## Abstract

It has been revealed that spontaneous coherent brain activity during rest, measured by functional magnetic resonance imaging (fMRI), self-organizes a “small-world” network by which the human brain could sustain higher communication efficiency across global brain regions with lower energy consumption. However, the state-dependent dynamics of the network, especially the dependency on the conscious state, remain poorly understood. In this study, we conducted simultaneous electroencephalographic recording with resting-state fMRI to explore whether functional network organization reflects differences in the conscious state between an awake state and stage 1 sleep. We then evaluated whole-brain functional network properties with fine spatial resolution (3781 regions of interest) using graph theoretical analysis. We found that the efficiency of the functional network evaluated by path length decreased not only at the global level, but also in several specific regions depending on the conscious state. Furthermore, almost two-thirds of nodes that showed a significant decrease in nodal efficiency during stage 1 sleep were categorized as the default-mode network. These results suggest that brain functional network organizations are dynamically optimized for a higher level of information integration in the fully conscious awake state, and that the default-mode network plays a pivotal role in information integration for maintaining conscious awareness.

## Introduction

Spontaneous coherent activity among brain regions measured by functional magnetic resonance imaging (fMRI) is known as functional connectivity (Fox and Raichle 2007). Recent studies have proposed that the functional connectivity during resting-state fMRI (rs-fMRI) optimizes the brain network to maintain higher cognitive functions (Achard and Bullmore 2007; van den Heuvel, Stam, et al. 2009). Furthermore, graph theoretical analysis of rs-fMRI has revealed that the functional network features “small-world” organization (Bullmore and Sporns 2009; Rubinov and Sporns 2010; Bullmore and Bassett 2011). An essential element of a small world is a short path length (Watts and Strogatz 1998) by which signals can reach other regions in fewer processing steps, and thus the network can underpin higher-level cognitive functions requiring the integration of information from specialized and divergent brain regions (Rubinov and Sporns 2010). In fact, several studies have reported that the functional network organization changes with aging (Achard and Bullmore 2007), neuropsychiatric disorders (Liu et al. 2008; Supekar et al. 2008), and intellectual performance (van den Heuvel, Stam, et al. 2009). However, these functional changes may be caused by alterations in anatomical network organization, but not in functional organization, because functional connectivity is fundamentally founded on anatomical connectivity (Honey et al. 2009; van den Heuvel, Mandl, et al. 2009; Sporns 2011).

A critical approach to settle this issue would be to examine whether changes in functional network organization depend on the transition of brain state over a short period during which the anatomical network organization cannot change. It is suitable for this purpose to measure rs-fMRI with simultaneous electroencephalographic (EEG) recordings and to investigate changes in functional network organization associated with the alteration of sleep stage. EEG is most sensitive to the change from the awake state to stage 1 sleep and conscious awareness. The latter is essential for integrative cognitive processing and considerably deteriorates during sleep (Tononi 2004; Dehaene and Changeux 2011). If functional network organization relates to higher cognitive functions, the efficiency of the functional network evaluated by the average path length would decrease during stage 1 sleep.

Another important issue is whether the efficiency decreases not only at the global level, but also in the key brain regions associated with consciousness during stage 1 sleep. So far, increasing evidence has suggested that the default-mode network (DMN) could play a key role in generating consciousness. For example, the DMN contains the most centrally connected regions in the whole-brain network (Buckner et al. 2009; Cole et al. 2010) and thus can be essential for integrating brain activity like consciousness. Recent rs-fMRI studies have shown that the connectivity inside the DMN decreased in altered states of consciousness, such as sleep (Horovitz et al. 2009; Sämann et al. 2011), general anesthesia (Boveroux et al. 2010), and clinical consciousness impairment (Vanhaudenhuyse et al. 2010). However, the interaction between the DMN and the whole-brain network was not taken into consideration in these previous studies. Thus, if the communication efficiency evaluated by path length decreases specifically in the DMN during stage 1 sleep, it would provide evidence that the DMN serves to integrate diverse brain regions for generating consciousness.

To the best of our knowledge, there are few neuroimaging studies focusing on brain activities during stage 1 sleep. A positron emission tomography study (Kjaer, Law, et al. 2002) showed that there is a relative regional cerebral blood flow increase in the occipital lobes and a relative decrease in the cerebellum, the posterior parietal cortex, the premotor cortex, and the thalamus during stage 1 sleep. An fMRI study (Picchioni et al. 2008) has shown that there is an activity increase in the parts of the DMN during early stage 1 sleep and an activity decrease in the hippocampus during late stage 1 sleep. As the most comparable study to ours, Spoormaker et al. (2010) reported the results of a graph theoretical analysis of rs-fMRI during non-rapid eye movement (NREM) sleep including stage 1 sleep. They observed that the main effect of light sleep (stages 1 and 2) was not on average path length (i.e. the efficiency), but on local clustering. In graph theoretical analysis, a whole-brain network is modeled as a graph consisting of a set of nodes and edges between nodes. The definition of nodes is arbitrary, and Spoormaker et al. (2010) defined nodes as 90 large parcels from the Automated Anatomical Labeling (AAL) brain atlas (Tzourio-Mazoyer et al. 2002). Although this is a common approach in rs-fMRI graph theoretical analysis, AAL-based partition is too coarse to distinguish most functional systems including the DMN (Power et al. 2011). Thus, we adopted a much finer brain partition as nodes (3781 nodes) to overcome this limitation, because we had a special interest in the system-specific effects (especially in the DMN) upon the efficiency.

## Materials and Methods

### Subjects

Eighteen healthy young adults (age, 25.1 ± 5.4 [mean ± SD]; gender: 14 males and 4 females) were recruited. None had any sleep, medical, or psychiatric disorders. None were employed in an occupation requiring “night shift” hours. None complained of any sleep disturbances or excessive daytime sleepiness. Subjects were not required to undergo experimental sleep deprivation. Data from 10 subjects were retained for final analysis as described below. All subjects gave informed consent and were compensated for their participation. The study was approved by the Ethics Committee of Kyushu University and the National Institute of Information and Communications Technology.

### Resting-State fMRI Recording

The fMRI measurements were performed using a 3-T scanner (Trio, Siemens Healthcare, Germany). Whole-brain T2*-weighted images were acquired using an echo planar imaging (EPI) sequence (repetition time = 2500 ms; echo time = 30 ms; flip angle = 79°; 42 axial slices; 3.0 mm isotropic voxels with no gap). During functional runs, subjects were required to keep alert with their eyes closed for 10 min. To avoid the effect of participants employing specific strategies to maintain alertness (e.g. reminiscing or counting scan number), participants were instructed not to think about anything in particular as much as possible. For each subject, 2–5 runs were recorded during daytime, resulting in a total of 76 rs-fMRI runs.

### EEG Recording

EEG data were acquired simultaneously with rs-fMRI using an MRI-compatible amplifier (BrainAmp MR plus, Brain Products GmbH, Munich, Germany) and an electrode cap (EASYCAP GmbH, Herrsching-Breitbrunn, Germany) with Ag/AgCl ring electrodes. A reference electrode was placed at the middle point between Fz and Cz. Either 32, or 14, electrodes were placed according to the international 10-20 system. A raw record was sampled at a rate of 5 kHz (bandpass filtered between 0.016 and 250 Hz) using the specialized recording software (Brain Vision Recorder, Brain Products GmbH). Brain Vision Analyzer (Brain Products GmbH) was used for the offline correction of scanning and ballistocardiogram artifacts. After down-sampling to 200 Hz, the reference channel was digitally replaced with an average of TP9 and TP10 electrodes, located behind the ears.

### Epoch Selection

We selected 10 subjects (age, 25 ± 6.1 [mean ± SD]; gender: 8 males and 2 females) who had both awake and stage 1 sleep epochs defined by EEG. Each epoch was 5 min long (120 scans). EEG recordings were visually scored according to the standard criteria (Rechtschaffen and Kales 1968) for 30 s intervals. A continuous 5-min recording was defined as an awake epoch if all 30-s segments were at sleep stage 0 (Fig. 1A,B), and was defined as a stage 1 sleep epoch if at least 4 min were at sleep stage 1 (Fig. 1C,D).

Figure 1.

Typical EEG power spectra and waveforms after removing artifacts. Both (A) and (C) show the power spectrogram of the entire epoch (300 s) from the O1 electrode of the same subject, both (B) and (D) show 5-s segments of EEG waveforms between the 2 dotted lines in the spectrograms. (A and C) Awake epoch characterized by continuous alpha waves. (B and D) Stage 1 sleep epoch characterized by low voltage theta waves with intermixed low voltage alpha waves.

Figure 1.

Typical EEG power spectra and waveforms after removing artifacts. Both (A) and (C) show the power spectrogram of the entire epoch (300 s) from the O1 electrode of the same subject, both (B) and (D) show 5-s segments of EEG waveforms between the 2 dotted lines in the spectrograms. (A and C) Awake epoch characterized by continuous alpha waves. (B and D) Stage 1 sleep epoch characterized by low voltage theta waves with intermixed low voltage alpha waves.

### Resting-State fMRI Preprocessing

The following preprocessing of fMRI data was performed by SPM5 (Wellcome Department of Imaging Neuroscience, http://www.fil.ion.ucl.ac.uk/spm/). After correcting for differences in slice timing within each image volume, each scan was aligned with the first scan, normalized according to the Montreal Neurological Institute (MNI) template, and resliced to 2-mm cubic voxels. Then, commonly applied preprocessing steps for rs-fMRI were performed (Fox et al. 2005). Data were temporally bandpass filtered (0.009Hz < f < 0.08 Hz), and the following sources of spurious variance along with their temporal derivatives were then removed through linear regression: (1) 6 parameters obtained by rigid-body correction of head motion, (2) the whole-brain signal averaged over gray matter, white matter, and ventricular regions, (3) signal from a ventricular region, and (4) signal from regions centered in the deep white matter. This regression procedure removes fluctuations unlikely to be involved in specific regional correlations (Van Dijk et al. 2010).

### Brain Network Construction

In graph theory, a complex system is modeled as a “graph,” which is defined as a set of “nodes” linked by “edges.” Then, important properties of the complex system are described by quantifying the topologies of the respective graphs (Boccalettia et al. 2006). In rs-fMRI analysis, nodes represent a set of regions of interest (ROIs) or voxels, and edges represent the functional connectivity between the nodes (Bullmore and Sporns 2009; Rubinov and Sporns 2010; Bullmore and Bassett 2011). In this study, to enhance spatial specificity we adopted a much larger number of partitions than was adopted in previous studies (Achard and Bullmore 2007; Spoormaker et al. 2010). Figure 2 schematically illustrates the graph theoretical analysis of rs-fMRI. As a first step, according to Meunier et al. (2009), we divided the AAL gray matter template (Tzourio-Mazoyer et al. 2002) into 3781 nodes covering the whole cortical and subcortical gray matter (Fig. 2A). Each node was a 6 mm × 6 mm × 6 mm cubic ROI containing 27 voxels (for more detail, see Meunier et al. 2009). As a second step, node time courses of fMRI signals for each epoch were extracted from the preprocessed EPI images by averaging the voxel time courses within the ROIs for each participant (Fig. 2B). Next, to estimate the functional connectivity, Pearson's correlation coefficients between all node pairs were calculated, which resulted in {3781 × 3781} correlation matrices (Fig. 2C). Following the practice undertaken by a majority of prior studies (for a review, see Bullmore and Bassett 2011), we then applied thresholds to the correlation matrices and eliminated weak correlations to evaluate the topological properties of functional brain networks using graph theoretical analysis. According to the recommendation of Bullmore and Bassett (2011), we set thresholds with reference to the connection density K, the ratio of the number of edges to all possible node pairs. For example, when we set a threshold with reference to K = 0.1, the strongest 10% of correlations were retained. Because there is no gold standard for a threshold, we applied a range of thresholds (0.01 ≤ K ≤ 0.2, 0.01 increments) to each correlation matrix and converted each to an adjacency matrix A, where the ai,j elements of A are 1, if the correlation coefficient ri,j is greater than a given threshold, or 0, if it is not (Fig. 2D). Each adjacency matrix defines a binary graph G, which represents a model of the whole-brain functional network (Fig. 2E). Finally, graphs of different connection densities were produced and the following parameters (see below) were calculated as a function of K (Fig. 2F).

Figure 2.

Procedure for graph theoretical analysis on rs-fMRI (see Materials and Methods). (A) Initially, the fine partitions of cortical and subcortical gray matter (3781 ROIs) are generated. (B) The mean time course of each ROI is extracted and bandpass filtered (0.009 Hz <f<0.08 Hz). Then, the sources of spurious variance along with their temporal derivatives are removed. (C) Pearson's correlation coefficients between all pairs of ROI time courses are calculated, which result in a 3781 × 3781 correlation matrix representing functional connectivity. (D) These correlation matrices are thresholded at different connection densities K (0.03 ≤ K ≤ 0.12) and binarized to generate adjacency matrices. (E) Each adjacency matrix defines a binary graph G, a model of the whole-brain functional network. (F) Important topological parameters such as path length, clustering coefficient, and modularity are then calculated from G and compared between the awake state and stage 1 sleep.

Figure 2.

Procedure for graph theoretical analysis on rs-fMRI (see Materials and Methods). (A) Initially, the fine partitions of cortical and subcortical gray matter (3781 ROIs) are generated. (B) The mean time course of each ROI is extracted and bandpass filtered (0.009 Hz <f<0.08 Hz). Then, the sources of spurious variance along with their temporal derivatives are removed. (C) Pearson's correlation coefficients between all pairs of ROI time courses are calculated, which result in a 3781 × 3781 correlation matrix representing functional connectivity. (D) These correlation matrices are thresholded at different connection densities K (0.03 ≤ K ≤ 0.12) and binarized to generate adjacency matrices. (E) Each adjacency matrix defines a binary graph G, a model of the whole-brain functional network. (F) Important topological parameters such as path length, clustering coefficient, and modularity are then calculated from G and compared between the awake state and stage 1 sleep.

### Network Analysis

To examine the differences in functional network organization between the awake and stage 1 sleep epochs, we computed and estimated the following parameters with the Brain Connectivity Toolbox (http://www.brain-connectivity-toolbox.net; Rubinov and Sporns 2010).

#### Small-World Organization

The small-world organization of a network can be quantified by 2 key parameters: The characteristic path length L and clustering coefficient C (Watts and Strogatz 1998). L is the average of the shortest path length between all pairs of nodes. Path length represents the number of processing steps along the routes of information transfer among the brain regions (Rubinov and Sporns 2010). Since low numbers of processing steps have the advantage in rapid and accurate communication (Kaiser and Hilgetag 2006), a lower L indicates a higher level of communication efficiency across global brain regions. To handle possibly infinite path lengths between disconnected nodes, we calculated L as the harmonic mean of the minimum path length (Latora and Marchiori 2001; Hayasaka and Laurienti 2010). Another parameter, C is the degree of interconnectedness in local networks, consisting of direct neighbors of each node. In brain networks, C is considered to be associated with locally specialized processing, fault tolerance, and economic pressure for minimal wiring cost (Kaiser and Hilgetag 2006; Rubinov and Sporns 2010; Bullmore and Bassett 2011). To avoid the influence of other network characteristics (Rubinov and Sporns 2010), normalized L and C, “lambda” and “gamma,” respectively, were then calculated as the ratio to values of a randomly rewired null model (Maslov and Sneppen 2002). Small-worldness “sigma” (Humphries et al. 2006) was calculated as the ratio of gamma to lambda. Compared with a randomly rewired network, small-world networks are known to have similar L and higher C, resulting in lambda ≈ 1, gamma > 1, and sigma =(gamma/lambda) > 1:

$$L = \displaystyle{{n(n - 1)} \over {\sum\limits_{i \ne j \in G} {1/d_{i,j} } }},\quad \hbox{Lambda} = \displaystyle{L \over {L_{{\rm random}} }},$$

$$C = \displaystyle{1 \over n}\sum\limits_{i \in G} {\displaystyle{{2e_i } \over {k_i (k_i - 1)}}} ,\quad \hbox{gamma} = \displaystyle{C \over {C_{{\rm random}} }},$$

where n is the number of nodes, di,j is the shortest path length between node i and j, ki is the number of edges connected to node i, and ei is the number of edges between the neighbors of node i, and Lrandom and Crandom are the averages of L and C calculated from 20 randomly rewired null models, respectively (Maslov and Sneppen 2002).

#### Modular Organization

Another feature of whole-brain functional networks is their modular organization (Bullmore and Sporns 2009; Meunier et al. 2010; Rubinov and Sporns 2010; Bullmore and Bassett 2011). A module is topologically defined as a group of highly interconnected nodes, which have relatively sparse connections to nodes in other modules (Fortunato 2010). Modular organization suggests that a functional network is suitable for specialized processing (Meunier et al. 2010; Rubinov and Sporns 2010), and the degree of modular organization can be estimated by a quantitative parameter called modularity Q (Newman 2004, 2006). Here, we applied the heuristic modularity maximizing algorithm proposed by Blondel et al. (2008). This method outputs an optimal partition, a set of modules, and optimized Q.

$$Q = \displaystyle{1 \over {2m}}\sum\limits_{i \ne j \in G} { \left(a_{i,j} - \displaystyle{{k_i k_j } \over {2m}} \right)} \delta (M_i ,M_j ),$$

where m is the number of edges, Mi is the module containing node i, and δ(Mi, Mj) = 1 if Mi = Mj, and 0 otherwise. Q measures the quality of network partitioning.

#### Physical Connection Distance

In brain networks, long-range connections are thought to be critical for generating short path lengths and high communication efficiency across global brain regions (Kaiser and Hilgetag 2006). Thus, we also calculated the physical connection distance D as the average of the Euclidean distance between nodes connected by edges as follows:

$$D = \displaystyle{1 \over m}\sum\limits_{i \ne j \in G} {w_{i,j} } ,$$
where m is the number of edges, and wi,j is the Euclidean distance between the center coordinates of nodes if ai,j = 1, and 0 if ai,j = 0.

#### Nodal Efficiency

We also estimated the communication efficiency at individual brain regions. Nodal efficiency Ei is the mean of the inverse shortest path length from node i to all other nodes and is defined as follows (Achard and Bullmore 2007):

$$E_i = \displaystyle{1 \over {n - 1}}\sum\limits_{\,j \in G} {\displaystyle{1 \over {d_{i,j} }}}$$

Since Ei is negatively correlated with the number of processing steps from the ith node to all other nodes, brain regions having high Ei suggest the existence of a high level of efficiency in communicating with the rest of the brain.

#### Group-Level Partition and Identification of DMN

To calculate nodal efficiency in the DMN, we identified this network by using a group-level partition. In accordance with He et al. (2009), we constructed a group-level graph by way of the statistical significance of the correlation coefficient. Fisher's transformed correlation matrix was averaged across the awake and stage 1 sleep epochs, then the significance of the correlation coefficient was tested by a 1-sample t-test, where the null hypothesis was a correlation coefficient = 0 at the group level. For multiple comparisons, we applied the false-discovery rate (FDR) and correlations where FDR ≤ 0.05, and a positive t-value (positive correlation) was defined as edges. This resulted in a sparse group-level graph (K ≈ 0.023). Thereafter, this graph was parceled into modules by using the modularity maximizing method as described above.

### Statistical Analysis

We compared the above described parameters in the nonrandom connection density range. As the threshold is relaxed and connection density increases, graph topology becomes increasingly random and less small world or modular. According to the notion that a high density random network is likely to be nonbiological (Lynall et al. 2010), we chose the nonrandom connection density range using 3 constraints: (1) at least 99% of nodes are connected, (2) small-worldness sigma > 1, and (3) modularity Q > 0.3. These criteria ensured that graphs retained small-world and modular topology. In practice, we empirically computed the number of connected nodes, sigma and Q over the rage of 0.01 ≤ K ≤ 0.2 (0.01 increments) to find the range over which all graphs met the criteria and resulted in 0.03 ≤ K ≤ 0.12. According to Lynall et al. (2010), all parameters were averaged over this range.

Since the distributional properties of graph theoretical parameters are not well known (Bullmore and Bassett 2011), differences in global network parameters (L, C, lambda, gamma, Q, and D) were examined by using a nonparametric permutation test adopted in other brain graph theoretical analysis studies (van den Heuvel et al. 2010; Fornito et al. 2011). We calculated the mean differences between the awake and stage 1 sleep epochs (observed difference). Then, in the permutation step, data from the awake epochs were exchanged for data from the same participants' stage 1 sleep epoch in all possible ways (210 = 1024), and mean differences were calculated in all of the permutated data. This resulted in a distribution under the null hypothesis in which there were no differences between the 2 states (null distribution). The 2-tail P-value was calculated as the proportion of permutations in which the absolute mean difference was greater than or equal to the observed absolute mean difference (Nichols and Holmes 2001).

For nodal efficiency, we applied the permutation test on a suprathreshold cluster size (Nichols and Holmes 2001) to obtain high sensitivity. As the first step, t-statistics were calculated for each node, and spatially extended clusters were estimated at a primary cluster-forming threshold of t > 2.82 (corresponding to P < 0.01, 1-tailed). Then, in a null distribution for multiple comparisons, a corrected P-value for cluster sizes was obtained by permutation of the data in all possible ways (210 = 1024). Finally, the suprathreshold clusters in the observed data with P < 0.025 (1-tailed) were defined as significant clusters. The same procedure in essence was adopted in a recent rs-fMRI graph theoretical analysis (Fornito et al. 2011).

To investigate whether each module (e.g., DMN or executive control network [ECN]) has a specific effect of sleep stage on the efficiency, we computed how many nodes overlap between each module (identified by the group-level partition) and the regions which have state-dependent effects on nodal efficiency. In addition, to test the statistical significance of these overlaps, we calculated the adjusted standardized residuals (Haberman 1973) for each overlap. Here, the null hypothesis was that the modules and the decreased nodal efficiency were independent. The adjusted standardized residuals represented the degree of the difference between the observed overlaps (number of nodes) and those of the expected ones if the null hypothesis was true. Under the null hypothesis, the adjusted standardized residuals will have a standard normal distribution, that is, the adjusted standardized residuals were Z-scores. Then, P-values were calculated. For multiple comparisons, we applied the Bonferroni method. If P < 0.01, we considered that the module had a specific effect of sleep stage on the efficiency.

## Results

### State-Dependent Functional Network Organization at the Global Level

Figure 3 shows the effects of brain state (awake state and stage 1 sleep) on the parameters as a function of connection density. Table 1 summarizes the statistical results of these parameters averaged over the nonrandom connection density range of 0.03 ≤ K ≤ 0.12. The characteristic path length L and normalized L (lambda) significantly increased in stage 1 sleep compared with the awake state (P = 0.0059 for L and P = 0.0059 for lambda, permutation test; Fig. 3A). In contrast, state-dependent effects on the degree of clustering were not evident (Fig. 3B). Although the clustering coefficient C was significantly increased in stage 1 sleep (P = 0.0039, permutation test), there was no significant difference when C was normalized by a null model (gamma; Table 1). The modular organization also showed no significant difference between the awake state and stage 1 sleep: There were no significant differences in modularity Q and number of modules (Fig. 3C, Table 1). On the contrary, the mean physical connection distance of edges D significantly decreased in the stage 1 sleep state compared with that of the awake state (P = 0.0019, permutation test; Fig. 3D).

Table 1

Differences in all parameters for network analysis between the awake state and stage 1 sleep

Awake

Stage 1 sleep

P-values Effect
Mean SD Mean SD
Characteristic path length L 2.035 0.034 2.083 0.047 0.0059* Stage 1 sleep > awake
Normalized L lambda 1.078 0.015 1.100 0.021 0.0059* Stage 1 sleep > awake
Clustering coefficient C 0.361 0.032 0.394 0.031 0.0039* Stage 1 sleep > awake
Normalized C gamma 3.326 0.299 3.296 0.503 0.8535
Modularity Q 0.453 0.038 0.457 0.034 0.6465
Number of modules 4.550 0.560 4.900 0.488 0.0723
Connection distance D (mm) 71.181 3.010 67.124 2.338 0.0019* Awake > stage 1 sleep
Awake

Stage 1 sleep

P-values Effect
Mean SD Mean SD
Characteristic path length L 2.035 0.034 2.083 0.047 0.0059* Stage 1 sleep > awake
Normalized L lambda 1.078 0.015 1.100 0.021 0.0059* Stage 1 sleep > awake
Clustering coefficient C 0.361 0.032 0.394 0.031 0.0039* Stage 1 sleep > awake
Normalized C gamma 3.326 0.299 3.296 0.503 0.8535
Modularity Q 0.453 0.038 0.457 0.034 0.6465
Number of modules 4.550 0.560 4.900 0.488 0.0723
Connection distance D (mm) 71.181 3.010 67.124 2.338 0.0019* Awake > stage 1 sleep

Note: Values are the mean over the nonrandom connection density range of 0.03 ≤ K ≤ 0.12 (see Materials and Methods).

*P < 0.05, permutation test.

Figure 3.

Network parameters (y axis) in the awake state and stage 1 sleep at various connection densities K (0.03 ≤ K ≤ 0.12). Solid red lines represent the average values of the awake state, while black lines represent stage 1 sleep. (A) Normalized characteristic path length (lambda) significantly increased in stage 1 sleep compared with the awake state (P = 0.0059, permutation test). (B and C) However, state-dependent effects on the normalized clustering coefficient (gamma) and modularity Q were not significant. (D) The mean connection distance of edges D is significantly decreased in stage 1 sleep compared with the awake state (P = 0.0019, permutation test). Error bars represent standard error of the mean.

Figure 3.

Network parameters (y axis) in the awake state and stage 1 sleep at various connection densities K (0.03 ≤ K ≤ 0.12). Solid red lines represent the average values of the awake state, while black lines represent stage 1 sleep. (A) Normalized characteristic path length (lambda) significantly increased in stage 1 sleep compared with the awake state (P = 0.0059, permutation test). (B and C) However, state-dependent effects on the normalized clustering coefficient (gamma) and modularity Q were not significant. (D) The mean connection distance of edges D is significantly decreased in stage 1 sleep compared with the awake state (P = 0.0019, permutation test). Error bars represent standard error of the mean.

### State-Dependent Efficiency at The Regional Level

To examine the effect of sleep stage on efficiency at the regional level, we compared the nodal efficiency Ei between the 2 states. As shown in Figure 4, 6 spatially extended clusters could be extracted where the nodal efficiency significantly decreased during stage 1 sleep: (1) Bilateral medial parietal cortex extended to the cingulate cortex, involving the precuneus, posterior and middle cingulate cortex (cluster size [number of nodes] = 70, P = 0.0019, corrected), (2) bilateral medial prefrontal cortex (cluster size = 28, P = 0.0107, corrected), (3) right lateral parietal cortex (mainly supramarginal gyrus; cluster size = 24, P = 0.0127, corrected), (4) left lateral parietal cortex (angular gyrus and superior parietal lobule; cluster size = 23, P = 0.0136, corrected), (5) right lateral parietal cortex (angular gyrus and superior parietal lobule; cluster size = 20, P = 0.0166, corrected), and (6) right lateral prefrontal cortex (cluster size = 19, P = 0.0166, corrected). There were no regions that showed significant increases in nodal efficiency during stage 1 sleep.

Figure 4.

Brain regions that showed statistically significant decreases in nodal efficiency Ei during stage 1 sleep (P < 0.025, corrected). (1) Bilateral medial parietal, (2) bilateral medial prefrontal, (3) right lateral parietal cortex (mainly supramarginal gyrus), (4) left lateral parietal cortex (angular gyrus and superior parietal lobule), (5) right lateral parietal cortex (angular gyrus and superior parietal lobule), and (6) right lateral prefrontal cortex.

Figure 4.

Brain regions that showed statistically significant decreases in nodal efficiency Ei during stage 1 sleep (P < 0.025, corrected). (1) Bilateral medial parietal, (2) bilateral medial prefrontal, (3) right lateral parietal cortex (mainly supramarginal gyrus), (4) left lateral parietal cortex (angular gyrus and superior parietal lobule), (5) right lateral parietal cortex (angular gyrus and superior parietal lobule), and (6) right lateral prefrontal cortex.

### Overlap of State-Dependent Regions and Segregated Modules

The modularity Q of a group-level graph was 0.601 and was high enough to separate whole-brain regions into several clustered modules. A module is topologically defined as a subset of highly interconnected nodes that are relatively sparsely connected to nodes in other modules (see Materials and Methods section for details). As shown in Figure 5, 5 primary modules could be segregated without any a priori assumptions, and the configuration of these 5 modules resembled the previously reported large-scale resting networks revealed by seed-based correlation analysis and independent component analysis (Raichle 2010). Thus, we labeled them as “DMN,” “ECN,” “salience network (SAN),” “sensorimotor network (SMN),” and “visual network (VN)” with reference to previous studies (Boly et al. 2012). The numbers of nodes were 1018, 704, 416, 710, and 706, respectively, and 94% of all nodes were involved in these 5 modules. Then, we embedded the nodes of each module into a region that showed a significant decrease in nodal efficiency during stage 1 sleep (Fig. 4) to demonstrate the positional relationship between them. As shown in Figure 6A,E, almost two-thirds of nodes that showed a significant decrease in nodal efficiency during stage 1 sleep were dominated by nodes categorized as DMN (64.7%, 119 nodes). The remaining nodes were occupied by ECN (14.7%, 27 nodes; Fig. 6B,E), SAN (15.2%, 28 nodes; Fig. 6C,E), SMN (4.3%, 8 nodes; Fig. 6D,E), and VN (0.5%, 1 nodes; Fig. 6E). To test the statistical significance of the overlaps, we created a 2 × 6 crosstab as shown in Table 2, then Haberman's residual analysis was performed. The overlap between the DMN and the nodes showing the significant decrease in nodal efficiency was significantly larger than the expected value (Z-score = 11.83, P = 3.0 × 10−31, corrected; Fig. 6F). The overlap between the SMN and the nodes showing the significant decrease in nodal efficiency was also significantly smaller than the expected value (Z-score = −5.13, P = 3.3 × 10−6, corrected; Fig. 6F). The overlap between the VN and the nodes showing that the significant decrease in nodal efficiency was significantly smaller than the expected value (Z-score = −6.46, P = 1.1 × 10−7, corrected; Fig. 6F).

Table 2

Overlapping regions between each module and the regions significantly decreased nodal efficiency during stage 1 sleep

DMN ECN SAN SMN VN Others
Significant decrease in Ei 119 27 28
Nonsignificant change in Ei 899 677 388 702 705 226
DMN ECN SAN SMN VN Others
Significant decrease in Ei 119 27 28
Nonsignificant change in Ei 899 677 388 702 705 226

Note: Values are the number of nodes.

Ei: nodal efficiency; DMN: default-mode network; ECN: executive control network; SAN: salience network; SMN: sensorimotor network; VN: visual network.

Figure 5.

Partition of a group-level graph by using the modularity maximizing method (see Materials and Methods). The 5 largest modules are segregated: “DMN (red, 1018 nodes),” “ECN (yellow, 704 nodes),” “SAN (green, 416 nodes),” “SMN (cyan, 710 nodes),” and “VN (blue, 706 nodes).” Ninety-four percent of all nodes are included in these 5 modules.

Figure 5.

Partition of a group-level graph by using the modularity maximizing method (see Materials and Methods). The 5 largest modules are segregated: “DMN (red, 1018 nodes),” “ECN (yellow, 704 nodes),” “SAN (green, 416 nodes),” “SMN (cyan, 710 nodes),” and “VN (blue, 706 nodes).” Ninety-four percent of all nodes are included in these 5 modules.

Figure 6.

Overlapping regions between each module (shown in Fig. 5) and the regions significantly decreased nodal efficiency during stage 1 sleep (shown in Fig. 4): (A) DMN, (B) ECN, (C) SAN, and (D) SMN. Regional colors correspond to those of Figure 5. (E) Numbers of nodes in these overlaps: DMN (red bar, 119 nodes, 64.7% of all nodes showing significantly decreased nodal efficiency during the stage 1 sleep), ECN (yellow bar, 27 nodes, 14.7%), SAN (green bar, 28 nodes, 15.2%), SMN (cyan bar, 8 nodes, 4.3%), and VN (blue bar, 1 nodes, 0.5%). (F) Z-scored overlaps (see Materials and Methods). Dotted lines indicate the Z-score = ±3.34 (P < 0.01, after Bonferroni correction).

Figure 6.

Overlapping regions between each module (shown in Fig. 5) and the regions significantly decreased nodal efficiency during stage 1 sleep (shown in Fig. 4): (A) DMN, (B) ECN, (C) SAN, and (D) SMN. Regional colors correspond to those of Figure 5. (E) Numbers of nodes in these overlaps: DMN (red bar, 119 nodes, 64.7% of all nodes showing significantly decreased nodal efficiency during the stage 1 sleep), ECN (yellow bar, 27 nodes, 14.7%), SAN (green bar, 28 nodes, 15.2%), SMN (cyan bar, 8 nodes, 4.3%), and VN (blue bar, 1 nodes, 0.5%). (F) Z-scored overlaps (see Materials and Methods). Dotted lines indicate the Z-score = ±3.34 (P < 0.01, after Bonferroni correction).

## Discussion

In this study, we applied graph theoretical analysis to rs-fMRI with simultaneous EEG recording to clarify the differences in the organization of spontaneous functional networks between the awake state and stage 1 sleep. Our major findings were as follows. First, the communication efficiency across global brain regions evaluated by the path length significantly decreased during stage 1 sleep. Secondly, the efficiency of several specific regions in the association cortices also significantly decreased during stage 1 sleep. Thirdly, these specific regions dominantly overlapped with the DMN. Our results provide evidence for a state-dependent alteration of brain network organization and decreased the ability of information integration during stage 1 sleep.

### Functional Network Organization Versus Anatomical Network Organization

In our results, average path length increased significantly depending on the shift in sleep stage within a short period of time over which anatomical network organizations could not respond. Thus, the modulation of functional network organizations, at least evaluated by some graph parameters, is independent of changes in anatomical network organization. This independency could provide an insight into the known discrepancy between anatomical and functional network reorganization. For example, Lo et al. (2010) reported that the average path length of an “anatomical” network increased (i.e. the efficiency decreased) in Alzheimer's disease (AD) patients, whereas Sanz-Arigita et al. (2010) reported that the average path length of a “functional” network decreased (i.e. the efficiency increased) in AD patients. Since our results suggested the dynamic modulation of functional network organization beyond anatomical constraints, the functional networks in AD patients may be reorganized to compensate for decreased anatomical network efficiency. This then raises the question of what is occurring in the brain during stage 1 sleep. In the following section, we discuss the alteration of functional network organization during stage 1 sleep from the viewpoint of the physiological and psychological changes.

### Functional Network Organization During Stage 1 Sleep

During stage 1 sleep, subjects unsteadily respond to external stimuli and their reaction times are prolonged (Ogilvie and Wilkinson 1984, 1988; Ogilvie et al. 1989). For example, Ogilvie et al. (1989) reported that subjects failed to respond to about 40% of presented faint auditory stimuli, and reaction times were considerably prolonged during stage 1 sleep. However, the neurophysiological evidence explaining such unstable and slow responsiveness during stage 1 sleep is scarce. In the small-world brain network, a short path length represents a small number of intermediate transmissions in the integrative pathway and thereby underpins the accurate and rapid transfer of information in integrative neural communications (Kaiser and Hilgetag 2006). Conversely, the larger number of intermediate transmissions causes greater signal loss, signal distortion, and slower processing speed. Therefore, unstable and slow responsiveness in stage 1 sleep could be explained by the increased path length demonstrated by this study.

In parallel with the increase in the average path length, the average physical connection distance decreased during stage 1 sleep. A decreased physical connection distance suggests a loss of connections between remote brain regions, that is, long-range connections that are critical for keeping path lengths short in brain networks and ensuring a highly efficient network organization (Kaiser and Hilgetag 2006). Therefore, the increase in average path length is likely caused by the loss of long-range connections during stage 1 sleep. The results of the combined transcranial magnetic stimulation (TMS) and EEG studies also support this notion: A TMS-evoked response efficiently spreads to long-distance distributed brain regions during the awake state, but do not spread beyond the stimulation site during stages 1 and 2 sleep (Massimini et al. 2005) or during anesthesia (Ferrarelli et al. 2010).

In contrast, we found no significant effects on the degree of clustering (Fig. 3B) and modular organization (Fig. 3C). Both are supposed to be associated with the network organization responsible for locally specialized processing. According to mathematical models (Watts and Strogatz 1998; Mathias and Gopal 2001), both parameters are interdependent with path length as a tradeoff between globally integrated organization and locally specialized organization. These parameters may be more robust than average path length for the alteration of network organization, that is, more constrained by anatomical network organization.

### Comparison with Previous rs-fMRI Studies

Spoormaker et al. (2010) reported on the changes in network organization from awake to deep NREM sleep using rs-fMRI. Their approach was very similar to ours. However, unlike in our study, they observed that the main effect of sleep was not on average path length, but also on local clustering: The normalized clustering coefficient was lowest in light NREM sleep (stages 1 and 2 > stage 0 > deep NREM sleep) and concluded that the functional network moved toward randomness in light sleep. Comparing their results with ours, some parts were consistent: The average path length increased in stage 1 sleep in some connection densities, and the normalized average path length increased in stage 2 sleep in some connection densities. However, the following 2 differences should be noted. First, according to the mathematical model of Watts and Strogatz (1998; WS model), when a small-world network moves toward randomness, the average path length decreases as the clustering coefficient decreases. Therefore, from the view point of the WS model, their results and ours were opposite in the direction of the changes in a small-world network organization. A possible cause for the discrepancy between the results of the 2 studies was the definition of nodes. They applied the AAL-based node definition (90 nodes), whereas we applied a much finer node definition (3781 nodes). The different node sets could represent the different aspects of the same network. For example, as the brain system is known as a hierarchical system (Mesulam 1998), different node sets could represent the different hierarchical levels in the functional network. Another possibility which could affect the results was the threshold selection. Whereas they were systemically analyzed over a full connection, we analyzed over a sparse connection density range. However, since the main effects of their study were observed throughout a wide range of connection densities, it is unlikely that the different threshold selections had an impact upon the divergence in the results of the 2 studies. Secondly, the specific involvement of the DMN during stage 1 sleep was demonstrated in our study, but not in their study. This could be due to our node definition, because our fine node set could distinguish the major functional systems including the DMN as shown in Figure 5, whereas the AAL-based node set could not (Power et al. 2011).

Recently, Boly et al. (2012) have reported on the changes in the functional brain network during stages 2–4 NREM sleep using rs-fMRI. Using information theoretical measures, they revealed a modification of the hierarchical organization of large-scale brain networks into smaller independent modules during stages 2–4 sleep. In line with our results, their results suggested that the brain's capacity to integrate information decreases during stages 2–4 sleep. Furthermore, they evaluated the modularity using graph theoretical analysis and revealed an increase in the modularity during stages 2–4 sleep. In contrast, we could not observe the increase in modularity during stage 1 sleep. This discrepancy could be explained by the difference in the stage of sleep between the 2 studies. The modularity could increase in proportion to the depth of sleep.

There have been several rs-fMRI studies that reported the change in functional connectivity during sleep and discussed the relationship to conscious awareness. However, the results are inconsistent: Connectivity within the DMN decreased throughout NREM sleep (Sämann et al. 2011), only in deep NREM sleep (Horovitz et al. 2009), remained constant in light NREM sleep (Horovitz et al. 2008; Larson-Prior et al. 2009), or throughout non-REM and REM sleep (Koike et al. 2011). Although it is hard to determine the cause of the discrepant results, the connectivity pattern of the whole-brain network was not taken into consideration in any of these studies. Since the changes in brain activity when shifting from wakefulness to sleep occur on the scale of the whole brain, a whole-brain analysis using graph theoretical analysis would be more suitable for this purpose.

### Role of DMN as a Center of Conscious Awareness

The regions showing a significant decrease in nodal efficiency during stage 1 sleep were extensively dominated by areas categorized as DMN (Fig. 6C). Nodal efficiency represents how efficiently a brain region communicates with the rest of the brain and reflects not only connectivity within modules (e.g. DMN or ECN), but also connectivity among whole-brain regions. For example, if a region has strong connectivity to regions in 2 or more modules, it has a higher nodal efficiency than that of another region having similar connectivity to regions in only one module. Therefore, our result suggests that DMN is indispensable for integrating whole-brain regions in a fully conscious awake state. So far, an increasing number of results have suggested that the DMN plays a key role in generating conscious awareness, summarized as follows. (1) The DMN regions show a metabolic reduction in various altered states of conscious awareness such as coma, general anesthesia, generalized seizures, and a vegetative state (for a review, see Baars et al. 2003; Laureys 2005). (2) Connectivity among the DMN regions decreased during sleep (Horovitz et al. 2009; Sämann et al. 2011), general anesthesia (Boveroux et al. 2010), and clinical consciousness impairment (Vanhaudenhuyse et al. 2010). (3) Coactivation of the DMN regions was related to self-awareness (Kjaer, Nowak, et al. 2002; Vanhaudenhuyse et al. 2011). Moreover, the DMN contains the most centrally connected regions in the whole-brain network (Buckner et al. 2009; Cole et al. 2010) and thus can be essential for consciousness as an integrating brain activity. However, these previous studies did not directly address the relationship between consciousness and the efficiency in communication with the DMN. By using graph theoretical analysis and simultaneous EEG recording with fMRI, we clearly demonstrated that efficient communications between regions in DMN and the rest of the brain were critical for the awake conscious state.

### Limitations of Our Study

One of the limitations of this study is that we have not analyzed the data acquired when the subjects reached deep NREM sleep. It is well known that conscious awareness degrades more in deep NREM sleep and in patients with consciousness disorders. Therefore, it is not yet clear whether the changes in the functional network organization reported here are specific to stage 1 sleep or if the change becomes more prominent in the same direction in deep NREM sleep. As mentioned earlier, the results of Spoormaker et al. (2010) suggested that light sleep was not a mere transient state from wakefulness to deep NREM sleep. Since their results in light sleep were quite different to ours, further systemic studies are needed to answer this issue.

The fine resolution nodes adopted in this study were useful to capture the DMN specific changes. However, at the same time, fine brain partition may reduce the signal-to-noise ratio and affect the overall results (Fornito et al. 2010). In this respect, several studies have sought for the ideal node definition (Fornito et al. 2010, Power et al. 2011), though no consensus has been established. Further theoretical and empirical studies are needed to overcome this limitation.

Interestingly, Picchioni et al. (2008) demonstrated that brain activities were different between early and late stage 1 sleep. It is possible that the functional network organizations are also different between early and late stage 1 sleep. However, because of the limited sampling rate of rs-fMRI, we could not estimate functional connectivity during such a short period. In this point, graph theoretical analysis using other modalities such as magnetoencephalography (Hipp et al. 2012) may be useful for obtaining a deep understanding of network organization during stage 1 sleep.

## Funding

This study was supported in part by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology (# 22390177 to S.T.) of the Government of Japan and CREST of Japan Science and Technology (JST).

## Notes

Conflict of Interest: None declared.

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