The Analysis Of Neural Signals By The Method Of Transfer Entropy

The brain is a complex system, characterized by consisting of interconnected modules (such as:cortical areas) that often perform very specific operation. A fundamental problem in neuroscience is to clarify how information is processed in such networks and how the networks generate corresponded cognitive functions. In order to investigate these issues, many researchers record neural signals simultaneously from various brain regions. Based on these recorded data, one question is how to measure and estimate the strength of function connectivity and information flow, or causal interaction, between brain regions.In previous studies, many methods have been proposed to estimate interaction between systems based on time series, such as Granger-causality, mutual information, and so on. However, Granger-causality and related methods come with a sever drawback as they specify a linear model of interaction a priori. Mutual information can deal with nonlinear systems from the view of information theory, but it cannot describe the direction of information. Transfer entropy is an effective tool for estimating causal interaction between two systems, without the use of a prior specification of the interaction mechanism itself. In this paper, we proposed a convenient, simple and easy-to-calculate method to estimate the transfer entropy (TE). To verify the efficiency of this approach, we utilized this method to calculate TE values of two simulated time series with nonlinear coupling, and found that the TE value increased with the increment of the coupling strength between the two signals, and decreased with the increasing strength of noise. We further calculated TE values in spectral domain, to estimate the information flow between two systems in a specific frequency band. We generated two signals interacting in a frequency band, and found the TE value was stronger in the frequency band than that out of this frequency band.We also calculated the TE value of LFPs recorded simultaneously from the lateral prefrontal cortex (LPFC) and the striatum of a monkey performing a stimulus-stimulus association task. The results showed that the TE value from the LPFC to the striatum was larger than the TE value from the striatum to the LPFC, consistent with anatomical evidence that prefrontal neurons have direct projections to striatal neurons, but striatal neurons do not Our results demonstrated that the TE was able to correctly estimate the strength of function connectivity and the direction of information flow between areas in the brain network.