Self-similarity and multifractality in human brain activity: A wavelet-based analysis of scale-free brain dynamics

Abstract

Altogether, our approach provides novel fine-grained characterizations of scale-free dynamics in human brain activity.

Dynamic Functional Connectivity between Order and Randomness and its Evolution across the Human Adult Lifespan

“…Quite on the contrary, it is well known that fMRI time-series at rest and during tasks display very characteristic multifractal spectral properties, relating to both behavioural performance and pathological alterations and modulated by task difficulty or aging (Maxim et al, 2005;Ciuciu et al, 2012;He, 2014;Churchill et al, 2016;Dong et al, 2018). Tools way more sophisticated than the ones we adopt here have been used to characterize and confirm multifractality in fMRI signals (Ciuciu et al, 2017;La Rocca et al, 2018). Furthermore, the multifractal properties of fMRI signals hold not only at the level of univariate spectra but also of cross-spectra therefore translating into specific signatures even at the level of static networks, once again with behavioural correlates (Ciuciu et al, 2014).…”

Revisiting Functional Connectivity for Infraslow Scale-Free Brain Dynamics Using Complex Wavelets

“…While exact scale-free dynamics remains debatable (Dehghani et al, 2010;Ignaccolo et al, 2010), it has been proposed by an abundant literature (cf. e.g., Vanhatalo et al, 2004;Dehghani et al, 2010;He et al, 2010;Van de Ville et al, 2010;He, 2011He, , 2014Zilber et al, 2012;Buzsáki and Mizuseki, 2014;Gadhoumi et al, 2015;La Rocca et al, 2018b) that infraslow macroscopic brain activity is better described by a scaling exponent (historically the power-law exponent of the Fourier spectrum and more recently and relevantly the selfsimilarity exponent H) that relates together dynamics across a large continuum of slow time scales (or low frequencies). While most oscillatory regimes are only observed in evoked activity, elicited by stimuli, infraslow scale-free brain temporal dynamics are persistent, observed both at rest and during task performance or even in unconscious states (e.g., sleep stages).…”

“…While most oscillatory regimes are only observed in evoked activity, elicited by stimuli, infraslow scale-free brain temporal dynamics are persistent, observed both at rest and during task performance or even in unconscious states (e.g., sleep stages). It was also shown that infraslow scale-free brain temporal dynamics are modulated when contrasting rest and task-related brain activity, task-inducing systematically a decrease in H and faster infraslow dynamics (Bhattacharya and Petsche, 2001;Linkenkaer-Hansen et al, 2004;Vanhatalo et al, 2004;Popivanov et al, 2006;Bianco et al, 2007;Buiatti et al, 2007;He et al, 2010;Zilber et al, 2013;La Rocca et al, 2018b). Infraslow scale-free brain activity has thus been hypothesized to be functionally associated with neural excitability (He, 2014).…”

“…It is also now well-established and documented that, while Fourier analysis can be used to assess 1/f power-law spectra at low frequencies, accurate and robust assessments of scale-free dynamics requires replacing Fourierbased spectral estimation with multiscale wavelet analysis. Interested readers are referred to Flandrin (1992), Muzy et al (1993), Veitch and Abry (1999), Kantelhardt (2008), and Abry et al (2019b) for methodological developments and to Ciuciu et al (2008Ciuciu et al ( , 2012Ciuciu et al ( , 2014, and La Rocca et al (2018b) for applications to neuroimaging data. Further, it has recently been shown that the self-similar description of scale-free temporal dynamics could be enriched by combining the concept of multifractality with that of selfsimilarity (Wendt et al, 2007;Abry et al, 2019b), requiring the use of wavelet-leaders, consisting of non-linear non-local transforms of wavelet coefficients, for practical analysis.…”

Dynamics of nested, self-similar winnerless competition in time and space

“…The feature of being nested refers to the interlocking of processes that run simultaneously on different temporal and spatial scales. Characteristics of self-similarity are seen in power spectra of brain activity [4], in self-similar wirings [5], and in computational motifs at the micro-, meso-, and macroscales [3]. Brain dynamics proceeds via sequential segmentation of information that is manifest in sequences of electroencephalography (EEG) microstates [6], which are brief periods of stable scalp topography with a quasistationary configuration of the scalp potential field.…”