International Journal of Neural Systems, Vol. 25, No. 2 (2015) 1550005 (18 pages) c World Scientific Publishing Company DOI: 10.1142/S0129065715500057

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A Longitudinal EEG Study of Alzheimer’s Disease Progression Based on A Complex Network Approach Francesco Carlo Morabito∗ , Maurizio Campolo and Domenico Labate DICEAM, University Mediterranea Reggio Calabria, Italy ∗ [email protected] Giuseppe Morabito University of Pavia, Faculty of Engineering, Italy Lilla Bonanno, Alessia Bramanti, Simona de Salvo, Angela Marra and Placido Bramanti IRCCS Centro Neurolesi “Bonino Pulejo” Messina, Italy Accepted 15 December 2014 Published Online 6 February 2015 A complex network approach is combined with time dynamics in order to conduct a space–time analysis applicable to longitudinal studies aimed to characterize the progression of Alzheimer’s disease (AD) in individual patients. The network analysis reveals how patient-speciﬁc patterns are associated with disease progression, also capturing the widespread eﬀect of local disruptions. This longitudinal study is carried out on resting electroence phalography (EEGs) of seven AD patients. The test is repeated after a three months’ period. The proposed methodology allows to extract some averaged information and regularities on the patients’ cohort and to quantify concisely the disease evolution. From the functional viewpoint, the progression of AD is shown to be characterized by a loss of connected areas here measured in terms of network parameters (characteristic path length, clustering coeﬃcient, global eﬃciency, degree of connectivity and connectivity density). The diﬀerences found between baseline and at follow-up are statistically signiﬁcant. Finally, an original topographic multiscale approach is proposed that yields additional results. Keywords: Alzheimer’s disease; complex networks; complexity; mutual information; longitudinal EEG database; multiscale temporal analysis.

1. Introduction Alzheimer disease (AD) is a degenerative disorder of cognitive and behavioral impairment characterized by a long and progressive course that markedly interferes with social life of both patients and caregivers. It is the most common cause of dementia, accounting for 60% to 80% of all dementia diagnoses.1 The related functional disturbances can be interpreted in terms of a disconnection syndrome of the brain cortex that is associated with deﬁciency of information transmission and altered cortico-cortical long

distance connections, rather than speciﬁc local alterations in neighboring areas.2,13,32,33 Neuroimaging techniques have conﬁrmed that features of AD progression follow neuronal pathways rather involving neighboring regions.3,33 Much evidence from these studies thus support the interpretation of AD as a disconnection syndrome.2–5 In order to infer neurodegeneration from connectivity data of individual patients, these should ideally be available from a time of relatively healthy clinical conditions up to a state of manifest disease.

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Future analyses of this type should become feasible for AD through large, ongoing, and multi-centric longitudinal studies. At present, it is largely unclear how mild cognitive impairment (MCI) converts to AD.7,11,12,34,35,38 The rationale of the present work to improve understanding the MCI → AD conversion and AD evolution is to start with patients already diagnosed as suﬀering AD. The study of the propagation of disrupted patterns along the brain network in AD patients could indeed suggest methods for anticipating the onset of the disease thus paving the way to a novel prognostic perspective and to the development of targeted therapeutic strategies. On the other hand, since deﬁcits and impairments evolve diﬀerently over time in patients, a personalized study should be pursued. Studies of disconnection diseases of human brain should necessarily take into account the network perspective.4,6–10 Recently, some authors have investigated graph analysis and complex networks as tools to identify brain organizations from both a structural and a functional viewpoint.9,14,48,52,54 They have been proposed to study reorganization of brain in aging in terms of variable connectivity patterns, resilience in terms of modular organization, local eﬃciency of related circuitry and changing small-world characteristics.17,31,39,54 In particular, alterations in graph topology and its corresponding metrics allow the examination of the evolving interactions among multiple brain areas and regions both in normal aging and in age-related diseases.8–10 Recent studies have reported interesting results on the use of complex networks and graph theory on brain networks in AD, particularly on neuroimaging data. These studies have reported altered global and local metrics in AD, supporting the potential clinical relevance of this kind of studies. In particular, it appears that AD patients have disrupted neural circuits integrity in structural and functional systems related to high-level cognitive functions, mostly interpreted as an altered small-world capacity observed in neuronal connectivity and that may ultimately explain cognitive deﬁcits in patients.3,4,9 Unfortunately, the interpretation of the results achieved is somewhat ambiguous also because of the diﬀerent imaging modalities used and of the kind of functional connectivity analyzed. A meta-analysis of the diﬀerent results published in the literature has been recently published.9

The considered studies mainly focus on a class comparison among healthy subjects, MCI and AD patients. In AD, they generally reported a longer path length with a relatively preserved (or slightly growing) clustering coeﬃcient, thus suggesting a loss of complexity and of small-worldness of the brain network.6,7,33 Since the small-world organization has been hypothesized to reﬂect a good balance between local segregated processing and global integration in the human brain, the alteration of these properties can be associated with the disruption of topological architecture in AD patients. However, some inconsistent results have also been reported. This can be a consequence of the heterogeneity and the diﬀerent progressive stages of the AD involved in the studies.9 In this work, the analysis is focused on just within-class (AD) measurements: individual modiﬁcations in longitudinal studies are compared at diﬀerent acquisition times. This approach has been proposed earlier but not within a complex network framework.49,50 Electroencephalographic (EEG) data allow to perform a noninvasive analysis of cortical neuronal synchronization, as revealed by resting state brain rhythms.15,16,38,40,41 Several studies support the idea that biomarkers derived from EEG rhythms, such as power spectral density, entropic complexity, and other quantitative features, diﬀer among normal elderly, MCI, and AD subjects, at least at group level.42–44 In particular, some authors have shown that the permutation entropy (PE) index, and its multiscale version, both in its univariate and multivariate version, is a good biomarker for discriminating among the three above-mentioned categories.19–22,24 It turns out that resting state EEG biomarkers are promising for large-scale, low-cost, fully noninvasive screening of elderly subjects at risk of AD. To investigate the variability in physiological signals across multiple time scales, Costa et al.28 proposed the use of a coarse-graining procedure. This analysis may possibly highlight history eﬀects in long-range temporal dynamics at multiple hierarchic levels of cortical processing.30,35 If functional connectivity in brain networks in AD originates at multiple hierarchic levels, the acquired EEG signals should be characterized at multiple scales. A multiscale study can be of interest also within the network approach, since the underlying

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A Longitudinal EEG Study of AD Progression

physiological mechanisms can be altered because of the disconnection syndrome and the related preserving actions originating brain resilience. In this work, a cohort of AD patients have been analyzed longitudinally, for a short follow-up time of three months in order to further investigate on the network hypothesis of AD as a disconnection syndrome.2 This paper is organized as follows: Sec. 2 gives information on materials, acquisition, and on the database preparation. Details on network construction and the methodologies used are given in Sec. 3. Section 4 reports the main results of the study both for weighted and binary networks, and compares them with previous studies on complexity of EEG recordings in AD. A novel multiscale approach is also proposed, where the above-mentioned coarsegraining procedure is combined with the network techniques. The results of the statistical analysis are also reported. Finally, Sec. 5 concludes the paper. 2. Materials 2.1. Study population (subjects) Fifteen consecutive outpatients with dementia (seven AD subjects, two males and ﬁve females, and eight MCI subjects, four males and four females) at several levels of clinical evolution were recruited from IRCCS Centro Neurolesi Bonino-Pulejo of Messina. All patients have been enrolled within an ongoing cooperation agreement that also includes a clinical protocol approved by the Ethic Committee of IRCCS. All patients signed the informed consent form. The inclusion criteria for enrollment of patients for statistical analysis are mainly standard and, at the ﬁrst level, they are based on MMSE scores. After diagnostic conﬁrmation, they were assessed for: gender, age, schooling, and estimated age of onset of dementia, marital status and scores on the Mini-Mental State Examination (MMSE). Current use of any medications, but particularly cholinesterase inhibitors (ChEis), Memantine, antidepressants, anti-psychotics and anti-epileptic drugs, was also quantiﬁed considering that patients had been receiving them for at least three months before the evaluation. The same examiners conducted all cognitive and clinical assessments. Diagnosis of AD was in accordance with the National Institute on Aging–Alzheimer’s Association criteria.

All patients were assessed at baseline (t0 ) and three months after the ﬁrst evaluation (t1 ). At t0 , the neuropsychological evaluation of patients showed a mean MMSE score ± SD was 16.6 ± 5.4 for AD patients and of 23.4 ± 6.6 for the MCI group. Overall, three AD patients were using drug treatment at survey time: among these, one used Donepezil, one used Venlafaxina and one used Sertraline. At t1 , the AD group increased (10 subjects, three males and seven females, with MMSE score of 14.6 ± 4.9): in fact, some subjects diagnosed as MCI at t0 , later showed a decrease of cognitive and neurological conditions. Among these, four subjects were using ChEis treatment: one used Rivastigmine, one used Memantine and two used Donepezil. At t1 , the MCI group, consisted of ﬁve subjects (three males and two females) with MMSE score of 21.6 ± 6.8. Among these, three subjects were using antidepressant treatment (one used Paroxetine and two used Sertraline). None of the used medications is expected to aﬀect the EEG. In this work, a subset of the available database is analyzed; in particular, only the portion that refers to the AD patients is considered. The patients converted from MCI to AD as well as the MCI stable group have not been included in the present study. This is because of the modiﬁcations in a threemonth’s period are often subtle, particularly for nonconverting patients. In spite to this, for many of the AD patients included in this work, it was possible to ﬁnd interesting modiﬁcations in such a short time course. In a future work, the study will be extended to the MCI converting to AD within the

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Table 1. The clinical data of patients with AD and MMSE Score at times t0 and t1 . ID

AD AD AD AD AD AD AD

MMSE

31 54 64 65 76 86 87

t0

t1

23 16 11 10 15 24 17

23 13 10 8 14 17 17

Gender

Age

M F F M F F F

74 83 74 76 79 83 78

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experimentation time span. Table 1 reports a summary of the participants’ characteristics.

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2.2. EEG recordings and preprocessing Each experimental EEG has been acquired through continuous recording on the scalp of all of the subjects. The EEG recordings have been collected, in comfortable resting state, according to the sites deﬁned by the standard 10–20 International System, channels (F p1, F p2, F 3, F 4, C3, C4, P 3, P 4, O1, O2, F 7, F 8, T 3, T 4, T 5, T 6, F z, Cz, and P z), at a sampling rate of 256 Hz, using a notch ﬁlter at 50 Hz. The reference electrode is A2, on the right ear lobe. Before EEG recordings, all patients and their caregivers underwent a semi-structured interview including questions about: (a) quality of the last night sleep, (b) quantity of the night before the recording, (c) meal timing and content. The EEG recordings were performed in the morning. Along the course of the experimental acquisition of the EEG, the patients kept closed eyes but remained awake. The technician, keeping the subject alert by calling her/him by name, prevented the drowsiness. The patients did indeed not sleep during the recording as conﬁrmed by the EEG traces devoid of sleep pattern. Each recording lasted approximately 5 min. The signals were band-pass ﬁltered between 0.5 and 32 Hz, to include the relevant bands for AD diagnosis. Manual cleaning of the recordings excluded those EEG sections with evident artifacts based on visual inspection. This step has been carried out in order to process artifact-free epochs only, and avoid losing potentially interesting information that might be lost in an automatic artifact rejection process. 2.3. Database preparation This study is carried out over a three months followup period. Diﬀerent patients do not necessarily show the same pathological state at the starting point of the investigation, as also highlighted by the MMSE score. In other worlds, the composition of AD patient samples is not homogeneous. This will certainly reﬂect in some variability of the reported ﬁndings. In particular, subtypes of AD are characterized by different atrophy patterns that have diﬀerent impacts

on memory loss. However, the present work focuses on a personalized study of the patients beyond the average results. It has been decided to exclude early-onset AD from the present study because of divergent results reported in the recent literature attributable to heterogeneity of the AD itself. 3.

Methods

3.1. Network construction A complex network can be represented as a graph, completely described by assigning a set of nodes, a set of edges (or links), and an adjacency (or connectivity) matrix.26 The electrodes of the EEG recording map that are spatially distributed along the scalp of the patient deﬁne the nodes of the complex network. The investigated network thus includes n = 19 nodes and, in the fully connected version, n(n − 1)/2 = 171 edges, representing links between pairs of nodes. Based on the strengths of connections, a number of edges will be canceled out in binary networks. The functional connectivity in the network is deﬁned in terms of temporal correlations between spatially distant neural events. A functional brain network is here generated from the multichannel EEG: a representative time series is associated with each node/electrode, and pairwise correlations between the respective time-series are considered as the measured connectivity between the corresponding brain zones. There is no uniﬁed consensus on how to better calculate cross-dependencies between nodes. In this work, the mutual information (MI) between pairs of nodes has been used. Other researchers have previously proposed MI.18,53 One of the advantages of this kind of metrics is the possibility it oﬀers to incorporate nonlinear correlations among variables, while some other popular criteria (e.g. correlation coeﬃcient) are limited to linear dependencies.53 As detailed in Appendix A, MI is expressed in terms of entropic measures that are estimated on the available database. The mutual information, MI(X, Y ), measures the average amount of common information, obtained in the variables X and Y . It represents, in a sense, the residual complexity (or, alternatively, the reduction of uncertainty) on the values of the signal X when the signal Y is known. If the signal X is strongly dependent from Y , the

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A Longitudinal EEG Study of AD Progression

term H(X | Y ) is relatively small, since the complexity of X aﬀected by the knowledge of Y . Indeed, the residual complexity of X, given Y , is low. As a consequence, MI(X, Y ) is relatively high, and it depends maximally on H(X), i.e. the complexity of channel X. If the channels X and Y , for example because of a pathological disconnection, become independent, the complexity of X is quite unaﬀected by Y , and MI(X, Y ) is reduced, since H(X | Y ) → H(X) and, thus, MI(X, Y ) → 0. However, it should be explicitly noted that the value of MI depends on two terms: the ﬁrst one measures the complexity of the signal (which has been shown to be reduced in AD and supposed to generally decline with the disease’s progression), and the second one that behaves as described above. This means that a reduction of the complexity of a channel implies in turn a reduction of MI independently on the conditional entropy term (see Sec. 4.4). The complex network associated with the available EEG recordings is generated by measuring the functional connectivity between spatially localized electrodes through the MI. The EEG time-series associated with each node are the basis for the calculation of MI (which is indeed measured on pairs of channels). The related (symmetric) connectivity matrix is generated by associating with each oﬀ-diagonal entry (i, j), the corresponding value of MI(i, j). A conventional value is assigned to the diagonal entries of the matrix, namely, the average MI(i, ·) computed on the corresponding row: MIEL (i) =

1 MI(i, j) i = 1, 19. 18 j=1,19

(1)

j=i

In the ﬁgures, for facilitating the visual inspection, the diagonal terms are ﬁxed to the MI value averaged on the upper triangular part of the matrix. For the practical computation of the node metrics in the software code, aside from the connectivity matrix, an intermediate distance work-matrix is also deﬁned, whose entries dij correspond to the “distance” between a source node i and a target node j. This distance is generally equal to the length of the shortest path between the nodes. In the case of “thresholded” network, if no path exists dij → ∞. The analysis of the complex networks is practically carried out as follows: for each patient, the original EEG is subdivided in nonoverlapping segments

(epochs) of length 5 s (corresponding to 1280 time samples); for each epoch, a 19 × 19 connectivity matrix has been derived; then, an averaged matrix has been obtained by taking into account all of the epochs’ matrices. The network parameters and properties were calculated on the resulting matrix. These quantities are thus mathematical functions of the connectivity matrix. The scripts of the software codes used in the present work can be downloaded from: http://neurolab.ing.unirc.it/ portale/ codes/ ijns 2014/.

3.2. Complex networks In order to characterize the underlying dynamical properties of the complex networks, a subset of the commonly used metrics have been used. They quantify the complexity of the dynamical processes supported by the patterns of functional activity of the cerebral cortex. In order to compare the network metrics of the functional brain network at two diﬀerent times (t0 and t1 ), the following quantities have been calculated: Global Eﬃciency (), Averaged (characteristic) Shortest Path Length (λ), Global Clustering Coeﬃcient (C), Betweenness Centrality (b), Node Degree Distribution, and Connectivity Density (here deﬁned as the global number of active links preserved in the binary networks generated at diﬀerent threshold levels). Some intermediate measures have also been considered; in particular, the topological distribution of the MI values and some derived quantities. For the sake of readability, deﬁnitions and formulas of interest have been collected in Appendix B. The values of the networks’ parameters has been calculated starting from the connection matrix, C, of the corresponding complex network. Each entry of this matrix, c(i, j), represents the MI between two EEG channels (ith and jth channels). The entries represent the strength of the functional connectivity between nodes (i.e. the relevance of the corresponding edges within the complex network). The modiﬁcations of the network parameters are then analyzed longitudinally and compared, for each patient and on the whole sample. The MI matrices, normalized to the interval 0–1, were also converted to binary matrices by applying a set of thresholds (from 0.1 to 0.9), and the

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network parameters were computed as a function of the threshold value at both times t0 and t1 . Accordingly, two diﬀerent kinds of network topologies have been considered: (i) in the case of weighted networks (WN), the entry (i, j) of the matrix represents the strength of correlation in the corresponding functional networks; consequently, in WN the parameter calculation keeps into account each link weight; (ii) if a threshold is applied to the connectivity matrix to remove links with low strengths, an adjacency (sparse) matrix is obtained, in which the entries are binary numbers; in the case of threshold networks (TN), the computational complexity is greatly reduced at the cost of some information loss. However, the thresholding can also be beneﬁcial, since it eliminates a possible over-evaluation of connectivity due to random noise. In the case of TN, it is common to represent the variations of network parameters as a function of diﬀerent threshold values. Although some considerations can be more easily done on TN, the strategy of “thresholding” may imply misleading results when comparing diﬀerent networks. This is mainly because of the disconnectedness of the corresponding graphs. The results achieved in TN by using a ﬁxed threshold strategy have been reported, well aware of the potential limitations of this approach. The results achieved with WN can be helpful in moderating those limitations; however, unfortunately, as of today, there is no general consensus on how WN properties can be characterized.26 Figure 1 gives a pictorial representation of the multi-step processing procedure designed for this study, both in terms of WN and TN. 3.3. Weighted networks The analysis of the WN starts from the generation of the connectivity matrix, C. Figure 2(a) reports the matrices representations for some of the AD patients at the two diﬀerent times (baseline and follow-up). The color scale goes from blue (0) to red (1). Figure 2(b) also reports the connection matrices, at times t0 and t1 , averaged on the cohort of patients. A visual inspection of the matrices allows us to claim that, on average, the evolution of

Fig. 1. Pictorial representation of the procedure for extracting networks’ parameters from EEG: the acquired EEG is subdivided in nonoverlapping epochs of 5 s; the corresponding connectivity matrix is generated by using the concept of mutual information and taking the average on all of the epochs. The average MI (formula 1 on the text) per row is computed which is used to form the background on the scalp. The adjacency matrix is also generated by applying a threshold (here Thr = 0.5); ﬁnally, the metrics are computed as described in Appendix B. WN is fully connected, while TN is sparse. The patient considered is AD 54.

the disease produces a reduction of the MI between channels, particularly for “long distance” ones. Some trends toward a local “block” aggregation is observed in some patients, at t1 .

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3.4. Threshold (binary) networks In TN, each link is deﬁned by a pair of nodes and it is associated with a binary level in dependence of its relative level with respect to a predeﬁned threshold. The entries of the adjacency matrix are thus valued 0 or 1. Since an optimal threshold value cannot be

deﬁned, and it could be diﬀerent for various patients, it was decided to work out TN matrices as follows:

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(i) the matrices for the patients’ cohort and for the two times considered have been normalized across patients to the interval 0–1;

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(ii) the network parameters have been calculated for diﬀerent threshold values (from 0.1 to 0.9).

Table 2. Modiﬁcations of network’s parameters from baseline to follow-up averaged over all subjects. Scale time

MS = 1

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3.5. Multiscale approach Measures of complexity at diﬀerent scales based on entropic indices have been proposed recently as an additional way to analyze the dynamics of physiological signals.27 The aim of this kind of analysis is to identify some possible abnormal complexity proﬁle across diﬀerent time scales and to interpret their relation to the severity of the AD status. It has been reported that AD may not only be characterized by decreased complexity in some EEG channel signals, but also by increased complexity at larger time scales.19,21 These measures of complexity have also been correlated with measures of cognitive impairment.21,29,30 In the present work, the multiscale approach is mapped on the complex network framework. The analysis is limited to scales 2 and 4, meaning that the coarse-graining procedure is carried out at level 2 (of 2 samples derive 1) and at level 4 (1 sample from 4 of the original time series). Thus, each original EEG recording of length N is coarse-grained by a scale factor MS = 2, or MS = 4, with nonoverlapping windows, generating two time series of length respectively N/2 and N/4. As for scale 1, on each multi-scaled EEG, the MI between channels is computed, and a connectivity matrix is generated accordingly. Then, the analysis is carried out similarly to scale MS = 1. 3.6. Statistical analysis The small size of the sample analyzed here prevents a full statistical analysis to be formally carried out. However, as in previous studies,53 the MI matrices can be used to analyze the statistical signiﬁcance comparisons between baseline and follow-up time. Indeed, the computed network metrics are functions of the MI’s entries. Furthermore, the signiﬁcance test can be carried out on some speciﬁc quantities like distribution degree and connectivity density. 4.

Results and Discussion

4.1. Weighted networks The network metrics have been computed for WN the achieved results are reported in Table 2 (in terms

λ C

MS = 2

MS = 4

t0

t1

t0

t1

t0

t1

3.59 0.35 1.57

4.51 0.28 1.58

2.82 0.43 2.05

3.30 0.36 2.08

2.37 0.49 2.59

2.36 0.47 2.62

Note: λ = Characteristic path length; = Averaged global eﬃciency; C = Global cluster coeﬃcient. Table 3. Modiﬁcations of network’s parameters from baseline to follow-up for each patients. Patient

λ(t0 )

λ(t1 )

(t0 )

(t1 )

C(t0 )

C(t1 )

AD AD AD AD AD AD AD

3.13 3.92 3.82 2.44 2.45 3.86 5.54

3.37 5.22 4.73 2.70 5.57 4.19 5.82

0.35 0.29 0.33 0.46 0.49 0.30 0.26

0.34 0.23 0.23 0.40 0.24 0.28 0.25

1.72 1.56 1.51 1.80 1.31 1.50 1.69

1.64 1.55 1.52 1.59 1.57 1.55 1.63

31 54 64 65 76 86 87

of averaged values) and Table 3 (values of λ, , and C for the cohort). On the average, it can be observed that the Global Eﬃciency () is reduced and the Averaged (Characteristic) Shortest Path Length (λ) is increased. This is also true for each single patient. This loss of small-worldness in AD has been observed in previous works in comparison to healthy control groups.6,7,54 This is reﬂected by a longer path length, and a reduced eﬃciency with a relatively preserved or increasing cluster coeﬃcient. These results can be seen as a conﬁrmation of the hypothesis that the patterns of gradual modiﬁcations continue with the progression of the disease. However, to the best of the authors’ knowledge, no previous AD patients followup results have been published on complex networks’ parameters longitudinal modiﬁcations. In particular, an increased value of λ is usually interpreted as a loss of long-range edges that, in turn, may be associated with a reduction of connectivity. This is coherent with the growing evidence of AD as a disconnection syndrome. On the average, this λ increase is coupled to a preservation of the clustering coeﬃcient (C), reﬂecting the prevalence of clustered connectivity around some nodes. Furthermore, it is

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noted that some nodes of the network increase their relative importance in terms of degree and centrality. In particular, an increased “Betweenness Centrality” (bi ) has been noted. This metric, deﬁned in Appendix B, basically represents, for each node, the

fraction of all shortest paths in the network that pass through this node. This growth could be interpreted as a compensatory reinforcement of some regions. The correct characterization of WN behavior is unfortunately in its early stage, and the available

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algorithmic tools need yet to be fully developed and understood. In general, the study of AD progression could beneﬁt from both WN and TN analysis.

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4.2. Threshold (binary) networks The number of preserved links (i.e. whose strength is above threshold) is a function of the threshold levels (Thr). Figure 3 shows the number of active links versus the threshold for the seven patients, at baseline and follow-up. For all but patients AD 31 and AD 87, the curves show a reduction of links for intermediate threshold levels, in spite of the short follow-up time. For patients AD 31, AD 54, AD 64, and AD 76, the diﬀerence is observed already at Thr = 0.1. For Thr > 0.8, there are very few left links active. Figure 4 represents the topographic distribution on the scalp of the MI at times t0 and t1 , for all the subjects. The background color map is generated as follows: at each electrode, it is attributed the level of MI obtained by averaging the MI values of the corresponding row MI(i, ·) (formula (1)). Then, the distribution is interpolated among the 19 “exact” values by using the EEGLab toolbox.37 A circle is associated with each electrode, whose radius is proportional to the node’s degree (k). The links reported are the ones above threshold (Thr = 0.5). In general, the averaged MI values decline with time,53 although, in some cases (e.g. AD 86), it is observed an apparent reorganization of the connections in different brain areas: this could be interpreted as a mechanism of resilience. This is also noted in the values of k: although the mean nodes’ degree is generally reduced from time t0 to t1 , some speciﬁc values are increased. In addition, some hubs are preserved (i.e. their “Betweennes Centrality” is roughly unchanged). The visual inspection suggests the idea of some underlying functional alterations. However, they also correlate well with the clinical evaluations. A highly signiﬁcant correlation between MMSE and the mean degree of nodes was indeed observed in TN at both t0 and t1 (r = 0.99, p < 0.001, and r = 0.99, p < 0.001, respectively). Figure 5 reports the decrease of the number of active links and global eﬃciency averaged on the cohort between baseline and follow-up. Keeping into account the relatively short time of the followup, this decrease is appreciable. Table 4 reports a

Fig. 4. Scalp distribution of normalized MI; selected threshold level = 0.5; the circles represent the nodes’ degree (the radius is proportional to the degree level). As above, time t0 on the left, follow-up at t1 on the right. Degree radius size: Kmin Kmedium Kmax .

quantiﬁcation of the change between t0 and t1 in terms of area of the surface between curves (globally, it is measured a percent reduction of 27%). Figure 6 shows the behavior of λ (averaged on the cohort) with respect to the threshold value: as observed in the case of WN, the growth of λ is evident. In summary, also TN yield interesting information on the behavior of the brain network at both global and local level.

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A Longitudinal EEG Study of AD Progression

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Fig. 6. Cohort-averaged characteristic path length (λ) versus threshold (MS = 1). Also for binary networks, on a wide threshold interval, λ is sensibly growing in the follow-up.

Table 4. Area of the surface under connectivity density curves (A) at times t0 and t1 and relative diﬀerence. Patient AD AD AD AD AD AD AD

31 54 64 65 76 86 87

A(t0 )

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∆(t0 − t1 )

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37.7 19.0 17.3 49.7 22.7 27.7 26.5

−2.05 11.9 19.3 11.4 43.3 4.1 1.1 %average

∆(t0 − t1 )/A(t0 ) −0.06 0.38 0.53 0.18 0.66 0.13 0.04 27%

4.3. Statistical signiﬁcance of diﬀerences in t0 and t1 The normality of data distribution has been evaluated using the Shapiro–Wilk normality test. The Wilcoxon signed-rank test was used in order to compare the distribution of MI(i, j) at t0 and MI(i, j) at t1 for each AD patients, and the mean values of MI(i, j) and MI(i, j) averaged on the cohort and on the residual links at the diﬀerent threshold levels at times t0 and t1 . Spearman’s Rank correlation has been used to assess whether a relationship between MMSE variance and the variance of the average network degree exists. The analyses have been performed using an open source R3.0 software package. The statistical signiﬁcance of the test has been set at p < 0.05.

Fig. 7. Boxplot of the MI in AD patients at t0 (above) and t1 (bottom).

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Figure 7 shows the distribution of the MI matrices’ entries in t0 and t1 for each patient. The diﬀerences between MI(i, j) at t0 and MI(i, j) at t1 showed a highly signiﬁcant decrease of MI values for 54 AD, 64 AD, 65 AD, and 76 AD (p < 0.001). Signiﬁcant diﬀerence are showed for 86 AD (p = 0.03); only for AD 31 (p = 0.63) and AD 87 (0.28) no signiﬁcant diﬀerence was highlighted (Table 4). It is worth noting that these two subjects showed unchanged MMSE over the three months (see Table 1). The diﬀerence between the mean of MI(i, j) at t0 and MI(i, j) at t1 (p < 0.001) is also highly signiﬁcant. These diﬀerences between baseline and follow-up are also highlighted by a diﬀerence of the number of preserved links (i.e. of the connectivity density). In particular, signiﬁcant diﬀerence are showed for 54 AD (p = 0.009), 64 AD (p = 0.004), 65 AD (p = 0.02), and 76 AD (p = 0.009), while, there are no signiﬁcant diﬀerences for AD 31 (p = 0.36), 86 AD (p = 0.13), and AD 87 (p = 0.57) (Table 5). There is a highly signiﬁcant diﬀerence between the mean number of links at t0 and t1 (p = 0.004). Table 5. Statistical signiﬁcance of diﬀerences for MI and connectivity density at baseline and follow-up times. Patient

AD AD AD AD AD AD AD

31 54 64 65 76 86 87

MI Median (t0 ) (I–III quartile)

Median (t1 ) (I–III quartile)

p-value

0.28 0.25 0.27 0.46 0.49 0.24 0.21

0.27 0.15 0.15 0.35 0.16 0.20 0.17

0.63