Synchronizability of EEG-based functional networks in ...

Synchronizability of EEG-based functional networks in early Alzheimer's disease Marzieh S. Tahaei, Mahdi Jalili, Member, IEEE and Maria G. Knyazeva  Abstract— Recently graph theory and complex networks have been widely used as a mean to model functionality of the brain. Among different neuroimaging techniques available for constructing the brain functional networks, electroencephalography (EEG) with its high temporal resolution is a useful instrument of the analysis of functional interdependencies between different brain regions. Alzheimer's disease (AD) is a neurodegenerative disease, which leads to substantial cognitive decline and, eventually, dementia in aged people. To achieve a deeper insight into the behavior of functional cerebral networks in AD, here we study their synchronizability in seventeen newly diagnosed AD patients compared to seventeen healthy control subjects at no-task, eyesclosed condition. The cross-correlation of artifact-free EEGs was used to construct brain functional networks. The extracted networks were then tested for their synchronization properties by calculating the eigenratio of the Laplacian matrix of the connection graph, i.e., the largest eigenvalue divided by the second smallest one. In AD patients, we found an increase in the eigenratio, i.e., a decrease in the synchronizability of brain networks across delta, alpha, beta, and gamma EEG frequencies within the wide range of network costs. The finding indicates the destruction of functional brain networks early in AD. Index Terms— EEG, Alzheimer's disease, functional connectivity, brain networks, graph theory, cross-correlation, synchronizability.

I. INTRODUCTION substantial proportion of neurological and psychiatric disorders including epilepsy [1], schizophrenia [2], Parkinson’s disease [3], and Alzheimer's disease (AD) [4] affect cerebral connectivity. AD is the most common cause of dementia accounting for the 50-70% of cases, named after German physician Alois Alzheimer, who first described it in 1906 [5]. Recent studies emphasize the role of early deterioration of cerebral circuitry in its pathogenesis (for review see [6-9]). To examine the functional and anatomical brain connectivity in AD various neuroimaging techniques

A

including diffusion tensor imaging (DTI), functional magnetic resonance imaging (fMRI), and electroencephalography (EEG) are used. EEG studies of functional connectivity in AD mostly apply synchronization measures including bivariate measures such as coherence [10, 11] and multivariate measures like phase synchronization [4]. A frequently demonstrated feature of AD is a reduction of power and coherence in EEG high frequency bands supposedly due to the abnormalities in local synchronization [11-13]. Additionally, AD is characterized by a decrease in general synchrony [14] and distant coherence [10]. At an early stage of the disease, patterns with both hypoand hyper-synchronization have been noticed [4, 15, 16]. This complex pattern of changes in functional connectivity suggests that the characteristics of dynamical brain circuits evolve in the disease and calls for an analysis of the relationship between network organization and function in AD. Such an analysis can be performed by applying the graph theory techniques to the signals recorded from the brain [1719]. Their first applications in AD revealed abnormal smallworld architecture in the structural and functional cortical networks [20, 21]. In this paper we investigated whether and how the synchronization properties of EEG-based brain networks are altered in AD. To this end, the cross-correlation matrices were calculated for all EEGs, and then, the connection networks were extracted through proper methods. We then compared the functional networks of AD patients with those of controls in terms of their synchronizability through a pure graph theoretic measure that is the largest eigenvalue of the Laplacian matrix of the connection graph divided by the second smallest eigenvalue [22]. The synchronizability mainly refers to the stability of synchronized state in the dynamical system within the wide range of the parameters of its dynamics. Our results showed widespread decrease of synchronizability in AD patients across all EEG frequency bands except theta band. II. METHODS AND MATERIALS

MSH and MJ are with Department of Computer Engineering, Sharif University of Technology, Tehran, Iran. MGK is with Laboratoire de Recherche en Neuroimagerie (Département des Neurosciences Cliniques) and Department of Radiology, Centre Hospitalier Universitaire Vaudois (CHUV), and University of Lausanne, Lausanne, Switzerland. * Corresponding author: Mahdi Jalili (Tel: 0098 21 66166636, Fax: 0098 21 66019246, Email: [email protected]) Copyright (c) 2012 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending an email to [email protected]

A. Subjects Seventeen newly diagnosed AD patients (mild AD with Clinical Dementia Rating (CDR) Scale in the range of 0.5–1 and Functional Assessment Staging (FAST) in the range of 3– 4) were recruited from the Memory Clinic of the Neurology Department (CHUV, Lausanne). The group included 6 women and 11 men (Table I). Seventeen control subjects (11 women and 6 men) were voluntarily enrolled in the study. The AD and control groups were almost matched for their age and

education level (Table I). All the patients, caregivers, and control subjects gave written informed consent. All the applied procedures conform to the Declaration of Helsinki (1964) by the World Medical Association concerning human experimentation and were approved by the local Ethics Committee of Lausanne University. The clinical diagnosis of AD was made according to the NINCDS–ADRDA criteria. Cognitive functions were assessed with the mini mental state examination (MMSE) [23], and the AD and control groups were significantly different in their MMSE scores (P = 0.001, Wilcoxon's ranksum test). The MMSE scores for the AD patients were in the range of 13 – 27.

beta (13-30 Hz), and gamma (30-40 Hz). To this end, digital filtering with no phase-shift was done off-line by applying an Elliptic filter with 0.5 db of peak-peak ripple and a minimum stop-band attenuation of 20 db. The filtered data were then analyzed by calculating the cross-correlation matrices to be used in the next step of the algorithm for extracting functional brain networks. A different aspect of this dataset (whole-head multivariate phase synchronization) has been previously published [4].

Table I. Demographic and clinical characteristics of the AD patients and control subjects. Second and third columns present group characteristics (mean ± standard deviation). Fourth column presents P-values for the statistical significance of the between-group differences (Wilcoxon’s ranksum test).

No of subject Gender Age Education MMSE

ADs 17 6 Women 11Men 69.4 ± 10.6 11.6 ± 3.3 21.8 ± 3.9

Controls P (Wilcoxon’s test) 17 11 Women 6 Men 67.6 ± 11.6 0.63 13.1 ± 3.2 0.18 28.5 ± 1.2 0.001

B. EEG recording and preprocessing The closed-eyes EEG data were collected while subjects were sitting relaxed in a semi-dark room. The 128-channel Geodesic Sensor Net (EGI, USA) machine was used for recording the EEGs. The duration of recording for each subject was 3-4 minutes. All the electrode impedances were kept under 30 k – that is, much lower than the recommended limit (50 k) for the high-input-impedance EGI amplifiers. The recordings were made with vertex reference at a sampling frequency of 500 Hz. They were filtered (FIR, band-pass of 1– 50 Hz; 50 Hz notch filter) and re-referenced against the common average reference that has been shown to closely approximate reference-free potentials in multichannel EEG applications. To obtain a higher confidence in the synchronization estimates, the signals were segmented into non-overlapping 1second epochs [24] and subsequent calculations were averaged over these artifact-free epochs. Artifacts in all channels were edited off-line: first, automatically, based on an absolute voltage threshold (100 V) and on a transition threshold (50 V), and then on the basis of a thorough visual inspection. The sensors that recorded artifactual EEG (> 20% of the recording time) were corrected using the bad channel replacement tool (NS 4.2 EGI, USA). We removed all of the sensors in the outer ring resulting in 111 sensors used for further processing (Fig. 1). Furthermore, in order to estimate correlation independently from the absolute power of the signals, each signal was mean de-trended and scaled to unit time variance. The EEG data were filtered in conventional frequency bands, i.e., delta (1-3 Hz), theta (3-7 Hz), alpha (7-13 Hz),

Figure 1: Head diagram of the EEG sensor positions and labeling. The diagram shows the correspondence between the high-density 129-channel Sensor Net (EGI, Inc.) and the International 10–10 System. The Sensor Net locations that match the positions of International 10–10 system are labeled. The 10–10 System names are followed by the numbers of the Sensor Net. The sensors corresponding to the 10–20 System are in bold. The gray background highlights all the sensors included in the analyses.

C. Constructing brain functional networks The filtered EEG time series were used to construct the connectivity matrices of the brain networks. We applied Pearson product momentum correlation coefficient as an index of the interdependence of the time series of two sensor locations. The first step was to calculate the weighted 111×111 correlation matrix (there are 111 sensor locations) based on Pearson cross-correlation coefficients. The correlation coefficient between sensors i and j can be obtained as

rij 

cov(i, j ) var(i ) var( j )

,

(1)

where cov(i,j) is the covariance between nodes i and j, and var(i) is the variance of node i. By averaging the correlation matrices over the artifact-free epochs, we computed the average weighted correlation matrices for each subject. Since

we were interested in identifying functional links between two sensor locations we considered the absolute value of the correlations. The next step was to construct the functional brain networks based on the correlation matrices. A possible approach is to consider the correlation matrix as the weighted adjacency matrix. In this case, the extracted weighted network is complete, and, thus, all the networks have the same topology but with different connection weights. Another approach is to binarize the connectivity matrices and to compute graph metrics for binary networks. We used conventional application of different threshold values to binarize the correlation matrix and to generate the adjacency matrix. This means that the elements of the graph are equal to 1, if the correlation value is larger than the threshold and to 0, if not. There are different threshold selection methods. When studying group differences, it is important to compare the networks of the same density. Otherwise, the observed phenomena might be due to the unbalanced number of links in the constructed networks. In order to obtain networks with similar density, we applied sparsity thresholding method [25-27]. Sparsity (or cost) of an undirected network of size N is the number of its edges divided by the number of edges in a complete network of size N, which is N(N – 1)/2. With a sparsity thresholding method, for each cost value one finds a subject-specific threshold resulting in a network with that particular cost. We applied this procedure to the correlation matrices of all subjects by repeating the thresholding over a range of cost values. In order to be able to study network synchronizability, in a network constructed from association matrix, all the component networks must be connected, i.e., there must be at least one path between any pair of nodes. The usual way to solve this problem is to restrict the analysis only to the cost values, at which all the networks are connected. However, the networks of our AD patients were disconnected for a considerable range of the cost values. So we addressed the issue of disconnectedness by means of maximum spanning tree [28, 29]. A maximum spanning tree is a spanning of a weighted graph having maximum weight. First, we computed the maximum spanning tree using original correlation matrix as a weight matrix. The maximum spanning tree was then used as a basis skeleton of the network. The edges required for constructing a network with specific cost, i.e. the strongest connections required to construct the network of that particular sparsity, were accordingly added to the maximum spanning tree. This way, the connectedness of the network was ensured [28, 29]. We considered two strategies for constructing the networks. The first, commonly used in brain network studies, was to construct binary brain networks. In order to generate networks of different cost values, unweighted edges were added to the binary maximum spanning tree. according to sparsity thresholding method. This strategy neglects weight values, which might contain useful information about the network. Therefore, in our second strategy, we added the number of edges needed to construct a network of a given cost, to the

weighted spanning tree, while preserving the weights of these edges, as was also done in [30]. A pseudo-code for construction of the network structure from EEG is as follows. - For each subject; - EEG is filtered in a desired frequency band; - For each epoch of EEG; o Absolute cross-correlation matrix is calculated; - Correlation matrices are averaged over artifact-free epochs resulting in average correlation C; - Maximum spanning tree T of weighted correlation matrix is calculated; - Considering a range (0.02-0.6) for network cost (density), for each density value d; o Threshold value at which the resulting binarized network has density value is found using sparsity thresholding method on (sparsity thresholding procedure): 1      ,   0   are added to o The edges of network maximum spanning tree  . The output binary network is denoted by A; o The edges of network are added to maximum spanning tree  . The output binary network is denoted by A; o The corresponding weighted network (W) is constructed by considering the original weights of non-zero elements of A; o The eigenratio is calculated for A and W; - Statistical test is performed at a group level. D. Network synchronizability There are various methods to quantify the degree of synchronization in dynamical networks, i.e., their synchronizability [31]. The most frequent measure accounting for the synchronizability of a network is its eigenratio [22, 32], which is a pure graph theoretical metric independent of individual dynamical system. In contrast to the metrics based on a specific dynamical system and estimated from numerical solutions of dynamical equations [33-35], the eigenratio does not need numerical simulation using dynamical systems. Let us consider a network with N nodes, adjacency matrix A = (aij), and Laplacian L = (aij), where N

lij  aij  i  j  ; lii   aij .

(2)

j 1

Let us denote the eigenvalues of the Laplacian matrix L as 0 = λ1 ≤ λ2 ≤ … ≤ λN (since L is a zero row-sum, we have λ1 = 0). The eigenratio λN /λ2 is a measure for synchronizability of the network (for connected networks we have λ2 ≠ 0), such that the smaller the eigenratio the better the synchronizability of the network [22, 32, 36]. Independent of a particular dynamical system, the eigenratio is the most frequent expression for the synchronizability of dynamical networks

[37-41]. E. Statistical analysis At each density value, the eigenratio of the functional networks of AD patients was compared to that of control subjects. The statistical significance was determined using a non-parametric Wilcoxon’s ranksum test. We set the significance level at P < 0.05. All computations were performed in MatLab. III. RESULTS Figure 2 shows the synchronizability of binarized networks as a function of cost for conventional frequency bands, i.e. delta (1-3 Hz), theta (3-7 Hz), alpha (7-13 Hz), beta (13-30 Hz), and gamma (30-40 Hz). As cost value increases, the networks become denser, and, hence, their synchronizability increases, i.e., the eigenratio decreases. On the other hand, for low values of cost, the networks are sparse and with few edges, and, hence, with weak synchronization properties. In our analysis cost values ranged from 0.02 to 0.6 with 0.02 intervals. Red asterisks in the figure indicate, where the

difference between AD patients and controls is significant. The results revealed widespread decreases in the synchronizability in AD patients compared to controls, i.e., increases in the eigenratio at the delta, beta, alpha, and gamma frequencies. Delta and alpha frequency bands showed the changes in a wide range of costs. At alpha band, the synchronizability of EEG brain functional networks in the control group was significantly higher than that in the AD patients for a broad range of cost values. At delta band, significant difference was observed for medium costs (0.10.48). The cost values at which the synchronizability of the networks in the control group was higher than that in the AD patients were lower in beta (0.11-0.18) and gamma (0.4-0.6) bands compared to the other two bands. We also computed synchronizability for weighted networks (Fig. 3). The results appear to be very similar to those for binarized networks. In fact, except for the theta band, all other frequencies revealed that the networks in controls had significantly higher synchronizability, i.e., lower eigenratio than that in AD patients.

Figure 2: The synchronizability (i.e., the eigenratio of the Laplacian matrix of the connection graph) of AD group (N = 17) and healthy control group (N = 17) in binarized networks as a function of cost. The synchronizability measure is applied to all conventional frequency bands, i.e. δ (delta 1-3 Hz), θ (theta 3-7 Hz), α (alpha 7-13 Hz), β (beta 13-30 Hz), and γ (gamma 30-40 Hz). Error bars correspond to standard errors. Red triangles indicate where the difference between AD patients and controls is significant (P < 0.05, permutation Hotelling's T2 test).

Figure 3: The synchronizability of AD and control groups in weighted networks as a function of cost for conventional frequency bands. Other designations are as in Fig. 2.

IV. DISCUSSION AND CONCLUSIONS Temporal synchronization of cerebral electrical activity plays an important role in brain function and its changes are linked to various brain pathologies. AD is among the brain disorders showing synchronization abnormalities [4, 10-16]. In this work we studied the synchronizability of brain functional networks extracted from EEGs of AD patients and matched healthy subjects. In contrast to previous studies, where the synchronization measures have been directly extracted out of the time series, we, first, extracted the network topology, and then, estimated a synchronizability measure for the extracted networks. To assess synchronizability, we used a conventional graphbased measure – the eigenratio that is the largest eigenvalue of the Laplacian matrix divided by the second smallest one [22, 32]. This measure quantifies the synchronizability of a network: the smaller the eigenratio, the better the synchronizability. The principal finding of this study is that the changes caused by AD result in the loss of

synchronizability in the EEG-based functional brain networks in all conventional frequency bands except theta. The synchronization properties of the AD networks were worse than those of controls in both binarized and weighted variants at delta, beta, and gamma frequencies, and, especially, in the alpha range. Indeed, in the latter frequency range, synchronizability of AD brain networks was lower than that of healthy controls for all the network densities. We have previously described the pattern of regional synchronization changes in the same dataset [4]. Our application of multivariate synchronization mapping to the analysis of functional connectivity revealed in AD specific changes in synchronization expressed by a landscape with both hypo- and hyper-synchronized regions. Its most prominent features included hypo-synchronization over the fronto-temporal brain region of the left hemisphere and hypersynchronization over the left temporal and bilateral parietal regions. The multivariate synchronization changes appeared to be significant across a broad frequency range, thus lending support to previous findings [4, 11-13, 15, 16]. Hyposynchronization frequently observed in AD was considered as

the effect of AD, while hyper-synchronization could be due to compensatory phenomena at the early stages of AD [4] or, alternatively, due to the impairment of cortical inhibition in AD [42]. An apparent inconsistency between increased functional connectivity (hyper-synchronization) shown in our previous study and decreased synchronizability revealed in the current network analysis may result from the fact that the latter provides a general characteristic of the brain networks, while synchronization changes previously studied in the same population are regional in nature [4]. The changes in functional connectivity raise questions about the properties of the brain networks in AD. The method that we use here allows an estimation of the synchronizability, which shows whether the synchronized state of a dynamical network is stable for a sufficiently large range of the parameters [43]. Therefore, low synchronizability indicates instability of the neural networks in mild AD. Considering the distributed nature of the brain cognitive functions, this property can be an important biomarker of disease progression, treatments, etc. Recent studies suggest that the large-scale functional brain networks in AD brain are of more random type, i.e., the average path length and clustering coefficient are closer to random networks in AD subjects compared to normal individuals [20]. Depending on the network structure, increasing the randomness in the network might enhance or worsen its synchronizability [44, 45]. For example, scale-free networks are less synchronizable than the corresponding random networks (with the same number of nodes and edges) [40]. However, increasing the randomness in small-world networks characteristic for the brain worsens their synchronizability, which is mainly due to the increase in network heterogeneity [40, 44]. Thus, the loss of smallworldness due to increased randomness could induce lower synchronizability in AD brain networks. The limitations of this study include relatively small size of the groups. However, clear results suggest a good potential of network analysis in AD. The replication of these findings on larger samples and with alternative imaging and analysis techniques is among the first tasks. Finally, it is no less important to understand to what extent network properties correlate with clinical picture in AD. V. ACKNOWLEDGMENTS The authors would like to thank Dr. Joseph Ghika for recruiting and diagnosing patients and Dr. Andrea Brioschi for their neuropsychological testing in the Neurology Dept. of Centre Hospitalier Universitaire Vaudois (CHUV). We also greatly appreciate participation of our patients and controls in the project. We are grateful to our peer-reviewers for insightful comments and suggestions. This work was partly supported by Swiss National Foundation Grant No 320030127538/1.

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Marzieh S. Tahaei received her M.Sc. degree in Artificial Intelligence (computer engineering) from Sharif University of Technology, Tehran, Iran, in 2011. Her thesis focused on network analysis of EEG data in Alzheimer’s disease. Since then she is a research assistant in Machine Learning group of Digital Media Lab (DML) at the Department of Computer Engineering, Sharif University of Technology, Tehran. She is currently working on unsupervised feature learning. Her research interests include machine learning and its applications in complex networks and computational neuroscience. Mahdi Jalili received his B.S. degree in Electrical Engineering from Tehran Polytechnique in 2001, his M.S. degree in Electrical Engineering from the University of Tehran in 2004, and his PhD from Swiss Federal Institute of Technology Lausanne (EPFL) in 2008. Since 2009, he has joined Department of Computer Engineering, Sharif University of Technology as an assistant professor. His research interests are in dynamical networks, synchronization in complex networks, computational neuroscience and human brain functional connectivity analysis. He received the 2009 presidential award of the 15th Razi Research Festival. Maria G. Knyazeva, PhD, is privat-docent and a leader of the research group “Connectivity Factors in Neurodegenerative Diseases” in the Department of Clinical Neurosciences, CHUV, Lausanne. Dr. Knyazeva has over 20 years of experience in developmental neurophysiology and about 10 years in neurophysiology of aging and neurodegenerative disease. She is the author of more than 50 scientific publications including peer-reviewed and conference papers and book chapters. Her research is focused on structural, functional, and effective aspects of cerebral connectivity across human lifespan and in Alzheimer’s disease. It is based on multimodal approaches combining MRI-based and high-density EEG methods.