Individual Differences in Dynamic Functional Brain Connectivity Across the Human Lifespan
Elizabeth N. Davison, Benjamin O. Turner, Kimberly J. Schlesinger, Michael B. Miller, Scott T. Grafton, Danielle S. Bassett, Jean M. Carlson
IIndividual Differences in Dynamic Functional BrainConnectivity Across the Human Lifespan
Elizabeth N. Davison , Benjamin O. Turner , Kimberly J. Schlesinger , Michael B. Miller , ScottT. Grafton , Danielle S. Bassett , Jean M. Carlson , Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NewJersey, United States of America Department of Psychological and Brain Sciences, University of California, Santa Barbara, SantaBarbara, California, United States of America Department of Physics, University of California, Santa Barbara, Santa Barbara, California, UnitedStates of America Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania, UnitedStates of America Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia,Pennsylvania, United States of America* [email protected]
Abstract
Individual differences in brain functional networks may be related to complex personal identifiers,including health, age, and ability. Understanding and quantifying these differences is a necessaryfirst step towards developing predictive methods derived from network topology. Here, we present amethod to quantify individual differences in brain functional dynamics by applying hypergraphanalysis, a method from dynamic network theory. Using a summary metric derived from thehypergraph formalism—hypergraph cardinality—we investigate individual variations in two separateand complementary data sets. The first data set (“multi-task”) consists of 77 individuals engaging infour consecutive cognitive tasks. We observed that hypergraph cardinality exhibits variation acrossindividuals while remaining consistent within individuals between tasks; moreover, one of thememory tasks evinced a marginally significant correspondence between hypergraph cardinality andage. This finding motivated a similar analysis of the second data set (“age-memory”), in which 95individuals of varying ages performed a memory task with a similar structure to the multi-taskmemory task. With the increased age range in the age-memory data set, the correlation betweenhypergraph cardinality and age correspondence becomes significant. We discuss these results in thecontext of the well-known finding linking age with network structure, and suggest that age-relatedchanges in brain function can be better understood by taking an integrative approach thatincorporates information about the dynamics of functional interactions.
Author Summary
Complex patterns of activity in each individual human brain generates the unique range of thoughtsand behaviors that person experiences. Individual differences in ability, age, state of mind, and othercharacteristics are tied to differences in brain activity, but determination of the exact nature of theserelationships has been limited by the intrinsic complexity of the brain. Here, we apply dynamicnetwork theory to quantify fundamental features of individual neural activity. We representfunctional connections between brain regions as a time varying network, and then identify groups ofthese interactions that exhibit similar behavior over time. The result of this construction is referred1 a r X i v : . [ q - b i o . N C ] J un o as a hypergraph, and each grouping within the hypergraph is called a hyperedge. We find thatthe number of these hyperedges in an individual’s hypergraph is a trait-like metric, with considerablevariation across the population of subjects, but remarkable consistency within each subject as theyperform different tasks. We find a significant correspondence between this metric and the subject’sage, indicating that the dynamics of functional brain activity in older individuals tends to be moredynamically segregated. This new insight into age-related changes in the dynamics of cognitiveprocessing expands our knowledge of the effects of age on brain function and confirms our methodsas promising for quantifying and examining individual differences. Introduction
Functional connectivity (FC) analyses based on fMRI data are effective tools for quantifying andcharacterizing interactions between brain regions. Many approaches borrow methods from the fieldof graph theory, in which FC is used to build graphs that model the brain as a complex network,treating brain regions as nodes and using functional connections (pairs of nodes with significantlyrelated BOLD signal dynamics) to determine the edge structure of the network [1, 2]. Individualdifferences in both underlying FC and the complex network structure resulting from graph theoryapproaches have been investigated for a variety of task states, developmental stages, and clinicaldiagnoses [3–5].Certain characteristics of FC have been found to vary consistently over the course of normalhuman aging. The loss of clear segmentation between neural systems is widely reported: manyintrinsic functional connectivity networks in the brain tend to become less internally coherent withage, and the functional differences between these intrinsic networks generally become lesspronounced [6–8]. These changes are most commonly reported in the default mode network(DMN) [9–15], although they have also been observed in other networks, including those associatedwith higher cognitive functions [9, 11, 14–16]. In addition, inter-network connectivity between theDMN and other regions of the brain has been found to increase, diminishing the ability todiscriminate between networks based on FC [13, 15]. There are some intrinsic functional networks,however, that show no changes or even increased intra-network conectivity with age, such as sensorynetworks [10, 12, 14].The bulk of studies on age-related changes and other individual differences in FC, including thosethat use methods from complex networks and graph theory to represent FC patterns, are performedusing static FC analysis, which represents the similarities of brain region activity (or some othermeasure of concordance) aggregated across an entire data set. Here, we build upon recent advancesin network science to study individual differences in human brain activity and behavior from adynamic network science perspective [17]. Dynamic functional connectivity (DFC) extends FC toexamine how functional organization evolves over time [18, 19], allowing investigation of the changesin FC during the course of a cognitive task or scanning session. Efforts to probe the dynamics offunctional brain networks have revealed that functional structure reconfigures over time in responseto task demands [20–24] and spontaneously at rest [18, 25]. DFC methods have also been used toinform understanding of individual differences related to aging. In particular, dynamic communitystructure was found to vary significantly with age [26] and amplitude of low-frequency fluctuations ofFC (ALFF-FC) was used to show age-dependent changes in the dynamics of interactions betweennetworks [27]. Both studies imply that functional dynamics should be considered when investigatinghow aging affects brain network organization.Here, we use hypergraph analysis to examine individual differences in DFC network structure infMRI data acquired as subjects perform cognitively demanding tasks. Compared to traditionalgraph theoretic techniques, hypergraphs address an existing methodological gap by characterizingnot only activity, but also the co-evolution of activity over time. Hyperedges group connections thatco-vary over both strong and weak interactions, thus enabling a more complete description ofactivity during both rest and cognitive tasks. Hypergraph methods extend standard graph methodsto incorporate information about co-evolution of activity; whereas standard methods operate on the2ode-node connectivity matrix, hypergraph methods operate on the edge-edge connectivity matrix.The particular method we utilize here identifies groups of FC connections with statistically similartemporal profiles and links them into groups called hyperedges [28]. Standard FC characterizesinteractions between pairs of brain regions and can be extended through DFC methods to capturethe dynamics of those interactions. The groups of brain regions that comprise hyperedges are notnecessarily strongly active or strongly interconnected brain regions. Rather, correlations in thedynamic connectivity of these regions are the defining characteristics that determine hyperedgestructure. As a result, hypergraph analysis is able to identify groups of dynamic connections thatchange from strong to weak (or vice versa ) cohesively together over time, providing complementaryinformation to other DFC methods that focus on only the strongest node-node correlations, such asdynamic community detection [26, 29, 30].In previous work, we demonstrated that hyperedges discriminate between diverse task states in agroup-level analysis of an fMRI data set spanning four tasks, which we refer to as the “multi-task”data set [24]. We also observed notable variation in descriptive hypergraph measures acrossindividuals. In this paper, we extend these results by developing and employing hypergraph measuresthat capture individual differences in functional brain dynamics to determine correspondencesbetween dynamics and specific demographic and behavioral measures. In the multi-task data set, wefind that hypergraph cardinality—the number of distinct hyperedges within a subject’shypergraph—exhibits marked variation across individuals. At the same time, we find this measure isconsistent within individuals, across overall hypergraphs and those associated with specific tasks.To elucidate the drivers of this striking variation in hypergraph metrics observed across subjects,we explore systematic relationships between hypergraph cardinality and individual differencemeasures spanning distinct domains such as demographics, cognitive strategy, and personality. Inthe multi-task data set, we find a suggestive relationship between hypergraph cardinality andparticipant age. This relationship is confirmed with an independent analysis of a data set withparticipants who range in age from 18 to 75, which we refer to as the “age-memory” data set. Wereport a strong positive relationship between age and hypergraph cardinality: older participants aresignificantly more likely to have a larger number of distinct hyperedges in their hypergraph. Thisagrees with the widely reported phenomenon of the loss of cohesion within intrinsic functional brainsystems, because an increase in the number of distinct hyperedges linking various brain regionspoints to interconnections between functional groups evolving in time [13, 15]. Thus, the hypergraphmethod agrees with previous descriptions of age-related brain changes, while capturing informationabout dynamics that adds a novel dimension to previous studies. This work further recommends thehypergraph as a useful tool in studying structure in dynamic functional connectivity.
Methods
Ethics Statement
Informed written consent was obtained from each participant prior to experimental sessions for themulti-task and age-memory experiments. All procedures were approved by the University ofCalifornia, Santa Barbara Human Participants Committee.
Background and Multi-Task Methods
Multi-Task Experimental Design
Participants were scanned at rest (task-free) and while engaging in three distinct tasks designed toelicit distinct cognitive functions: an attention-demanding task, a memory task with lexical stimuli,and a memory task with face stimuli. Participants were instructed to lie still and look at a blankscreen for the duration of the rest period. During the attention task, participants were instructed toattend to sequences of images on a screen and detect the presence or absence of a target stimulus indesignated test displays. Prior to the test display, a cue arrow provided probabilistic information on3hether and where the target stimulus might appear. The test display was flashed for approximately50 ms, after which participants chose whether or not the target stimulus had been present. In bothmemory tasks, participants were presented with 180 previously examined stimuli and 180 novelstimuli and were asked to discriminate between the two. The memory tasks also includedprobabilistic cues indicating the probability that the stimulus was novel. For additional experimentaldetails, see [31] and [32].After completing the scans described above, the following individual difference measures wereobtained for study participants: self-reported demographic information, self-reported state of mind(including physical and mental comfort) information, results from the Beck Depression InventoryII [33], tests for cognitive style (Santa Barbara Learning Style Questionnaire [34], Object SpatialImagery Questionnaire [35], The Need for Cognition Questionnaire [36], Verbalizer-VisualizerQuestionnaire [37], Card Rotation and Paper Folding Tests [38]), personality tests (Big FiveInventory [39] BIS/BAS scales [40], and PANAS mood assessment [41]). More individual differencemeasures were also collected, but do not match the individual difference measures collected fromsubjects in the age-memory study.
Image Acquisition and Processing
The MRI data were acquired from 116 participants at the UCSB Brain Imaging Center using aphased array 3T Siemens TIM Trio with a 12 channel head coil. In addition to functional data, athree dimensional high-resolution T1-weighted structural image of the whole brain was obtained foreach participant. Functional MRI data were collected from 116 healthy adult participants over thefour states described above. Due to various sources of attrition, only 77 participants completed thefunctional scan and accompanying survey of detailed in [32]. The sampling period (TR) was 2 s forthe rest and attention tasks and 2.5 s for both memory tasks (TE = 30ms, FA = 90).The functional data is parcellated into regions using a “hybrid” adaptation of themulti-resolution Lausanne2008 atlas registered to MNI space [42] in order to apply the hypergraphanalysis. This 194 region “hybrid” anatomical atlas minimizes variability in region size betweensubjects and brain regions [24].The functional data are preprocessed using FSL [43], AFNI [44] and Matlab [45]. Preprocessingincludes head motion correction with MCFLIRT [46], non-brain removal and spatial smoothing withAFNI 3dAutomask/3dDespike, slice-timing correction with AFNI 3dTshift, and additional motionartifact correction with AFNI 3dDetrend. Additionally, each participant’s time-averaged fMRI imageis aligned to their structural T1 scan using FSL’s FLIRT with boundary-based registration [46, 47].The inverse of this transformation is applied to all participants’ parcellation scales (generated instructural space) and parcellations are down-sampled into functional space with AFNI 3dfractionize.The mean signal across all voxels within a given brain region is calculated to produce a singlerepresentative time series. Time series for each task are concatenated to produce a single time seriesfor each brain region.
Construction of Temporal Networks
For each subject, we construct a dynamic network model of brain function that accounts for changesin connectivity over time. Each of the N = 194 brain regions is a node in the network. The BOLDsignal time series from each brain region is bandpass filtered to obtain data in the 0.06-0.125 Hzfrequency range that contains task-related brain activity [48–51]. This bandpassed time series isthen windowed into one-minute sections. Node-node adjacency matrices of size N × N areconstructed by taking Pearson’s correlations between each pair of the N = 194 nodes in each of thetime windows. Given the lengths of each scan, this windowing yields four rest, 18 attention, 18 wordmemory, and 18 face memory node-node adjacency matrices. The set of node-node adjacencymatrices, one for each windowed section of time, represents the dynamic functional connectivitynetwork; each edge, or pairwise connection between nodes, has an edge weight time series describingits temporal evolution across time windows, as depicted in Figure 1.4 ig 1. Hypergraph construction: Illustration of the method used to identify hyperedges. Edgeweights are computed separately for each time window (A) and joined together to form edge weighttime series (B). Significantly correlated edge time series are cross-linked to form a hyperedge (C).The group of hyperedges for an individual, with singletons removed, forms a hypergraph (D).
Hypergraph Construction
Since hyperedges link edges in this dynamic network that have related temporal profiles, hypergraphstructure is determined from the correlations between time-evolving weights of network edges [28](See Figure 1 for a schematic illustration of hypergraph construction). These are represented in anedge-edge adjacency matrix X , of size E × E , where E = N ( N − / X is given by the Pearson correlationbetween the corresponding pair of edge weight time series in the DFC network. The p -values fromthese correlations are thresholded by a false discovery rate correction, which is more sensitive thanother corrections for multiple comparisons and is thus effective for such neuroimaging networkanalyses [52]. When the correlation between edges i and j is significant ( p < . ξ ij = X ij ,to form the thresholded matrix ξ . All other elements of ξ are set to zero. We binarize thisthresholded matrix and obtain ξ (cid:48) ij , where ξ (cid:48) ij = (cid:40) , if ξ ij (cid:54) = 0;0 , if ξ ij = 0 . (1)Each connected component in the thresholded edge-edge correlation matrix ξ (cid:48) – that is, each setof edges with correlations between any two edges in the set but no significant correlation with edgesin any other set – forms a hyperedge. Taken together, all hyperedges in ξ form a hypergraph. Sincethe edge weight time series are never thresholded and both high and low edge weights are preserved,hypergraphs provide information about edge dynamics without restricting the analysis to strongcorrelations in regional time series.Our results are compared with a null model designed to ensure that hyperedges identified in ouranalysis can be attributed to system dynamics, rather than overall statistical properties of thedata [29]. To destroy temporal correspondences between edges but retain the mean and variance ofeach edge weight time series, the null model randomly reorders each edge time series individuallyand calculates correlations between the reordered edges.Once hypergraphs are identified for each individual in the multi-task data set, hyperedges areclassified according to whether the correlation in a cognitive state (i.e., rest or one of three cognitivetasks) is significant compared to a permutation null model over all states [24]. The hyperedges thatsatisfy these requirements are denoted as task-specific hyperedges, which we combine to formtask-specific hypergraphs. 5 ypergraph Metrics In this analysis, we examine several complementary measures on individual hypergraphs and focuson one method to extract meaningful information from the overall hyperedge distribution.
Hyperedge size:
The size, s ( h ), of a hyperedge h , is defined by s ( h ) = (cid:88) i,j ∈ h ξ (cid:48) i,j , (2)where the sum is over the upper triangular elements of ξ (cid:48) , the binarized edge-edge adjacency matrixdefined above. This is equivalent to the number of edges that are designated as part of thishyperedge. Singletons:
Singletons are hyperedges with s ( h ) = 1, edges with no significant correlation withany other edge in the network. We exclude singletons from the following analyses. Hypergraph cardinality:
The cardinality of an individual hypergraph is the number ofnon-singleton hyperedges present in the hypergraph.
Hyperedge node degree:
The hyperedge degree of a node is the total number of hyperedges thatcontain that node.
Task-specific hyperedges:
Hyperedges that exhibit a significantly higher correlation within oneparticular task are grouped into task-specific sets. The sets are calculated by using a permutationtest to compare the correlation between edge time series for groups of edges in hypereges in a singletask to the same correlation with edge time series data chosen randomly from all tasks. ABonferroni correction for false positives due to multiple comparisons is employed to selecttask-specific hyperedges using the most stringent requirements [53].
Regression Procedure
To investigate possible correlates of variability in individual hypergraph metrics, we perform a seriesof regression analyses. In each analysis, we use the hypergraph metric as the dependent variable andfactors representing individual difference measures from the psychometric tests as the independentvariables.
Behavioral data categorization:
Behavioral and performance data for the multi-task study consistof 231 measures, while there are 115 measures for the age-memory study participants. There are 42individual difference measures common to both studies, which we group into five categories, given inTable 1. These categories are comprised of differing numbers of individual difference measures,which are summarized in Table S1.
Table 1. Information retained for multi-task study:
Categories, number of factors for each,and how much overall variance from the multi-task individual difference data was retained for eachcategory. Each category represents a subset of the 42 individual difference measures and the factorsrepresent a percentage of the variance contained in the category for the multi-task data.
Category Factors Information Retained
Performance 2 91.41%Demographics 2 92.62%State of Mind 3 80.45%Cognitive Factors 4 77.64%Personality 6 77.79%
Singular value decomposition:
Once the individual difference measures have been categorized, wedemean all measures and perform a singular value decomposition (SVD) separately for each category.We choose the minimum number of factors from the SVD for each category that retain at least 75%of the variance across the category of measures from the multi-task study. Results from this processare presented in Table 1. 6 change: The number of factors retained is not constant across categories, so we implement anadapted multivariate hierarchical regression [54, 55] to establish the comparative informativeness ofeach category. To assess the explanatory power of a given category, all factors in that category areheld out for a “control” regression, and the difference in model R between this reduced model andthe full model is denoted as the contribution for that category. This corresponds to repeatedlyperforming a hierarchical regression with each category computed last, which gives a conservativeestimate for the amount of variance attributable to the category [55]. Significance test:
To determine the significance of the regression coefficients, we use the p -valuesfrom t -tests on each multiple regression performed. The Bonferroni procedure for correcting for falsepositives due to multiple comparisons is used to adjust the t -test p -values over all regressionsperformed in this study [53]. We employ the Bonferroni correction for multiple comparisons in allregression analyses because it is the most stringent test for significance. Age-Memory Methods
The majority of the methods are identical to those discussed for the multi-task data set. Below, wepoint out aspects that differ between the two analyses.
Age-Memory Experimental Design
The word memory task in the age-memory study is constructed similarly to the word memory taskin the multi-task data set. In addition to the memory task, participants completed a resting statescan and diffusion-tensor imaging, which we do not analyze further. Participants did not completethe face memory or attention tasks described in the first data set. The BOLD data were acquiredwhile adult participants performed a recognition memory task with probabilistic cues. Prior to thescanning session, the participants studied 153 common English words, which were mixed with 153novel lexical stimuli during the task. Participants were asked to determine whether the stimuli werestudied or unstudied, with font color cues indicating whether the word had a 70% probability or a30% probability of having been previously studied [56].
Image Acquisition and Processing
Functional and structural data were collected from 126 healthy participants engaged in the wordmemory task. All functional data was acquired with a 3T Siemens TIM Trio MRI system with a12-channel head coil. Scans consisted of T2*-weighted single shot gradient echo, echo-planarsequences sensitive to BOLD contrast (TR = 1.6 s; TE = 30 ms; FA = 90) with generalizedautocalibrating partially parallel acquisitions (GRAPPA). In additon to the functional scans,high-resolution anatomical scans were performed for each participant using an MPRAGE sequence(TR = 2.3 s; TE = 2.98 ms; FA = 9; 160 slices; 1.1 mm thickness). Study participants alsounderwent behavioral assessments and psychological testing. Functional data from 31 participantswere excluded due to technical issues, metal screening issues, claustrophobia, attrition, or lack of acomplete individual differences survey. The results presented here are from 95 participants withusable functional and individual difference data.The functional data are preprocessed using FSL [43], AFNI [44], and Matlab [45]. Preprocessingincludes head motion correction (MCFLIRT) [46], non-brain removal (BET) [57], high-pass temporalfiltering ( σ = 50s), spatial smoothing, and grand mean intensity normalization (FEAT) [58]. Eachvoxel’s time series is further denoised using a nuisance regression. The nuisance regression includesregressors for the six motion correction terms returned by MCFLIRT, their temporal derivatives,and the mean signal time series from the cerebrospinal fluid. The denoised data is registered to MNIspace using FLIRT [59, 60]. The T1 scan is first registered to the MNI template (12 df affinetransformation), the functional data are registered with the T1 image (6 df affine transformation,trilinear interpolation), and the transformations are combined. As in the multi-task study, the mean7OLD signal across all voxels within a given brain region is calculated to produce a singlerepresentative time series. Construction of Temporal Networks
Time series are demeaned and concatenated across the three functional runs of the word memorytask to produce a single time series for each brain region. DFC networks are constructed hereanalogously to the multi-task study, with one key difference. In the age-memory analysis, we removea single node-node adjacency matrix (i.e., a single time window) from the beginning and end of eachfunctional run. This is to counteract edge effects from processing and ensure continuity across runs.We address this choice further in the Methodological Considerations section of the SupportingInformation.
Regression Procedure
The regression procedure is similar to the analysis performed on the multi-task data. The individualdifference data is kept in the common format, where only the 42 measures common to both studiesare used and the categories are the same. Furthermore, the R change and significance tests arecalculated as above. Singular value decomposition:
We demean all measures and perform a singular valuedecomposition (SVD) on the combined multi-task and age-memory data separately for each category.This differs from the multi-task analysis, where we only consider the variance retained over themulti-task data. We choose the minimum number of factors from each SVD that retain at least 75%of the variance across both studies. Results from this process are presented in Table 2.
Table 2. Factors common to the mutli-task and age-memory trials:
Categories, number offactors assigned to each, and how much of the overall variance was retained in each category. Eachcategory represents a subset of the 42 individual difference measures and the factors represent apercentage of the variance contained in the category.Category Factors Information RetainedPerformance 1 87.18%Demographics 1 86.14 %State of Mind 3 77.09%Cognitive Factors 3 81.25%Personality 4 78.56%
Results
As mentioned above, the hyperedge method has been applied to the multi-task data set in a previousstudy [24]. Here, we recapitulate the key findings from that investigation and provide results ofexploratory analyses that motivate the followup analyses on the age-memory data set. We thenpresent results from the age-memory analysis.
Summary of Prior Results
A previous study of the multi-task data identified measures that capture significant differences inpopulation-level hypergraph structure across tasks [24]. Furthermore, extensive variation wasobserved in several hypergraph measures, including hypergraph cardinality, across individuals. Theseresults emphasize that hypergraph structure can be used to differentiate between task states andmotivates our investigation of the correspondence between hypergraph structure and individualdifference measures. 8igure 2 depicts the empirical cumulative hyperedge size distributions for all hyperedges foundacross all subjects in the multi-task data set. As a null test, we shuffle the data over time and findno hyperedges of size greater than one. There is a rough power law for the smaller sizes ( s < s = (cid:0) (cid:1) = 18721). The shape of the distribution is due to the consistent hypergraph structureacross individuals; the majority of subjects in this study have a hypergraph composed of one largehyperedge and many small hyperedges. While this characteristic structure is common to mostsubjects in the study, the size of the largest hyperedge varies across individuals. This size is closelyrelated to the hypergraph cardinality, defined as the number of hyperedges in a hypergraph, ameasure which also exhibits large variation. Fig 2. Multi-task cumulative size distribution:
The empirical cumulative distributionfunction of hyperedge sizes for all subjects in the multi-task study. Also shown is a trace for theempirical cumulative distribution functions of hyperedge sizes over all subjects for each of the fourtask-specific hypergraphs.Figure 2 also depicts task-dependent differences in the cumulative size distributions oftask-specific hyperedges. Memory-specific hyperedges tend to be more numerous than those specificto the rest and attention tasks. However, the total number of task-specific hyperedges for any task isat least ten times fewer than the total number of hyperedges. Our strict definition of task specificityincludes only hyperedges specific to a single task and discards those associated with more than onetask. This approach is conservative, and likely leaves some meaningfully task-related hyperedgesunclassified. However, it reduces the complexity of the task-specific results, and provides greaterconfidence that any hyperedges classified as task-specific are indeed providing truly task-driveninformation due to coherence within that task alone, rather than coherence due to an unrelateddriver that is common to several tasks.There are significant differences in the spatial organization of task-specific hyperedges over allindividuals that are visualized in Figure 3. The plots depict task-specific hyperedge degree acrossthe brain for each of the four tasks. In addition to the differences in magnitude between word9emory and the other tasks, the locations of high hyperedge concentration vary with task.
Fig 3. Node degree spatial distribution:
Here, the number of hyperedges at each node over allindividuals in the multi-task study is plotted on the brain. The scale is logarithmic, and highervalues in a region indicate that there are more hyperedges that include the region.These significant differences in hypergraph structure between the tasks confirm that hypergraphstructure varies between task states. However, persistent variability in hypergraph measures acrossindividuals indicates that the hypergraph method reflects innate differences beyond the current taskstate. The work presented here follows this line of inquiry, beginning with an analysis of individualdifferences in the multi-task data set.
Multi-Task Results: Individual Differences
Here, we illustrate and quantify the wide variation in hypergraph measures across individuals in themulti-task data. In brief, we identify a particular measure, hypergraph cardinality, thatdemonstrates large variance across all individuals but is consistent within individuals. Following this,we investigate relationships between the variation in individual difference measures and the variationin hypergraph cardinality. The results from this study are not statistically significant due to thelimited variation in individual difference measures and strict corrections for multiple comparisons.However, we report a marginally significant result relating demographics and word-memoryhyperedge cardinality that motivates further analyses on the age-memory data set.
Individual Variability and Consistency in Hypergraph Metrics
Although our previous study focused on group-level properties of hypergraphs across tasks, notableindividual differences in functional dynamics were also seen [24]. Here, we confirm those preliminaryobservations by investigating the hypergraph cardinality measure and finding that it displaysextreme variations across subjects in the multi-task data set, as shown in panel (A) of Figure 4.These individual variations in hypergraph cardinality span several orders of magnitude.Despite this large variation between participants, hypergraph cardinality follows a consistentpattern within each participant across tasks. Panel (B) of Figure 4 depicts individual measures ofhypergraph cardinality for hyperedges specific to each task, with subjects sorted by rest hypergraphcardinality. Within participants, the task-specific hypergraph cardinality is consistent across taskstates and follows the distribution for rest-specific hyperedges, which further emphasizes theconsistency of hypergraph cardinality within individuals.Consistent hypergraph cardinality within participants over all tasks indicates that there arecharacteristics specific to individuals that drive hypergraph properties, even in designatedtask-specific hypergraphs. These patterns imply the existence of driving influences on hypergraphstructure that are independent of performance on a specific task. To investigate this further, weexamine how individual difference measures from demographic and behavioral data relate tohypergraph cardinality. 10 ig 4. Individual variability:
Hypergraph cardinality for overall hyperedges (A), sorted fromsmallest to largest cardinality. The plot also includes task-specific cardinalities sorted by overallcardinality. Panel (B) depicts the cardinality for task-specific hyperedges, sorted by rest cardinality.The number of hyperedges across tasks is fairly consistent within individuals, in contrast to therange of hyperedge number across individuals.
Drivers of Individual Variability
To investigate possible sources of the large variation in hypergraph cardinality seen above, as well asto quantify the extent of the consistency of hyperedge cardinality across tasks, we perform a series ofmultiple regression analyses on the multi-task data, as described in Methods.First, using the cardinality of task-specific hypergraphs as the dependent variable, we perform aregression analysis for each non-resting task (attention, word memory, and face memory) thatincludes the cardinality of the rest-specific hypergraph and the factors shown in Table 1 asindependent variables. Table 3 gives the R change values and p -values associated with the restpredictor for each task-specific regression. In all three tasks, the rest predictor alone significantlyexplains the variance in task-specific hypergraph cardinality. This confirms and quantifies ourobservation in Figure 4 that hypergraph cardinality is consistent across each individual’stask-specific hypergraphs—i.e., it is trait-like. The individual difference measures used asindependent variables are not significant after the Bonferroni correction for multiple comparisonsover all tests. However, including the rest-specific hypergraph cardinality, which is closely linked tooverall hypergraph cardinality, as an independent variable in the regression accounts for thevariation across individuals that is consistent across tasks.To identify possible drivers of this individual variation, we perform another regression analysis,using the individual difference measures from Table 1 as independent variables and overallhypergraph cardinality as the dependent variable. Figure 5 depicts the R changes from this analysisfor each category of factors. The t -test identifies no factors with significant correspondence tohypergraph cardinality, but we observe that the demographics category has the largest R change.The t -test p -value for one of the factors in the demographics category is < .
05 and is by far thelowest p -value in this stage of the analysis. However, due to our stringent requirements for correctingfor multiple comparisons and the number of tests we performed, this correlation is not statisticallysignificant. The marginally significant demographics factor has a loading of − .
95 for the agemeasure and − .
31 for the years of education measure; the loading for sex and handednessdemographic measures are comparatively negligible, with magnitudes < . able 3. Rest regression R values: R values for the regression between rest-specifichyperedge cardinality and hyperedge cardinality for each of the other three tasks. Attention Word Memory Face Memory R change p -value < . < . < . Fig 5. Multi-task R changes: Normalized R changes with respect to hypergraph cardinalityacross individuals in the multi-task study. R changes are calculated from the regression procedureoutlined in Methods, with five distinct categories common to the multi-task and age-memory studies.The largest normalized R change is from the demographics factor. Summary of Multi-task Results
On the basis of our previous results applying hyperedge analysis to this data set, which hints atsubstantial variability across individuals in hypergraph structure (Figure 2), we carry out severalregression analyses designed to identify individual drivers of this variability. There were two keyresults. The first result is that overall and task-specific hypergraph cardinality show notablevariation between subjects, but remarkable consistency within subjects for all tasks (Figure 4).The second key result from this exploratory analysis is the finding of a marginally significantrelationship between the demographics category and hyperedge cardinality. Limits to theexplanatory power of the multi-task data set may be determined by limited variation in somedemographic measures – particularly the small range (27–45) and variance (19) in subject age, whichpoorly represents the ages observed in the entire population. We thus extend our analysis to acomplementary data set collected on a longer study of the word memory task with participants aged18–75. In the next section, we report the results of our independent analysis of this age-memorydata set, which confirm the relationship between age and hypergraph cardinality suggested by themulti-task results.
Age-Memory Results
To supplement the findings from the multi-task data set, we perform a parallel set of analyses on theage-memory data set. The data set includes participants with ages ranging from 18 to 75, a rangethree times larger than the range of ages in the multi-task study. Furthermore, the age-memorystudy uses an almost identical task to the multi-task word-memory task. In this section, we combinehypergraph results for all participants in the age-memory data set and obtain a distribution of12yperedge size over all participants with similar features to the hyperedge size distribution from theword-memory task of the multi-task data. We then identify and test specific drivers of individualvariation in hypergraph cardinality for the age-memory study participants. We find a strongcorrespondence between age and hypergraph cardinality that confirms the preliminary result fromthe multi-task study.
Hypergraph Statistics
The cumulative size distribution of hyperedges for all individuals in the age-memory study isdepicted in blue in Panel (A) of Figure 6. To compare these age-memory hyperedges with the wordmemory portion of the multi-task study, we identify a new set of hyperedges using only the portionof the multi-task functional time series recorded during the word-memory task for each subject; thedistribution of sizes for these hyperedges are plotted in pink. Note that these new word-memoryhyperedges from the multi-task data are fundamentally different from the “word memory-specific”hyperedges depicted in Figure 2. The “word memory-specific” hyperedges are those hyperedgescomputed over all tasks, but classified to be driven by correlations in the word memory task alone.In contrast, the new word-memory hyperedges in Figure 6 are found by using just the word-memorysubset of the multi-task data, with no further classification applied.The distributions of sizes are similar at smaller size scales, but differ somewhat at larger sizescales. There are many more hyperedges close to the system size in the age-memory task, while theword-memory hyperedges from the multi-task data set tend to be smaller. The length of themulti-task word-memory time series is shorter than the age-memory time series, which maycontribute to this effect [61]. To investigate the size distributions without the effect of full-brainhyperedges, we remove the largest hyperedge from each subject’s hypergraph and plot the resultingdistribution in Panel B of Figure 6. With this adjustment, the distribution of age-memory hyperedgesizes has a striking agreement with the size distribution of hyperedges constructed from themulti-task word memory data. In both distributions, there is power law behavior for small sizes,similar to that observed in Figure 2. Furthermore, the distributions without the largest hyperedgesare almost identical; the power of the fit to multi-task word memory data is − .
21 and the interceptis 7 . × , while the power of the fit to the age-memory data is − .
37 and the intercept is1 . × .We construct a null model, as detailed in the multi-task Methods section, by temporally shufflingthe data and find no hyperedges with size greater than one, indicating that the hyperedges identifiedin the unshuffled data are capturing statistically significant aspects of brain dynamics. In addition,the close correspondence between these two distributions of word-memory hyperedges suggests thatthe analysis captures aspects of brain dynamics that are robust across imaging sessions andpopulations. Fig 6. Comparison of cumulative size distribution:
Panel (A) depicts the cumulativedistribution of hyperedge sizes over all individuals in the age-memory study compared with the sizesof the set of hyperedges constructed from only the word-memory task of the multi-task data set.Panel (B) illustrates the cumulative distribution of sizes for all individuals in both studies with thelargest hyperedge for each individual subject removed. When this is done, the distributions overlapand are well described by a power law with close alignment in slope and magnitude across studies.The inter-subject variability in multi-task hypergraph cardinality spanned several orders ofmagnitude and followed consistent patterns within subjects for differing cognitive states. Wecompare the individual hypergraph cardinality for the age-memory and multi-task word-only studiesin Figure 7. In the age-memory data, hypergraph cardinality ranges from 0 to 1817, which is asimilar range of variability as that observed for the complete overall multi-task data set in Figure 4.There are 79 subjects with nonzero hyperedge cardinality, indicating that significant non-singletonhyperedges are present in less than two thirds of the subjects. For the remaining analyses, we onlyconsider the 79 subjects with nonzero hypergraph cardinality. For the overall hypergraphs,13ypergraph cardinality ranges from 0 to 1832. The maximum hypergraph cardinality for themulti-task word-only data is 1408, which is markedly less than that observed for the age-memorydata and may be a result of the shorter time series for the multi-task word task. The presence ofnear-system size hyperedges, which may also be due to the shorter multi-task word time series,affects hypergraph cardinality by resulting in hypergraphs with cardinality near one.
Fig 7. Sorted hypergraph cardinality:
Increasing hyperedge cardinality for individualmulti-task word-only and age-memory hypergraphs. The variability for both studies is similar to thevariability in multi-task overall hypergraph cardinality, depicted in Panel (A) of Figure 4.
Age-Memory Hypergraph Correspondence With Age
Having confirmed that hypergraph composition is similar for the multi-task word study and theage-memory study, we investigate whether the individual variability in hypergraph cardinality seenin Figure 7 corresponds to individual difference factors for the age-memory study.We perform a multiple regression on the 12 factors distributed across five categories in Table 2.Head motion has been found to induce correlations in FC analyses [62], and a previous study usingthis data found a significant correlation between age and amount of head motion during theexperiment [56]. To ensure that excessive head motion is not contributing to our result in any way,we include head motion (operationalized as the average relative movement as computed byMCFLIRT) as a predictor in this regression.The overall R value for the multiple regression analysis was 0.3452, indicating that thepredictors explain about a third of the variance in the overall data. After a Bonferroni correction formultiple comparisons across all regression studies included in this paper [53], the demographicsfactor is the only significant predictor of hyperedge cardinality. The normalized R changes forhypergraph cardinality can be seen in Figure 8; the demographics factor has the largest normalized R change and the only significant p -value ( < . Fig 8. Age-memory R changes: Normalized R changes with respect to hypergraph cardinalityacross individuals in the age-memory study. The largest normalized R changes are from thedemographics factor and head motion measure. The demographics factor is the only significantpredictor of hypergraph cardinality, which we denote with a bold outline.Much of the variation in the demographics factor (73.5%) is directly attributable to age. Weattempt to isolate the specific relationship between age and hypergraph cardinality by performing aseparate regression. In this regression, hypergraph cardinality is the dependent variable and theindependent variables are age and head motion. The relationship between age and hypergraphcardinality is significant, with the t -test p -value well below the Bonferroni correction over allregression analyses presented in this work, at p < . ρ = 0 .
32, and the p -value for this correlation, p < − , is significant when we use the Bonferroni correction over allanalyses presented in this paper. Discussion
Improving our understanding of the drivers of individual differences in functional brain imaging datacan give insight into the mechanisms that lead to individual behavior. Dynamic FC has been usedover groups to explain changes in the brain attributed to individual differences in learning [30, 49, 63].Hypergraphs in particular have been used to analyze how long-term learning impacts the functionalnetwork structure [30] and how the brain switches between cognitive states [24]. Here, we extendprevious dynamic FC studies that showed common properties of the dynamics at the level of thegroup [24] to investigate the drivers of strong individual variations in certain hypergraph metrics.15 ig 9. Hypergraph cardinality and age:
Scatter plot of hypergraph cardinality as a function ofage for the age-memory data set and word memory task of the multi-task data set. Thecorrespondence between increasing age and larger hypergraph cardinality can be observed.
Disparate Sources of Variability in Hypergraph Structure
As we showed in the Multi-Task Analysis, the hypergraph cardinality varies widely acrossindividuals, but is consistent between task states. Previous work on the multi-task data set foundthat the probability for hypergraphs to appear in a particular network configuration over individualswas significantly different depending on task state [24]. Consistent spatial organization rules for eachtask existed at the level of the group. There were similarities in the spatial arrangement ofhyperedges in the brain for differing tasks, but certain properties were found to vary significantlybetween tasks. Brain areas in the occipital lobe in particular were highly likely to participate in thehypergraph network across individuals and across tasks, likely due to the visual nature of most ofthe cognitive tasks studied.Here, we study hypergraph cardinality, which displays high variability across individuals andconsistency across tasks within individuals (Figure 4). This indicates that hypergraph cardinalityserves as an individual signature of a subject’s brain dynamics. The similarities across subjects inthe spatial distributions of hypergraphs described in [24] capture information orthogonal to theinformation summarized by hypergraph cardinality. For example, there are some individuals forwhom the visual brain regions are linked by many hyperedges, and some for whom those same regionsare linked by relatively few hyperedges, but these regions are more likely than others to be includedin hypergraphs in the majority of subjects. This suggests that, for some subjects, brain regions tendto be more dynamically integrated in general, with co-varying functional relationships across manybrain circuits; in other subjects, connectivity dynamics are more fragmented across the brain.The high degree of variability in hypergraph cardinality across subjects and consistency withinsubjects, combined with the significant differences in spatial hyperedge arrangement across tasks,indicate that hypergraphs are a useful analysis tool for investigating both individual and task-based16ifferences in brain function in a variety of settings. At the same time, hypergraphs can provide aview of dynamic patterns that complements other commonly used DFC methods. For example,many FC methods exclusively investigate the structure of strong correlations in functionaldata [29, 64–66]; hypergraph analysis captures information about both strongly and weaklycorrelated dynamics and how sets of brain regions transition between them [28].Although they are highly informative, many of the hypergraph metrics we study here arerepresentative measures that greatly reduce the complexity of the hypergraph and only reveal asmall part of the information contained in its structure. Further development of methods to utilizemore of the information that hypergraphs provide will allow characterization of the consistency ofparticular hyperedges and dynamic modes, an understanding of which are important for behavior, orinfluenced by demographics or disease. Future work is also needed to further quantify the spatialdifferences in hypergraph arrangement across both individuals and tasks, to clarify the extent ofoverlap between the two types of information, and to determine whether the individual variability incardinality can be mapped to individual spatial differences in hypergraph structure.
Relationship Between Age and Changes in DFC Networks
FC studies have established clear trends associated with aging, including a decrease in connectivitywithin functional networks and an increase in connectivity across different functional networks inresting and task states [15, 67–70]. Many of these studies have considered resting-state FC, becausethe absence of task stimulus provides a simple and reliable setting for comparison betweensubjects [71], although recent studies have successfully used FC networks to study various cognitiveproceses [72]. The default mode network (DMN) and similar resting-state analyses may missfunctional changes evoked by task states; while the DMN FC decreases with age, task-relatedsensorimotor network FC has been shown to increase with age [12, 14]. Similarly, FC in memorytasks shows increased segmentation with age [73]. Extending these analyses to incorporate thedynamics of functional interactions is a necessary step towards quantifying individual changes infunctional brain dynamics associated with age.Several efforts have been made to capture individual age-related differences with methods fromdynamic FC. Dynamic community structure and amplitude of low-frequency fluctuation of FC wereboth found to be strongly correlated with age, illustrating that functional dynamics are closelylinked with aging [26, 27]. In the dynamic community detection analysis, functional communitieswere found to be more fragmented with age, which agrees with the hypergraph cardinality resultpresented here [26]. A multi-scale community detection analysis uncovered similar fragmentationwith age for small scales [74]. Our finding that hypergraph cardinality also increases with age alignswith this result and provides further information based upon its ability to capture higher-orderdynamic patterns across larger ensembles of brain regions. Not only do the functional similarities ofcommunities of brain regions themselves become less distinct as humans age, but the temporalprofiles of these functional similarities also become less integrated across brain regions. Theagreement of this result with known age-related changes in FC [6–8, 13, 15] demonstrates the abilityof hypergraph methods to capture and quantify major brain changes. Moreover, since thehypergraph analysis is not limited to strong correlations, our analysis further suggests that age isrelated not only to the organization of functional activity in groups of brain regions with stronglycoherent activity, but also to the coordination between groups of regions that transition from beingstrongly to weakly correlated over time (or vice versa ).The reported correspondence between age and hypergraph cardinality is significant in theage-memory data set, but our analysis did not include data that could verify this relationship forcognitive tasks other than the word memory task. Although memory is a cognitive ability known todecline with age in many individuals, it is unlikely that the specific task studied in the age-memorydata set drives this result. Rather, the consistency of hypergraph cardinality across tasks seen in themulti-task data set in Figure 4(B) suggests that similar hypergraph cardinalities may be foundduring other tasks in data sets with higher age variability, and that the relationship between age andcardinality is unlikely to depend primarily on the behavioral task. Further investigation is needed to17etermine whether individual differences in hyperedge structure have any significant relationship tobehavioral or cognitive performance on any particular task.
Conclusion
Here, we have shown that the considerable differences in functional connectivity dynamics acrossindividuals are closely linked with age. The hypergraph method is presented as a complex analysistool that captures information about group-level similarities that differ between task states as wellas individual differences that are consistent within individuals, across tasks. Further investigationinto a single hypergraph metric (hypergraph cardinality) that varies across individuals uncovers asignificant relationship between hypergraph cardinality and age. Specifically, there are a greaternumber of hyperedges in older individuals’ hypergraphs, suggesting that there are more small groupsof regions with cohesively evolving dynamics and indicating a loss of coherence across larger,spatially distributed intrinsic functional connectivity networks. This complements widely reportedrelationships between FC and human aging by providing new insight into how FC activity and theco-evolution of FC activity are altered with increasing age, including the loss of large groups ofco-evolving brain regions in older individuals. The correspondence with and extension of classic FCresults to new dynamic regimes, along with the unique capacity of hypergraphs to probe multipledimensions of both strong and weak dynamic variability, show that hypergraph analysis is a valuabletool for understanding age-related changes and other individual differences in dynamic brainfunction.
Supporting Information
The following information is included in this supplementary document to support the claimspresented in the main work:1. A discussion of observed effects of concatenating multiple time series.2. Figure S1 and Figure S2: Cumulative size distributions for several methods for minimizing theeffect of concatenation.3. A discussion of the effect of time series length on hyperedge size distributions for theage-memory data set.4. Tables S1, S2, and S3: Tables of individual difference measures grouped by category for thefull analysis, multi-task data, and age-memory data.5. Figure S3: R changes for the task-specific hypergraph cardinality regression analysis. Methodological Considerations. Edge Effects in Task Concatenation:
In this paper, weinvestigate dynamic functional connectivity changes across multiple cognitive tasks and two separateimaging data sets. In order to capture changes across tasks in the multi-task data set, weconcatenate the time series for all tasks, as in [24]. In our analysis of the age-memory data, weconcatenate time series from three functional runs of the word memory task, and remove timewindows from the ends of the time series of each task to reduce edge effects. Edge effects appear tobe confined to the data points adjacent to the beginning and end of each run, but we remove the full N × N adjacency matrix to ensure we are not including any edge effects in the analysis. Theresulting change in the cumulative size distribution is depicted in Figure S1. With the edge blocksremoved, there are fewer system-size hyperedges and more small hyperedges.Figure S1 includes a comparison with another method for treating edge effects. In this case, thetime series data for each of the three tasks is filtered separately before concatenation. This approachdramatically reduces the number of hyperedges. If filtering is responsible for introducing edge effects18hat drive hyperedges, the number of hyperedges are likely to increase when we employ this method.Instead, only 13 subjects had non-singleton hyperedges. We choose to not analyze these resultsfurther because there are too few subjects with hyperedge data.Two further efforts to understand the effects of concatenating across functional runs on thecumulative size distribution are depicted in Figure S2. In the trial-by-trial analysis, we performedthe hypergraph method separately on each edge time series (10 data points each) for the three trials.Only 30 subjects have significant non-singleton hyperedges in at least one of the three trials and thenumber of large hyperedges is much lower than the original result. This decrease may be a result ofour removal edge effects, but it is likely the shorter task length is driving the difference, as wediscuss in the next Methodological Considerations section. To explicitly investigate the effect on thesize distribution caused by each transition, we also split the time series data into three sets of 18edge time series data points. The first includes the transition between the first and second trials, thelast includes the transition between the second and third trials, and the middle includes bothtransitions. These distributions are also plotted in Figure S2. We see that the overall number ofhyperedges is greater than both the original age-memory hypergraph over all individuals, which isdriven by a decrease in the number of system-size hypergraphs in the 18-split analysis. Thedistributions for all three follow similar patterns, indicating there is not a large discontinuity in thepattern of the distribution when we include both transitions. Fig S1. Edge compensation comparison:
Cumulative size distributions for the originalage-memory data set (with no changes to remove effects of the edges) and two methods for removingpotential effects from the edges. The “edge blocks removed” method is used in all analyses in themain text.
Methodological Considerations. Edge Time Series Length in HypergraphConstruction:
When we construct hypergraphs from the much shorter single task measurementswithin the multi-task data set, the number of large hyperedges is greatly reduced, with fewerhyperedges in the population near the system size (see Panel A of Figure 6). We see a similar effectwhen we compare the distributions seen in Figure S2 for the split data sets. The trial-by-trialhypergraphs contain fewer hyperedges overall and far fewer system-size hyperedges than the 18-splithypergraphs. However, this increase is not driven by inclusion of the transitions alone, since themiddle 18-split hypergraph contains approximately half the number of system-size hyperedges when19 ig S2. Trial separation comparison:
Cumulative size distributions for two different methodsfor separating edge effects. In the trial-by-trial method, hypergraphs are constructed separately foreach trial, while in the 18-split analysis, hypergraphs are constructed from the first, middle, or last18 edge time series data points.compared to the full analysis. Since both hypergraphs are constructed across both transitions, thisindicates that the edge time series length is more influential to population-level hypergraphproperties than concatenation.Further work is needed to elucidate the relationships between hyperedge size and the overalllength and composition of the data set. Additionally, it remains to be determined whether there isan analogue to the scan length proposed for reliable FC estimates [61]; an edge time series lengththat ensures minimal fluctuations in the size distributions for longer scans. However, the very closecorrespondence between small-size hyperedges found during the word memory task in both data setssuggests that these hyperedges are capturing important characteristics of the dynamics within thistask that are robust across imaging sessions and populations.Performance (Word) Demographics Personality Cognitive Factors State of MindCriterion shift score Age PANAS (6) OSIQ-S/O Arrival timeLiberal Dprime Sex Big 5 (5) VVQ-W/P Meal (hours since)Conservative Dprime Education (years) BIS/BAS (4) Need for cognition Hours of sleepOverall Dprime Dominant hand SBCSQ visual Physical/mental comfortSBCSQ verbal Beck Depression InventoryPaper folding Alcohol (Y/N)Card rotation Exercise (Y/N)Smoking (Y/N)Caffeine (Y/N)
Table S1. Common behavioral measures in both data sets:
Categories containing measuresof interest (42). For the state of mind measures, (Y/N) indicates measures where participants wereasked whether they had performed the activity in the past 24 hours.20erformance Demographics Personality Cognitive Factors State of MindAttention CS Military rank EPQ-R (4) Working memory MSW/MSFFace memory CS Vocabulary test PTSD ScoreAttention Dprime PTSD (Y/N)Face memory Dprime Concussion scoreConcussion 5 inventory
Table S2. Additional behavioral measures in multi-task data:
Categories containingmeasures of interest. For the state of mind measures, (Y/N) indicates measures where participantswere asked whether they had performed the activity in the past 24 hours.Performance Demographics Personality Cognitive Factors State of MindHit rates Height Distracted Stressed (Y/N)Failure rates Weight Motivated Days since periodReaction time Contraceptive use Usual hours of sleepChildren (Y/N) Drugs past 48h (Y/N)Number of children MMSE (dementia)
Table S3. Additional behavioral and brain measures in age-memory data:
Categoriescontaining measures of interest. For the state of mind activity measures, yes indicates measureswhere participants were asked whether they had performed the activity in the past 24 hours.Questions about daily, weekly, and monthly amounts of activity, including whether activity in thepast 24 hours were more or less than usual were also recorded for all (Y/N) state of mind activitiesin the age-memory study.
Fig S3. Task-specific multi-task R changes: Normalized R changes with respect totask-specific hypergraph cardinality for each of the four task-specific hypergraphs. Rest-specifichypergraph cardinality is included as an independent variable for the other three tasks and is theonly significant predictor, which is denoted with a bold outline. Acknowledgments
We would like to thank John Bushnell for technical support.21 eferenceseferences