Abnormal dynamic functional connectivity in Alzheimer’s disease

Abstract Aims Alzheimer's disease (AD) is a progressive neurodegenerative disorder. Previous studies have demonstrated abnormalities in functional connectivity (FC) of AD under the assumption that FC is stationary during scanning. However, studies on the FC dynamics of AD, which may provide more insightful perspectives in understanding the neural mechanisms of AD, remain largely unknown. Methods Combining the sliding‐window approach and the k‐means algorithm, we identified three reoccurring dynamic FC states from resting‐state fMRI data of 26 AD and 26 healthy controls. The between‐group differences both in FC states and in regional temporal variability were calculated, followed by a correlation analysis of these differences with cognitive performances of AD patients. Results We identified three reoccurring FC states and found abnormal FC mainly in the frontal and temporal cortices. The temporal properties of FC states were changed in AD as characterized by decreased dwell time in State I and increased dwell time in State II. Besides, we found decreased regional temporal variability mainly in the somatomotor, temporal and parietal regions. Disrupted dynamic FC was significantly correlated with cognitive performances of AD patients. Conclusion Our findings suggest abnormal dynamic FC in AD patients, which provides novel insights for understanding the pathophysiological mechanisms of AD.

brain regions. 4 In relation to AD, abnormal FC has been found in functional hub regions, 5,6 neural circuits, 7,8 and the whole-brain level. 9,10 Despite these advances, previous studies mostly assumed that the FC was constant during MRI scanning, ignoring its dynamic nature. 11,12 Compared to stationary FC, dynamic FC allows investigating the R-fMRI time series on a much finer scale (eg, at specific time points or within predefined time windows), which provides two exclusive advantages. On one hand, dynamic FC facilitates the observation of details that are averaged out in stationary FC and may offer greater insight into the fundamental mechanisms of FC. On the other hand, dynamic FC enables the capture of spontaneously reoccurring FC patterns (ie, FC states), which is essential for understanding the temporal variability in the intrinsic organization of the brain. Based on these advantages, researchers have found that dynamic FC is a potential sensitive biomarker for neuropsychiatric disorders, such as schizophrenia, 13 autism, 14 and Parkinson's disease. 15 To our knowledge, only a few studies have examined the FC dynamics associated with AD. [16][17][18] Among these studies, Jones et al 17  To fill this gap, we first employed the sliding-window approach and the k-means algorithm to identify FC states that reoccur over time. Then, the FC patterns under each state and the temporal properties of the FC states were explored. Furthermore, we evaluated the temporal variability of regional FC along the entire time series.
Finally, the correlation analyses between the above indicators of FC dynamics and AD cognitive performances were performed.

| Participants
Twenty-six AD patients and twenty-six age-and sex-matched HCs with resting-state fMRI data from the Alzheimer's Disease

| Data acquisition and preprocessing
All participants were scanned on a 3.0 T Philips scanner. MRI acquisitions were performed according to the ADNI acquisition protocol. 19 R-fMRI was obtained using an echo-planar imaging (EPI) sequence and the following parameters: repetition time (TR) = 3000 ms, echo

| Construction of dynamic functional networks
Dynamic functional brain network construction was carried out using graph theoretical network analysis 21

| Detection of dynamic functional connectivity states
To assess the architecture and the frequency of reoccurring FC patterns, the k-means algorithm 26 was applied to group correlation matrices according to their L1 distances. First, a subsampling procedure was carried out to facilitate determining the optimal cluster number and the initial cluster centroids. Similar to EEG microstate analysis, 26 the subsampling procedure first chose the correlation matrices with locally maximal FC variance (ie, matrices whose L1norm was 1.5 standard deviation away from the L1-norm of the mean correlation matrix) for each participant. 12 Thus, 767 matrices of the 52 participants (14.3 ± 3.3 matrices per AD patient, 15.2 ± 3.5 matrices per HC) were obtained. Second, the k-means algorithm was used to group these 767 matrices into k clusters. To determine the optimal cluster number, we varied k from two to nine and repeated the k-means procedure 100 times for each k value. The validity of the clustering results was evaluated using the Silhouette score and the Calinski-Harabasz index. 27 The elbow criterion based on the Silhouette score and the peak value of the Calinski-Harabasz index both indicated three as the most appropriate cluster number (k = 3).
Finally, initiated by the three cluster centroids obtained from the 767 matrices, the k-means algorithm was further used to group the 6552 correlation matrices derived from all participants into three clusters (ie, dynamic FC states).
Based on the dynamic FC states identified from k-means clustering, we calculated a participant-specific FC matrix for each participant at each state. Specifically, each element in the matrix was the median of the corresponding elements in the participant's matrices belonging to one state. Then, the differences between AD and HC in the participant-specific FC matrices were evaluated for each state.
We also examined the between-group differences in the temporal properties of the dynamic FC states from three aspects, including the mean dwell time of each state (ie, the average number of windows that participants spent on one state), the mean number of state transitions (ie, the average number of transitions that occurred between any two states), and the distribution of transition frequency (ie, the fraction of state transitions with a specific source and target). 15

| Temporal variability of regional functional architecture
After investigating the differences in FC dynamics between the AD and HC groups from the perspective of dynamic FC states at the whole-brain level, we further investigated the between-group differences from the perspective of the temporal variability of FC in each brain region. Specifically, for each participant, we first measured the temporal stability of FC in brain region k by the average Pearson correlation coefficient between the k-th row of every two correlation matrices. Then, the temporal variability V k of region k can be described by one minus the temporal stability, 28 that is, where n = 126 is the total number of windows and F i,k ,F j,k is the Pearson correlation coefficient between the FC profiles of region k in the correlation matrices derived from the i-th and the j-th windows (i, j = 1, 2, …, n; i ≠ j; k = 1, 2, …, 625).

| Statistical analyses
comparison of nodal temporal variability (ie, V k ) was performed using the GLM with age and sex controlled (P < .05, FDR corrected).
Finally, to investigate whether FC dynamics were related to the clinical performance of AD, we set age and sex as controlled variables and computed the partial correlation coefficients between the clinical measures (ie, MMSE and NPI) and the following three indicators: (a) the median strength of FC with significant between-group differences at each state; (b) the three temporal properties of the dynamic FC states (ie, mean dwell time, mean transition number, and transition frequencies between states); and (c) the temporal variability of the regions that exhibited significant between-group differences.

| Validation analysis: Effect of head motion
Recent studies have suggested that head motion can produce a marked influence on R-fMRI. 29,30 To validate our results, we added bad time points as an additional regressor into the nuisance covariate regression model, with the threshold of bad time points set as the framewise displacement of head motion above 0.5 mm as well as one back and two forward neighbors. 31 Then, we reanalyzed our data to examine our main results.

| Identification of dynamic functional connectivity states
Using the k-means algorithm, we identified three reoccurring FC states and found that windows were more likely to be in States I and II but less likely to be in State III ( Figure 1A). Significant betweengroup differences were found in the FC of States I and II (P < .05, FDR corrected, Figure 1B,C). In State I, five edges exhibited significant between-group differences ( Figure 1B). Among them, the to have significant between-group differences, most of which were associated with the frontal cortex (eg, superior frontal cortex and middle frontal cortex), temporal cortex (eg, middle temporal cortex and hippocampus), insula, and amygdala ( Figure 1C).
Intriguingly, detailed examinations of the FC with significant between-group differences in States I and II found that their signs were consistently opposite between AD and HC ( Figure 2). This finding suggested that FC with significant between-group differences may be useful for distinguishing AD and HC. As a validation, we performed ROC analyses that classified AD and HC according to the median strength of the significantly different (either increased/decreased) FC in each state as input features. The area under the ROC curve (AUC) was above 0.95, suggesting that abnormalities in dynamic FC could serve as potential biomarkers for distinguishing AD from HC. Figure 3A shows that significant between-group differences were found in the mean dwell time of States I and II but not State III.

| Analyses of the temporal properties of dynamic functional connectivity states
Specifically, among the three states, AD had significantly longer  Figure 3B shows that AD had significantly more state transitions than HC (AD: 6.1 ± 0.89; HC: 3.7 ± 0.84, P = .010). The distribution of state transition frequencies is shown in Figure 3C. Visual inspection indicated that most of the transitions occurred between States I and II, and State I was associated with the largest fraction of transitions in both AD and HC.
However, it is worth noting that AD transitioned from/to State II more frequently than HC did.  Table S1).

| Validation results
We validated the reliability of our main findings with respect to the influence of head motion. After using regression to correct for head motion, three reoccurring dynamic FC states were extracted, and they resembled those found in the main analyses ( Figure S1).
Similarly, the ROC analyses based on FC with significant betweengroup differences achieved good performance (AUC ≥ 0.99). The between-group comparison of the mean dwell time of the three states also produced highly compatible results ( Figure S2). With respect to the regional temporal variability, 55 of the 57 regions that showed significant decreases in the main analyses had recovered in the validation analyses. In addition, the validation analyses found some additional regions with significantly decreased regional temporal variability, mainly in the SMN and frontal cortex ( Figure S3 and Table S2).

| Temporal properties of dynamic functional connectivity states
The finding that the most loosely connected baseline state had the highest occurrence was also reported by previous studies. 12,38 Since FC in the resting state was suggested to support information transfer between brain regions, 39,40 the high occurrence of the baseline shorter dwell time on the weakest state compared to HC. 16 Notably, a study that used a similar method found the opposite pattern. 18 This discrepancy could be attributed to the instability of the independent component analysis method, in which it is inherently difficulty to determine the number of independent components and distinguish the true signal from noise. 40 Additionally, we found that the median strength of the FC with significant between-group differences in the AD-abnormality state was significantly correlated with the NPI scores of AD patients. Specifically, the significantly increased FC had a positive correlation with the NPI, while the significantly decreased FC had a negative correlation with the NPI. Our findings were thus supportive of the suggestion that connectivity changes in dynamic FC states may be behaviorally relevant. 45 In addition, since the NPI score can reflect the severity of neuropsychiatric characteristics in AD, our findings also imply that the AD-abnormality state may be closely associated with aberrant motor behaviors and neuropsychiatric symptoms, such as apathy, disinhibition, and dysphoria in AD patients. The longer dwell time on the AD-abnormality state in AD suggested that it may cost them more energy to cope with neuropsychiatric symptoms. Taking the above findings together, we concluded that the AD-abnormality state might be a specific, core working state of AD.
Additionally, we also observed that the state transition number of AD was larger than that of HC, indicating that AD transitioned more frequently than HC did. Furthermore, the distribution of transition frequencies showed that AD was more likely to transition between the AD-abnormality state and the baseline state than HC.
We speculated that AD may not have enough energy to transition to the spiking state, which could be partially supported by a growing number of studies that have consistently reported hypometabolism in AD. [46][47][48]

| Regional temporal variability and its correlations with clinical scores
Although AD experienced more state transitions than HC, the regional temporal variability of AD was lower than that of HC, probably because the FC matrices derived from the AD group tended to have lower overall diversity due to a common disease, despite that they were clustered into different states.  51 and especially influences memory consolidation, 8 and the CN is involved in cognitive control and has also been reported to have hypoconnectivity during AD progression. 49 In addition, a significantly negative correlation was found between the NPI scores of the AD patients and the regional temporal variability F I G U R E 4 Brain regions showing significant differences in temporal variability between AD and HC (P < .05, FDR corrected) of the left inferior temporal cortex, right middle temporal cortex, left caudate lobe, and left superior frontal cortex. Thus, we suggest that regional temporal variability might be a potential biomarker to distinguish AD from HC.

| Limitations and further considerations
The present work has a few limitations that should be noted.
First, although our results suggested that the AD-abnormality state might be a core and specific state of AD, further confirmatory studies in larger datasets are needed. Second, since previous studies have found different levels of brain damage at different diagnostic stages of AD, 52 FC dynamics may also exhibit different characteristics as the disease progresses. As the initial goal was to investigate the FC dynamics in AD, the diagnostic stages were not considered in this article. A prominent future direction would be to investigate the change in FC dynamics during the progression of AD. Finally, we adopted the widely used sliding-window approach to extract FC dynamics in the current study. To avoid potential bias, future studies can consider using other extraction methods, such as the point-process method, 53 to analyze FC dynamics in AD.

ACK N OWLED G M ENTS
This work wass supported by the National Natural Science

CO N FLI C T O F I NTE R E S T
None of the authors has any conflicts of interest to disclosure.