In this study, we investigated whether global functional brain organization is disrupted in AD. To our knowledge, this is the first study to examine alterations in global functional organization and connectivity in AD patients using fMRI data. Graph metrics–clustering coefficient and characteristic path length—were used to measure and characterize global functional organization in the brain. The main finding of our study is that functional brain networks in AD consistently showed lower clustering but similar characteristic path lengths compared to controls, which suggests disrupted global functional organization in AD. Our findings also suggest that small-world network characteristics might be useful as an imaging biomarker for AD.
The characteristic path lengths were low (λ~1) and showed no significant differences between the AD group and the control group, suggesting short distances between distinct brain regions in both groups. This finding suggests an organization consisting of multiple short alternative paths between nodes in functional brain networks in both groups.
The most interesting finding of our study was the lower levels of clustering observed in the AD group. Clustering coefficient is a measure of local efficiency or the fault-tolerance of a network 
. The difference in clustering coefficients in the AD group as compared to the control group was observed at a correlation threshold at or near a subject's average correlation (to ensure an equivalent number of edges across subjects), and the clustering coefficient was significantly lower in the AD group, suggesting loss of local efficiency in AD. Similarly, values for σ, a measure of small-worldness, were significantly lower in the AD group compared to the control group, suggesting loss of small-world properties in AD.
Analysis of global efficiency in functional brain networks showed that the networks exhibit small-world properties indicated by smaller Eglobal values compared to random networks, but this measure was not significantly different. This finding parallels results obtained with measures of characteristic path length.
Regional analysis of differences in clustering coefficients as a function of correlation thresholds showed that the left and the right hippocampal regions differed significantly between groups. In contrast, the clustering coefficient of the precentral gyrus did not differ between groups. This suggests disrupted connectivity from the hippocampus to other regions of the brain in AD. This finding is consistent with our previous study 
showing that AD reduced functional connectivity of the hippocampus within a specific network of regions—the default mode network 
that includes the posterior cingulate and lateral temporoparietal cortices. It is also consistent with the study by Wang et al. 
showing altered hippocampal connectivity to several neocortical regions in the early stages of AD. Other studies have reported decreased intrahippocampal synchrony of low frequency BOLD fluctuations 
during a task-free scan. Taken together, these findings point to significantly altered local and global hippocampal network connectivity in AD.
Analysis of the group differences in the regional connectivity across several broadly defined anatomical regions demonstrate that AD patients not only showed decreased intratemporal, temporo-thalamus, temporo-corpus striatum, thalamo-occipital and thalamo-frontal connectivity but, surprisingly, also showed increased intrafrontal, frontal-prefrontal, and fronto-corpus striatum connectivity. These findings are in line with the recent study by Wang et al. 
which not only reported decreased connectivity between a number of regions, but also increased prefrontal connectivity in AD. As suggested by fMRI studies showing increased prefrontal activation in AD during task performance 
, these findings suggest that patients with AD may rely on increased prefrontal connectivity to compensate for reduced temporal connectivity. An intriguing (and testable) hypothesis is that the ability to make such compensatory changes in frontal lobe connectivity may account in part for the “cognitive reserve” phenomenon 
that allows some patients to perform better than others despite equivalent pathological burdens.
Small-world characterization is well-suited for analyzing anatomical and functional brain networks at the system level because these networks are complex and optimally connected to minimize information processing costs 
. Anatomical connectivity networks of the brain obtained from tracer studies in the primate cortical visual system 
, primate cerebral cortex 
, and macaque cortex 
have been shown to exhibit small-world characteristics. Functional connectivity networks of human brain constructed from EEG as well as MEG data have also been shown to have small-world architecture 
. Salvador et al. 
built a whole-brain functional connectivity network from task-free human functional MRI data. This network of intrinsic, task-free functional interactions between 90 cortical regions was also shown to have small-world properties–high clustering coefficient and low characteristic path length. The small-world architecture was confirmed by Achard et al., who also reported that the small-world properties were salient in the frequency interval 0.03 to 0.06 Hz 
. These findings suggest that the structural and functional organization of the brain has a small-world architecture; these characteristics may assist in robust and dynamic information processing. Recently, Stam et al 
. reported that the architecture of whole-brain functional networks derived using scalp EEG is disrupted in AD. They observed that a 21-node network constructed using EEG data collected from subjects with AD showed loss of small-world properties characterized by longer characteristic path length with relative sparing of the local clustering.
provides a comparison of results obtained from our study to all of the above-mentioned results on the small-world characterization of functional brain networks. Our results are largely comparable to small-world metrics reported by Salvador et al. also using task-free fMRI in healthy human subjects 
. The small-world metrics reported by Stam et al. analyzing beta-band EEG in controls and AD subjects are also largely consistent with our results 
. It is interesting to note that whereas we report similar characteristic path lengths but different cluster coefficients between AD and controls, the EEG study found the converse (characteristic path lengths differed between AD subjects and controls but cluster coefficients did not). We believe that this discrepancy may be related to significant volume conduction in scalp EEG data 
which may reduce sensitivity to detect differences in short-range connectivity while enhancing the relative sensitivity to detect differences in long-range connectivity. Other methodological differences may also contribute–the use of synchronization likelihood as their association measure, which unlike wavelet correlation is sensitive to non-linear coupling. Also, the poor spatial resolution of scalp EEG limits the network to mainly cortical regions, unlike our fMRI study where the network comprised of cortical as well as sub-cortical regions, which is a relative strength of our study.
Table 2 Comparison of number of nodes in the graph (N), normalized characteristic path length (λ), normalized clustering coefficient (γ), and small-world measure (σ) from our study with previously published results on small-world characterization (more ...)
To address the extent to which clustering coefficients serve as a sensitive biomarker to distinguish AD from healthy aging, we examined γ values in the two subject groups. The clustering coefficient is a measure of efficiency in network connectivity. It distinguished AD subjects from controls with a sensitivity of 72% and specificity of 78%. These values approach the sensitivity and specificity reported for other imaging biomarkers 
and are close to the range considered clinically relevant by a recent Working Group on biomarkers in AD 
. With some improvements in the technique—decreasing the number of nodes in the network for example—the clustering coefficient may therefore prove to be an effective biomarker for AD, though prospective studies will be required to validate its effectiveness. In addition to its promise as a diagnostic aid, the clustering coefficient merits investigation as a functional marker of response to treatment.
This study has two main limitations. First, in evaluating its efficacy as a biomarker, it will be critical to assess this metric not only in AD and normal subjects, but in subjects with non-AD dementias and related conditions to ensure that these findings are specific to AD and not to dementia or other neurodegenerative disorders more generally. The second limitation pertains to the fact that most of the AD patients (14 of 21), and none of the controls, were taking an acetylcholinesterase inhibitor. Similarly, 12 of 21 AD patients, and none of the controls, were taking memantine, an NMDA-receptor antagonist. While we doubt that these differences in medication exposure could account for the differences in clustering coefficients in AD subjects we cannot exclude that possibility in the current study.
In conclusion, we have demonstrated that fMRI-derived functional brain networks in AD show loss of small-world properties. Our findings suggest that cognitive decline in AD is associated with disrupted global functional organization in the brain.