Whether the balance between integration and segregation of information in the brain is damaged in Mild Cognitive Impairment (MCI) subjects is still a matter of debate. Here we characterize the functional network architecture of MCI subjects by means of complex networks analysis. Magnetoencephalograms (MEG) time series obtained during a memory task were evaluated by synchronization likelihood (SL), to quantify the statistical dependence between MEG signals and to obtain the functional networks. Graphs from MCI subjects show an enhancement of the strength of connections, together with an increase in the outreach parameter, suggesting that memory processing in MCI subjects is associated with higher energy expenditure and a tendency toward random structure, which breaks the balance between integration and segregation. All features are reproduced by an evolutionary network model that simulates the degenerative process of a healthy functional network to that associated with MCI. Due to the high rate of conversion from MCI to Alzheimer Disease (AD), these results show that the analysis of functional networks could be an appropriate tool for the early detection of both MCI and AD.

To our best knowledge, no previous characterizations of the topological properties of functional brain networks in MCI subjects with MEG were attempted so far. We here apply methods from complex networks theory to compute macroscopic and mesoscopic parameters of the functional networks in a group of nineteen MCI patients and a group of control participants of the same size. Brain activity was measured by means of MEG during a Sternberg's letter-probe memory task [15] , [16] and functional connectivity was calculated using the synchronization likelihood (SL), a measure to evaluate the generalized synchronization based on the theory of nonlinear dynamical systems [17] . We will show that an increase in global network synchronization in MCI patients occurs, as compared to healthy controls, and that an evolution of the MCI functional network towards a more random structure takes place. Interestingly, MCI patients feature an increased synchronization between brain areas [14] , and AD patients a corresponding decrease in connectivity [18] . Finally, based on the experimental observations, we offer a computational evolutionary network model that simulates the transition from healthy to MCI topology, and satisfactorily reproduces the changes in the network metrics observed in MCI subjects.

On the other side, Mild Cognitive Impairment (MCI) is an intermediate state between healthy aging and dementia [11] . In fact, 12 to 15 of MCI subjects develop some form of dementia per year. This makes MCI patients an ideal population to search for neurophysiological profiles of prediction of who will develop dementia. In amnestic MCI, cognitive abilities are mildly impaired, and patients are able to carry out everyday activities, but there are pronounced deficits in memory tasks. Whether MCI subjects show a similar network profile than AD patients is still a matter of debate. Neuropathological studies indicate that MCI patients share some of the AD pathophysiological characteristics, such as the presence of neurofibrillary tangles, loss of dendritic spines and the accumulation of beta-amyloid protein in the associative cortex [12] . fMRI studies show higher blood flow values in medial temporal lobe regions during a memory task in MCI, as compared to controls [13] . Bajo et al. [14] described higher functional connectivity values from MEG recordings in MCI subjects than in age-matched controls.

A key issue in neuroscience is the understanding of the coexistence of local specialization and long distance integration in the complex structure of the brain. Graph theory provides valuable tools to describe the topological organization supporting cognitive processes [1] . In particular, the approach led to a characterization of structural and functional networks in the brain [2] – [4] , typically endowed with high clustering and short non-Euclidean distance between nodes, the fingerprint of a Small World (SW) architecture [5] . In addition, graph analysis may help to identify network signatures of impairment in pathological conditions, such as the network organization in Alzheimer's Disease (AD) [6] . AD, the most frequent cause of dementia, is characterized by accumulation of beta-amyloid proteins, degeneration of neurons, loss of synaptic contacts, and it has been described as a disconnection syndrome [7] . Stam et al. [6] demonstrated that functional networks of AD patients show a loss of SW properties [6] , [8] , [9] , resulting in an increase in the mean path length between nodes [8] , with an associated decrease in local synchrony [9] . A crucial point is whether the pathophysiology of AD would be detected long before the actual diagnosis of the disease [10] . Indeed, the identification of preclinical AD could significantly enhance the benefit of new drugs and vaccines, at the time when the severe brain damage, such as widespread brain atrophy, associated with AD, has not taken place yet.

The node outreach relates the distance and the weight of the connections of node , being the set of nearest neighbors of node and the physical (Euclidean) distance of the links (obtained from the distance between sensors). The network mean outreach reflects whether the network activity is dominated by short-range (low outreach) or long-range (high outreach) connections. Finally, the network modularity quantifies the existence of topological communities inside the network [22] . Its value is , where is the sum of all terms of , is the Kronecker delta and and are the communities of nodes and , respectively. In what follows, we focus on assuming the classical network partition into six lobes (central, frontal-left, frontal-right, temporal-left, temporal-right and occipital).

As for the network parameters, the average degree of a node is obtained as , and the mean degree is . The mean shortest path can be obtained as follows: the length associated to the link connecting nodes and is defined as the inverse of its probability , being when . By applying the Dijkstra's algorithm [21] , the shortest distance matrix is found. The value tells us how far is node from the rest of the network, while the average gives the average shortest path of the whole network. The mean clustering reflects the probability of finding triangles in the network. It can be calculated through the probability matrix as . The average clustering coefficient is obtained by averaging [20] .

Functional networks from a representative control volunteer. A broad-band filter was applied. (A) Weighted SL matrix obtained from the SL between 148 sensors. (B) Unweighted adjacency network after converting the SL matrix (shown in A) into a binary matrix using as a threshold , which leaves the 5% of all possible links. (C) Probability matrix after normalizing as explained in the text (note the contrast enhancement). In all panels, nodes/sensors are grouped according to the lobe they belong to: frontal left (FL), frontal right (FR), temporal right (TR), central (C), temporal left (TL) and occipital (O).

The SL between the 148 sensors yields a (symmetric and weighted) 148 148 correlation matrix . The values of the matrix elements range from to , which corresponds to a difference of one order of magnitude between the maxima and the minima. The matrix is fully connected, and all pairs of nodes (sensors) have a SL higher than zero. Traditionally, two different techniques are used in order to study weighted brain networks. The first method involves thresholding the matrix to obtain an unweighted network , so that the link between node an is if the weight of the connection is above the threshold, and otherwise. In some other occasions, a fraction of the total number of links is kept [19] (e.g., the of the highest weighted links). In both cases, information is lost by thresholding. Our approach relies in a normalization technique recently proposed [20] that allows using the measures applied to unweighted networks to the weighted case without losing the information contained in the weights distribution. In addition, this normalization facilitates comparison between networks obtained from different individuals. By mapping the weights of the correlation matrix with a continuous bijective map [0,1] it is possible to obtain a probability matrix . In our case, we linearly normalize the weights . The matrix reflects the probability of existence of a link between node and , and an ensemble of unweighted matrices can be generated on the basis of the probabilities given by . The power of the approach is that any polynomial function calculated as the average of an ensemble of adjacency matrices obtained from , is equal to the value of the polynomial of the matrix itself [20] . Therefore, one can extend several classical measures for unweighted networks to . To visualize the advantage of this method, we have plotted in Fig. 1 the matrices , (with of the links) and for a control individual, grouping nodes according to the lobe they are over. We can see that in the case of the adjacency matrix, Fig. 1B , we lose information, which is specially relevant for the inter-lobe correlations (e.g., see connections between central and occipital lobe). In addition, by comparing and , we observe how the matrix normalization enhances the contrast between low and high correlated nodes.

MEG scans were obtained from nineteen MCI patients and nineteen healthy volunteers during a Sternberg's letter-probe task (see Materials and Methods in File S1 for details). Before the MEG recordings, all participants or legal representatives gave written consent to participate in the study, which was approved by the local ethics committee of the Hospital Clnico San Carlos. Data segments free of artifacts corresponding to eye blinks, eye movements of muscular activity were chosen by visual inspection. Five frequency bands [ Hz, Hz, Hz, Hz, Hz] were considered. Synchronization Likelihood (SL) [17] was calculated between all channel pairs for each frequency band. A normalization was applied to obtain a probability matrix from which the topological network parameters are extracted. In what follows we define the normalization method and the metrics calculated over all networks.

Results

Network structure and global properties For each individual, we construct a probability matrix from the broadband signal and five probability matrices from each considered frequency band ( , , , and ). Next, we compute the network parameters described in the previous section and average them by groups (control and MCI). File S1 summarizes the results obtained for each group along with the percentage of variation from the control group. The average degree of the network shows an increase of 15.9 for the MCI group. Since only positive recognition trials during the memory paradigm are considered, these results confirm that MCI patients require higher synchronization in their functional networks in order to perform a memory task [14]. We also observe that differences between both groups are more evident in the broadband signal, a signature that will be constantly present for all network parameters. As a consequence of the higher number of connections in the MCI group, the average shortest path decreases, although differences between both groups are less significant. It is interesting to note that the normalized shortest path in both controls and MCI, revealing that the average distance between nodes is twice as large as for an equivalent random graph. Since , the organization of the shortest paths within the MCI network is slightly shifted towards more random configurations. The outreach parameter is the most affected parameter. We observe a 23.4 increase for the broadband signal, which is higher than the 15.9 increase in mean degree for both networks. This indicates that the increase in correlation between nodes in the MCI networks becomes more pronounced at long-range connections, and the combination of both alterations makes the outreach parameter the one with the highest differences between both groups. This suggests that individuals suffering from MCI incur in a higher energetic cost than controls to perform the same memory task, since they have to maintain high correlations at longer distances. The normalized outreach is in both cases lower than in the random case ( ) since the existing correlations between nearby brain regions are spread around the whole network when randomizing it. Nevertheless, we observe that the MCI group has a closer to one, which again reveals that the functional structure is more random than in the control group. Finally, there is a decrease in the modularity that is in accordance with an evolution towards random topologies. This reduction of in the MCI group, larger again for the broadband signal, indicates a degradation of the modular structure of the functional networks, and it is an inherent property of random networks, whose modularity is close to zero. Figure 2 shows the behavior of the degree distribution, clustering, outreach and neighbour's mean degree – as a function of the node average degree for control (green circles) and MCI groups (red squares) computed from the broadband signal. In Fig. 2(A) we report the cumulative degree distribution which, in turn, corresponds to the average degree of an ensemble of unweighted networks generated using the probability matrix. The figure makes it evident the likelihood of finding highly connected nodes within the MCI group. As for the clustering distribution , both groups have positive correlations (see [Fig. 2(B)]), a behaviour that has been previously reported in healthy individuals and Alzheimer patients [8]. Notice that individuals suffering from MCI have lower clustering coefficient, entailing an evolution towards random structures, where the number of triangles is much lower than in the networks analyzed here [2]. The outreach distribution [Fig. 2(C)] shows that the MCI group features higher values of the outreach. Since (where indicates ensembles average), the latter feature comes from an increase in the probabilities of long distant links. In other words, the evolution of the disease has, somehow, increased the weight of long-range connections. Finally, in Fig. 2(D) we report the average degree of the nearest neighbours of nodes with degree , . This distribution characterizes the assortativity of the network [23]. Both groups show a positive degree correlation, revealing the assortative nature of the networks. Interestingly, assortative organization has been already reported in functional connectivity networks obtained with fMRI [24]. Despite both networks being assortative, the MCI group exhibits higher values, as a result of the much larger levels of synchronization between nodes. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 2. Network parameter distributions. Several network parameter distributions for the control (green circles) and MCI (red squares) groups. (A) Probability distribution of finding a node with a degree higher than , (B) clustering coefficient , (C) outreach and (D) average nearest neighbors degree . https://doi.org/10.1371/journal.pone.0019584.g002 To compare the mentioned network parameters between the two groups, each parameter value was first averaged across epochs for each participant and channel pair. Then, nonparametric permutation testing [25]–[27] was applied to find channel pairs with significant differences between groups. In brief, a two-sample non-parametric test (Kruskal-Wallis test) between groups was performed. Next, non-parametric permutations were calculated by randomly dividing the participants into groups of members to match the numbers in the original groups. This was repeated times for each channel pair. Subsequently, the threshold was obtained from the percentile of this set of -values. After the application of this statistical method to SL raw data (i.e., without band-pass filtering) there are parameters showing significant differences between the two groups: outreach ( ), normalized clustering ( ), modularity (p = 0.0033), mean degree ( ), normalized shortest path ( ) and normalized outreach ( ) (see File S1 for details).

Mesoscale analysis: inter-lobe communication, community structure and roles From a holistic point of view, it is well known that the processing abilities of the brain rely on the segregation and integration of information [28]. Since both mechanisms depend on the modular structure of the network, any alteration of the interplay between the existing clusters may lead to a deterioration of the functional network performance. With the aim of evaluating how MCI modifies the modular structure, we have measured the internal lobe strength , the external lobe strength and the lobe modularity , being the lobe index. The two former parameters measure, respectively, the total weight of the connections inside lobe , and those going to other lobes . Figure 3 summarizes the variation of these parameters in the MCI group for the classical cortical division into six lobes (central, frontal left, frontal right, temporal left, temporal right and occipital). With regard to the internal lobe strength [Fig. 3(A)], we can see that three lobes have a significant increase of their internal activity, specifically, the central ( ), the frontal left ( ) and the temporal right ( ), and only the frontal right lobe has slightly reduced its internal synchronization ( ). Differences in the external lobe strength are more important [Fig. 3(B)], with an increase higher than in all lobes, indicating that, besides an evolution towards random structures, there is an increase in the weight of the connections between lobes in MCI. As a consequence, the modularity of all lobes decreases [Fig. 3(C)], since the restructuring of the network is dominated by the increase of the inter-lobe connections. Therefore, despite the increase in communication between lobes, the segregated structure of the brain is dramatically reduced and the balance between segregation and integration present in a healthy brain is lost. Finally, we have plotted the percentage of variation of the lobe-to-lobe strength [Fig. 3(D)], which shows in all cases a positive value. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 3. Mesoscale analysis. Percentages of variation in the MCI group with respect to the control one of: the strength inside each lobe (A), the strength of the links going out from each lobe (B), and the lobe modularity (C). In (D), percentages of variation of the lobe-to-lobe strength. Lobe code: 1 = central, 2 = frontal left, 3 = frontal right, 4 = temporal left, 5 = temporal right and 6 = occipital. https://doi.org/10.1371/journal.pone.0019584.g003 Next, we have gone down to the lowest scale (i.e., the node level). We have used the classification of nodes introduced by Guimerà et al. [29], which is based in the computation of the within-module degree and the participation coefficient . The first parameter, quantifies the importance of node inside its community and it is defined as , where and are, respectively, the degree and the community of the node , is the mean degree of the community and is the standard deviation of in . On the other hand, the participation coefficient indicates how connections of the node are distributed among the existing communities, where is the number of connections between node and community and is the total number of communities. The participation coefficient is zero when all links of a node are inside its own community and close to one when they are distributed among all modules of the network. Figure 4(A) shows the position of the nodes with higher influence in their communities (circles) and higher participation coefficients (triangles) in the healthy group. We can observe that, during a memory task, most participating nodes are located over the two frontal lobes, while nodes with higher relevance (i.e., those with higher weights) are located over the occipital lobe. Figure 4(B) shows those nodes which have suffered the highest variation of both parameters in the MCI group. We observe a generalized increase of the participation coefficient, while the within-module degree has both positive and negative changes, which indicates that a certain reorganization is occurring inside each lobe. Note that nodes with higher increases in the participation coefficient are located over the occipital, temporal right and central lobes, while nodes for which the within-module degree has increased the most are spread over the whole network (see File S1 for more details). PPT PowerPoint slide

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larger image TIFF original image Download: Figure 4. Community structure and roles. (A) Nodes with higher within-module degree and participation coefficient in healthy individuals. Only the first 13 nodes with the highest and are labelled. Those with the highest are marked with circles and triangles indicate those with the highest . (B) Nodes with higher variation at the within-module degree and participation coefficient in the MCI group. Again, only the first 13 nodes with the highest differences are labelled: nodes with higher increase of (circles) and (triangles). Lobe color scheme: red (central), blue (frontal right), black (frontal left), magenta (temporal right), green (temporal left), and cyan (occipital). https://doi.org/10.1371/journal.pone.0019584.g004