Avalanche Dynamics and Correlations in Neural Systems

Abstract

The existence of power law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression of a system acting close to a critical point. This chapter focuses on temporal correlations and avalanche dynamics in the spontaneous activity of cortex slice cultures and in the resting fMRI BOLD signal. Long-range correlations are investigated by means of the scaling of power spectra and of Detrended Fluctuations Analysis. The existence of 1/ f decay in the power spectrum, as well as of power-law scaling in the root mean square fluctuation function for the appropriate balance of excitation and inhibition suggests that long-range temporal correlations are distinctive of "healthy brains". The corresponding temporal organization of neuronal avalanches can be dissected by analyzing the distribution of inter-event times between successive events. In rat cortex slice cultures this distribution exhibits a non-monotonic behavior, not usually found in other natural processes. Numerical simulations provide evidences that this behavior is a consequence of the alternation between states of high and low activity, leading to a dynamic balance between excitation and inhibition that tunes the system at criticality. In this scenario, inter-times show a peculiar relation with avalanche sizes, resulting in a hierarchical structure of avalanche sequences. Large avalanches correspond to low-frequency oscillations, and trigger cascades of smaller ones that are part of higher frequency rhythms. The selfregulated balance of excitation and inhibition observed in cultures is confirmed at

Beyond pulsed inhibition: Alpha oscillations modulate attenuation and amplification of neural activity in the awake resting-state

“…Power-law regimes (A) and (B) are followed by a faster decay of the probability P (Δ t ) for Δ t ’s longer than 1 s, which may be related to delta oscillations. The non-exponential, power-law quiet time distribution implies that neural cascades of activity are strongly correlated [63, 12, 35, 31, 33, 30]. Indeed, the distribution P (Δ t ) calculated after random phase shuffling (Materials and Methods) of the original brain signals is exponential (Figs.…”

“…The double power-law, non-exponential quiet time distribution, as well as the autocorrelation C ( t ), implies that neural cascades of activity are strongly correlated [50, 51, 37, 52, 53, 54], and indicates that the nature of correlations in the cascading process depends on the time scales. Indeed, the distribution P (Δ t ) calculated after random phase shuffling (STAR Methods) of the original brain signals is exponential (Figs.…”

“…In this paper, we provided a description of the resting-state brain activity that uncovers the dynamic organization of neural activity cascades underlying brain oscillations, unifying two complementary approaches to neural synchronization—neuronal avalanches and oscillations [8, 22, 32, 39, 30, 34]. Our analysis shows that the collective neural dynamics underlying resting-state brain activity is governed by attenuation-amplification principles across timescales—which we link with prominent features of the alpha oscillations.…”

Taming the Unknown Unknowns in Complex Systems: Challenges and Opportunities for Modeling, Analysis and Control of Complex (Biological) Collectives

“…In contrast, for single power law distributed inter-event times, the rate of change in one state variable requires the introduction of a fractional order derivative (Shlesinger, 1987; West, 2010; Svenkeson et al, 2016). Of note, as demonstrated in Lombardi et al (2019), the distribution of inter-event times (among successive events) can not only shed light on the nature of the operator governing the rate of change (dynamics), but also allow us to study the hierarchical temporal organization of the neuronal avalanches (i.e., an ensemble of neurons that fire close-in-time) and the existence of a critical behavior. Nevertheless, the set of critical exponents characterizing the neuronal spontaneous activity in control conditions and in the presence of folic acid are different (Yaghoubi et al, 2018) suggesting the existence of different universality classes.…”

“…Rigorous mathematical analysis shows that many such genomic, proteomic and physiological processes possess time dependent, long-range dependence, and multi-fractal characteristics (Goldberger and West, 1987; Ivanov et al, 2001; Wink et al, 2008; Bassingthwaighte et al, 2013; Ghorbani and Bogdan, 2013; Bohara et al, 2017; Akhrif et al, 2018; Ghorbani et al, 2018; Racz et al, 2018b). For instance, Lombardi et al (2019) demonstrated that the existence of long-range temporal correlations (dependence) is an accurate marker of “healthy brains.” Moreover, mathematical investigations of physiological processes collected from the individuals suffering from various diseases revealed specific patterns, for example, a decrease in correlation in both temporal and fractal behavior (Ivanov et al, 1999; Stanley et al, 1999; Kotani et al, 2005; Gierałtowski et al, 2012). For instance, the ratio between the short-term and long-term scaling exponents was demonstrated in Platiša et al (2019) to discriminate between patients experiencing heart failure, providing crucial information where the levels of the cardiac autonomic nervous system control, age, or the left ventricular ejection fraction could not.…”