Brain Rhythms Reveal a Hierarchical Network Organization

Abstract

Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or “virtual brains”, whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease.

Information gain in the brain's resting state: A new perspective on autism

“…The presence of background noise does not allow the system to quench at the fixed point but perturbs the system in a continuous manner, so that it fluctuates around the equilibrium (Galán, 2008). Thus, consistent with the approach used by several authors (Tononi et al, 1999; Sporns et al, 2000; Galán, 2008; Barnett et al, 2009; Steinke and Galán, 2011; García Domínguez et al, 2013), large-scale spontaneous brain activity is accurately described as a linear stochastic process that is formally equivalent to a mOUP. $x_i(t+dt)=x_i(t)+dt{\displaystyle \sum _{j=1}^N{W}_{ij}}{x}_j(t)+{\eta }_i(t+dt),$ where W ij is the functional connectivity matrix, i.e., the coupling between the j -th and the i -th nodes; x i ( t ) is the neural activity of the i -th node with respect to baseline, measured as the signal from the i -th MEG channel at time t ; η i are the residuals (background, uncorrelated white noise) of the i -th channel; N is the number of nodes (sensors) and dt is the sampling interval (1.6 ms).…”

Functional Connectivity Estimated from Intracranial EEG Predicts Surgical Outcome in Intractable Temporal Lobe Epilepsy

“…In recent computational studies, virtual brains modeling diseased states like epilepsy displayed lower structural complexity compared to models of normal neural function [23]. A measure of neuronal complexity loss estimated from subdural electrodes during presurgical evaluation of epilepsy correctly identified 86.7% of the patients with respect to seizure outcome [24], consistently with other reports [25].…”

“…Analysis of loss of neuronal complexity has been used to lateralize unilateral TLE and to predict outcome in neocortical lesional epilepsy [24], [25]. Loss of variability and increased excitability was recently noted in virtual brains modeled to simulate pathological states like epilepsy [23]. The correlation matrices of the patients give a strikingly visual representation of decrease in strength and loss of heterogeneity of connectivity in patients with a good outcome (Figure S2).…”

Sustained oscillations, irregular firing, and chaotic dynamics in hierarchical modular networks with mixtures of electrophysiological cell types

“…Experimental and theoretical work suggests that this ongoing resting state activity may have an important role to endow the brain with flexibility in dealing with diverse cognitive and behavioral situations (Lakatos et al, 2008; Gong and van Leeuwen, 2009; Lewis et al, 2009; Luczak et al, 2009; Sadaghiani et al, 2010; Destexhe, 2011; Steinke and Galán, 2011). …”