Approximate Entropy of Spiking Series of a Neuronal Network in Either Subcritical or Critical State

Abstract

Spontaneous activity of neural networks depends on their stage of development. Computational performances of a network increase when the maturation leads to a self-organized criticality. Thus, an increasing complexity in the behavior of the network is expected when it enters in this developmental stage, called critical state. We tested this hypothesis investigating with a Micro-Electrodes Array of 60 electrodes a neuronal culture that during maturation exhibited first a subcritical and then a critical state. We found that in the critical state the local complexity (measured in terms of Approximate Entropy) was larger than in subcritical conditions ($\mathbf{mean}\pm \mathbf{std}$, ApEn about $\mathbf{1.03}+\mathbf{0.10},\mathbf{0.77}+\mathbf{0.18}$ in critical and sub-critical states, respectively; differences statistically significant), but only if the embedding dimension is at least 3 and the tolerance is fixed (we considered it equal to 1 ms, which is close to the characteristic time of neural communications).