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. 2018 Aug 16;39(12):4949–4961. doi: 10.1002/hbm.24336

Sustained versus instantaneous connectivity differentiates cognitive functions of processing speed and episodic memory

Jace B King 1,2,✉, Jeffrey S Anderson 1,2,3
PMCID: PMC6218279  NIHMSID: NIHMS992245  PMID: 30113114

Abstract

Synchrony of brain activity over time describes the functional connectivity between brain regions but does not address the temporal component of this relationship. We propose a complementary method of analysis by introducing the width of cross‐correlation curves between functional MRI (fMRI) time series as a metric of the relative duration of synchronous activity between brain regions, or “sustained connectivity”. Using resting‐state fMRI, cognitive, and demographics data from 1,003 subjects included in the Human Connectome Project, we find that sustained connectivity is a reproducible trait in individuals, heritable, more transient in females, and shows changes with age in early adulthood. Sustained connectivity in sensory brain regions is specifically associated with differences in processing speed across subjects, particularly in men. In contrast, traditional functional connectivity was correlated with a measure of episodic memory, but not with processing speed. Individual differences in hemodynamic response function (HRF) are closely approximated by sustained connectivity and width of the HRF is also correlated with processing speed across individuals, suggesting that variability in hemodynamic response may be influenced by transient versus sustained neural activity rather than simply differences in vascularity and signal transduction. Sustained connectivity may provide new opportunities to study brain dynamics in clinical populations.

Keywords: fMRI, human connectome project, processing speed, resting‐state, sustained connectivity

1. INTRODUCTION

Functional connectivity, a computational technique derived from resting‐state functional magnetic resonance imaging (fMRI) data, measures synchrony of intrinsic activity between brain regions. This metric is commonly used to investigate architectural, cognitive, behavioral, and clinical properties of brain function. However, traditional functional connectivity (fcMRI) measures synchrony between brain regions averaged over an extended period of time, and the duration of connectivity between brain regions is not captured. The majority of fMRI analysis methods that do incorporate a temporal component either attempt to elucidate the directionality of the relationship between brain regions, effective connectivity, or measure changes in connectivity over time, such as with sliding window and other dynamical connectivity approaches. None of these methods directly assess the duration of functional connections.

Several methods aim to describe effective connectivity for fMRI data, including Granger causality (Goebel, Roebroeck, Kim, & Formisano, 2003), structural equation modeling (McIntosh & Gonzalez‐Lima, 1994), Patel's conditional dependence (Patel, Bowman, & Rilling, 2006), and dynamic causal modeling (Friston, Harrison, & Penny, 2003). Granger causality uses vector autoregressive modeling to estimate directed interactions between brain regions (Wu, Liao, Stramaglia, Chen, & Marinazzo, 2013; Goebel et al., 2003). Time‐series data from a set of brain regions are time shifted and examined for their relationship such that if past time points from two brain regions allow for a better prediction of future time points from that of only one region than predictions made using the past time point from that one region alone, the cooperating brain region is said to have a Granger causal relationship. However, this method is confounded when applied to fMRI data by the regional variability of the hemodynamic response (Schippers, Renken, & Keysers, 2011) as well as brain vasculature (Webb, Ferguson, Nielsen, & Anderson, 2013). Structural equation modeling examines causal relationships between multiple variables by utilizing the covariance structure in fMRI data to provide estimates of path directions and coefficients (McIntosh & Gonzalez‐Lima, 1994). Patel's pairwise conditional activation probability provides hierarchical functional brain networks by considering the joint activation probabilities of A given B, and B given A, with probability ascendency being interpreted as representing causality (Patel et al., 2006). Dynamic causal modeling is an fMRI data analysis method used to estimate the directional strength of edges incorporated into a node‐based network model of neural activity thereby inferring the causal architecture of dynamical systems (Friston et al., 2003; Friston, Kahan, Biswal, & Razi, 2014).

Dynamical functional connectivity methods investigate how the strength of functional connections between brain regions change over time (Calhoun, Miller, Pearlson, & Adali, 2014; Hutchison et al., 2013; Preti, Bolton, & Van De Ville, 2017). One popular class of methods for estimating this change uses a sliding window approach (Allen et al., 2014; Chang & Glover, 2010; Jones et al., 2012; Sakoglu et al., 2010). This analysis technique partitions fMRI time series into sections, or windows, and functional connectivity strength is calculated separately for each window across brain regions. Despite the popularity of this approach, windowed analyses are estimated from short time series resulting in decreased accuracy of individual measurements (Hindriks et al., 2016), although this may create a richer sample of connectivity measurements from which patterns may be estimated in brain networks using component analysis techniques (Leonardi et al., 2013). Windowed analysis has been proposed as a method to elucidate quasi‐stable cognitive states (Gonzalez‐Castillo et al., 2015). An alternate approach using multiplication of temporal derivatives may show greater sensitivity than sliding window approaches to estimate network structure in nonstationary data (Shine et al., 2015).

Dynamical aspects of functional connectivity have also been assessed at the network level by evaluating nonstationary network interactions. One approach has been used to analyze transient coactivation patterns of functional networks (J. E. Chen, Chang, Greicius, & Glover, 2015; Karahanoglu & Van De Ville, 2015). Temporal functional modes have also been described corresponding to independent temporal components (Smith et al., 2012). Mitra and colleagues have proposed using lag‐based information in fMRI time series to study sequences of propagated activity present in the brain that they have termed “lag threads” that also incorporate the temporal dimension of resting‐state fMRI data (Mitra, Snyder, Blazey, & Raichle, 2015; Mitra, Snyder, Hacker, & Raichle, 2014). Extending temporal connectivity analysis to the frequency domain has motivated descriptions of harmonic brain modes that vary by brain network (Atasoy, Deco, Kringelbach, & Pearson, 2017). Another approach has been used to estimate static functional connectivity between regions and perform simulations of dynamical connectivity using in silico models to evaluate dynamical stability of networks, oscillators, meta‐stable states, and temporal patterns of activity (Cabral, Kringelbach, & Deco, 2017; Deco, Jirsa, McIntosh, Sporns, & Kotter, 2009; Deco, Kringelbach, Jirsa, & Ritter, 2017; M. A. Ferguson & Anderson, 2011; Ponce‐Alvarez et al., 2015).

Despite the promise of the previously mentioned analysis methods, there remains a need for intuitive and straightforward analysis methods to assess temporal patterns embedded within resting‐state data. Here we introduce an approach that utilizes the width of cross‐correlation curves between fMRI time series as a metric of the relative duration of synchronous activity between brain regions that we term “sustained connectivity.” This measurement presents an opportunity for new insights in the study of cognition as well as psychopathology in patient groups by providing a simple, complementary metric related to the dynamical relationships of functional brain connectivity. To validate sustained connectivity, we present findings using resting‐state data from typically developing individuals included in the Human Connectome Project (HCP) to test the hypothesis that duration of functional connectivity between pairs of time series can be used to describe distinctive aspects of cognitive function from those described using traditional measures of functional connectivity.

2. METHODS

Data were derived from 1,003 (534 females, mean age = 29.45 ± 3.61 (SD); 469 males, mean age 27.87 ± 3.65) participants from the 1,200 Subjects Data Release of the HCP (Van Essen et al., 2013). For information regarding recruitment, quality control and assurance standards, see Van Essen et al. (2013) and Marcus et al. (2013). All neuroimaging data were acquired with a 3.0 Tesla Siemens Skyra scanner (Siemens, Erlangen Germany) using a 32‐channel head coil. See Ugurbil et al. (2013) for a detailed description of the HCP fMRI acquisition protocols. The current study utilized FIX ICA cleaned blood‐oxygen‐level dependent (BOLD) resting‐state data (Griffanti et al., 2014; Salimi‐Khorshidi et al., 2014; Smith et al., 2013) acquired over four 15‐min multiband BOLD resting‐state scans over 2 days. Only subjects who fully completed all four resting‐state scans are included in this analysis.

Resting‐state functional MRI data were analyzed using both network level and finer‐grained brain parcellation schemes. Time series from each of four resting‐state scans, containing 1,180 volumes, were averaged after excluding the first 20 volumes of each run. Time series from each of the 17 distributed brain networks included in the cortical parcellation of Yeo et al. (2011) were extracted for analysis with each network treated as a single region of interest (ROI). These 17 networks describe functional connectivity organization, labeled for convenience as follows: (1) Central visual; (2) Peripheral visual; (3) Dorsal somatomotor; (4) Ventral somatomotor; (5) Posterior dorsal attention; (6) Somatomotor association; (7) Posterior ventral attention; (8) Anterior ventral attention; (9) Medial temporal–limbic; (10) Orbitofrontal–limbic; (11) Medial superior parietal; (12) Medial frontoparietal; (13) Lateral frontoparietal; (14) Lateral temporal–default mode network (DMN); (15) Ventral–DMN; (16) Dorsal–DMN; and (17) Lateral–DMN.

A finer parcellation was also analyzed that consisted of 333 regions in the cerebral cortex (Gordon et al., 2016), 14 subject‐specific subcortical regions from FreeSurfer derived segmentation (Fischl et al., 2002) (bilateral thalamus, caudate, putamen, amygdala, hippocampus, pallidum, and nucleus accumbens), and 14 bilateral cerebellar representations of a 7‐network parcellation (Buckner, Krienen, Castellanos, Diaz, & Yeo, 2011). This combined parcellation scheme incorporates major cortical, subcortical, and cerebellar gray matter ROIs numbering 361 regions in total (M.A. Ferguson, Anderson, & Spreng, 2017; Shah, Cramer, Ferguson, Birn, & Anderson, 2016).

A matrix consisting of correlation coefficients representing functional connectivity for 17 × 17 networks or 361 × 361 ROIs was averaged for each subject across the four runs for that subject. In addition to the FIX ICA cleaning procedure already performed on the BOLD time series, a general linear regression analysis was performed on each of the 17 networks and each ROI's time series in which 12 detrended head motion time series, obtained from the minimally preprocessed data release for the same subjects, were used as regressors. Volumes before and after mean head motion greater than 0.2 mm were censored from the data after the residuals were linearly detrended. The remaining time series were then concatenated (Power, Barnes, Snyder, Schlaggar, & Petersen, 2012). Analyses were conducted in the Matlab computing environment (MathWorks, Natick, Massachusetts) and SPSS software (version 23) for Mac OS X was used for additional statistical analyses. Multiple comparison corrections were completed for all data included in the results section as described. Brain images included in figures were created using BrainNet Viewer (Xia, Wang, & He, 2013). This software is freely available on the NITRC website (http://www.nitrc.org/projects/bnv/). For display purposes, a smoothed gray matter mask was used and each gray matter voxel was assigned to one of the 333 regions based on nearest proximity.

In order to calculate sustained connectivity MRI (scMRI) values, cross‐correlation curves were calculated for each of four scans in each individual subject between pairs of time series for each of the 17 networks and 361 ROIs using the resting‐state acquisition repetition time (TR = 720 ms) as lag values (see Figure 1). Data points from volumes before and after volumes with a mean head motion value of ≥ 0.2 mm were treated as missing data in scMRI calculations analogous to volume censoring or scrubbing in traditional functional connectivity analysis.

Figure 1.

Figure 1

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Traditional functional connectivity measures the synchrony of intrinsic activity between region pairs. Sustained connectivity uses the full width at half maximum value of cross correlation curves between time series as a measure of relative duration of synchrony. Examples of “transient” versus a more “sustained” connectivity are depicted by differences in cross‐correlation curve width. Peak values were determined by locating the maximal absolute value of the cross‐correlation curve allowing for peak values to be either positive or negative [Color figure can be viewed at http://wileyonlinelibrary.com]

Cross‐correlation curves were constructed by taking the Pearson correlation coefficient between two time series at each of −8 to +8 lags, such that autocorrelations at zero lag were valued at 1.0. To better characterize the distribution of peak lag positions across the population, we calculated the maximal absolute value of the cross‐correlation curve for the entire data range tested (±8 TR = 5.76 s) and noted the position of the peak for every pair of brain regions in every subject. Only 3% of the peak locations for individual subjects returned values for the peak at the edges of the tested interval (±5.76 s), even when including weakly connected region pairs.

Group averages revealed that the position of the peak was within 1.5 s of zero‐lag for every connection (361 x 361 regions) and was within one second of zero‐lag for the vast majority of connections (see Figure 2). In calculating the location of the peak for individual subject results, we doubled the lag range of the population averages (± 3 s) and selected peak values for individual subject cross‐correlation curves as the maximal absolute value of the cross‐correlation curve between −3 s and + 3 s lag. When averaged across the four scans for each individual, this aligned more than 97% of the time with the location of the peak lag using the full lag range of −5.76 to +5.76 s.

Figure 2.

Figure 2

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(a) Peak locations in relation to lag value overlaid across the cortex. (b) Representation of peak location across 361 gray matter regions of interest and (c) A 17‐network parcellation [Color figure can be viewed at http://wileyonlinelibrary.com]

For subject‐level results 21.7% of peak values were negative, many of which were weakly negative and associated with relatively unconnected region pairs. When averaged across the entire population, only 2.4% of peak values were negative for the population mean. Interestingly, there were certain brain regions that showed consistently slight positive or slight negative lag compared to other brain regions. These were well described by proximity to either dural venous sinuses (phase delayed time series) or Circle of Willis arterial structures (phase advanced time series), reflecting delays related to movement of blood flow from arteries to veins across the brain in the relative timing of the BOLD signal (Webb et al., 2013).

The resulting cross‐correlation curves were then interpolated using a cubic spline function. The peak of the resulting cross correlation curves is identical to traditional fcMRI if the peak is located at zero lag. In this study, cross‐correlation curves including both peak and width measurements were obtained from motion‐censored data (after scrubbing). Sustained connectivity values were defined as the full width at half maximum (FWHM) value of the cross‐correlation curve (see Figure 1).

In order to establish the relationship between the hemodynamic response function (HRF) and scMRI, a method for estimating HRF offset and width in resting‐state fMRI data (Wu, Liao, Stramaglia, Ding, et al., 2013; Wu & Marinazzo, 2016) for a given voxel, based on various spontaneous point process events, was fitted across all 361 ROIs and 17 network time series.

Behavioral data used in this study contained scores from the 12 cognition domain measures included in the HCP battery of behavioral and individual difference measures—Cognition Domain (WU‐Minn Consortium Human Connectome Project, March 2017). For details related to the development of the cognitive batteries that are included in the HCP, see Barch et al. (2013). A brief description of each measure can be found in the Supporting Information related to this article. Reaction times from the task‐based fMRI data included in the HCP dataset (Barch et al., 2013) were also included in post hoc analyses related to cognition as detailed below. As access to HCP restricted data was necessary for the full scope of analyses conducted in this study, appropriate approval was acquired from HCP administrators. Additionally, approval to access and use restricted data was given by the Institutional Review Board at the University of Utah. No results contain information that could be used to publicly identify any individual included in the HCP dataset.

3. RESULTS

Sustained connectivity uses the width of cross‐correlation curves, extracted from resting‐state fMRI time series between two regions, or the width of the autocorrelation curve from a single region's time series as a relative measure of the duration of connectivity between brain regions. For the purposes of this report, the peak of cross‐correlation curves represents traditional fcMRI (see Figure 1). There were persistent associations between scMRI and fcMRI related to factors known to influence functional MRI signals such as age, sex and head motion (see Supporting Information Figure S1), even after an extensive postprocessing pipeline designed to mitigate head motion and physiological artifacts (Griffanti et al., 2014). Measures of scMRI were less sensitive to effects of head motion compared to fcMRI, whereas scMRI appears to be more variable with age. Both scMRI and fcMRI covary with sex however, all effects appear to differ in their spatial relationship within 17 networks examined (Yeo et al., 2011) as well as within a more granular 361 region gray matter parcellation (Gordon et al., 2014; Lopez‐Larson et al., 2017).

3.1. Sustained connectivity and the hemodynamic response function

Mean scMRI autocorrelation and HRF offset and width, averaged across all 361 and ROIs and 17 networks showed strong positive correlations (r = .743, p ≪ .001; r = .863, p ≪ .001, respectively) (see Figure 3a) as did mean scMRI autocorrelation and HRC offset and width, averaged across all 1,003 subjects (r = .863, p ≪ .001; r = .872, p ≪ .001, respectively) (see Figure 3b). Taken together, the strength of these correlations suggests that scMRI is a simple metric effectively reproducing the information contained within individual and regional variation of the HRF.

Figure 3.

Figure 3

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Comparison of averaged sustained connectivity values and hemodynamic response function offset and width values across 361 gray matter regions of interest and a 17‐network parcellation (a) and across subjects (b)

3.2. Reproducibility of sustained connectivity

In order to confirm that scMRI is a reproducible individualized trait, scMRI autocorrelation values from the 17‐network parcellation were compared between resting‐state acquisitions (two aggregate 30‐min scans). Sustained connectivity values were found to be significantly correlated between scans suggesting scMRI is highly reproducible (see Figure 4). This significant reproducibility of scMRI extended to the finer parcellation of 361 cortical and subcortical ROIs. An image of the reproducibility as measured by intra‐class correlation coefficient for four scans and 1,003 subjects across the cortex is shown in Figure 4a, calculated using AFNI's 3dLME, which uses a restricted maximum likelihood algorithm to estimate the intra‐class correlation coefficient using a Bayesian approach with Gamma priors in order to avoid negative ICC values (G. Chen et al., 2018; Zuo et al., 2013). Reproducibility was excellent (0.75–1) for 261 of 361 gray matter regions and good (0.6–0.74) for an additional 49 regions (Cicchetti, 1994), with higher reproducibility within networks and across sensory and motor cortex. Areas of lower reproducibility were found in the orbitofrontal and anterior temporal cortex, regions known to exhibit higher susceptibility artifact on functional MRI images.

Figure 4.

Figure 4

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(a) Intra‐class correlation coefficients for mean sustained connectivity autocorrelation values between resting‐state scans overlaid across the cortex. (b) Representation of intra‐class correlation coefficient across 361 gray matter regions of interest and (c) A 17‐network parcellation [Color figure can be viewed at http://wileyonlinelibrary.com]

3.3. Heritability of sustained connectivity

In order to establish whether scMRI is a heritable trait, heritability estimates were calculated across the 17 networks and 361 ROIs for 120 monozygotic and 64 dizygotic twin pairs included in the larger dataset. Only subjects with confirmation of zygosity by genotyping were included in this analysis. Heritability was estimated using Falconer's formula [h 2 = 2*(r MZ ‐ r DZ)] which estimates trait heritability of based on the difference between monozygotic and dizygotic twin correlations (Falconer, 1960). This heritability estimate takes into account additive genetic effects as well as effects related to common environment.

Distribution of the estimated heritability of scMRI across the cortex can be found in Figure 5a. No significant differences in magnitude were found between heritability estimates for fcMRI and scMRI averaged across the 17 networks (scMRI mean: 42.36% ±5.0% (SD); fcMRI mean: 39.7% ±7.6%; t(32) = .85, p = .40). However, divergent patterns of heritability were found between scMRI and fcMRI such that increased heritability was more concentrated in sensory networks in fcMRI compared to scMRI, which demonstrated highest heritability in default mode, frontoparietal, and dorsal and ventral attention networks (see Figure 5). Common environmental influence estimates were also calculated across the 17 networks using Falconer's formula [c 2 = (2*r DZ) – r MZ]. Significantly increased common environmental influence estimates were found for fcMRI compared to scMRI (scMRI mean: −6.0% ±4.4%(SD); fcMRI mean: 2.0% ±4.9%; t(32) = −2.75, p = .01). However, caution should be used in interpreting these values as a negative c2 value suggests that the assumption of equal environments may be violated in this sample.

Figure 5.

Figure 5

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(a) Heritability estimates for sustained connectivity for gray matter regions of interest overlaid across the cortex. (b) Heritability (h 2) and common environmental influence (c 2) estimates for sustained connectivity and (c) Peak connectivity values for the 17‐network parcellation. (d) Comparison of sustained connectivity and traditional functional connectivity across the 17‐network parcellation for heritability (h 2) and common environmental influence (c 2) [Color figure can be viewed at http://wileyonlinelibrary.com]

3.4. Sustained connectivity and cognition

Of the 12 cognitive domain measures included in the HCP battery of behavioral and individual difference measures—Cognition Domain, only the measure of processing speed passed multiple comparison correction for a significant correlation with scMRI in the 17‐network parcellation. All comparisons to cognitive domain measures included age, Sex and mean head motion as subject‐level covariates using a general linear model. The NIH Toolbox Pattern Comparison Processing Speed Test (Carlozzi, Tulsky, Kail, & Beaumont, 2013) was used to assess processing speed. This assessment requires participants to determine whether or not two pictures, presented side‐by‐side, differ in appearance. The number of correct responses is recorded over a period of 90 s. A significant negative correlation was found between processing speed and scMRI within the visual association, attention, parietal, lateral frontoparietal, and dorsal default mode networks. The finer 361 ROI parcellation of scMRI also demonstrated significant, corrected, widespread relationships with processing speed suggesting individuals with faster processing speed have decreased scMRI (see Figure 6).

Figure 6.

Figure 6

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(a) T‐statistic between sustained connectivity versus processing speed for gray matter ROIs overlaid across the cortex. (b) T‐statistic values for sustained connectivity between pairs of 361 gray matter ROIs and (c) A 17‐network parcellation and processing speed. (d) T‐statistic for functional connectivity (peak) versus episodic memory for gray matter ROIs overlaid across the cortex. (e) T‐statistic values for traditional functional connectivity (peak) between pairs of 361 gray matter ROIs and (f) 17‐networks versus episodic memory. Only values meeting multiple comparison correction (pFDR < 0.05) are included. Seventeen networks: (1) central visual; (2) peripheral visual; (3) dorsal somatomotor; (4) ventral somatomotor; (5) posterior dorsal attention; (6) Somatomotor association; (7) posterior ventral attention; (8) anterior ventral attention; (9) medial temporal–limbic; (10) orbitofrontal–limbic; (11) medial superior parietal; (12) medial frontoparietal; (13) lateral frontoparietal; (14) lateral temporal–default mode network (DMN); (15) ventral–DMN; (16) dorsal–DMN; and (17) lateral ‐ DMN [Color figure can be viewed at http://wileyonlinelibrary.com]

We also calculated the correlation between width and offset of the HRF and processing speed, controlling for effects of age, sex and mean head motion, and found significant positive correlation across subjects (HRF width vs. processing speed: t[998] = −3.06; p = .002; HRF offset vs. processing speed: t[998] = −3.87; p = .0001). Post hoc analyses were then conducted using reaction times extracted from six of seven task‐based fMRI scans from which this performance variable was available. Reaction times within each task were significantly correlated with each other for all six tasks (see Supporting Information Figure S2). Average reaction times within tasks were then compared with all 12 of the cognitive domain measures. Reaction times for all six tasks were negatively correlated with processing speed score (see Supporting Information Figure S3). Reaction times for two of the six tasks demonstrated widespread correlations with scMRI (see Supporting Information Figures S4 and S5) providing independent confirmation of the relationship between scMRI and processing speed.

Processing speed was not significantly correlated with fcMRI for any network or region pairs after multiple comparison correction; however, a positive relationship was found between fcMRI and episodic memory in peripheral visual, posterior ventral attention, medial temporal, lateral temporal default mode, and ventral default mode networks as well sensory regions across the cortex (see Figure 6). No other cognitive domain measures showed significant correlation to fcMRI measurements after multiple comparison correction. Episodic memory was assessed using the NIH Toolbox Picture Sequence Memory task (Dikmen et al., 2014), in which participants are asked to recall the sequence of a series of illustrated objects and activities presented in a set order from two learning trials.

3.5. Sex differences in sustained connectivity

In order to directly compare scMRI between males and females, autocorrelation scMRI values for the 17 networks were included in a general linear model analysis that also accounted for effects of age and mean head motion. A significant increase in scMRI was evident in males compared to females for 16 of the 17 networks (see Table 1). Additionally, when scMRI was averaged across the 361 ROIs into a single global scMRI value, scMRI was significantly increased in males relative to females (F[1,999] = 100.42; p = 1.38e−22) (see Figure 7a). These differences in scMRI between sexes were also independent of height, weight, hematocrit, handedness, blood pressure, and education when included as covariates in a partial correlation analysis.

Table 1.

Sex differences in sustained connectivity (auto‐correlation) values, controlling for age and mean head motion, across a 17‐network parcellation (Yeo et al., 2011)

Male Female
(N = 469) (N = 534)
Network Mean SD Mean SD F p Cohen's d
Central visual 7.12 1.31 6.33 1.33 80.10 1.70e−18 .60
Peripheral visual 6.54 1.41 5.54 1.31 130.14 2.01e−28 .74
Dorsal somatomotor 7.25 1.68 6.09 1.70 106.49 8.59e−24 .69
Ventral somatomotor 6.82 1.53 5.67 1.46 135.58 1.79e−29 .77
Posterior dorsal attention 7.55 1.38 6.61 1.36 105.66 1.26e−23 .69
Somatomotor association 7.65 1.39 6.58 1.40 131.28 1.21e−28 .77
Posterior ventral attention 6.96 1.40 5.88 1.24 145.28 2.48e−31 .82
Anterior ventral attention 6.97 1.39 5.99 1.29 107.24 6.10e−24 .73
Medial temporal–limbic 2.09 1.46 1.57 0.85 36.21 2.48e−09 .44
Orbitofrontal–limbic 1.37 0.78 1.28 0.55 NS NS .13
Medial superior parietal 6.35 1.20 5.75 1.13 56.13 1.49e−13 .52
Medial frontoparietal 7.62 1.33 6.67 1.19 120.72 1.37e−26 .76
Lateral frontoparietal 7.37 1.29 6.60 1.11 85.12 1.63e−19 .64
Lateral temporal–DMN 6.73 1.74 5.42 1.65 127.36 6.94e−28 .77
Ventral–DMN 5.68 1.47 5.19 1.27 24.17 1.03e−06 .36
Dorsal–DMN 7.37 1.23 6.78 1.15 53.21 6.08e−13 .50
Lateral–DMN 7.43 1.37 6.39 1.26 134.53 2.85e−29 .79
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Figure 7.

Figure 7

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General linear model comparing global sustained connectivity, controlling for effects of age and mean head motion, revealed significantly increased sustained connectivity in males relative to females (a). In males, decreasing process speed was significantly correlated with increased sustained connectivity. This relationship was not evident in females (b) [Color figure can be viewed at http://wileyonlinelibrary.com]

In order to evaluate whether sex differences in scMRI might be modulated by sex hormones, the relationship between ovarian cycle and scMRI were explored using self‐reported menstrual history in females relative to their fMRI scans. No trends were found for regularly cycling females in scMRI with respect to days since last menstrual period. Female participants were then grouped into phases of the ovarian cycle based on expected dates. No differences were found between follicular phase (days 1–10), peri‐ovulatory phase (days 13–15) or luteal phase (days 20–26) using a one‐way anova with mean whole‐brain scMRI values (F[2,257] = 1.83; p = .16). Additionally, no differences were found for women with and without current birth control (two‐tailed t‐test: t[369] = .81; p = .42) (see Supporting Information Figure S6). Taken together, these data suggest sex differences are less likely to be due to transient fluctuations in sex hormones, although effects of testosterone were not considered.

As scMRI demonstrated a significant relationship with processing speed, this cognitive measure was also evaluated for differences in relationship to sex. No significant differences were found between males and females in processing speed score; however, when comparing the relationship between processing speed and scMRI autocorrelation values in the 17 networks, males demonstrated a significant negative relationship between processing speed and scMRI in all but the orbitofrontal and medial temporal networks. No significant correlations were found in females. Additionally, when scMRI was averaged across the 361 ROIs into a single global scMRI value, scMRI was negatively correlated with processing speed again only in males relative to females (Males: r = −.136, p = .003; Females: r = −.054, p = .182) suggesting the overall relationship may be influenced largely by male participants (see Figure 7b).

4. DISCUSSION

Sustained connectivity is a straightforward measurement of how long, on average, functional activity or connectivity persists in a region or connection and can be calculated as the width of the cross‐correlation curve of the time series for a connection between two regions or the width of the autocorrelation curve for a single region's time series. This measurement queries not how strongly connected brain regions are, but rather how transient or sustained those connections are. Longer scMRI may represent a more stable connection between brain regions whereas shorter scMRI suggests a more transient connection. Sustained connectivity is closely related to individual differences in hemodynamic response function and is correlated with different aspects of neurophysiology than traditional fcMRI. This study suggests that scMRI is a reproducible trait in individuals, is highly heritable, shows changes with age in early adulthood, and is more transient in females. Sustained connectivity is specifically associated with differences in processing speed across subjects, particularly in males, with more robust associations between processing speed and scMRI in sensory regions.

Sustained connectivity is highly correlated with the HRF implying that differences in duration of functional connections inform the hemodynamic response. The BOLD response is believed to be an indicator of local field potentials (Goense & Logothetis, 2008), and as regional blood flow increases proportionate with neuronal metabolism, neural signaling to blood vessels via astrocytes leads to increases in the production of nitric oxide, which is required for neurovascular coupling (Lee et al., 2010; Petzold & Murthy, 2011). Despite the well characterized relationship between neural activation and changes in cerebral blood flow, factors contributing to differences in temporal aspects of signal transduction are less well understood.

If sustained connectivity can recapitulate individual differences in HRF, which are both correlated with speed of cognitive processing, it seems likely that a significant component of BOLD signal transduction may be related to neural dynamics rather than simply signal transduction through the vasculature. For example, if local cortical microcircuitry results in oscillations or sustained neuronal activity differentially in individuals, this may be observed as a prolongation of the HRF once convolved with other elements in the neurovascular coupling pathway. While scMRI may closely approximate parameters of the HRF for individual brain regions, scMRI is easily and intuitively calculated using existing resting‐state fMRI analysis methods whereas the estimate of HRF in resting‐state data requires a more computationally intense approach. Moreover, scMRI can be applied not only to individual brain regions (using autocorrelation) but also to region pairs or even distributed brain networks more flexibly than can be performed with traditional functional connectivity.

Sustained connectivity captures different aspects of cognitive function than that of fcMRI. In the current study, scMRI was significantly correlated with processing speed in a number of functional networks including sensory, attentional, frontoparietal control, and default networks. Decreased scMRI suggests that the functional link between brain regions is more transient for those individuals or networks. A negative correlation between processing speed and connectivity width suggests that when functional connectivity is more sustained between two regions, processing speed is slower. Intuitively, more transient connectivity may be associated with moving information between brain regions more quickly or with shorter duration of individual connections, an attractive hypothesis for the biophysical basis of individual differences in processing speed. Taken together, these data suggest scMRI may capture cognitive functions that rely on faster information transfer in brain networks or regions.

Whereas our study found no significant relationship between fcMRI and processing speed, other studies have linked the two. For instance, Shaw, Schultz, Sperling, and Hedden (2015) found positive relationships between processing speed and fcMRI in the default network, salience network, and frontoparietal control network. However, their findings were specific to older adults (aged 65–90) and a different fcMRI analysis method was used (template‐based rotation). In a study utilizing spectral decomposition to define overlapping networks in resting‐state fMRI data, processing speed was found to be significantly correlated with scaled eigenvalues throughout the brain (M.A. Ferguson et al., 2017).

Functional connectivity in this cohort was positively correlated with a measure of episodic memory while scMRI was not. Strength of traditional functional connectivity has been linked to performance in episodic memory tasks in aging populations (Fjell et al., 2015; Fjell et al., 2016), bipolar disorder (Oertel‐Knochel et al., 2015), and schizophrenia (Haut et al., 2015). In a study measuring availability of dopamine D2 receptors, caudate‐hippocampal connectivity was associated with D2 receptor availability and episodic memory, but not processing speed (Nyberg et al., 2016). It is possible that while processing speed reflects the speed at which the brain traverses through microstates underlying cognitive tasks associated with different sets of synchronous brain regions, that episodic memory in contrast is more reflected in the strength of connections between cortical regions in which semantic memory information is stored. Further studies are needed to elucidate the ability of scMRI to detect aspects of cognition that may be missed by more established fMRI analysis methods.

Recent emphasis has been placed on evaluating sex differences in terms of a continuum rather than attempting to treat the human brain as either distinctly female or male (Joel et al., 2015). Certainly, biological differences between sexes exist and the literature is rife with studies detailing structural, functional, and cognitive differences between males and females (Ruigrok et al., 2014; Scheinost et al., 2015; van der Linden, Dunkel, & Madison, 2017). The purpose of exploring sex differences in the current study initially was to rule sex out as a confounding factor related to scMRI. However, we found substantial differences in scMRI between males and females such that autocorrelation of scMRI values across the 17‐network parcellation was significantly increased in males in all but the orbitofrontal limbic network. These findings suggest sex differences in the extent to which more transient versus sustained connections are employed as a cognitive strategy to achieve faster processing speed. However, when further examining the relationship between scMRI and processing speed, it appeared that the significant relationship was only maintained in males. A number of explanations may account for these differences in cortical functioning between the sexes. No hormonal effects were revealed as measured by of birth control use or ovarian cycle phase. Males and females have been shown to follow differential development trajectory with age related to functional connectivity (Scheinost et al., 2015); however, sex differences related to scMRI were consistent whether age was controlled for or not. It may be possible that these sex differences are related to effects not easily detectable using brain imaging techniques such as training effects or cultural traits that differ by sex. This study found a significant relationship between age and both scMRI and fcMRI. Due to the limited age range of participants included in this study, it is beyond the scope of this investigation to track age related changes in scMRI across the lifespan. In a recent review highlighting life‐span connectomics, it was suggested that such connectomics shift across the lifespan (Zuo et al., 2017), from an ‘anatomically driven’ organization to a more ‘topological’ organization. Future research should investigate age related changes in scMRI in relation to brain development and aging.

Reproducibility of scMRI was excellent for both the coarse and finer parcellations across the cortex with the lowest ICC values expressing in the orbitofrontal and anterior temporal cortex. These regions are known to exhibit higher susceptibility artifact and poorer signal quality on functional MRI images (Deichmann, Gottfried, Hutton, & Turner, 2003; Weiskopf, Hutton, Josephs, Turner, & Deichmann, 2007). Lower reproducibility in those regions may partially explain why we see greater effects of age and mean head motion in relation to scMRI. Demonstrable reproducibility of scMRI is in keeping with the excellent reproducibility of traditional fcMRI, which has previously been described (Zuo & Xing, 2014), and may be due in part to the extended resting‐state scan acquisition lengths included in the current study. Reproducibility of traditional fcMRI has been directly tied to length of scan acquisition (Anderson, Ferguson, Lopez‐Larson, & Yurgelun‐Todd, 2011; Shah et al., 2016). For example, in a sample of HCP subjects, Shah et al. (2016) reported that reproducibility for single connections in fcMRI is a linear function of the square root of imaging time for both individual subjects and population estimates.

Functional connectivity network dynamics are influenced by genetics (Yang et al., 2016). As a result, data from systems‐level connectivity analyses may provide phenotypic data for imaging genetics (Meyer‐Lindenberg, 2009). The current study found heritability estimates for scMRI equivalent to those found in fcMRI though the distribution of strong heritability estimates varied between scMRI and fcMRI. Sustained connectivity demonstrated higher heritability estimates in default mode, frontoparietal, and dorsal and ventral attention networks whereas higher heritability estimates in fcMRI were more concentrated in sensory and frontoparietal networks. Heritability of functional networks have been reported in the literature in both resting‐state and task‐based fMRI studies using a variety of heritability estimates (Blokland et al., 2011; Ge, Holmes, Buckner, Smoller, & Sabuncu, 2017; Glahn et al., 2010; Yang et al., 2016). The current study also found increased estimates of common environmental influence in fcMRI compared to scMRI. Future research may help elucidate genetic components that contribute to both fcMRI and scMRI.

Autocorrelation of BOLD data has been studied in the context of task fMRI signal processing. Early studies showed that temporal autocorrelation could be generated by physiological noise and stimulus paradigms (Purdon & Weisskoff, 1998), and removing temporal autocorrelation, or “prewhitening” has been proposed as a postprocessing step for fMRI data analysis (Bullmore et al., 1996; Woolrich, Ripley, Brady, & Smith, 2001). Much of this autocorrelation, from the perspective of brief responses to discrete stimuli, is likely a reflection of neural responses convolved with a slower hemodynamic response, resulting in temporal smoothing by the vasculature of neural activity. Individual and spatial differences in neurovascular coupling have been described (Schippers et al., 2011), and autocorrelation effects have predominantly been treated as a source of noise in the functional imaging literature. However, a previous study evaluating the relationship between autocorrelation of fMRI time series and traditional functional connectivity found that correcting for autocorrelation had little effect on traditional functional connectivity (Arbabshirani et al., 2014). Our results suggest that at least a component of the autocorrelative structure of BOLD signal may be due to differences in neural activity and could be related to cognition.

It is probable that sustained connectivity, similar to traditional functional connectivity, is nonstationary and may dynamically vary throughout the scan, and future methods may apply dynamical approaches to sustained connectivity already tested with traditional functional connectivity. The temporal dynamics of functional connectivity on the order of seconds are subject to the effects of vascularity, and inter‐subject differences in sustained connectivity may reflect contributions of differences in brain perfusion and BOLD signal transduction. Future research into scMRI should attempt to address this by correlating non‐BOLD related brain activation methods, such as MEG and EEG, with scMRI. It may also be possible that scMRI is sensitive to sampling frequency and acquisition technique, limiting comparisons in multisite datasets with variable acquisition parameters. We note that effect sizes are small, both for sex differences as well as differences in processing speed described in this study in relation to individual differences in sustained connectivity, contributing only a portion of the inter‐individual variation. Finally, scMRI, like many MR techniques, may be susceptible to artifact often found in functional MRI images. This may make it more difficult to define weaker connections such as those found in the orbitofrontal and medial temporal networks in this study.

One potential advantage of sustained connectivity is that it can be applied both to individual brain regions as well as to inter‐regional connections. Other methods that provide a single estimate for each brain region include regional homogeneity (Zang, Jiang, Lu, He, & Tian, 2004), fractional amplitude of low frequency fluctuations (Zou et al., 2008), voxel‐mirrored homotopic connectivity (Anderson, Druzgal, et al., 2011; Zuo et al., 2010), seed‐based correlation maps, and graph‐theoretic properties such as modularity or clustering coefficient (Bullmore & Sporns, 2009). These methods allow application of traditional functional imaging clustering approaches and partially mitigate the multiple comparison problems arising from pairwise connectivity metrics.

Sustained connectivity may be a promising new metric for evaluating brain function associated with neurodevelopmental or neuropsychiatric disease, particularly in conditions where prevalence differs with sex or for conditions associated with abnormal processing speed. In one functional imaging study, individuals with Down syndrome exhibited widened autocorrelation of the signal in the dorsal attention network, and this effect was greatest for individuals with the lowest IQ (Anderson et al., 2015). Sustained connectivity may be uniquely situated to provide additional information related to network dysfunction in psychopathology due to its sensitivity to processing speed which has been associated with a variety of psychopathologies (Nigg et al., 2017). Aberrant functional connectivity between and within networks has also been associated with a number of psychopathologies (Anderson, Nielsen, et al., 2011; Fox & Greicius, 2010; Hutchison et al., 2013; Jones et al., 2012; Keilholz, Caballero‐Gaudes, Bandettini, Deco, & Calhoun, 2017; Lopez‐Larson et al., 2017; Mitra, Snyder, Constantino, & Raichle, 2017; Sakoglu et al., 2010). Understanding the temporal dynamics related to dysfunction in resting‐state networks in mental illness may help to further elucidate the pathophysiology of these disorders, and potentially, constrain development of targeted therapies.

5. CONCLUSIONS

We found that decreases in the cross‐correlation curve width of fMRI time series data between regions are associated with increases in processing speed across the cerebellum and cortex and that episodic memory was associated with increased cross correlation peak in corticostriatal and striato‐cerebellar connections. Taken together, these data indicate that slower processing speed may be related to more transient relationships between cortical regions, an increase that may be modulated by sex. We believe that these distinctive aspects of functional connectivity may encode different cognitive domains. Cross correlation curve width, a measure of sustained connectivity, may represent an opportunity for new insights in the study of cognition as well as psychopathology in patient groups by informing about a specific aspect of dynamical functional brain connectivity.

CONFLICT OF INTERESTS

The authors declare no competing interests.

Supporting information

Appendix S1: Supporting Information

Click here for additional data file. (5.3MB, docx)

ACKNOWLEDGMENTS

Data were provided by the Human Connectome Project, WU‐Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. Preparation of this manuscript was made possible by support from the National Institute of Mental Health (R01 MH080826).

King JB, Anderson JS. Sustained versus instantaneous connectivity differentiates cognitive functions of processing speed and episodic memory. Hum Brain Mapp. 2018;39:4949–4961. 10.1002/hbm.24336

Funding information National Institute of Mental Health, Grant/Award Number: R01MH080826; McDonnell Center for Systems Neuroscience; NIH Blueprint for Neuroscience Research, Grant/Award Number: 1U54MH091657; WU‐Minn Consortium, Grant/Award Number: 1U54MH091657

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