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Journal of Alzheimer’s Disease 41 (2014) 1239–1249 DOI 10.3233/JAD-140090 IOS Press

Human Brain Networks in Physiological Aging: A Graph Theoretical Analysis of Cortical Connectivity from EEG Data Fabrizio Vecchioa,∗ , Francesca Miragliaa , Placido Bramantib and Paolo Maria Rossinia,c a Brain

Connectivity Laboratory, IRCCS San Raffaele Pisana, Rome, Italy Centro Neurolesi Bonino-Pulejo, Messina, Italy c Institute of Neurology, Catholic University, Rome, Italy b IRCCS

Accepted 15 March 2014

Abstract. Modern analysis of electroencephalographic (EEG) rhythms provides information on dynamic brain connectivity. To test the hypothesis that aging processes modulate the brain connectivity network, EEG recording was conducted on 113 healthy volunteers. They were divided into three groups in accordance with their ages: 36 Young (15–45 years), 46 Adult (50–70 years), and 31 Elderly (>70 years). To evaluate the stability of the investigated parameters, a subgroup of 10 subjects underwent a second EEG recording two weeks later. Graph theory functions were applied to the undirected and weighted networks obtained by the lagged linear coherence evaluated by eLORETA on cortical sources. EEG frequency bands of interest were: delta (2–4 Hz), theta (4–8 Hz), alpha1 (8–10.5 Hz), alpha2 (10.5–13 Hz), beta1 (13–20 Hz), beta2 (20–30 Hz), and gamma (30–40 Hz). The spectral connectivity analysis of cortical sources showed that the normalized Characteristic Path Length (λ) presented the pattern Young > Adult>Elderly in the higher alpha band. Elderly also showed a greater increase in delta and theta bands than Young. The correlation between age and λ showed that higher ages corresponded to higher λ in delta and theta and lower in the alpha2 band; this pattern reflects the age-related modulation of higher (alpha) and decreased (delta) connectivity. The Normalized Clustering coefficient (␥) and small-world network modeling (σ) showed non-significant age-modulation. Evidence from the present study suggests that graph theory can aid in the analysis of connectivity patterns estimated from EEG and can facilitate the study of the physiological and pathological brain aging features of functional connectivity networks. Keywords: Delta and alpha bands, EEG, eLORETA, functional connectivity, graph theory, small-world networks

INTRODUCTION Understanding the relationship between the structure and function of the brain is one of the basic goals of neuroscience. Regarding the brain as a complex network of dynamically interacting neuronal assemblies—that mold stable (maintained in time) or unstable (changing in time) networks on the basis of daily experience—offers new insights into higher-level ∗ Correspondence to: Dr. Fabrizio Vecchio, PhD, Brain Connectivity Laboratory, IRCCS San Raffaele Pisana, Via Val Cannuta, 247, 00166 Rome, Italy. Tel.: +39 06 52253767; E-mails: [email protected], [email protected].

brain processes, such as memory, planning, problem solving, decision making, sensorimotor skills, emotions, language, and abstract reasoning, as well as various types of brain/mind pathophysiology. Watts and Strogatz introduced the concept of the so-called ‘small-world’ networks, which allow for an optimal balance between local specialization and global integration [1]. This novel approach, which applies concepts from graph theory (a branch of the mathematical field of complex network theory) to neurophysiological data, is a promising way to characterize brain functional organization [2–5]. It provides a method to evaluate whether the functional connectivity patterns between brain areas reproduce

ISSN 1387-2877/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved

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the organization of theoretically efficient, flexible, or robust networks (based on the strength of synchronization in the time-varying oscillatory electromagnetic activity of different brain regions, as measured by EEG or MEG). The human brain consists of complex inhibitory and excitatory circuits of functionally specialized areas with a continuous, time-varying interplay—with epochs lasting mere milliseconds—for sharing and integrating information. The white-matter (axonal) fibers provide the anatomical basis for signal transfer and communication. These connections are not random, but are organized in a so-called small-world network topology. The topology of a small-world network is characterized by a high degree of local clustering (segregation) and the presence of long-distance connections (integration) that secure a high level of global communication efficiency. Numerous studies suggested implementing small-world network organization in the brains of healthy humans [3, 6–11]. However, few have investigated the impact of brain diseases on the normal small-world architecture [12–14]. Biologically speaking, networks that are highly integrated are strongly synchronized, since the activity of one node will largely influence most of the nodes in the network, given their relative proximity in terms of network distance. Integration and segregation properties combine functional specialization with higher-order processing like multisensory integration, cognition, and executive functions that require large-scale integration. Such a global network may be more vulnerable to disruptions due to age-related neuropathological changes in any part of the network, resulting in a loss of efficiency and leading to a decline in processing speed that is typically associated with aging. Resting EEG characteristics are known to change across physiological aging, with gradual modifications in spectral power profile indicating a pronounced amplitude decrease of alpha (8–13 Hz) and a global “slowing,” with increases in power and changes in topographic location in the slower delta (2–4 Hz) and theta (4–8 Hz) frequency ranges [15–18]. Aging processes affect posterior alpha rhythms, presumably because of the progressive degradation of the activity of dominant oscillatory thalamo-cortical circuits in the resting, awake adult brain [19–21]. Although a large body of knowledge about both young and elderly brain structure and function has been gathered in recent decades, we still have a poor understanding of the exact relationship between structure and function. A fundamental hypothesis is that cogni-

tive dysfunction can be illustrated and/or explained by a disturbed functional organization. There is a general consensus that cognition is maintained and supported by a highly distributed and dynamic process. Thus, it depends on coordinated, time-varying interactions between many brain regions. It is therefore reasonable to argue that, by exclusively focusing on structural (dis)organization, it will be difficult to fully explain cognitive (dys)function, since the complex interactions and interdependencies between different regions need to be addressed via techniques with high temporal resolution in order to be fully understood and explained. An intriguing perspective would be to take into account both local and global structural changes, as well as the spatio-temporal dynamics of the brain and the way these different aspects are related [22–25]. The modulation of such parameters could be related to morphomolecular changes in neurons, axons, dendrites, and synapses, as well as the accumulation of neuropathologies that occur with age. A recent study [26] investigated brain developmental changes from childhood to adulthood by analyzing the strength and patterning in long-range connectivity on the basis of synchronization likelihood (SL) between electroencephalographic (EEG) signals simultaneously recorded at distant electrodes. The study was based on scalp data, the functional connectivity was arbitrary in terms of threshold (an unweighted graph was used), and the graph data were not normalized in order to avoid the dependence of the graph degrees. Indeed, the results of the present paper were obtained with a method based on estimating the sources of EEG signals (exact Low Resolution Electromagnetic Tomography (eLORETA); therefore most likely not affected by the ambiguity of localization and reference-dependence), and omitted zero phase angle coherences to avoid the undue inflation of coherence by volume conduction [27, 28]. This method is artifacts-free, since artifacts—such as eye blinking and muscle activity—were identified and excluded by the independent component analysis (ICA) composition. By directly using the current density obtained from the inverse methods, the weights for the brain network parameters were extracted. Although integration/segregation balance and small-worldness have been extensively investigated in relation to brain diseases, even if the small world properties are typically preserved in pathological conditions, the integration or segregation is often altered. It is difficult to give a univocal interpretation to this effect, and conclusions should be drawn according to the specific study and complementary (e.g.,

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multimodal) information. A disruption of integration properties may be linked to long-range and associative fiber damage, while a concomitant alteration of integration and segregation may be related to both short and long connection damages, including intracortical involvement. Altogether, the aim of the present study was to investigate physiological brain aging from both cortical source powers (by standardized Low Resolution Electromagnetic Tomography, sLORETA) and connectivity (by graph theory from eLORETA) based on EEG signals. SUBJECTS AND METHODS Participants 113 healthy human volunteers were recruited and divided in three groups with respect to their ages: 36 young (Young; aged 15–45 years, mean age = 29.3 ± 1.1 (Standard Error) years, 17 male), 46 adult (Adult; aged 50–70 years, mean age = 60.5 ± 0.8 years, 16 male), and 31 elderly (Elderly; aged over 70 years, mean age = 77.4 ± 0.9 years, 17 male). Demographic data are reported in Table 1. Of note, gender, education, and Mini-Mental State Exam values were used as covariates in the subsequent statistical analysis to make sure that the small differences in these variables would not influence the subsequent statistical analysis. All subjects were determined to be righthanded though the Handedness Questionnaire [29]. Exclusion criteria included a history of neurological or psychiatric disorders and current treatment with vasoactive or psychotropic medication. The study was approved by a local ethical committee. Experimental procedures were conformed to the Declaration of Helsinki and to national guidelines.

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tional 10–20 system. Two separate channels, vertical and horizontal electrooculograms, were used to monitor eye blinks. Impedance was kept below 5 K, and the sampling rate frequency was set up at 512 Hz. EEG signals were measured at rest, for at least 5 minutes (while the eyes were close and no task conditions were being executed). During the recording, subjects were seated and relaxed in a sound attenuated and dimly lit room. We are well aware that high-density arrays of electrodes would improve spatial discrimination. However, such recording systems are hardly employable in diseased patients, particularly in those with cognitive decline and a low collaboration level. The large number of electrode positionings and impedance checks would increase the preparation time, thereby running a high risk of highly degrading the overall quality of the recorded EEG signal, due, for example, to muscular contamination. The data were processed in Matlab R2011b (MathWorks Natick, MA) using scripts based on EEGLAB 11.0.5.4b toolbox (Swartz Center for Computational Neurosciences, La Jolla, CA; http://www.sccn.ucsd.edu/eeglab). The EEG recordings were band-pass filtered from 0.1 to 47 Hz using a finite impulse response (FIR) filter. Imported data were divided in 2 s epochs, and visible artifacts in the EEG recordings (i.e., eye movements, cardiac activity, and scalp muscle contraction) were removed using an ICA procedure allowing for the identification and extraction of ocular artifact components from the EEG data. ICA is a blind source decomposition algorithm that enables the separation of statistically independent sources from multichannel EEG recordings [30–33]. ICA was performed using the Infomax ICA algorithm [34], as implemented in the EEGLAB. Artifact free EEG signals were used for further analyses.

Data recordings and preprocessing EEG recordings were carried out with a digital EEG machine from 19 electrodes (Fp1, Fp2, F7, F8, F3, F4, T3, T4, C3, C4, T5, T6, P3, P4, O1, O2, Fz, Cz, and Pz) positioned in accordance with the Interna-

Functional connectivity of cortical sources analysis Selected artifact-free EEG segments (129.2 ± 2.3 trials of 2 s) were used to calculate the eLORETA

Table 1 Demographic data of Young, Adult, and Elderly subjects n Age (years) Education (years) Mini-Mental State Exam Gender (M/F)

Young 36

Adult 46

Elderly 31

29.3 (±1.1 SE) 16.4 (±0.4 SE) 29.9 (±0.03 SE) 17/19

60.5 (±0.8 SE) 10.2 (±1.0 SE) 28.8 (±0.2 SE) 16/30

77.4 (±0.9 SE) 8.5 (±0.8 SE) 28.2 (±0.3 SE) 17/14

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intracranial spectral density, with a resolution of 0.5 Hz, from 0.5 to 45 Hz. All EEG data epochs were normalized and recomputed into time series at 6,239 cortical voxels using eLORETA [35], available as free academic software package. Brain connectivity was computed by eLORETA software on 84 regions-of-interest (ROIs) defined according to the 42 Brodmann areas (BAs: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, and 47) for the left and right hemispheres. ROIs are needed for the estimation of the electric neuronal activity used to analyze brain functional connectivity. Among the eLORETA current density time series of the 84 ROIs, the intracortical Lagged Linear Coherence, extracted through the “all nearest voxels” method [35, 36], was computed between all possible pairs of the 84 ROIs for each of the seven independent EEG frequency bands [37, 38] of delta (2–4 Hz), theta (4–8 Hz), alpha 1 (8–10.5 Hz), alpha 2 (10.5–13 Hz), beta 1 (13–20 Hz), beta 2 (20–30 Hz), and gamma (30–45 Hz), for each subject. Starting with the definition for the complex valued coherence [28, 39] between time series x and y in the frequency band ω, which is based on the crossspectrum given by the covariance and variances of the signals, the lagged linear coherence in the frequency band ω is reported on in the following equation [35, 36]: LagR2xyw

[ImCov(x, y)]2 = Var(x)Var(y) − [ReCov(x, y)]2

where Var and Cov are variances and covariance of the signals. This equation was developed to provide a measure of true physiological connectivity not affected by volume conduction and with low spatial resolution, as shown in Pascual-Marqui et al. [35]. The values of connectivity computing between all pairs of ROIs for each frequency band and for each subject were used as measure of weight of the graph in the follow graph analyses. Graph analysis A network is a mathematical representation of a real-world complex system defined by a collection of nodes (vertices) and links (edges) between pairs of nodes. Nodes in large-scale brain networks represent brain regions, while links represent anatomical, func-

tional, or effective connections [40], depending on the dataset. Anatomical connections typically correspond to white matter fiber tracts between pairs of grey matter relays (cortical areas or subcortical relays). Functional connections correspond to magnitudes of temporal correlations in activity and may occur between pairs of anatomically unconnected regions. The nature of nodes and links in individual brain networks is determined by combinations of brain mapping methods, anatomical parcellation schemes, and measures of connectivity. Many combinations occur in various experimental settings [41]. Nodes should ideally represent brain regions with coherent patterns of extrinsic anatomical or functional connections [42]. An undirected and weighted network, based on the connectivity between the 84 ROIs—the nodes of the network being ROIs and the edges of the network being weighted by the lagged linear connectivity—was built [27]. The software instrument used here for the graph analysis was the Brain Connectivity Toolbox (http://www.brain-connectivitytoolbox.net/), which was adapted by Matlab scripts. Two core measures of graph theory were computed: characteristic path length (L) and weighted clustering coefficient. These were representative of global connectedness and local interconnectedness, respectively; L is reported in the following [1]:  1
1
j⊂N,j = / i& dij L= Li = n n n−1 i⊂N

i⊂N

where Li is the average distance between node i and all other nodes. This is the average shortest path connecting any nodes couple of the graph: the length of a path is indicated by the number of connections it contains. The characteristic path length L (averaged shortest path length between all node pairs) is a graph property, which describes how well its elements are integrated/interconnected. The clustering coefficient C of a node is reported in the following [1]: 1
1
2ti C= Ci = n n ki (ki − 1) i⊂N

i⊂N

where Ci is the clustering coefficient of node i (Ci = 0 for ki < 2). This is the ratio of all existing connections between the ‘neighbors’ of a node (nodes that are one step away) and the maximum possible number of edges between the neighbors. The mean clustering coefficient is computed for all nodes of the graph and then averaged. It is a measure for the tendency of network elements to form local clusters [43].

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To obtain normalized measures, the vales of the characteristic path length and of the clustering coefficient were divided by the mean values obtained from a set of 1,000 random digraphs (obtained by randomization of all actual matrices) with the same number of nodes and connections as the actual graphs. The set of 1,000 random digraphs was obtained using software taken from the above-mentioned website. These functions randomize the network while preserving the degree distribution. The respective distributions of global (Lrandom) and local (C-random) connectedness values were calculated and averaged to obtain a mean value for each core measure. The scale-free values Gamma (␥) was evaluated from the normalized C (C/C-random), and Lambda (λ) was evaluated from the normalized L (L/L-random). ’Small-worldness’ (Sigma σ) is the ␥:λ ratio; it is used to describe the balance between the local connectedness and the global integration of a network. When this ratio is larger than 1, a network is said to have small-world properties. Statistical evaluation Analysis of variance (ANOVA) was used between the ROIs indices computed in the three populations for all the frequency bands. ANOVA was chosen because it is known to be robust with respect to the departure of normality and homoscedasticity of data being treated [44, 45]. The Greenhouse and Geisser correction was used to protect against the violation of the sphericity assumption in the repeated measure ANOVA. Additionally, a post-hoc analysis with the Duncan’s test and significance level at 0.05 was performed. All the statistical analysis was performed with the software Statistica v.7 (StatSoft Inc., http://www.statsoft.com). Separate ANOVAs were conducted for each of the variables: Gamma (␥), Lambda (λ), and Sigma (σ). These were computed in each group of subjects and frequency band relevant for this study. The significance level was set at p < 0.05, and the ANOVAs were performed between two factors: Group (Young, Adult, Elderly; independent variable) and Band (delta, theta, alpha 1, alpha 2, beta 1, beta 2, and gamma). Furthermore, we tested the Pearson’s linear correlations between age and the variables; the results were significant in the previous ANOVAs, considering all subjects as a whole group (Bonferroni corrected to obtain p < 0.05). Finally, in order to evaluate the within-subject test-retest variability, each ANOVA result that was sig-

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nificant in the main analyses was performed on the recordings of a 10-subject sub-group. These subjects came back for a second recording two weeks later, at which point the factor Time was introduced (First and Second recording session). RESULTS EEG cortical sources connectivity as estimated by eLORETA For illustrative purpose, we report in Fig. 1 the eLORETA connectivity maps for the three groups of subjects in the explored frequencies. The maps illustrate only the connections (among the mentioned 84 ROIs: 42 left and 42 right BAs) that resulted in a higher than arbitrary threshold for each band. The arbitrary threshold was selected through a visual inspection conducted in order to show the differences among the groups. No statistical analysis was evaluated regarding the functional connections in the groups, as the aim of the present study was to test the variation on graph pattern, not on single connection. Elderly subjects present a higher number of connections in the lower frequency bands than the other two groups. Moreover, the alpha 2 band presents a focalized localization in the posterior areas that decreases its number of tracts along Young, Adult, and Elderly groups. Graph theory based on the EEG cortical sources as estimated by eLORETA The ANOVA for the evaluation of the normalized characteristic path length (λ) showed a statistically significant interaction (F(12,660)=3.24; p < 0.0001) among the factors Group (Young, Adult, and Elderly) and Band (delta, theta, alpha 1, alpha 2, beta 1, beta 2, and gamma). Figure 2 shows the λ values relative to this statistical interaction in the ANOVA. The Duncan post-hoc testing showed that the pattern Young > Adult>Elderly was fitted in the higher alpha band (p < 0.04). Furthermore, elderly subjects also showed an increase of the same parameter in delta and theta bands only with respect to young subjects (p < 0.05). The normalized Clustering coefficient (␥) showed a non-significant interaction (p > 0.05) between the three groups and the seven frequency bands considered. Finally, small-world (σ) showed a non-significant interaction (p > 0.05), even if the mean of each group presented small-world network properties, as expressed by values of σ larger than 1.

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Fig. 1. eLORETA connectivity maps for delta, theta, alpha1, alpha 2, beta1, beta 2 and gamma bands, in the Young, Adult, and Elderly groups. Each red tract among the 84 ROIs reports only the connectivity value higher than the cut-off threshold.

Fig. 2. ANOVA interaction of the normalized characteristic path length (λ) among the factors Group (Young, Adult, and Elderly) and Band (delta, theta, alpha 1, alpha 2, beta 1, beta 2, gamma). The right panel of the figure shows the concomitant cerebral connectivity, mapped by eLORETA, for the alpha 2 band in the three groups, in which the red tract representation belongs to ROIs well connected over the cut-off threshold.

Correlation between network characteristic and age Correlation analyses were performed only on the statistically significant values of interest: the normalized characteristic path length (λ) in the delta, theta, and

alpha 2 bands. The Bonferroni correction for the three correlations led to a statistical threshold of p < 0.016. Considering all subjects as a group, this analysis between age and λ showed a positive correlation in delta (p < 0.004, r = 0.26) and theta (p < 0.01, r = 0.24) associated with a negative correlation in the alpha 2

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cortical sources, were performed on the recordings of the 10-subject sub-group, introducing the factor Time (First and Second recording). The statistical analyses showed that no interaction including Time resulted in significance. This highlights the stability of the present methodology when carried out on clinically stable subjects. Control analysis on subgroups of gender-matched subjects We also performed a control analysis using subgroups of 16 gender-matched subjects (8 male and 8 female for each subgroup). The obtained results were very similar to those of the main analysis (F(12,270)=5.83; p < 0.00001). As was already reported in the manuscript, at least one paper [28] was cited in which connectivity between source localized signals was estimated using eLORETA software (beginning with the 19 channel EEG). However, in order to understand the improvement of the present method with respect to the standard scalp analysis, we added a further control analysis using the mentioned subgroups of gendermatched subjects in which we evaluated the scalp connectivity as reported in a recent manuscript [26]. The obtained results were only partially similar to those obtained in the main analysis. In particular, only delta (F(2,45)=4.77; p < 0.0132) and tendentially alpha 2 (F(2,45)=1.93; p < .1566) bands showed a similar trend. This second control analysis confirmed the limitations of the evaluation of a network comprising a few nodes. Control analysis on the topography of the EEG cortical sources as estimated by sLORETA

Fig. 3. Scatterplots showing the correlation between age and λ in the delta, theta and alpha 2 bands for all subjects as a whole group. The r- and p-values relative to the Pearson’s correlation are reported within the diagram.

(p < 0.003, r = −0.27) band. Namely, higher subject ages corresponded to higher λ in delta and theta and lower in the alpha 2 band (see Fig. 3). Within-subject Test-retest analysis Two ANOVAs, evaluating the spectral power density and the normalized characteristic path length of EEG

In order to verify the goodness of the EEG data, the maps of the grand average of the sLORETA [46] solutions (i.e., relative power current density at cortical voxels) modeling the distributed EEG cortical sources for delta, theta, alpha 1, alpha 2, beta 1, beta 2, and gamma bands in the Young, Adult, and Elderly groups were evaluated. The results showed that, in line with literature, Adult and Elderly groups showed a reduction of the frontal delta sources and an increase of the occipital theta sources, unlike the Young group. With respect to the Young and Elderly groups, the Adult group showed an intermediate magnitude of the frontal delta sources and of the occipital alpha 1 sources. Meanwhile, the younger and older groups had a comparable magnitude of occipital alpha 1 sources.

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These results showed that the most evident differences were observed in the delta, theta, and alpha bands. This observation is perfectly in line with previous evidence on resting EEG changes across physiological aging, with gradual modifications in the spectral power profile indicating a pronounced amplitude decrease of alpha (8–13 Hz) and a global “slowing” of the background EEG, with an increase in power and topographic changes in delta (2–4 Hz) and theta (4–8 Hz) frequency ranges [15–18].

DISCUSSION Brain connectivity datasets comprise networks of cerebral regions directly connected by anatomical tracts or by functional associations. Brain networks are invariably complex. They also share a number of common features with networks from other biological and physical systems, and, accordingly, they may be characterized by using complex network mathematical methods. The concept of functional connectivity is viewed as pivotal for understanding the organized behavior of anatomical regions in the brain during their activity. This organization is probably based on the interaction between different and variably specialized cortical sites. Cortical functional connectivity estimate aims to describe these interactions as connectivity patterns that reflect the strength of the information flow among the involved cortical areas. The theoretical graph approach can be a very useful tool, intercepting some global and local features in the functional connectivity patterns estimated from the EEG along the physiological aging. The main results showed that—for the normalized Characteristic Path Length (λ)—the pattern Young > Adult>Elderly nicely fits in the higher alpha band. Also, elderly subjects showed an increase in delta and theta band connectivity, unlike young subjects. Considering all subjects as a group, the correlation between age and λ showed that the older the age, the higher the λ values in delta and theta, and the lower the λ in the alpha 2 band. Instead, the normalized Clustering coefficient (␥) showed non-significant modulation in the three groups. Finally, the small-world (σ) also showed non-significant modulation presenting smallworld network properties, as expressed by values of σ larger than 1. The present alpha result extends those of previous clinical EEG studies [43, 47] in which it was demonstrated that, in Alzheimer’s disease patients, the characteristic path length decreased in the alpha

band with respect to normal elderly subjects; this observation was confirmed by a recent magnetoencephalographic study [10]. The increase of normalized alpha path length characterizing Alzheimer’s disease [48] was also interpreted as a loss of efficiency of communication between distant brain regions. With regard to the low frequencies (the delta and theta bands), alpha rhythms dominate in the posterior areas of the awake brain. Moreover, the delta rhythms are low in amplitude, thus reflecting a condition of likely alpha-delta “reciprocal inhibition” [49]. However, it is well known that anatomical or functional disconnection from related cortical areas generates spontaneous slow oscillations in the delta range in virtually all recorded neurons [50]. An increase of delta connectivity might therefore reflect a progressive disconnection process of the aging brain. Regarding the effects observed at a high alpha rhythm (10.5–12 Hz), while low-frequency alpha rhythms (about 8–10 Hz) are supposed to reflect the regulation of global cortical arousal [17, 20], there is a consensus that the high-frequencies alpha rhythms reflect the functional modes of thalamo-cortical and cortico-cortical loops. These loops facilitate/inhibit the transmission and retrieval of sensorimotor information into the brain [19–21] and reflect the oscillation of specific neural systems for the elaboration of semantic information [17, 51, 52]. With decreasing global network parameters in elderly subjects—as was shown in the present study—the large-scale functional brain network structure also deviates towards a more “random” type. The loss of structure, as partially expressed by the lower path length in the higher alpha frequency bands, supports, together with the well-known slowing of brain activity and the loss of functional connectivity, the idea of brain aging as a disconnection process. Namely, decreases in path length mean a shift toward network randomness [12]. Of note, a shorter path length related to physiological aging seems counter-intuitive. However, at least in theory, a shorter path length is not necessarily an advantage in a complex network corrupted by age, since it might increase the processing time and the background “noise,” and because the overall structure must maintain an effective balance between local specialization and global integration. In this context, the modulation of the global but not of the local network parameters during the aging process could be considered a loss in the balancing of the most efficacious type of brain connectivity of the Adult group. This is also in line with the aging brain functions [53], which

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include a slower processing speed [54], difficulty with both episodic and working memory, reduced ability to learn and retrieve both non-verbal and verbal material [55–58], decreased attention [59–61], and difficulty task switching [62–64]. The present results are in line with those of a recent study [26] investigating the development from childhood to adulthood through strength and patterning in long-range connectivity. While in the cited paper the highest statistical differences were observed from childhood to adolescence, and the present work was more centered on adult aging, both focused on decreases in network randomness in the young brain following a new increase in randomness in the elderly (as revealed by the decrease in the alpha band of the characteristic path length). The imperfect similarity between the present result and the cited paper could be due to several factors: i) they based their analyses on scalp data, ii) the functional connectivity was thresholded, iii) the graph data were not normalized in order to avoid the dependence of the graph degrees, iv) the population was aged from 5 years. This last factor ought to be clarified further. That is, the population was divided, with steps of a few years, into nine groups. Accordingly, the meaningful results were mainly concentrated between childhood and adolescence, while in the present work the subjects were divided into three groups that begin with subjects aged at least 18 years (the mean age of the younger group was about 29 years), and the results were more focused on adult aging. Finally, here the results were obtained through a method based on estimating the sources of EEG signals (eLORETA) minimally or not affected at all by the ambiguity of localization and referencedependence. This method omitted zero phase angle coherences to avoid undue inflation of coherence by volume conduction [27, 28]. Our method is artifactsfree, since artifacts such as eye blinking and muscle activity were identified and excluded by the ICA composition and directly using the current density obtained from the inverse methods extracting the weights for the brain network parameters. It is worth mentioning that the test-retest variability analysis showed that no interaction, including Time, resulted in significance. This highlights the stability of the present measurements.

CONCLUSIONS Evidence from the present study—comparing the cortical sources of the EEG signals and the

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graph theory approach on the physiological brain aging—confirm the utility to adopt a mathematical approach to investigate relevant age-related features in real complex brain networks. Results are compatible with the hypothesis that processes, such as those revealed by changes in functional networks, may be an aspect of normal human adult brain aging. In this sense, graph theory applied to EEG can help the analysis of connectivity patterns, particularly regarding their dynamic properties, thanks to the high temporal resolution of the EEG signals. A possible interpretation of the present results is that aging processes provoke progressive disconnection among brain areas. This effect has been revealed in older subjects by the increase of low and the decrease of high frequency characteristic path length (λ) values, which measure the average shortest path length of a network. This indicates a global index of ease of travel from one part of the network to another. Further studies should address the correlation analyses between these index and the neuropsychological test scores altered by the aging process to better understand how brain network organization may be responsible for different cognitive performances. In conclusion, the graph analysis tools described here represent an interesting probe to study the distinctive features of physiological aging through a focus on functional connectivity networks. Applied to patient data, this technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection. It might aid in monitoring the impact of eventual pharmacological and rehabilitative treatments.

ACKNOWLEDGMENTS Dr. Francesca Miraglia participated to this study in the framework of her Ph.D. program at the Doctoral School in Neuroscience, Department of Neuroscience, Catholic University of Rome, Italy. The article is partially funded by the Italian Ministry of Instruction, University and Research MIUR (“Approccio integrato clinico e sperimentale allo studio dell’invecchiamento cerebrale e delle malattie neurodegenerative: basi molecolari, epidemiologia genetic, neuroimagnig multimodale e farmacogenetica” and “Functional connectivity and neuroplasticity in physiological and pathological aging” PRIN project). Authors’ disclosures available online (http://www.jalz.com/disclosures/view.php?id=2216).

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