Introduction Alzheimer's disease (AD) is a neurodegenerative disorder characterized by progressive impairment of episodic memory and other cognitive domains resulting in dementia and, ultimately, death. Imaging studies in AD have begun a shift from studies of brain structure [1],[2] to more recent studies highlighting focal regions of abnormal brain function [3]–[6]. Most recently, fMRI studies have moved beyond focal activation abnormalities to dysfunctional brain connectivity. Functional connectivity is defined as temporal correlations between spatially distinct brain regions [7]. PET studies, restricted to across-subject connectivity measures, have shown that AD patients have decreased hippocampus connectivity with prefrontal cortex [8] and posterior cingulate cortex [9] during memory tasks. Using fMRI, we demonstrated that AD patients performing a simple motor task had reduced intra-subject functional connectivity within a network of brain regions—termed the default-mode network—that includes posterior cingulate cortex, temporoparietal junction, and hippocampus [10]. Bokde et al. reported abnormalities in fusiform gyrus connectivity during a face-matching task in subjects with mild cognitive impairment—frequently a precursor to AD [11]. Three recent studies have reported reduced default-mode network deactivation in MCI and/or AD patients during encoding tasks [12],[13] and during a semantic classification task [14]. Celone et al also reported increased default-mode network deactivation in a subset of “less impaired” MCI patients. In addition to analyzing functional connectivity during task performance, functional connectivity has also been investigated during task-free (“resting-state”) conditions. Task-free functional connectivity MRI detects interregional correlations in spontaneous blood oxygen level-dependent (BOLD) signal fluctuations [15]. Using this approach, Wang et al. found disrupted functional connectivity between hippocampus and several neocortical regions in AD [16]. Similarly, Li et al. reported reduced intrahippocampal connectivity during task-free conditions [17]. Most recently Sorg et al. [18] reported reduced resting-state functional connectivity in the default-mode network of MCI patients. Although evidence is accumulating that AD disrupts functional connections between brain regions [19], it is not clear whether AD disrupts global functional brain organization. Graph metrics–the clustering coefficient and the characteristic path length—are useful measures of global organization of large-scale networks [20]. Graphs are data structures which have nodes and edges between the nodes. The clustering coefficient is a measure of local network connectivity. A network with a high average clustering coefficient is characterized by densely connected local clusters. The characteristic path length is a measure of how well connected a network is. A network with a low characteristic path length is characterized by short distances between any two nodes. Small-world network is characterized by a high clustering coefficient and a low characteristic path length [20],[21]. In a graphical representation of a brain network, a node corresponds to a brain region while an edge corresponds to the functional interaction between two brain regions. Functional connectivity networks of the human brain derived from electroencephalograms (EEGs), magnetoencephalograms and task-free fMRI data exhibit small-world characteristics [22]–[24]. In a recent EEG study, Stam et al. reported that small-world architecture in functional networks in the brain is disrupted in AD [25]. Here we examined the global functional organization of the brain in AD by (1) creating whole-brain functional connectivity networks from task-free fMRI data, (2) characterizing the organization of these networks using small-world metrics, and (3) comparing these characteristics between AD patients and age-matched controls. We hypothesized that global functional brain organization would be abnormal in AD. Further, given the need for a reliable, non-invasive clinical test for AD [26], we sought to determine whether a small-world metric obtained from task-free fMRI data might provide a sensitive and specific biomarker in AD. Results Subjects Demographic data is shown in Table 1. Subject groups did not differ significantly in age (p = 0.73), gender distribution (p = 0.62), or years of education (p = 0.58). The mean MMSE was significantly lower (p 1) showed a linear increase in small-worldness as the threshold increased (degree decreased). σ values for higher correlation thresholds are difficult to interpret, as at higher threshold values, graphs of functional brain networks have fewer edges (smaller degree) and tend to split into isolated sub-graphs. Graph metrics such as clustering coefficient, characteristic path length, and small-world property do not meaningfully characterize network structures that are not composed of a single, large group of interconnected nodes [20]. 10.1371/journal.pcbi.1000100.g001 Figure 1 Graph metrics–degree, λ (L/Lran), γ (C/Cran), σ (γ/λ), for the AD group (Δ) and the control group (○) at three frequency intervals–0.01 to 005 Hz (green), 0.06 to 0.12 Hz (blue), and 0.13 to 0.25 Hz (red). (A) For both groups, the mean degree–a measure of network connectivity is highest at Scale 3 for a wide range of correlation thresholds (0.01 1) showed a linear increase in small-worldness as the threshold increased (degree decreased). σ values for higher correlation thresholds are hard to interpret as at higher threshold values graphs of functional brain networks have fewer edges (smaller degree) and tend to split into isolated sub-graphs. Since functional connectivity and small-world properties were salient at lower-frequencies (0.01 to 0.05 Hz) for the AD group and the control group, we only report results for this frequency interval in subsequent analyses. Comparison of small-world metrics in the AD and control groups In the frequency interval between 0.01 to 0.05 Hz, we examined λ and γ values in the two groups. For group comparison, we controlled for the average correlation value (r). r is different across groups. Thus, for a given correlation threshold, the number of edges in the graph are likely to be less in AD, resulting in high λ and low γ values. To ensure that graphs in both groups had the same number of edges, individual correlation matrices were thresholded such that the resultant graph had exactly K′ edges. K′ is the average number of edges in the graph obtained by thresholding individual correlation matrices with R = ri (ri is the average correlation value for subject i, i = 1 to 39). The value of K′ selected according to this procedure was 40 for both the groups. Mean λ, mean γ, and mean σ values for the networks of the AD group and control group were derived by thresholding the correlation matrices such that the network has K′ ( = 40) edges (shown in Figure 2). Results were: (i) No significant differences in the mean λ values were observed, Mean γ values in the AD group were significantly lower than in the control group (p 0.6, mainly due to the large variance observed at higher threshold values. This analysis was extended to the remaining 86 regions of the whole brain functional network (see Table S1 to find regions that showed significant differences in clustering coefficient values between the two subject groups). 10.1371/journal.pcbi.1000100.g005 Figure 5 Small-world property γ (C/Cran), the normalized clustering coefficient, for four regions of interest–left hippocampus (Hippocampus - Left), right hippocampus (Hippocampus - Right), left precentral gyrus (Precentral Gyrus - Left), right precentral gyrus (Precentral Gyrus - Right)–for the AD group (red) and the control group (blue) as a function of the correlation threshold. In the left and the right hippocampus, for threshold values from 0.1 to 0.6, the clustering coefficient values in the AD group were significantly lower (p 172) was assumed to be a symmetric reflection of itself. At each of the three scales, wavelet correlations between signals in the 90 anatomical regions were determined by computing the correlation coefficient between the transformed signals at that scale. For each subject, a 90-node, scale-specific, undirected graph of the functional connectivity network was constructed by thresholding the wavelet correlation matrix computed at that scale. If the wavelet correlation value between two anatomical regions represented by nodes i and j in the network exceeded a threshold then an edge was drawn between node i and node j. There is currently no formal consensus regarding threshold selection, so we computed networks for threshold values from 0.01 to 0.99 with an increment of 0.01. Once a whole-brain functional connectivity network was constructed from the correlation matrix, we characterized this network in terms of its small-world properties. Small-world analysis of the whole-brain functional connectivity network Small-World properties of a network are described by the clustering coefficient and the characteristic path length of the network. The clustering coefficient and characteristic path length of functional brain networks generated from the task-free fMRI data obtained from 21 AD subjects and 18 age-matched controls were computed. The clustering coefficient of every node was computed as the ratio of the number of connections between its neighbors divided by the maximum possible connections between its neighbors. The clustering coefficient (C) of the network was calculated as the mean of the clustering coefficients of all the nodes in the network. The mean minimum path length of a node was computed as the average of minimum distances from that node to all the remaining nodes in the network. The characteristic path length (L) of the network was the average of the mean minimum path lengths of all the nodes in the network. The clustering coefficient and path length of nodes completely disconnected with the network were set as 0 and Inf respectively, and these nodes were excluded while computing C and L. To evaluate the network for small-world properties, we compared the clustering coefficient and the characteristic path length of the network with corresponding values (Cran, Lran) obtained and averaged across 1000 random networks with the same number of nodes and degree distribution [48]. Degree of a network is a measure of its connectivity. The degree of every node was computed by counting the number of edges incident on that node. Small world networks are characterized by high normalized clustering coefficient γ (C/Cran)>1 and low normalized characteristic path length λ (L/Lran)∼1 compared to random networks [24]. A cumulative metric σ–the ratio of normalized clustering coefficient (γ) to the characteristic path length (λ), a measure of small-worldness–is thus greater than 1 for small world networks. Analysis of global efficiency of whole-brain functional connectivity network Small-world networks are characterized by high clustering coefficient and low characteristic path length. These small-world metrics, particularly the path length, are not meaningful when the graph contains disconnected nodes. To address this issue, we ensured that only small-world metrics computed on connected graphs were considered in our analysis. Specifically, the algorithm used to choose the correlation threshold (R) guaranteed that disconnected graphs were excluded from the analysis. Also, in the node-wise clustering coefficient comparison analysis, we only considered thresholds from 0.1 to 0.6. We chose these thresholds because beyond 0.6 the network gets divided into disconnected subset of nodes. To determine if our characteristic path length findings were robust and reliable, we computed efficiency of functional brain networks. It has been previously reported that efficiency as a graph metric (1) is not susceptible to disconnected nodes, (2) is applicable to unweighted as well as weighted graphs, and (3) is a more meaningful measure of parallel information processing than path length [49]. Efficiency of a graph (Eglobal-net) [50] is inverse of the harmonic mean of the minimum path length between each pair of nodes, Lij, and was computed as, (1) To evaluate the network for its global efficiency of parallel information processing, we compared the global efficiency of the network (Eglobal-net) with corresponding values (Eglobal-ran) obtained and averaged across 1000 random networks with the same number of nodes and degree distribution. A network with small-world properties is characterized by global efficiency value that is lower than the random network–Eglobal (Eglobal-net/Eglobal-ran)<1. Regional profile of clustering coefficient In the frequency interval 0.01 to 0.05 Hz, we next examined small world metric values of four anatomical regions of interest in the two groups. These four regions included the left hippocampus, the right hippocampus, the left precentral gyrus, and the right precentral gyrus. These were chosen because we hypothesized significant differences in the hippocampus (a region targeted early in AD), but not in the precentral gyrus (which is typically spared even in the advanced stages of AD) [51]. This regional profiling analysis was performed on the clustering coefficient (and not the path length) because only the former differed significantly between the AD and control groups. Growth curve modeling, with an intercept (baseline), linear and quadratic terms, was used to compare the clustering coefficient values for threshold values from 0.1 to 0.6 in the two subject groups. We chose these thresholds because beyond 0.6 the network divides into disconnected subsets of nodes and small-world metrics are then no longer meaningful [20]. This analysis was performed using the Mplus software (http://www.statmodel.com). Growth curve models describe change (growth) with respect to a control variable. They are well-suited for analyzing group-level differences in biomedical data, particularly in cases where capturing and analyzing individual growth trajectories is important. In our study, the growth trajectories of clustering coefficient of a subject carry important information about the variance within the group and needs to be incorporated in the model. The coefficients of growth curve models capture the baseline performance, instantaneous growth rate, and the acceleration of the variable of interest–γ. Regional connectivity We then examined regional correlation values (connectivity) in the two groups. Wavelet correlation values of 4005 pairs of anatomical regions were first z-normalized and then compared between the two subject groups. T-test with a false discovery rate of 0.01 was used to test if the difference was significant. For the frequency range 0.01 to 0.05 Hz, the correlation values of 108 pairs of anatomical regions out of a total 4005 pairs were significantly lower in the AD group as compared to the control group while only 42 correlation values showed a significant increase in the AD group (p<0.01, corrected for multiple comparisons). To get an idea of average differences in the global functional organization in the two groups, we investigated the regional connectivity at a coarser level of granularity. Ninety anatomical regions of our network were grouped into eight higher-level anatomical regions using the grouping defined by Tzourio-Mazoyer et al. [45]. The prefrontal lobe region consists of the superior frontal gyrus (dorsolateral, orbital, medial, medial orbital), the middle frontal gyrus, the middle frontal gyrus (orbital), the inferior frontal gyrus (opercular, triangular, orbital), the olfactory gyrus, the gyrus rectus, and the anterior cingulate. The other parts of frontal lobe region consists of the precentral gyrus, the supplementary motor area, the median cingulate, and the rolandic operculum. The occipital lobe region consists of the calcarine fissure, the cuneus, the lingual gyrus, the superior occipital gyrus, the middle occipital gyrus, and the inferior occipital gyrus. The temporal lobe and the medial temporal region consists of the superior temporal gyrus, the temporal pole (superior, middle), the middle temporal gyrus, the inferior temporal gyrus, the heschl gyrus, the fusiform gyrus, the hippocampus, the parahippocampal gyrus, and the amygdala. The parietal lobe region consists of the postcentral gyrus, the superior parietal lobule, the inferior parietal lobule, the supramarginal gyrus, the angular gyrus, the precuneus, the paracentral lobule, and the posterior cingulate gyrus. The corpus striatum region consists of the caudate nucleus, the putamen, and the pallidum. Each higher level anatomical region consists of regions from both the hemispheres. Differences in mean correlation coefficients for 4005 pairs were aggregated into 32 pairs and the resulting differences were then normalized. (see also [52]). In the aggregation step, the number of decreased (−1) or increased connectivities (+1) for each of the 32 pairs ( = (8×8)/2) was counted. For example, to identify differential connectivity between the prefrontal lobe region and the occipital lobe region the number of decreased or increased connectivities between all pairs of sub-regions belonging to the prefrontal lobe region and occipital lobe region was counted. Since each brain region has a different number of sub-regions, the aggregated differential connectivity count was normalized by the number of possible connections between pairs of sub regions belonging to the two brain regions under investigation. Supporting Information Table S1 Regions of whole brain functional network ranked in ascending order of the p-value (computed using growth curve modeling) and then descending order of absolute difference between the clustering coefficient values of the AD group and the control group. (0.18 MB DOC) Click here for additional data file.
