism of oscillatory self-organization in large-scale brain networks

Communication and oscillatory synchrony between distributed neural populations are believed to play a key role in multiple cognitive and neural functions. These interactions are mediated by long-range myelinated axonal fiber bundles, collectively termed as white matter. While traditionally considered to be static after development, white matter properties have been shown to change in an activity-dependent way through learning and behavior-a phenomenon known as white matter plasticity. In the central nervous system, this plasticity stems from oligodendroglia, which form myelin sheaths to regulate the conduction of nerve impulses across the brain, hence critically impacting neural communication. We here shift the focus from neural to glial contribution to brain synchronization and examine the impact of adaptive, activity-dependent changes in conduction velocity on the large-scale phase synchronization of neural oscillators. Using a network model based on primate large-scale white matter neuroanatomy, our computational and mathematical results show that such plasticity endows white matter with self-organizing properties, where conduction delay statistics are autonomously adjusted to ensure efficient neural communication. Our analysis shows that this mechanism stabilizes oscillatory neural activity across a wide range of connectivity gain and frequency bands, making phase-locked states more resilient to damage as reflected by diffuse decreases in connectivity. Critically, our work suggests that adaptive myelination may be a mechanism that enables brain networks with a means of temporal self-organization, resilience, and homeostasis.

Dimensional reduction of emergent spatiotemporal cortical dynamics via a maximum entropy moment closure

Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.

Mechanisms of competitive selection: A canonical neural circuit framework

Competitive selection, the transformation of multiple competing sensory inputs and internal states into a unitary choice, is a fundamental component of animal behavior. Selection behaviors have been studied under several intersecting umbrellas including decision-making, action selection, perceptual categorization, and attentional selection. Neural correlates of these behaviors and computational models have been investigated extensively. However, specific, identifiable neural circuit mechanisms underlying the implementation of selection remain elusive. Here, we employ a first principles approach to map competitive selection explicitly onto neural circuit elements. We decompose selection into six computational primitives, identify demands that their execution places on neural circuit design, and propose a canonical neural circuit framework. The resulting framework has several links to neural literature, indicating its biological feasibility, and has several common elements with prominent computational models, suggesting its generality. We propose that this framework can help catalyze experimental discovery of the neural circuit underpinnings of competitive selection.

Emergent Spaces for Coupled Oscillators

Systems of coupled dynamical units (e.g., oscillators or neurons) are known to exhibit complex, emergent behaviors that may be simplified through coarse-graining: a process in which one discovers coarse variables and derives equations for their evolution. Such coarse-graining procedures often require extensive experience and/or a deep understanding of the system dynamics. In this paper we present a systematic, data-driven approach to discovering “bespoke” coarse variables based on manifold learning algorithms. We illustrate this methodology with the classic Kuramoto phase oscillator model, and demonstrate how our manifold learning technique can successfully identify a coarse variable that is one-to-one with the established Kuramoto order parameter. We then introduce an extension of our coarse-graining methodology which enables us to learn evolution equations for the discovered coarse variables via an artificial neural network architecture templated on numerical time integrators (initial value solvers). This approach allows us to learn accurate approximations of time derivatives of state variables from sparse flow data, and hence discover useful approximate differential equation descriptions of their dynamic behavior. We demonstrate this capability by learning ODEs that agree with the known analytical expression for the Kuramoto order parameter dynamics at the continuum limit. We then show how this approach can also be used to learn the dynamics of coarse variables discovered through our manifold learning methodology. In both of these examples, we compare the results of our neural network based method to typical finite differences complemented with geometric harmonics. Finally, we present a series of computational examples illustrating how a variation of our manifold learning methodology can be used to discover sets of “effective” parameters, reduced parameter combinations, for multi-parameter models with complex coupling. We conclude with a discussion of possible extensions of this approach, including the possibility of obtaining data-driven effective partial differential equations for coarse-grained neuronal network behavior, as illustrated by the synchronization dynamics of Hodgkin–Huxley type neurons with a Chung-Lu network. Thus, we build an integrated suite of tools for obtaining data-driven coarse variables, data-driven effective parameters, and data-driven coarse-grained equations from detailed observations of networks of oscillators.

The Bayesian Virtual Epileptic Patient: A probabilistic framework designed to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread

Despite the importance and frequent use of Bayesian frameworks in brain network modeling for parameter inference and model prediction, the advanced sampling algorithms implemented in probabilistic programming languages to overcome the inference difficulties have received relatively little attention in this context. In this technical note, we propose a probabilistic framework, namely the Bayesian Virtual Epileptic Patient (BVEP), which relies on the fusion of structural data of individuals to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread. To invert the individualized whole-brain model employed in this study, we use the recently developed algorithms known as No-U-Turn Sampler (NUTS) as well as Automatic Differentiation Variational Inference (ADVI). Our results indicate that NUTS and ADVI accurately estimate the degree of epileptogenicity of brain regions, therefore, the hypothetical brain areas responsible for the seizure initiation and propagation, while the convergence diagnostics and posterior behavior analysis validate the reliability of the estimations. Moreover, we illustrate the efficiency of the transformed non-centered parameters in comparison to centered form of parameterization. The Bayesian framework used in this work proposes an appropriate patient-specific strategy for estimating the epileptogenicity of the brain regions to improve outcome after epilepsy surgery.

Brain network constraints and recurrent neural networks reproduce unique trajectories and state transitions seen over the span of minutes in resting-state fMRI

Large-scale patterns of spontaneous whole-brain activity seen in resting-state functional magnetic resonance imaging (rs-fMRI) are in part believed to arise from neural populations interacting through the structural network (Honey, Kötter, Breakspear, & Sporns, 2007). Generative models that simulate this network activity, called brain network models (BNM), are able to reproduce global averaged properties of empirical rs-fMRI activity such as functional connectivity (FC) but perform poorly in reproducing unique trajectories and state transitions that are observed over the span of minutes in whole-brain data (Cabral, Kringelbach, & Deco, 2017; Kashyap & Keilholz, 2019). The manuscript demonstrates that by using recurrent neural networks, it can fit the BNM in a novel way to the rs-fMRI data and predict large amounts of variance between subsequent measures of rs-fMRI data. Simulated data also contain unique repeating trajectories observed in rs-fMRI, called quasiperiodic patterns (QPP), that span 20 s and complex state transitions observed using k-means analysis on windowed FC matrices (Allen et al., 2012; Majeed et al., 2011). Our approach is able to estimate the manifold of rs-fMRI dynamics by training on generating subsequent time points, and it can simulate complex resting-state trajectories better than the traditional generative approaches.

Brain network models have become a promising theoretical framework for simulating signals that are representative of whole-brain activity such as resting-state fMRI. However, it has been difficult to compare the complex brain activity obtained from simulations with empirical data. Previous studies have used simple metrics to characterize coordination between regions such as functional connectivity. In this manuscript, we extend this work by utilizing modern machine learning techniques to fit the brain network models to observed data and train on the mismatch between the model and observed signal. Our results show that our system training on these new metrics generalizes to a system that is able to reproduce trajectories and complex state transitions seen in rs-fMRI over the span of minutes. Our results will be useful in constraining and developing more realistic simulations of whole-brain activity.

Smooth interpolation of covariance matrices and brain network estimation: Part II

This work focuses on the modeling of time-varying covariance matrices using the state covariance of linear systems. Following concepts from optimal mass transport, we investigate and compare three types of covariance paths which are solutions to different optimal control problems. One of the covariance paths solves the Schrödinger bridge problem (SBP). The other two types of covariance paths are based on generalizations of the Fisher-Rao metric in information geometry, which are the major contributions of this work. The general framework is an extension of the approach in [1] which focuses on linear systems without stochastic input. The performances of the three covariance paths are compared using synthetic data and a real-data example on the estimation of dynamic brain networks using functional magnetic resonance imaging.

The role of node dynamics in shaping emergent functional connectivity patterns in the brain

The contribution of structural connectivity to functional brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure–function issue, treating a system of Jansen–Rit neural mass nodes with heterogeneous structural connections estimated from diffusion MRI data provided by the Human Connectome Project. Via direct simulations we determine the similarity of functional (inferred from correlated activity between nodes) and structural connectivity matrices under variation of the parameters controlling single-node dynamics, highlighting a nontrivial structure–function relationship in regimes that support limit cycle oscillations. To determine their relationship, we firstly calculate network instabilities giving rise to oscillations, and the so-called ‘false bifurcations’ (for which a significant qualitative change in the orbit is observed, without a change of stability) occurring beyond this onset. We highlight that functional connectivity (FC) is inherited robustly from structure when node dynamics are poised near a Hopf bifurcation, whilst near false bifurcations, and structure only weakly influences FC. Secondly, we develop a weakly coupled oscillator description to analyse oscillatory phase-locked states and, furthermore, show how the modular structure of FC matrices can be predicted via linear stability analysis. This study thereby emphasises the substantial role that local dynamics can have in shaping large-scale functional brain states.

Patterns of oscillation across the brain arise because of structural connections between brain regions. However, the type of oscillation at a site may also play a contributory role. We focus on an idealised model of a neural mass network, coupled using estimates of structural connections obtained via tractography on Human Connectome Project MRI data. Using a mixture of computational and mathematical techniques, we show that functional connectivity is inherited most strongly from structural connectivity when the network nodes are poised at a Hopf bifurcation. However, beyond the onset of this oscillatory instability a phase-locked network state can undergo a false bifurcation, and structural connectivity only weakly influences functional connectivity. This highlights the important effect that local dynamics can have on large-scale brain states.

Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches

Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. ​Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks.

Ghost Attractors in Spontaneous Brain Activity: Recurrent Excursions Into Functionally-Relevant BOLD Phase-Locking States

Functionally relevant network patterns form transiently in brain activity during rest, where a given subset of brain areas exhibits temporally synchronized BOLD signals. To adequately assess the biophysical mechanisms governing intrinsic brain activity, a detailed characterization of the dynamical features of functional networks is needed from the experimental side to constrain theoretical models. In this work, we use an open-source fMRI dataset from 100 healthy participants from the Human Connectome Project and analyze whole-brain activity using Leading Eigenvector Dynamics Analysis (LEiDA), which serves to characterize brain activity at each time point by its whole-brain BOLD phase-locking pattern. Clustering these BOLD phase-locking patterns into a set of k states, we demonstrate that the cluster centroids closely overlap with reference functional subsystems. Borrowing tools from dynamical systems theory, we characterize spontaneous brain activity in the form of trajectories within the state space, calculating the Fractional Occupancy and the Dwell Times of each state, as well as the Transition Probabilities between states. Finally, we demonstrate that within-subject reliability is maximized when including the high frequency components of the BOLD signal (>0.1 Hz), indicating the existence of individual fingerprints in dynamical patterns evolving at least as fast as the temporal resolution of acquisition (here TR = 0.72 s). Our results reinforce the mechanistic scenario that resting-state networks are the expression of erratic excursions from a baseline synchronous steady state into weakly-stable partially-synchronized states - which we term ghost attractors. To better understand the rules governing the transitions between ghost attractors, we use methods from dynamical systems theory, giving insights into high-order mechanisms underlying brain function.

Decoding Task-Specific Cognitive States with Slow, Directed Functional Networks in the Human Brain

Flexible functional interactions among brain regions mediate critical cognitive functions. Such interactions can be measured using functional magnetic resonance imaging (fMRI) data either with instantaneous (zero-lag) or lag-based (time-lagged) functional connectivity. Because the fMRI hemodynamic response is slow, and is sampled at a timescale (seconds) several orders of magnitude slower than the underlying neural dynamics (milliseconds), simulation studies have shown that lag-based fMRI functional connectivity, measured with approaches like Granger–Geweke causality (GC), provides spurious and unreliable estimates of underlying neural interactions. Experimental verification of this claim is challenging because neural ground truth connectivity is often unavailable concurrently with fMRI recordings. Here we demonstrate that, despite these widely held caveats, GC networks estimated from fMRI recordings contain useful information for classifying task-specific cognitive states. We estimated instantaneous and lag-based GC functional connectivity networks using fMRI data from 1000 participants (Human Connectome Project database). A linear classifier, trained on either instantaneous or lag-based GC, reliably discriminated among seven different task and resting brain states, with >80% cross-validation accuracy. With network simulations, we demonstrate that instantaneous and lag-based GC exploited interactions at fast and slow timescales, respectively, to achieve robust classification. With human fMRI data, instantaneous and lag-based GC identified complementary, task–core networks. Finally, variations in GC connectivity explained inter-individual variations in a variety of cognitive scores. Our findings show that instantaneous and lag-based methods reveal complementary aspects of functional connectivity in the brain, and suggest that slow, directed functional interactions, estimated with fMRI, may provide useful markers of behaviorally relevant cognitive states.

Electrocortical dynamics differentiate athletes exhibiting low- and high- ACL injury risk biomechanics

Anterior cruciate ligament (ACL) injuries are physically and emotionally debilitating for athletes,while motor and biomechanical deficits that contribute to ACL injury have been identified, limited knowledge about the relationship between the central nervous system (CNS) and biomechanical patterns of motion has impeded approaches to optimize ACL injury risk reduction strategies. In the current study it was hypothesized that high-risk athletes would exhibit altered temporal dynamics in their resting state electrocortical activity when compared to low-risk athletes. Thirty-eight female athletes performed a drop vertical jump (DVJ) to assess their biomechanical risk factors related to an ACL injury. The athletes' electrocortical activity was also recorded during resting state in the same visit as the DVJ assessment. Athletes were divided into low- and high-risk groups based on their performance of the DVJ. Recurrence quantification analysis was used to quantify the temporal dynamics of two frequency bands previously shown to relate to sensorimotor and attentional control. Results revealed that high-risk participants showed more deterministic electrocortical behavior than the low-risk group in the frontal theta and central/parietal alpha-2 frequency bands. The more deterministic resting state electrocortical dynamics for the high-risk group may reflect maladaptive neural behavior-excessively stable deterministic patterning that makes transitioning among functional task-specific networks more difficult-related to attentional control and sensorimotor processing neural regions.

Linking Structure and Function in Macroscale Brain Networks

Structure-function relationships are a fundamental principle of many naturally occurring systems. However, network neuroscience research suggests that there is an imperfect link between structural connectivity and functional connectivity in the brain. Here, we synthesize the current state of knowledge linking structure and function in macroscale brain networks and discuss the different types of models used to assess this relationship. We argue that current models do not include the requisite biological detail to completely predict function. Structural network reconstructions enriched with local molecular and cellular metadata, in concert with more nuanced representations of functions and properties, hold great potential for a truly multiscale understanding of the structure-function relationship.

Delayed correlations improve the reconstruction of the brain connectome

The brain works as a large-scale complex network, known as the connectome. The strength of the connections between two brain regions in the connectome is commonly estimated by calculating the correlations between their patterns of activation. This approach relies on the assumption that the activation of connected regions occurs together and at the same time. However, there are delays between the activation of connected regions due to excitatory and inhibitory connections. Here, we propose a method to harvest this additional information and reconstruct the structural brain connectome using delayed correlations. This delayed-correlation method correctly identifies 70% to 80% of connections of simulated brain networks, compared to only 5% to 25% of connections detected by the standard methods; this result is robust against changes in the network parameters (small-worldness, excitatory vs. inhibitory connection ratio, weight distribution) and network activation dynamics. The delayed-correlation method predicts more accurately both the global network properties (characteristic path length, global efficiency, clustering coefficient, transitivity) and the nodal network properties (nodal degree, nodal clustering, nodal global efficiency), particularly at lower network densities. We obtain similar results in networks derived from animal and human data. These results suggest that the use of delayed correlations improves the reconstruction of the structural brain connectome and open new possibilities for the analysis of the brain connectome, as well as for other types of networks.

Intrinsic connectome organization across temporal scales: New insights from cross-modal approaches

The discovery of a stable, whole-brain functional connectivity organization that is largely independent of external events has drastically extended our view of human brain function. However, this discovery has been primarily based on functional magnetic resonance imaging (fMRI). The role of this whole-brain organization in fast oscillation-based connectivity as measured, for example, by electroencephalography (EEG) and magnetoencephalography (MEG) is only beginning to emerge. Here, we review studies of intrinsic connectivity and its whole-brain organization in EEG, MEG, and intracranial electrophysiology with a particular focus on direct comparisons to connectome studies in fMRI. Synthesizing this literature, we conclude that irrespective of temporal scale over four orders of magnitude, intrinsic neurophysiological connectivity shows spatial similarity to the connectivity organization commonly observed in fMRI. A shared structural connectivity basis and cross-frequency coupling are possible mechanisms contributing to this similarity. Acknowledging that a stable whole-brain organization governs long-range coupling across all timescales of neural processing motivates researchers to take "baseline" intrinsic connectivity into account when investigating brain-behavior associations, and further encourages more widespread exploration of functional connectomics approaches beyond fMRI by using EEG and MEG modalities.

Electrophysiological dynamics of antagonistic brain networks reflect attentional fluctuations

Neuroimaging evidence suggests that the default mode network (DMN) exhibits antagonistic activity with dorsal attention (DAN) and salience (SN) networks. Here we use human intracranial electroencephalography to investigate the behavioral relevance of fine-grained dynamics within and between these networks. The three networks show dissociable profiles of task-evoked electrophysiological activity, best captured in the high-frequency broadband (HFB; 70-170 Hz) range. On the order of hundreds of milliseconds, HFB responses peak fastest in the DAN, at intermediate speed in the SN, and slowest in the DMN. Lapses of attention (behavioral errors) are marked by distinguishable patterns of both pre- and post-stimulus HFB activity within each network. Moreover, the magnitude of temporally lagged, negative HFB coupling between the DAN and DMN (but not SN and DMN) is associated with greater sustained attention performance and is reduced during wakeful rest. These findings underscore the behavioral relevance of temporally delayed coordination between antagonistic brain networks.