Clinical Neurophysiology xxx (2014) xxx–xxx

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Clinical Neurophysiology journal homepage: www.elsevier.com/locate/clinph

Structure and dynamics of functional networks in child-onset schizophrenia Guilherme Ferraz de Arruda a, Luciano da Fontoura Costa b, Dirk Schubert c, Francisco A. Rodrigues a,⇑ a

Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, CEP: 13566-590, São Carlos, SP, Brazil Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970, São Carlos, SP, Brazil c Radboud University Medical Centre, Nijmegen, Donders Institute for Brain, Cognition and Behaviour, Department of Cognitive Neuroscience, Postbus 9101 6500 HB Nijmegen, The Netherlands b

a r t i c l e

i n f o

Article history: Accepted 26 November 2013 Available online xxxx Keywords: Cortical networks Schizophrenia Child-onset schizophrenia Complex networks

h i g h l i g h t s  Cortical networks in healthy and child-onset schizophrenic subjects differ significantly in only a small

number of large-scale network properties.  Classification of networks of healthy and schizophrenic subjects yields sensitivity of 90% and specific-

ity of 74%.  Our analysis allows reliable automatic diagnostics in patients with child-onset schizophrenia based

on cortical network properties and data mining methods.

a b s t r a c t Objective: Schizophrenia is a neuropsychiatric disorder characterized by cognitive and emotional deficits and associated with various abnormalities in the organization of neural circuits. It is currently unclear how and to which extend the global network organization is changed due to such disorder. In this work, we analyzed cortical networks of healthy subjects and patients with child-onset schizophrenia to address this issue. Methods: We performed a comparison of cortical networks extracted from functional MRI data of patients with schizophrenia and healthy subjects considering their topological and dynamical properties. Results: Among 54 network measures tested, only four contributed substantially to a discrimination between the classes of healthy and schizophrenic subjects, with a sensitivity of 90% and specificity of 74%. However, such classes of networks did not differ significantly with respect to the level of network resilience and synchronization. Conclusions: Schizophrenic subjects have cortical regions with higher variance of network centrality, but less modular structure. Significance: Our findings suggest that it is possible to establish data analysis routines that allow automatic diagnosis of a multifaceted disease like child-onset schizophrenia based on fMRI data of individual subjects and extracted network properties. Ó 2013 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

1. Introduction The structural and functional mapping of human brain networks using functional magnetic resonance imaging (fMRI) and magnetoencephalographic data has shown that cortical networks present small-worldness, high efficiency of information transfer, modularity, and the existence of hubs (Chen et al., 2008; Bullmore and Sporns, 2009; Sporns, 2010). The description of the large-scale ⇑ Corresponding author. Tel.: +55 1633738626. E-mail address: [email protected] (F.A. Rodrigues).

human brain organization has allowed studying the hypothesis that some neuropsychiatric disorders are related to disarrays of connectivity between cortical areas. Indeed, aberrant structural patterns have been verified in the brain organization of subjects with autism, schizophrenia, depression, anxiety disorders, Alzheimer’s disease and frontotemporal dementia (Supekar et al., 2008; He et al., 2008; Bassett et al., 2008; Bassett and Bullmore, 2009; Lynall et al., 2010; Menon, 2011). Revealing these disorder related differences has improved the understanding of how dysfunction of cognitive and emotion regulation processes are related to the altered brain network organization.

1388-2457/$36.00 Ó 2013 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.clinph.2013.11.036

Please cite this article in press as: de Arruda GF et al. Structure and dynamics of functional networks in child-onset schizophrenia. Clin Neurophysiol (2014), http://dx.doi.org/10.1016/j.clinph.2013.11.036

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In addition, analysis of brain network properties derived from fMRI data has been considered for developing methods of non-invasive diagnosis of neurological disorders (Supekar et al., 2008). Diagnosis of neurological disorders is often hampered by ambiguous symptoms and the necessity for long-lasting monitoring of the patients. The analysis of brain network properties may provide a way to facilitate and accelerate diagnosis of such disorders. Neural network properties derived from resting-state fMRI data have already successfully been used for distinguishing between healthy subjects and patients with different neurological disorders, such as amyotrophic lateral sclerosis (Welsh et al., 2013) major depression (Zeng et al., 2013) antisocial personality disorder (Tang et al., 2013). In our study we focused on child-onset schizophrenia, which is a rare form of schizophrenia having its onset before age of 13. From first medical consultation to correct diagnosis of child-onset schizophrenia it can take years (Schaeffer and Ross, 2002) partially because the diagnostic challenges are with differentiating childhood-onset schizophrenia from other neurological disorders or acute, transient syndromes (for review see (Masi et al., 2006)). In case of schizophrenia in general, data obtained from fMRI suggest that cortical networks of schizophrenic adults are less small-world type, less hierarchical, less clustered, less efficiently wired (Bassett et al., 2008; Bullmore and Sporns, 2009) and have a less hub-dominated configuration (Lynall et al., 2010). Moreover, Basset et al. (Bassett et al., 2008) showed that multimodal network organization of patients with schizophrenia are abnormal, presenting increased connection distance and reduced hierarchy. In adult schizophrenic patients previous studies already illustrated the usefulness of non-invasive diagnosis based on the analysis of restingstate fMRI data. Such analysis of brain network properties achieved values for correct classification of up to 94% with 75% accuracy (Tang et al., 2012; Venkataraman et al., 2012; Shen et al., 2010). However, similar analysis of fMRI data from patients with childonset schizophrenia is currently lacking. Analysis of data from patients presenting child-onset schizophrenia is very important, since it allows early diagnosis and disease monitoring. Moreover, although these studies confirmed various structural differences in cortical networks of schizophrenic subjects, they have not determined which network properties are most consistently affected by schizophrenia. The two main objectives of our study are (i) analysis and evaluation of the topological and dynamical properties of brain networks of patients with child-onset schizophrenia and healthy subjects and (ii) determining which network properties are most consistently affected by schizophrenia. One of our main findings suggests that the networks in healthy and schizophrenic subjects differ significantly in only a small number of large-scale network properties. On the other hand, healthy and schizophrenic networks do not differ significantly with respect to dynamical processes such as resilience to attacks and synchronization. Therefore, the main structural alterations in the cortical networks of patients with schizophrenia do not affect the general network resilience and synchronization of the brain. Finally, we showed that network measures and data-mining methods can be useful as an imaging-based diagnosis method to distinguish patients presenting child-onset schizophrenia from healthy subjects. In this case, a sensitivity of 74% and specificity of 90% were obtained. Therefore, our findings suggest that it is possible to establish a data analysis routine that allows automatic diagnosis of this multifaceted disease based on functional MRI data of individual subjects and the resulting cortical network properties.

2. Materials and methods In this section, we describe the main concepts adopted in this work regarding data mining. The concepts of network

characterization and dynamical processes are presented as supplementary material. These concepts are considered to develop a network-based approach for diagnosis of child-onset schizophrenia. 2.1. Data set Our study is based on cortical network data obtained from a study by Vértes et al. (Vértes et al., 2012). The authors used resting-state fMRI to measure low-frequency neural network oscillations in 140 cortical brain regions at the right hemisphere. The data was obtained from a group of adolescent healthy volunteers (n = 20, mean age 19.7 years; 11 male) and a group of adolescent participants with childhood-onset schizophrenia (n = 19, mean age 18.7 years; 9 male). The subjects were scanned using a General Electric Signa MRI scanner operating at 1.5 Tesla. The authors considered only regions in the right hemisphere to facilitate the approximation of the wiring length by the Euclidean distance between brain regions. Cortical networks of each subject were constructed by determining the functional connectivity from the correlation between each pair of regional time series using a band-pass filter in order to define the frequency interval in the range 0.05 – 0.111 Hz. Binary graphs were constructed by thresholding the wavelet correlation matrix estimated for each subject. In order to prevent disconnection of nodes, Vértes et al. considered the minimum spanning tree as a backbone. This procedure resulted in 140 cortical regions whose average time series were used to construct brain functional networks. These preprocessed data can be downloaded via http://intramural.nimh.nih.gov/chp/articles/ matlab.html. Additional details about the database can be found in (Vértes et al., 2012). These functional networks were used to develop mathematical models of functional human brain networks based on distance penalty and connections between regions sharing similar output. Vertés and coworkers suggested that some network properties can be explained by an economical selection pressure to establish connections between different brain areas. Moreover, the authors also verified that clustering and modularity are reduced in schizophrenic patients (Vértes et al., 2012). 2.2. Data mining Before performing the classification of the cortical networks, some pre-processing is required in order to avoid scaling effects, since the network measures varies in different ranges. That is, while the degree is an integer larger than zero, the clustering coefficient varies in the interval ½0; 1 (see the supplementary material). One possible method for standardization is the so called z-score (Costa and Cesar Jr, 2000; Theodoridis and Koutroumbas, 2003). For each observation i; i ¼ 1; . . . ; N, the transformation of the attribute xi is performed as

yi ¼

xi  x

rx

;

ð1Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P PN 2 where x ¼ Nj¼1 xj =N and rx ¼ j¼1 ðxj  xÞ =N are the average and standard deviation of the values of the measure x, respectively. The probability distribution of each transformed measurement, y, presents zero mean and unit variance. Pre-processing is also necessary for obtaining classes with the same number of objects, since a class with the highest number of elements can be favored in the classification process (Theodoridis and Koutroumbas, 2003). In this way, we performed a random sampling, which allows obtaining classes with the same number of elements. After the pre-processing, we analyzed the topology of functional networks via data mining methods in order to find the most important features, i.e., those that best discriminate between the two

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types of networks. This procedure, called feature ranking, performs a ranking of all features according to a given criterion. Here we used two different criteria: (i) symmetrical uncertainty (U) and (ii) the v2 statistical test. The former is based on information theory, and is defined as (Yu and Liu, 2003; Witten and Frank, 2005)

UðC; AÞ ¼

2ðHðCÞ  HðCjAÞÞ ; HðCÞ þ HðAÞ

ð2Þ

where C is the class (i.e., networks of healthy subjects or patients presenting child-onset schizophrenia), A is the network measure (attribute) and HðpÞ is the Shannon entropy (Shannon and Weaver, 1948) — the entropy of a discrete random variable X is given by P HðXÞ ¼  i Pðxi Þlogb ðPðxi ÞÞ, where b is the base of the logarithm used (see the supplementary material). Symmetrical uncertainty yields values in range [0,1] with the value 1 indicating that the network measure can predict the class of the subject. The second criterion is a statistical test (Theodoridis and Koutroumbas, 2003), which evaluates the worth of an attribute by computing the value of the Pearson’s v2 test with respect to the class. This test-statistic measures the lack of independence between the attribute and the class (Yang and Pedersen, 1997; Jin et al., 2006). Both criteria give a higher value for the attributes that provide better discrimination between the classes. Note that the ranking procedures are performed considering each individual measurement at a time. Since some of the network measures evaluated here are continuous, it is necessary to consider a discretization procedure. We used the minimal description length principle (MDLP) algorithm (Fayyad and Irani, 1993; Witten and Frank, 2005), which is considered to be one of the best general techniques for supervised discretization (Witten and Frank, 2005) and is also used in data mining software, such as Weka (Hall et al., 2009). Such supervised approach was considered since the classes are known. This heuristic uses the minimization of the entropy with a criterion based on the minimum description length for definition of the partition intervals. The formal derivation of this criterion has been described previously (Fayyad and Irani, 1993). The feature ranking procedure was performed by using the Weka software (Hall et al., 2009) and the FSelector toolbox available by the R language. After the ranking procedure, we performed the network classification by taking into account three classifiers: (i) naive Bayes (Witten and Frank, 2005), (ii) Bayesian networks (Witten and Frank, 2005) and (iii) C4.5 decision tree (Witten and Frank, 2005). These classifiers are based on information theory and Bayesian concepts. Naive Bayes assumes that the attributes are statistically independent, which is not verified for most application cases (Theodoridis and Koutroumbas, 2003). The Bayes network classifier tries to overcome this deficiency by considering some dependency on the attributes. On the other hand, the decision tree divides the attribute space in hyper-rectangles based on the information gain provided by the attribute. We evaluated the classification using the leaveone-out procedure (Witten and Frank, 2005), which consists of using a single sample from the original data set, i.e., a cortical network of a healthy subject or a patient presenting child-onset schizophrenia, as the validation sample, and the remaining networks as the training data. This process was repeated considering the whole data set by considering each observation at a time. In order to evaluate the accuracy of the classifiers, we took into account the indices true positive (TP), true negative (TN), false positive (FP) and false negative (FN). The metrics based on these indices are (Theodoridis and Koutroumbas, 2003): (i) Accuracy summarizes the performance of our classifier. It is formally defined as:

Accuracy ¼

TP þ TN : n

ð3Þ

Table 1 Feature ranking of network measures calculated by using symmetrical uncertainty (U) and chi-squared test (v2 ). The features are ordered according to the symmetrical uncertainty. UðC; AÞ

v2

Feature

0.326 0.289 0.263 0.258

15.55 10.13 12.88 12.74

Variance of the closeness centrality First moment of K-core Modularity Variance of the accessibility

The error is defined as  ¼ 1  Accuracy. (ii) Precision is the proportion of positive samples classified correctly considering all samples defined as positive. Formally,

Precision ¼

TP : TP þ FP

ð4Þ

(iii) Recall is the accuracy rate on the positive class, i.e.,

Recall ¼

TP : TP þ FN

ð5Þ

Recall is called sensitivity when the positive class is defined as schizophrenic subjects. On the other hand, when the positive class is healthy subjects, it is called specificity. (iv) F-measure is defined in terms of precision and recall, i.e.,

F¼

2  Precision  Recall : Precision þ Recall

ð6Þ

The classification of networks of healthy and schizophrenic subjects was performed by considering the whole set of measures, as well as only the measures selected by the ranking procedure. 3. Results 3.1. Network structure After the standardization and random sampling procedures, we ranked a set of 54 measures extracted from the cortical networks in order to find those that provide the best discrimination between healthy and schizophrenic subjects. These measures are the first two statistical moments,1 the variance and entropy of the probability distribution of (i) degree (the first statistical moment is the mean degree and it is fixed for all networks, so it was excluded in our analysis), (ii) clustering coefficient, (iii) closeness centrality, (iv) node betweenness centrality, (v) edge betweenness centrality, (vi) shortest path length, (vii) K-core, (viii) communicability, (ix) access information, (x) hidden information, (xi) accessibility and (xii) average degree of the nearest neighbors. Note that we calculated all statistical moments of the distributions of network measures before applying the z-score (Eq. (1)). Other measurements related to the large-scale network organization were also considered, including the first two spectral moments, assortativity, central point dominance, efficiency, average search information as well as the maximum network modularity. Introduction of these measures is given in the supplementary material. Table 1 presents the values of U and v2 for the four measurements that contribute substantially to the discrimination between the healthy and schizophrenic cortical networks. The remaining 50 networks measures (data not shown) present U and v2 equal to 1 The statistical moment of order m of a random variable X is defined as R1 E½X m  ¼ 1 X m PðX ¼ xÞdx. The first moment is the mean and the second is related to the variance, E½X 2  ¼ VðXÞ þ ðEðXÞÞ2 . See the supplementary material for additional information.

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zero. Consequently these measures did not contribute to the discrimination between the two classes of networks. Note that a measure presenting similar values in different data classes has U ¼ 0 and v2 ¼ 0 (Theodoridis and Koutroumbas, 2003). Therefore, based on these criteria, out of the 54 original network measures, only four contributed significantly to a discrimination between the two classes of networks, which indicates that these properties can be related to abnormalities in cortical networks of patients presenting child-onset schizophrenia. These measures are the variance of the closeness centrality, the first moment of K-core, the maximum modularity and the variance of the accessibility (see Table 1). Our finding that only 4 of the tested measures contributed to discrimination at the same time indicates that the network properties quantified by the other 50 measures were similar in networks of schizophrenic and healthy subjects. Fig. 1 presents the probability distributions of these measurements. For better visualization, we considered a kernel density estimation (Gaussian kernel) to smooth the densities (Parzen, 1962; Rosenblatt, 1956). Cortical networks of schizophrenic subjects tended to present higher values of variance of the closeness centrality and accessibility, but small values of average K-core and modularity. Therefore, such networks have cortical regions displaying a higher variance of central properties, but less modular structure. Note that the separations of the distributions in Fig. 1 agree with the rankings presented in Table 1. Note that U ¼ 0 and v2 ¼ 0 are zero mainly due to the discretization method applied to the dataset during the feature ranking procedures. For additional information about the discretization procedure see Section 2.2 and (Fayyad and Irani, 1993).

3.2. Dynamical processes In addition to the structural evaluation, we performed a comparison between the networks obtained from healthy and schizophrenic subjects in terms of two dynamical processes, i.e., the synchronization of coupled oscillators and resilience to failures and attacks. The synchronization of non-identical oscillators, i.e., the Kuramoto model, can be considered as being related with lesion recovery in cortical networks (Honey and Sporns, 2008). The Kuramoto model (Acebrón et al., 2005) was considered by Honey and Sporn (Honey and Sporns, 2008) for simulation of the effects of cortical lesions. This model is described in the supplementary material. The evolution of the order parameter was similar in healthy and schizophrenic networks (Fig. 2). The differences observed may be

6

1200

Healthy Schizophrenia

1000

f(E[K−core])

600

4 3

400

2

200

1

0 0

1

2

3

4

0 2.8

5 −3

V[Cc ]

Healthy Schizophrenia

5

800 f(V[Cc ])

Having identified the most relevant features for discrimination of the two classes of networks, we performed a supervised classification. We evaluated the data set by considering three different supervised classifiers, i.e., naive Bayes, Bayesian network and C4.5 decision tree (see Section 2.2). We compared the results of two supervised classifications: (i) a classification based on the four most relevant measures only and (ii) a classification based on all 54 network measures. As shown in Table 2, the analysis based on the 4 most important attributes always yielded more precise classifications. Indeed, the decision tree was the most sensible one to the selection procedure, improving the accuracy from 44.74% to 71.05%.

3

x 10

12

3.4 3.6 E[K−core]

3.8

4

(b)

(a) 14

3.2

2

x 10

−3

Healthy Schizophrenia

Healthy Schizophrenia

1.5 f(V[Acc])

f(Q)

10 8 6 4

1

0.5

2 0

0.4

0.5

0.6

0.7

0.8

0

Q

0

1000

2000 3000 V[Acc]

(c)

(d)

4000

5000

Fig. 1. Probability distributions of the network measures with the highest rankings for networks in healthy and schizophrenic subjects: (a) variance of the closeness centrality, (b) first statistical moment of the K-core, (c) maximum modularity, and (d) variance of the accessibility. We considered a kernel density estimation (Gaussian kernel) to smooth the densities for better visualization.

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Table 2 Percentage of correct classification of networks obtained from healthy and schizophrenic subjects considering 4 or 54 measures. PC is the positive class, H. indicates the healthy class and S., schizophrenic subjects. Naive Bayes

Accuracy Precision (PC: H.) Specificity: Recall (PC: H.) F-Measure (PC: H.) Precision (PC: S.) Sensitivity: Recall (PC: S.) F-Measure (PC: S.)

Bayesian network

C4.5 Decision tree

54 meas.

4 meas.

54 meas.

4 meas.

54 meas.

4 meas.

0.74 0.68 0.90 0.77 0.85 0.58 0.69

0.76 0.73 0.84 0.78 0.81 0.68 0.74

0.71 0.70 0.74 0.72 0.72 0.68 0.70

0.78 0.76 0.84 0.80 0.82 0.74 0.78

0.45 0.46 0.58 0.51 0.43 0.32 0.36

0.71 0.68 0.79 0.73 0.75 0.63 0.69

1

0.8

0.8

0.8

0.6

0.6

0.6

r

r

1

r

1

0.4

0.4

0.2

0.4

0.2 Healthy Mean

0 0

20

40

60

σ

80

100

0.2 Schizophrenia Mean

0 0

20

40

(a)

60

σ

80

100

Healthy Schizophrenia

0 0

20

(b)

40

σ

60

80

100

(c)

Fig. 2. Phase coherence calculated for networks of (a) healthy subjects and (b) patients with schizophrenia. Each point is a network. In (c), it is shown the average phase coherence for each class, for a better visualization.

1.6

Another analysis concerning the robustness of networks was done by simulating random failures and attacks. Both types of network had similar behaviors (Fig. 4). In order to verify these results deeper, we calculated the second moment of the degree distribu-

Healthy Schizophrenia

1.4 1.2

2

tion of the networks (E½k ), which is related to the heterogeneity of network organization. The emergence of some dynamical pro-

f(Hd)

1 0.8

cesses shows a critical value depending on the ratio

0.6

synchronization, percolation and spreading processes (Barrat et al., 2008). Since our data has a fixed mean degree, the second statistical moment of the degree distribution is enough to define the behavior of the networks. Fig. 5 presents the probability distri-

0.4 0.2

E½k , E½k2 

such as

2

0

bution of E½k . 2

2.5

3

3.5

4

4.5

5

Hd Fig. 3. Probability distribution of the dynamical entropy measure for healthy and schizophrenic cortical networks.

pffiffiffiffi due to the fluctuations in r, which are of order Oð1= N Þ (Arenas et al., 2008). At an N ¼ 140, we observed a fluctuation of 8.5%, which indicates that the order parameter, which measures the network synchronization, did not allow a discrimination between the two classes of networks. We quantified the resilience of the networks in terms of the dynamic entropy (Demetrius and Manke, 2005), which can be considered as a measure of robustness against random failures (see the supplementary material). Fig. 3 presents the probability distribution of this measurement obtained from cortical networks of healthy and schizophrenic subjects. Interestingly, networks of patients with schizophrenia were slightly more robust than the networks of healthy subjects, confirming the results by Lynall et al. (Lynall et al., 2010). However, this difference was not statistically significant as we verified by performing a chi-squared statistical test and by evaluating the symmetrical uncertainty.

4. Discussion In this study we show that cortical network measures based on fMRI data and data-mining methods can be used to reliably distinguish between brain networks of patients presenting child-onset schizophrenia and those of healthy subjects. We observed that cortical networks of patients with child-onset schizophrenia presented higher values of variance of the closeness centrality and accessibility, but small values of average K-core and modularity (see Fig. 1 and Table 1). This fact indicates that networks of schizophrenic patients contain cortical regions with higher variance of central properties, but have less modular structure than networks of healthy subjects. In addition, schizophrenic patients contain some cortical regions with higher values of closeness centrality and accessibility than the healthy ones. In contrast, large-scale properties of the brain organization, such as small-worldness and degree distribution, have very similar values in healthy and schizophrenic subjects. This suggests that key aspects of brain topology are highly preserved even in the presence of this putative neurodevelopmental disorder. One can speculate that such variations are at

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1

1

Healthy Schizophrenia

0.8

0.6

0.6 E/E0

E/E0

0.8

Healthy Schizophrenia

0.4

0.4

0.2

0.2

0

0

0.2

0.4 0.6 Fraction failed

0.8

(a)

0

0

0.1

0.2 0.3 Fraction attacked

0.4

0.5

(b)

Fig. 4. Relative efficiency obtained from (a) random removal of nodes and (b) attacks.

0.08

Healthy Schizophrenia

0.07

f(E[k2])

0.06 0.05 0.04 0.03 0.02 0.01 0 20

40

60

80

100

E[k2] Fig. 5. Probability distribution of the second statistical moment of the degree distribution for healthy and schizophrenic subjects.

least partially responsible for the disease pattern of schizophrenia, but in order to test this hypothesis more accurate databases and further studies are needed. Regarding the remaining 50 network measures we tested in this study, the two classes of networks were not significantly different. Although Supekar et al. (Supekar et al., 2008) verified that the measure of the clustering coefficient could distinguish patients with Alzheimer from the controls with a sensitivity of 72% and specificity of 78%, we observed that this measure was not able to reliably discriminate healthy patients from subjects with child-onset schizophrenia. Moreover, our results contradict previous analysis of networks in healthy and schizophrenic adults which showed reduced clustering coefficient and modularity in schizophrenic networks (Vértes et al., 2012; Liu et al., 2008). According to our results, only the modularity could discriminate reliably between both types of networks. Moreover, we also observed that the average shortest paths were similar in these two classes of networks. Our findings imply that the schizophrenic cortical networks are less modular but the efficiency in communication is almost the same for both classes of networks. Therefore, network communities, formed by densely connected nodes, might be better defined in healthy subjects than in schizophrenic ones, whereas the communication between brain areas is supposed to be similar in both classes of networks. Our results also suggest that there is a weak statistical dependence between the four selected discriminating measures, since the performance of the naive Bayes and the Bayesian network methods was very similar (see Table 2). This outcome was

expected since these features are all related to different networks properties. More specifically, closeness centrality is based on shortest paths, accessibility on random walks, K-core on connectivity and the modularity is related to the network modular structure. The comparison of the networks in terms of dynamical processes revealed that the two classes of networks do not differ significantly with respect to synchronization and resilience (see Figs. 2 and 3). The distribution of the second moment of the degree distribution for schizophrenic cortical networks presents higher average, which indicates that these networks were less heterogeneous than the healthy networks (see Fig. 5). However, the probability distributions did not allow discriminating between the networks, as we verified by a chi-squared test. Therefore, the variations on the network topology did not affect the dynamics of networks in schizophrenia, since the second moment of the degree distribution was similar in both classes of networks. These results agree with the simulation of synchronization and node removal (see Figs. 2 and 4). Therefore, the networks of healthy and schizophrenic subjects are not significantly different with respect to their level of resilience and synchronization. Our findings also indicate that the revealed differences in cortical network organization can be explored for developing a diagnostic aid method based on network measures. Indeed, our classification of patients with child-onset schizophrenia achieved a sensitivity of 90% and specificity of 74%. This finding supports the notion that analysis based on network measures and data mining methods may present a possible strategy for automatic diagnostics for neurological disorders Previous studies on restingstate fMRI achieved similar levels of specificity and accuracy, not only for schizophrenia in adults (Tang et al., 2012; Venkataraman et al., 2012; Shen et al., 2010), but also for other neurological disorders (Welsh et al., 2013; Zeng et al., 2013; Tang et al., 2013). Regarding the limitations of our analysis, note that more accurate results could be obtained if one considers data from both hemispheres of a brain. However, such data sets are currently not available. In addition, the use of the low-frequency oscillations, as addressed here (0.05–0.111 Hz), may not be suitable to model actual information transfer but probably reflect gross anatomical connectivity plus large-scale regulation processes. A limitation in terms of reliable and early diagnosis of child-onset schizophrenia lies in the fact that our analysis was focused on comparing brain networks of healthy subjects with those of child-onset schizophrenic patients. A complication in diagnostics of this disease is based on the need for differentiating child-onset schizophrenia from other diseases such as affective disorders (both depression and bipolar disorder) with psychotic symptoms, pervasive developmental disorders, severe personality disorders, nonpsychotic

Please cite this article in press as: de Arruda GF et al. Structure and dynamics of functional networks in child-onset schizophrenia. Clin Neurophysiol (2014), http://dx.doi.org/10.1016/j.clinph.2013.11.036

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Please cite this article in press as: de Arruda GF et al. Structure and dynamics of functional networks in child-onset schizophrenia. Clin Neurophysiol (2014), http://dx.doi.org/10.1016/j.clinph.2013.11.036