Abstract

This work aims at assessing the maturational changes in the interdependence between the activities of different cortical areas in neonates during active sleep (AS) and quiet sleep (QS). Eight electroencephalography (EEG) channels were recorded in 3 groups of neonates of increasing postmenstrual age. The average linear (AVL) and average nonlinear (AVN) interdependencies of each electrode region with the remaining ones were calculated using the coherence function and a recently developed index of nonlinear coupling between 2 signals in their state spaces, respectively. In theta band, AVL increased with neonate's age for central and temporal regions during QS. In beta band, AVL increased for most cortical regions during QS and a parallel decrease of AVL with neonate's age was found during AS. For all regions, beta AVL was greater in AS than in QS in preterm neonates but the reverse happened in older term neonates. Contrarily to AVL, AVN decreased with age during QS for most cortical regions. Surrogate data test showed that the interdependencies were nonlinear in preterm and younger term neonates but in older term both linear and nonlinear interdependencies coexisted. It is concluded that neonatal maturation is associated with changes in the magnitude and character of the EEG interdependencies during sleep.

Introduction

During a neonate's first months of life, the electroencephalography (EEG) constitutes a valuable tool for the evaluation of the degree of brain maturity because in this ontogenical period the signal presents major changes (Mizrahi and others 2004). The quantification of such changes is relevant from the diagnostic point of view, because they are characteristic of the process of cerebral maturation, and hence, can provide information about its alterations. Quantitative EEG analysis based on spectral measures is a good candidate for such aim, as it has proved useful as a noninvasive method to assess cerebral damage (Thakor and Tong 2004). In addition, recent results suggest that quantitative EEG may be more effective than some methods of diagnosis for image in the detection of anomalies in the cerebral function of neonates (Mandelbaum and others 2000). As a result, several frequency domain measures have been used to assess the degree of neonate's maturation from the EEG. For instance, a recent work (Burdjalov and others 2003) proposes a method based on the integrated EEG amplitude of the parietal electrodes P1 and P3. Other authors (Holthausen and others 2000) reported an index of neonatal maturation based on the spectral amplitudes of various frequency bands (δ, θ, and β/θ ratios), whereas Scher and others (2003) have used the power in these bands as well as spectral correlations between central and parietal regions to establish differences between premature and full-term neonates.

Despite their usefulness, all these methods present the drawback of assuming a linear behavior of the EEG activity and hence, they take into account only its more regular variations. But the EEG is a complex, irregular signal, and other procedures of analysis that take into account these characteristics might be used to better characterize it (Quian Quiroga and others 2002; David and others 2004). In this line, the application of nonlinear time series analysis has been useful to study neonate's maturation from EEG records. For instance, the correlation dimension (a measure of the signal complexity or irregularity) calculated from the waking EEG, increased with age from neonates to adults (Meyer-Lindenberg 1996) and within neonates of increasing age during active sleep (AS) and quiet sleep (QS) (Scher and others 2005; Pereda and others 2006). As far as multivariate analysis concerns, nonlinear methods have been useful to assess the interdependence between the EEG signals of different brain areas in both neonates (Pereda and others 2003) and adult subjects (Pereda and others 2001; Terry and others 2004) during sleep, which suggests the usefulness of these methods to study changes in cortical connectivity from this signal.

As the EEG is a signal that reflects the integrated brain activity, it seems sensible to use multivariate analysis techniques to establish how the interdependence between different brain areas changes during maturation. On the other hand, neonatal EEG records are quite irregular during both AS and QS and exhibit, during QS and in the period of postmenstrual age (PMA) ranging from 36 to 38 weeks until about 44 weeks, the pattern of relatively short-duration called “tracé alternant” (see, e.g., Mizrahi and others 2004). In addition, neonate EEG changes its morphology from one electrode to another as well as from premature to full-term neonates (Mandelbaum and others 2000; Pereda and others 2003, 2006; Scher and others 2003). In consequence, our objective is 2-fold: on the one hand, we aim at determining whether neonate's maturation is accompanied by changes in the magnitude and nature of the global interdependence between the activities of each cortical area and the remainder during sleep; on the other hand, we try to get insight into the usefulness of multivariate techniques to assess the maturational process in neonates as a method that might help in the detection of neonatal neurological disorders. We demonstrate that the simultaneous use of multivariate linear and nonlinear interdependence measures is relevant to detect dynamical changes in the structure of the sleep EEG activity during neonate's maturation.

Materials and Methods

Data Recording and Preprocessing

Polysomnographic records of 21 healthy neonates were obtained during approximately one hour between 12:00 and 14:00 PM in a quiet, soundproofed, and temperature-controlled room. All subjects were neurologically normal at the time of the record and showed normal psychomotor development at follow up. They were divided into 3 groups of 7 subjects each according to their PMA (Engle 2004), taking into account previous studies (Duffy and others 1990; Huppi and others 1996; Scher 1997) that reported evidences of altered brain development in preterm neonates when comparing with term neonates of similar PMA. Thus, the 3 groups of neonates are group 1, preterm neonates (32 weeks (w.) ≤ PMA < 37 w., average: 35.2 ± 0.9 w.); group 2, young term neonates (37 w. ≤ PMA < 42 w., average: 39.5 ± 0.8 w.); and group 3, older term neonates (42 w. ≤ PMA < 47 w., average: 45.1 ± 0.7 w.).

After obtaining informed written consent from the neonates' parents or legal tutors, 8 monopolar EEG channels (average as reference) were recorded from each subject from electrodes located at Fp1, Fp2, C3, C4, T3, T4, O1, and O2 sites according to the International 10–20 System of Electrode Placement modified for recording neonates (Mizrahi and others 2004) (0.5- and 30-Hz high- and low-pass frequency filters, 128-Hz sampling frequency). The entire experimental protocol was approved by the University's Ethical Committee and was conducted in accordance with the Declaration of Helsinki.

The choice of a proper reference is very important in EEG studies using the coherence function, and this issue has been addressed in several works (see, e.g., Rappelsberger 1989; Nunez and others 1997, 1999, and references therein). Their main conclusion regarding the use of average reference is that it provides a reliable, partly independent measure of neocortical dynamical function in those cases—such as the neonates—where a high degree of coherent activity across the scalp is not likely to be present. Indeed, previous studies in neonates (Eiselt and others 2001; Pereda and others 2003, 2006) also indicate that this reference produces reliable results that are reproducible by using, for example, bipolar noncephalic common reference derivations and can be used to compare the degree of cortical integration across different situations.

The first preprocessing stage consisted of rejecting all the segments showing artifacts, which was carried out by using a 2-step procedure: first, the segments were visually inspected by an expert neurophysiologist and those presenting artifacts, which were apparent by the naked eye, were removed. Then, the remaining segments were automatically analyzed, and those presenting more than a 5% of samples out of the range mean ± 3 standard deviations (SDs) were also discarded. The rest of the segments were manually scored as AS and QS by using the chin electromyogram (EMG), the electrooculogram, the respiration, and the electrocardiogram (ECG) as auxiliary signals from the polysomnographic records following standardized techniques in neonates (Anders and others 1971). A segment was considered AS if it presented low-to-moderate voltage, continuous EEG pattern with rapid eye movements, irregular respirations and cardiac rate, decreased chin EMG activity, and quick irregular movements of the fingers, hand, or face; it was considered QS if it presented an absence of lateral eye movements, increased chin EMG activity, and regular respirations and ECG. Only those segments univocally identified as belonging to any of these 2 states were included in the analysis.

As the EEG is an intrinsically nonstationary signal, some criterion must be defined to select sufficiently stationary segments for the analysis. With this aim, the previously scored segments were divided into nonoverlapping subsegments of 1 s. Then, in each subsegment, the mean and the SD of the corresponding 128 samples were calculated. For each epoch of 16 consecutive subsegments (2048 samples), the variance of the 16 means (σMEAN2) and that of the 16 SD (σSD2) were calculated. The 5 epochs showing the lowest joint variance (i.e., the lowest value of the sum of (σMEAN2) and (σSD2) for the 8 EEG channels) were selected during both AS and QS. By using this criterion of weak stationarity, we reach a trade off between stationarity and the length of each segment in agreement with previous works (Pereda and others 1999, 2003, 2006). The selected segments were then detrended by subtracting from the data a second-order polynomial previously fitted by the least-squares method and finally normalized to zero mean and unit variance.

Assessment of the Linear Interdependencies

To study the linear interdependencies within the cortex, we used the coherence function, also termed as the magnitude square coherence. It is a symmetric measure of the linear correlation between 2 signals as a function of the frequency, which ranges from 0 (independent signals) to 1 (completely linearly dependent signals). Thus, it is a useful tool for the quantitative study of the synchronization between EEG channels in different frequency bands and can be interpreted as a linear measure of the functional coupling between different brain cortical areas that depend mainly on structural connections (Tucker and others 1986; Ruchkin 2005).

The coherence function between 2 EEG channels i and j (i, j = 1, …, 8; ij) is defined as 

(1)
graphic
where Cij(f) is the cross spectrum between both signals (i.e., the power that both signals have in common at the considered frequencies), Cii(f) and Cjj(f) are the respective auto spectra, f are the discrete frequencies where the coherence function is calculated, and <•> represents ensemble average. The coherence function was estimated using the Welch's averaged periodogram method, considering segments of 256 data tapered with a Hanning window with a 62.5% of overlap, and then averaged in the EEG frequency bands δ (0.5–3.9 Hz), θ (4–7.9 Hz), α (8–12.9 Hz), and β (13–30 Hz).

The mean coherence between each electrode, i = 1, …, 8, and the others, which reflects the functional coupling between each brain cortical area and the remaining ones, is 

(2)
graphic

For each neonate, the global average coherence (average linear [AVL]) used in the analysis was the average of the 5 CFi(f) values obtained for the 5 selected EEG segments.

Nonlinear Interdependence Measure

An alternative approach for measuring the interdependence between 2 signals makes use of their reconstructed state spaces. Thus, from the time series X and Y simultaneously measured for EEG channels i and j (i, j = 1, …, 8; ij), we first reconstructed their state spaces by using Takens' method (Takens 1980) to form delayed state vectors such as the following ones: 

graphic
 
(3)
graphic
where N′ is the total number of vectors, m is the embedding dimension—chosen as the dimension for which the percentage of false nearest neighbors was lower than 5%—and τ is the delay time—chosen as the first minimum of the mutual information function—(for details on how to choose these embedding parameters, see, e.g., Pereda and others 2003; Stam 2005). As the values of these parameters presented small differences among the situations (e.g., τ was normally greater for QS than for AS), we took for all the segments the maximal values m = 7 and τ = 10 to avoid any possible bias in the calculation of the nonlinear indexes due to a different number of reconstructed vectors in each segment (Pereda and others 2001).

Rulkov and others (1995) have demonstrated that if 2 systems synchronize, there exists a functional relationship between their state spaces, whereby state vectors that are close in one of the state spaces are simultaneous to vectors of the other space that are also close to each other. Although this work only dealt with nonlinear chaotic systems with unidirectional coupled, the concept has been afterward extended to study the interdependence between real-life systems from the signals they generate (see, e.g., Quian Quiroga and others 2002). Thus, this result has been successfully used in EEG studies to assess the interdependence between cortical brain areas by means of different indexes, in applications such as epilepsy (Arnhold and others 1999), schizophrenia (Breakspear and others 2003), working memory tasks (Stam and others 2002), visual imaginary (Bhattacharya and Petsche 2005), and sleep studies (Pereda and others 2001, 2003), to name a few. In this work, we make use of one of these indexes, N(X|Y), that has shown to be robust against noise and relatively insensitive to the complexity of the individual signals (Quian Quiroga and others 2002), 2 features that are very useful in EEG analysis (see., e.g., Pereda and others 2001). This index measures the interdependence of channel X on channel Y from their reconstructed state spaces and is defined as 

(4)
graphic
where Rn(X) is the mean squared Euclidean distance of all the state vectors X to the nth reference vector, forumla, and Rn(k)(X|Y) is the mean squared Euclidean distance of that reference vector to its k mutual neighbors. The mutual neighbors of forumla are those state vectors of X bearing the same time indexes of the nearest neighbors of forumla As outlined above, in the presence of synchronization they are closer to the reference vectors than the average (Rulkov and others 1995) so that the index is positive (the greater the synchronization, the greater its value). On the other hand, if the signals are independent, Rn(k)(X|Y) ≈ Rn(X) and the index is very close to 0. The dependence of Y on X, N(k)(Y|X), can be assessed in complete analogy.

The index N(Y|X) is sensitive to both linear and nonlinear interdependencies and asymmetric, that is, in general, N(X|Y) ≠ N(Y|X), with N(X|Y) < N(Y|X) indicating that Y depends more on X (i.e., X influences more on Y) than vice versa. From these 2 bivariate indexes, we calculated the global indexes N(X|ALL Y) and N(ALL Y|X)—which reflect how a brain area (X) is influenced by and influences on the remaining ones (ALL Y), respectively—and the average global nonlinear interdependence (average nonlinear [AVN]) in analogy with equation (2) and the AVL, respectively.

The aforementioned features of N(X|Y), that is, its sensitivity to both linear and nonlinear correlations and its asymmetry, make it a valuable tool for the study of EEG interdependencies. Indeed, the correlations between EEG signals mediated by neuronal coupling, which reflect brain functional connectivity, can be linear or nonlinear in nature (Pereda and others 2001; Stam 2005). Moreover, the index N allows identifying the existence of asymmetric interdependence between 2 brain cortical areas, with N(X|Y) ≠ N(Y|X) suggesting that X influences on Y with a different strength than vice versa.

It is important to note that the AVN index is obtained from nonlinear interdependence indexes calculated in the state space by considering the signal as a whole and is able to assess the interaction (if any) between different frequencies of 2 electrode sites (the so-called cross-frequency synchronization [Palva and others 2005]). The relationship between different frequencies is one of the characteristics of nonlinear interdependence between 2 signals, which cannot be captured by the coherence function (AVL), and would remain undisclosed if we filtered the signals in a given band before calculating the nonlinear indexes.

Surrogate Analysis

Univariate Surrogates

Theoretic results have shown that the difference between N(X|Y) and N(Y|X) might also depend, in addition to the asymmetric nature of coupling, on the differences in structures of individual signals (Quian Quiroga and others 2000; Pereda and others 2001). To test the significance of the indexes as well as the nature (linear or nonlinear) of the interdependencies, we use multivariate surrogate data (Pereda and others 2001, 2003; Andrzejak and others 2003) (see Fig. 1). Thus, we checked that the values of the nonlinear index were measuring the interdependence between 2 EEG signals by comparing, for each pair of electrodes (e.g., O1 and O2), the value of N estimated from the original data with those obtained from univariate surrogate data pairs. In these pairs, one of the EEG signals (say, O2) remains unchanged, whereas the other one (O1) is replaced by surrogate signals preserving all its linear structure but completely independent from the other one. The following Z-score is then obtained: 

(5)
graphic
where Nor is the value of the index for the original pair of data and forumla and σs,u are the mean and the SD, respectively, of the set of indexes calculated from 19 univariate surrogate pairs. We consider that N(O2|O1) was measuring the dependence of O2 on O1—at the 95% level of confidence—if equation (5) was greater than 2 (Schreiber and Schmitz 2000). The topside of the blank box in Figure 1 (left) represents this threshold. The significance of N(O1|O2) was tested accordingly by keeping O1 unchanged and surrogating O2.

Figure 1.

Left: Two EEG channels (electrode O1 [solid line] and O2 [dashed line]) from a neonate of group 3 (older neonates) during AS. (A) Original segments. (B) The O1 segment has been replaced by one of its surrogates, producing a univariate surrogate pair where the interdependence has been destroyed. (C) Both segments have been replaced by one of their surrogates, producing a bivariate surrogate pair that preserves the linear interdependence. Right: The circles are the nonlinear interdependence index N(O2|O1) from the original segments (A), as well as its mean value for 19 univariate pairs such as (B) and 19 bivariate pairs such as (C). The boxes stand for 2 SDs of the mean. As the original N is above the topsides of both boxes, interdependence is considered significant and nonlinear at the 95% level of confidence.

Figure 1.

Left: Two EEG channels (electrode O1 [solid line] and O2 [dashed line]) from a neonate of group 3 (older neonates) during AS. (A) Original segments. (B) The O1 segment has been replaced by one of its surrogates, producing a univariate surrogate pair where the interdependence has been destroyed. (C) Both segments have been replaced by one of their surrogates, producing a bivariate surrogate pair that preserves the linear interdependence. Right: The circles are the nonlinear interdependence index N(O2|O1) from the original segments (A), as well as its mean value for 19 univariate pairs such as (B) and 19 bivariate pairs such as (C). The boxes stand for 2 SDs of the mean. As the original N is above the topsides of both boxes, interdependence is considered significant and nonlinear at the 95% level of confidence.

Bivariate Surrogates

Following a similar line of reasoning, it is possible to test whether the measured interdependence was nonlinear by calculating the following Z-score: 

(6)
graphic
with Nor as above, and where forumla and σs,b are the mean and the SD, respectively, of the set of indexes calculated from 19 bivariate surrogate pairs, which are constructed in such a way that they preserve the linear interdependencies between the original signals (i.e., the coherence function) but devoid of any nonlinear interdependency (if any) (Prichard and Theiler 1994). As with equation (5), if equation (6) is greater than 2 (topside of the solid box in Fig. 1, left), we can reject—at the 95% level of significance—the hypothesis that the 2 signals are linearly correlated bivariate time series (Andrzejak and others 2003).

In all cases, surrogate signals were generated using the Iterative Amplitude Adjusted Fourier Transform algorithm, which presents a good trade off between statistical accuracy and computational cost (Schreiber and Schmitz 2000).

Statistical Comparisons

An analysis of variance test for repeated measures (with a Scheffé post hoc test and Bonferroni corrections for multiple comparisons) was used to check for differences among the 3 groups and the 2 sleep states, with the group as independent factor and the sleep state as dependent factor. Global differences were considered significant if P < 0.05.

Results

AVL Interdependence

The average coherence AVL was calculated in the δ, θ, α, and β frequency bands. Only the coherence in the θ and β bands presented differences with the PMA. Significant statistical differences between groups 1 and 2 and groups 1 and 3 are shown in the Figures.

θ Band

The results of AVL in θ band are shown in Figure 2. Significant changes with the PMA were only found for electrodes C3, T3, and T4.

Figure 2.

Average coherence (±95% confidence interval) between each electrode and the remaining ones (AVL) in the θ band during AS and QS for the groups 1 (G1), 2 (G2), and 3 (G3). Asterisks stand for the statistical significance of the difference between groups 2 or 3 and group 1 in both AS and QS (***P < 0.001; **P < 0.01; *P < 0.05). Top: Electrodes of the right hemisphere. Bottom: Electrodes of the left hemisphere. Electrodes: Fp1, Fp2 (frontopolar), C3, C4 (central), T3, T4 (temporal), and O1, O2 (occipital).

Figure 2.

Average coherence (±95% confidence interval) between each electrode and the remaining ones (AVL) in the θ band during AS and QS for the groups 1 (G1), 2 (G2), and 3 (G3). Asterisks stand for the statistical significance of the difference between groups 2 or 3 and group 1 in both AS and QS (***P < 0.001; **P < 0.01; *P < 0.05). Top: Electrodes of the right hemisphere. Bottom: Electrodes of the left hemisphere. Electrodes: Fp1, Fp2 (frontopolar), C3, C4 (central), T3, T4 (temporal), and O1, O2 (occipital).

During QS, we found an increase with PMA for these electrodes, for which AVL was greater in group 3 than in group 1, but no difference was found between groups 2 and 1 except for C3, in which coherence was lower in the preterm group.

During AS, AVL increased with PMA for T3 (from group 1 to group 3).

QS versus AS comparisons: AVL during QS was greater than during AS in group 1 for C4 and T4 (P < 0.01 for both electrodes) and in group 3, for C3 (P < 0.05), O2 (P < 0.01), C4, T3, and T4 (P < 0.001 for the 3 electrodes). However, AVL was greater during AS than during QS in group 2 for C3 (P < 0.01).

β Band

The results of AVL in β band are shown in Figure 3 (Top). Most of the electrodes showed changes with PMA during QS as well as during AS.

Figure 3.

Top: Topographic changes of the mean values (gray scale bar) of the AVL in the β band during AS and QS for the 3 groups of neonates. Bottom: The same but for the global AVN interdependence for the unfiltered data.

Figure 3.

Top: Topographic changes of the mean values (gray scale bar) of the AVL in the β band during AS and QS for the 3 groups of neonates. Bottom: The same but for the global AVN interdependence for the unfiltered data.

During QS, the AVL was greater in group 2 than in group 1 for the electrodes C3 (P < 0.01), T3 (P < 0.05), O1 (P < 0.01), and Fp2 (P < 0.05), and it was greater in group 3 than in group 1 for all the electrodes (P < 0.001).

During AS, AVL was greater in group 1 than in group 2 for C3 (P < 0.001), T3 (P < 0.05), C4 (P < 0.001), T4 (P < 0.001), and O2 (P < 0.05), and it was greater in group 1 than in group 3 for C3, C4, and T4 (P < 0.01 in all cases).

QS versus AS comparisons: For all the electrodes, AVL during AS was greater than QS in group 1 (P < 0.01 for Fp1, T3, O1, Fp2, C4 and P < 0.001 for C3, T4, O2), whereas the reverse occurred for group 3 (P < 0.01 for C3, T3 and P < 0.001 for Fp1, O1, Fp2, C4, T4, O2). For group 2, no differences between AS and QS were found.

The overall topographic changes of AVL in β band during QS and AS with neonates' PMA can be seen in Figure 3 (Top). In that Figure, the AVL increase during QS and the corresponding decrease during AS are stressed by the changes in the gray level representing the mean values of AVL.

AVN Interdependence

The results for the interdependence index N are shown in Figure 3 (Bottom). Only the N(X|ALL Y) was considered to calculate the AVN, as in general the N(ALL Y|X) indexes were almost identical (i.e., no asymmetries in the interdependence were found).

During QS, the AVN was greater in group 1 than in group 2 for T3 (P < 0.05), O1, C4 (P < 0.01 for both electrodes), and O2 (P < 0.001), and it was greater in group 1 than in group 3 for Fp1, T3, O1, Fp2, C4, T4, and O2 (P < 0.001 in all cases).

During AS, the index AVN did not change with PMA for any electrode.

QS versus AS comparisons: AVN was greater in QS than in AS in group 1 for the electrodes Fp1, C3, T3, Fp2, C4, and T4 (P < 0.001 in all cases), in group 2 for the electrodes Fp1 (P < 0.01), T3, C4, and T4 (P < 0.001 in all cases), and in group 3 for the electrodes C4 (P < 0.01), T3, and T4 (P < 0.001 for both electrodes).

The topographic changes of AVN during QS and AS with neonates' PMA can be seen in Figure 3 (bottom). In that Figure, the AVN decrease during QS is apparent in the changes of the gray level representing the AVN means.

Surrogate Data

The surrogate data test showed that the average interdependence between each electrode and the remainder was significant for all the electrodes and groups, as shown in Figure 4. It can be seen that SIGMAU was greater than 2 in all cases.

Figure 4.

Average values (±95% confidence interval) of the SIGMAU statistics for testing the significance of the interdependence among each electrodes and the remaining ones, during AS and QS for the groups 1 (G1), 2 (G2), and 3 (G3). The 95% level of significance (SIGMAU = 2) is indicated by the horizontal dashed arrow. Top: Electrodes of the left hemisphere. Bottom: Electrodes of the right hemisphere. Electrodes: Fp1, Fp2 (frontopolar), C3, C4 (central), T3, T4 (temporal), and O1, O2 (occipital).

Figure 4.

Average values (±95% confidence interval) of the SIGMAU statistics for testing the significance of the interdependence among each electrodes and the remaining ones, during AS and QS for the groups 1 (G1), 2 (G2), and 3 (G3). The 95% level of significance (SIGMAU = 2) is indicated by the horizontal dashed arrow. Top: Electrodes of the left hemisphere. Bottom: Electrodes of the right hemisphere. Electrodes: Fp1, Fp2 (frontopolar), C3, C4 (central), T3, T4 (temporal), and O1, O2 (occipital).

Finally, the results of SIGMAB are shown in Figure 5. During QS, and for groups 1 and 2, its value was greater than the threshold level of 2 for all the electrodes, indicating that the interdependence was of nonlinear nature. However, for group 3, part of the 95% confidence interval of the SIGMAB value falls below this threshold, which indicates that for this group the interdependence for some of the EEG segments was of linear nature. The later was also true for groups 2 and 3 during AS.

Figure 5.

Same as in Figure 4 but for the SIGMAB statistics.

Figure 5.

Same as in Figure 4 but for the SIGMAB statistics.

Discussion

Our study aimed to demonstrate that EEG interdependence measures among different brain regions during sleep are sensitive to the neonate brain development, and thus, they can inform about the dynamical changes in cortical activity during maturation. Two measures of interdependence were used here: the first one, spectral coherence, assesses the linear correlation between the EEG activity of 2 brain cortical regions as a function of the frequency; the second one, N(X|Y), measures the interdependence between the reconstructed state spaces of 2 signals. This latter measure, when applied to the EEG, is an estimate of the synchronization between 2 recorded areas and is sensitive to both linear and nonlinear correlations.

The most important result from our coherence analysis is that the magnitude of coherence increases from preterm to term neonates, albeit only in the θ band and for central and temporal regions during QS in term neonates (Fig. 2). Furthermore, the AVL in the higher frequency band β (Top Fig. 3) increased for all the cortical regions during QS and, which is more relevant, whereas in the preterm neonates it is greater in AS than in QS, the reverse happens in the older term neonates. No differences between the 2 sleep stages were found in the younger term neonates. Therefore, AVL in the β band during AS and QS allows to clearly discriminate the stage of the neonates' cortical brain maturation. The reason why the later result was not always found in the θ band can be attributed to the fact that slow waves during QS are not permanently present in the neonate EEG recording and their incidence varies with the neonates' age. On the contrary, higher frequency β waves are present in all the EEG derivations of all the neonates during AS and QS, although in different proportion. Probably, the increase of AVL in the β band during QS parallels the development of the cerebral cortex during the first growth stages and the lesser irregularity of the EEG traces. The reverse holds true during AS, possibly due to the fact that this sleep stage is the predominant one during the first months of life and presents lesser irregularities than QS. In a recent work (Duffy and others 2003), the authors were able to significantly predict gestational age at birth by means of multiple regression analysis applied to 40 factors extracted from coherence EEG measures during QS in a large group of neonates of 42 weeks of PMA. They also found an increase of the left 6- to 24-Hz central–temporal coherence with the gestational age. Our study, with a lower number of neonates and using a lower number of coherence factors, was able to find significant differences among the 3 groups of neonates. In addition, our method showed that there are differences between the 2 sleep states in the β band AVL, which depends on the PMA.

The surrogate data test showed that the interdependencies among the different cortical regions were significant during AS and QS in the 3 groups of neonates (Fig. 4). This result is in agreement with that reported in term neonates (Pereda and others 2003).

As for the AVN index, we found that for most cortical regions the interdependence decreased with the PMA during QS (Bottom Fig. 3). However, during AS no changes appeared with the PMA and the interdependence was lower than in QS. Thus, AS does not present relevant changes in the nonlinear cortical interdependencies in the state space during maturation. The results from the surrogate data test suggested a decrease of the nonlinear character of the interdependence in AS and QS with the PMA (Fig. 5). In a previous work (Pereda and others 2003), it was shown that in term neonates with ages similar to those of groups 2 and 3, the interdependence was of nonlinear nature and showed differences among cortical areas and between the 2 sleep stages, although in this case we used a different nonlinear interdependence index, which is more dependent on the structure of the individual state space than the one we used here. In the present work, we observed that the nonlinear nature of the interdependence is evident in the preterm neonates group during AS and QS, but it is only present during QS and only for some cortical areas in the younger term neonates. In the older term neonates, linear and nonlinear interdependencies apparently coexist in both AS and QS. But it is in the QS where we detected the decrease of the AVN with the PMA, with a parallel trend of the interdependence to become linear and without any change in the significance of the global interdependence. This decrease in the nonlinearity of the cortical interdependencies with maturation parallels the increase of the linear interdependence (i.e., the AVL) in the θ and β bands, the latter one only in QS. These dynamical changes in the nature of the cortical interdependence with maturation have not been reported yet. Nevertheless, in adult subjects interdependencies in the state space—as assessed by AVN—between C3 and C4 have been indeed reported to be mostly of nonlinear nature during slow wave sleep, although linear correlations are also present (Pereda and others 2001).

Preterm neonates, in which the cortex is still far from reaching a complete development, exhibit nonlinear correlations among their cortical areas during both AS and QS. The linear interdependencies assessed by AVL increase during QS and decrease during AS as the PMA increase. The reason why this occurs may be linked to the underlying brain processes related with the development of the cortex, which have a clear effect on the dynamics of the sleep stages.

Concerning the weak EEG interdependencies reported by both AVL and AVN, low values for similar global measures of interdependence were also found in a previous EEG study (Pereda and others 2003), which is consistent with findings from magnetic resonance (MR) studies in neonates (Paus and others 2001; Forbes and others 2002). These MR studies also reveal major age-related changes in the human brain during the first year of life that reflects brain maturation. Thus, diffusion-weighted MR imaging has reported interesting results for the infant apparent diffusion coefficient (ADC), which measures random water diffusion within tissue, varying with both overall water content and cellular location, during the first year of life (Forbes and others 2002). The ADC was significantly higher in white than in gray matter and showed a logarithmic decline with age since birth (most pronounced during the first few months of life) in all the brain regions, although its value changes significantly from one brain region to another. Reduction in brain water content, cellular maturation, and white matter myelination, among other factors, can account for this age-related decrease in the ADC.

These results are consistent with those about the time course of the gray–white matter contrast and the degree of myelination reported by T1- and/or T2-weighted MR imaging in neonates (for a review see, Paus and others 2001), which reflect significant changes during the first year of life. Thus, 3 developmental patterns (infantile [<6 months], isointense [8–12 months], and early-adult [>12 months] patterns) were distinguished in the gray–white differentiation, and a temporal sequence in the myelination was reported. In particular, MR imaging showed that the corpus callosum appears isointense at birth and does not acquire the appearance of that of an adult until around 8 months of age (Barkovich and others 1988). Therefore, the weak interdependencies among cortical brain areas found in the present study are consistent with the early stage of brain maturation of neonates whose PMAs are lower than 47 weeks.

In summary, we have shown that the overall interdependencies among different cortical areas in healthy neonates evolve from nonlinear to linear character with increasing PMA during QS. The results also indicate that measuring the changes in the overall linear correlations in the β band during QS and AS could be an important tool for the follow up of neonatal brain development. Furthermore, when the interdependencies among cortical areas are measured in the reconstructed state spaces of the EEG signals, the neonate's maturation degree can be assessed from the changes in the magnitude and the character of these interdependencies that take place during QS. Finally, as a general conclusion of the work, it can be said that the joint use of both linear and nonlinear approaches for measuring cortical interdependencies during neonate's sleep seems to be essential to get a complete insight into the degree of brain development from the EEG in the earliest stages of life.

The authors acknowledge the financial support of the Spanish Ministry of Science and Technology (Grant number: BFI2002-01159) and of the European Regional Development Fund (F.E.D.E.R.) through a grant of the Health Research Fund (F.I.S., Spanish Ministry of Health and Consumption, Grant number: PI05/2166). The authors are also truly indebt to the staff of the Unit of Clinical Neurophysiology of the University Hospital Nuestra Señora de la Candelaria for their assistance during the polysomnographic records. Conflict of Interest: None declared.

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