Abstract
Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been observed in neural systems, particularly, in neuronal cultures. However, the presence of critical states in the awake brain remains controversial. Here, we compared avalanche analyses performed on different in vivo preparations during wakefulness, slow-wave sleep, and REM sleep, using high density electrode arrays in cat motor cortex (96 electrodes), monkey motor cortex and premotor cortex and human temporal cortex (96 electrodes) in epileptic patients. In neuronal avalanches defined from units (up to 160 single units), the size of avalanches never clearly scaled as power-law, but rather scaled exponentially or displayed intermediate scaling. We also analyzed the dynamics of local field potentials (LFPs) and in particular LFP negative peaks (nLFPs) among the different electrodes (up to 96 sites in temporal cortex or up to 128 sites in adjacent motor and premotor cortices). In this case, the avalanches defined from nLFPs displayed power-law scaling in double logarithmic representations, as reported previously in monkey. However, avalanche defined as positive LFP (pLFP) peaks, which are less directly related to neuronal firing, also displayed apparent power-law scaling. Closer examination of this scaling using the more reliable cumulative distribution function (CDF) and other rigorous statistical measures, did not confirm power-law scaling. The same pattern was seen for cats, monkey, and human, as well as for different brain states of wakefulness and sleep. We also tested other alternative distributions. Multiple exponential fitting yielded optimal fits of the avalanche dynamics with bi-exponential distributions. Collectively, these results show no clear evidence for power-law scaling or self-organized critical states in the awake and sleeping brain of mammals, from cat to man.
Highlights
Self-organized criticality (SOC) is a dynamical state of a system which maintains itself at a phase transition point
AVALANCHE DEFINITION Figure 1 illustrates the definition of avalanche for discrete and continuous (LFP) data, as they are used in this study
POWER-LAW FIT It has been shown that that cumulative distribution function (CDF) provides a better measure than probability density function (PDF) as it avoids erroneous measures at the far end of the distribution tail of probability curve
Summary
Self-organized criticality (SOC) is a dynamical state of a system which maintains itself at (or close to) a phase transition point. This family of systems were initially described by Bak et al (1987), and have been found in many natural systems (reviewed in Bak, 1996; Jensen, 1998). SOC systems are characterized by scale invariance, which is usually identified as a power-law distribution of characteristics of the system’s dynamics such as event size or the waiting time between events. The temporal fingerprint of SOC systems is often 1/f or 1/f 2 noise. Avalanche sizes are typically distributed as a power-law, where the probability of occurrence p(x) of a given avalanche size x scales as:
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