Characterizations of resting-state modulatory interactions in the human brain

Abstract

Functional connectivity between two brain regions, measured using functional MRI (fMRI), has been shown to be modulated by other regions even in a resting state, i.e., without performing specific tasks. We aimed to characterize large-scale modulatory interactions by performing region-of-interest (ROI)-based physiophysiological interaction analysis on resting-state fMRI data. Modulatory interactions were calculated for every possible combination of three ROIs among 160 ROIs sampling the whole brain. Firstly, among all of the significant modulatory interactions, there were considerably more negative than positive effects; i.e., in more cases, an increase of activity in one region was associated with decreased functional connectivity between two other regions. Next, modulatory interactions were categorized as to whether the three ROIs were from one single network module, two modules, or three different modules (defined by a modularity analysis on their functional connectivity). Positive modulatory interactions were more represented than expected in cases in which the three ROIs were from a single module, suggesting an increase within module processing efficiency through positive modulatory interactions. In contrast, negative modulatory interactions were more represented than expected in cases in which the three ROIs were from two modules, suggesting a tendency of between-module segregation through negative modulatory interactions. Regions that were more likely to have modulatory interactions were then identified. The numbers of significant modulatory interactions for different regions were correlated with the regions' connectivity strengths and connection degrees. These results demonstrate whole-brain characteristics of modulatory interactions and may provide guidance for future studies of connectivity dynamics in both resting state and task state.

studies on connectivity between spatially remote brain regions have strengthened our knowledge on brain functions and organizations (Bullmore and Sporns 2009, 2012; Friston 2011; Sporns et al. 2005). Until recently, a majority of the studies investigating brain connectivity focused on the anatomical connections using diffusion-weighted imaging (Hagmann et al. 2008; Jones et al. 1999; Xue et al. 1999) and functional connectivity using functional MRI (fMRI) in a resting state, i.e., without explicit tasks performed (Biswal et al. 1995, 2010; Fox et al. 2005; Greicius et al. 2003). In both cases, it is assumed that the connections are stable and do not vary significantly over short time scales (hours). However, accumulating evidence has suggested functionally meaningful, dynamic connectivity in the resting state (Chang and Glover 2010; Handwerker et al. 2012; Kang et al. 2011; Kiviniemi et al. 2011), and theoretically, the dynamics of resting-state functional connectivity and task-related connectivity changes are one of the key components to understand brain functions better (Friston 2011; Park and Friston 2013).

The dynamics of brain connectivity are currently thought to be driven and manipulated by task demands designed by an experiment (Friston 2011), and therefore, a majority of studies of dynamic connectivity has focused on task-related connectivity differences (Büchel and Friston 1997; Di et al. 2013; McIntosh et al. 1994; Mechelli et al. 2003; Rao et al. 2008; Rissman et al. 2004). However, these modulations, generally considered as a “task,” should be encoded in activities of other brain regions; that is, a region that supports the task may directly modulate the connectivity between other two regions (den Ouden et al. 2010; Stephan et al. 2008; van Schouwenburg et al. 2010). Therefore, it is critical to study directly the modulation of connectivity between two regions by a third region, using models such as physiophysiological interaction (PPI) (Friston et al. 1997) and nonlinear dynamic causal modeling (DCM) (Stephan et al. 2008).

The PPI approach (Friston et al. 1997) applies a linear-regression framework to identify regions in the whole brain that are correlated with an interaction between two predefined regions, which reflects a modulation of connectivity between two regions by a third region (Fig. 1A) (Di and Biswal 2013; Friston et al. 1997). The exploratory nature of PPI analysis is suitable for the current stage of research compared with model-driven methods, such as nonlinear DCM, because the knowledge of connectivity modulation is still quite limited. A few studies have been conducted to investigate modulatory interactions under various task conditions (Asari et al. 2010; Baumgartner et al. 2012; Das et al. 2005; Griffiths et al. 2009; Longe et al. 2009; Menon and Levitin 2005; Tadic et al. 2008; Williams et al. 2006). However, these analyses are limited by defining regions that are only related to their task activations. With the application of PPI analysis on resting-state data, we have demonstrated that the modulation of connectivity by a third region could take place in multiple networks, even in a resting state (Di and Biswal 2013, 2014, 2015). Because the resting state accounts for the preponderance of the brain's energy consumptions (Raichle 2011), it provides a complementary approach to study connectivity modulations. We note that although we have chosen to frame our analysis in terms of PPIs, this characterization could be framed, in general, in terms of high-order correlations, which quantify dependency of a correlation on another variable. Another form of such high-order correlations is termed psychophysiological interaction (also abbreviated as PPI, but throughout this paper, PPI is used for physiophysiological interaction, as defined above), which models the effect of a psychological manipulation on effective connectivity between regions (Friston et al. 1997).

Fig. 1.

Illustrations of the modulatory interaction effect (A) and the 160 regions of interest (ROIs) that were used in the current analysis (B). A: a modulatory interaction characterizes the modulation of connectivity between 2 regions, A and C, by a third region, B. B: in the current analysis, we calculated modulatory interactions among any combinations of 3 regions out of the 160 ROIs that sampled the whole brain. The colors of ROIs represent 6 network modules: red, cerebellar; green, cingulo-opercular; blue, default mode network (DMN); cyan, frontoparietal; violet, occipital; yellow, sensorimotor.

Despite our demonstration of modulatory interactions between regions from the same network (Di and Biswal 2013) and from different networks (Di and Biswal 2014), the characterization of modulatory or state (time)-dependent interactions remains largely unknown. Therefore, the goal of the present study was to characterize modulatory interactions in the resting state across the whole brain. One factor that limits the explorations of whole-brain modulatory interactions is the exponentially increased number of effects and computational workloads, because a modulation of connectivity involves three regions. In the present study, we performed region-of-interest (ROI)-based PPI analysis using 160 ROIs that sampled the whole brain (Fig. 1B) and calculated modulatory interactions among every combination of three regions (two regions and their modulator). An open-access, resting-state fMRI dataset of 123 subjects was analyzed. We calculated statistical properties of modulatory interaction effects and compared them with those of simple correlations between two regions (i.e., functional connectivity). Next, we sought to gain insight of the architecture of modulatory interactions by examining network affiliations of the three regions in significant modulatory interactions. The 160 ROIs were assigned into six networks based on their functional relationships (Fig. 1B) (Dosenbach et al. 2010). Three scenarios were examined: whether the three regions of a significant modulatory interaction were from the same network, two networks, or three different networks. Based on the notion that dynamic connectivity may be important in large-scale, functional integration (Bullmore and Sporns 2012), we predicted that modulatory interactions might, more likely, take place among regions from different networks. Lastly, we studied spatial distributions of significant modulatory effects and identified regions that were more likely to show modulatory interactions.

MATERIALS AND METHODS

Subjects and fMRI data.

We analyzed an open-access, resting-state fMRI dataset from the Nathan Kline Institute/Rockland Sample (http://fcon_1000.projects.nitrc.org/indi/pro/nki.html) (Nooner et al. 2012). This dataset originally contained 207 subjects, ranging from 4 to 85 yr old. We only included the subjects who were >17 yr old. After additionally removing subjects, due to missing files and large head motions [maximum framewise displacement (FD) >2 mm or 2°], the final data included 123 subjects (49 women). The mean age of this sample was 40.8 yr (18–85 yr).

Resting-state fMRI images (260) were scanned for each subject with a repetition time (TR) of 2.5 s. Other imaging parameters were as follows: echo time (TE), 30 ms; flip angle, 80°; voxel size, 3 × 3 × 3 mm³; 38 slices. High-resolution anatomical images were also acquired using the magnetization-prepared rapid acquisition gradient echo sequence. Imaging parameters were as follows: TR, 2.5 s; TE, 3.5 ms; flip angle, 8°; voxel size, 1 × 1 × 1 mm³; 192 slices. More information about this dataset can be found online (http://fcon_1000.projects.nitrc.org/indi/pro/nki.html) and in Nooner et al. (2012).

Image preprocessing.

MRI image processing and PPI analysis were performed using SPM8 software [Statistical Parametric Mapping (SPM); http://www.fil.ion.ucl.ac.uk/spm/] under MATLAB7.7 environment (MathWorks; http://www.mathworks.com/). The first two functional images were discarded for analysis. For each subject, functional images were realigned to the first image to correct head motion effects. The head position (HP) parameters relative to the first image as a function of scan time t are denoted as HP = [hp_x,t, hp_y,t, hp_z,t, hp_α,t, hp_β,t, hp_γ,t], where x, y, and z represent three translation directions, and α, β, and γ represent three rotation directions. FD was calculated in translation and rotation separately using the following equations

$$F{D}_{translation,t}=\sqrt{{\left(h{p}_{x,t}-h{p}_{x,t-1}\right)}^2+{\left(h{p}_{y,t}-h{p}_{y,t-1}\right)}^2+{\left(h{p}_{z,t}-h{p}_{z,t-1}\right)}^2}$$ (1)

$$F{D}_{rotation,t}=\sqrt{{\left(h{p}_{\alpha ,t}-h{p}_{\alpha ,t-1}\right)}^2+{\left(h{p}_{\beta ,t}-h{p}_{\beta ,t-1}\right)}^2+{\left(h{p}_{\gamma ,t}-h{p}_{\gamma ,t-1}\right)}^2}$$ (2)

Imaging data were removed from analysis if the maximum FD in either translation or rotation of a subject exceeded 2 mm or 2°. Then, the functional images were coregistered to the subject's own high-resolution anatomical image. The anatomical images were segmented into gray matter, white matter (WM), cerebrospinal fluid (CSF), and other tissues using the new segment tool in SPM8. The deformation field maps obtained from the new segment step were applied to the functional images to normalize them into standard Montreal Neurological Institute space. The functional images were not smoothed, because the current analysis was ROI based rather than voxel based.

Regions of interest.

We adopted Dosenbach's 160 ROIs (Dosenbach et al. 2010) that covered much of the brain for the current analysis and were defined from a series of meta analyses of functional activations. The ROIs were assigned into six networks by a modularity analysis of resting-state fMRI data, including the cingulo-opercular, frontoparietal, default mode (DMN), sensorimotor, occipital, and cerebellar networks (Fig. 1B) (Dosenbach et al. 2010).

Time series extraction.

To extract ROI time series for further analysis, a general linear model (GLM) was defined for each subject using SPM. The GLM included a dummy condition with an onset at the middle of scan time and a duration of one-half of the scan time (Di and Biswal 2013). In addition, two regressors of the first eigen variate within the WM and CSF masks were included in the GLM model. Lastly, 24 regressors of the autoregressive head motion model were also included (Friston et al. 1996; Yan et al. 2013). The autoregressive head motion model included six rigid body head motion parameters obtained from the realign step, six head motion parameters of one time point before, and their square. A high-pass filter of 1/128 Hz was used to minimize low-frequency scanner drift. After model estimation, the first eigen variate of all of the voxels in an ROI was extracted for the above-mentioned 160 ROIs. The signals of WM and CSF, head motion parameters, and low-frequency drift were all removed when extracting time series.

PPI analysis.

Pair-wise PPI terms were defined using the PPI function in SPM8, resulting in 12,720 PPI effects [160 × (160 − 1)/2]. To calculate a PPI term, two time series were deconvolved with the canonical hemodynamic response function (hrf), resulting in a time series that represented neural activity instead of blood oxygen level-dependent (BOLD) activity (Gitelman et al. 2003). The two time series were demeaned, multiplied, and then convolved with the hrf to result in a PPI prediction at the level of BOLD responses. PPI effects were tested for all other ROIs. Therefore, the total number of tested PPI effects was 12,720 × (160 − 2) = 2,009,760. The linear-regression model was as follows

$$y={\beta }_0+{\beta }_1·x_1+{\beta }_2·x_2+{\beta }_{PPI}·x_{PPI}+\epsilon$$ (3)

Where x₁ and x₂ represented the time series of the two ROIs, and y represented the time series of a tested ROI, which was different from x₁ and x₂. A significant β_PPI value indicates a modulatory interaction effect among the regions x₁, x₂, and y. Note that in this equation, we have ignored the deconvolution procedure (which can usually be omitted if neuronal activity fluctuates slowly).

Statistical analysis.

One sample t-test across subjects was used to test whether a PPI effect was statistically significant. False discovery rate (FDR) was used to correct for a total of 2,009,760 multiple comparisons. Because the total number of PPI effects was large, the application of a multiple comparison correction raised another problem of false negative, reporting only extremely large effects. This may be inappropriate for characterizing overall properties of modulatory interactions. Hence, we applied different thresholds at P < 0.05, P < 0.10, P < 0.15, and P < 0.20 of FDR correction. With the use of these thresholds, we included more true modulatory interactions, whereas we still made sure that the numbers of false-positive effects were at small proportions. In addition, because we observed a majority of negative PPI effects, one speculation was that the large amount of negative PPI effects might be due to the DMN, since regions in the DMN typically showed negative correlations with task-positive regions (Chai et al. 2012; Fox et al. 2005, 2009). Therefore, we additionally excluded the DMN regions and repeated the analyses.

Each modulatory interaction involves three regions. Because the model used to estimate PPI effects was a simple regression model, it is difficult to differentiate which region modulates the connectivity of the other two regions. Therefore, for visualization of the interaction effects, we plotted all significant PPI effects across all three connections among the three regions. Positive and negative modulatory interactions were illustrated separately using BrainNet Viewer (http://www.nitrc.org/projects/bnv/) (Xia et al. 2013). The large number of connections plotted onto the brain still made it difficult to differentiate patterns of modulatory interactions. Therefore, we performed principle component (PC) analysis on significant positive or negative modulatory interaction effects to identify most representative patterns of modulatory interactions. Significant positive and negative effects were analyzed separately. For all significant positive or negative effects at P < 0.10 of FDR correction, β values for each subject were concatenated into one vector, resulting in a number of subjects (n)-by-number of significant effects (m) matrix. The matrix was submitted to PC analysis using MATLAB. The first several PCs were calculated. To visualize them, each PC vector was correlated with the original n-by-m matrix to identify specific modulatory interaction effects that were correlated with that PC (r > 0.4 was used). We used the correlations of PCs on the original matrix but not the principle component coefficients, because the thresholds for the coefficients were difficult to determine.

To identify regions that were more likely to exhibit modulatory interactions, we counted how many times a region revealed significant positive or negative modulatory interactions at the four P thresholds, respectively. At each significant level and positive or negative effects, means and SD of the numbers of significant effects across the 160 ROIs were calculated. Regions that showed a greater number of significant effects than the means + 1 SD were reported. In addition, the numbers of significant modulatory interactions across the 160 ROIs were correlated with the connection strengths and connection degrees of the ROIs using Spearman's rank correlation coefficient. Connectivity strength of an ROI was calculated by taking the average of mean correlation coefficients between this ROI with all other 159 ROIs. Connection degree of an ROI was calculated by counting the number of connections with all other 159 ROIs from the binarized mean correlation matrix thresholded at a 20% sparsity level (i.e., 20% of total connections remaining).

Network affiliations.

Lastly, we tested whether modulatory interactions were more likely to reflect within module functional integrations or between module functional integrations. To do so, we categorize significant PPI effects as three categories: 1) all three ROIs were from the same network module, 2) two ROIs were from the same module, whereas the third ROI was from another module, and 3) all three ROIs were from different modules (see Fig. 3A). Network modules were derived from Donsenbach et al. (2010), which included the cingulo-opercular, frontoparietal, DMN, sensorimotor, occipital, and cerebellar networks (Fig. 1B). The number of significant PPI effects for the three network affiliation categories was calculated for positive and negative PPI effects separately and in the four threshold levels. Expected numbers of significant PPI effects were also calculated from all possible combinations of PPI effects. Statistics (χ²) was used to determine whether an observed pattern of numbers of significant PPI effects in the three categories was different from expected. To rule out the potential influence of DMN regions on network affiliations of negative PPI effects, the same analyses were performed again, excluding all of the DMN regions.

Fig. 3.

Numbers of significant and expected modulatory interactions in 3 different network affiliation conditions. A: the 3 scenarios of network affiliations of 3 regions. B: significant positive effects across the whole brain. C and D: significant negative effects across the whole brain and excluding DMN regions, respectively.

The effects of age and biological sex.

To examine the potential effects of age and biological sex on modulatory interactions, we performed an additional group-level analysis of all PPI effects using a regression model with two variables representing age and biological sex as covariates (mean centered). We checked whether there were any PPI effects that were correlated with subjects' age or sex. Additionally, we compared the group mean effects, after taking into account age and sex, with the results of a simple one-sample t-test to examine the influence of age and sex on group mean effects.

The influence of ROI systems on modulatory interactions.

To test robustness of the current results with respect to spatial sampling, we also used another set of ROIs from Craddock's 200 ROI system (Craddock et al. 2012). Several ROIs that were located in the anterior temporal lobe and at the bottom of prefrontal regions were excluded because of fMRI signal dropout in these regions. In addition, ROIs that were mainly located in the cerebellum were excluded. As a result, 169 ROIs covering the majority part of the cerebral cortex and subcortical structures, such as the thalamus and basal ganglia, were used. The number of ROIs was close to that of Dosenbach et al. (2010) so that multiple comparison corrections were roughly comparable. The 169 ROIs were assigned into five modules based on a modularity analysis of a binarized mean correlation matrix, including the DMN, visual, sensorimotor, cingulo-opercular, and thalamic modules.

The effects of collinearity between the PPI term and main effects.

The ROI time series were demeaned before calculating the interaction term so that in principle, the correlations between the main effects of ROI time series and their interaction should be low. However, due to the large amount of PPI terms examined in the current analysis, there was the possibility that some PPI effects would be correlated with their main effects. To estimate the potential influence of collinearity between an interaction term and main effects, we also calculated the PPI effects without adding the two main effects in the regression model using the following equation

$$y={\beta }_0+{\beta }_{PPI}\cdot x_{PPI}+\epsilon$$ (4)

The resulting β_PPI estimates were compared with those calculated from the full model (Eq. 3).

RESULTS

Histograms of modulatory interactions and simple correlations.

We first computed modulatory interactions for every combination of three ROIs, resulting in 2,009,760 [160 × (160 − 1)/2 × (160 − 2)] effects. The histogram of all group mean modulatory interactions is illustrated in Fig. 2A. The average of the mean group PPI β values was −0.0012 (SD, 0.0056), indicating that the whole distribution of mean modulatory interactions shifted toward the negative direction by 0.22 SD. To rule out the possibility that the large number of negative modulatory interactions was due to negative correlations between the DMN and other task-positive regions, the distributions of mean PPI effects were also calculated after excluding the PPI effects that involved DMN ROIs. The average of the mean modulatory interactions was −0.00082 (SD, 0.0053) after excluding the DMN ROIs, which still shifted toward the negative direction by 0.15 SD. These distributions were in contrast with the distribution of simple mean correlation coefficients (i.e., functional connectivity) across the 160 ROIs (mean, 0.19; SD, 0.11). The whole distribution of correlations shifted toward the positive direction by 1.73 SD (Fig. 2B).

Fig. 2.

Histograms of group mean modulatory interactions and correlations. A and B: distributions of all mean modulatory interactions (A) and correlations (B) across the whole brain and excluding the DMN regions. C and D: distributions of significant modulatory interactions at the 4 significant levels across the whole brain (C) and excluding the DMN regions (D). The 4 significant levels represent critical P values of false discovery rate (FDR) correction. PPI, physiophysiological interaction.

We next calculated distributions of only significant modulatory interaction effects using FDR correction for multiple comparisons. Because the total number of PPI effects was large, the application of a multiple comparison correction raised another problem of false negative, reporting only extremely large effects. This may be inappropriate for characterizing overall properties of modulatory interactions. Hence, we applied different thresholds at P < 0.05, P < 0.10, P < 0.15, and P < 0.20 of FDR correction. The distributions of significant group mean modulatory interactions across the whole brain at different threshold levels are shown in Fig. 2C. It showed clearly that there were more significant negative PPI effects than positive effects at all four threshold levels. This trend was still present when the modulatory interactions that were associated with the DMN were removed (Fig. 2D).

Network affiliations.

To differentiate further the role of positive and negative modulatory interactions, we calculated the numbers of significant effects where the three regions were from the same module, from two modules, or from three different modules (Fig. 3A). The numbers of significant PPI effects in the three network affiliation scenarios at all four thresholds, i.e., FDR P < 0.05, P < 0.10, P < 0.15, and P < 0.20, were significantly different from the expected numbers calculated from all possible PPI effects in the three network affiliation scenarios (χ² test P < 0.05). The patterns were generally consistent across the four significant thresholds. However, due to the small number of significant effects at P < 0.05 of FDR correction, the results at this level showed some variations with those at other levels. Therefore, we presented the results of P < 0.10 of FDR correction in Fig. 3. For positive PPI effects, there were more significant effects than expected in that the three ROIs were from one single module but less significant effects in that the three ROIs were from two different modules than expected (Fig. 3B). In contrast, for negative PPI effects, there were more significant effects than expected in that the three ROIs were from two modules but less significant effects in that the three ROIs were from three different modules (Fig. 3C). The large number of significant negative effects from two modules could be due to generally negative relationships between DMN and task-positive regions. However, the same pattern could still be observed when the DMN regions were excluded from analysis (Fig. 3D).

Spatial distributions of modulatory interactions.

The spatial distributions of positive and negative modulatory interactions at P < 0.10 of FDR correction are shown in Fig. 4. There were 173 significant positive modulatory interactions (Fig. 4A), mainly involving posterior regions of the brain but not prefrontal and anterior temporal lobe regions. The network affiliations of the three regions of significant positive modulatory interactions are also shown in Fig. 4A. The overall pattern was difficult to summarize; however, we observed that a majority of effects involved one region from the cerebellar network, one region from the cingulo-opercular network, and one region from the sensorimotor network. In contrast, there were 1,291 significant negative modulatory interactions (Fig. 3B) that involved regions that were widely distributed across the whole brain. The network affiliations of the three regions of the significant negative modulatory interactions also showed a complex pattern (Fig. 4B). The spatial distributions of modulatory interactions at other thresholds showed similar patterns, with different numbers of significant effects.

Fig. 4.

Spatial distributions of positive (A) and negative (B) modulatory interactions at P < 0.10 of FDR correction. The colors of nodes encode the 6 network modules. The sizes of regions and the thickness of connections reflect the number of significant modulatory interaction effects. Network affiliations of the 3 regions of significant modulatory interactions (right). Each row represents a modulatory interaction effect, with 3 regions involved (3 columns). The colors in the matrices represent the 6 networks modules, which correspond to the node colors on the left.

We next performed PC analysis to identify characteristic modulatory interaction patterns among these significant effects. The first PC of significant positive modulatory interactions explained 11.4% of the total variance. This component was associated with a cluster of modulatory interactions, mainly involving three regions from three different networks of the cerebellar, cingulo-opercular, and sensorimotor networks (Fig. 5A). There were also a small number of effects that involved three regions from three different networks of the cingulo-opercular, occipital, and sensorimotor networks. The remaining several PCs only had a small number of correlated effects without clear patterns and therefore, were not reported. For the negative modulatory interactions, the first two PCs were identified to have clear patterns. The first PC explained 10.6% of the total variance and mainly involved two regions from bilateral sensorimotor regions and a region from widely distributed regions from the cingulo-opercular network or DMN (Fig. 5B). The second PC explained 5.9% of the total variance and mainly involved posterior regions from the occipital network and DMN (Fig. 5C). A large number of these effects involved two regions from the occipital network and one region from the DMN, and the second large number of these effects involved two regions from the DMN and one region from the occipital network.

Fig. 5.

The first principle component (PC) of significant positive modulatory interactions (A) and the first 2 PCs (B and C) of significant negative modulatory interactions at P < 0.10 of FDR correction. The colors of nodes encode the 6 network modules. The sizes of regions and the thickness of connections reflect the number of significant modulatory interaction effects. Network affiliations of the 3 regions of modulatory interactions of the corresponding PCs (right). Each row represents a modulatory interaction effect, with 3 regions involved (3 columns). The colors in the matrices represent the 6 networks modules, which correspond to the node colors on the left.

We next sought to pinpoint the regions that were more likely to show modulatory interactions. Because the regions that showed the greater number of modulatory interaction effects were fairly consistent across different thresholds, we therefore identified regions that had a consistently larger number of significant effects (greater than means + 1 SD) across P < 0.05, P < 0.10, P < 0.15, and P < 0.20 of FDR levels (Fig. 6 and Table 1). Regions that showed a consistent, larger number of positive modulatory interactions could be grouped into four sets based on their module affiliations. The first set consisted of the basal ganglia, thalamus, and middle insula of the cingulo-opercular network. The second set of regions was located in bilateral sensorimotor regions and the supplementary motor area of the sensorimotor network. The third set of regions was located in the medial portion of the cerebellum, and the last region was located in the medial portion of the occipital network. Regions that showed a consistent, greater number of negative modulatory interactions across threshold levels of P < 0.05, P < 0.10, P < 0.15, and P < 0.20 are shown in Fig. 6B and Table 1. Firstly, four regions were located in the bilateral portions of the occipital network. The second set of regions was located in the bilateral portions of the sensorimotor network. We noted that two of these regions also showed more positive modulatory interactions (as highlighted in Table 1). Lastly, one region in the left angular gyrus of the DMN and one region in the right basal ganglia of the cingculo-opercular network also revealed a large number of negative modulatory interactions.

Fig. 6.

Regions that showed a consistent, greater number (greater than means + 1 SD) of modulatory interactions of positive (A) and negative (B) effects across P < 0.05, P < 0.10, P < 0.15, and P < 0.20 of FDR correction. Node colors encode the 6 network modules.

Table 1.

Regions that showed consistently more modulatory interaction effects (greater than means + 1 SD) at P < 0.05, P < 0.10, P < 0.15, and P < 0.20 of false discovery rate correction

Label	x	y	z	Module
Positive Effects
Med cerebellum	1	−66	−24	Cerebellum
Med cerebellum	−16	−64	−21	Cerebellum
Med cerebellum	−11	−72	−14	Cerebellum
Basal ganglia	−20	6	7	Cingulo-opercular
Mid insula	−30	−14	1	Cingulo-opercular
Thalamus	−12	−12	6	Cingulo-opercular
Thalamus	11	−12	6	Cingulo-opercular
Post-occipital	−4	−94	12	Occipital
Parietal	18	−27	62	Sensorimotor
Precentral gyrus	−54	−9	23	Sensorimotor
Precentral gyrus	58	−3	17	Sensorimotor
SMA	0	−1	52	Sensorimotor
Negative Effects
Basal ganglia	14	6	7	Cingulo-opercular
Angular gyrus	−48	−63	35	DMN
Occipital	36	−60	−8	Occipital
Occipital	39	−71	13	Occipital
Occipital	29	−73	29	Occipital
Occipital	−29	−75	28	Occipital
Frontal	53	−3	32	Sensorimotor
Parietal	−47	−12	36	Sensorimotor
Precentral gyrus	−54	−9	23	Sensorimotor
Precentral gyrus	46	−8	24	Sensorimotor
Precentral gyrus	58	−3	17	Sensorimotor

The regions denoted in bold represent those that have more modulatory interaction effects in both positive and negative effects. x, y, and z represent center coordinates of each region of interest in Montreal Neurological Institute space.

Med, medial; Mid, middle; SMA, supplementary motor area; DMN, default mode network.

We next tried to gain insight into why these regions showed a larger number of modulatory interactions than other regions. The numbers of significant modulatory interactions across the 160 ROIs were correlated with connectivity strengths and connection degrees of the ROIs. The connectivity strengths were calculated from the unthresholded continuous mean correlation matrix, and the connection degrees were calculated from the binarized mean correlation matrix thresholded at a sparsity level of 20%. We observed positive linear relationships between the numbers of significant positive or negative modulatory interactions with connectivity strengths or connection degrees, respectively (Fig. 7). These trends can be observed for both positive and negative modulatory interactions and for all four threshold levels.

Fig. 7.

Relationships between the numbers of significant modulatory interactions [square rooted (Sqrt)] and the connectivity strengths (A and C) and connection degrees (B and D) across nodes. Positive (A and B) and negative (C and D) modulatory interactions are presented separately. Numbers of significant modulatory interaction were calculated at P < 0.10 of FDR correction. The lines in the scatter plots indicate linear fits.

The effects of age and biological sex.

No significant effects of age or sex were observed at the liberal threshold of P < 0.20 of FDR correction. In addition, the inclusion of age and sex as covariates had very limited effects on group mean effects. For example, with the use of a threshold of P < 0.10 of FDR correction, 177 significant positive PPI effects and 1,335 significant negative PPI effects were identified. These numbers of significant effects were very close to the numbers when not using age and sex as covariates (173 and 1,291 correspondingly).

The influence of ROI systems on PPI results.

To rule out the possibility that the current results were biased due to spatial sampling, we also used 169 ROIs from Craddock's method (Craddock et al. 2012) (Fig. 8A). The overall distributions of PPI effects (Fig. 8B) and the distributions of significant PPI effects (Fig. 8D) were similar to those observed using Dosenbach's ROI system (Dosenbach et al. 2010). The resulting distributions after excluding DMN ROIs still showed negative bias (Fig. 8E), which was also similar to what was observed using Dosenbach's 160 ROIs.

Fig. 8.

A: ROIs (169) based on a different ROI system of Craddock et al. (2012). With the use of these 169 ROIs, the distributions of all mean modulatory interactions (B) and mean correlations (C) across the whole brain and excluding the DMN regions are demonstrated. Distributions of significant modulatory interactions at 4 significant levels across the whole brain (D) and excluding the DMN regions (E) are demonstrated. The 4 significant levels represent critical P values of FDR correction.

The effects of collinearity between the PPI term and main effects.

To rule out the possibility that the larger number of negative rather than positive modulatory interaction effects was due to the collinearity between the PPI term and main effects, the PPI effects were also calculated from a model with only the PPI effect, without the two main effects. The resulting distribution of β estimates of PPI effects is shown in Fig. 9A, along with the distribution of β estimates calculated from the full model. The distribution was still negatively biased, and the correlation of mean β estimates, with and without main effects, was very high (Spearman's rank correlation ρ = 0.785, P < 0.001; Fig. 9B). We next checked whether the mean β estimates changed signs when using the PPI-only model compared with the full model. We identified significant PPI effects using the full model at different thresholds and found that only a small portion of mean β estimates demonstrated an opposite direction when using the PPI-only model (7.00% at P < 0.05, 4.80% at P < 0.10, 3.51% at P < 0.15, and 2.76% at P < 0.20 of FDR correction). Therefore, collinearity between the PPI term and main effects was unlikely a confounding variable that caused the predominantly large number of negative modulatory interactions.

Fig. 9.

A: distributions of mean modulatory interactions across the whole brain when using a full interaction model and when using an interaction model without main effects. B: scatterplot of mean β estimates of the PPI effects using interaction models with and without main effects.

DISCUSSION

With the application of ROI-based PPI analysis across the whole brain, the current analysis identified large-scale modulatory interactions. The characterizations of modulatory interactions can be summarized as follows. First, there were more negative modulatory interactions in the whole brain than positive modulatory interactions. Second, positive modulatory interactions were more representative in the scenario that the three regions were from a single network module, whereas negative modulatory interactions were more representative in a scenario that the three regions were from two different network modules. Last, the numbers of significant modulatory interactions of different regions were correlated with their connectivity strengths and connection degrees.

Across the whole brain, there were more negative modulatory interactions than positive effects. This trend was still observed when DMN regions were excluded from analysis, when using a different ROI system, and when not including main effects in the interaction model. In addition, the preponderance of negative modulatory interactions was in contrast with simple correlations that had more positive than negative values. Therefore, even though the absolute correlation values are found to be subject to different preprocessing strategies (Chai et al. 2012; Fox et al. 2009; Weissenbacher et al. 2009), the larger number of negative modulatory interactions is not likely introduced due to preprocessing steps. The predominately larger number of negative modulatory interactions than positive effects is reasonable at the whole-brain level, because in a system point of view, negative modulatory interactions, which may serve as negative feedback, ensure that the whole brain as a system is stable.

Further insights of the functions of positive and negative modulatory interactions can be drawn from the analysis of the network affiliations of the three ROIs of significant modulatory interactions. The three ROIs of a modulatory interaction may come from a single network module, two networks, or three different networks. There were more numbers of positive modulatory interactions than expected for the scenario that the three regions of an effect were from the same network; i.e., increased activity of one region was associated with enhanced connectivity of the same network. This suggests that a potential function of positive modulatory interaction is to facilitate within network collaborations. The number of positive modulatory interactions, in which the three regions were from three different networks, was similar to the number expected but still constitutes the largest number of all positive modulatory interactions. This suggests a possible function of modulating large-scale intersystem communications of three systems through positive modulatory interactions. In contrast, negative modulatory interactions were more representative in the scenario that the three ROIs of an effect were from two different networks; that is, increased activity of a region in one network inhibited connectivity between one region in the same network and another region in a different network. This suggests that negative modulatory interactions may serve as a function to facilitate segregations of different modules. These proposed functions of positive and negative modulatory interaction seem in line with the previous notion regarding the functions of positive and negative correlations (Fox et al. 2005), whereas the current analysis focused on higher-order modulations on connectivity but not on single regions.

There were a small number of regions that showed a very large number of significant modulatory interactions with other regions. In the context of recent advances of studies on dynamic connectivity in a resting state (Calhoun et al. 2014; Hutchison et al. 2013), these regions may be responsible for dynamically modulating communications between other brain regions. The modulation of connectivity may be important to understand certain brain regions. For example, the basal ganglia are among the regions that had the highest number of both positive and negative modulatory interactions. Studies of effective connectivity using nonlinear DCM based on fMRI data (den Ouden et al. 2010; van Schouwenburg et al. 2010) have suggested a role of modulation by the basal ganglia on cortical connectivity. Similar to the “hub regions” that generally have a disproportionally higher number of connections with other regions (Buckner et al. 2009; Hagmann et al. 2008), these regions with a higher number of modulatory interactions may play an important role in modulating whole-brain, large-scale communications. Further analysis revealed that the numbers of significant (positive and negative) modulatory interactions with different regions were correlated with the connectivity strengths and connection degrees (number of connections) of these regions, suggesting an overlap between the network hubs and modulating hubs.

The current analysis replicated several findings of our previous studies (Di and Biswal 2013, 2014, 2015). For example, one main finding of our previous studies was the positive modulatory interactions among the salience network, frontoparietal network, and DMN (Di and Biswal 2014). In the current analysis, we indeed found a region in the right inferior frontal gyrus, which was part of the salience network, showing positive modulatory interactions with several regions in the DMN and frontoparietal network. However, these effects were small in number so that they are not easy to be observed among other effects (for example, in Fig. 4A).

One representative cluster of modulatory interactions in the current analysis was positive modulatory interactions among the medial cerebellum, thalamus/basal ganglia, and widely spread regions in the sensorimotor network. The cerebellar regions are mainly located in the left hemisphere and vermis of lobule VI, according to a probabilistic cerebellar atlas (Diedrichsen et al. 2009). Interestingly, these regions are activated during cognitive tasks but not a motor task (Stoodley et al. 2012) and are functionally correlated with the ventral attention network but not the motor network in a resting state (Buckner et al. 2011). The thalamus, on the other hand, is the key region to relay information transmissions between the cerebellum and cortex (Buckner et al. 2011; Yuan et al. 2015). Therefore, it seems that there are no direct functional relationships between the medial cerebellar regions and sensorimotor regions, but their functional relationships are modulated by the thalamus and basal ganglia. The functional implications of such modulatory interactions need further studies.

For negative modulatory interactions, approximately one-half of the significant effects involved regions in the DMN. This seems in line with the observations of simple correlations that the regions in DMN generally revealed negative correlations with task-positive networks (Fox et al. 2005). However, the regions showing negative modulatory interactions with DMN regions are different from the regions that showed negative correlations with DMN regions. The regions in DMN typically showed negative correlations with higher-order association regions of task-positive networks, such as dorsal attention, frontoparietal, and salience networks, but not unimodal regions, such as primary visual and motor regions (Fox et al. 2005). In contrast, the regions in DMN typically showed negative modulatory interactions with unimodal regions, such as bilateral sensorimotor regions (Fig. 5B) and occipital regions (Fig. 5C). This extended our understanding of the relationship between the DMN and other brain regions.

Recent studies have shown that regions in the visual system were dynamically connected to executive regions and DMN regions upon task demands (Chadick and Gazzaley 2011; Karten et al. 2013), which emphasized a modulating role of the DMN on the visual system. The modulatory interaction model may open a new avenue to study the role of DMN in cognitive processes. In addition to visual areas, several regions in the bilateral sensorimotor areas showed negative modulatory interactions with regions in the DMN and other networks. These sensorimotor regions are located in the inferior portion of the sensorimotor network and may be responsible for higher-order somatosensory processing and motor controls. These results suggested a very special role of these regions in dynamic modulations of connectivity. However, it is still largely unknown about the functions of these modulatory interactions.

The current results of modulatory interactions may be considered in the context of neuronal oscillations and cross-frequency coupling. Specifically, the large amount of negative modulatory interactions may imply a link between negative modulatory interaction and alpha band modulation, given its inhibitory role (Palva and Palva 2007; Pfurtscheller et al. 1996). A direct examination of posterior alpha power, measured by EEG modulation on functional connectivity, measured by resting-state fMRI signals, revealed negative modulations of the alpha power on connectivity between primary visual area and other occipital regions (Scheeringa et al. 2012). Interestingly, the posterior alpha power was positively correlated with the BOLD signals in the DMN (Scheeringa et al. 2012). Therefore, these results mirrored the current results of negative modulatory interactions between the DMN regions and posterior occipital regions (Fig. 5C) and suggested possible neurophysiological mechanisms underlying negative modulatory interactions. It is reasonable to speculate that positive and negative modulatory interactions may be associated with neural oscillations in different frequency bands (Bastos et al. 2012; Friston et al. 2015), although it warrants future studies to examine the relationships directly between these two.

Note that the sizes of the PPI regression coefficients are smaller than the main effects of correlations of one region or the other. Unlike the main effects, the effect size encoded by the PPI coefficient is sensitive to the scaling of the data. Therefore, one should not overinterpret the relative sizes of the interaction and main effects. However, the interaction term does have an interesting interpretation. If we substitute the x_PPI variable as the multiplication of variables x₁ and x₂, then Eq. 3 can be rewritten as

$$y={\beta }_0+{\beta }_1\cdot x_1+{\beta }_2\cdot x_2+{\beta }_{PPI}\cdot x_1\cdot x_2+\epsilon$$ (5)

$$y={\beta }_0+\left({\beta }_1+{\beta }_{PPI}\cdot x_2\right)\cdot x_1+{\beta }_2\cdot x_2+\epsilon$$ (6)

We can see that β_PPI plays a sensitive role in the connection from area x₁ to area y that depends on the activity in area x₂. In other words, for a unit increase in area x₂, the linear-directed effective connectivity increases by β_PPI.

The results demonstrated that spontaneous fluctuations of a region could modulate connectivity between two other regions. It is reasonable to assume that similar modulation may take place when the same region is activated by a task instead of fluctuated spontaneously. However, it is still largely unknown regarding the similarities and the extent of differences between modulatory interactions in a resting state and those when performing specific tasks. The PPI analysis, in principle, can be applied to task data with alternating task conditions. However, the differences of modulatory interactions between different task conditions are needed to be considered in this circumstance. Higher-order interaction models have been proposed to study whether the modulatory interaction is modulated by task designs (Stamatakis et al. 2005). However, the higher the order of interaction, the less reliable the interaction term would be. A large sample size may be needed to explore such kinds of higher-order interactions (Gorka et al. 2014).

GRANTS

Support for this research was provided by the National Institute on Aging Grant R01AG032088 and the National Institute on Drug Abuse Grant R01DA038895.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

Author contributions: X.D. and B.B.B. conception and design of research; X.D. performed experiments; X.D. analyzed data; X.D. interpreted results of experiments; X.D. prepared figures; X.D. and B.B.B. drafted manuscript; X.D. and B.B.B. edited and revised manuscript; X.D. and B.B.B. approved final version of manuscript.