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Small-worldness and modularity of the resting-state functional brain network decrease with aging
Neuroscience Letters 556 (2013) 104–108
Contents lists available at ScienceDirect
Neuroscience Letters journal homepage: www.elsevier.com/locate/neulet
Small-worldness and modularity of the resting-state functional brain network decrease with aging Keiichi Onoda ∗ , Shuhei Yamaguchi Department of Neurology, Shimane University, 89-1 Enyacho, Izumo, Shimane 693-8501, Japan
h i g h l i g h t s • • • • •
Graph theory can be used to estimate brain network efficiency. We investigated the effects of aging on small-worldness and modularity of the functional brain network. Small-worldness and modularity were negatively correlated with age. Node strengths for sensorimotor regions showed positive correlations with age. Efficiency of the human functional brain network gradually decreases with age.
a r t i c l e
i n f o
Article history: Received 8 July 2013 Received in revised form 3 October 2013 Accepted 11 October 2013 Keywords: Aging Resting-state fMRI Small-worldness Modularity Functional network
a b s t r a c t The human brain is a complex network that is known to be affected by normal aging. Graph-based analysis has been used to estimate functional brain network efficiency and effects of normal aging on small-worldness have been reported. This relationship is further investigated here along with network modularity, a statistic reflecting how well a network is organized into modules of densely interconnected nodes. Modularity has previously been observed to vary as a function of working memory capacity, therefore we hypothesized that both small-worldness and modularity would show age-related declines. We found that both small-worldness and modularity were negatively correlated with increasing age but that this decline was relatively slow. © 2013 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Human cognitive decline reflects various brain changes in a complex network [6]. Each brain region has its own function and different regions are continuously sharing information with each other. Functional connectivity is defined as a temporal dependency between spatially separate regions, and is calculated as the coactivation level of spontaneous BOLD time series recorded during rest. Functional connectivity changes as individuals age [4,12]. In graph theory, the functional brain network is defined as a graph with nodes and edges, reflecting brain regions and connections between the regions. Graph-based analyses of the functional brain network have shown that the brain forms an integrative complex network [7,13]. Functional segregation is the occurrence of specialized processing within densely interconnected groups of regions, and is quantified using a clustering coefficient or
∗ Corresponding author. Tel.: +81 853 20 2198. E-mail addresses: [email protected] (K. Onoda), [email protected] (S. Yamaguchi). 0304-3940/$ – see front matter © 2013 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.neulet.2013.10.023
modularity value. Higher values for these indices are interpreted as the presence of clusters or modules within the functional brain network. Functional integration is the ability to rapidly combine specialized information from distributed brain regions and is quantified as characteristic path length or global efficiency. Shorter paths and higher global efficiency mean higher integration in the brain. The brain network simultaneously reconciles opposing demands of functional segregation and integration. A well-designed network could therefore combine functionally specialized modules with a robust number of intermodular connections. Such a network is called a small-world network, defined as a network that is more clustered than a random network yet has approximately the same characteristic path length as a random network. Few studies have investigated potential changes in resting-state network properties with aging. Bullmore and his colleague examined the efficiency of functional networks in younger and older adults, and found that older adults show decreases in global and local efficiency [1]. This research team has also studied whether age affects functional network modularity [10], reporting that the modularity of the older brain network was not significantly different from that of the younger, implying that whole brain module
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organization is conserved over the adult age range. However, they also reported decreased intermodular connections to frontal modular regions. The absence of a significant aging effect on whole brain modularity might be due to the relatively small sample size (n = 17 for young and 13 for old) used in this study. In the present study we used a larger sample size to explore the effects of aging on the properties of the resting-state functional network. A recent study showed that resting-state network modularity is associated with working memory capacity [17]. We hypothesized that both smallworldness and functional network modularity would decrease with age, consistent with a general reduction in cognitive functioning typically observed in the elderly.
2. Materials and methods Two hundred and eight adult and elderly individuals without a history of neurological or psychiatric disorders participated in the present study. We discarded from our analyses the participants whose images showed excessive head movement (over 2 mm or 2◦ ) during acquisition. We also removed participants whose images indicated bran atrophy, silent bran infarction and/or pathological subcortical white matter lesions. After such removals our study included 193 participants (115 men, 78 women). The mean age was 60.1 ± 12.1 (sd) years old, and the age range was 34–87 years old. The Shimane University Medical Ethics Committee approved the study and all participants gave their written informed consent. Imaging data were acquired using a Siemens AG 1.5 T scanner. Twenty axial slices parallel to the plane connecting the anterior and posterior commissures were measured using a T2*-weighted gradient-echo spiral pulse sequence (TR = 2000 ms, TE = 46 ms, flip angle = 90◦ , scan order = interleave, matrix size = 64 × 64, FOV = 256 mm × 256 mm, slice thickness = 5 mm, gap = 1 mm). All participants underwent this five-minute rs-fMRI scan only after being instructed to remain awake with their eyes closed. After the functional scan, T1-weighted images (MPRAGE) of the entire brain were measured (192 sagittal slices, TR = 2170 ms, TE = 3.93 ms, inversion time = 1100 ms, flip angle = 15◦ , matrix size = 256 × 256, FOV = 256 mm × 256 mm, slice thickness = 1 mm). We used Statistical Parametric Mapping (SPM8, http://www.fil.ion.ucl.ac.uk/spm/) for spatial preprocessing. The first 10 functional images for each participant were discarded for magnetic field stabilization. The remaining 140 functional images were realigned to remove any artifacts from head movement and to correct for differences in image acquisition time between slices. Next, the functional images were normalized to the standard space defined by a template T1-weighted image (MNI) and then resliced with a voxel size of 3 mm × 3 mm × 3 mm to agree with the gray matter probability maps. Spatial smoothing was applied with the FWHM equal to 8 mm. After the spatial preprocessing, we did temporal preprocessing using the functional connectivity toolbox (conn, http://www.alfnie.com/software). Temporal smoothing was performed using a band-pass filter (0.01–0.08 Hz). Head movement time series, white matter signal, and cerebral spinal fluid signal were regressed out from each voxel, based on CompCor Strategy [2]. To define brain nodes, an automated anatomical labeling atlas (AAL) was employed to divide the whole brain into 90 volumes of interest. The mean time course of the voxels within each atlas region was extracted for network construction. A Pearson correlation coefficient matrix was calculated for all time course pairs. We then applied a power adjacency function called ‘soft thresholding’:
wij =
rij + 1 2
ˇ
Fig. 1. The soft thresholding approach aims to retain all edges, replacing the thresholding operation with a continuous mapping of correlation (r) into edge weights (w) using the power adjacency function. Top: matrixes of correlation r [−1 1] and edge weight w [0 1] for a sample participant (A and D). Middle: edge r/w distributions of the original and soft-thresholded networks (B and E). Different colored lines indicate different participants. Bottom: distributions of node strength in the original (r) and soft-thresholded (w) networks (C and F).
where wij = f (rij ) describes a continuous, non-linear mapping of correlation coefficients. Correlation coefficients in the range [−1 1] were translated to edge weights [0 1] with a power law [14]. Based on evidence provided by Schwarz and McGonigle [14], we set 12 as  because small-worldness of soft-thresholded networks is demonstrated at parameter values of ˇ ≥ 12. Edge histograms (rij /wij ) before and after soft-thresholding transformations are illustrated in Fig. 1B and E. In the soft-thresholded networks, the edge weight distributions became skewed toward lower values of wij . The resulting histograms of node strength distribution are shown in Fig. 1C and F. The soft-thresholded distribution approached a profile similar to the power law observed with binary networks. We estimated small-worldness and modular organization using the brain connectivity toolbox (BCT, https://sites.google.com/site/bctnet/). Small-worldness was quantified using characteristic path length and the clustering coefficient [20]. Characteristic path length is defined as the average of the shortest path length between all pairs of nodes, and the path length represents the number of steps along the route between the pairs. A shorter characteristic path length indicates a higher level of communication efficiency between global brain regions. The clustering coefficient is defined as the fraction of the node’s neighbors that are also neighbors of each other, and reflects the prevalence of clustered connectivity around individual nodes. We normalized the characteristic path length and the clustering coefficient by dividing by the value for the same variable calculated for a randomly rewired null model. The characteristic path length and the clustering coefficient of the random network were the average of the values calculated from 100 randomly rewired null models. Small-worldness “sigma” was computed as the ratio of
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the normalized clustering coefficient “gamma” to the normalized characteristic path length “lambda”. Modularity, another important feature of the whole brain functional network, is defined as the degree to which a network may be subdivided into delineated and nonoverlapping groups [11]. A higher modularity indicates that a functional network is more suitable for specialized processing. We estimated modularity using the heuristic modularity maximizing algorithm [3]. We examined correlations between global network properties and age, and compared mean brain functional network modular structure across middle age (under 50, n = 42) and old age (over 70, n = 38) participants. To examine the effect of age on each region, we also estimated node strength, which is defined as the sum of all neighboring link weights. In addition, we explored the relationship between aging effects and anatomical distance at a region involving the strongest effects of age on node strength. The distance was defined as the Euclidean distance between the centers of each ROI.
3. Results We calculated Spearman’s correlation coefficients to examine the relationships between the metrics from the graph analysis of the resting-state functional network and age. Small-worldness (“sigma”; r = −0.165, p = 0.022) and modularity (r = −0.155, p = 0.031) were significantly correlated with age, such that older study participants showed both a lower sigma and reduced modularity (Fig. 2A and B). There was no significant correlation between number of modules and age (r = −0.020, p = 787). Modular structures for average middle age and old age brain networks are illustrated in Fig. 2C and D. The middle and old age brain functional networks were comprised of 6 and 7 modules, respectively. One module of the middle age brain was comprised of the posterior cingulate and ventral medial prefrontal cortices, and corresponded to a portion of the default mode. However, the elderly posterior cingulate cortex appears to be integrated into a visual module. In addition, the regions comprising the sensorimotor sub cortex module of the middle age brain network were segregated into two modules in the older age brain network, and the intramodule edges of the sensorimotor area were closely aggregated in the latter. Finally, the front-parietal module was smaller for the older brain network. To examine the effect of age on each region, we calculated correlations between age and node strength. Regions were credited with a significant correlation at a threshold of FDR corrected p < 0.05. As shown in Fig. 3A and B, node strength of the bilateral sensorimotor areas including the pre/postcentral gyrus, supplementary motor area, paracentral lobule, and precuneus increased as age increased. Furthermore, we examined the relationship between age and anatomical distance. Fig. 3C shows correlation coefficients for age and connectivity with the right precentral gyrus, and Fig. 3D shows a scatter plot depicting the correlations and anatomical distance. There were weak correlations between age and distance (whole brain: r = −0.200, p = 0.060; left hemisphere: r = -0.329, p = 0.027; right hemisphere: r = −0.268, p = 0.078). These indicate that short distance connectivity tends to be strong in the elderly for this region.
4. Discussion The aim of the present study was to investigate aging effects on two organizational properties (small-worldness and modularity) of the functional brain network. We found that small-worldness and modularity decreased with normal aging, while node strength of the sensorimotor regions in the elderly was notably increased.
Fig. 2. Top: scatter plots of small-worldness “sigma” (A) and modularity (B) with age. Middle and bottom: anatomical representations of module structure for average middle age (C) and old age (D) networks. If w > 0.02, edges were described as connected lines. The intra- and inter-module connections are shown in colored and black lines, respectively.
Achard et al. [1] reported that normal aging is associated with reduced global and local efficiencies, which are indices of smallworldness. We confirmed that small-worldness declines with aging using another metric (sigma) [1]. Meunier et al. [10] studied agerelated changes in module structure between younger and older groups, and found that module size and composition differed between them. However, in their study, overall modularity failed to show a significant age-related difference. Employing the soft threshold method [14], we observed significant aging effects on the modularity of the functional brain network. These results suggest that normal aging is associated with alterations of brain functional organization. However, the effect size on overall network properties was small compared with that for the local regions. In a previous graph theory-based anatomical network study smallworldness was relatively preserved across the age range, local efficiency was decreased in older people [5]. More global properties of the brain network might not be sensitive to normal aging. In contrast to global properties, aspects of regional topology including default mode, front-parietal, and sensorimotor modules
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Fig. 3. ROIs that showed significant correlations between node strength and age. Scatter plot of node strength in right precentral gyrus with age. (C) Color of each ROI indicates aging effect (correlation between age and connectivity (w) with right precentral gyrus). Red shows that right precentral gyrus connectivity is higher for elderly than younger participants, and blue shows the opposite. (D) X-axis indicates anatomical distance (mm) between centers of each ROI and right precental gyrus, and y-axis indicates aging effect which is shown in (C).
might be more sensitive to aging. Consistent with our results, earlier work has found that major modules in the middle age brain network corresponded to smaller and more local modules in the older brain network [10]. In particular, we found that sensorimotor region connectivity was closely aggregated in the older brain network, which was corroborated by node strength analysis. We explored the distribution of aging effects on node strength and found increased strength in the sensorimotor area. Age-related decreases in functional brain connectivity have been reported in many studies, although some studies have found age-related increases [4]. A study using a support vector machine reported that the accuracy for distinguishing between brains of young and old adults was 84%, with the sensorimotor regions providing the greatest contribution to this accuracy [9]. In this study, the older group showed stronger connections among the sensorimotor brain regions. As our evidence showed that aging preferentially affects long-range connections, one possible interpretation for this finding is that the sensorimotor areas that are relatively more isolated from anatomically long-distance regions show increased short-distance connectivity. In other words, the functional independence of each sensorimotor region in fact declines with aging. Song et al. [16] reported that global efficiency of the default mode network was different in a superior-intelligence as compared to an average-intelligence group. This difference indicates that small-worldness of a partial network is related to individual intelligence. Local but not global changes in the functional network may reflect cognitive declines with aging. There is a limitation of the present study. Our participants were instructed to keep awake with their eyes closed, but the possibility that they fell asleep cannot be eliminated due to a lack of autonomic nerve or EEG measurements. However, Uehara et al. [19] reported that clustering coefficients and modularity of the resting-state bran network were not significantly different between an awake state and stage 1 sleep. We speculate that the effects of consciousness level on global indexes are smaller than that of aging.
In conclusion, our study demonstrated that small-worldness and modularity of the functional brain network are attenuated by normal aging, although this age-related decline appears to occur relatively slowly. Some studies have suggested that global properties of functional brain networks are disrupted by neurodegenerative diseases in the elderly [8,18]. Small-worldness and modularity might be good markers for studies of aging and dementia, because such functional changes in the brain network typically precede anatomical changes such as atrophy [15].
References [1] S. Achard, E. Bullmore, Efficiency and cost of economical brain functional networks, PLoS Comput. Biol. 3 (2007) e17. [2] Y. Behzadi, K. Restom, J. Liau, T.T. Liu, A component based noise correction method (CompCor) for BOLD and perfusion based Fmri, Neuroimage 37 (2007) 90–101. [3] V.D. Blondel, J.-L. Guillaume, R. Lambiotte, E. Lefebvre, Fast unfolding of communities in large networks, J. Stat. Mech. Theor. Exp. 10 (2008) P10008. [4] L.K. Ferreira, G.F. Busatto, Resting-state functional connectivity in normal brain aging, Neurosci. Biobehav. Rev. 37 (2013) 384–400. [5] G. Gong, P. Rosa-Neto, F. Carbonell, Z.J. Chen, Y. He, A.C. Evans, Age- and genderrelated differences in the cortical anatomical network, J. Neurosci. 29 (2009) 15684–15693. [6] T. Hedden, J.D.E. Gabrieli, Insights into the ageing mind: a view from cognitive neuroscience, Nat. Rev. Neurosci. 5 (2004) 87–96. [7] C.J. Honey, R. Kötter, M. Breakspear, O. Sporns, Network structure of cerebral cortex shapes functional connectivity on multiple time scales, Proc. Natl. Acad. Sci. U. S. A. 104 (2007) 10240–10245. [8] Z. Liu, Y. Zhang, H. Yan, L. Bai, R. Dai, W. Wei, C. Zhong, T. Xue, H. Wang, Y. Feng, Y. You, X. Zhang, J. Tian, Altered topological patterns of brain networks in mild cognitive impairment and Alzheimer’s disease: a resting-state fMRI study, Psychiatr. Res. 202 (2012) 118–125. [9] T.B. Meier, A.S. Desphande, S. Vergun, V. a Nair, J. Song, B.B. Biswal, M.E. Meyerand, R.M. Birn, V. Prabhakaran, Support vector machine classification and characterization of age-related reorganization of functional brain networks, Neuroimage 60 (2012) 601–613. [10] D. Meunier, S. Achard, A. Morcom, E. Bullmore, Age-related changes in modular organization of human brain functional networks, Neuroimage 44 (2009) 715–723. [11] M. Newman, Analysis of weighted networks, Phys. Rev. E 70 (2004) 056131.
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[12] K. Onoda, M. Ishihara, S. Yamaguchi, Decreased functional connectivity by aging is associated with cognitive decline, J. Cogn. Neurosci. 24 (2012) 2186–2198. [13] M. Rubinov, O. Sporns, Complex network measures of brain connectivity: uses and interpretations, Neuroimage. 52 (2010) 1059–1069. [14] A.J. Schwarz, J. McGonigle, Negative edges and soft thresholding in complex network analysis of resting state functional connectivity data, Neuroimage. 55 (2011) 1132–1146. [15] Y.I. Sheline, M.E. Raichle, Resting state functional connectivity in preclinical Alzheimer’s disease, Biol. Psychiatr. (2013) 340–347. [16] M. Song, Y. Liu, Y. Zhou, K. Wang, C. Yu, T. Jiang, Default network and intelligence difference, Conf. Proc. IEEE Eng. Med. Biol. Soc. 2009 (2009) 2212–2215.
[17] A. Stevens, S. Tappon, A. Garg, D. Fair, Functional brain network modularity captures inter- and intra-individual variation in working memory capacity, PLoS ONE 7 (2012) e30468. [18] K. Supekar, V. Menon, D. Rubin, M. Musen, M.D. Greicius, Network analysis of intrinsic functional brain connectivity in Alzheimer’s disease, PLoS Comput. Biol. 4 (2008) e1000100. [19] T. Uehara, T. Yamasaki, T. Okamoto, T. Koike, S. Kan, S. Miyauchi, J.I. Kira, S. Tobimatsu, Efficiency of a “Small-World” brain network depends on consciousness level: a resting-state fMRI study, Cereb. Cortex (2013). [20] D.J. Watts, S.H. Strogatz, Collective dynamics of “small-world” networks, Nature 393 (1998) 440–442.
Contents lists available at ScienceDirect
Neuroscience Letters journal homepage: www.elsevier.com/locate/neulet
Small-worldness and modularity of the resting-state functional brain network decrease with aging Keiichi Onoda ∗ , Shuhei Yamaguchi Department of Neurology, Shimane University, 89-1 Enyacho, Izumo, Shimane 693-8501, Japan
h i g h l i g h t s • • • • •
Graph theory can be used to estimate brain network efficiency. We investigated the effects of aging on small-worldness and modularity of the functional brain network. Small-worldness and modularity were negatively correlated with age. Node strengths for sensorimotor regions showed positive correlations with age. Efficiency of the human functional brain network gradually decreases with age.
a r t i c l e
i n f o
Article history: Received 8 July 2013 Received in revised form 3 October 2013 Accepted 11 October 2013 Keywords: Aging Resting-state fMRI Small-worldness Modularity Functional network
a b s t r a c t The human brain is a complex network that is known to be affected by normal aging. Graph-based analysis has been used to estimate functional brain network efficiency and effects of normal aging on small-worldness have been reported. This relationship is further investigated here along with network modularity, a statistic reflecting how well a network is organized into modules of densely interconnected nodes. Modularity has previously been observed to vary as a function of working memory capacity, therefore we hypothesized that both small-worldness and modularity would show age-related declines. We found that both small-worldness and modularity were negatively correlated with increasing age but that this decline was relatively slow. © 2013 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Human cognitive decline reflects various brain changes in a complex network [6]. Each brain region has its own function and different regions are continuously sharing information with each other. Functional connectivity is defined as a temporal dependency between spatially separate regions, and is calculated as the coactivation level of spontaneous BOLD time series recorded during rest. Functional connectivity changes as individuals age [4,12]. In graph theory, the functional brain network is defined as a graph with nodes and edges, reflecting brain regions and connections between the regions. Graph-based analyses of the functional brain network have shown that the brain forms an integrative complex network [7,13]. Functional segregation is the occurrence of specialized processing within densely interconnected groups of regions, and is quantified using a clustering coefficient or
∗ Corresponding author. Tel.: +81 853 20 2198. E-mail addresses: [email protected] (K. Onoda), [email protected] (S. Yamaguchi). 0304-3940/$ – see front matter © 2013 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.neulet.2013.10.023
modularity value. Higher values for these indices are interpreted as the presence of clusters or modules within the functional brain network. Functional integration is the ability to rapidly combine specialized information from distributed brain regions and is quantified as characteristic path length or global efficiency. Shorter paths and higher global efficiency mean higher integration in the brain. The brain network simultaneously reconciles opposing demands of functional segregation and integration. A well-designed network could therefore combine functionally specialized modules with a robust number of intermodular connections. Such a network is called a small-world network, defined as a network that is more clustered than a random network yet has approximately the same characteristic path length as a random network. Few studies have investigated potential changes in resting-state network properties with aging. Bullmore and his colleague examined the efficiency of functional networks in younger and older adults, and found that older adults show decreases in global and local efficiency [1]. This research team has also studied whether age affects functional network modularity [10], reporting that the modularity of the older brain network was not significantly different from that of the younger, implying that whole brain module
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organization is conserved over the adult age range. However, they also reported decreased intermodular connections to frontal modular regions. The absence of a significant aging effect on whole brain modularity might be due to the relatively small sample size (n = 17 for young and 13 for old) used in this study. In the present study we used a larger sample size to explore the effects of aging on the properties of the resting-state functional network. A recent study showed that resting-state network modularity is associated with working memory capacity [17]. We hypothesized that both smallworldness and functional network modularity would decrease with age, consistent with a general reduction in cognitive functioning typically observed in the elderly.
2. Materials and methods Two hundred and eight adult and elderly individuals without a history of neurological or psychiatric disorders participated in the present study. We discarded from our analyses the participants whose images showed excessive head movement (over 2 mm or 2◦ ) during acquisition. We also removed participants whose images indicated bran atrophy, silent bran infarction and/or pathological subcortical white matter lesions. After such removals our study included 193 participants (115 men, 78 women). The mean age was 60.1 ± 12.1 (sd) years old, and the age range was 34–87 years old. The Shimane University Medical Ethics Committee approved the study and all participants gave their written informed consent. Imaging data were acquired using a Siemens AG 1.5 T scanner. Twenty axial slices parallel to the plane connecting the anterior and posterior commissures were measured using a T2*-weighted gradient-echo spiral pulse sequence (TR = 2000 ms, TE = 46 ms, flip angle = 90◦ , scan order = interleave, matrix size = 64 × 64, FOV = 256 mm × 256 mm, slice thickness = 5 mm, gap = 1 mm). All participants underwent this five-minute rs-fMRI scan only after being instructed to remain awake with their eyes closed. After the functional scan, T1-weighted images (MPRAGE) of the entire brain were measured (192 sagittal slices, TR = 2170 ms, TE = 3.93 ms, inversion time = 1100 ms, flip angle = 15◦ , matrix size = 256 × 256, FOV = 256 mm × 256 mm, slice thickness = 1 mm). We used Statistical Parametric Mapping (SPM8, http://www.fil.ion.ucl.ac.uk/spm/) for spatial preprocessing. The first 10 functional images for each participant were discarded for magnetic field stabilization. The remaining 140 functional images were realigned to remove any artifacts from head movement and to correct for differences in image acquisition time between slices. Next, the functional images were normalized to the standard space defined by a template T1-weighted image (MNI) and then resliced with a voxel size of 3 mm × 3 mm × 3 mm to agree with the gray matter probability maps. Spatial smoothing was applied with the FWHM equal to 8 mm. After the spatial preprocessing, we did temporal preprocessing using the functional connectivity toolbox (conn, http://www.alfnie.com/software). Temporal smoothing was performed using a band-pass filter (0.01–0.08 Hz). Head movement time series, white matter signal, and cerebral spinal fluid signal were regressed out from each voxel, based on CompCor Strategy [2]. To define brain nodes, an automated anatomical labeling atlas (AAL) was employed to divide the whole brain into 90 volumes of interest. The mean time course of the voxels within each atlas region was extracted for network construction. A Pearson correlation coefficient matrix was calculated for all time course pairs. We then applied a power adjacency function called ‘soft thresholding’:
wij =
rij + 1 2
ˇ
Fig. 1. The soft thresholding approach aims to retain all edges, replacing the thresholding operation with a continuous mapping of correlation (r) into edge weights (w) using the power adjacency function. Top: matrixes of correlation r [−1 1] and edge weight w [0 1] for a sample participant (A and D). Middle: edge r/w distributions of the original and soft-thresholded networks (B and E). Different colored lines indicate different participants. Bottom: distributions of node strength in the original (r) and soft-thresholded (w) networks (C and F).
where wij = f (rij ) describes a continuous, non-linear mapping of correlation coefficients. Correlation coefficients in the range [−1 1] were translated to edge weights [0 1] with a power law [14]. Based on evidence provided by Schwarz and McGonigle [14], we set 12 as  because small-worldness of soft-thresholded networks is demonstrated at parameter values of ˇ ≥ 12. Edge histograms (rij /wij ) before and after soft-thresholding transformations are illustrated in Fig. 1B and E. In the soft-thresholded networks, the edge weight distributions became skewed toward lower values of wij . The resulting histograms of node strength distribution are shown in Fig. 1C and F. The soft-thresholded distribution approached a profile similar to the power law observed with binary networks. We estimated small-worldness and modular organization using the brain connectivity toolbox (BCT, https://sites.google.com/site/bctnet/). Small-worldness was quantified using characteristic path length and the clustering coefficient [20]. Characteristic path length is defined as the average of the shortest path length between all pairs of nodes, and the path length represents the number of steps along the route between the pairs. A shorter characteristic path length indicates a higher level of communication efficiency between global brain regions. The clustering coefficient is defined as the fraction of the node’s neighbors that are also neighbors of each other, and reflects the prevalence of clustered connectivity around individual nodes. We normalized the characteristic path length and the clustering coefficient by dividing by the value for the same variable calculated for a randomly rewired null model. The characteristic path length and the clustering coefficient of the random network were the average of the values calculated from 100 randomly rewired null models. Small-worldness “sigma” was computed as the ratio of
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the normalized clustering coefficient “gamma” to the normalized characteristic path length “lambda”. Modularity, another important feature of the whole brain functional network, is defined as the degree to which a network may be subdivided into delineated and nonoverlapping groups [11]. A higher modularity indicates that a functional network is more suitable for specialized processing. We estimated modularity using the heuristic modularity maximizing algorithm [3]. We examined correlations between global network properties and age, and compared mean brain functional network modular structure across middle age (under 50, n = 42) and old age (over 70, n = 38) participants. To examine the effect of age on each region, we also estimated node strength, which is defined as the sum of all neighboring link weights. In addition, we explored the relationship between aging effects and anatomical distance at a region involving the strongest effects of age on node strength. The distance was defined as the Euclidean distance between the centers of each ROI.
3. Results We calculated Spearman’s correlation coefficients to examine the relationships between the metrics from the graph analysis of the resting-state functional network and age. Small-worldness (“sigma”; r = −0.165, p = 0.022) and modularity (r = −0.155, p = 0.031) were significantly correlated with age, such that older study participants showed both a lower sigma and reduced modularity (Fig. 2A and B). There was no significant correlation between number of modules and age (r = −0.020, p = 787). Modular structures for average middle age and old age brain networks are illustrated in Fig. 2C and D. The middle and old age brain functional networks were comprised of 6 and 7 modules, respectively. One module of the middle age brain was comprised of the posterior cingulate and ventral medial prefrontal cortices, and corresponded to a portion of the default mode. However, the elderly posterior cingulate cortex appears to be integrated into a visual module. In addition, the regions comprising the sensorimotor sub cortex module of the middle age brain network were segregated into two modules in the older age brain network, and the intramodule edges of the sensorimotor area were closely aggregated in the latter. Finally, the front-parietal module was smaller for the older brain network. To examine the effect of age on each region, we calculated correlations between age and node strength. Regions were credited with a significant correlation at a threshold of FDR corrected p < 0.05. As shown in Fig. 3A and B, node strength of the bilateral sensorimotor areas including the pre/postcentral gyrus, supplementary motor area, paracentral lobule, and precuneus increased as age increased. Furthermore, we examined the relationship between age and anatomical distance. Fig. 3C shows correlation coefficients for age and connectivity with the right precentral gyrus, and Fig. 3D shows a scatter plot depicting the correlations and anatomical distance. There were weak correlations between age and distance (whole brain: r = −0.200, p = 0.060; left hemisphere: r = -0.329, p = 0.027; right hemisphere: r = −0.268, p = 0.078). These indicate that short distance connectivity tends to be strong in the elderly for this region.
4. Discussion The aim of the present study was to investigate aging effects on two organizational properties (small-worldness and modularity) of the functional brain network. We found that small-worldness and modularity decreased with normal aging, while node strength of the sensorimotor regions in the elderly was notably increased.
Fig. 2. Top: scatter plots of small-worldness “sigma” (A) and modularity (B) with age. Middle and bottom: anatomical representations of module structure for average middle age (C) and old age (D) networks. If w > 0.02, edges were described as connected lines. The intra- and inter-module connections are shown in colored and black lines, respectively.
Achard et al. [1] reported that normal aging is associated with reduced global and local efficiencies, which are indices of smallworldness. We confirmed that small-worldness declines with aging using another metric (sigma) [1]. Meunier et al. [10] studied agerelated changes in module structure between younger and older groups, and found that module size and composition differed between them. However, in their study, overall modularity failed to show a significant age-related difference. Employing the soft threshold method [14], we observed significant aging effects on the modularity of the functional brain network. These results suggest that normal aging is associated with alterations of brain functional organization. However, the effect size on overall network properties was small compared with that for the local regions. In a previous graph theory-based anatomical network study smallworldness was relatively preserved across the age range, local efficiency was decreased in older people [5]. More global properties of the brain network might not be sensitive to normal aging. In contrast to global properties, aspects of regional topology including default mode, front-parietal, and sensorimotor modules
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Fig. 3. ROIs that showed significant correlations between node strength and age. Scatter plot of node strength in right precentral gyrus with age. (C) Color of each ROI indicates aging effect (correlation between age and connectivity (w) with right precentral gyrus). Red shows that right precentral gyrus connectivity is higher for elderly than younger participants, and blue shows the opposite. (D) X-axis indicates anatomical distance (mm) between centers of each ROI and right precental gyrus, and y-axis indicates aging effect which is shown in (C).
might be more sensitive to aging. Consistent with our results, earlier work has found that major modules in the middle age brain network corresponded to smaller and more local modules in the older brain network [10]. In particular, we found that sensorimotor region connectivity was closely aggregated in the older brain network, which was corroborated by node strength analysis. We explored the distribution of aging effects on node strength and found increased strength in the sensorimotor area. Age-related decreases in functional brain connectivity have been reported in many studies, although some studies have found age-related increases [4]. A study using a support vector machine reported that the accuracy for distinguishing between brains of young and old adults was 84%, with the sensorimotor regions providing the greatest contribution to this accuracy [9]. In this study, the older group showed stronger connections among the sensorimotor brain regions. As our evidence showed that aging preferentially affects long-range connections, one possible interpretation for this finding is that the sensorimotor areas that are relatively more isolated from anatomically long-distance regions show increased short-distance connectivity. In other words, the functional independence of each sensorimotor region in fact declines with aging. Song et al. [16] reported that global efficiency of the default mode network was different in a superior-intelligence as compared to an average-intelligence group. This difference indicates that small-worldness of a partial network is related to individual intelligence. Local but not global changes in the functional network may reflect cognitive declines with aging. There is a limitation of the present study. Our participants were instructed to keep awake with their eyes closed, but the possibility that they fell asleep cannot be eliminated due to a lack of autonomic nerve or EEG measurements. However, Uehara et al. [19] reported that clustering coefficients and modularity of the resting-state bran network were not significantly different between an awake state and stage 1 sleep. We speculate that the effects of consciousness level on global indexes are smaller than that of aging.
In conclusion, our study demonstrated that small-worldness and modularity of the functional brain network are attenuated by normal aging, although this age-related decline appears to occur relatively slowly. Some studies have suggested that global properties of functional brain networks are disrupted by neurodegenerative diseases in the elderly [8,18]. Small-worldness and modularity might be good markers for studies of aging and dementia, because such functional changes in the brain network typically precede anatomical changes such as atrophy [15].
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