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This protocol is extracted from research article:

NetDI: Methodology Elucidating the Role of Power and Dynamical Brain Network Features That Underpin Word Production

**
eNeuro**,
Jan 5, 2021;
DOI:
10.1523/ENEURO.0177-20.2020

NetDI: Methodology Elucidating the Role of Power and Dynamical Brain Network Features That Underpin Word Production

Procedure

DI was estimated in a model free manner using the computationally efficient Kraskov, Stögbauer, and Grassberger (KSG) estimator (Kraskov et al., 2004; Gao et al., 2018), which is based on a k-nearest neighbors (kNN) approach to measuring mutual information (MI). DI was estimated between every pair of channels in each SA and AA time window in a data-driven manner. Every trial was considered to be an independent sample path of an unknown underlying random process, and pairwise DI was estimated using all the trials in a given window. Given two raw time series from a pair of electrodes ${X}_{1}^{N}=\{{X}_{1},{X}_{2},.\hspace{0.17em}.\hspace{0.17em}.\hspace{0.17em},{X}_{N}\}$ and ${Y}_{1}^{N}=\{{Y}_{1},{Y}_{2},.\hspace{0.17em}.\hspace{0.17em}.\hspace{0.17em},{Y}_{N}\}$, where ${X}_{i},{Y}_{i}\in \mathbb{R}$, DI from ${X}_{1}^{N}$ to ${Y}_{1}^{N}$ is denoted as $I({X}_{1}^{N}\to {Y}_{1}^{N})$, and is defined as the following:

where the right hand side of Equation 2 is the conditional MI between time series ${X}_{1}^{i}$ and single sample point *Y _{i}*, conditioned on the past

Also, a conditional differential entropy term can be expressed as a difference of two differential entropies:

From Equations 2, 4, DI can be expanded as the following:

Each entropy term in Equation 5 was estimated using the KSG estimator (Kraskov et al., 2004), which uses a kNN approach, similar to the methodology described in Murin (2017). The implementation of DI was written in MATLAB using the kNN tools from Trentool (Lindner, 2011; Lindner et al., 2011). ECoG data were assumed to be Markovian of order *m*, i.e., samples only depend on the past *m* samples. Based on a non-parametric method of estimating memory order for ECoG (Murin et al., 2019), and from other similar work (Malladi et al., 2016; Murin et al., 2016), a memory order of 150 ms was used, achieved by using downsamples of the data for estimation. The final equation used for estimation of DI rate $\widehat{I}({X}_{1}^{\stackrel{~}{N}}\to {Y}_{1}^{\stackrel{~}{N}})$ is given by:

where *m* is the number of past samples, $\stackrel{~}{X}$ and $\stackrel{~}{Y}$ are the downsampled versions of *X* and *Y*, respectively, $\widehat{h}$’ s are the estimated differential entropies, and $\stackrel{~}{N}$ is the length of the downsampled signal.

This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International license, which permits unrestricted use, distribution and reproduction in any medium provided that the original work is properly attributed.

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