Decreased Complexity in Alzheimer's Disease: Resting-State fMRI Evidence of Brain Entropy Mapping

Alzheimer's disease (AD) is a frequently observed, irreversible brain function disorder among elderly individuals. Resting-state functional magnetic resonance imaging (rs-fMRI) has been introduced as an alternative approach to assessing brain functional abnormalities in AD patients. However, alterations in the brain rs-fMRI signal complexities in mild cognitive impairment (MCI) and AD patients remain unclear. Here, we described the novel application of permutation entropy (PE) to investigate the abnormal complexity of rs-fMRI signals in MCI and AD patients. The rs-fMRI signals of 30 normal controls (NCs), 33 early MCI (EMCI), 32 late MCI (LMCI), and 29 AD patients were obtained from the Alzheimer's disease Neuroimaging Initiative (ADNI) database. After preprocessing, whole-brain entropy maps of the four groups were extracted and subjected to Gaussian smoothing. We performed a one-way analysis of variance (ANOVA) on the brain entropy maps of the four groups. The results after adjusting for age and sex differences together revealed that the patients with AD exhibited lower complexity than did the MCI and NC controls. We found five clusters that exhibited significant differences and were distributed primarily in the occipital, frontal, and temporal lobes. The average PE of the five clusters exhibited a decreasing trend from MCI to AD. The AD group exhibited the least complexity. Additionally, the average PE of the five clusters was significantly positively correlated with the Mini-Mental State Examination (MMSE) scores and significantly negatively correlated with Functional Assessment Questionnaire (FAQ) scores and global Clinical Dementia Rating (CDR) scores in the patient groups. Significant correlations were also found between the PE and regional homogeneity (ReHo) in the patient groups. These results indicated that declines in PE might be related to changes in regional functional homogeneity in AD. These findings suggested that complexity analyses using PE in rs-fMRI signals can provide important information about the fMRI characteristics of cognitive impairments in MCI and AD.

(F=0.436, P=0.728) among the four groups. At the regional levels, 5 clusters were found to exhibit significant differences in PE among the four groups, as illustrated in Figure S1. The complexity differences among the four groups were mainly observed in the frontal lobes.

ROI analysis
We obtained 5 ROIs for the next analysis as presented in Table S1. Specifically, as presented in Table S1, the following regions exhibited significant differences:the left fusiform gyrus(FFG.L),the left rectus gyrus (REC.L), the inferior Frontal Gyrus (ORBinf.L, ORBinf.R), the right middle frontal Gyrus(MFG.R). The results of one-way ANOVAs revealed significant effects of group in 5 brain regions that exhibited significantly decreased complexity in the AD group compared with the MCI groups and the NC group ( Figure S2).

Relationships between PE and clinical measurements
First, we performed correlation analyses of the MMSE scores with the mean PEs of the whole brain in the patient groups (EMCI+LMCI+AD) and found that no correlations. We also examined the correlations of the MMSE scores with the PEs of the 5 ROIs in the pooled patient groups (EMCI+LMCI+AD). The results were presented in Table S2. 4 ROIs exhibited positive correlations between the PEs and MMSE scores (r>0.189, P<0.076). A higher MMSE score indicates higher cognitive ability. There were no correlations of the FAQ scores with the mean PEs of the whole brain in patient groups. The PEs of 5 ROIs exhibited strong negative correlations with the FAQ scores (r<-0.236, P<0.026).A higher FAQ score indicates poorer functional performance. There were no correlations of the CDR scores with the mean PE of the whole brain in the patient groups. The PEs of 5 ROIs exhibited strong negative correlations with the CDR scores (r<-0.238, P<0.025). A higher CDR score indicates the presence of dementia. The correlation analyses were performed between the PE and the clinical measurements in the four groups (Table S3). Consistent significant correlations were found.

Relationships between PE and ReHo
We extracted the ReHos of 5 ROIs according to the peak MNI coordinates (Table  S1), and the sphere radius was 8 mm. We explored the relationship between PE and ReHo in the pooled groups (EMCI+LMCI+AD). The results were presented in Table  S4. 3 ROIs (FFG.L, ORBinf.L, and MFG.R) exhibited significant negative correlations between the PE and ReHo in the patient groups. The results illustrated that high regional spontaneous activities may be associated with a decrease in complexity.
Correlation analyses in the four groups (NC+EMCI+LMCI+AD) were also performed between the PE and ReHo (Table S5 ). Consistent significant correlations were found.

Relationships between PE and the gray matter volume, FDG-PET
We extracted the gray matter volumes of 5 ROIs according to the peak MNI coordinates, and the sphere radius was 8 mm. Then, we explored the relationships between the PEs and the gray matter volumes in the patient groups. The FFG.L(r=0.024, P=0.019) and MFG.R(r=0.270, P=0.008) exhibited a positive correlation between the PE and the gray matter volume in the patient groups (Table  S4). Correlation analyses in the four groups (NC+EMCI+LMCI+AD) were also performed between the PE and gray matter volume, and the MFG.R exhibited a significant positive correlation (r=0.185, P=0.041) between the PE and the gray matter volume (Table S5 ).
Finally, the FDG-PET data of the 5 ROIs from the same group of subjects were extracted. Pearson's correlation analyses of the PE and FDG-PET were performed and no correlations were found in the patient groups (Table S4) and in the four groups (Table S5). Figure S1. Surface-rendered images showed the differences between the control and patient groups after adjusting for age and sex. The regions showed exhibited different complexities among the four groups (threshold P<0.01, uncorrected). See Table S1 for a complete list of these regions.   Table S2. Results of the correlation analyses between the PE maps and the MMSE, FAQ, and CDR scores in the patient groups (EMCI+LMCI+AD).