Abstract
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 altered in Alzheimer's disease (AD). Here we employed resting-state functional MRI and graph theory approaches to investigate the fitting of degree distributions of the whole-brain functional networks and seven subnetworks in healthy subjects and individuals with amnestic mild cognitive impairment (aMCI), i.e., the prodromal stage of AD, and whether they are altered and correlated with cognitive performance in patients. Forty-one elderly cognitively healthy controls and 30 aMCI subjects were included. We constructed functional connectivity matrices among brain voxels and examined nodal degree distributions that were fitted by maximum likelihood estimation. In the whole-brain networks and all functional subnetworks, the connectivity degree distributions were fitted better by the Weibull distribution [f(x)~x(β−1)e(−λxβ)] than power law or power law with exponential cutoff. Compared with the healthy control group, the aMCI group showed lower Weibull β parameters (shape factor) in both the whole-brain networks and all seven subnetworks (false-discovery rate-corrected, p < 0.05). These decreases of the Weibull β parameters in the whole-brain networks and all subnetworks except for ventral attention were associated with reduced cognitive performance in individuals with aMCI. Thus, we provided a short-tailed model to capture intrinsic connectivity structure of the human brain functional networks in health and disease.
Highlights
Resting-state functional magnetic resonance imaging studies have suggested that the human brain can be considered an efficiently integrated network that is divided into several functionally linked subnetworks
For the fittings compared between Weibull and power law, in all networks, both the HC and the amnestic mild cognitive impairment (aMCI) groups, all of the averaged R ratios were positive and sufficiently larger than zero, indicating that the Weibull is better than the power law in human brain Resting-state functional magnetic resonance imaging (rsfMRI) networks
For the 48 times fitting compared between Weibull and power law with exponential cutoff, in all generated networks, 85.4% of the R-values were positive, suggesting that the Weibull is better than the power law with exponential cutoff
Summary
Resting-state functional magnetic resonance imaging (rsfMRI) studies have suggested that the human brain can be considered an efficiently integrated network that is divided into several functionally linked subnetworks. One view is that the degree distribution follows the heavy-tailed power law (Van Den Heuvel et al, 2008; Hanson et al, 2016; Forlim et al, 2019) based on the simple growth mechanisms, such as preferential attachment (Barabási and Albert, 1999) Another view is that the degree distribution can be better fitted by a short-tailed distribution such as power law with exponential cutoff (Bassett et al, 2006; Hayasaka and Laurienti, 2010; Cao et al, 2016) and Weibull distribution (Nakamura et al, 2009; Gupta and Rajapakse, 2018), considering the wiring-cost constrains (Bullmore and Sporns, 2012) in the human brain. These suggest that power law, power law with exponential cutoff ( called truncated power law), and Weibull distribution ( called stretched exponential) are the three most frequently reported models for fitting the degree distribution of human brain networks, but the findings are not conclusive
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