The Foraging Brain: Evidence of Lévy Dynamics in Brain Networks

Progress in Neurobiology, 2009

Frontiers in Physiology, 2012

The continuous interaction between brain regions "at rest" defines the so-called resting state networks (RSN) which can be reconstructed from the analysis of functional magnetic resonance imaging (fMRI) data. What dynamical mechanism allow for a flexible large-scale organization of the RSN still remains an important challenge. Here, three key novel properties of the RSN are uncovered. First, the correlation length (i.e., the length at which correlation between two regions vanishes) diverges with the cluster's size considered. Second, this divergence it is observed also for measures of mutual information. Third, the variance of the fMRI mean signal remains constant across the entire range of observed clusters sizes, in contrast with naive expectations. The unveiled scale invariance exposes the RSN optimal information-sharing properties across very diverse networks sizes, architectures and functions, which can be an important marker of healthy brain dynamics.

Journal of Neuroscience, 2013

Brain fluctuations at rest are not random but are structured in spatial patterns of correlated activity across different brain areas. The question of how resting-state functional connectivity (FC) emerges from the brain's anatomical connections has motivated several experimental and computational studies to understand structure-function relationships. However, the mechanistic origin of resting state is obscured by large-scale models' complexity, and a close structure-function relation is still an open problem. Thus, a realistic but simple enough description of relevant brain dynamics is needed. Here, we derived a dynamic mean field model that consistently summarizes the realistic dynamics of a detailed spiking and conductance-based synaptic large-scale network, in which connectivity is constrained by diffusion imaging data from human subjects. The dynamic mean field approximates the ensemble dynamics, whose temporal evolution is dominated by the longest time scale of the system. With this reduction, we demonstrated that FC emerges as structured linear fluctuations around a stable low firing activity state close to destabilization. Moreover, the model can be further and crucially simplified into a set of motion equations for statistical moments, providing a direct analytical link between anatomical structure, neural network dynamics, and FC. Our study suggests that FC arises from noise propagation and dynamical slowing down of fluctuations in an anatomically constrained dynamical system. Altogether, the reduction from spiking models to statistical moments presented here provides a new framework to explicitly understand the building up of FC through neuronal dynamics underpinned by anatomical connections and to drive hypotheses in task-evoked studies and for clinical applications.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Slow coherent spontaneous fluctuations (<0.1 Hz) in functional magnetic resonance imaging blood-oxygen-level-dependent signals have been observed for a resting state of the human brain. In this paper, considering feed-forward inhibition in addition to excitation between brain areas, which we assume to be in up (active) or down (quiescent) states, we propose a model for the generation and organization of the slow fluctuations. Connectivity with feed-forward excitation and inhibition between the areas makes the system have multiple stable states and organized slow fluctuations manifest as noise-induced slow transitions between the states. With various connectivities, we observe slow fluctuations and various organizations, including anticorrelated clusters, through numerical simulations.

Endogenous brain activity supports spontane- ous human thought and shapes perception and behavior. Connectivity-based analyses of endogenous, or resting- state, functional magnetic resonance imaging (fMRI) data have revealed the existence of a small number of robust networks which have a rich spatial structure. Yet the temporal information within fMRI data is limited, moti- vating the complementary analysis of electrophysiological recordings such as electroencephalography (EEG). Here we provide a novel method based on multivariate time– frequency interdependence to reconstruct the principal resting-state network dynamics in human EEG data. The stability of network expression across subjects is assessed using resampling techniques. We report the presence of seven robust networks, with distinct topographic organi- zations and high frequency (*5–45 Hz) fingerprints, nes- ted within slow temporal sequences that build up and decay over several orders of magnitude. Interestingly, all seven networks are expressed concurrently during these slow dynamics, although there is a temporal asymmetry in the pattern of their formation and dissolution. These analyses uncover the complex temporal character of endogenous cortical fluctuations and, in particular, offer an opportunity to reconstruct the low dimensional linear subspace in which they unfold.

NeuroImage, 2014

Studies employing functional connectivity-type analyses have established that spontaneous fluctuations in functional magnetic resonance imaging (fMRI) signals are organized within large-scale brain networks. Meanwhile, fMRI signals have been shown to exhibit 1/f-type power spectraa hallmark of scale-free dynamics. We studied the interplay between functional connectivity and scale-free dynamics in fMRI signals, utilizing the fractal connectivity frameworka multivariate extension of the univariate fractional Gaussian noise model, which relies on a wavelet formulation for robust parameter estimation. We applied this framework to fMRI data acquired from healthy young adults at rest and while performing a visual detection task. First, we found that scaleinvariance existed beyond univariate dynamics, being present also in bivariate cross-temporal dynamics. Second, we observed that frequencies within the scale-free range do not contribute evenly to interregional connectivity, with a systematically stronger contribution of the lowest frequencies, both at rest and during task. Third, in addition to a decrease of the Hurst exponent and interregional correlations, task performance modified crosstemporal dynamics, inducing a larger contribution of the highest frequencies within the scale-free range to global correlation. Lastly, we found that across individuals, a weaker task modulation of the frequency contribution to interregional connectivity was associated with better task performance manifesting as shorter and less variable reaction times. These findings bring together two related fields that have hitherto been studied separatelyresting-state networks and scale-free dynamics, and show that scale-free dynamics of human brain activity manifest in cross-regional interactions as well.

Journal of Magnetic Resonance Imaging, 2009

Purpose-To examine spatiotemporal dynamics of low frequency fluctuations in rat cortex.

Physics Uspekhi , 2023

The article deals with the influence of stochastic dynamics of the brain's neural ensembles on the perception and processing of sensory information, as well as on decisionmaking based on it. The review considers sources of noise in the nervous system during sensory information processing, as well as some nervous system strategies of compensating for or taking into account stochastic processes. Experiments and mathematical models are discussed in which stochastic brain dynamics begins to play a significant role in the perception of sensory information. Particular attention is paid to brain noise research paradigms such as the perception of weak stimuli close to the sensitivity threshold and bistable ambiguous stimuli. Methods for assessing brain noise using both psychophysical experiments and direct analysis of neuroimaging data are described. Finally, some issues in applying the concept of stochastic brain dynamics to problems in the biomedical diagnosis of various neurological diseases are considered.

International Journal of Bifurcation and Chaos, 2010

Nonlinear time series analyses have suggested that the human electroencephalogram (EEG) may share statistical and dynamical properties with chaotic systems. During slow-wave sleep or pathological states like epilepsy, correlation dimension measurements display low values, while in awake and attentive subjects, there is no such low dimensionality, and the EEG is more similar to a stochastic variable. We briefly review these results and contrast them with recordings in cat cerebral cortex, as well as with theoretical models. In awake or sleeping cats, recordings with microelectrodes inserted in cortex show that global variables such as local field potentials (local EEG) are similar to the human EEG. However, neuronal discharges are highly irregular and exponentially distributed, similar to Poisson stochastic processes. To reconcile these results, we investigate models of randomly-connected networks of integrate-and-fire neurons, and also contrast global (averaged) variables, with neuronal activity. The network displays different states, such as "synchronous regular" (SR) or "asynchronous irregular" (AI) states. In SR states, the global variables display coherent behavior with low dimensionality, while in AI states, the global activity is high-dimensionally chaotic with exponentially distributed neuronal discharges, similar to awake cats. Scale-dependent Lyapunov exponents and -entropies show that the seemingly stochastic nature at small scales (neurons) can coexist with more coherent behavior at larger scales (averages). Thus, we suggest that brain activity obeys a similar scheme, with seemingly stochastic dynamics at small scales (neurons), while large scales (EEG) display more coherent behavior or high-dimensional chaos.

The Journal of neuroscience : the official journal of the Society for Neuroscience, 2014

Ongoing neuronal activity in the CNS waxes and wanes continuously across widespread spatial and temporal scales. In the human brain, these spontaneous fluctuations are salient in blood oxygenation level-dependent (BOLD) signals and correlated within specific brain systems or "intrinsic-connectivity networks." In electrophysiological recordings, both the amplitude dynamics of fast (1-100 Hz) oscillations and the scalp potentials per se exhibit fluctuations in the same infra-slow (0.01-0.1 Hz) frequency range where the BOLD fluctuations are conspicuous. While several lines of evidence show that the BOLD fluctuations are correlated with fast-amplitude dynamics, it has remained unclear whether the infra-slow scalp potential fluctuations in full-band electroencephalography (fbEEG) are related to the resting-state BOLD signals. We used concurrent fbEEG and functional magnetic resonance imaging (fMRI) recordings to address the relationship of infra-slow fluctuations (ISFs) in sca...