Approximate Entropy of Spiking Series Reveals Different Dynamical States in Cortical Assemblies

Self-organized criticality theory proved that information transmission and computational performances of neural networks are optimal in critical state. By using recordings of the spontaneous activity originated by dissociated neuronal assemblies coupled to Micro-Electrode Arrays (MEAs), we tested this hypothesis using Approximate Entropy (ApEn) as a measure of complexity and information transfer. We analysed 60 min of electrophysiological activity of three neuronal cultures exhibiting either sub-critical, critical or super-critical behaviour. The firing patterns on each electrode was studied in terms of the inter-spike interval (ISI), whose complexity was quantified using ApEn. We assessed that in critical state the local complexity (measured in terms of ApEn) is larger than in sub-and super-critical conditions (mean ± std, ApEn about 0.93 ± 0.09, 0.66 ± 0.18, 0.49 ± 0.27, for the cultures in critical, sub-critical and super-critical state, respectively—differences statistically significant). Our estimations were stable when considering epochs as short as 5 min (pairwise cross-correlation of spatial distribution of mean ApEn of 94 ± 5%). These preliminary results indicate that ApEn has the potential of being a reliable and stable index to monitor local information transmission in a neuronal network during maturation. Thus, ApEn applied on ISI time series appears to be potentially useful to reflect the overall complex behaviour of the neural network, even monitoring a single specific location.