Abstract
The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent . Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.
Highlights
Neuronal avalanches are bouts of scale-invariant spatiotemporal electrical activity first recorded by Beggs and Plenz from cortical cultures via multi-electrode arrays (MEAs) [1]
We have simulated two-dimensional networks of excitable elements modeled by cellular automata, which have been used in recent works to mimic the propagation of neuronal avalanche [1,23,24,25]
The effects of the investigated topologies can be summarized as follows: two-dimensional and small-world networks are more severely affected by decreasing sampling densities because they have a well defined local neighborhood, in contrast to random graphs, whose size distributions do not change significantly when sampling density decreases
Summary
Neuronal avalanches are bouts of scale-invariant spatiotemporal electrical activity first recorded by Beggs and Plenz from cortical cultures via multi-electrode arrays (MEAs) [1]. It coincides with the exponent governing a critical branching process [3] This coincidence has been held as evidence that neuronal avalanches are a statistical signature that the brain as a dynamical system operates near a critical point, a conjecture that has spurred intense research (for recent reviews, see [4] and [5]). In light of this conjecture, several models for this type of brain activity have been proposed, in which a phase transition occurs between an inactive state and an active collective state. When coupling is strong enough, activity propagates from neuron to neuron in a never-ending process: self-sustained activity is collectively stable
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