Background

Living a happy and meaningful life is a major topic in positive psychology, which have a great impact on individuals’ physical and mental health and help people flourish in their lives, in their communities, and in the world [1,2,3]. Researchers have proved that healthy people with higher levels of well-being tend to have better emotional states, better interpersonal relationships, and stronger senses of belonging to a group [2, 4, 5], thus they were less likely to suffer from mental illnesses [6]. Compared with other models of well-being mostly focusing on emotional (or subjective) aspect of well-being, Keyes [7, 8] developed the mental health continuum model composed of three well-being components: emotional (subjective) well-being, psychological well-being, and social well-being. Specifically, emotional well-being reflect the hedonic aspect of well-being that encompassed pleasure attainment, positive affective states, and high levels of life satisfaction [9]. Psychological well-being and social well-being together are considered as eudaimonic well-being, which refer to the actualization of individuals’ potential or true value and evaluation of one’s circumstance and functioning in society [10, 11]. Previous studies have shown that these three dimensions of well-being were moderately correlated with each other, and they were interrelated but distinct constructs [12,13,14].

Recently, neuroimaging studies have used different experimental approaches to enrich our understanding of both anatomical and functional substrates of different dimensions of well-being and showed a variety of association results [15]. For instance, a result from an electroencephalography study showed that the greater left than right superior frontal activation was associated with the higher levels of both hedonic and eudaimonic well-being [16]. MRI studies revealed many correlations between different dimensions of well-being and human brain structural metrics [e.g., the regional gray matter volume (rGMV) or regional gray matter density (rGMD)]. In more detail, social well-being was correlated with both rGMV in the left dorsolateral prefrontal cortex [17] and rGMD in the left orbitofrontal cortex [18], which were both involved in emotional regulation [19,20,21] and social-cognitive processes [22, 23]. Besides, several other studies reported the associations between emotional well-being and rGMV in the precuneus [24, 25], the rostral anterior cingulate [25, 26] and the left dorsolateral prefrontal cortex [26, 27]; as well as the correlation between psychological well-being and rGMV in the insula [27, 28]. Meanwhile, several resting-state fMRI studies also reported the links between (1) emotional well-being and human brain functional measurements [e.g., regional homogeneity (ReHo) and amplitude of low-frequency fluctuations (ALFF)] in the prefrontal cortex [28,29,http://volbrain.upv.es) [113]; (2) image intensity inhomogeneity correction; (3) tissue segmentation of cerebrospinal fluid (CSF), white matter (WM) and deep gray matter (GM); (4) generation of the GM-WM (white surface) and GM-CSF interface (pial surface); (5) spatial registration via matching of the cortical folding patterns across participants by recon-all in FreeSurfer and Gaussian spatial smoothing (FWHM = 6mm, Full Width at Half Maxima); (6) Finally, the 3D (dimensional) structure images were projected onto the fsaverage5 standard cortical surface with 10,242 vertices per hemisphere.

Quality control procedure

Quality control is very significant for solid data analysis. The CCS provided quality control procedures for both functional and structural images. For structural MRI in this study, the quality control procedure (QCP) was as follows: (1) brain extraction or skull strip**; (2) image tissue segmentation; (3) reconstruction of pial and white surface; and (4) head motion. We performed the visual inspection on all the original structural images and excluded participants with obvious structural brain abnormalities and significant motor artifacts during the scan. The CCS provides screenshots of the brain tissue segmentation as well as screenshots of pial and white surface reconstruction. We visually checked the screenshots, and participants with bad brain tissue segmentation and surface reconstruction were excluded from the subsequent analysis. All the participants passed the quality control. The final sample included 65 participants and their descriptive information and inter-variable correlations were shown in Table 1.

Morphological similarity network construction

In the study, we used a macro-scale brain network parcellation, which subdivided the entire cortical surface into 51 spatially connected parcels which were derived from a clustering approach on MRI images of 1000 subjects to identify networks of functionally coupled regions across the cerebral cortex [114], to construct human brain morphological network based on their distributions, and then we calculated mean cortical thickness of each parcel. We excluded the parcels whose vertex number was less than 50, and finally got 32 parcels reserved for final group analysis: expanding across all the Yeo-7 networks: visual network, somatomotor network, dorsal attention network, ventral attention network, limbic network, frontoparietal (control) network, and default mode network (see Table 2).

Table 2 The vertex number of reserved 32 brain regions
Full size table

As in our previous study [47], we estimated distribution similarity of cortical thickness for each pair of parcels to construct human brain morphological similarity network. Firstly, for each pair of parcels, we segmented both of their cortical thickness into 30 bins. Secondly, we calculated the vertex frequency for each bin of the two parcels, and then we got the frequency distribution histogram for each parcel. Finally, we computed the Pearson’s correlation to estimate the similarity of cortical thickness distribution, and then we obtained a 32 × 32 morphological correlation matrix for each participant. There were both positive and negative connections between different brain regions which respectively demonstrated co-varying and anti-correlated distribution curves, and the negative connections only occupied a tiny proportion of the entire connection matrix. Therefore, in the study, we considered the absolute values of connections to computing network topological measurements considering the little effects of negative connections on the whole brain network topology. Then, we used orthogonal minimal spanning trees (OMST) analysis, which was a threshold-free method to derive the strongest connections of a network and reserve important information about brain network organization [115], to get an undirected weighted graph, and then the topological measurements could be computed based on the binary (unweighted) correlation matrix.

Topological measurements

We computed network efficiency including global efficiency (Eglob), nodal efficiency (Enodal) and local efficiency (Elocal) as well as network centrality including degree centrality (DC), betweenness centrality (BC), eigenvector centrality (EC) and pagerank centrality (PC) based on the binary (unweighted) correlation matrix using the Brain Connectivity Toolbox (http://www.brain-connectivity-toolbox.net) [48] and the CCS scripts [108].

Network efficiency

Global efficiency for network G is defined as:

$${E}_{glob}\left(G\right)=\frac{1}{N(N-1)}\sum_{i,j,i\ne j\in G}\frac{1}{{L}_{ij}}$$
(1)

where N is the number of nodes and Lij is the shortest path length between node i and node j in graph G [52]. Global efficiency is a global measurement of the parallel ability of information transfer within the whole network.

Nodal efficiency of node i is defined as:

$${E}_{nodal}(i)=\frac{1}{N-1}\sum_{j,i\ne j\in G}\frac{1}{{L}_{ij}}$$
(2)

where N and Lij are the same as that in Eq. (1), respectively representing the number of nodes and the shortest path length between node i and node j in graph G. Nodal efficiency measures the ability of the node for information transfer within the whole network and is also a global measurement.

Local efficiency of node i is defined as:

$${E}_{local}(i)={E}_{glob}\left({G}_{i}\right)$$
(3)

where Gi is a subgraph and is composed of the nodes that connect to node i (not including node i) directly and interconnected edges. Local efficiency indicates how well the information is exchanged in the given brain region and hence is a local measurement.

Network centrality

Degree centrality of node i is defined as:

$$DC\left(i\right)=\sum_{j\in N}{a}_{ij}$$
(4)

where N is the set of all nodes in the network, and aij is the connection status between i and j: aij = 1 when i and j were connected and aij = 0 when i and j weren’t connected. DC identifies the nodes with the most connected links and is the most common quantifiable local centrality measure [48, 49, 116].

Betweenness centrality of node i is defined as:

$$BC\left(i\right)=\sum_{k,j\in N, k\ne j,k\ne i,i\ne j}\frac{{L}_{kj}(i)}{{L}_{kj}}$$
(5)

where Lkj is the number of shortest paths between node k and node j, and Lkj(i) is the number of shortest paths between k and j that pass through node i. BC represents the fraction of all shortest paths in the network that pass through a given node. High BC indicated the nodes were important in connecting disparate parts of the network [48, 117] and were global measuremens.

Eigenvector centrality of node i is defined as:

$$EC\left( i \right) = \mu_1 \left( i \right) = \frac{1}{\lambda_1 }\mathop \sum \limits_{j = 1}^N a_{ij} \mu_1 (j)$$
(6)

where \({\mu }_{j}\left(i\right)\) is the i-th component of the j-th eigenvector of the adjacency matrix aij, and \({\lambda }_{1}\) is the corresponding j-th eigenvalue. N is the set of all nodes in the network, and aij is the connection matrix. EC considers the nodes connecting to other high degree nodes as highly central and indicates a central and important role of the node in the network [118, 119].

Pagerank centrality of node i is defined as:

$$PC\left( i \right) = r\left( i \right) = 1 - d + d\mathop \sum \limits_{j = 1}^N \frac{{a_{ij} r(j)}}{DC(j)}.$$
(7)

Pagerank centrality was introduced originally by Google to rank web pages. In graph theory, PC represents the importance of nodes assuming that the importance of a node is the expected sum of the importance of all connected nodes and the direction of edges [120, 121]. The PC algorithm is a variant of EC, which introduces a small probability (1—d = 0.15, d is dam** factor) of random dam** to handle walking traps on a graph [122]. Both EC and PC are global centrality measurements.

Statistics

To investigate the associations between topological measurements (i.e., network efficiency Effi and centrality Cent) of human brain morphological similarity network and different dimensions of well-being, we applied general linear model that took age, sex, education, intracranial volume (ICV), mean cortical thickness (CT) as covariates. The detailed statistical model was shown in Eq. (8).

$$Well-being\,=\, {\alpha }_{1}\times age+{\alpha }_{2}\times sex+{\alpha }_{3}\times education+{\alpha }_{4}\times ICV+{\alpha }_{5}\times {CT}_{mean}+\beta \times Effi/Cent+\gamma$$
(8)

False discovery rate (FDR, q < 0.05) correction for 32 parcels was used to control type 1 error over multiple tests. And the General Linear Model statistical analysis and FDR correction were performed using MATLAB scripts in the study.