An Information-Theoretic Framework to Measure the Dynamic Interaction Between Neural Spike Trains

• Published in: IEEE transactions on biomedical engineering Vol. 68; no. 12; pp. 3471 - 3481
• Main Authors: Mijatovic, Gorana, Antonacci, Yuri, Loncar-Turukalo, Tatjana, Minati, Ludovico, Faes, Luca
• Format: Journal Article
• Language: English
• Published: United States IEEE 01-12-2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Atmospheric measurements; Biomedical measurement; Entropy; Firing pattern; information dynamics; Information theory; mutual information; Nervous system; neural synchrony; Neurons; Neurosciences; Particle measurements; point processes; Statistical analysis; Time measurement; transfer entropy
• ISSN: 0018-9294; 1558-2531
• DOI: 10.1109/TBME.2021.3073833

Objective: While understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience, existing methods either do not consider the inherent point-process nature of spike trains or are based on parametric assumptions. This work presents an information-theoretic framework for the model-free, continuous-time estimation of both undirected (symmetric) and directed (Granger-causal) interactions between spike trains. Methods: The framework computes the mutual information rate (MIR) and the transfer entropy rate (TER) for two point processes <inline-formula><tex-math notation="LaTeX">X</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">Y</tex-math></inline-formula>, showing that the MIR between <inline-formula><tex-math notation="LaTeX">X</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">Y</tex-math></inline-formula> can be decomposed as the sum of the TER along the directions <inline-formula><tex-math notation="LaTeX">X \rightarrow Y</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">Y \rightarrow X</tex-math></inline-formula>. We present theoretical expressions and introduce strategies to estimate efficiently the two measures through nearest neighbor statistics. Results: Using simulations of independent and coupled point processes, we show the accuracy of MIR and TER to assess interactions even for weakly coupled and short realizations, and demonstrate the superiority of continuous-time estimation over the standard discrete-time approach. We also apply the MIR and TER to real-world data, specifically, recordings from in-vitro preparations of spontaneously-growing cultures of cortical neurons. Using this dataset, we demonstrate the ability of MIR and TER to describe how the functional networks between recording units emerge over the course of the maturation of the neuronal cultures. Conclusion and Significance: the proposed framework provides principled measures to assess undirected and directed spike train interactions with more efficiency and flexibility than previous discrete-time or parametric approaches, opening new perspectives for the analysis of point-process data in neuroscience and many other fields.