A Novel Quantitative Metric Based on a Complete and Unique Characterization of Neural Network Activity: 4D Shannon's Entropy.

Here, we present a novel entropy metric for neural network characterization, 4D Shannon's entropy, based on triple correlation, which measures interactions among up to three neurons in time and space. Per the Triple Correlation Uniqueness (TCU) theorem, our 4D entropy approach is based on a complete and unique characterization of network activity. We first outline the method to obtain 4D Shannon's entropy using a simulated spike raster of feedforward three-neuron configurations. We then apply this metric to an open-source, experimental dataset of rat cortical cultures over time to show that while first- and second-order interactions (spike rate and cross-correlation) show similar trends to published results, the TCU-based 4D Shannon's entropy metric provides greater insights into later-stage network activity compared to the published pairwise entropy. As this metric is computed from a 4D distribution unique to the network, we propose that utilization of 4D entropy offers a clear advantage compared to currently utilized pairwise entropy metrics for neural network analyses. For this reason, neuroscientific and clinical applications abound - these may include analysis of distinct dynamical states, characterizing responses to medication, and identification of pathological brain networks, such as seizures.