Inferring correlations associated to causal interactions in brain signals using autoregressive models

Abstract

The specific connectivity of a neuronal network is reflected in the dynamics of the signals recorded on its nodes. The analysis of how the activity in one node predicts the behaviour of another gives the directionality in their relationship. However, each node is composed of many different elements which define the properties of the links. For instance, excitatory and inhibitory neuronal subtypes determine the functionality of the connection. Classic indexes such as the Granger causality (GC) quantifies these interactions, but they do not infer into the mechanism behind them. Here, we introduce an extension of the well-known GC that analyses the correlation associated to the specific influence that a transmitter node has over the receiver. This way, the G-causal link has a positive or negative effect if the predicted activity follows directly or inversely, respectively, the dynamics of the sender. The method is validated in a neuronal population model, testing the paradigm that excitatory and inhibitory neurons have a differential effect in the connectivity. Our approach correctly infers the positive or negative coupling produced by different types of neurons. Our results suggest that the proposed approach provides additional information on the characterization of G-causal connections, which is potentially relevant when it comes to understanding interactions in the brain circuits.

Functional Interactions between Entorhinal Cortical Pathways Modulate Theta Activity in the Hippocampus

“…Guo and colleagues [25] proposed a partial GC, which estimates the GC after removing the influence of unknown variables (i.e., time-series that were not included in the analysis). It can be estimated whether the receiver follows directly or inversely the activity of the sender, what was applied in computational models to distinguish two circuits with different mechanisms (excitation and inhibition) but identical GC values [26]. Baccalá and Sameshima introduced a new approach, termed Partial Directed Coherence (PDC) [27], to estimate a frequency-domain representation of the direct GC between two nodes, i.e., controlling the influence of other variables included in the model.…”

Community detection in the human connectome: Method types, differences and their impact on inference

“…Coordinated functional activity between brain areas can be described mathematically by a graph $$$ \mathcal{G}\left(E,V\right) $$$, in which discretized brain regions represent nodes $$$ V $$$ and functional interactions between their edges $$$ E $$$. Brain graphs are typically estimated from regional measurements of electrical/electromagnetic activity (EEG and MEG) or blood oxygenation (fMRI) using various correlation techniques, from simple pairwise correlation in the time or frequency domains (e.g., peak cross‐correlation and coherence) to probabilistic (information theoretic) methods (Bastos & Schoffelen, 2016; Li et al, 2009; Rossini et al, 2019), and directional techniques for effective connectivity (Harush & Baruch, 2017; Lopez‐Madrona et al, 2019; Stephan & Friston, 2010). Connectivity matrices are further processed (e.g., via thresholding or model‐related approaches (Bielczyk et al, 2018)) to eliminate edges that represent weak and/or artifact‐related regional interactions and obtain binary or weighted adjacency matrices, based on which communities and other topological graph characteristics can be estimated.…”

Uncorrelated bilateral cortical input becomes timed across hippocampal subfields for long waves whereas gamma waves are largely ipsilateral

“…As such, their interpretation should be approached with caution as they do not directly correspond to true elementary waves or their intervals. To minimize overinterpretation by relying on a single aspect (Hillebrand et al, 2012;López-Madrona et al, 2017), we have utilized several tests exploring different temporal, frequency, and leadership characteristics.…”

“…Theoretical studies have found that effective connectivity in the hippocampus can be strongly modulated by multiple factors, including the interaction between common afferents, average firing frequency, or intrinsic excitability (Battaglia et al, 2012;Han et al, 2015;López-Madrona et al, 2017;Pariz et al, 2018). On the one hand, experimental studies conducted on single subfields will be highly dependent on the study conditions, and on the other hand, theoretical studies show that unless structural and functional constraints are incorporated, almost any parameter can be decisive in one range or another (Migliore et al, 1995;López-Aguado et al, 2000;Ibarz et al, 2006).…”