Phenomenological Renormalization Group Applications to Brain Data

Abstract

The critical brain hypothesis has emerged in the last decades as a fruitful theoretical framework for understanding collective neuronal phenomena. Lending support to the idea that the brain operates near a phase transition, Beggs and Plenz were the first to report experimentally recorded neuronal avalanches, whose distributions coincide with the mean-field directed percolation (DP) universality class, which comprises a variety of models in which a phase transition occurs between an absorbing (silent) and an active phase. However, this hypothesis is highly debated, as neuronal avalanches analyses and other common statistical mechanics tools may struggle with challenges ubiquitous in living systems, such as subsampling and the absence of an explicit model for a complete theory of neuronal dynamics. In this context, Meshulam et al. recently proposed a phenomenological renormalization group (PRG) method to deal with neural networks with a model independent analysis. The procedure consists of recursively manipulating the data, obtaining an increasingly coarse-grained description of the activity after each iteration. Under a critical regime, non-trivial correlations and scale-free behavior should be unveiled as we simplify our description. This can be inferred from a series of statistical features of the data, which lead us to different scaling relations. Here, we apply the PRG in two different experimental setups: spiking data from the anesthetized rat visual cortex and functional magnetic resonance imaging (fMRI) time series from young and aging humans. In the first, we investigate the interplay between scale invariance and cortical states, as assessed by populational spiking variability coefficient of variation (CV). In the latter, we find empirical relations between PRG phenomenological exponents and explore connections between those exponents and clinical traits of the experiment participants.