In recent years, functional connectivity in the developmental science received increasing attention. Although it has been reported that the anatomical connectivity in the preterm brain develops dramatically during the last months of pregnancy, little is known about how functional and effective connectivity change with maturation. The present study investigated how effective connectivity in premature infants evolves. To assess it, we use EEG measurements and graphtheory methodologies. We recorded data from 25 preterm babies, who underwent longEEG monitoring at least twice during their stay in the NICU. The recordings took place from 27 weeks
The brain can be seen as a complex network of interacting regions and hierarchical communications, which are constrained by the anatomy, but not limited to it [
Different datasets were used. A simulated dataset was also employed in order to show how connectivity analysis performs in a controlled case. In particular, the main objective of the simulation was to illustrate the meaning of the most common graph indices used in the literature. A dataset comprised of EEG signals was the main part of the maturation study.
The first experiment of the study consisted of a simulation based on a linear Gaussian regression model (derived from [
The parameter
The figure displays the graph associated with model (
The second dataset comprised 25 preterm infants, with gestational age (GA) ≤ 32 weeks, who were recruited for a larger EEG study to assess brain development and automatically detect quiet sleep epochs [
The literature about effective connectivity presents different methods to assess coupling among time series, such as
The first method employed to assess the
The second method applied to assess the
With respect to (
The first equation explains
The effective connectivity methods generate an adjacency matrix
An overview of all graph metrics that have been used in the study.
Overview of graph indices  

Path length  Mean of the nodes’ shortest paths 
Clustering coefficient  Mean of the nodes’ triangles intensity around each node 
Diameter  Maximum graph eccentricity 
Causal density  Sum of all significant couplings in 
Spectral radius 

Spectral gap 

Algebraic connectivity 

According to different authors [
In the following paragraphs, the results obtained in both the simulated and the real dataset are discussed. In particular, we will show how the network indices behave in both examples, the simulated data and the EEG maturation dataset. The last part summarizes the predictive power of those graph metrics to infer the
Figures
The figure shows the results for the simulation dataset. (a, b, c) show how the graph indices behave for different level of coupling in model (
Figure
The main integration and spectral features in three discrete time points. The table shows the indices for both sleep states (QS = quiet sleep, NQS = nonquiet sleep) and they were computed on the transfer entropy connectivity graph. The results are reported as median (IQR), where IQR stands for
Network indices: transfer entropy in three age groups  

Median (IQR), PMA weeks  ≤31 

≥37 

Clustering coefficient  
QS  .025 (.008)  .021 (.005)  .017 (.002) 

NQS  .025 (.006)  .020 (.006)  .018 (.002) 

Path length  
QS  3.73 (.30)  3.89 (.22)  4.07 (.10) 

NQS  3.71 (.20)  3.91 (.25)  4.04 (.14) 

Spectral radius  
QS  .18 (.07)  .16 (.05)  .12 (.01) 

NQS  .18 (.05)  .15 (.04)  .13 (.02) 

Spectral gap  
QS  .15 (.09)  .12 (.04)  .10 (.02) 

NQS  .15 (.06)  .12 (.04)  .11 (.02) 



Network indices: transfer entropy, CCA  
Median (IQR)  ≤31 

≥37 



Clustering coefficient  
QS ( 
9.82 (6.1)  6.21 (3.3)  4.98 (0.9) 

NQS ( 
9.13 (3.5)  6.29 (2.0)  5.90 (1.0) 

Path length  
QS  4.70 (.57)  5.11 (.47)  5.32 (.18) 

NQS  4.73 (.40)  5.09 (.27)  5.16 (.18) 

Spectral radius  
QS ( 
8.20 (4.7)  4.68 (3.1)  3.63 (.6) 

NQS ( 
6.94 (2.8)  4.74 (1.6)  4.30 (.7) 

Spectral gap  
QS ( 
5.84 (3.1)  3.93 (2.0)  3.30 (.6) 

NQS ( 
5.84 (3.1)  3.93 (2.0)  3.30 (.6) 

The main integration and spectral features in three discrete time points. The table shows the indices for both sleep states (QS = quiet sleep, NQS = nonquiet sleep) and they were computed on the Granger causality connectivity graph. The results are reported as median (IQR), where IQR stands for
Network indices: Granger causality  

Median (IQR), PMA weeks  ≤31 

≥37 

Clustering coefficient  
QS  .024 (.006)  .019 (.006)  .015 (.002) 

NQS  .024 (.007)  .019 (.005)  .016 (.002) 

Path length  
QS  3.77 (.20)  3.95 (.25)  4.17 (.13) 

NQS  3.75 (.33)  3.95 (.27)  4.10 (.14) 

Spectral radius  
QS  .18 (.06)  .15 (.04)  .10 (.02) 

NQS  .18 (.05)  .14 (.03)  .10 (.01) 

Spectral gap  
QS  .14 (.06)  .13 (.04)  .09 (.02) 

NQS  .15 (.05)  .11 (.03)  .11 (.01) 



Network indices: Granger causality, CCA  
Median (IQR), PMA weeks  ≤31 

≥37 



Clustering coefficient  
QS ( 
12.87 (4.8)  9.34 (3.2)  7.39 (1.2) 

NQS ( 
12.29 (3.4)  9.08 (2.1)  8.51 (1.2) 

Path length  
QS  4.36 (.37)  4.69 (.33)  4.92 (.16) 

NQS  4.41 (.28)  4.71 (.21)  4.77 (.14) 

Spectral radius  
QS ( 
9.52 (3.5)  6.79 (2.6)  5.28 (.8) 

NQS ( 
8.98 (2.5)  6.50 (1.5)  6.05 (.9) 

Spectral gap  
QS ( 
7.28 (2.4)  5.87 (2.3)  4.91 (1.1) 

NQS ( 
6.91 (3.0)  6.07 (1.0)  5.35 (1.4) 

Multivariate regression model performances. The table shows the error on the test set (Error),
Multivariate regression performances  

Median (IQR)  Error (weeks) 



Simple filtering  
TE, QS  2.54 (0.41)  0.57 (0.07)  11.64 (3.46) 

TE, NQS  2.88 (0.39)  0.40 (0.07)  6.23 (1.72) 






GC, NQS  2.79 (0.53)  0.44 (0.07)  7.20 (2.09) 



CCA  
TE, QS  2.23 (0.29)  0.63 (0.06)  12.90 (3.14) 

TE, NQS  2.54 (0.51)  0.57 (0.06)  10.36 (2.66) 






GC, NQS  2.35 (0.42)  0.63 (0.04)  13.38 (2.61) 

The figure shows the results for EEG data. (a, b, c, d) show OLS regression between 4 main graph indices versus the age (PMA in weeks) for GC in QS. The grey area is the confidence interval at
The figure shows the average connectivity graph (GC for three different age groups). The strength of the coupling among the electrodes is decoded by the color (the closer to the red color, the higher the coupling) and by the width of the arrow. The connectivity values have been normalized between 0 and 1 for the three groups together. The panels clearly show the weakening of the coupling among EEG channels with maturation. The consequence is the increase of path length and the decrease of the clustering coefficient (Figure
In the present study, we quantified the effective brain connectivity in preterm infants to track their maturation. Although there are some studies that investigate connectivity in the neonates [
According to [
In the literature, a number of studies can be found to have assessed the brain maturation in children and adolescents by graph theory [
In the present study, we investigated effective EEGbased brain connectivity in premature infants, whose PMA ranged from 27 to 42 weeks. Results showed that the EEGgraphs changed with age in terms of topology. In particular, the clustering coefficient and the spectral radius decreased with maturation, while the path length increased. This perspective suggests that the EEG graph shifted from a smallworld network to a random network. This apparent nodes’ segregation can be a consequence of the thalamocortical connections development and the strengthening of the longrange cortical connections. The lowest ageprediction error was 2.11 PMA weeks (obtained with GC in QS), which is in line with literature results. Application of source filtering methods, like CCA, can improve the performance of the connectivity analysis.
This paper reflects only the authors’ views and the Union is not liable for any use that may be made of the contained information.
The authors declare that there are no conflicts of interest regarding the publication of this paper. The received funding stated in the Acknowledgments does not lead to any conflicts of interest.
This research is supported by Bijzonder Onderzoeksfonds KU Leuven (BOF): The Effect of Perinatal Stress on the Later Outcome in Preterm Babies (no. C24/15/036); iMinds Medical Information Technologies (SBO, 2016); Belgian Federal Science Policy Office, IUAP no. P7/19/(DYSCO, “Dynamical Systems, Control and Optimization,” 2012–2017); Belgian Foreign AffairsDevelopment Cooperation (VLIR UOS Programs (2013–2019)); and EU: the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Advanced Grant: BIOTENSORS (no. 339804). A. Caicedo is a post doc fellow at Fonds voor Wetenschappelijk OnderzoekVlaanderen (FWO), supported by Flemish government. M. Lavanga is a SB Ph.D. fellow at Fonds voor Wetenschappelijk OnderzoekVlaanderen (FWO), supported by Flemish government.