Altered structural and functional brain network overall organization predict human intertemporal decision‐making

Abstract

Intertemporal decision‐making is naturally ubiquitous to us: individuals always make a decision with different consequences occurring at different moments. These choices are invariably involved in life‐changing outcomes regarding marriage, education, fertility, long‐term well‐being, and even public policy. Previous studies have clearly uncovered the neurobiological mechanism of the intertemporal decision in the schemes of regional location or sub‐network. However, it still remains unclear how to characterize intertemporal behavior with multimodal whole‐brain network metrics to date. Here, we combined diffusion tensor image and resting‐state functional connectivity MRI technology, in conjunction with graph‐theoretical analysis, to explore the link between topological properties of integrated structural and functional whole‐brain networks and intertemporal decision‐making. Graph‐theoretical analysis illustrated that the participants with steep discounting rates exhibited the decreased global topological organizations including small‐world and rich‐club regimes in both functional and structural connectivity networks, and reflected the dreadful local topological dynamics in the modularity of functional connectome. Furthermore, in the cross‐modalities configuration, the same relationship was predominantly observed for the coupling of structural–functional connectivity as well. Above topological metrics are commonly indicative of the communication pattern of simultaneous global and local parallel information processing, and it thus reshapes our accounts on intertemporal decision‐making from functional regional/sub‐network scheme to multimodal brain overall organization.

1. INTRODUCTION

Intertemporal decision‐making exists ubiquitously in our real life. Such choices require us to tradeoff between alternatives varying both in our expected consequences and time of delivery. In general, benefits available in the near future are prone to be chosen compared with even larger rewards in the far future. Such preferences for the immediate but short‐term outcomes consistently refer to delay discounting (Bickel, Odum, & Madden, 1999; Kable & Glimcher, 2010). Steep discounting behavior in intertemporal decision‐making frequently reflects substantial harmful trends, such as drug abuse (Alessi & Petry, 2003), alcohol addiction (Kirby & Petry, 2004), obesity (Weller, Cook, Avsar, & Cox, 2008), and nonresponse to climate change (Bickel, Quisenberry, Moody, & Wilson, 2015). To clarify the precise neurobiological underpinnings of intertemporal decision‐making, cumulative studies have utilized multi‐scale neuroimaging approaches to characterize the delay discounting, such as regions‐based task‐state functional magnetic resonance imaging (fMRI) (Kable & Glimcher, 2007; McClure, Laibson, Loewenstein, & Cohen, 2004), subnetwork‐based resting‐state function connectivity MRI (rs‐fcMRI) (Chen, Guo, & Feng, 2017; Li et al., 2013), and even subnetwork‐interaction scheme (Chen, Guo, & Feng, 2018). However, little concern to how the overall organization of the whole‐brain network, namely, a complex integrated system, accounts for this scenario.

To date, the bulk of available evidence has predominantly converged on the notion that delay discounting did not recruit in any isolated brain regions but a battery of subnetworks and the communication/synergism of them. With regard to subnetwork scheme in the task‐state fMRI studies, some reliable findings have manifested that the neuronal activation pattern of delay discounting can be reconsidered to divide into three distinct functional subnetworks: reward‐coding network (e.g., ventral striatum [VS], orbitofrontal cortex [OFC], and ventromedial prefrontal cortex [vmPFC]), top‐down control network (e.g., anterior‐lateral PFC [alPFC], dorsolateral prefrontal cortex [dlPFC]), and prospection network (e.g., bilateral hippocampus [Hip], amygdala [Amy]), which underlay the key subprocesses of intertemporal decision‐making respectively (Peters & Büchel, 2011). More specifically, the reward‐coding network mainly engages in the encoding of the subjective value of the reward, whereas these elicited signals would be controlled and regulated from the top‐down cognitive network (Kable & Glimcher, 2007; Peters & Büchel, 2011). Afterward, prospection network is taken into account for the representation of future outcomes when individuals make decisions in the context of time‐related rewards (Hassabis, Kumaran, Vann, & Maguire, 2007; Peters & Büchel, 2010). Furthermore, the findings derived from rs‐fcMRI studies substantiate this idea that delay discounting should be characterized with network‐based regimen instead regional dynamics, showing the predictive role of specific large‐scale functional subnetworks (i.e., default mode network and salience network) on one's temporal devaluing (Achard & Bullmore, 2007; Chen et al., 2017; Li et al., 2013). Also, existing studies have identified the neuroanatomical understructure of discounting behavior into a series of structural subnetworks (i.e., reward network [including striatal area and right ventromedial prefrontal cortex] and prospection network [including the hippocampus and parahippocampus gyrus] as well (Dombrovski et al., 2012; Yu, 2012). Taken together, increasing attention have been directed toward the subnetwork‐based framework to ascertain the local neuronal pattern of delay discounting, but little is known about how the global and local communication of whole‐brain network simultaneously work in the human intertemporal decision‐making.

Human brain serves as a highly complexly integrated network system in both structural and functional domains. Notably, several influential researches aiming at the brain network's in‐depth overall mechanisms increasingly advocate a notion that brain function is not solely attributable to the nature of isolated regions or plain connections (i.e., subnetworks) but rather emerges from the overall network organization of the brain as a whole, namely human connectome (Sporns, 2010; van den Heuvel, Kahn, Goñi, & Sporns, 2012; van den Heuvel, Stam, Boersma, & Pol, 2008). There is mounting evidence that connectome‐based analysis can yield a better comprehension on the nature of the cognitive‐biological mechanism of behaviors straightforward (Bullmore & Bassett, 2011; Sporns, 2011; Sporns, Tononi, & Kötter, 2005). Encouragingly, the graph‐theoretical analysis of complex network induces a potent mathematical tool to quantify a collection of comprehensive topological dynamics in such human functional and structural connectomes (Bullmore & Sporns, 2009; Iturria‐Medina et al., 2007; Tononi, Sporns, & Edelman, 1994). On the basis of graph‐theoretical accounts, human whole‐brain networks (connectomes) can be mathematically described as a graph G = <V, E>, comprising of a set of nodes V (brain regions) and an array of edge E (connectivity). Hence, the analysis makes it possible to quantitatively describe brain's overall organization and communicative processes as a variety of physical topological properties (Bullmore & Bassett, 2011; Sporns, 2010; Van Den Heuvel & Pol, 2010). Due to the methodological advances in neuroscience, we can predictably shift from one's whole‐brain network dynamics to multiple graph‐theoretical metrics.

Specifically, the graph‐theoretical algorithms to combine topological metrics of brain connectomes in the small‐world organization, network efficiency, modularity dynamic, hierarchical structure, assortativity, the rich‐club regime, and leverage the estimation for cardinal nodal attributes in degree and betweenness centrality would be undertaken in this work. Ordinarily, the small‐world organization of network is synchronously characterized by the dramatically increased local cliquishness of connectivity between adjacent nodes and comparatively shorter path length between each pair of nodes than random/regular network, which has been proven to dominate one's high‐order cognitive function (Bassett & Bullmore, 2006; He, Chen, & Evans, 2007; Uehara et al., 2014). A considerable amount of unambiguous evidence manifested that this nontrivial property of brain connectomes dedicates to illuminate the underpinning of generating and integrating information from multiple sources in real time (Rubinov & Sporns, 2010). Notwithstanding this, the algorithm of this small‐world metric centers on the absolutely communicative pattern of information from various systems, thus neglecting the efficient behavior of the informative transmission in such small‐world networks (Latora & Marchiori, 2001). To this end, we further leverage the estimated network efficiency to provide a clearly quantitative gauge (i.e., global and local efficiency) for preventing this drawback in terms of information flow theory (Latora & Marchiori, 2001, 2003). Encouragingly, the high‐performance topological modularity was proven to entail an advantageous wiring‐cost premium, and can reap huge fruits in restraint of network cost as well (Bullmore & Sporns, 2012; Daianu, Jahanshad, Nir, Toga, Jack Jr, Weiner, Thompson,, & for the Alzheimer's Disease Neuroimaging Initiative, 2013; Newman, 2006). A barrel of systematic analyses concerning neuropsychiatric disorders have highlighted the vulnerability of the modularity of brain networks to pathological attack or abnormal behaviors (e.g., decision‐making, working memory, and leaning) (Arnemann et al., 2015; Meunier, Achard, Morcom, & Bullmore, 2009; Meunier, Lambiotte, Fornito, Ersche, & Bullmore, 2009). In this vein, we postulate that the individuals with promising topological modularity would be prone to make a better choice in intertemporal decision‐making resulting from the economic‐efficient pattern of brain structural and functional connectomes. In addition, we seek to estimate the topological hierarchy and assortativity as the measure to represent the synchronization dynamics and homogeneity of high‐degree nodes respectively. Highly hierarchical organization of brain connectomes reflect a biologically plausible regime in favor of the processing and assignment of information, whereas the strong assortativity between hub regions can predominately elevate robustness of brain networks (Barthélemy, Barrat, Pastor‐Satorras, & Vespignani, 2004; Bullmore & Sporns, 2009, 2012). Ultimately, given the remarkable productivity of the measure of high‐level topological metric, we further gauge the parameter of rich‐club dynamic. Brain organization with rich‐club regime produces the weights for high‐degree regions to be more intimately connected among themselves than regions with the comparatively lower degree, which is widely considered to integrate the parallel information among the diverse portions of whole‐brain connectivity network (Bullmore & Sporns, 2012; Collin, Scholtens, Kahn, Hillegers, & van den Heuvel, 2017; Grayson et al., 2014; Van Den Heuvel & Sporns, 2011). In this vein, there is also merit in exploring the association between the rich‐club regime of brain connectomes and one's cardinal intertemporal decision‐making in this work.

Taking into account the potential dedication of some hub regions on human decision, we further probe this issue of interests with specific respect to nodal metrics, namely, degree and betweenness centrality. The degree serves as the most original and vital measure to describe nodal characteristic for a graph. In human brain functional/structural connectome, it is defined as the number of connectivity which is directly connected with the regions (Bondy & Murty, 1976). Naturally, the high degree of the region predominantly exhibits its importance and backbone position in the network. Notwithstanding this, it is self‐evident that the degree fails to highlight which node own relative centrality in the network. Thus, the betweenness is examined in this work based on the fraction of shortest paths which alleviates the drawback found in other nodal measures, with the higher betweenness centrality for superior standing in this network (Borgatti & Everett, 2006; Freeman, Borgatti, & White, 1991).

Thus far, a robust body of studies have indicated that the widespread alterations of brain overall organization (e.g., small‐worldness, modularity, and rich‐club regime) rather specific disruption in subnetworks were more intimately associated with psychiatry and psychological behaviors, such as Alzheimer's disease (Lo et al., 2010), schizophrenia (Liu et al., 2008; Zalesky et al., 2011), major depression (Korgaonkar, Fornito, Williams, & Grieve, 2014; Sacchet, Prasad, Foland‐Ross, Thompson, & Gotlib, 2015), epilepsy (Ji et al., 2016; Li et al., 2016; Liao et al., 2012), attention‐deficit/hyperactivity disorder (Ahmadlou, Adeli, & Adeli, 2012), autism spectrum disorder (Peters et al., 2013), gambling (Tschernegg et al., 2013), and smoking (Zhang et al., 2017). Meanwhile, some neuropathologic dysfunctions were invariably attributed to the topological dynamics of hub regions as well, such as Alzheimer's disease (Daianu et al., 2015), first‐episode major depressive disorder (Zhang et al., 2011), obsessive–compulsive disorder (Shin et al., 2014) and http://www.neurology.org/content/81/2/134.short (Agosta et al., 2013). Consequently, we formally propose the hypotheses that intertemporal decision‐making, as a crucial neuropsychological phenomenon, could indeed be predicted by widespread alteration of brain network overall organizations. Specifically, the stochastic communicative pattern of small‐worldness would entail the steep delay discounting rates in both functional and structural whole‐brain connectomes, whereas the same scenario would be observed in the vulnerable rich‐club organization. What's more, we also conjecture that the rational choices in the intertemporal decision‐making would largely depend on stationary hierarchy, assortativity, and modularity of whole‐brain connectomes. Aside from the overall organization of brain connectomes, we also posit the presence of the association between the nodal topological metrics (i.e., degree and betweenness centrality) and intertemporal decision‐making.

In addition, topics in human brain connectomes have been strongly driven another quantitative brain network attribute that roots on exploring the efforts of the structural and functional connectivity coupling (SC–FC coupling) to one's behaviors (Passingham, Stephan, & Kötter, 2002). From a network‐based perspective, the functionality of brain regions is heavily determined by the physical pattern of them in the network (Hagmann et al., 2008; Koch, Norris, & Hund‐Georgiadis, 2002; Sporns, Honey, & Kötter, 2007). That is, the structural connectivity is not only highly predictable for brain morphology but also places constraints on functional interactions yield in the network, and thus it allows us to investigate the relationship between them (Sporns, 2013). Moreover, a compelling body of studies has also demonstrated the high spatial resemblances between these multi‐modalities within the whole‐brain network (Hagmann et al., 2008; Marder & Goaillard, 2006). Previously, disrupted coupling of whole‐brain structural and functional connectivity network is widely observed in psychiatric diseases and suboptimal behaviors, such as schizophrenia (Cocchi et al., 2014), bipolar disorder (Collin et al., 2017), cocaine abuse (Hu, Salmeron, Gu, Stein, & Yang, 2015), and internet addiction (Bi et al., 2015). Accordingly, we also harbor the idea that the communication of structural and functional connectomes can provide a more worthwhile predictor for human discounting behavior relative to either one.

In the current study, we first applied both automated anatomical labeling (AAL‐90, Tzourio‐Mazoyer et al., 2002) and 264‐region functional (Power‐264, Power et al., 2011) parcellation scheme to product functional and structural connectivity networks (matrices). Of note, a novel advance in multiscale parcellation approaches potently overcomes the potential shortcomings in the differences of connectome resolution (Bassett, Brown, Deshpande, Carlson, & Grafton, 2011; Cammoun et al., 2012). In addition, networks in AAL‐90 and Power‐264 parcellation schemes naturally shared common topological metrics as well (Power et al., 2011; Power, Schlaggar, Lessov‐Schlaggar, & Petersen, 2013). Then, the threshold‐band (Sparsity: 5%–40%, step‐to‐step width: 1%, a total of 36 cutoff points) was performed for shifting connectivity networks to adjacency matrices. Afterward, these processed matrices were characterized by a series of topological properties: clustering coefficient, C; characteristic shortest path length, L; normalized clustering coefficient, γ; normalized shortest path length, λ; small‐worldness, σ; local efficiency, E _loc; global efficiency, E _glob; rich‐club behavior, Φ; modularity, Q; hierarchy, β; and assortativity, r. Aside from network‐based topological metrics, these overarching nodal properties of brain connectomes were examined in the current study as well, namely, nodal degree (k) and betweenness centrality (be). As aforementioned, we further wonder whether the interactive communication between structural and functional connectomes was associated with one's complex high‐order cognitive decision (i.e., intertemporal choice). Thus, we then correlated functional connectivity networks into nonzero structural connectomes by using Pearson product–moment correlation for characterizing the degree of SC–FC coupling. Finally, a partial bivariate correlation model was conducted to explore how the topological dynamics (extended to SC–FC coupling) of the human whole‐brain network link to the intertemporal decision‐making. To further ensure the reproducibility of our findings, all the tests would be cross‐verified across two independent data sets.

2. MATERIALS AND METHODS

2.1. Participants

Two completely independent data sets were recruited for this study (a total of 119 participants): a principal data set (including 60 participants) and an independent replication data (including 59 participants). A total of 14 participants were excluded for further analyses after quality control due to excessive frame‐to‐frame displacement (FD > 0.2 mm; Power, Barnes, Snyder, Schlaggar, & Petersen, 2012, Power, Schlaggar, et al., 2013), and 105 participants were remained (principal data set: 53 participants, replication data set: 52 participants; for more details, please see below). Subsequently, the sample size was determined by detecting medium‐size effect (effect size d = 0.5, type I error α = 0.05, power 1 − β = 0.7) based on the G*Power calculation (http://www.softpedia.com/get/Science-CAD/G-Power), which could ensure the adequate power in our study and finally a minimum sample size of 49 participants was used for our current analysis (Faul, Erdfelder, Lang, & Buchner, 2007) (Supporting Information Method). The detailed demographic characteristics of both data sets have been summarized in Table 1. No significant difference in all behavioral measures between genders was found (Supporting Information Figure S1). There was no history of psychiatric or neurological illness in these participants, which was confirmed by the standardized psychiatric clinical assessment; all the participants were paid for participation with actual money as what they chose in one trial in the experimental task. The experimental protocol has been approved by the Institutional Review Board (IRB) of the Southwest University.

Table 1.

Participants' demographic information for the current study

			Principal data set				Replication data set
											p
			Male		Female		Male		Female
Numbers			29		24		27		25		–
Age			19.89 (1.73)		20.25 (1.70)		20.26 (1.93)		20.20 (1.21)		n.s
Education			15.21 (2.01)		14.89 (1.44)		13.86 (0.76)		13.83 (1.86)		n.s
Trait anxiety			54.14 (10.4)		55.33 (10.7)		52.85 (9.81)		53.94 (9.09)		n.s
Personality
Conscientious.			42.20 (6.41)		42.32 (4.93)		41.13 (6.74)		44.01 (6.39)		n.s
Extraversion.			40.71 (5.34)		37.98 (6.59)		41.61 (6.20)		39.97 (5.11)		n.s
Neuroticism.			34.56 (8.40)		38.14 (8.68)		34.31 (7.65)		34.93 (9.11)		n.s
Agreeableness.			40.13 (5.12)		40.53 (5.47)		41.01 (6.14)		39.68 (6.53)		n.s
Openness.			41.26 (5.77)		40.17 (5.42)		40.66 (5.83)		40.12 (6.26)		n.s

Participants' demographic for the current study. Measurements: Age and education (years); trait anxiety (assessed by trait anxiety inventory, TAI; Spielberger, Sharama, & Singh, 1973) and personality (scores) (assessed by NEO personality inventory, NEO‐PI; Costa & McCrae, 1992). The “n.s” indicated the no significant difference between two samples under the nonparametric permutation test (n = 10,000) (all the corresponding p values are largely greater than.05).

2.2. Monetary intertemporal decision‐making task

In the current study, we performed the classical monetary intertemporal decision‐making task, which refers to a series of fictitious monetary choices between one fixed smaller‐but‐soon reward and another mutative larger‐but‐delayed reward (Kable & Glimcher, 2007). The immediate option was hardened as ¥ 20 (≈$3.15) for all the trials, as previously reported (Halfmann, Hedgcock, Kable, & Denburg, 2015; Miglin, Kable, Bowers, & Ashare, 2017). The larger‐but‐delayed option was generated with the combinations of five respective time (7, 15, 30, 60, and 120 days) and 10 add‐percentages (10, 20, 40, 80, 120, 160, 240, 320, 400, and 500%) of the immediate option (¥ 20), resulting in a total of 50 trials in one session. To make the choices more realistic, four sessions were contained in the entire task, yielding a total of 200 trials (Kim‐Spoon, McCullough, Bickel, Farley, & Longo, 2015; McColgan et al., 2015). All the participants would be informed to make choices between two alternatives as what they truly wanted without any time limitation (see Figure 1a for detailed experimental design).

Figure 1.

The systematic view for the procedures of monetary intertemporal decision‐making task (a) and the typical example for the remuneration procedures (b) and distributions of the amount of final monetary remuneration (c). Participants are instructed to make decisions in this task before scanning. Each trial started with a white fixation (duration: 1,000 ms) and subsequently present blank screen (duration: 2,000 ms). Next, the immediate and delayed choices were presented for fixed 4,000 ms, followed by another blank screen (duration: 2,000 ms). Then, during the choice, the symbol of triangle and tetragonum instructed participants on how to choose, without time limits. Triangle represents the alternative of immediate rewards while tetragonum indicated delayed ones. Finally, the decision in this trial was really feedback in a screen for 1,000 ms. in the feedback stage, if participant prefers immediate rewards, the triangle would turn to red; in contrast, the tetragonum would turn to red when participant choose delayed alternative. After the presentation of feedback, the next trial will start with the new fixation. Panel (b) shows a really complete remuneration procedure in the Subject 9 as the didactic example. The top presents records of all the actual responses in the task from subject 9. As the remuneration procedures specified before, this subject would receive ¥ 20 with cash immediately and further obtain ¥ 64 via Alipay account (i.e., a prevailing mode of electronic payment in CHINA) after 1 week when the Trial 3 is randomly selected (orange); if the Trial 17 was randomly extracted out, the Subject 9 would be paid with ¥ 40 (cash) immediately (fixed reward ¥ 20 + task reward ¥ 20) according to his real decision in this trial (blue). We have been informed of these remuneration procedures for each participant and double‐check whether they thoroughly understood these procedures prior to formal experiment in favor of the high ecological validity in this study. Panel (c) shows the distributions of the amount of actual monetary remunerations of all the participants. The top of the c indicates the distribution of remuneration in the principal sample (Brown), whilst the bottom of c illustrates the distribution in the replicated sample (cerulean). Panel (d) indicated the distributions of AUC for the principal and replicated sample, respectively [Color figure can be viewed at http://wileyonlinelibrary.com]

To ensure the higher ecological validity of this research, we instructed the special remuneration procedures for each participant in detail prior to the formal experiment. Specifically, participants would be paid with actual money derived from two parts: fixed reward and task‐related reward. In the first part, participants could receive the fixed reward (¥ 20 [≈$3.15]) with cash as remuneration immediately for their participation. In the second part, to duly motivate the real decisions in this task they would make, one of the trials from their real responses would be randomly picked out and participants would be paid with actual money according to the real decision in this trial, at the delay specified. That is, a total of ¥ 20 would be paid with cash for the participants who choose the immediate option in the trial that was randomly selected as the task‐related reward. Otherwise, the participant could receive the larger amount of actual money (that equate to the amount in the delayed option of this trial) as remuneration in this part after the delayed time had elapsed (see Figure 1b for details). Furthermore, the distributions of the amount of final monetary remuneration are examined to be normal in the principal (K–S z = 0.73, p = .66) and replicated sample (K–S z = 1.10, p = .18), partly acknowledging the ecological validity of our study (Figure 1c).

The degree of individuals' delay discounting in the intertemporal decision‐making was quantified by the area under the curve (AUC) in the current study. As widely suggested in prior researches, the AUC was considered to be a more valuable measure to the analysis of discounting behaviors relative to hyperbolic fitting parameter, which could overcome potential problems created by the lack of consensus in the mathematical form of the model‐based discounting function (e.g., the skew distribution of the estimates of the parameters, less powerful and flexible in theoretical discounting function and potential collinearity) (Dixon, Marley, & Jacobs, 2003; Madden, Begotka, Raiff, & Kastern, 2003). Furthermore, the AUC has been broadly adopted in numerous economics studies as well due to its reliable psychometric properties (Harrison & McKay, 2012; Jimura, Chushak, & Braver, 2013) (details can be seen in Supporting Information Method). In addition, we had conducted One‐sample Kolmogorov–Smirnov test to examine the distribution of AUCs. The results showed that no skewness was observed in both principal and replicated data sets (K–S z _{(Principal sample)} = 0.61, p = .85; K–S z _{(Replicated sample)} = 0.51, p = .96; Figure 1d).

2.3. fMRI data acquisition

Both data sets were acquired with a 3‐Tesla scanner (Siemens Magneton Trio TIM, Erlangen, Germany) in the Key Laboratory of Cognition and Personality, Southwest University. A circularly polarized head coil was used, with foam padding to restrict head motion. During the scans, subjects were instructed to keep their eyes close, relax their mind, not to sleep, and remain motionless as much as possible (see Supporting Information Method for more detailed information).

2.4. Head‐motion censoring

Given the potential confound of head‐motion on further analyses, all the images were corrected by the frame‐to‐frame head‐motion displacement (FD) strategy to rigorously control motion‐related effects. Specifically, we first calculated the FD value for every volume (time point) of each participant. The FD was broadly considered to be a robust measure for instantaneous head motion, and can be estimated as a scalar quantity for six‐dimensional rigid body parameters by an empirical equation, FD_i = | Δd_ix | + | Δd_ix | + | Δd_iz | + | Δd_iy | + | Δα_i | + | Δβ_i | + | Δγ_i |, where Δ_ix = d_{(i − 1)x ‐} d_ix and similarly for the other rigid body parameters ([d_iy, d_iz, α_i, β_i, γ_i]) (Power et al., 2012). Then, these frames (volumes), whose the FD value was greater than 0.2 mm (as well as 1 back and 2 forward neighbors of them) were excluded from the participant's time series in the analysis (Power, Schlaggar, et al., 2013; Supporting Information Method).

2.5. Brain network construction

2.5.1. Parcellation

As mentioned above, the graph‐theoretical analysis would illustrate the brain network as a collaborative graph model (G = <V, E>), where V indicated a set of defined nodes, and E represented a set of the pairs of these vertices (connectivity). Obviously, how to determine the nodes of the brain network was the paramount methodological issue in the present study. Thus, as indicated in the prior researches, we first utilized the automated anatomical labeling [AAL‐90] atlas to parcellate the whole brain into 90 noncerebellar anatomical regions with low resolution (Tzourio‐Mazoyer et al., 2002). Furthermore, given that the relatively large regions from anatomical AAL‐90 would distort or obscure the nature of the functional and structural network by mixing distinct signals (Craddock, James, Holtzheimer, Hu, & Mayberg, 2012; Fornito, Zalesky, & Bullmore, 2010), we also performed a high‐resolution parcellation scheme based on a large meta‐analysis of whole‐brain functional connectivity maps to define nodes for whole‐brain network construction (Power‐264; Power et al., 2011). A total of 264 putative functional regions were included in this parcellation strategy, which has been proven to be robust for brain network construction relative to voxel‐wise parcellation approach (Cole, Pathak, & Schneider, 2010; Gordon et al., 2014; Power, Barnes, Snyder, Schlaggar, & Petersen, 2013). To this end, both AAL‐90 and Power‐264 atlas were applied to parcellation for the node definition. The complete workflow of these analyses had been illustrated in Figure 2.

Figure 2.

The complete workflow. (a) Participants were instructed to the structural magnetic resonance imaging (sMRI) scan, and corresponding T1 images were automatically segmented to gray and white matter tissue and parcellation with two distinct resolution schemes (low resolution: AAL‐90 atlas; high resolution: Power‐264 atlas), determining the nodes of the brain structural network. Meanwhile, the fiber assignment by continuous tracking (FACT) deterministic tractography was performed to diffusion‐weighted for diffusion tension imaging (DTI) data, generating the white matter pathways to reconstruct the edge of this network. From these defined nodes with 90 or 264 regions and edges between a pair of vertices, i and j, the DTI‐based structural connectivity matrix (network) for each participant were constructed. (b) The same parcellation procedure was applied for resting‐state functional connectivity MRI (rs‐fcMRI) data for defining the nodes of a human functional brain network. The corresponding edge was determined to the functional connectivity (FC) between node i and j, and the correlation coefficient between their blood oxygenation level dependent (BOLD) time series was computed as their connectivity (edge), resulting in the functional connectivity matrix (network). (c) These well‐established structural connectivity matrices (top) and functional connectivity matrices (below) were thresholded to a set of adjacency matrices over a range of sparsity or k for the estimation of graph‐theoretical metrics: small‐worldness (efficiency, E; clustering coefficient, C; characteristic shortest path length, L; normalized clustering coefficient, γ; normalized shortest path length, λ), rich‐club regimen, modularity, hierarchy and assortativity organization as well as two nodal topological properties (degree and betweenness). (d) the coupling of structural and functional connectivity (SC‐FC coupling) was examined by correlating the nonzero structural connectivity vectors to functional counterparts, thus a total of n (the number of participants) coupling values were calculated. (e) In the group analysis, the correlation between the value of SC‐FC coupling and intertemporal choices (reflected by AUC) would be calculated across two samples (the principal data set and replicated data set) [Color figure can be viewed at http://wileyonlinelibrary.com]

2.5.2. Functional connectivity network construction

The preprocessing of functional neuroimaging was undertaken in the light of routine procedures (Crinion et al., 2007). We discarded the first 10 volumes from each participant to prevent magnetization disequilibrium. Then, we conducted slice‐time and head‐motion correction successively. Afterward, these realigned images were warped into the normalized Montreal Neurological Institute (MNI) echo‐planar imaging (EPI) template and resampled into 3 × 3 × 3 mm³ resolution, and were further smoothed with 8 mm FWHM Gaussian kernel. As indicated by previous studies (Auer, 2008; Ciric et al., 2017; Fox et al., 2005), to potently restrict the potential distortion due to the head motion and nonneuronal BOLD fluctuations, we hereby estimated the white matter (WM) signal, cerebrospinal fluid signal (CSF) signal, Friston 24‐parameters of head motion and mean frame‐to‐frame displacement (FD) as nuisance regressors of no interest for elimination. Finally, to further remove the physiological and artificial noises, the temporal band‐pass filter (0.01–0.08 Hz) and linear detrending were implemented as well. For functional brain network construction, the mean resting‐state fMRI time series across all voxels in the regions [nodes] was calculated as the representative time series for them. Then, we correlated time series between each pair of brain regions (nodes) and calculated the correlation coefficients to generate whole‐brain functional connectivity matrices (N × N, where N = 90 was the number of regions (nodes) in low‐resolution AAL‐90, and N = 264 for high‐resolution Power‐264; whose elements were e _ij) for each participant. To determine the available edges, sparsity thresholding process was applied to binarize these functional connectivity matrices to adjacency scheme (Achard & Bullmore, 2007; Rudie et al., 2013; Supekar, Menon, Rubin, Musen, & Greicius, 2008).

2.5.3. Structural connectivity network construction

First, the diffusion‐weighted images (DWI) of each participant were preprocessed to diffusion tensor images (DTI) data. Afterward, we performed whole‐brain deterministic fiber tracking with the Fiber Assignment by Continuous Tracking (FACT) algorithm in native diffusion space using the Pipeline for Analyzing brain Diffusion imAges (PANDA) Toolbox (https://www.nitrc.org/projects/panda; Cui, Zhong, Xu, Gong, & He, 2013). To construct the structural connectivity matrix, segmented regions would be defined as nodes in the native diffusion space (Gong et al., 2008). To this end, each participant's T1*‐weight MPRAGE images were coregistered to the native space of diffusion tensor images (b ₀ images) with the linear transformation (Collignon, Vandermeulen, Suetens, & Marchal, 1995; Woods et al., 1998). Then, the affine transformation was applied to map these coregistered images into MNI‐152 T1*‐template. These obtained parameters were transposed and conducted to warp the regions of AAL‐90/Power‐264 atlas from ICBM‐152 MNI space into the native diffusion tensor space. Above procedures had been widely adopted for preprocesses of DTI data in the graph‐theoretical analysis (Gong et al., 2008; Lo et al., 2010; Shu et al., 2011; Wen et al., 2011). In the native diffusion tensor space, the region (i) and another region (j) were connected by an edge (e _ij = [i, j]), in case of at least one fiber existed between them (Gong et al., 2008; Hagmann et al., 2008). A fiber was commonly considered as the connectivity of two regions if the endpoints of it terminated within both regions (Hagmann et al., 2008; Pierpaoli & Basser, 1996). Consequently, given the definition of the edges for structural connectivity network (matrix), the number of fibers (FN) connecting a pair of regions was calculated as an edge (e) for each participant.

2.6. Graph theoretical‐based network analysis

Graph‐theoretical analyses were performed to quantify the topological metrics of functional and structural connectivity networks by the Graph Theoretical Network Analysis (GRETNA) Toolbox (https://www.nitrc.org/projects/gretna; Wang et al., 2015). As aforementioned, the graph‐theoretical analyses were widely considered as a potent mathematical tool for characterizing the overall topological properties of human brain connectivity networks (Bullmore & Sporns, 2009; Rubinov & Sporns, 2010). To date, how to set a reasonable cutoff (thresholds) was still a major methodological hurdle in the graph theoretical‐based neuroimaging domain. As indicated in previous studies, the binarizing threshold should ensure that the network density was less than 50%, and the average degree (k) was simultaneously required to greater than the natural logarithm of the number of nodes (Rubinov, Sporns, van Leeuwen, & Breakspear, 2009; Rudie et al., 2013):

$\frac{1}{\mathrm{i}}\sum _{\mathrm{i}>1}{k}_i>ln\left(N\right)$

To this end, we applied this sparsity‐band, which ranged from 5% to 40% (step‐to‐step width = 1%), as thresholds to determine whether an edge exists between nodes (regions) in the functional and structural networks. The upper sparsity of 40% was set for threshold in the current study, showing the acceptable network density within 50%. In addition, the natural logarithms of the number of nodes from AAL‐90 and Power‐264 atlas (ln [90] = 4.49; ln [264] = 5.57) were largely less than average degree of these corresponding networks across all the cutoff points, indicating the justification of this threshold‐band setting.

2.7. Network‐based graph theoretical metrics

2.7.1. Small‐world properties

Small‐world properties were initially proposed by Watts and Strogatz (1998). There were a typical network that owned relatively high local clustering (neighboring nodes were connected with each other) and relatively short mean paths (little paths were needed to connect one and another one node) for the reconcilable coexistence of segregation and integration of information, which was consistently referred as a small‐world network. In the current study, we had investigated a series of small‐world characteristics in both functional and structural brain network, including clustering coefficient, shortest path length, Lambda, Gamma, Sigma, and efficiency. The clustering coefficient of a node (C _i) was defined as the ratio of the number of existing connections to the number of all possible connections, whose formula was denoted as below:

$C_{\mathrm{i}}=\frac{2e_i}{k_i\left(k_i-1\right)}$

where e _i represented the number of edges in the sub‐graph G _i (Strogatz, 2001; Watts & Strogatz, 1998), and k _i was the degree of node i. Obviously, if the node was isolated or within only one connection, the C _i would be NaN.

The clustering coefficient of the network was calculated as the average of the clustering coefficients of all nodes:

$C_{\mathrm{net}}=\frac{1}{N}\sum _{\mathrm{i}\in G}{C}_{\mathrm{i}}$

The characteristic shortest path length was considered as the least sum of the edge lengths between node i and node j, which was estimated as:

$L_{\mathrm{i}}=\frac{1}{N-1}\sum _{i\ne j\in G}min\left\{L_{i,j}\right\}$

in which {L _i,j} measured the shortest absolute path length between the i ^th node and the j ^th node. Formally, the characteristic path length of a network was the average value of the shortest path lengths between the nodes:

$L_{\mathrm{net}}=\frac{1}{N}\sum _{\mathrm{i}\in G}{L}_{\mathrm{i}}$

To reflect the small‐worldness of functional and structural connectivity networks, we normalized the clustering coefficient and the average shortest path length as Gamma (γ) and Lambda (λ), respectively. These parameters were calculated as follow:

$\gamma =\frac{C_{\mathrm{net}}}{C_{\mathrm{rand}}};\lambda =\frac{L_{\mathrm{net}}}{L_{\mathrm{rand}}}$

where C _rand and L _rand indicated the clustering coefficient and the average shortest path length for a random network. For generating the comparable random network, we began with a real network and further randomly swapped the double edge with the constraint that such a randomized procedure would not disrupt the natures of this network. We built a total of 200 of these random networks and further estimated the average of them as the representative random network for characterization of C _rand and L _rand. This algorithm maintained the degree of each node in the real network with equal natures, which had been applied in a prior study (Rudie et al., 2013). This randomized process was implemented with the script “gretna_RUN_SmallWorld.m” embedded in GRETNA toolbox.

Ordinarily, relative to the random network, the small‐world network would show the similar shortest path length but relatively higher clustering coefficient, namely, γ > 1 and λ ≈ 1 (Watts & Strogatz, 1998). Furthermore, these conditions were also summarized into a scalar quantitative measurement, σ (= γ / λ), which was typically >1 in the case of the small‐world network (Humphries, Gurney, & Prescott, 2006). Nevertheless, the clustering coefficient ignored the indirect connection between neighbor nodes whereas the shortest path length would not work if any isolated node existed in the network (Latora & Marchiori, 2001). Thus, to overcome the shortcomings of these measures (i.e., C and L), the (global/local) efficiency of the network were further proposed for characterizing small‐worldness.

Global efficiency (E _glob), was estimated for quantifying the efficiency of parallel information transfer in the overall network, which was defined by the inverse of the average harmonic of the absolute shortest path length between each pair of nodes (Latora & Marchiori, 2001, 2003):

$E_{\text{glob}}=\frac{\sum _{\mathrm{i}\ne \mathrm{j}\in \mathrm{G}}\mathrm{G}\in \mathrm{i},\mathrm{j}}{\mathrm{N}\left(\mathrm{N}‐1\right)}=\frac{1}{\mathrm{N}\left(\mathrm{N}‐1\right)}\sum _{\mathrm{i}\ne \mathrm{j}\in \mathrm{G}}\frac{1}{{\mathrm{L}}_{\mathrm{ij}}}$

Then, local efficiency (E _loc), could also be calculated for the information processing efficiency of node i:

$E_{\mathrm{loc}\_i}=\frac{1}{N_{G_i}\left(N_{G_i}-1\right)}\sum _{j,k\in G_i}\frac{1}{L_{j,k}}$

The quantity of E _{loc_i} played a similar role to the clustering coefficient of node i in the network C _i. Given that the node i was not an element for the subgraph G _i, the local efficiency could be considered as a measure of the fault tolerance for a system, it reflected how much information swapped when the node i was removed (Achard & Bullmore, 2007; Latora & Marchiori, 2001). In this vein, the E _loc of a network could be calculated with the average efficiency of the local subgraphs, reflecting the ability of local communication in the network:

$E_{\mathrm{loc}}=\frac{1}{N}\sum _{i\in G}{E}_{\mathrm{loc}\_\mathrm{i}}$

The efficiency‐based indices rephrased our understanding of small‐world properties in term of the information flow, indicating that the small‐world network was significantly efficient in global and local communication (Latora & Marchiori, 2001).

2.7.2. Rich‐club organization

The so‐called “rich club” organization would be formed in the brain network when the high‐connected (reflected by high degree) hubs of this network were more massively connected among themselves than that expected by the high‐degree node alone (Van Den Heuvel & Sporns, 2011) (see Supporting Information Method and Figure S2). For a given unweighted matrix (network), the rich‐club coefficient, Φ(k), was estimated as the ratio of the number of connections between the subset of selected nodes and the number of possible maximized connections between them. Thus, this was formally denoted as the following formula (Colizza, Flammini, Serrano, & Vespignani, 2006; McAuley, da Fontoura Costa, & Caetano, 2007; Zhou & Mondragón, 2004):

$\varphi \left(k\right)=\frac{2E_{>\mathrm{k}}}{N_{>\mathrm{k}}\left(N_{>\mathrm{k}}-1\right)}$

where E _>k indicated the number of connections between the subset of node i in the network, and N _>k(N _>k − 1)/2 represented the maximized possible connections between them.

In the same way, we could also normalize the Φ(k) as a more informative measure for quantifying the rich‐club behavior. Basing on the Erdos–Renyi (ER) random model, the rich‐club coefficient was considered to be normalized with the comparable random network of equal size and similar connectivity distribution (Colizza et al., 2006; McAuley et al., 2007). Consequently, about 200 randomized networks were generated and the average network of them was applied in normalization (detailed procedure see above). The formal computational formula of the normalized rich‐club coefficient (Φ_norm[k]) was described as below:

${\mathrm{\Phi }}_{\mathrm{norm}}\left(k\right)=\frac{{\mathrm{\Phi }}_{\text{real}}\left(k\right)}{{\mathrm{\Phi }}_{\text{random}}\left(k\right)}$

in which (Φ_random[k]) reflected the rich‐club coefficient of the established random network. The existence of the rich‐club effect would be determined if the normalized coefficient Φ_norm exceeded 1 over the range of k (Rubinov & Sporns, 2010; Van Den Heuvel & Sporns, 2011).

2.7.3. Modularity

In the functional connections, the communities nature of connectome could devote to a set of modules, which reflected the denser connections of the subset of vertices within the graph (network) relative to peripheral subgraph (Fletcher Jr et al., 2013). To estimate the optimal Modularity value (Q) of a network, the Newman's spectral optimization algorithm was performed to mathematically quantify the communities of connectome (Newman, 2006):

$Q=\frac{1}{L}\times \frac{1}{S_{i,j\in N}\left(a_{\mathrm{ij}}-\frac{k_i{k}_j}{L}\right){\delta }_{\mathrm{mi},\mathrm{mj}}}$

where L referred to the number of edges. The a _ij was the element of the matrix (network), indicating whether the connection between node i and node j would exist (a _ij = 1 meant the presence of an edge, otherwise a _ij = 0).

2.7.4. Hierarchy

Many real networks, particularly in brain networks, commonly shared a natural topological property, which was called a hierarchy organization. In a hierarchy network, the low‐degree nodes in the graph typically exhibited a higher clustering coefficient compared with high‐degree nodes (and vice versa), yielding the efficient network communication (Smith, Abdala, Koizumi, Rybak, & Paton, 2007). Due to the strict scaling law and scale‐free properties, the hierarchy coefficient could be described in the distribution of the ratio, and was quantified with the following equation:

C~k^−β

in which the C still represented the clustering and k indicated the degree of a node in a network. β, as the coefficient of hierarchy organization, was calculated fitting a linear regression with the ratio between log‐transformed C and log‐transformed k.

2.7.5. Assortativity

The network‐based graph theoretical metric could also be measured by the assortativity organization. This topological characteristic aimed at the measurement of how many connections between a pair of nodes with the similar degree. In this vein, the assortativity coefficient could be computed by correlating the degree of nodes on the mean degree of the graph (M):

$r=\frac{1}{{\sigma }_q^2}\sum _{\mathit{jk}}\mathit{jk}\left(e_{\mathrm{jk}}-q_{\mathrm{j}}{q}_{\mathrm{k}}\right)=\frac{M^{-1}\sum _i{j}_i{k}_i-{\left[M^{-1}\sum _i\frac{1}{2}\left(j_i+k_i\right)\right]}^2}{M^{-1}\sum _i\frac{1}{2}\left({j_i}^2+{k_i}^2\right)-{\left[M^{-1}\sum _i\frac{1}{2}\left(j_i+k_i\right)\right]}^2}$

where e _jk was defined to be the joint probability distribution of the remaining degrees of the two vertices at either end of a randomly chosen edge, as well as σ² _q was equal to the variance of q _k/q _j (Newman, 2002; Pastor‐Satorras & Vespignani, 2002).

2.8. Node‐based graph theoretical metrics

In the current study, we utilized both degree (k) and betweenness centrality (be) to quantitatively characterize the nodal dynamics of human brain networks. The degree was the most original and vital measure to describe nodal characteristic for a graph (Bondy & Murty, 1976), whereas betweenness centrality basing on the information flow perspective provided a more sensitive measure to recognize the position of the node in the network (Freeman, 1977). To maximize the original information of data for the further study, even though we have examined the between‐group effect in the correlation model with normalized betweenness coefficient, yet reported the original values in the figure.

2.9. Coupling of the structural‐functional connectivity network

With respect to the communication of cross‐modal regimen, we assessed the coupling level of structural–functional connectivity network (SC–FC Coupling). To overcome the drawback concerning the asymmetrical network density between the anatomical and functional connectomes (Rubinov & Sporns, 2010; see Discussion for more details), the correlations between them were corrected with a mathematical strategy that constrained functional connectivity network with edges from nonzero structural connectivity network (Zhang et al., 2011). In this vein, we extracted the edges from nonzero structural connectivity network for generating the vectors, and further rescaled them into a Gaussian distribution (Hagmann et al., 2010; Honey et al., 2009; van den Heuvel et al., 2013). Similarly, the functional connectivity was also selected to form the corresponding vectors. Finally, the coupling of SC–FC was quantified by the Pearson product–moment correlation between structural and functional vectors. SC–FC coupling has been proven to be one of the most valuable topological properties for characterizing one's overall organization (Collin et al., 2017; Rudie et al., 2013; Zhang, Liao, et al., 2011).

2.10. Statistical analysis

We utilized MATLAB 2014b (MathWorks, Natick, MA) and supplemented IBM PASW Statistics 21, Release Version 21.1.1 (SPSS, Inc., Chicago, IL) to explore the association between graph‐theoretical overall metrics of functional–structural brain connectome and one's intertemporal decision‐making. We examined a set of small‐world properties of both functional and structural matrices (i.e., clustering coefficient, C; characteristic shortest path length, L; normalized clustering coefficient, γ; normalized shortest path length, λ; small‐worldness, σ; local efficiency, E _loc; global efficiency, E _glob) over a range of sparsity (5%–40%, step‐to‐step width = 0.01), calculated them in each threshold point as well. This threshold‐band ensured no isolated node exists in the network and also maximally restored the low‐cost but high‐performance brain network (Achard & Bullmore, 2007; He et al., 2007). Subsequently, the partial Pearson product–moment correlation between these metrics and AUC (a robust measure for individuals' intertemporal decision) was performed, whereas the genders, ages, education, trait anxiety, big‐five personality and mean FD were involved as covariates of no interests for control. On the other hand, to quantify the other topological dynamics (i.e., rich‐club organization, hierarchy, modularity and assortativity organization) in the networks, we replaced sparsity with degree k (ranging from 1 to the maximum degree value in the network) as the thresholds for the construction of adjacency matrix (binarization). Similarly, we also correlated the value of these metrics to delay discounting rates by partial Pearson correlation. For the nodal characteristics (i.e., degree, k; primordial betweenness, B _i), we extracted the average values of each node that was parceled by AAL‐90/Power‐264 atlas and further utilized them to the partial correlation model, respectively. Finally, the coupling of SC–FC connectivity that had been already quantified by the correlation coefficient was used to correlate the off‐line intertemporal behavior of interests (i.e., delay discounting). In addition, the nonparametric Permutation test was applied to examine the between‐group differences between two data sets (principal sample and replication sample) in demographic characteristics. Of note, all the tests were replicated in an independent data set to certify the reproducibility of our results. For the exploratory purpose, the level of significance was set at p < .05 for all the statistical tests without multiple comparison correction. In line with a vast majority of previous studies, the uncorrected p value at .05 was widely adopted as the empirical significant level for the statistical model with multiple comparisons to deal with the multiple threshold points of adjacency matrices (networks) in the graph‐theoretical analysis of brain connectomes (Liu et al., 2008; Liu, Chen, Lin, & Wang, 2015; Smit, Stam, Posthuma, Boomsma, & De Geus, 2008; Stam, Jones, Nolte, Breakspear, & Scheltens, 2006). Furthermore, for the sake of the rounded exploration on the whole‐brain organization pattern of human intertemporal decision‐making, the liberal statistical threshold could entail huge fruits for more informative comprehension relative to unduly conservative multiple comparisons correction. On the other hand, to moderately alleviate the potential risk of false‐positive rates yielded by the lack of multiple comparison corrections and comparatively liberal statistical threshold, we further undertaken the statistical strategy with the AUC value of topological regimes of brain connectomes (i.e., gamma [γ], sigma [σ], global efficiency [E _glob], local efficiency [E _loc], degree [k], and betweenness centrality [be]) to link for delay discounting rates basing on the same partial bivariate correlation model. This work would re‐confirm the association between the delay discounting rates and these topological regimes based on AUC value, which overcomes the inflated false‐positive rates found in original graph‐theoretical measures without multiple comparison corrections.

What's more, to further address the potential concerns on the presumable inflation of the false‐positive rates stemming from the multiple comparisons, all the raw data pertaining to the statistical tests for the associations between these graph‐theoretical measures and delay discounting rates of intertemporal decision‐making have been encapsulated and submitted in the Open Science Framework (OSF, https://osf.io/x4z2j) without any limitation on the access for readers to scrutinize and leverage those findings straightforwardly.

3. RESULTS

3.1. Functional and structural connectivity network construction

We have produced the average matrices of both functional and structural connectivity networks with AAL‐90 and Power‐264 parcellation scheme across two independent data sets (Figure 3a–d). For the visual inspection of these matrices, all the averaged matrices were reconstructed in a three‐dimensional (3D) glass ICBM152 brain with native space, implemented by BrainNet Viewer Toolbox (Xia, Wang, & He, 2013; Figure 4a–d). These visualized matrices have shown the empirically classical connectivity pattern in both functional and structural brain network, indicating the well‐established connectivity networks that we have constructed (Achard & Bullmore, 2007; Rudie et al., 2013; van den Heuvel et al., 2008; Zhang, Liao, et al., 2011). Furthermore, to evaluate the reproducibility of our results, the correlations between these mean matrices of the two data sets were examined. Meanwhile, we also reported 95% confidence intervals (CI) of these correlation coefficients with a bootstrapping procedure (with 5,000 bootstrap samples). The results showed the highly positive correlation between mean connectivity matrices of two independent data sets (r _{[AAL‐based functional matrix]} = 0.92, p < 1 × 10⁻⁵, 95% CI: 0.91–0.92; r _{[Power‐based functional matrix]} = 0.93, p < 1 × 10⁻⁵, 95% CI: 0.93–0.94; r _{[AAL‐based structural matrix]} = 0.80, p < 1 × 10⁻⁴, 95% CI: 0.79–0.81; r _{[Power‐based structural matrix]} = 0.73, p < 1 × 10⁻⁴, 95% CI: 0.70–0.75), reflecting the robust repeatability of these established functional and structural connectivity networks (Figure 3e,f). Above all, these findings highlighted that we had successfully constructed the reliable brain connectomes for further graph theoretical analysis.

Figure 3.

Reproducible results of structural (a/b) and functional connectivity (c/d) matrices construction. Panel (a) represented the group‐averaged functional connectivity matrices with AAL‐90 node‐defined scheme across two samples (principal data set and replication data set), and the color bar indicated the corresponding correlation coefficient between the BOLD time‐series of these nodes. Panel (b) showed the group‐averaged functional connectivity matrices with Power‐264 node‐defined scheme across two samples. Panel (c) reflected the group‐averaged structural connectivity matrices with AAL‐90 node‐defined scheme across two sample, and the color bar indicated the number of white matter connections. Panel (d) showed the mean structural connectomes with Power‐264 within two samples. Panel (e) provided the scatter plot for the generated functional connectomes correlation between two samples with AAL‐90 (left) and Power‐264 scheme (right), showing the high reproducibility of network construction. Panel (f) offered the scatter plot for the generated structural connectomes correlation between two samples with AAL‐90 (left) and Power‐264 (right) scheme, also showing the high correlation of these networks. The corresponding p value and the 95% confidence intervals (CI) of correlation coefficients with a bootstrapping procedure (with 5,000 bootstrap samples) have been reported in the bottom of e and f [Color figure can be viewed at http://wileyonlinelibrary.com]

Figure 4.

Reconstruction of group‐averaged matrices in functional (top) and structural (bottom) connectome with AAL‐90 (left) and Power‐264 (right) scheme. Axial rendering map was rebuilt into the 3D glass brain model with ICBM‐152 MNI space for visualization. “Node” in the figure reported the number of nodes in corresponding connectivity network (n = 90 for AAL‐90 scheme; n = 264 for Power‐264 scheme), while the “edge” indicated the number of all possible connectivity in graph (e = 4,005 for AAL‐90 scheme; e = 34,716 for Power‐264 scheme). FN = functional network; SN = structural network [Color figure can be viewed at http://wileyonlinelibrary.com]

3.2. Network‐based topological metrics of functional and structural connectomes

Small‐world organization (γ > 1, λ ≈ 1, σ > 1) had been observed in both structural and functional connectivity networks that we established over a range of 6–40% sparsity (covering almost all the threshold cutoff points), irrespective of which the parcellation scheme (i.e., low‐resolution AAL‐90 atlas and high‐resolution Power‐264 atlas) was applied. Together, the same results were also found in the replication data set. In accordance with the purpose of our research, group‐analysis indicated the significantly positive correlation between small‐world properties (γ and σ) of functional connectivity network and AUC values of delay discounting in nearly all sparsity points across both two parcellation schemes, indicating that increased delay discounting might be paralleled by the aberrant small‐world organization (Figure 5a,b). Simultaneously, we obtained the parallel results in the structural connectomes as well (Figure 5c,d).

Figure 5.

Small‐world properties in both functional (a/b) and structural (c/d) connectome. Top showed the values (Mean ± SD) of small‐world properties (clustering coefficient, characteristic path length, lambda, gamma and sigma) and the degree over a range of sparsity (5% and 40% network sparsity in 1% increments) for functional connectivity networks with AAL‐90 (a) and Power‐264 (b) scheme, where the pink line indicated the values for principal data set while blue one reflect them for replication data set. The bottom also reflects the same measures (Mean ± SD) for the small‐world properties and the degree over a range of sparsity (5% and 40% network sparsity in 1% increments) in structural connectivity networks with AAL‐90 (c) and Power‐264 (d) scheme. * indicates the significant correlation (p < .05) between the intertemporal choices and the metric under this threshold constraint in both data sets, whereas * showed the significant correlation (p < .05) in either principal data set or replication one [Color figure can be viewed at http://wileyonlinelibrary.com]

Afterward, E _loc, as a more precise measure for small‐worldness, was also found to be significantly associated with AUC value of delay discounting in functional connectivity networks with both AAL‐90 and Power‐264 parcellation schemes but was not observed in structural connectomes (e.g., when sparsity = 18%, r _{[Eloc in functional network with AAL‐90]} = 0.43, p < .001, 95% CI: 0.16–0.66; r _{[Eloc in functional network with Power‐264]} = 0.34, p < .01, 95% CI: 0.08–0.55; r _{[Eloc in structural network with AAL‐90]} = 0.02, p > .05, 95% CI:−0.33–0.31; r _{[Eloc in structural network with Power‐264]} = 0.04, p > .05, 95% CI:−0.26–0.41). Conversely, E _glob was hardly correlated to delay discounting in neither functional nor structural connectomes. Encouragingly, these significant correlations were almost all confirmed in the replicated data set.

Notably, the findings derived from the statistical scheme with the AUC values of these small‐world metrics of brain functional and structural connectomes showed the parallel results as above across two independent samples (e.g., r _{[γ of functional network in principal sample]} = 0.34, p < .01, 95% CI: 0.03–0.58; r _{[γ of functional network in replicated sample]} = 0.47, p < .01, 95% CI: 0.17–0.59; r _{[σ of functional network in principal sample]} = 0.41, p < .01, 95% CI: 0.25–0.67; r _{[σ of functional network in replicated sample]} = 0.52, p < .01, 95% CI: 0.38–0.76; r _{[Eloc of functional network in principal sample]} = 0.49, p < .01, 95% CI: 0.25–0.67; r _{[Eloc of functional network in replicated sample]} = 0.64, p < .01, 95% CI: 0.47–0.82), substantially strengthening the robustness and reproducibility of these outcomes concerning the significant association between the small‐world organization of brain connectomes and delay discounting, with high‐performance small‐worldness for less temporal devaluation (see Supporting Information Figure S3 for more details).

Unexpectedly, our analysis only captured a positive correlate of modularity organization of functional connectome on AUC value of delay discounting (when k = 23, r _{[principal data set]} = 0.44, p < .001, 95% CI: 0.22–0.62; r _{[replication data set]} = 0.48, p < .001, 95% CI: 0.29–0.64; Supporting Information Figure S4). There is no more evidence to corroborate our hypothesis regarding the function of hierarchy and assortativity of whole‐brain connectomes on discounting behavior in the absence of significant correlations (e.g., when k = 23, r _[hierarchy] = −0.05, p > .05, 95% CI:−0.32–0.22; r _{[assortativity]} = 0.01, p > .05, 95% CI: −0.26 to 0.26; Supporting Information Figure S4). These results pertaining to small‐worldness (λ, γ, and σ), local efficiency, global efficiency, hierarchy, modularity, and assortativity, had been sorted in Table 2 in detail. In brief, regarding above overall topological dynamics in functional and structural connectomes, we had clarified the significantly negative linking between small‐world/modularity organization of brain connectomes and devaluation of delays, which underscored this notion that the enhanced overall organization of whole‐brain network could potentially facilitate the high‐performance decision in intertemporal choices.

Table 2.

Group‐average characteristics of functional and structural graph matrices (threshold‐average) with two atlases (AAL‐90 Atlas/Power‐264 Atlas) across two independent samples (principal sample/replication sample)

Characteristic			Principal data set (n = 53)								Replication data set (n = 52)
			Mean			SD				p			Mean			SD			p
Functional graph matrices
	Small‐world properties
		Clustering coefficient, C real	0.62 (0.61)			0.028 (0.030)				–			0.65 (0.63)			0.034 (0.029)			–
		Characteristic path length, L real	1.75 (1.68)			0.106 (0.115)				–			1.77 (1.78)			0.124 (0.110)			–
		C of random networks, C rand	0.57 (0.59)			0.186 (0.159)				–			0.58 (0.51)			0.244 (0.214)			–
		L of random networks, L rand	1.34 (1.29)			0.034 (0.031)				–			1.34 (1.49)			0.189 (0.193)			–
		Normalized C, gamma, γ	1.30 (1.30)			0.040 (0.048)				**			1.32 (1.19)			0.056 (0.029)			**
		Normalized L, lambda, λ	1.07 (1.02)			0.150 (0.136)				n.s			1.08 (1.07)			0.139 (0.135)			n.s
		Small‐worldness, sigma, σ	1.22 (1.24)			0.162 (0.201)				**			1.23 (1.22)			0.160 (0.156)			**
Efficiency properties
		Global efficiency, E glob	0.45 (0.47)			0.011 (0.008)				n.s			0.44 (0.49)			0.014 (0.017)			n.s
		Local efficiency, E loc	0.66 (0.71)			0.020 (0.032)				**			0.66 (0.61)			0.020 (0.011)			**
Modularity			0.46 (0.41)			0.020 (0.037)				*			0.47 (0.44)			0.022 (0.020)			*
Hierarchy			0.31 (0.27)			0.071 (0.054)				n.s			0.31 (0.29)			0.069 (0.072)			n.s.
Assortativity			−6 × 10−3 (−5 × 10−3)			−4 × 10−4 (−3 × 10−4)				n.s			−5 × 10−3 (−5 × 10−3)			−3 × 10−4 (−3 × 10−4)			n.s
Structural graph matrices
Small‐world properties
		Clustering coefficient, C real	0.50 (0.61)			0.023 (0.066)				–			0.49 (0.57)			0.024 (0.193)			–
		Characteristic path length, L real	1.72 (1.64)			0.064 (0.071)				–			1.55 (1.69)			0.091 (0.142)			–
		C of random networks, C rand	0.35 (0.42)			0.104 (0.145)				–			0.40 (0.47)			0.289 (0.333)			–
		L of random networks, L rand	1.54 (1.56)			0.114 (0.165)				–			1.51 (1.59)			0.070 (0.018)			–
		Normalized C, gamma, γ	1.42 (1.45)			0.162 (0.194)				**			1.21 (1.19)			0.319 (0.191)			**
		Normalized L, lambda, λ	1.11 (1.05)			0.093 (0.085)				n.s			1.02 (1.06)			0.043 (0.059)			n.s.
		Small‐worldness, sigma, σ	1.27 (1.38)			0.128 (0.195)				**			1.18 (1.12)			0.067 (0.016)			**
Efficiency properties
		Global efficiency, E glob	0.44 (0.43)			0.012 (0.007)				n.s			0.39 (0.41)			0.007 (0.006)			n.s
		Local efficiency, E loc	0.63 (0.66)			0.028 (0.019)				n.s			0.64 (0.61)			0.084 (0.071)			n.s
Modularity			0.48 (0.45)			0.020 (0.014)				n.s			0.49 (0.48)			0.022 (0.201)			n.s
Hierarchy			0.55 (0.52)			0.093 (0.092)				n.s			0.60 (0.58)			0.105 (0.081)			n.s
Assortativity			−2 × 10−3 (−2 × 10−3)			−4 × 10−4 (−3 × 10−4)				n.s			−6 × 10−3 (−4 × 10−3)			−6 × 10−4 (−1 × 10−4)			n.s

“Mean” reported the group‐averaged value of the graph‐theoretical properties for both atlas “AAL‐90 (Power‐264)” across all the threshold points. “SD” indicated the corresponding standard deviation for these characteristics “AAL‐90 (Power‐264)”. The nonparametric permutation test (n = 10,000) was performed to identify the correlation between these graph‐theoretical characteristics and delay discounting rate (significant level was set at 0.05). The “n.s.” meant that “no significant correlation” was found. “**” reflected the significant correlation between delay discounting rate and the characteristic in both AAL‐90 and Power‐264 atlas. “*” reflected such significant correlations in either atlas.

Encouragingly, in line with prior studies (Collin et al., 2017; van den Heuvel et al., 2013), the rich‐club organization (a portion of Φ_norm exceeded 1 over the range of k) was observed across all the generated functional/structural connectivity networks, irrespective of which parcellation scheme was used. The Figure 6 illustrated the group‐averaged normalized/randomized/real rich‐club curves (Φ_norm, Φ_rand, and Φ_real) of the functional and structural connectomes with AAL‐90 atlas across two data sets, and reconstructed the hub organization into 3D glass brain from ICBM‐152 MNI space for visualization as well. Specifically, in the group‐averaged functional connectivity network with AAL‐90 parcellation scheme, the bilateral superior frontal, left superior parietal, right precuneus and left insula were figured out as rich‐club regions (hubs; Figure 6a). Similarly, those regions, including bilateral superior frontal, right superior parietal, bilateral precuneus and bilateral putamen, also exhibited the hub organization in the AAL‐based mean structural connectome (Figure 6c). These findings were almost confirmed in the replication data set (Figure 6b,d). Group‐analysis presented a significant positive correlation between rich‐club regimen in the AAL‐based functional connectivity network and AUCs of delay discounting (r _{[Φnorm‐AUC]} = 0.34, p < .01, 95% CI: 0.11–0.54), indicating that the increased rich‐club communication in functional connectome can restrain one's future discounting tendencies. The parallel finding was also observed in the structural connectome, showing the positive correlates of rich‐club behavior on AUCs (r _{[Φnorm‐AUC]} = 0.33, p < .01, 95% CI: −0.19 to 0.35). In other words, the aberrant rich‐club organization in structural connections can also bias one's intertemporal choice for short‐termism. Moreover, the above findings were all replicated in the independent replication data set, substantially acknowledged the reproducibility of these outcomes. Thus collectively, the enhanced rich‐club regime could bolster the robust global communication pattern, and further promote long‐term beneficial choices in one's intertemporal decision‐making.

Figure 6.

Rich‐club regime in the both functional (a,b) and structural (c,d) connectivity network with AAL‐90 parcellation scheme. Panel (a) reflects the rich‐club ϕ (k) curve for the group‐averaged functional connectomes over a range of k (15 and 50 network degree in 1 increments). The whole‐brain functional network showed the typical rich‐club behavior for the range of k from 27 to 47. The normalized rich‐club ϕ_norm (k) is denoted as red, whereas rich‐club ϕ_real (k)/ϕ_random (k) from group‐averaged networks/generated random networks are plotted with dark and light gray, respectively, and the rich‐club regime is also highlighted with the light brown background. On the right of this figure, the rich‐club organization is reconstructed into the 3D glass brain model with ICBM‐152 MNI space for visualization. Panel (b) shows the results of the same measures in replication data for examining the reproducibility of our finding. Panel (c) reflects the same measures for the group averaged structural connectomes over the range of k from 1 to 36 whereas “d” shows this reproducible result in replication data set. In the visualized reconstruction of rich‐club, the dark red regions represent hubs (rich‐club nodes) while the dark yellow regions indicate nonhubs (nonrich club nodes) [Color figure can be viewed at http://wileyonlinelibrary.com]

3.3. Node‐based characteristics for functional and structural connectomes

In the current study, we respectively evaluated the degree (k) and primordial/normalized betweenness centrality (be) to characterize nodal properties. As mentioned above, the average degree and betweenness centrality of regions from both structural and functional connectomes were extracted out and further conducted for the partial bivariate correlation model to investigate the correlates of them on delay discounting respectively. However, there were no significant correlations between delay discounting and the degree/betweenness centrality of any regions over the entire range of threshold. Based on the structural and functional connectivity matrices with AAL‐90 parcellation scheme, the group‐average values of all the nodes (regions) were sorted in Figure 7 with descending order. We further highlighted a series of regions that were intimately related to delay discounting (Bartra, McGuire, & Kable, 2013; Kable & Glimcher, 2007; Peters & Büchel, 2010, 2011). In addition, there were still null findings concerning the association between these momentous nodal metrics of brain connectomes generated by multi‐scale parcellation schemes and delay discounting behaviors (e.g., r _{[k of functional network in principal sample]} = −0.03, p > .05, 95% CI: −0.22 to −0.17; r _{[k of functional network in replicated sample]} = −0.02, p > .05, 95% CI: −0.03 to −0.02); r _{[be of functional network in principal sample]} = −0.01, p > .05, 95% CI: −0.02 to −0.01; r _{[be of functional network in replicated sample]} = −0.01, p > .05, 95% CI: −0.02 to 0.03), even though we implemented the statistical strategy with the AUC values for characterizing these topological attributes in the partial bivariate correlation model (see Supporting Information Figure S3 for more details). In brief, with regard to nodal topological metrics of human functional and structural connectomes, these alterations might rarely explain the observed variance in one's intertemporal decision‐making.

Figure 7.

Node‐based topological characteristics of graph matrices. The figure showed the degree and original betweenness (rather than normalized values) for the group‐averaged functional connectivity matrices (a) and structural connectomes (b) with AAL‐90 parcellation scheme. All the regions (nodes) were listed with reverse order by their values, showing relatively high repeatability across neural modalities. Meanwhile, these regions (nodes) that are intimately related to intertemporal choices have been marked with the yellow bar [Color figure can be viewed at http://wileyonlinelibrary.com]

3.4. Dynamics for structural–functional connectivity coupling

As indicated by prior studies (Collin et al., 2017; Liao et al., 2013; Liao et al., 2016; Zhang, Wang, et al., 2011), we also explored the potential association between the coupling of SC–FC connectomes and one's intertemporal decision‐making in the current study. When making a correlation between functional and structural connectome, the moderate positive correlation between them was observed regardless of which parcellation schemes were applied (the r values almost covered in a range of 0.2–0.4). To construct an exact correlation model, the outliers (2 standard deviations outside the average) of coupling value were excluded. Group‐analysis suggested that the whole‐brain SC–FC coupling was slightly correlated with the AUCs of discounting behavior (r _(AAL‐90) = 0.28, p < .05, 95% CI: 0.05–0.53); this finding was also cross‐validated in the generated brain connectomes with high‐resolution parcellation scheme (r _{[Power‐264]} = 0.36, p < .01, 95% CI: 0.05–0.59), indicating that increased coupling of cross‐modalities organization was propitious to one's optimal decision‐making behavior in intertemporal choice. Furthermore, these findings were all verified in the replication data set (r _[AAL‐90] = 0.34, p < .05, 95% CI: 0.03–0.57; r _{[Power‐264]} = 0.31, p < .05, 95% CI: 0.08–0.55; Figure 8). In conclusion, our findings revealed that the delay discounting was indeed negatively correlated to the SC–FC coupling, suggesting that the steep delay discounting in intertemporal decision‐making, in part, might be characterized by the aberrance of structural–functional connectome communication.

Figure 8.

Scatter plots for the correlates of SC‐FC coupling on intertemporal choices. The intertemporal choice for each participant is quantified by delay discounting rate with an area under the curve (AUC). Top shows the significant correlations between AUC and SC‐FC coupling across two independent data sets with AAL‐90 parcellation scheme (“a” for principal sample and “b” for replicated sample), whereas bottom reflects the similar association across two samples with Power‐264 parcellation scheme (“a” for principal sample and “b” for replicated sample), thus cross‐validating our findings [Color figure can be viewed at http://wileyonlinelibrary.com]

4. DISCUSSION

In this study, we performed an exploration by linking the higher‐level topological properties of whole‐brain functional and structural connectivity network to human intertemporal decision‐making via the graph‐theoretical analysis. Our findings revealed that the alteration in a set of overall metrics of human structural and functional connectomes including small‐world properties, modularity, and the rich‐club organization was robustly associated with this decision‐making behavior, which indicated that steep delay discounting would be predominantly observed in randomized (disrupted) whole‐brain global and local communication. Furthermore, taking into account the cross‐modalities profile, we also found that the decoupling of SC–FC communication was significantly more marked in individuals with the higher discounting rate. Collectively, our findings might thus converge on the notion that not only the information processes of sole regions or sub‐networks but also high‐performance overall global and local communication of whole‐brain complex network underline one's intertemporal decision‐making.

4.1. Bridge between the network‐based topological dynamics and intertemporal decisions

Human brain network broadly exhibited the greater cliquishness but relatively shorter path length, which was the so‐called “small‐world” organization. In line with numerous prior connectome‐based studies (Achard, Salvador, Whitcher, Suckling, & Bullmore, 2006; Horstmann et al., 2010; Van Dellen et al., 2009), we observed the presence of small‐world organization in all the established human brain connectivity networks, irrespective of which parcellation scheme was conducted. Encouragingly, a significantly negative relation between this topological metric and delay discounting was found here. Ordinarily, the small‐world organization was inevitably involved in simultaneous communicative behavior on parallel information processing, largely determining the efficiency of both local and global high‐order cognitive communication in the brain system (Bassett & Bullmore, 2017). In other words, this small‐world overall organization has been regarded as a striking contributor to one's high‐performance cognitive function when participants are required to deliberation processes (Bassett et al., 2011; Yu et al., 2011). As a key index for checking the shifts capability of network communication in functional and structural connectomes enhanced small‐world overall organization was widely considered to intensify the fault tolerance of randomized attacks toward both parallel and sequential system. Such improvements can benefit for the integration of high‐level cognitive resources straightforward (He et al., 2007; He & Evans, 2010; Huang, Zou, Tan, Shao, & Jin, 2003; Latora & Marchiori, 2001). To the best of our knowledge, widespread deficiencies in cognitive function, particularly in top‐down cognitive processes, has been proven to be a robust predictor for future discounting (Bickel, Yi, Landes, Hill, & Baxter, 2011; Miller & Cohen, 2001). Emerging evidence has further indicated the predictive role of cognitive function recruited in human connectomes on complex intertemporal decisions (Gonzalez‐Castillo et al., 2015; Mobini, Grant, Kass, & Yeomans, 2007). In this vein, an arbitrary small‐world organization in the topological space of brain connectomes could simultaneously disrupt the local and global communication toward distributed cognitive processes. As we mentioned above, these deficits would further hamper the regulation of cognitive resources, resulting in the suboptimal behaviors in intertemporal decision‐making.

As aforementioned, to overcome the shortcomings resulting from the obtuse measure on the transmissible ability/efficiency of information in the light of information flow theory, we further quantitatively gauged the global and local efficiency to represent the small‐world organization that concentrated upon the relatively parallel transfer of information. However, with respect to our preliminary findings on the small‐world organization, the significant correlate of local efficiency on delay discounting was just proven in the functional connectivity networks but not in the structural connectomes. As a matter of fact, the asymmetry of two modalities on this graph‐theoretical metric has frequently been reported in previous studies (Park, Kim, Kim, & Kim, 2008; Rudie et al., 2013; Zhang, Liao, et al., 2011). Here, we could cautiously interpret it in terms of the neurophysiological asymmetry between functional and structural networks. As was well‐known to us, the functional connectivity largely depended on relatively dynamic and mutable blood oxygenation level‐dependent (BOLD) fluctuations, whereas structural connectivity was consistently determined by intrinsic and stable synaptic junction (Bullmore & Sporns, 2009; Caroni, Chowdhury, & Lahr, 2014; Park et al., 2008). Consequently, we may speculate that the subtle alteration of cognitive function could be rapidly captured by the functional MRI (BOLD signals) yet exhibited relatively changes‐insensitive in the fiber‐based structural connectome. Taken together, our exploratory findings may converge on the conjecture that individuals' discounting behavior in intertemporal decision‐making was presumably characterized by an altered small‐world communicative pattern of overall brain networks.

There was cumulative evidence that the transitions of complex cognitive information might be largely organized by the relative extent of local communication of functional brain networks in favor of the constraints of wiring‐cost premium, referring to “modularity” (Chen, Abrams, & D'esposito, 2006; Rubinov et al., 2009). Consistent with previous researches (He & Evans, 2010; Meunier, Lambiotte, & Bullmore, 2010), the modularity organization had been detected in functional connectivity networks that we re‐established in the current study. Group‐analysis further uncovered the inverse correlation between this topological metric and delay discounting. Based on the graph‐theoretical literature, modularity organization was considered as a manager to constrain the stream of information processes throughout the whole brain during the resting‐state stage, this attribute that generally involved in the rapid reconfigure on responses of behavioral tasks and concomitant changes with past experience (Bassett & Bullmore, 2006; Simon, 1991, 1995). In other words, the modularity organization can determine how the brain network processes the parallel information within integrated and segregated communication patterns, reflecting the capacity of deliberative cognitive processes toward high‐load tasks (Arnemann et al., 2015; Kitzbichler, Henson, Smith, Nathan, & Bullmore, 2011; Rubinov & Sporns, 2010). Naturally, the enhanced functional modularization of complex brain system can potently facilitate efficient communicative behaviors in the collectivized information transmission in favor of cognitive control. As an emblematical high‐order cognitive task, it was essential to efficiently regulate cognitive resources for complex parallel processes of neural coding (e.g., valuation signals and cognitive control) when participants made decisions in intertemporal choice (Halfmann et al., 2015; Smith et al., 2016). What's more, some direct evidence has highlighted the crucial role of such cognitive ability in discounting behaviors (Hirsh, Morisano, & Peterson, 2008; Wittmann, Leland, & Paulus, 2007). From what has been mentioned above, we may infer that the modularity organization of functional connectome can directly influence how overall brain system paralleled multidimensional cognitive information; it can further determine the capability of cognitive function and thus bias one's performance in intertemporal decision‐making. In brief, our findings suggested that the modularity organization in brain network might partially underlie the superior neuronal substrate of this high‐level cognitive decision, namely intertemporal decision‐making.

Rich‐club regime was increasingly advocated to be a cardinal topological property in human whole‐brain network, which has been proven to play a fundamental role in the global communication among organized parallel subsystems in both functional and structural connectomes basing on the specific structure with the “Matthew effect” (van den Heuvel et al., 2012; Van Den Heuvel & Sporns, 2011). In the current study, our findings were in almost agreement with prior works (McColgan et al., 2015; van den Heuvel et al., 2013), showing the representative rich‐club organization in established human whole‐brain networks. Encouragingly, our results further showed the significant negative correlation between this topological metric and the discounting behavior. It was clear that rich‐club organization embedded in brain network's infrastructure was mainly responsible for the integration of neural coding information derived from a subset of local communities (de Reus & van den Heuvel, 2014; Zamora‐López, Zhou, & Kurths, 2011). Emerging research has documented a more straightforward idea that the rich‐club behavior may directly determine how well the brain network worked in the global communication system (Liang et al., 2017). In the cognitive processes, global communication reflected the flexible interaction among specific functional or structural modules; such patterns automatically ensured the duly comprehensive information for a repertoire of top‐down cognitive function (Park & Friston, 2013; Santarnecchi, Galli, Polizzotto, Rossi, & Rossi, 2014). Hence, the aberrant rich‐club organization might dramatically disrupt the informative fluency of global communication in the whole‐brain network system, thereby triggering more short‐sighted choices in intertemporal decision‐making due to the inhibition of cognitive function. Collectively, the rich‐club organization has been speculated to constitute a backbone for brain global communication. Thus, our findings suggested that the alteration in this metric might provide a novel topological hallmark for intertemporal decision‐making.

4.2. Bridge between the nodal topological metrics and intertemporal decisions

Degree and betweenness centrality were proven to be the most pivotal nodal measures to quantitatively describe the position of nodes (regions) within the network (whole‐brain), reflecting the capability of regions on parallel information processes in brain connectomes (Hagmann et al., 2008; Sporns, 2010). Quite unexpectedly, there were null findings in our node‐based analysis. No significant correlations between degree/betweenness centrality of brain regions and delay discounting rates were found in neither functional nor structural connectivity networks, indicating a complex association between the topological properties of regions and behavioral performance. However intriguingly, although no positive results were captured, these regions with high degree/betweenness centrality were largely converged to a set of hubs for intertemporal decision‐making, such as bilateral superior frontal (e.g., in the AAL‐based functional connectome, k _[left] = 24.65, be _[left] = 14.52; k _[right] = 27.16, be _[right] = 49.64; in the AAL‐based structural connectome, k _[left] = 3.49, be _[left] = 14.52; k _[right] = 3.98, be _[right] = 29.49), bilateral putamen (e.g., in the AAL‐based functional connectome, k _[left] = 14.74, be _[left] = 44.85; k _[right] = 24.79, be _[right] = 40.82; in the AAL‐based structural connectome, k _[left] = 6.16, be _[left] = 108.31; k _[right] = 6.88, be _[right] = 125.86) and caudate; these areas were all confirmed to be involved in subjective value coding and cognitive control function in intertemporal choices (Kable & Glimcher, 2009; McClure et al., 2004; Peters & Büchel, 2011). Yet in the case of the absence of significant correlations, one could carefully propose the explanation that not only contribution in isolated region's function but also the distributed communication within brain network as a whole might account for the differences in the complicated cognitive‐directed behavior (i.e., intertemporal decision‐making).

4.3. Coupling of structural–functional connectivity on intertemporal decision

As a novel and valuable measure for brain network's topological attribute, the structural–functional connectivity coupling (SC–FC coupling) exhibited the high priority to detect the subtle alterations of brain integration in cognitive function or pathological state (Collin et al., 2017; Honey et al., 2009; van den Heuvel et al., 2013). In the current exploratory study, we have revealed the significant correlates of SC–FC coupling on the delay discounting across multi‐scale parcellation schemes, suggesting that the disturbance of SC–FC coupling might link to more myopic decisions in one's intertemporal choice. As indicated by previous works, SC‐FC coupling was generally considered to represent the degree of neuroanatomical constraint over functional brain dynamics, thus determining the capacity of robust reconfigurations for distributed network organization pattern (Griffa et al., 2015; van den Heuvel et al., 2013). Emerging evidence further attested this idea that the decoupling of SC–FC might be indicative of more vulnerable and less sustainable reconfigurations function in the network, further resulting in the aberrant in aspects of cognitive ability, such as the function of executive control and cognitive inhibition (Braun et al., 2015; Collin et al., 2017; Hutchison & Morton, 2015). Of note, the failure to resist the temptation of attractive immediate reward, to a large extent, could be attributed to the impaired cognitive function, particularly to executive control ability (Sasse, Peters, & Brassen, 2017; Wang et al., 2017). As aforementioned, widespread alterations in cognitive function, reflected by reliable reconfigurations, had been indicated to be intimately associated with one's high‐order cognitive‐behavioral functioning (e.g., intertemporal decision‐making; Collin et al., 2017; Park & Friston, 2013). In this vein, we may elucidate this finding that decreased SC–FC coupling in human connectomes was widely involved in the broad disruption of cognitive functioning due to the deviated communication pattern, such aberrance that thus predisposed participants to the steep discounting tendency. Taken together, our outcomes in SC–FC coupling analysis indicated that the underlying communication pattern across multi‐modalities of brain connectomes might offer a novel comprehension to account one's cognitive‐directed intertemporal decision‐making.

However, it was still worthwhile noting that the robustness of these outcomes would presumably be exposed to the risk of the methodological drawback pertaining to the pronounced asymmetry between the brain anatomical and functional connectomes. Thus far, it was universally acknowledged that the functional connectomes of the whole brain emerged from the linear or nonlinear correlations between time‐series of all the possible pairs of regions (nodes) but the connectomes of brain structural networks can only occur in the intrinsic anatomical connections (Honey et al., 2009; Rubinov & Sporns, 2010). Ordinarily, the higher network density would be prone to be observed in the brain functional connectomes, as it incorporates considerably redundant connectivity of anatomically unconnected regions (Damoiseaux & Greicius, 2009). Comparatively speaking, the structural connectomes were broadly considered to show the sparser density in the intrinsic anatomical network, deviating significantly from functional one (Costa et al., 2007; Sharan & Ideker, 2006). Consequently, the straightforward examinations between them may heavily obscure the comprehensive elucidation of information flow in the brain system (Rubinov & Sporns, 2010). Notwithstanding this, the previous studies still substantiated this cardinal idea that the comparisons and coupling between anatomical and functional connectomes naturally shared the sound meanings and implications to depict the topological dynamics of brain (Collin et al., 2017; Sporns et al., 2005; Zhang, Liao, et al., 2011; Zhou & Mondragón, 2004). To this end, even though the mathematical emendation with Gaussian space was undertaken in the current study (see above), spreading our conclusions regarding the bridge between the structural–functional coupling of brain connectomes and intertemporal decision‐making still need to warrant some caution.

4.4. Methodological concerns

In the present study, several inherent limitations still should be considered. First, as suggested in previous studies (Lo et al., 2010; Shu et al., 2011; Yan et al., 2010), the FACT deterministic tractography algorithm was performed to yield the white matter (WM)‐based structural connectome. Nevertheless, this fiber tracking algorithm might be exposed to the risk of the detection loss (Zhang, Wang, et al., 2011). Deterministic tracking pathway toward cortical regions would be terminated when the angle between the current and the previous path segment exceed 35°, thus potentially erasing a portion of intrinsic anatomical connectome information (Mori & van Zijl, 2002). Due to this practical risk factor, future research could benefit from the probabilistic tractography approach to determine the connectivity as the probe for brain structural connectomes. Second, it is an ongoing debate whether weighting connectivity network could provide more sensitive information to capture the subtle topological dynamics for brain graph relative to the conventional binary network (Rubinov & Sporns, 2010). In the current study, a battery of binarized matrices rather than weighted networks was produced for graph‐theoretical analysis, providing the fairly realistic arithmetical operator to brain connectomes (Rubinov et al., 2009). On the other hand, the weighted network was considered to more directly represent topological information related to the graph, indicating the high‐performance evaluation of network dynamics in weighted profile (Rubinov et al., 2009; Rubinov & Sporns, 2010). As a result, it is still valuable to further explore this issue in the context of weighted networks. Third, with special respect to our exploratory purpose, a rather permissive statistical significant level (p < .05, uncorrected) was set here. Of note, the partial Bonferroni strategy was gradually encouraged to perform for multiple comparison corrections in the graph‐theoretical analysis, which could balance Type I and Type II error comparing to family‐wise Bonferroni correction (de Reus & van den Heuvel, 2014). Aside from this, the pre‐registration for the methodological designs (e.g., statistical model) of the research is increasingly prevalent in the both psychological and brain science to address the potential reproducibility crisis stemming from the multiple comparisons (Lindsay, 2015; Martin & Clarke, 2017). Finally, with the open‐access of partial large‐scale neuroimaging databases, such as Human Connectome Project (HCP, Sotiropoulos et al., 2013) and 1,000 Functional Connectivity Project (FCP), this investigation could benefit from the advances in the cross‐platforms collaboration in the future.

5. CONCLUSION

Our primary findings showed the decline in specific overall brain network dynamics, including small‐world properties (i.e., normalized clustering coefficient, small‐worldness, and local efficiency), modularity regimen and rich‐club organization, were almost linked to steeper delay discounting in intertemporal decision‐making. These outcomes thus indicated this notion that the differences in one's sophisticated intertemporal decision‐making might be characterized by the altered global and local parallel communication capacity concerning widespread high‐level cognitive function. Furthermore, we also ascertained the significant association between the structural–functional connectivity coupling and one's devaluing trends, suggesting the potential influence of cross‐modalities communicative pattern on one's complex cognitive‐directed discounting behavior, with decoupling of SC–FC interaction for steeper temporal discounting. To the best of our knowledge, the current exploratory study obtained the first evidence linking the altered overall organization of both structural and functional connectomes to one's discounting function in intertemporal decision‐making. Ultimately, such a comprehensive framework for the whole‐brain overall organization could substantially extend our understanding on the neurobiological underpinnings of intertemporal decision‐making, shedding light on the novel topological biomarker for such behavior.

CONFLICT OF INTEREST

All the co‐authors declare that they have no conflict of interest.

Supporting information

Appendix S1: Supporting Information

Chen Z, Hu X, Chen Q, Feng T. Altered structural and functional brain network overall organization predict human intertemporal decision‐making. Hum Brain Mapp. 2019;40:306–328. 10.1002/hbm.24374