On the intersection between data quality and dynamical modelling of large-scale fMRI signals.

Large-scale dynamics of the brain are routinely modelled using systems of nonlinear dynamical equations that describe the evolution of population-level activity, with distinct neural populations often coupled according to an empirically measured structural connectivity matrix. This modelling approach has been used to generate insights into the neural underpinnings of spontaneous brain dynamics, as recorded with techniques such as resting state functional MRI (fMRI). In fMRI, researchers have many degrees of freedom in the way that they can process the data and recent evidence indicates that the choice of pre-processing steps can have a major effect on empirical estimates of functional connectivity. However, the potential influence of such variations on modelling results are seldom considered. Here we show, using three popular whole-brain dynamical models, that different choices during fMRI preprocessing can dramatically affect model fits and interpretations of findings. Critically, we show that the ability of these models to accurately capture patterns in fMRI dynamics is mostly driven by the degree to which they fit global signals rather than interesting sources of coordinated neural dynamics. We show that widespread deflections can arise from simple global synchronisation. We introduce a simple two-parameter model that captures these fluctuations and performs just as well as more complex, multi-parameter biophysical models. From our combined analyses of data and simulations, we describe benchmarks to evaluate model fit and validity. Although most models are not resilient to denoising, we show that relaxing the approximation of homogeneous neural populations by more explicitly modelling inter-regional effective connectivity can improve model accuracy at the expense of increased model complexity. Our results suggest that many complex biophysical models may be fitting relatively trivial properties of the data, and underscore a need for tighter integration between data quality assurance and model development.

Stochastic synchronization of dynamics on the human connectome.

Synchronization is a collective mechanism by which oscillatory networks achieve their functions. Factors driving synchronization include the network's topological and dynamical properties. However, how these factors drive the emergence of synchronization in the presence of potentially disruptive external inputs like stochastic perturbations is not well understood, particularly for real-world systems such as the human brain. Here, we aim to systematically address this problem using a large-scale model of the human brain network (i.e., the human connectome). The results show that the model can produce complex synchronization patterns transitioning between incoherent and coherent states. When nodes in the network are coupled at some critical strength, a counterintuitive phenomenon emerges where the addition of noise increases the synchronization of global and local dynamics, with structural hub nodes benefiting the most. This stochastic synchronization effect is found to be driven by the intrinsic hierarchy of neural timescales of the brain and the heterogeneous complex topology of the connectome. Moreover, the effect coincides with clustering of node phases and node frequencies and strengthening of the functional connectivity of some of the connectome's subnetworks. Overall, the work provides broad theoretical insights into the emergence and mechanisms of stochastic synchronization, highlighting its putative contribution in achieving network integration underpinning brain function.

Mapping how local perturbations influence systems-level brain dynamics.

The human brain exhibits a distinct spatiotemporal organization that supports brain function and can be manipulated via local brain stimulation. Such perturbations to local cortical dynamics are globally integrated by distinct neural systems. However, it remains unclear how local changes in neural activity affect large-scale system dynamics. Here, we briefly review empirical and computational studies addressing how localized perturbations affect brain activity. We then systematically analyze a model of large-scale brain dynamics, assessing how localized changes in brain activity at the different sites affect whole-brain dynamics. We find that local stimulation induces changes in brain activity that can be summarized by relatively smooth tuning curves, which relate a region's effectiveness as a stimulation site to its position within the cortical hierarchy. Our results also support the notion that brain hubs, operating in a slower regime, are more resilient to focal perturbations and critically contribute to maintain stability in global brain dynamics. In contrast, perturbations of peripheral regions, characterized by faster activity, have greater impact on functional connectivity. As a parallel with this region-level result, we also find that peripheral systems such as the visual and sensorimotor networks were more affected by local perturbations than high-level systems such as the cingulo-opercular network. Our findings highlight the importance of a periphery-to-core hierarchy to determine the effect of local stimulation on the brain network. This study also provides novel resources to orient empirical work aiming at manipulating functional connectivity using non-invasive brain stimulation.

Neural decoding of visual stimuli varies with fluctuations in global network efficiency.

Functional magnetic resonance imaging (fMRI) studies have shown that neural activity fluctuates spontaneously between different states of global synchronization over a timescale of several seconds. Such fluctuations generate transient states of high and low correlation across distributed cortical areas. It has been hypothesized that such fluctuations in global efficiency might alter patterns of activity in local neuronal populations elicited by changes in incoming sensory stimuli. To test this prediction, we used a linear decoder to discriminate patterns of neural activity elicited by face and motion stimuli presented periodically while participants underwent time-resolved fMRI. As predicted, decoding was reliably higher during states of high global efficiency than during states of low efficiency, and this difference was evident across both visual and nonvisual cortical regions. The results indicate that slow fluctuations in global network efficiency are associated with variations in the pattern of activity across widespread cortical regions responsible for representing distinct categories of visual stimulus. More broadly, the findings highlight the importance of understanding the impact of global fluctuations in functional connectivity on specialized, stimulus driven neural processes. Hum Brain Mapp 38:3069-3080, 2017. © 2017 Wiley Periodicals, Inc.

Time-resolved resting-state brain networks.

Neuronal dynamics display a complex spatiotemporal structure involving the precise, context-dependent coordination of activation patterns across a large number of spatially distributed regions. Functional magnetic resonance imaging (fMRI) has played a central role in demonstrating the nontrivial spatial and topological structure of these interactions, but thus far has been limited in its capacity to study their temporal evolution. Here, using high-resolution resting-state fMRI data obtained from the Human Connectome Project, we mapped time-resolved functional connectivity across the entire brain at a subsecond resolution with the aim of understanding how nonstationary fluctuations in pairwise interactions between regions relate to large-scale topological properties of the human brain. We report evidence for a consistent set of functional connections that show pronounced fluctuations in their strength over time. The most dynamic connections are intermodular, linking elements from topologically separable subsystems, and localize to known hubs of default mode and fronto-parietal systems. We found that spatially distributed regions spontaneously increased, for brief intervals, the efficiency with which they can transfer information, producing temporary, globally efficient network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time, possibly achieving a balance between efficient information-processing and metabolic expenditure.

Connectome sensitivity or specificity: which is more important?

Connectomes with high sensitivity and high specificity are unattainable with current axonal fiber reconstruction methods, particularly at the macro-scale afforded by magnetic resonance imaging. Tensor-guided deterministic tractography yields sparse connectomes that are incomplete and contain false negatives (FNs), whereas probabilistic methods steered by crossing-fiber models yield dense connectomes, often with low specificity due to false positives (FPs). Densely reconstructed probabilistic connectomes are typically thresholded to improve specificity at the cost of a reduction in sensitivity. What is the optimal tradeoff between connectome sensitivity and specificity? We show empirically and theoretically that specificity is paramount. Our evaluations of the impact of FPs and FNs on empirical connectomes indicate that specificity is at least twice as important as sensitivity when estimating key properties of brain networks, including topological measures of network clustering, network efficiency and network modularity. Our asymptotic analysis of small-world networks with idealized modular structure reveals that as the number of nodes grows, specificity becomes exactly twice as important as sensitivity to the estimation of the clustering coefficient. For the estimation of network efficiency, the relative importance of specificity grows linearly with the number of nodes. The greater importance of specificity is due to FPs occurring more prevalently between network modules rather than within them. These spurious inter-modular connections have a dramatic impact on network topology. We argue that efforts to maximize the sensitivity of connectome reconstruction should be realigned with the need to map brain networks with high specificity.

Mechanisms of zero-lag synchronization in cortical motifs.

Zero-lag synchronization between distant cortical areas has been observed in a diversity of experimental data sets and between many different regions of the brain. Several computational mechanisms have been proposed to account for such isochronous synchronization in the presence of long conduction delays: Of these, the phenomenon of "dynamical relaying"--a mechanism that relies on a specific network motif--has proven to be the most robust with respect to parameter mismatch and system noise. Surprisingly, despite a contrary belief in the community, the common driving motif is an unreliable means of establishing zero-lag synchrony. Although dynamical relaying has been validated in empirical and computational studies, the deeper dynamical mechanisms and comparison to dynamics on other motifs is lacking. By systematically comparing synchronization on a variety of small motifs, we establish that the presence of a single reciprocally connected pair--a "resonance pair"--plays a crucial role in disambiguating those motifs that foster zero-lag synchrony in the presence of conduction delays (such as dynamical relaying) from those that do not (such as the common driving triad). Remarkably, minor structural changes to the common driving motif that incorporate a reciprocal pair recover robust zero-lag synchrony. The findings are observed in computational models of spiking neurons, populations of spiking neurons and neural mass models, and arise whether the oscillatory systems are periodic, chaotic, noise-free or driven by stochastic inputs. The influence of the resonance pair is also robust to parameter mismatch and asymmetrical time delays amongst the elements of the motif. We call this manner of facilitating zero-lag synchrony resonance-induced synchronization, outline the conditions for its occurrence, and propose that it may be a general mechanism to promote zero-lag synchrony in the brain.

Modeling positive Granger causality and negative phase lag between cortical areas.

Different measures of directional influence have been employed to infer effective connectivity in the brain. When the connectivity between two regions is such that one of them (the sender) strongly influences the other (the receiver), a positive phase lag is often expected. The assumption is that the time difference implicit in the relative phase reflects the transmission time of neuronal activity. However, Brovelli et al. (2004) observed that, in monkeys engaged in processing a cognitive task, a dominant directional influence from one area of sensorimotor cortex to another may be accompanied by either a negative or a positive time delay. Here we present a model of two brain regions, coupled with a well-defined directional influence, that displays similar features to those observed in the experimental data. This model is inspired by the theoretical framework of Anticipated Synchronization developed in the field of dynamical systems. Anticipated Synchronization is a form of synchronization that occurs when a unidirectional influence is transmitted from a sender to a receiver, but the receiver leads the sender in time. This counterintuitive synchronization regime can be a stable solution of two dynamical systems coupled in a master-slave (sender-receiver) configuration when the slave receives a negative delayed self-feedback. Despite efforts to understand the dynamics of Anticipated Synchronization, experimental evidence for it in the brain has been lacking. By reproducing experimental delay times and coherence spectra, our results provide a theoretical basis for the underlying mechanisms of the observed dynamics, and suggest that the primate cortex could operate in a regime of Anticipated Synchronization as part of normal neurocognitive function.

Measuring neuronal avalanches to inform brain-computer interfaces.

Large-scale interactions among multiple brain regions manifest as bursts of activations called neuronal avalanches, which reconfigure according to the task at hand and, hence, might constitute natural candidates to design brain-computer interfaces (BCIs). To test this hypothesis, we used source-reconstructed magneto/electroencephalography during resting state and a motor imagery task performed within a BCI protocol. To track the probability that an avalanche would spread across any two regions, we built an avalanche transition matrix (ATM) and demonstrated that the edges whose transition probabilities significantly differed between conditions hinged selectively on premotor regions in all subjects. Furthermore, we showed that the topology of the ATMs allows task-decoding above the current gold standard. Hence, our results suggest that neuronal avalanches might capture interpretable differences between tasks that can be used to inform brain-computer interfaces.

Detection of Cross-Frequency Coupling Between Brain Areas: An Extension of Phase Linearity Measurement.

The current paper proposes a method to estimate phase to phase cross-frequency coupling between brain areas, applied to broadband signals, without any a priori hypothesis about the frequency of the synchronized components. N:m synchronization is the only form of cross-frequency synchronization that allows the exchange of information at the time resolution of the faster signal, hence likely to play a fundamental role in large-scale coordination of brain activity. The proposed method, named cross-frequency phase linearity measurement (CF-PLM), builds and expands upon the phase linearity measurement, an iso-frequency connectivity metrics previously published by our group. The main idea lies in using the shape of the interferometric spectrum of the two analyzed signals in order to estimate the strength of cross-frequency coupling. We first provide a theoretical explanation of the metrics. Then, we test the proposed metric on simulated data from coupled oscillators synchronized in iso- and cross-frequency (using both Rössler and Kuramoto oscillator models), and subsequently apply it on real data from brain activity. Results show that the method is useful to estimate n:m synchronization, based solely on the phase of the signals (independently of the amplitude), and no a-priori hypothesis is available about the expected frequencies.

Flexibility of Fast Brain Dynamics and Disease Severity in Amyotrophic Lateral Sclerosis.

BACKGROUND AND OBJECTIVES: Amyotrophic lateral sclerosis (ALS) is a multisystem disorder, as supported by clinical, molecular, and neuroimaging evidence. As a consequence, predicting clinical features requires a description of large-scale neuronal dynamics. Normally, brain activity dynamically reconfigures over time, recruiting different brain areas. Brain pathologies induce stereotyped dynamics which, in turn, are linked to clinical impairment. Hence, based on recent evidence showing that brain functional networks become hyperconnected as ALS progresses, we hypothesized that the loss of flexible dynamics in ALS would predict the symptoms severity. METHODS: To test this hypothesis, we quantified flexibility using the "functional repertoire" (i.e., the number of configurations of active brain areas) as measured from source-reconstructed magnetoencephalography (MEG) in patients with ALS and healthy controls. The activity of brain areas was reconstructed in the classic frequency bands, and the functional repertoire was estimated to quantify spatiotemporal fluctuations of brain activity. Finally, we built a k-fold cross-validated multilinear model to predict the individual clinical impairment from the size of the functional repertoire. RESULTS: Comparing 42 patients with ALS and 42 healthy controls, we found a more stereotyped brain dynamics in patients with ALS (p < 0.05), as conveyed by the smaller functional repertoire. The relationship between the size of the functional repertoire and the clinical scores in the ALS group showed significant correlations in both the delta and the theta frequency bands. Furthermore, through a k-fold cross-validated multilinear regression model, we found that the functional repertoire predicted both clinical staging (p < 0.001 and p < 0.01, in the delta and theta bands, respectively) and symptoms severity (p < 0.001, in both the delta and theta bands). DISCUSSION: Our work shows that (1) ALS pathology reduces the flexibility of large-scale brain dynamics, (2) subcortical regions play a key role in determining brain dynamics, and (3) reduced brain flexibility predicts disease stage and symptoms severity. Our approach provides a noninvasive tool to quantify alterations in brain dynamics in ALS (and, possibly, other neurodegenerative diseases), thus opening new opportunities in disease management and a framework to test, in the near future, the effects of disease-modifying interventions at the whole-brain level.

Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays.

Multielectrode recordings have revealed zero time lag synchronization among remote cerebral cortical areas. However, the axonal conduction delays among such distant regions can amount to several tens of milliseconds. It is still unclear which mechanism is giving rise to isochronous discharge of widely distributed neurons, despite such latencies. Here, we investigate the synchronization properties of a simple network motif and found that, even in the presence of large axonal conduction delays, distant neuronal populations self-organize into lag-free oscillations. According to our results, cortico-cortical association fibers and certain cortico-thalamo-cortical loops represent ideal circuits to circumvent the phase shifts and time lags associated with conduction delays.

Single-neuron dynamical effects of dendritic pruning implicated in aging and neurodegeneration: towards a measure of neuronal reserve.

Aging is a main risk factor for neurodegenerative disorders including Alzheimer's disease. It is often accompanied by reduced cognitive functions, gray-matter volume, and dendritic integrity. Although age-related brain structural changes have been observed across multiple scales, their functional implications remain largely unknown. Here we simulate the aging effects on neuronal morphology as dendritic pruning and characterize its dynamical implications. Utilizing a detailed computational modeling approach, we simulate the dynamics of digitally reconstructed neurons obtained from Neuromorpho.org. We show that dendritic pruning affects neuronal integrity: firing rate is reduced, causing a reduction in energy consumption, energy efficiency, and dynamic range. Pruned neurons require less energy but their function is often impaired, which can explain the diminished ability to distinguish between similar experiences (pattern separation) in older people. Our measures indicate that the resilience of neuronal dynamics is neuron-specific, heterogeneous, and strongly affected by dendritic topology and the position of the soma. Based on the emergent neuronal dynamics, we propose to classify the effects of dendritic deterioration, and put forward a topological measure of "neuronal reserve" that quantifies the resilience of neuronal dynamics to dendritic pruning. Moreover, our findings suggest that increasing dendritic excitability could partially mitigate the dynamical effects of aging.

Flexible brain dynamics underpins complex behaviours as observed in Parkinson's disease.

Rapid reconfigurations of brain activity support efficient neuronal communication and flexible behaviour. Suboptimal brain dynamics is associated to impaired adaptability, possibly leading to functional deficiencies. We hypothesize that impaired flexibility in brain activity can lead to motor and cognitive symptoms of Parkinson's disease (PD). To test this hypothesis, we studied the 'functional repertoire'-the number of distinct configurations of neural activity-using source-reconstructed magnetoencephalography in PD patients and controls. We found stereotyped brain dynamics and reduced flexibility in PD. The intensity of this reduction was proportional to symptoms severity, which can be explained by beta-band hyper-synchronization. Moreover, the basal ganglia were prominently involved in the abnormal patterns of brain activity. Our findings support the hypotheses that: symptoms in PD relate to impaired brain flexibility, this impairment preferentially involves the basal ganglia, and beta-band hypersynchronization is associated with reduced brain flexibility. These findings highlight the importance of extensive functional repertoires for correct behaviour.

Dynamic control for synchronization of separated cortical areas through thalamic relay.

Binding of features and information which are processed at different cortical areas is generally supposed to be achieved by synchrony despite the non-negligible delays between these areas. In this work we study the dynamics and synchronization properties of a simplified model of the thalamocortical circuit where different cortical areas are interconnected with a certain delay, that is longer than the internal time scale of the neurons. Using this simple model we find that the thalamus could serve as a central subcortical area that is able to generate zero-lag synchrony between distant cortical areas by means of dynamical relaying (Vicente et al., 2008). Our results show that the model circuit is able to generate fast oscillations in frequency ranges of the beta and gamma bands triggered by an external input to the thalamus formed by independent Poisson trains. We propose a control mechanism to turn "On" and "Off" the synchronization between cortical areas as a function of the relative rate of the external input fed into dorsal and ventral thalamic neuronal populations. The current results emphasize the hypothesis that the thalamus could control the dynamics of the thalamocortical functional networks enabling two separated cortical areas to be either synchronized (at zero-lag) or unsynchronized. This control may happen at a fast time scale, in agreement with experimental data, and without any need of plasticity or adaptation mechanisms which typically require longer time scales.

Active dendrites enhance neuronal dynamic range.

Since the first experimental evidences of active conductances in dendrites, most neurons have been shown to exhibit dendritic excitability through the expression of a variety of voltage-gated ion channels. However, despite experimental and theoretical efforts undertaken in the past decades, the role of this excitability for some kind of dendritic computation has remained elusive. Here we show that, owing to very general properties of excitable media, the average output of a model of an active dendritic tree is a highly non-linear function of its afferent rate, attaining extremely large dynamic ranges (above 50 dB). Moreover, the model yields double-sigmoid response functions as experimentally observed in retinal ganglion cells. We claim that enhancement of dynamic range is the primary functional role of active dendritic conductances. We predict that neurons with larger dendritic trees should have larger dynamic range and that blocking of active conductances should lead to a decrease in dynamic range.

Spatially resolved dendritic integration: towards a functional classification of neurons.

The vast tree-like dendritic structure of neurons allows them to receive and integrate input from many neurons. A wide variety of neuronal morphologies exist, however, their role in dendritic integration, and how it shapes the response of the neuron, is not yet fully understood. Here, we study the evolution and interactions of dendritic spikes in excitable neurons with complex real branch structures. We focus on dozens of digitally reconstructed illustrative neurons from the online repository NeuroMorpho.org, which contains over 130,000 neurons. Yet, our methods can be promptly extended to any other neuron. This approach allows us to estimate and map specific and heterogeneous patterns of activity observed across extensive dendritic trees with thousands of compartments. We propose a classification of neurons based on the location of the soma (centrality) and the number of branches connected to the soma. These are key topological factors in determining the neuron's energy consumption, firing rate, and the dynamic range, which quantifies the range in synaptic input rate that can be reliably encoded by the neuron's firing rate. Moreover, we find that bifurcations, the structural building blocks of complex dendrites, play a major role in increasing the dynamic range of neurons. Our results provide a better understanding of the effects of neuronal morphology in the diversity of neuronal dynamics and function.

Exploring atypical timescales in the brain.

Identifying activity imbalances in specific brain regions may help to diagnose and treat psychiatric disorders.

Hierarchical and Nonlinear Dynamics in Prefrontal Cortex Regulate the Precision of Perceptual Beliefs.

Actions are shaped not only by the content of our percepts but also by our confidence in them. To study the cortical representation of perceptual precision in decision making, we acquired functional imaging data whilst participants performed two vibrotactile forced-choice discrimination tasks: a fast-slow judgment, and a same-different judgment. The first task requires a comparison of the perceived vibrotactile frequencies to decide which one is faster. However, the second task requires that the estimated difference between those frequencies is weighed against the precision of each percept-if both stimuli are very precisely perceived, then any slight difference is more likely to be identified than if the percepts are uncertain. We additionally presented either pure sinusoidal or temporally degraded "noisy" stimuli, whose frequency/period differed slightly from cycle to cycle. In this way, we were able to manipulate the perceptual precision. We report a constellation of cortical regions in the rostral prefrontal cortex (PFC), dorsolateral PFC (DLPFC) and superior frontal gyrus (SFG) associated with the perception of stimulus difference, the presence of stimulus noise and the interaction between these factors. Dynamic causal modeling (DCM) of these data suggested a nonlinear, hierarchical model, whereby activity in the rostral PFC (evoked by the presence of stimulus noise) mutually interacts with activity in the DLPFC (evoked by stimulus differences). This model of effective connectivity outperformed competing models with serial and parallel interactions, hence providing a unique insight into the hierarchical architecture underlying the representation and appraisal of perceptual belief and precision in the PFC.

Metastable brain waves.

Traveling patterns of neuronal activity-brain waves-have been observed across a breadth of neuronal recordings, states of awareness, and species, but their emergence in the human brain lacks a firm understanding. Here we analyze the complex nonlinear dynamics that emerge from modeling large-scale spontaneous neural activity on a whole-brain network derived from human tractography. We find a rich array of three-dimensional wave patterns, including traveling waves, spiral waves, sources, and sinks. These patterns are metastable, such that multiple spatiotemporal wave patterns are visited in sequence. Transitions between states correspond to reconfigurations of underlying phase flows, characterized by nonlinear instabilities. These metastable dynamics accord with empirical data from multiple imaging modalities, including electrical waves in cortical tissue, sequential spatiotemporal patterns in resting-state MEG data, and large-scale waves in human electrocorticography. By moving the study of functional networks from a spatially static to an inherently dynamic (wave-like) frame, our work unifies apparently diverse phenomena across functional neuroimaging modalities and makes specific predictions for further experimentation.