Corrigendum: Spectral Entropy Based Neuronal Network Synchronization Analysis Based on Microelectrode Array Measurements.

[This corrects the article DOI: 10.3389/fncom.2016.00112.].

On electrophysiological signal complexity during biological neuronal network development and maturation.

Developing neuronal populations are assumed to increase their synaptic interactions and generate synchronized activity, such as bursting, during maturation. These effects may arise from increasing interactions of neuronal populations and increasing simultaneous intra-population activity in developing networks. In this paper, we investigated the neuronal network activity and its complexity by means of self-similarity during neuronal network development. We studied the phenomena using computational neuronal network models and actual in vitro microelectrode array data measured from a developing neuronal network of dissociated mouse cortical neurons. To achieve this, we assessed the spiking and bursting characteristics of the networks, and computed the signal complexity with Sample Entropy. The results show that we can relate increasing simultaneous activity in a neuronal population with decreasing entropy, and track the network development and maturation using this. We can conclude that the complexity of neuronal network signals decreases during the maturation. This can emerge from the fact that as networks mature, they exhibit more synchronous activity, thus decreasing the complexity of its signaling. However, increasing the number of interacting populations has lesser effect on the signal complexity. The entropy based measure provides a tool to assess the complexity of the neuronal network activity, and can be useful in the assessment of developing networks or the effects of drugs and toxins on their functioning.

Network-Wide Adaptive Burst Detection Depicts Neuronal Activity with Improved Accuracy.

Neuronal networks are often characterized by their spiking and bursting statistics. Previously, we introduced an adaptive burst analysis method which enhances the analysis power for neuronal networks with highly varying firing dynamics. The adaptation is based on single channels analyzing each element of a network separately. Such kind of analysis was adequate for the assessment of local behavior, where the analysis focuses on the neuronal activity in the vicinity of a single electrode. However, the assessment of the whole network may be hampered, if parts of the network are analyzed using different rules. Here, we test how using multiple channels and measurement time points affect adaptive burst detection. The main emphasis is, if network-wide adaptive burst detection can provide new insights into the assessment of network activity. Therefore, we propose a modification to the previously introduced inter-spike interval (ISI) histogram based cumulative moving average (CMA) algorithm to analyze multiple spike trains simultaneously. The network size can be freely defined, e.g., to include all the electrodes in a microelectrode array (MEA) recording. Additionally, the method can be applied on a series of measurements on the same network to pool the data for statistical analysis. Firstly, we apply both the original CMA-algorithm and our proposed network-wide CMA-algorithm on artificial spike trains to investigate how the modification changes the burst detection. Thereafter, we use the algorithms on MEA data of spontaneously active chemically manipulated in vitro rat cortical networks. Moreover, we compare the synchrony of the detected bursts introducing a new burst synchrony measure. Finally, we demonstrate how the bursting statistics can be used to classify networks by applying k-means clustering to the bursting statistics. The results show that the proposed network wide adaptive burst detection provides a method to unify the burst definition in the whole network and thus improves the assessment and classification of the neuronal activity, e.g., the effects of different pharmaceuticals. The results indicate that the novel method is adaptive enough to be usable on networks with different dynamics, and it is especially feasible when comparing the behavior of differently spiking networks, for example in developing networks.

Spectral Entropy Based Neuronal Network Synchronization Analysis Based on Microelectrode Array Measurements.

Synchrony and asynchrony are essential aspects of the functioning of interconnected neuronal cells and networks. New information on neuronal synchronization can be expected to aid in understanding these systems. Synchronization provides insight in the functional connectivity and the spatial distribution of the information processing in the networks. Synchronization is generally studied with time domain analysis of neuronal events, or using direct frequency spectrum analysis, e.g., in specific frequency bands. However, these methods have their pitfalls. Thus, we have previously proposed a method to analyze temporal changes in the complexity of the frequency of signals originating from different network regions. The method is based on the correlation of time varying spectral entropies (SEs). SE assesses the regularity, or complexity, of a time series by quantifying the uniformity of the frequency spectrum distribution. It has been previously employed, e.g., in electroencephalogram analysis. Here, we revisit our correlated spectral entropy method (CorSE), providing evidence of its justification, usability, and benefits. Here, CorSE is assessed with simulations and in vitro microelectrode array (MEA) data. CorSE is first demonstrated with a specifically tailored toy simulation to illustrate how it can identify synchronized populations. To provide a form of validation, the method was tested with simulated data from integrate-and-fire model based computational neuronal networks. To demonstrate the analysis of real data, CorSE was applied on in vitro MEA data measured from rat cortical cell cultures, and the results were compared with three known event based synchronization measures. Finally, we show the usability by tracking the development of networks in dissociated mouse cortical cell cultures. The results show that temporal correlations in frequency spectrum distributions reflect the network relations of neuronal populations. In the simulated data, CorSE unraveled the synchronizations. With the real in vitro MEA data, CorSE produced biologically plausible results. Since CorSE analyses continuous data, it is not affected by possibly poor spike or other event detection quality. We conclude that CorSE can reveal neuronal network synchronization based on in vitro MEA field potential measurements. CorSE is expected to be equally applicable also in the analysis of corresponding in vivo and ex vivo data analysis.