Conceived and designed the experiments: KS VM MG. Performed the experiments: KS. Analyzed the data: KS. Contributed reagents/materials/analysis tools: KS MM. Wrote the paper: KS MG. Edited the paper: DR.
The authors have declared that no competing interests exist.
Functional brain networks detected in task-free (“resting-state”) functional magnetic resonance imaging (fMRI) have a small-world architecture that reflects a robust functional organization of the brain. Here, we examined whether this functional organization is disrupted in Alzheimer's disease (AD). Task-free fMRI data from 21 AD subjects and 18 age-matched controls were obtained. Wavelet analysis was applied to the fMRI data to compute frequency-dependent correlation matrices. Correlation matrices were thresholded to create 90-node undirected-graphs of functional brain networks. Small-world metrics (characteristic path length and clustering coefficient) were computed using graph analytical methods. In the low frequency interval 0.01 to 0.05 Hz, functional brain networks in controls showed small-world organization of brain activity, characterized by a high clustering coefficient and a low characteristic path length. In contrast, functional brain networks in AD showed loss of small-world properties, characterized by a significantly lower clustering coefficient (p<0.01), indicative of disrupted local connectivity. Clustering coefficients for the left and right hippocampus were significantly lower (p<0.01) in the AD group compared to the control group. Furthermore, the clustering coefficient distinguished AD participants from the controls with a sensitivity of 72% and specificity of 78%. Our study provides new evidence that there is disrupted organization of functional brain networks in AD. Small-world metrics can characterize the functional organization of the brain in AD, and our findings further suggest that these network measures may be useful as an imaging-based biomarker to distinguish AD from healthy aging.
Alzheimer's disease (AD) is a brain disorder characterized by progressive impairment of episodic memory and other cognitive domains resulting in dementia and, ultimately, death. Functional neuroimaging studies have identified brain regions that show abnormal brain function in AD. Although there is converging evidence about the identity of these regions, it is not clear how this abnormality affects the functional organization of the whole brain. In order to characterize the functional organization of the brain, our approach uses small-world measures, which have also been used to study systems such as social networks and the internet. We use graph analytical methods to compute these measures of functional connectivity brain networks, which are derived from fMRI data obtained from healthy elderly controls and AD patients. The AD patients had significantly lower regional connectivity, and showed disrupted global functional organization, when compared to healthy controls. Moreover, our results indicate that cognitive decline in Alzheimer's disease patients is associated with disrupted functional connectivity in the entire brain. Our findings further suggest that small-world measures may be useful as an imaging-based biomarker to distinguish AD from healthy aging.
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
Functional connectivity is defined as temporal correlations between spatially distinct brain regions
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
Graph metrics–the
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
Demographic data is shown in
AD (n = 21) | Controls (n = 18) | |
Age | 63.97 (range: 48 to 83) | 62.84 (range: 37 to 77) |
Sex | 10 males, 11 females | 10 males, 8 females |
Years of Education | 15.89 (range: 12 to 22) | 16.53 (range: 12 to 21) |
MMSE | 22.14* (range: 12 to 29) | 29* (range: 27 to 30) |
MMSE scores are significantly different in AD patients compared with control subjects (*denotes significant differences between groups).
We first examined graph metrics obtained for the functional brain networks constructed by thresholding (threshold values ranged from 0.01 to 0.99 with an increment of 0.01) the wavelet correlation matrix computed at three scales (frequencies in the range from 0.01 to 0.25 Hz) for the AD group and the control group (see
(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<R<0.7), (B) The mean characteristic path length (λ) is low (1<λ<1.27) and shows similar trends at all the scales (C) The clustering coefficient (γ) for both groups is highest at Scale 3. (D) Due to higher mean γ values, the small-world measure σ (γ/λ) is highest at Scale 3 for both groups. The small-world property (σ>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.
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
Error bars represent values two standard deviations from the mean. (A) Mean λ (L/Lran) values for the AD group and the control group. No significant differences in the mean λ values are observed. (B) Mean γ (C/Cran) values for the AD group and the control group. γ values in AD group were significantly lower (indicated by *) than that in the control group (p<0.01). (C) Mean σ (γ/λ) values for the AD group and the control group. σ values in AD group were significantly lower (indicated by *) than that in the control group (p<0.01).
We examined global efficiency (Eglobal) values obtained for the functional brain networks constructed by thresholding (threshold values ranged from 0.01 to 0.99 with an increment of 0.01) the wavelet correlation matrix computed at three scales (frequencies in the range from 0.01 to 0.25 Hz) for the AD group and the control group (see
(A) Global efficiency measure (Eglobal), 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). The mean Eglobal value is low (0.78<λ<1) and shows similar trends at all the scales. (B) For the frequency interval 0.01 to 005 Hz (green)–mean Eglobal values for the AD group and the control group for networks derived by thresholding the correlation matrices such that the network has K′ edges. No significant differences in the mean Eglobal values were observed. Error bars represent values two standard deviations from the mean.
In the frequency interval 0.01 to 0.05 Hz (scale 3), mean Eglobal values for the AD group and the control group for the networks derived by thresholding the correlation matrices such that the network has K′ ( = 40) edges are shown in
Here, we examined whether γ (normalized clustering coefficient) might prove sufficiently sensitive and specific to serve as a biomarker for AD. Using the cut-off value (γ = 1.57) that maximizes sensitivity and specificity, γ correctly classified 14 out of 18 controls and 15 of 21 AD subjects, yielding 72% sensitivity and 78% specificity respectively. A receiver operating characteristic curve for various cut-off values is shown in
Using a cut-off value of 1.57, γ correctly classified 14 out of 18 controls and 15 of 21 AD subjects yielding 72% sensitivity and 78% specificity. The Area under the curve was 0.754 (95% CI Area 0.602 to 0.906).
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<0.01) than in the control group, while for the left and the right precentral gyrus, no significant differences in the clustering coefficient values were observed at any correlation threshold.
To determine whether the differences observed in γ values reflect true differences and not artifacts of different average correlation values, we repeated our analysis by computing γ values as a function of the number of edges in the graph. Mean γ values of four anatomical regions of interest for the AD group and the control group for networks derived by thresholding the individual correlation matrices such that the network has K′ edges were computed and compared. Results were consistent with the initial analysis–significantly lower clustering coefficient values (p<0.01) in the left and right hippocampus in AD, and no significant differences in the left and right precentral gyrus.
We next examined regional correlation values (connectivity) in the two groups. Results show that compared to the control group, the AD group had decreased correlation values (1) within the temporal lobe, (2) between the temporal lobe and thalamus, (3) between the temporal lobe and corpus striatum, (4) between the thalamus and occipital lobe, and (5) between the thalamus and other parts of the frontal lobe, but increased correlations (1) within the prefrontal areas, (2) within other parts of frontal lobe, (3) between the prefrontal areas and other parts of the frontal lobe, and (4) between other parts of frontal lobe and the corpus striatum.
To determine if our findings were robust–reproducible across datasets–we repeated our entire analysis on a second resting-state fMRI dataset (rest2 scans) acquired from the same set of subjects. Results were consistent with previous analysis (performed on data from rest1 scan): (i) Functional brain connectivity and small-world metrics including the global efficiency were salient in the low frequency interval–0.01 to 0.05 Hz (Scale 3), (ii)No significant differences in the mean λ values were observed, (iii) Mean γ values in the AD group were significantly lower than in the control group (p<0.01), (iv) Mean σ values in the AD group were significantly lower than that in the control group (p<0.01), (v) No significant differences in the mean Eglobal values were observed, and (vi) significantly lower clustering coefficient values were found in the left and right hippocampus in AD, with no significant differences in the left and right precentral gyrus.
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
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
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.
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
Data | N | λ | γ | σ |
fMRI of healthy human subjects (Our study) | 90 | 1.05 | 1.74 | 1.66 |
fMRI of human subjects with AD (Our study) | 90 | 1.042 | 1.56 | 1.497 |
EEG of healthy human subjects (Stam 2006) | 21 | 1.07 | 1.58 | 1.476 |
EEG of human subjects with AD (Stam 2006) | 21 | 1.12 | 1.6 | 1.428 |
EEG of healthy human subjects (Micheloyannis 2006) | 28 | 1.0 | 2.0 | 2.0 |
MEG of healthy human subjects (Stam 2004) | 126 | 1.8 | 4.2 | 2.3 |
fMRI of healthy human subjects (Salvador 2005) | 90 | 1.09 | 2.08 | 1.91 |
fMRI of healthy human subjects (Achard 2006) | 90 | 1.09 | 2.37 | 2.18 |
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
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.
Twenty one subjects with AD and eighteen age-matched control subjects participated in this study after giving written, informed consent. For those AD patients who were unable to give informed consent, written, informed consent was obtained from their legal guardian. The study protocol was approved by the Stanford University Institutional Review Board. The AD subjects (10 males, 11 females) ranged in age from 48 to 83 (mean age 63.97) with 12 to 22 years of education (mean years of education 15.89). The subjects were recruited from memory disorder clinics in Stanford University and the University of California San Francisco (UCSF). All AD subjects met the NINDS-ADRDA criteria for probable AD
For the task-free scan, subjects were instructed to keep their eyes closed and try not to move. The scan lasted for 6 minutes (rest1 scan). All the subjects (except for one control subject and two AD subjects) also underwent another task-free scan that lasted for 6 minutes (rest2 scan) and was acquired immediately after the first task-free scan. Functional images were acquired on a 3-T General Electric Signa scanner using a standard whole-head coil. Twenty-eight axial slices (4 mm thick, 1mm skip) were acquired parallel to the plane connecting the anterior and posterior commissures and covering the whole brain using a T2* weighted gradient echo spiral in/out pulse sequence (TR = 2000 msec, TE = 30 msec, flip angle = 80° and 1 interleave)
Data (rest1 and rest2 scans) were preprocessed using statistical parametric mapping (SPM2) software (
The preprocessed task-free functional MRI datasets were parcellated into 90 regions using anatomical templates defined by Tzourio-Mazoyer et al.
Wavelet analysis was used to construct correlation matrices from the regional fMRI time series data. These matrices described frequency-dependent correlations, a measure of functional connectivity, between spatially-distinct brain regions. Correlation matrices were then thresholded to generate a whole-brain functional connectivity network.
Wavelets are mathematical functions that transform the input signal into different frequency components
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 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
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
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.
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)
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
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.
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.
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The authors would like to acknowledge Drs. Bruce Miller and Gary Glover for their assistance in recruiting the subjects and acquiring the fMRI data (respectively), Dr. Booil Jo and Shih-jui Lin for advice on statistical analysis, and Meghan Meyer for her insightful comments.