The ability to cognitive control of emotions is critical to behavioral flexibility and well-being (Ochsner et al., 2012; Marek et al., 2015). Although patterns of activation during cognitive control of emotions have been well-characterized, graph theory-based connectivity research has shown that the brain network composes of functionally separate subnetworks or modules (Buckner et al., 2009; Barret and Satpute, 2013; Sripada et al., 2014). Furthermore, functional connectome research has revealed that affective processing at least contains frontoparietal subnetwork (e.g., dorsolateral prefrontal cortex, inferior and superior parietal lobule), salience subnetwork (e.g., insula, middle, and posterior cingulate cortex), visual subnetwork (within the occipital lobe), and cerebellum (Wolf et al., 2009; Lindquist and Barrett, 2012; Oosterwijk et al., 2012). However, with the emergence of chronnectome (Calhoun et al., 2014), little is known about how affective information is dynamically represented through distributed large-scale brain networks.

During affective processing, cognitive control relies on not only short-distance intramodular processing but also long-distance intermodular communications (Mesulam, 1990; Wager et al., 2008; Barret and Satpute, 2013). As a matter of fact, whole-brain networks contain some important long-distance communications (e.g., long intra/inter-hemispheric connections) (Sepulcre et al., 2010; Hermundstad et al., 2013). In graph-theoretic research, hubs integrate and distribute information in powerful ways and are further classifies into provincial and connector hubs (Power et al., 2013; Van den Heuvel and Sporns, 2013). Different from provincial hubs that connect nodes within a module, connector hubs with high participant coefficients connect to multiple communities and have access to a variety of types of different information (Power et al., 2011). Particularly, the focal damage to a connector hub (e.g., a frontoparietal hub) caused large-scale long-distance functional deficits (Gratton et al., 2012). Therefore, focusing on the role of connector hubs is crucial for understanding of intermodular communication during cognitive control of affective pictures. However, static connectomics did not capture temporal structure of brain activity (Calhoun et al., 2014). Recently, more and more research has become interested in understanding network dynamics that support emotional or cognitive states (Fornito et al., 2012; Shine et al., 2016; Betzel et al., 2017), learning (Mantzaris et al., 2013), development (Gu et al., 2015), aging (Betzel et al., 2014), and disease progression (Raj et al., 2015). Time-vary features of functional network (e.g., connector hubs) are import for understanding how functional network dynamically evolute during information communication (Sizemore and Bassett, 2018), which further deepens our understanding the nature of temporal dynamics of brain activity (Vidaurre et al., 2018).

To obtain a sparse adjacent matrix in graph theoretic analysis, the traditional hard-thresholding approach eliminates weak and negative couplings between nodes because these negative links are often conceived as noise or minor (Rubinov and Sporns, 2010, 2011). However, not all negative connections are biologically meaningless (Chang and Glover, 2009; Fornito et al., 2013). For instance, during cognitive reappraisal of affective pictures, there exist strong anticorrelations between prefrontal cortex (PFC) (e.g., dorsomedial PFC or dorsolateral PFC) and salience/limbic areas (e.g., insula or amygdala) (Ochsner et al., 2002; Urry et al., 2006; Drabant et al., 2009). Undeniably, negative connections between modules are quite pervasive in functional network architectures and play an important role in behavior (Fox et al., 2005; De pisapia et al., 2012; Fornito et al., 2013), particularly in the task-evoked networks, although they were rarely mentioned. Simply removing these negative links lead to inaccurate representation of affective networks. The reservation of internetwork anti-correlations are critical for the precise representation of connector hubs in graph theoretical analysis because connector hubs are responsible for intermodular communication (Buckner et al., 2009; Van den Heuvel and Sporns, 2011). In contrast, the soft-thresholding approaches to mapping [−1,1] to [0, 1] not only avoid issues related to network fragmentation but also simply suppress rather than remove weaker connections (Schwarz and McGonigle, 2011). Here we aimed to use soft-thresholding approach to explore time-varying features of connector hubs in intermodular communication during affective information processing.

This study aimed to explore how connector networks dynamically evolute during cognitive control of affective processing. We collected fMRI data from 26 right-handed healthy undergraduates while they performed a cognitive task (silently counting backward) during the viewing of affective (positive, negative, and neutral) pictures. After preprocessing, time-series of 278 whole-brain parcels were extracted and subjected to a wavelet decomposition (Shen et al., 2013). Then, we estimated the dynamic correlation coefficients (DCCs) of all possible pairs of 278 parcels (Lindquist et al., 2014) and obtained 27 group-averaged DCC matrices. These DCC matrices were subsequently Fisher z-transformed and subjected to soft-thresholding. Next, we used the BCT toolbox¹ to calculate graph theoretic features of these full-connected matrices. Finally, we constructed and characterized connector networks for affective pictures across 9 time points. Based on the previous study of dynamic networks (Fornito et al., 2012; Shine et al., 2016; Betzel et al., 2017; Sizemore and Bassett, 2018; Vidaurre et al., 2018), we expected that connector networks would exhibit valence-dependent dynamic connectivity patterns over times; in order to coordinate the stability and the flexibility of connector networks during dynamic affective processing, we expected that the shared connector would keep robust connections and form the functional backbone correspondent with structural backbone (Hagmann et al., 2008; Liang et al., 2013; Zhang et al., 2015).

The current study used graph theory approach to explore how connector hubs dynamically evolute during cognitive control of affective pictures. We used soft-thresholding to reserve negative connections (Schwarz and McGonigle, 2011). Results revealed that connector networks consisted of cross-modular negative connectivities, which is impossible to be unveiled by hard-thresholding. This might be because we were the first time to use edge betweenness centrality to sparse connector networks, different from traditional hard-thresholding that just removes weak links (Rubinov and Sporns, 2010, 2011). Edge betweenness centrality is the fraction of all shortest paths in the network that contain a given edge and reflects an edge’ centrality of in a network but not link strength (Brandes, 2001). Thus, negative links between connector hubs is not noise or spurious connections but take an important role in intermodular long-distance communications. Overall, this study not only provides a novel method to sparse functional networks but also reveals that there exist negatively linking connector networks during intermodular integration of affective information.

Connector networks exhibited valence-related dynamic connectivity patterns over times, e.g., dynamic community affiliations and time-varying connections with other parts of whole-brain networks. These dynamic changes facilitate intermodular communications of affective information. However, connector networks did not exhibit small-worldness because of low cluster coefficient but high characteristic path length, regardless of picture valences. This implies that these connector networks contain less direct links but more indirect links. For example, the frontoparietal subnetwork does not receive direct afferents from the visual system, but executes top–down control indirectly via the ventral attention/salience network, which contains the anterior insula (Seeley et al., 2007; Vossel et al., 2012; Palaniyappan et al., 2013). This study requested participants to perform the silent-counting task while they viewed pictures on the screen. Participants needed to inhibit visually affective information when pictures appeared on the screen. Behavioral results indicated that the counting task significantly decreased arousal rating for positive and negative pictures but not neutral pictures compared with offline viewing. Consistent with behavioral findings, the frontoparietal system (e.g., superior frontal gyrus and superior parietal lobe) through negative connections dynamically top–down inhibited the neural activities from salience subnetwork (e.g., insula) and visual area (e.g., cuneus).

Affective picture processing also exhibited different nodal betweenness patterns in connector networks. The present study found that the left superior parietal lobe (BA7.4) in the frontoparietal system exhibited larger nodal betweenness for positive and neutral pictures, although connector networks contained less hubs in the neutral picture condition than in the positive picture condition. In contrast, connector networks of negative pictures included larger nodal betweenness in the superior medial frontal gyrus (BA10.6). These results were consistent with the frontoparietal control system consisting of flexible hubs that integrate information from the external environment (e.g., visual stimuli) with stored internal representations (e.g., silently counting) and regulate distributed systems (e.g., visual, salience) according to affective valences (Vincent et al., 2008; Woolgar et al., 2015). Moreover, the left insula (BA44.2) had larger nodal betweenness centrality in the salience system of all connector networks. This might be attributed to that the insula regulates the interaction between the salience of the selective attention created to achieve a task and the salience of emotional arousal and has an important role in the experience of emotions (Taylor et al., 2009; Quarto et al., 2016).

In particular, five cerebellar hubs participated in network processing of negative pictures while fewer cerebellar connector hubs for positive and neutral pictures. As being famous for sensorimotor control (Bastian, 2011), the human cerebellum has connections with other brain areas involved in affective regulation, including the insula, amygdala, hypothalamus, as well as the neocortex (Baumann and Mattingley, 2012). Patients with cerebellar diseases had significant higher depressive scores relative to healthy comparison groups (Wolf et al., 2009). Neuroimaging studies revealed that the cerebellum was involved in control processing of aversive stimuli and other basic emotions (Moulton et al., 2011). However, cerebellar hubs were ignored by several cortical parcellations (e.g., Power et al., 2011; Yeo et al., 2011; Gordon et al., 2014). Future studies should follow in interest the centrality of cerebellar hubs in whole-brain network processing of affective information.

The shared 11 connectors kept robust connections and formed the functional backbone. The functional backbone mainly consisted of connector hubs with high metabolic activity and might be constrained by cortical structural cores (Hagmann et al., 2008). Different from structural connections, functional connectivities reflect statistical dependence between nodes and thus functional hubs have unnecessarily direct structural connection with other hubs (Sporns, 2014). Under the disturbing of active tasks, metabolic energy is necessarily redistributed more to task-specific hubs to complete tasks (Liang et al., 2013; Zhang et al., 2015). The present functional backbone exhibited different connectivity patterns among positive, negative, and neutral pictures, which reconfigured during cognitive control of differently-valenced affective processing.

From a perspective of temporal dynamics, the existence of the functional backbone helps not only maintain network integrity (or task set) across full trials but also flexibly integrate different types of information from different modules during cognitive processing. Therefore, the functional backbone plays a critical role in coordinating both the stability and the flexibility of cognitive control networks during dynamic processing of affective information. In particular, the connector lesions influence processing in multiple systems and produces impairment across several cognitive domains (Gratton et al., 2012). Therefore, the functional backbone concept has important implications for the understanding the relationship between disruption of whole-brain network architecture and functional deficits in neurological or psychiatric disorders. Future work will need to further examine the importance of functional backbone of connector networks in clinical research with other experimental paradigms.

The limitations in this study must be mentioned as follows. First, the sample size is small and future studies should use larger sample to confirm the results. Second, dynamic networks are a very active and fast field. Recently, some novel approaches on temporal dynamic of brain networks have been put forward (Sizemore and Bassett, 2018; Vidaurre et al., 2018). Future studies should use these new approaches to further investigate how connector networks dynamically evolute and verify the importance of the functional backbone. Third, since the hard- and soft-thresholding have different ideas about how to deal with weak and negative connections, future studies might use the simulating methods to completely compare the soft-thresholding approach with the traditional approach so as to further clarify their appropriateness.

In the summary, the present findings lay stress on the necessity of conserving negative connections between multiple modules in chronnectome research, and provide evidence for the existence of functional backbone during dynamic evolution of the connector networks. These results deepen the understanding of the relationship between structural and functional connectivity during dynamic processing of affective information.

The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the Ethical Committee of School of Psychology at East China Normal University.

QL, GR, and WZ designed and performed the study and analyzed the data. WZ wrote the manuscript. FT, HL, GR, and JC reviewed and modified the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.