Cerebral Cortex March 2007;17:583--590
doi:10.1093/cercor/bhk002
Advance Access publication April 20, 2006
Maturational Changes in the
Interdependencies between Cortical Brain
Areas of Neonates during Sleep
Dulce M. de la Cruz1, Soledad Mañas2, Ernesto Pereda3,
José M. Garrido2, Santiago López4, Luis De Vera1 and
Julián J. González1
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.
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.
Keywords: coherence, interdependence, neonates, nonlinear analysis,
sleep electroencephalogram
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 (d, h, and b/h ratios),
whereas Scher and others (2003) have used the power in these
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1
Laboratory of Biophysics, Department of Physiology,
University of La Laguna, Tenerife, Spain, 2Unit of Clinical
Neurophysiology, University Hospital Nuestra Señora de la
Candelaria, Tenerife, Spain, 3Electrical Engineering and
Bioengineering group, Department of Basic Physics,
University of La Laguna, Tenerife, Spain and 4Unit of
Pediatrics, University Hospital Nuestra Señora de la
Candelaria, Tenerife, Spain
Materials and Methods
the least-squares method and finally normalized to zero mean and unit
variance.
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-tomoderate 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 (r2MEAN ) and that of the 16 SD (r2SD ) were
calculated. The 5 epochs showing the lowest joint variance (i.e., the
lowest value of the sum of (r2MEAN ) and (r2SD ) 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
584 Cortical Interdependencies during Neonate’s Sleep
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de la Cruz and others
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;
i 6¼ j) is defined as
CFij ðf Þ =
j < Cij ðf Þ > j2
;
j < Cii ðf Þ > k < Cjj ðf Þ > j
ð1Þ
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 d (0.5--3.9 Hz), h (4--7.9 Hz),
a (8--12.9 Hz), and b (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
d
8
+ CFij ð f Þ
j =1
j 6¼ i
:
CFi ðf Þ =
7
ð2Þ
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; i 6¼ j), we first reconstructed their state spaces by
using Takens’ method (Takens 1980) to form delayed state vectors such
as the following ones:
~n = ðxðnÞ; xðn – sÞ; . . . ; xðn – ðm – 1ÞsÞÞ
x
~
yn = ðyðnÞ; yðn – sÞ; . . . ; yðn – ðm – 1ÞsÞÞ;
n = 1; . . . ; N 9;
ð3Þ
where N9 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 s 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., s was normally greater for QS
than for AS), we took for all the segments the maximal values m = 7 and
s = 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(XjY), 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
N
ðkÞ
ðX jY Þ =
1 N 9 Rn ðX Þ – Rn ðkÞ ðX jY Þ
+
;
N9n=1
Rn ðX Þ
ð4Þ
where Rn(X) is the mean squared Euclidean distance of all the state
~n ; and RnðkÞ ðX jY Þ is the mean
vectors X to the nth reference vector, x
squared Euclidean distance of that reference vector to its k mutual
~n are those state vectors of X
neighbors. The mutual neighbors of x
bearing the same time indexes of the nearest neighbors of ~
yn : 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).
ðkÞ
On the other hand, if the signals are independent, Rn ðX jY Þ Rn ðX Þ
and the index is very close to 0. The dependence of Y on X, N (k)(Y jX),
can be assessed in complete analogy.
The index N (Y jX) is sensitive to both linear and nonlinear interdependencies and asymmetric, that is, in general, N (X jY ) 6¼ N (Y jX ),
with N (X jY ) < N (Y jX ) 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 jALL Y ) and N (ALL Y jX )—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 jY ), 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 jY ) 6¼ N (Y jX ) 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 jY ) and
N (Y jX ) 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:
SIGMAU =
Nor – N̂s;u
;
rs;u
ð5Þ
where Nor is the value of the index for the original pair of data and N̂s;u
and rs,u are the mean and the SD, respectively, of the set of indexes
calculated from 19 univariate surrogate pairs. We consider that
N(O2jO1) 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(O1jO2) was tested accordingly by
keeping O1 unchanged and surrogating O2.
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:
SIGMAB =
Nor – N̂s;b
rs;b
ð6Þ
with Nor as above, and where N̂s;b and rs,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
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(O2jO1) 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.
Cerebral Cortex March 2007, V 17 N 3 585
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 d, h, a, and b
frequency bands. Only the coherence in the h and b bands
presented differences with the PMA. Significant statistical
differences between groups 1 and 2 and groups 1 and 3 are
shown in the Figures.
u Band
The results of AVL in h band are shown in Figure 2. Significant
changes with the PMA were only found for electrodes C3, T3,
and T4.
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).
b Band
The results of AVL in b band are shown in Figure 3 (Top). Most
of the electrodes showed changes with PMA during QS as well
as during AS.
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 b 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.
Figure 2. Average coherence (±95% confidence interval) between each electrode and the remaining ones (AVL) in the h 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).
586 Cortical Interdependencies during Neonate’s Sleep
d
de la Cruz and others
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.
Discussion
Figure 3. Top: Topographic changes of the mean values (gray scale bar) of the AVL in
the b band during AS and QS for the 3 groups of neonates. Bottom: The same but for
the global AVN interdependence for the unfiltered data.
AVN Interdependence
The results for the interdependence index N are shown in
Figure 3 (Bottom). Only the N (X jALL Y ) was considered to
calculate the AVN, as in general the N (ALL Y jX ) 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.
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
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 jY ), 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 h band and for central and temporal
regions during QS in term neonates (Fig. 2). Furthermore, the
AVL in the higher frequency band b (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 b 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 h 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 b 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 b
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 b 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
Cerebral Cortex March 2007, V 17 N 3 587
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 5. Same as in Figure 4 but for the SIGMAB statistics.
588 Cortical Interdependencies during Neonate’s Sleep
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de la Cruz and others
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 h and b 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, diffusionweighted 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 b 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.
Notes
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.
Address correspondence to Julián J. González, Department of
Physiology, Faculty of Medicine, University of La Laguna, Ctra. La
Cuesta-Taco s/n, 38071 La Laguna, S/C de Tenerife, Spain. Email:
[email protected].
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