Intrinsic overlapping modular organization of human brain functional networks revealed by a multiobjective evolutionary algorithm

Functional network modules overlap and are linked to interindividual connectome differences during human brain development

The modular structure of functional connectomes in the human brain undergoes substantial reorganization during development. However, previous studies have implicitly assumed that each region participates in one single module, ignoring the potential spatial overlap between modules. How the overlapping functional modules develop and whether this development is related to gray and white matter features remain unknown. Using longitudinal multimodal structural, functional, and diffusion MRI data from 305 children (aged 6 to 14 years), we investigated the maturation of overlapping modules of functional networks and further revealed their structural associations. An edge-centric network model was used to identify the overlapping modules, and the nodal overlap in module affiliations was quantified using the entropy measure. We showed a regionally heterogeneous spatial topography of the overlapping extent of brain nodes in module affiliations in children, with higher entropy (i.e., more module involvement) in the ventral attention, somatomotor, and subcortical regions and lower entropy (i.e., less module involvement) in the visual and default-mode regions. The overlapping modules developed in a linear, spatially dissociable manner, with decreased entropy (i.e., decreased module involvement) in the dorsomedial prefrontal cortex, ventral prefrontal cortex, and putamen and increased entropy (i.e., increased module involvement) in the parietal lobules and lateral prefrontal cortex. The overlapping modular patterns captured individual brain maturity as characterized by chronological age and were predicted by integrating gray matter morphology and white matter microstructural properties. Our findings highlight the maturation of overlapping functional modules and their structural substrates, thereby advancing our understanding of the principles of connectome development.

Abnormal Dynamic Reconstruction of Overlapping Communities in Schizophrenia Patients

OBJECTIVE

This study aims to explore the changes in dynamic overlapping communities in the brains of schizophrenia (SZ) patients and further investigate the dynamic restructuring patterns of overlapping communities in SZ patients.

MATERIALS AND METHODS

A total of 43 SZ patients and 49 normal controls (NC) were selected for resting-state functional MRI (rs-fMRI) scans. Dynamic functional connectivity analysis was conducted separately on SZ patients and NC using rs-fMRI and Jackknife Correlation techniques to construct dynamic brain network models. Based on these models, a dynamic overlapping community detection method was utilized to explore the abnormal overlapping community structure in SZ patients using evaluation metrics such as the structural stability of overlapping communities, nodes' functional diversity, and activity level of overlapping communities.

RESULTS

The stability of communities in SZ patients showed a decreasing trend. The changes in the overlapping community structure of SZ patients may be related to a decrease in the diversity of overlapping node functions. Additionally, compared to the NC group, the activity level of overlapping communities of SZ patients was significantly reduced.

CONCLUSION

The structure or organization of the brain functional network in SZ patients is abnormal or disrupted, and the activity of the brain network in information processing and transmission is weakened in SZ patients.

A Hybrid Routing Pattern in Human Brain Structural Network Revealed By Evolutionary Computation

The human brain functional connectivity network (FCN) is constrained and shaped by the communication processes in the structural connectivity network (SCN). The underlying communication mechanism thus becomes a critical issue for understanding the formation and organization of the FCN. A number of communication models supported by different routing strategies have been proposed, with shortest path (SP), random diffusion (DIF), and spatial navigation (NAV) as the most typical, respectively requiring network global knowledge, local knowledge, and both for path seeking. Yet these models all assumed every brain region to use one routing strategy uniformly, ignoring convergent evidence that supports the regional heterogeneity in both terms of biological substrates and functional roles. In this regard, the current study developed a hybrid communication model that allowed each brain region to choose a routing strategy from SP, DIF, and NAV independently. A genetic algorithm was designed to uncover the underlying region-wise hybrid routing strategy (namely HYB). The HYB was found to outperform the three typical routing strategies in predicting FCN and facilitating robust communication. Analyses on HYB further revealed that brain regions in lower-order functional modules inclined to route signals using global knowledge, while those in higher-order functional modules preferred DIF that requires only local knowledge. Compared to regions that used global knowledge for routing, regions using DIF had denser structural connections, participated in more functional modules, but played a less dominant role within modules. Together, our findings further evidenced that hybrid routing underpins efficient SCN communication and locally heterogeneous structure-function coupling.

Evaluating functional brain organization in individuals and identifying contributions to network overlap

Individual differences in the spatial organization of resting state networks have received increased attention in recent years. Measures of individual-specific spatial organization of brain networks and overlapping network organization have been linked to important behavioral and clinical traits and are therefore potential biomarker targets for personalized psychiatry approaches. To better understand individual-specific spatial brain organization, this paper addressed three key goals. First, we determined whether it is possible to reliably estimate weighted (non-binarized) resting state network maps using data from only a single individual, while also maintaining maximum spatial correspondence across individuals. Second, we determined the degree of spatial overlap between distinct networks, using test-retest and twin data. Third, we systematically tested multiple hypotheses (spatial mixing, temporal switching, and coupling) as candidate explanations for why networks overlap spatially. To estimate weighted network organization, we adopt the Probabilistic Functional Modes (PROFUMO) algorithm, which implements a Bayesian framework with hemodynamic and connectivity priors to supplement optimization for spatial sparsity/independence. Our findings showed that replicable individual-specific estimates of weighted resting state networks can be derived using high quality fMRI data within individual subjects. Network organization estimates using only data from each individual subject closely resembled group-informed network estimates (which was not explicitly modeled in our individual-specific analyses), suggesting that cross-subject correspondence was largely maintained. Furthermore, our results confirmed the presence of spatial overlap in network organization, which was replicable across sessions within individuals and in monozygotic twin pairs. Intriguingly, our findings provide evidence that network overlap is indicative of linear additive coupling. These results suggest that regions of network overlap concurrently process information from all contributing networks, potentially pointing to the role of overlapping network organization in the integration of information across multiple brain systems.

Trade-offs among cost, integration, and segregation in the human connectome

The human brain structural network is thought to be shaped by the optimal trade-off between cost and efficiency. However, most studies on this problem have focused on only the trade-off between cost and global efficiency (i.e., integration) and have overlooked the efficiency of segregated processing (i.e., segregation), which is essential for specialized information processing. Direct evidence on how trade-offs among cost, integration, and segregation shape the human brain network remains lacking. Here, adopting local efficiency and modularity as segregation factors, we used a multiobjective evolutionary algorithm to investigate this problem. We defined three trade-off models, which represented trade-offs between cost and integration (Dual-factor model), and trade-offs among cost, integration, and segregation (local efficiency or modularity; Tri-factor model), respectively. Among these, synthetic networks with optimal trade-off among cost, integration, and modularity (Tri-factor model [Q]) showed the best performance. They had a high recovery rate of structural connections and optimal performance in most network features, especially in segregated processing capacity and network robustness. Morphospace of this trade-off model could further capture the variation of individual behavioral/demographic characteristics in a domain-specific manner. Overall, our results highlight the importance of modularity in the formation of the human brain structural network and provide new insights into the original cost-efficiency trade-off hypothesis.

The resting-state causal human connectome is characterized by hub connectivity of executive and attentional networks

We demonstrate a data-driven approach for calculating a "causal connectome" of directed connectivity from resting-state fMRI data using a greedy adjacency search and pairwise non-Gaussian edge orientations. We used this approach to construct n = 442 causal connectomes. These connectomes were very sparse in comparison to typical Pearson correlation-based graphs (roughly 2.25% edge density) yet were fully connected in nearly all cases. Prominent highly connected hubs of the causal connectome were situated in attentional (dorsal attention) and executive (frontoparietal and cingulo-opercular) networks. These hub networks had distinctly different connectivity profiles: attentional networks shared incoming connections with sensory regions and outgoing connections with higher cognitive networks, while executive networks primarily connected to other higher cognitive networks and had a high degree of bidirected connectivity. Virtual lesion analyses accentuated these findings, demonstrating that attentional and executive hub networks are points of critical vulnerability in the human causal connectome. These data highlight the central role of attention and executive control networks in the human cortical connectome and set the stage for future applications of data-driven causal connectivity analysis in psychiatry.

The overlapping modular organization of human brain functional networks across the adult lifespan

Previous studies have demonstrated that the brain functional modular organization, which is a fundamental feature of the human brain, would change along the adult lifespan. However, these studies assumed that each brain region belonged to a single functional module, although there has been convergent evidence supporting the existence of overlap among functional modules in the human brain. To reveal how age affects the overlapping functional modular organization, this study applied an overlapping module detection algorithm that requires no prior knowledge to the resting-state fMRI data of a healthy cohort (N = 570) aged from 18 to 88 years old. A series of measures were derived to delineate the characteristics of the overlapping modular structure and the set of overlapping nodes (brain regions participating in two or more modules) identified from each participant. Age-related regression analyses on these measures found linearly decreasing trends in the overlapping modularity and the modular similarity. The number of overlapping nodes was found increasing with age, but the increment was not even over the brain. In addition, across the adult lifespan and within each age group, the nodal overlapping probability consistently had positive correlations with both functional gradient and flexibility. Further, by correlation and mediation analyses, we showed that the influence of age on memory-related cognitive performance might be explained by the change in the overlapping functional modular organization. Together, our results revealed age-related decreased segregation from the brain functional overlapping modular organization perspective, which could provide new insight into the adult lifespan changes in brain function and the influence of such changes on cognitive performance.

Biomarkers Derived from Alterations in Overlapping Community Structure of Resting-state Brain Functional Networks for Detecting Alzheimer's Disease

Recent studies show that overlapping community structure is an important feature of the brain functional network. However, alterations in such overlapping community structure in Alzheimer's disease (AD) patients have not been examined yet. In this study, we investigate the overlapping community structure in AD by using resting-state functional magnetic resonance imaging (rs-fMRI) data. The collective sparse symmetric non-negative matrix factorization (cssNMF) is adopted to detect the overlapping community structure. Experimental results on 28 AD patients and 32 normal controls (NCs) from the ADNI2 dataset show that the two groups have remarkable differences in terms of the optimal number of communities, the hierarchy of communities detected at different scales, network functional segregation, and nodal functional diversity. In particular, the frontal-parietal and basal ganglia networks exhibit significant differences between the two groups. A machine learning framework proposed in this paper for AD detection achieved an accuracy of 76.7% when using the detected community strengths of the frontal-parietal and basal ganglia networks only as input features. These findings provide novel insights into the understanding of pathological changes in the brain functional network organization of AD and show the potential of the community structure-related features for AD detection.

Nodal Memberships to Communities of Functional Brain Networks Reveal Functional Flexibility and Individualized Connectome

Human brain network is organized as interconnected communities for supporting cognition and behavior. Despite studies on the nonoverlapping communities of brain network, overlapping community structure and its relationship to brain function remain largely unknown. With this consideration, we employed the Bayesian nonnegative matrix factorization to decompose the functional brain networks constructed from resting-state fMRI data into overlapping communities with interdigitated mapping to functional subnetworks. By examining the heterogeneous nodal membership to communities, we classified nodes into three classes: Most nodes in somatomotor and limbic subnetworks were affiliated with one dominant community and classified as unimodule nodes; most nodes in attention and frontoparietal subnetworks were affiliated with more than two communities and classified as multimodule nodes; and the remaining nodes affiliated with two communities were classified as bimodule nodes. This three-class paradigm was highly reproducible across sessions and subjects. Furthermore, the more likely a node was classified as multimodule node, the more flexible it will be engaged in multiple tasks. Finally, the FC feature vector associated with multimodule nodes could serve as connectome "fingerprinting" to gain high subject discriminability. Together, our findings offer new insights on the flexible spatial overlapping communities that related to task-based functional flexibility and individual connectome "fingerprinting."

Cost-efficiency trade-offs of the human brain network revealed by a multiobjective evolutionary algorithm

It is widely believed that the formation of brain network architecture is under the pressure of optimal trade-off between reducing wiring cost and promoting communication efficiency. However, the questions of whether this trade-off exists in empirical human brain structural networks and, if so, how it takes effect are still not well understood. Here, we employed a multiobjective evolutionary algorithm to directly and quantitatively explore the cost-efficiency trade-off in human brain structural networks. Using this algorithm, we generated a population of synthetic networks with optimal but diverse cost-efficiency trade-offs. It was found that these synthetic networks could not only reproduce a large portion of connections in the empirical brain structural networks but also embed a resembling small-world organization. Moreover, the synthetic and empirical brain networks were found similar in terms of the spatial arrangement of hub regions and the modular structure, which are two important topological features widely assumed to be outcomes of cost-efficiency trade-offs. The synthetic networks had high robustness against random attacks as the empirical brain networks did. Additionally, we also revealed some differences between the synthetic networks and the empirical brain networks, including lower segregated processing capacity and weaker robustness against targeted attacks in the synthetic networks. These findings provide direct and quantitative evidence that the structure of human brain networks is indeed largely influenced by optimal cost-efficiency trade-offs. We also suggest that some additional factors (e.g., segregated processing capacity) might jointly determine the network organization with cost and efficiency.

Understanding neural flexibility from a multifaceted definition

Flexibility is a hallmark of human intelligence. Emerging studies have proposed several flexibility measurements at the level of individual regions, to produce a brain map of neural flexibility. However, flexibility is usually inferred from separate components of brain activity (i.e., intrinsic/task-evoked), and different definitions are used. Moreover, recent studies have argued that neural processing may be more than a task-driven and intrinsic dichotomy. Therefore, the understanding to neural flexibility is still incomplete. To address this issue, we propose a multifaceted definition of neural flexibility according to three key features: broad cognitive engagement, distributed connectivity, and adaptive connectome dynamics. For these three features, we first review the advances in computational approaches, their functional relevance, and their potential pitfalls. We then suggest a set of metrics that can help us assign a flexibility rating to each region. Subsequently, we present an emergent probabilistic view for further understanding the functional operation of individual regions in the unified framework of intrinsic and task-driven states. Finally, we highlight several areas related to the multifaceted definition of neural flexibility for future research. This review not only strengthens our understanding of flexible human brain, but also suggests that the measure of neural flexibility could bridge the gap between understanding intrinsic and task-driven brain function dynamics.

The relationship between spatial configuration and functional connectivity of brain regions revisited

Previously we showed that network-based modelling of brain connectivity interacts strongly with the shape and exact location of brain regions, such that cross-subject variations in the spatial configuration of functional brain regions are being interpreted as changes in functional connectivity (Bijsterbosch et al., 2018). Here we show that these spatial effects on connectivity estimates actually occur as a result of spatial overlap between brain networks. This is shown to systematically bias connectivity estimates obtained from group spatial ICA followed by dual regression. We introduce an extended method that addresses the bias and achieves more accurate connectivity estimates.