Effective brain connectivity for fNIRS data analysis based on multi-delays symbolic phase transfer entropy

Recently, effective connectivity (EC) calculation methods for functional near-infrared spectroscopy (fNIRS) data mainly face two problems: the first problem is that noise can seriously affect the EC calculation and even lead to false connectivity; the second problem is that it ignores the various real neurotransmission delays between the brain region, and instead uses a fixed delay coefficient for calculation.

To overcome these two issues, a delay symbolic phase transfer entropy (dSPTE) is proposed by developing traditional transfer entropy (TE) to estimate EC for fNIRS. Firstly, the phase time sequence was obtained from the original sequence by the Hilbert transform and state-space reconstruction was realized using a uniform embedding scheme. Then, a symbolization technique was applied based on a neural-gas algorithm to improve its noise robustness. Finally, the EC was calculated on multiple time delay scales to match different inter-region neurotransmission delays.

A linear AR model, a nonlinear model and a multivariate hybrid model were introduced to simulate the performance of dSPTE, and the results showed that the accuracy of dSPTE was the highest, up to 74.27%, and specificity was 100% which means no false connectivity. The results confirmed that the dSPTE method realized better noise robustness, higher accuracy, and correct identification even if there was a long delay between series. Finally, we applied dSPTE to fNIRS dataset to analyse the EC during the finger-tapping task, the results showed that EC strength of task state significantly increased compared with the resting state.

The proposed dSPTE method is a promising way to measure the EC for fNIRS. It incorporates the phase information TE with a symbolic process for fNIRS analysis for the first time. It has been confirmed to be noise robust and suitable for the complex network with different coupling delays.