Statistical Analysis of Single-Trial Granger Causality Spectra

Andrea Brovelli

doi:10.1155/2012/697610

Abstract

Granger causality analysis is becoming central for the analysis of interactions between neural populations and oscillatory networks. However, it is currently unclear whether single-trial estimates of Granger causality spectra can be used reliably to assess directional influence. We addressed this issue by combining single-trial Granger causality spectra with statistical inference based on general linear models. The approach was assessed on synthetic and neurophysiological data. Synthetic bivariate data was generated using two autoregressive processes with unidirectional coupling. We simulated two hypothetical experimental conditions: the first mimicked a constant and unidirectional coupling, whereas the second modelled a linear increase in coupling across trials. The statistical analysis of single-trial Granger causality spectra, based on t-tests and linear regression, successfully recovered the underlying pattern of directional influence. In addition, we characterised the minimum number of trials and coupling strengths required for significant detection of directionality. Finally, we demonstrated the relevance for neurophysiology by analysing two local field potentials (LFPs) simultaneously recorded from the prefrontal and premotor cortices of a macaque monkey performing a conditional visuomotor task. Our results suggest that the combination of single-trial Granger causality spectra and statistical inference provides a valuable tool for the analysis of large-scale cortical networks and brain connectivity.

Highlights

The study of linear dependence between time series is central in many fields of science inferring causal relations among components of complex systems
To assess the sensitivity of the statistical analysis with respect to the number of trials analysed in each session, we reduced the number of trials used in the statistical analysis, from 150 to 3 stepped every trial (i.e., 148 values)
The results show that the statistical analysis is able to correctly infer the directional influence from X2 to X1

Summary

Introduction

The study of linear dependence between time series is central in many fields of science inferring causal relations among components of complex systems. Current literature suggests that oscillations in neural populations activity, such as the local field potentials (LFPs), play a key role in modulating, filtering, and redirecting information in the nervous system [10,11,12]. Within this framework, Granger causality analysis is employed to reveal directional influences within oscillatory networks, such as during motor maintenance behaviours [13], and, more generally, it represents a crucial tool for the investigation of the neurophysiological substrate of cognitive functions [14]

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