Altered Weibull degree distribution in resting‐state functional brain networks in Alzheimer’s disease

Background The topological organization of human brain networks can be mathematically characterized by the connectivity degree distribution of network nodes. However, there is no clear consensus on whether the topological structure of brain networks follows a power law or other probability distributions, and whether it is disrupted in Alzheimer’s disease(AD) and its prodromal stage, mild cognitive impairment(MCI). We investigated on the fitting of nodal degree distribution of the whole‐brain functional networks and 7 subnetworks in healthy controls(HC) and individuals with MCI and AD. Method We included 40 HCs, 34 MCI and 34 early‐stage AD subjects who were recruited from a memory clinic at the Peking University Sixth Hospital. Resting‐state fMRI scans underwent standard preprocessing and were spatially normalized to the standard space. For each subject, we built whole‐brain FC matrices by computing Pearson’s correlations among brain voxels, followed by a threshold process( r from 0.4 to 0.6). Seven pre‐defined subnetworks were obtained from previous studies, including visual, sensorimotor, dorsal attention, ventral attention, limbic, frontoparietal and default mode (DMN). For a given subnetwork, degree distributions were calculated within and between subnetworks, respectively. Maximum likelihood estimation was used to determine model parameters. The goodness of fit of each fitting was evaluated by bootstrapping and the Kolmogorov‐Smirnov test. Group differences in the estimated parameters were tested by ANCOVAs, controlled for age, gender and education. Result In the whole‐brain networks and all subnetworks, the connectivity degree distributions were fitted better by a Weibull distribution( f ( x )∼ x ^( β ‐1) e ^(‐ λx ^ β )) than power law or alternative models. Compared with the HC group, the MCI group showed lower Weibull β parameter (shape factor) in both the whole‐brain and subnetworks, especially in visual, somatomotor and DMN across all threshold( p s<0.05), some of which were distributed in within‐network(somatomotor), between‐networks(dorsal attention and limbic), or both(visual, ventral attention, frontoparietal and DMN). In the AD group, the β parameters were lower in the frontalparietal( p <0.05) and DMN( p <0.05, except for r =0.6) than those in the HC. Conclusion We show that the Weibull model fits human brain functional networks better than a power law model, and this network structure is disrupted in AD and MCI. Such a short‐tailed model may capture intrinsic network structure of the human brain in health and disease.