Altered Small-World Brain Networks in Temporal Lobe in Patients with Schizophrenia Performing an Auditory Oddball Task

The functional architecture of the human brain has been extensively described in terms of complex networks characterized by efficient small-world features. Recent functional magnetic resonance imaging (fMRI) studies have found altered small-world topological properties of brain functional networks in patients with schizophrenia (SZ) during the resting state. However, little is known about the small-world properties of brain networks in the context of a task. In this study, we investigated the topological properties of human brain functional networks derived from fMRI during an auditory oddball (AOD) task. Data were obtained from 20 healthy controls and 20 SZ; A left and a right task-related network which consisted of the top activated voxels in temporal lobe of each hemisphere were analyzed separately. All voxels were detected by group independent component analysis. Connectivity of the left and right task-related networks were estimated by partial correlation analysis and thresholded to construct a set of undirected graphs. The small-worldness values were decreased in both hemispheres in SZ. In addition, SZ showed longer shortest path length and lower global efficiency only in the left task-related networks. These results suggested small-world attributes are altered during the AOD task-related networks in SZ which provided further evidences for brain dysfunction of connectivity in SZ.

Schizophrenia is a chronic, disabling, and one of the most mysterious, costliest mental disorder which impairs multiple cognitive domains including memory, attention, and executive function (Calhoun et al., 2009a;Danielyan and Nasrallah, 2009;Javitt, 2009;van Os and Kapur, 2009;Hugdahl and Calhoun, 2010). Previous neuroimaging studies have found both structural and functional abnormalities in temporal lobe brain regions for SZ (Iritani, 2007;Calhoun et al., 2009a;Palmer et al., 2009). One of the most robust functional abnormalities in SZ is a different "oddball response" compared with HCs, reported for both event-related potential (ERP) and fMRI data. For example, reduced P300 amplitude in SZ is usually found in ERP studies during auditory oddball tasks (Bramon et al., 2004;O'Donnell et al., 2004;Doege et al., 2009). Aberrant activations in auditory cortex for SZ are often reported in fMRI studies during auditory oddball tasks (Pearlson, 1997;Calhoun et al., 2006;Sui et al., 2009). However, it is not clear if there are altered properties of auditory oddball task-related small-world networks in auditory cortex. The present study was designed to address this issue. Disturbed brain asymmetry is another important determinant for schizophrenic pathophysiology (Ribolsi et al., 2009). Disturbances in hemispheric lateralization are widely reported in SZ, including electrophysiological (Gruzelier et al., 1999), structural (Schlaepfer et al., 1994), and functional Ross and Pearlson, 1996; domains. The default mode network (DMN) also shows lateral differences during auditory oddball tasks (Swanson et al., in press). As both hemispheres involve auditory cortex, it is natural to inquire whether both auditory cortices show altered network properties in SZ during an auditory oddball task.
In this study, group independent component analysis (ICA) was used to detect the strongest auditory oddball task-related component. A left and a right task-related network were constructed by using the top 95 task-related voxels in the left auditory cortex and the top 95 task-related voxels in the right auditory cortex respectively. Some previous small-world brain network studies (Liu et al., 2008;Wang et al., 2009b;Liao et al., 2010) parcellated brain images into 90 anatomical regions of interest using the anatomical automatic labeling (AAL) template (Tzourio-Mazoyer et al., 2002). Because temporal lobe was one of the regions most implicated in previous work in SZ we hypothesized that there would be group difference in the local small-world network properties (Calhoun et al., 2004;Micheloyannis et al., 2006;Liu et al., 2009;Palmer et al., 2009;Zhang et al., 2009). In addition, because previous work suggested temporal lobe changes in both structure and function may be lateralized, we assessed small-world network properties separately for left and right temporal lobe. To determine if the information processing pattern was different between HCs and SZ in a strongly task-related brain region which consisted of temporally coherent voxels within the temporal lobe (Calhoun et al., 2008a) during an auditory oddball detection (AOD) task, we used 95 voxels from each hemisphere and assessed their small-world network properties. All voxels were selected from the most task-related component based on the Z-maps from the group ICA results. Properties of the left and the right task-related networks including clustering coefficient, shortest path length, local efficiency, global efficiency, and the smallworldness as a function of threshold or degree (defined below) were computed from the partial correlation matrices. Two-sample t-tests were used to detect any possible group difference. Since most graph studies based on fMRI data found less clustering coefficient, less local efficiency, less global efficiency, longer path length, and less small-worldness in SZ (Liu et al., 2008;Bullmore and Sporns, 2009;Lynall et al., 2010), we predicted the patients group in the present study would show the same trend in these metrics.

PartIcIPants
Subjects consisted of 20 (four females) HCs and 20 (three females) SZ. All of them gave written, informed, IRB-approved consent at Hartford Hospital and were compensated for their participation. Schizophrenia was diagnosed according to the DSM-IV TR criteria on the basis of a structured clinical interview (First et al., 1995). administered by a research nurse and by review of the medical records. All patients had chronic schizophrenia [PANSS: positive score 16 ± 6 (SD); negative score 16 ± 5 (SD)] and all were taking medication (including the atypical antipsychotic medications aripiprazole, clozapine, risperidone, quetiapine, and olanzapine, first-generation antipsychotics including fluphenazine, and miscellaneous mood-stabilizing, hypnotic, and anti-cholinergic medications including zolpidem, zaleplon, lorazepam, benztropine, divalproex, trazodone, clonazepam). Patients were on average about 7 years older (but not significantly, P = 0.085) than controls (SZ: mean age 36.7, range 19-59; HCs: mean age 29.9, range 18-56). All participants except two patients were right-handed. Exclusion criteria included auditory or visual impairment, mental retardation (full scale IQ < 70), traumatic brain injury with loss of consciousness greater than 15 min, and presence or history of any central nervous system (CNS) neurological illness. Participants were also excluded if they met criteria for alcohol or drug dependence within the past 6 months or showed a positive urine toxicology screen (screening was for cocaine, opioids including methadone, cannabis, amphetamine, barbiturates, PCP, propoxyphene, and benzodiazepines) on the day of scanning. All participants were able to perform the AOD task successfully during practice prior to the scanning session. Healthy participants were free of any DSM-IV TR Axis I disorder or psychotropic medication.

exPerIMental desIgn
All participants were scanned during an AOD task. The AOD consisted of detecting an infrequent sound within a series of regular and different sounds. The task consisted of two runs of auditory stimuli presented to each participant by a computer stimulus presentation system via insert earphones embedded within 30-dB sound attenuating MR compatible headphones. The standard stimulus was a 500-Hz tone, the target stimulus was a 1000-Hz tone, and the novel stimuli consisted of non-repeating random digital noises (e.g., tone sweeps, whistles). The target and novel stimuli each occurred with a probability of 0.10; the standard stimuli occurred with a probability of 0.80. The stimulus duration was 200 ms with a 1000-, 1500-, or 2000-ms inter-stimulus interval randomly chosen with equal probability. All stimuli were presented at 80 dB above the standard threshold of hearing. All participants reported that they could hear the stimuli and discriminate them from the background scanner noise. Prior to entry into the scanning room, each participant performed a practice block of 10 trials to ensure understanding Frontiers in Systems Neuroscience www.frontiersin.org principal component analysis (PCA), followed by an independent component estimation using the infomax algorithm (Bell and Sejnowski, 1995). Group ICA was performed separately on HCs and SZ. A temporal multiple regression of the ICA time courses and an SPM5 general linear model (GLM) design matrix coded for the target stimuli was performed. This resulted in a set of beta weights for each regressor associated with a particular subject and component. The resulting beta weights represent the degree to which the component was associated with the AOD task (i.e., a high beta weight represents a large task-related modulation of component for a given regressor; White et al., 2010). One sample t-tests of beta values for each component were performed to define task-related components (Calhoun et al., 2008b). The most task-related component for HCs (P < 0.0001, t = 11.81, df = 19) and the most task-related component for SZ (P < 0.0001, t = 8.80, df = 19) were averaged into one Z-map (McKeown et al., 1998;Calhoun et al., 2001).

estIMatIon of the PartIal correlatIons
Partial correlation could be used as a measure of connectivity between a given pair of voxels by attenuating the contribution of other sources of covariance (Hampson et al., 2002;Marrelec et al., 2006). In this case, following a previous study (Liu et al., 2008), we used partial correlation to reduce indirect dependencies by other voxels, and built undirected graphs respectively in the left and the right network. Given a set of N random variables, the partial correlation matrix is a symmetric matrix, where each off-diagonal element is the correlation coefficient between a pair of variables after filtering out the contributions of all other variables included in the dataset. In the present study, therefore, the partial correlation between any pair of voxels filters out the effects of the other 93 voxels (Salvador et al., 2005). The first step was to estimate the sample covariance matrix S from the data matrix Y = (x i ), i = 1,…,95, of observations for each individual. Here x i was the time series of each ith voxel. If we introduce X = (x j , x k ) to denote the observations in the jth and kth voxels, Z = Y\X denotes the other 93 time series matrices. Each component of S contains the sample covariance value between two voxels (say j and k). If the covariance matrix of [X, Z] was in which S 11 was the covariance matrix of X, S 12 was the covariance matrix of X and Z and S 22 was the covariance matrix of Z, then the partial correlation matrix of X, controlling for Z, could be defined formally as a normalized version of the covariance matrix, of the instructions. The participants were instructed to respond as quickly and accurately as possible with their right index finger every time they heard the target stimulus and not to respond to the nontarget stimuli or the novel stimuli. An MRI compatible fiber-optic response device (Lightwave Medical, Vancouver, BC, USA) was used to acquire behavioral responses. The stimulus paradigm data acquisition techniques and previously found stimulus-related activation were described more fully elsewhere . Healthy controls had a success average of 99.8% and an average total reaction time of 397 ms for performing the AOD task, while SZ had a 98.3% success rate average, with an average total reaction time of 462 ms. Two-sample t-tests indicated only reaction time had significant group difference (for success rate, t = 1.874, P = 0.069; for reaction time, t = −2.524, P = 0.008). Both patients and controls were able to perform the task well.

IMage acquIsItIon
Scans were acquired at the Olin Neuropsychiatry Research Center at the Institute of Living/Hartford Hospital on a Siemens Allegra 3T dedicated head scanner equipped with 40 mT/m gradients and a standard quadrature head coil. The functional scans were acquired transaxially using gradient-echo echo-planar-imaging with the following parameters: repeat time (TR) 1.50 s, echo time (TE) 27 ms, field of view 24 cm, acquisition matrix 64 × 64, flip angle 70°, voxel size 3.75 mm × 3.75 mm × 4 mm, slice thickness 4 mm, gap 1 mm, 29 slices, ascending acquisition. Six "dummy" scans were acquired at the beginning to allow for longitudinal equilibrium, after which the paradigm was automatically triggered to start by the scanner. The AOD consisted of two 8-min runs.

PreProcessIng
Functional magnetic resonance imaging data were preprocessed using the SPM5 1 software package. Data were motion corrected using INRIalign -a motion correction algorithm unbiased by local signal changes (Freire et al., 2002), spatially normalized into the standard Montreal Neurological Institute (MNI) space using a symmetric template , and spatially smoothed with a 10 mm × 10 mm × 10 mm full width at half-maximum Gaussian kernel. Following spatial normalization, the data (originally acquired at 3.75 mm × 3.75 mm × 4 mm) were resliced to 3 mm × 3 mm × 3 mm, resulting in 53 × 63 × 46 voxels. Group spatial ICA (Calhoun et al., 2009b) was used to decompose all the data into components using the GIFT software 2 as follows. Dimension estimation, to determine the number of components, was performed using the minimum description length criteria, modified to account for spatial correlation (Li et al., 2007). Using this approach, the data were estimated to have 19 components. A more complete explanation of the ICA algorithm and its theoretical constructs, as well as choosing the appropriate number of components, can be found elsewhere (Bell and Sejnowski, 1995;Calhoun et al., 2001;Stevens et al., 2007). Once the estimate of the number of components was determined, we applied ICA to the data using group ICA (Calhoun et al., 2001(Calhoun et al., , 2009b as follows. Data from HCs or SZ were concatenated and the aggregate data set reduced to 19 temporal dimensions using E global , a measure of the global efficiency of parallel information transfer in the network, was defined by the inverse of the harmonic mean of the minimum path length between each pair of nodes (Latora andMarchiori, 2001, 2003;Achard and Bullmore, 2007): The local efficiency of the ith node could be calculated: In fact, since the ith node was not an element of the subgraph G i , the local efficiency could also be understood as a measure of the fault tolerance of the network, indicating how well each subgraph exchanges information when the index node was eliminated (Achard and Bullmore, 2007). In addition, based on its definition, it was a measure of the global efficiency of the subgraph G i . The mean local efficiency of a graph, was the mean of all the local efficiencies of the nodes in the graph.

sMall-worldness
Compared with random networks, small-world networks have similar path lengths but higher clustering coefficients, that is γ = C net / C random > 1, λ = L net /L random ≈1 (Watts and Strogatz, 1998). These two conditions can also be summarized into a scalar quantitative measurement, small-worldness, σ = γ/λ, which is typically >1 for smallworld networks Humphries et al., 2006;He et al., 2007). To examine the small-world properties, the values of C net and L net of the functional brain network need to be compared with those of random networks. As suggested by , statistical comparisons should generally be performed between networks that have equal (or at least similar) degree sequences. Whereas theoretical random networks have Gaussian degree distributions that may differ from the degree distribution of the brain networks that we discovered in this study. To obtain a better control for the functional brain networks, following previous studies (Liu et al., 2008;Liao et al., 2010), we generated 100 random networks for each degree K and threshold T of each individual network by a Markov-chain algorithm (Maslov and Sneppen, 2002;Milo et al., 2002;Sporns and Zwi, 2004). In the original network, if node i 1 was connected to j 1 and i 2 was connected to j 2 , for the corresponding randomized matrices, we removed the edges between i 1 j 1 , and i 2 j 2 but added new edges between i 1 j 2 , and i 2 j 1 . That means two pairs of vertices (i 1 , j 1 ) and (i 2 , j 2 ) in the existing network were selected where e i j The matrices were randomly permuted which assured that the random matrices had the same degree distribution as the original matrix. This procedure was repeated until the topological structure of the original matrix was randomized . Finally, we averaged across all 100 generated random networks to obtain a mean C random and a mean L random for each degree K and threshold T.
Finally, a Fisher's r-to-z transformation (Fisher, 1914(Fisher, , 1921Liu et al., 2008) was used on the partial correlation matrix in order to induce normality on the partial correlation coefficients.

graPh theoretIcal analysIs
An N × N (N = 95 in the present study) binary graph brain network, G, consisting of nodes (brain voxels) and undirected edges (connectivity) between nodes, could be constructed by applying a correlation threshold T (Fisher's r-to-z) to the partial correlation coefficients: That was, if the absolute z(i, j) (Fisher r-to-z of the partial correlation coefficient) of a pair of voxels, i and j, exceeds a given threshold T, an edge was said to exist; otherwise it did not exist. We defined the subgraph G i as the set of nodes that were the direct neighbors of the ith node, i.e., directly connected to the ith node with an edge. The degree of each node, K i , i = 1,2,…,95, was defined as the number of nodes in the subgraph G i . The degree of connectivity, K net , of a graph was the average of the degrees of all the nodes in the graph: which was a measure to evaluate the degree of sparsity (or density, cost) of a network.
The clustering coefficient of a node was the ratio of the number of existing connections to the number of all possible connections in the subgraph G i : where E i was the number of edges in the subgraph G i (Watts and Strogatz, 1998;Strogatz, 2001). The clustering coefficient of a network was the average of the clustering coefficients of all nodes: where C net was a measure of the extent of the local density or cliquishness of the network. The mean shortest path length of a node was: in which min{L i,j } was the shortest path length between the ith node and the jth node, and the path length was the number of edges included in the path connecting two nodes. The mean shortest path length of a network was the average of the shortest path lengths between the nodes: L net was a measure of the extent of average connectivity of the network.
Frontiers in Systems Neuroscience www.frontiersin.org correlation results for both left and right 95 voxels. Figure A3 shows the histogram for absolute partial correlation (Fisher's z) values of one subject in the left task-related network. When looking at the topological indices as a function of threshold T, in both left and right task-related networks, the higher threshold resulted in a lower clustering coefficient, lower local efficiency, lower global efficiency, lower degree, and higher shortest path length because more and more edges were being lost with an increase in the threshold. Two-sample t-tests (FDR correction for multiple comparisons) indicated only shortest path length had significant group differences in the left task-related networks. As shown in Figure 3A, SZ had higher shortest path length at higher threshold points (0.098-0.110). Effect size (Cohen, 1988;Hartung et al., 2008) of shortest path length at threshold 0.104 was 0.9619. No group difference was found in the right task-related networks.
For the topological indices as a function of degree K, with an increase in the degree, the global efficiency, local efficiency, clustering coefficient increased whereas shortest path length decreased in both left and right task-related networks. Significant group differences (two-sample t-tests, FDR correction for multiple comparisons) were only found in the left hemisphere. As shown in Figures 3B,C, SZ showed lower global efficiency and higher shortest path length at most K values (10.5-15.0). Effect size (Cohen, 1988;Hartung et al., 2008) of global efficiency at degree point K = 13.0 is −0.91, effect size of shortest path length at degree point K = 13.0 is 0.91. Figure 4 displays original distributions of global efficiency and shortest path length across subjects of the two groups at that degree point.
The small-world attribute was evident in both left and right networks for both groups: γ was significantly greater than 1 while λ was near 1 over the whole range of T or K. Significant group differences were found in both left and right hemisphere networks. γ values and σ values were significantly decreased in SZ at all T and K values in the left network ( Figure 5) and at most T and K values in the right network (Figure 6). See Figures A1,A2 for example graph (in form of nodes and edges) of networks.
Two-sample t-tests were performed to compare strength (Lynall et al., 2010) of connectivity between HCs and SZ. There was no group difference (the left task-related network: t = 0.897, P = 0.375; the right task-related network: t = −0.117, P = 0.907). Two-sample Kolmogorov-Smirnov tests indicated the distribution of connectivity strengths was similar in the two groups (the left task-related network: P = 0.497, the right task-related network: P = 0.275). Associations between network properties and clinical symptom severity (PANSS scale) were explored using Pearson's correlation coefficient. We found no significant result. Pearson's correlation coefficient was also used to evaluate associations between network properties and task performance, no significant result was found either.

dIscussIon
In this fMRI study, topological properties of an AOD task-related networks as a function of threshold and degree were examined for both HCs and SZ. First, group ICA was performed to detect task-related networks in left and right hemisphere, both of which consisted of top 95 activated voxels during an AOD task. Then partial correlation matrix of the network was used to generate binary adjacency matrix. Both left and right task-related networks statIstIcal analysIs and sMall-world regIMe Statistical comparisons of C net , L net , E global , E local , γ, λ, and σ between the two groups were performed for the left and the right taskrelated networks separately. Following the approach of Liu, et al. (2008), a two-sample two-tailed t-test was performed to detect possible group difference for each value over a range of T or K. False discovery rate (FDR) correction (Benjamini and Hochberg, 1995) was used for multiple comparisons.
In the present study, we investigated the topological properties of the left and right task-related network as a function of T and K, following the studies by Liao et al. (2010), , and Liu et al. (2008). All matrices were thresholded using a single, conservative threshold chosen to construct a sparse graph with mean degree K net ≥ 2logN ≈ 9.1. (1) The maximum threshold (T) was selected also to assure that each network was fully connected with N = 95 nodes. This allowed us to compare the topological properties between the two groups in a way that was relatively independent of the size of the network. (2) The minimum threshold was selected to ensure that the brain networks have a lower global efficiency and a larger local efficiency compared to random networks with relatively the same distribution of the degree of connectivity (Achard and Bullmore, 2007). We selected the threshold range, T min ≤ T ≤ T max by intersecting the upper criteria. In both left and right network, we selected the small-world regime as 0.086 ≤ T ≤ 0.110 and repeated the full analysis for each value of T with increments of 0.002, corresponding to the degree of connectivity threshold 9.5 ≤ K ≤ 17.5 (cost range: 0.101-0.186) and did analysis with steps of 0.5.

results
In line with prior findings (Calhoun et al., 2008a,b), group ICA results indicated the most task-related component for HCs and the most task-related component for SZ involving both left and right temporal lobe. Figure 1 displays schematic location of top 95 task-related voxels in both hemispheres selected based on the average of the most taskrelated component for HCs and the most task-related component for SZ. Figure 2 shows mean absolute Fisher's z-score matrices of partial  3D spatial organization of 95 voxels were transformed into 1D alignment organized by slice (z-coordinate). The diagonal running from the upper left to the lower right is intentionally set to zero (L: the left task-related network; R: the right task-related network).

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showed "small-world" pattern in the selected range of threshold and degree in HCs and SZ which provided further support for the presence of small-world features in complex brain networks (Sporns and Zwi, 2004;Stam and Reijneveld, 2007). However, SZ showed some different small-world characteristics. In the left task-related network, when examining topological properties as a function of threshold, SZ showed longer shortest path length; when looking at the topological properties as a function of degree, SZ had lower global efficiency, and longer shortest path length. Moreover, SZ showed lower γ and small-worldness σ when looking at them as a function of threshold or degree. In the right task-related network, only γ and small-worldness σ had significant group difference. SZ had lower value when looking at γ and σ as a function of threshold or degree. Our results suggest that during this AOD task, in the task-related networks consisting of activated voxels, SZ have different functional connectivity pattern from HCs. This finding is consistent with prior studies (Friston, 2005;Honey et al., 2005) which reported functional disconnectivity in SZ and provides further evidence for brain dysfunction associated with this disease. The structure of the absolute connection matrix for the left and right task-related network for HCs and SZ can be directly compared by visual inspection in Figure 2.  Frontiers in Systems Neuroscience www.frontiersin.org 2010) reported reduced clustering coefficient and local efficiency in SZ, no significant group difference were found for the two measures in this study. That may suggest information processing efficiencies are equal robust in local in the networks consisted of task-related voxels for HCs and SZ during this AOD task. Most interestingly, that γ and small-worldness σ values were decreased at the same threshold T or degree K in SZ in both hemispheres suggests that the task-related networks in both left and right hemispheres for SZ are closer to the random networks that have equal degree sequences. These group differences imply that the small-world AOD task-related networks are altered in SZ. That some significant group differences (including shortest path length and global efficiency) are restricted to the left hemisphere is compatible with previous contributions reporting predominantly left hemisphere abnormalities in SZ Ribolsi et al., 2009).
Overall, we built "equi-threshold" networks using threshold T and "equi-sparse" networks using degree K. Similar results were found in the two separated ways might be due to the average partial correlation (connectivity strength) and the distribution of it showed no significant difference between the two groups.
However, several limitations should be concerned for this study. The first consideration is medication of patients may possibly influence the results. The types of medications used to treat SZ are A short average path length and high global efficiency in graph system is of significance in minimizing noise, shortening signaling delay and increasing synchrony (Kaiser and Hilgetag, 2004). In a network of Hodgkin-Huxley neurons, (Lago-Fernandez et al., 2000) showed the structural and functional robustness of neural systems increases when path lengths are shorter. Short path lengths have also been demonstrated to promote effective interactions both between and across different cortical regions Achard and Bullmore, 2007). Consistent with previous studies (Micheloyannis et al., 2006;Bassett et al., 2008;Liu et al., 2008), SZ showed lower global efficiency at most K values and longer path length at some T values and most K values. That group differences were significant only for the left hemisphere, may indicate information interactions between interconnected task-related voxels were slower and less efficient in the left hemisphere in SZ during the AOD task.
Clustering coefficient and local efficiency of a graph system assess efficiency of communication between the first neighbors of a node when it is removed (Latora and Marchiori, 2001). Brain networks with high clustering and high local efficiency are robust in local information processing even if some neurons are inefficient or damaged (Zhao et al., 2008). Lower clustering coefficient and lower local efficiency imply relatively sparse local connectedness of brain functional networks (Micheloyannis et al., 2006). Although previous studies (Bassett et al., 2008;Liu et al., 2008;Lynall et al., λ (B), and σ (C) of the right task-related networks for HCs (blue circles) and SZ (red squares) as a function of threshold T. γ (D), λ (e), and σ (F) of the right task-related networks for HCs (blue circles) and SZ (red squares) as a function of degree K. Error bars correspond to SEM (across 20 subjects of each group), Black triangles indicate where the group difference is significant (t-test, df = 38, P < 0.05, FDR correction for multiple comparisons).

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www.frontiersin.org effects during AOD tasks. One more concern is the limitation to perform group comparisons in standard space. As SZ consistently show decreased brain volume (Meyer-Lindenberg, 2010), voxels in patients may not correspond anatomically to controls. Future studies in native space are needed to confirm the findings of this study. To our knowledge, this is the first fMRI study to examine the topological properties of AOD task-related small-world networks in HCs and SZ, using ICA and graph theoretical analysis methods. SZ showed longer path length and lower global efficiency in the left task-related network, suggests altered robustness of global information processing in SZ. In addition, γ and small-worldness σ values were decreased in SZ in both hemispheres, indicating the task-related networks of SZ are closer to random networks having equal degree sequences. Taken together, these results suggest altered properties of AOD taskrelated networks in SZ, which helps advance our understanding of the underlying pathophysiology of the disorder from functional brain architecture.

acknowledgMent
This work was supported by NIH grant RO1 EB000840 (PI: Calhoun).
complex, therefore, we are unable to perform a treatment similar to van Dellen et al. (2009) which divided temporal lobe epilepsy patients into two groups. But in further studies we may perform an analysis in first-episode, never medicated patients before and after antipsychotic treatment as Lui et al. (2010). Secondly, undirected, unweighted networks are built in the present study like most previous researches (Liu et al., 2008;Bullmore and Sporns, 2009;Lynall et al., 2010). Further studies may perform a weighted network analysis which could supply more information (van den Heuvel and Hulshoff Pol, 2010;Wang et al., 2010a). The third issue is smooth during preprocessing. It has been pointed out that spatial smoothing could introduce artificial correlations between voxels by previous voxel-based network analysis studies in which graphs were built based on correlation matrices (van den Heuvel et al., 2008;Hayasaka and Laurienti, 2010). However, Partial correlation in this study would remove the local correlation (including that caused by smoothing) but preserve the unique voxel variance. Further studies are required to determine the full impact of smoothing on correlation and partial correlation including its relationship to the variability from subject to subject. Moreover, two hemispheres were compared separately in this study. The two left handed patients might bias the results. Further studies are necessary to assess any relationship between handedness and lateralization of network Frontiers in Systems Neuroscience www.frontiersin.org