Resting-state directed brain connectivity patterns in adolescents from source-reconstructed EEG signals based on information flow rate

Quantifying the brain’s effective connectivity offers a unique window onto the causal architecture coupling the different regions of the brain. Here, we advocate a new, data-driven measure of directed (or effective) brain connectivity based on the recently developed information flow rate coefficient. The concept of the information flow rate is founded in the theory of stochastic dynamical systems and its derivation is based on first principles; unlike various commonly used linear and nonlinear correlations and empirical directional coefficients, the information flow rate can measure causal relations between time series with minimal assumptions. We apply the information flow rate to electroencephalography (EEG) signals in adolescent males to map out the directed, causal, spatial interactions between brain regions during resting-state conditions. To our knowledge, this is the first study of effective connectivity in the adolescent brain. Our analysis reveals that adolescents show a pattern of information flow that is strongly left lateralized, and consists of short and medium ranged bidirectional interactions across the frontal-central-temporal regions. These results suggest an intermediate state of brain maturation in adolescence.


Introduction
neuronal networks. EEG studies have been extensively used to infer the nature of the functional 48 connectivity --i.e. the linear or nonlinear statistical interdependence between the electrical activity 49 in the different brain regions (Stam and Van Straaten, 2012) -during resting state or during task 50 related activities. In this paper, we focus our attention on the former. 51 The resting-state or persistent background activity, previously dismissed as background noise, 52 has been shown to comprise coherent patterns of functional connectivity and appears to play a 53 critical role in mediating complex functions such as memory, language, speech and emotional 54 states (Raichle et al., 2001; Raichle and Mintun, 2006). There has been considerable progress in 55 mapping out the key resting-state functional brain networks as well as tracking how they change 56 over development. These functional connectivity studies indicate that the resting-state brain 57 networks are sparsely connected in childhood (Fair et al., 2008) and evolve towards increased 58 connectivity in adolescence (Smit et al., 2012). However, a more complete description remains 59 elusive. For one, very little is known about how information flows within these networks, and how 60 these flow patterns change with maturation. 61 Several different approaches are in use for quantifying the brain's effective connectivity. Struc-62 tural approaches such as Structural Equation Modeling (SEM) (McLntosh and Gonzalez-Lima, 1994) 63 and Dynamic Causal Modeling (Friston et al., 2003) involve a neuranatomical model of the brain 64 and a connectivity model. Other measures are data-driven and involve a statistical model, such using the information flow rate, in order to identify connectivity patterns in the adolescent brain. 83 Only one prior study that focuses on this age group is available in the literature, and the connectivity 84 analysis in that study is carried out in sensor space (Marshall et al., 2014). 85 The information flow rate was developed by Liang using the concept of information entropy 86 and the theory of dynamical systems (Liang, 2008(Liang, , 2013b(Liang, , 2014(Liang, , 2015 and based on earlier work 87 with Kleeman (Liang and Kleeman, 2005). While the the initial formulation of the information flow 88 rate was derived for two-dimensional (bivariate) systems, Liang (2016,2018) recently showed that 89 the formulation is also valid for -dimensional systems as well. The Liang-Kleeman coefficient can 90 measure the transfer of information between time series at different locations and thus between 91 different brain regions. Unlike empirical measures of causality, e.g., transfer entropy and Granger 92 causality, the information flow rate is derived from general, first-principles equations for the 93 time evolution of stochastic dynamical systems (Liang, 2016(Liang, , 2018. Owing to its definition, which 94 involves only the time series and their temporal derivatives (or their finite-difference approximations 95 for discretely sampled systems), the information flow rate has computational advantages over 96 other entropy-based measures such as transfer entropy, that require the estimation of additional 97 information (e.g., conditional probabilities) from the data. In addition, the information flow rate 98 concept does not require stationarity (Liang, 2015) or a specific model structure, and can also be 99 applied to deterministic nonlinear systems (Liang, 2016). These are important advantages, since information flow rate instead of the non-normalized → , because we aim to capture interactions 174 between brain regions that significantly affect the receiver region (denoted by the index ). The 175 advantage of → is its ability to measure the relative importance of causal relations (Liang, 2015). 176 We use the second-neighbor differencing scheme (i.e., = 2, see Box 1) to calculate the informa-177 tion flow rates as suggested by Liang (2014). We further comment on this choice in Materials and 178 methods (section on the impact of differencing scheme). 179 Our analysis focuses on the mean information flow rate calculated over all the individuals in the 180 study cohort, but we also explore variations of connectivity between individuals. 181 Brain connectivity based on mean information flow rate 182 To study the information flow across brain regions we want to characterize connections that exhibit 183 significant levels of activity (as measured by the information flow rate) over all the individuals. We  wherê , is the sample cross-covariance of the series and , and̂ = √̂ , is the sample standard deviation of the series ( = 1, … , ). Botĥ , and̂ , (often used to measure functional connectivity) are non-directional and symmetric under the index interchange ⇆ . The sample cross-covariancê , is defined bŷ where the "overline" denotes the sample time average, i.e., wherê , is the sample covariance of the time series and the first derivative, d ∕d , of the series . Due to the discrete nature of sampling, the first derivative d ∕d is unknown a priori.
Hence, a finite difference approximation based on the Euler forward scheme, with a time step equal to Δ , is used, i.e., The differencing orders = 1 and = 2 are the two most common choices (Liang, 2013a) which we also consider herein. Herein we refer to as the transmitter series and to as the receiver series with respect to → .
We adopt the term transmitter instead of "source" for the series that "sends" information in order to avoid confusion, since all the time series represent current dipole moments obtained from scalp EEG by means of source reconstruction. for selecting a threshold value above which connections are considered important (Cohen, 2014). 204 Hereafter, we will consider that a connection → between two dipoles is active in the ensemble 205 sense if the magnitude of the normalized information flow rate | → | exceeds the arbitrary threshold 206 of = 0.05. This means that the entropic rate of change at the receiver due to its interaction 207 with the transmitter located at is at least 5% of the total rate of entropy change at . The latter involve only connections such that → ≥ 0.05. As evidenced in this plot, 92 out of the 210 211 inter-dipole pairs are connected on average, i.e., they exhibit → ≥ .

212
The top thirty (30) active connections, ranked on the basis of → , are listed in Table 1  The last column of       rates of individuals is by counting for how many individuals each connection is active. Hereafter, we 230 will consider that a connection → between two dipoles is individually active if the magnitude of the 231 normalized information flow rate | → | exceeds the threshold , which means that the percentage 232 of the total entropy rate of the receiver due to its interaction with the transmitter is at least 5%. We 233 assume that the threshold for individually active connections is the same as the threshold used for 234 the ensemble mean of the information flow rate. However, this is not necessary in general. 235 We define the frequency of activity, → ( ), for the connection → as the number of individuals 236 in the study cohort for which the specific connection is active. Hence, where (⋅) is the unit step function, i.e., To study the information flow across brain regions in individuals, we focus on the individually active 254 source dipole pairs. As stated above, these are dipole pairs with → whose magnitude (absolute      The maximum → observed among individuals is ≈ 0.36. This is about three times higher than 273 the highest ensemble mean → which is equal to 0.116 (cf. Table 1 (Liang, 2008, 2013b,a, 2014). However, the information flow 385 formalism can be derived using either absolute or relative entropy. In two dimensions (i.e., for a  (Muetzel et al., 2016). 488 The fact that both functional and effective connectivity changes as the brain matures is not 489 entirely surprising. It is well known that the brain undergoes considerable structural changes during regions of the brain, continues well into the twenties. Functionally, these long association fibers are 498 correlated with increasing long-range EEG coherence and synchronization (Miskovic et al., 2015). 499 Finally, we have also identified significant variability of effective connectivity between individuals 500 based on the patterns of information flow rate between brain regions. We have presented and 501 discussed graphical tools for visualizing and characterizing variability between individuals including 502 dipole-dipole connectivity plots that account for all the individuals in the cohort, e.g., Figure 8. The the connectivity matrix between individuals is not due to noise but is associated with individual 507 variances in mental/vigilance states and cognitive function. They also note that there are reports 508 of the temporal dynamics of the connectivity matrix being affected by brain health, which raises 509 the exciting possibility that, in the future, the associated features could serve as disease/injury 510 biomarkers. The significant advantages of the new data-driven measure of effective brain connectiv-511 ity discussed in this paper (i.e., ease of calculation, sensitivity to both linear and nonlinear relations, 512 independence from a specific model structure and the stationarity assumptions), make it especially 513 well suited for exploring these exciting new directions.

515
In this section we briefly describe the EEG dataset. We then present the Liang-Kleeman directional 516 information flow rate that will be used for the analysis of resting-state EEG brain connectivity. We 517 also discuss how to numerically calculate and evaluate the statistical significance of the information 518 flow rate obtained from the EEG data.  ., 2002). The interpolation offers a consistent way of dealing with occasional bad channels 551 while maintaining a common montage across all the individuals. Thereafter, we use the BESA 552 montage method (Scherg et al., 2002) to compute source waveforms. Since resting-state activity 553 is not localized, we used the BR_Brain Regions montage which is derived from 15 pre-defined 554 regional sources that are symmetrically distributed over the entire brain. The respective brain 555 regions involved in this montage are listed in Table 2 and shown in Figure 2. BESA uses a linear 556 inverse operator of the lead field matrix, which accounts for the topography of the sources included 557 in the BR_Brain Regions montage, to calculate the source waveforms (Scherg et al., 2002). The 558 composite source activity in each brain region is represented by a single regional source. Each 559 source is modeled as a current dipole whose moment is specified in terms of a local orthogonal In order to infer connectivity patterns, it is necessary to know if the estimated values → are 665 statistically significant. Each estimate of an inter-dipole → is a statistic, i.e., a random variable that 666 fluctuates between samples. If the sampling distribution of the statistic is known, the significance 667 of a particular estimate can be assessed using a suitably constructed parametric statistical test. 668 In the case of → such a test can be constructed (Liang, 2014  the inter-dipole information flow rates calculated from the EEG data, we find that all except for 11 694 out of the 210×32=6720 dipole pairs show information flow rates outside the above interval. In fact, 695 the majority of the normalized information flow rates are two orders or more higher in magnitude. 696 Hence, given the size of the above confidence interval, we can conclude that most of the observed 697 → are statistically significant even at the = 0.1% level. 698 The above result indicates a low-level global connectivity linking most of the brain regions in the 699 resting state. However, small normalized information flow rates, albeit statistically significant, imply studies. Hence, we did not consider values of higher than two. 713 We have experimented with synthetic data obtained from the simulation of two coupled stochas-714 tic differential equations for which → admits explicit expressions (Liang, 2014). We used similar 715 length = 60000 − 80000) for the synthetic time series as that of the EEG series and a number of 716 repetitions equal to the number of individuals in the study ( = 32). Our results show practically no 717 difference between the mean → estimated from the time series whether = 1 or = 2 is used. 718 In the case of the source-reconstructed EEG data, we repeated the entire analysis using = 1.