Brain Rhythms Reveal a Hierarchical Network Organization

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. Author Summary: The fact that the brain generates weak but measurable electromagnetic waves has intrigued neuroscientists for over a century. Even more remarkable is the fact that these oscillations of brain activity correlate with the state of awareness and that their frequency and amplitude display reproducible features that are different in health and disease. In healthy conditions, oscillations of different frequency bands tend to minimize interference. This is similar to radio stations avoiding overlap between frequency bands to ensure clear transmission. During epileptic seizures, mutual entrainment, analogous to interference of radio signals, has also been reported. Moreover, in schizophrenia and autism, there is a loss of higher frequency oscillations. Most studies thus far have focused on the mechanisms generating the oscillations, as well as on their functional relevance. In contrast, our study focuses on what brain rhythms tell us about the functional network organization of the brain. Using a reverse-engineering approach, we construct abstract networks (virtual brains) that display oscillations of actual brains. These networks reveal that brain rhythms reflect different levels of hierarchical organization in health and disease. We predict specific alterations in brain connectivity in the aforementioned diseases and explain how clinicians and experimentalists can test our predictions.