Network communication models improve the behavioral and ...Apr 21, 2020 · models. Communication...

Network communication models improve the behavioral and functional predictiveutility of the human structural connectome

Caio Seguin1,∗ Ye Tian1, and Andrew Zalesky1,2

1Melbourne Neuropsychiatry Centre, The University of Melbourne and Melbourne Health, Melbourne, VIC 3010, Australia and2Department of Biomedical Engineering, Melbourne School of Engineering,

The University of Melbourne, Melbourne, VIC 3010, Australia(Dated: April 21, 2020)

The connectome provides a structural substrate facilitating communication between brain re-gions. We aimed to establish whether accounting for polysynaptic communication paths in structuralconnectomes would improve prediction of interindividual variation in behavior as well as increasestructure-function coupling strength. Structural connectomes were mapped for 889 healthy adultsparticipating in the Human Connectome Project. To account for polysynaptic signaling, connec-tomes were transformed into communication matrices for each of 15 different network communicationmodels. Communication matrices were (i) used to perform predictions of five data-driven behavioraldimensions and (ii) correlated to interregional resting-state functional connectivity (FC). While FCwas the most accurate predictor of behavior, network communication models, in particular com-municability and navigation, improved the performance of structural connectomes. Accounting forpolysynaptic communication also significantly strengthened structure-function coupling, with thenavigation and shortest paths models leading to 35-65% increases in association strength with FC.Combining behavioral and functional results into a single ranking of communication models posi-tioned navigation as the top model, suggesting that it may more faithfully recapitulate underlyingneural signaling patterns. We conclude that network communication models augment the functionaland behavioral predictive utility of the human structural connectome and contribute to narrowingthe gap between brain structure and function.

INTRODUCTION

Communication between gray matter regions is cru-cial for brain functioning. The complex topology of thestructural connectome [1, 2] provides the scaffold on topof which neural signaling unfolds. While region pairsthat share a connection in the structural connectomemay communicate directly, polysynaptic paths compris-ing two or more connections are required to establishcommunication between anatomically unconnected re-gions. Network communication models describe strate-gies to delineate putative signaling paths between re-gions, based on aspects of connectome topology and ge-ometry [3].

Several network communication models have been pro-posed to describe large-scale neural signaling, rangingfrom naive random walk processes to optimal routing viashortest paths [4]. By considering polysynaptic paths,these models quantify the putative efficiency of commu-nication between both connected and unconnected nodes,thus enabling a high-order structural description of inter-actions among every pair of regions in the connectome [5].Recent studies report that network communication mod-els can improve the strength of coupling between struc-tural and functional connectivity in the human connec-tome [6], explain established patterns of cortical lateral-ization [7], and infer the directionality of effective con-nectivity from structural connectomes [8].

∗ [email protected]

Building on this previous work, we aimed to investigatethe utility of a range of candidate models of network com-munication in structural brain networks. First, we soughtto determine whether accounting for polysynaptic (multi-hop) paths in structural brain networks using models ofnetwork communication would: i) improve the predic-tion of interindividual variation in behavior, compared topredictions based on direct structural connections alone;and, ii) improve the strength of structure-function cou-pling. Second, we aimed to establish a ranking of com-munication models with respect to their predictive util-ity, with the goal of determining which models may morefaithfully capture biological signaling patterns related tobehavior and FC.

We considered five previously proposed communica-tion measures: (i) shortest paths [9, 10], (ii) naviga-tion [11, 12], (iii) diffusion [13], (iv) search information[6, 14], and (v) communicability [15–17]. Collectively,these models cover a wide-range of neural signaling con-ceptualizations. Shortest paths and navigation determin-istically route information using centralized and decen-tralized strategies, respectively. In contrast, diffusionand search information model communication from thestochastic perspective of random walk processes. Finally,communicability implements a broadcasting model of sig-naling, in which signals are simultaneously propagatedalong multiple network fronts. While all these candidatemodels have been investigated in the human connectome,which particular models provide the most parsimoniousrepresentation of large-scale neural signaling remains un-clear.

Using diffusion-weighted MRI and tractography, we

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mapped structural connectivity (SC) matrices for n =889 healthy adults participating in the Human Connec-tome Project (HCP) [18]. Each individuals SC ma-trix was then transformed into a communication matrix,which represented the efficiency of communication be-tween each pair of regions under a particular candidatemodel of network communication. For each model, com-munication matrices were fed to statistical techniques toperform out-of-sample prediction of individual variationin five behavioral dimensions [19], and also correlatedwith FC matrices mapped using resting-state functionalMRI. This enabled a systematic ranking of network com-munication models in terms of behavior prediction andstructure-function coupling. While these criteria do notconstitute direct biological validation of signaling strate-gies, we hypothesize that the higher the predictive utilityof a communication model, the more likely it is to parsi-moniously recapitulate the signaling mechanisms of thehuman brain.

RESULTS

Brain network communication matrices

Structural connectomes were mapped using white mat-ter tractography applied to diffusion MRI data acquiredfor 889 healthy adults participating in the Human Con-nectome Project [18] (Materials and Methods). We focuson reporting results for connectomes comprising N = 360cortical regions [20] that were thresholded to eliminatepotentially spurious connections [21]. Results for alterna-tive cortical parcellations and connection density thresh-olds are reported in the Supplementary Information.

Connectome mapping yielded a structural connectivity(SC) matrix for each individual. These matrices repre-sented connectivity between directly connected regionsand were generally sparse due to an absence of whitematter tracts between a majority of region pairs. Tomodel the impact of polysynaptic neural signaling, eachindividual’s connectivity matrix was transformed into acommunication matrix (Fig. 1a). Communication matri-ces were of the same dimension as the SC matrices, butfully connected in most cases, and they quantified the effi-ciency of communication between indirectly (polysynap-tic) as well as directly connected pairs of regions undera given network communication model. In contrast, theSC matrices only characterized directly connected pairsof regions.

We considered three connectivity weight definitions:(i) Weighted: connection weights defined as the num-ber of tractography streamline counts between regions;(ii) Binary: non-zero connection weights set to one; and(iii) Distance: non-zero connection weights set to the Eu-clidean distance between regions. Network communica-tion models computed on these connectomes operational-ize metabolic factors conjectured to shape large-scale sig-naling: (i) adoption of high-caliber, high-integrity white

matter projections to enable fast and reliable signal prop-agation (weighted); (ii) reduction of the number of synap-tic crossings (binary); and (iii) reduction of the physicallength traversed by signals (distance).

Predicting behavior with models of connectomecommunication

Statistical models were trained to independently pre-dict five dimensions of behavior (cognition, illicit sub-stance use, tobacco use, personality-emotional traits,mental health) based on features comprising an individ-ual’s communication matrix (Fig. 1b,c). Training andprediction were performed separately for a total of 15communication matrices representing different connec-tion weight definitions (binary, weighted, distance) andnetwork communication models (shortest paths, navi-gation, diffusion, search information, communicability).Additionally, predictions based on an individual’s SC andFC were computed to provide a benchmark. The fivebehavioral components represent orthogonal dimensionsthat were parsed from a comprehensive set of behavioralmeasures using independent component analysis (Mate-rials and Methods).

Out-of-sample prediction accuracy was evaluated for10 repetitions of a 10-fold cross-validation scheme. ThePearson correlation coefficient between the actual andout-of-sample predicted behavior was used to quantifyprediction accuracy for each behavioral dimension. Toensure that our results were not contingent on theadoption of a particular statistical model, predictionswere independently performed using lasso regression [22]and a regression model based on features identified bythe network-based statistic (NBS) [23] (Materials andMethods). Prediction accuracies were averaged acrosscross-validation folds and repetitions, and visualized inthe form of a matrix comprising behavioral dimensions(rows) and communication models (columns) (Fig. 2a,c).

We found that individual variation in some behav-ioral dimensions could be predicted with greater accu-racy than others (lasso: F(4,80) = 10.67, p = 5 × 10−7;

NBS: F(4,80) = 47.18, p = 2 × 10−20). Dimensions char-acterizing cognition (respective lasso and NBS accuraciesaveraged across all predictors: 0.068, 0.101) and tobaccouse (0.061, 0.089) could be predicted more accuratelyon average, whereas comparably weaker predictions of il-licit substance use (-0.003, -0.002), personality-emotion(-0.008, -0.003) and mental health (-0.014, -0.0003) wereevident (Fig. 2b,d).

Prediction accuracies were consistent between the twostatistical models (NBS, lasso), both when pooling thefive behavioral dimensions (Spearman rank correlationcoefficient r(83) = 0.60, p = 2 × 10−9; Fig. 2e), as wellas separately for cognition (r(16) = 0.56, p = 0.022; Fig.2f) and tobacco use (r(16) = 0.67, p = 0.004; Fig. 2h).However, lasso and NBS diverged for the dimensions thatwere less accurately predicted (e.g., p = 0.313; Fig. 2g).



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FIG. 1. Methodology overview. (a) For each participant in our sample, structural connectomes comprising N cortical regionswere mapped using white matter tractography applied to diffusion MRI. Structural connectivity matrices were transformed intocommunication matrices C ∈ RN×N , where C(i, j) denotes the communication efficiency from region i to region j. For eachparticipant, a total of 15 communication matrices were derived representing different combinations of network communicationmodels (shortest paths, navigation, diffusion, search information, communicability) and connection weight definitions (binary,weighted, distance). To assess structure-function coupling, communication matrices were correlated with FC matrices com-puted from resting-state functional MRI data. (b) Communication, FC and SC matrices were vectorized and aggregated acrossn = 889 participants, resulting in 17 n × N(N − 1)/2 matrices of explanatory variables. A set of five behavioral dimensionswas computed by applying independent component analysis (ICA) to the HCP dataset of behavioral phenotypes. (c) Commu-nication, SC and FC matrices were used to predict behavior. An entry in the resulting 17× 5 prediction matrix corresponds tothe mean cross-validated association between a communication or connectivity matrix and a behavioral dimension.

Focusing on lasso regression, we sought to determinewhether behavioral predictions were robust to variationsin our methodological settings. First, we found thatadopting the mean square error to quantify predictiveutility led to accuracies significantly associated to theones computed based on Pearson correlation (Fig. S1).Second, we tested whether prediction accuracies weresensitive to changes in our connectome mapping pipeline.To this end, we recomputed behavioral predictions forthree additional sets of connectomes: (i) N = 360 regions

without connection thresholding, (ii) N = 68 regionswith connection thresholding, and (iii) N = 68 regionswithout connection thresholding (Materials and Meth-ods). Prediction accuracies were typically significantlycorrelated across low- and high-resolution, as well asthresholded and unthresholded, connectomes (Fig. S2).This was the case both when considering all behaviorsand when restricting the analyses to the cognition andtobacco use dimensions.

Together, these findings suggest that network commu-



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FIG. 2. Predicting individual variation in human behavioral dimensions using models of connectome communication, as wellas structural and functional connectivity (N = 360 thresholded connectomes). (a) Matrix of Pearson correlation coefficientsbetween actual and out-of-sample predicted behavior using lasso regression for five orthogonal behavioral dimensions (rows) and15 connectome communication models as well as SC and FC (columns, predictors). (b) Lasso regression prediction accuracies(correlation coefficients) stratified by behavioral dimensions. Each boxplot summarizes a row of the prediction accuracy matrixand the superimposed data points are colored accordingly. Top and bottom edges boxplots indicate, respectively, the 25thand 75th percentiles, while the central mark shows the distribution median. Mean prediction accuracies significantly differedbetween the five behavioral dimensions (F(4,80) = 10.67, p = 5 × 10−7). (c-d) Same as (a-b), but for predictions carried outusing a regression model based on featured identified by the NBS. Again, mean prediction accuracies were significantly differentbetween behavioral dimensions (F(4,80) = 47.18, p = 2 × 10−20). Scatter plots showing the correspondence (Spearman rankcorrelation coefficient and p-value) between lasso and NBS prediction accuracies for (e) all behavioral dimensions, (f) cognition,(g) illicit substance use, (h) tobacco use, and (i) the average between cognition and tobacco use prediction accuracies. SPE:shortest path efficiency, NE: navigation efficiency, DE: diffusion efficiency, SI: search information, CMY: communicability, bin:binary, wei: weighted, dis: distance.

nication models (as well as SC and FC) can explain out-of-sample inter-individual variance in behavior. Morespecifically, cognition and tobacco use were the most ac-curately and robustly predicted behavioral dimensions.

For this reason, we henceforth focus subsequent analy-ses on the averaged prediction accuracy obtained for thecognition and tobacco use dimensions. This provides uswith a single measure of how connectome communication



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relates to behavior by considering only the behavioraltraits that can be predicted with relevant accuracy. Theobtained prediction accuracy average was also consistentacross the lasso and NBS (r(16) = 0.50, p = 0.041; Fig.2i).

Communication models improve the behavioralpredictive utility of the human connectome

We sought to compare communication models, as wellas SC and FC, in terms of their behavioral predictionaccuracy. Figure 3a shows the distributions of out-of-sample accuracies (10 repetitions of 10-fold cross valida-tion, averaged for the cognition and tobacco use dimen-sions) obtained for the each predictor using lasso regres-sion. Accuracy distributions were ranked based on theirmedians. FC (median accuracy: 0.24) provided markedlygreater prediction accuracy than all communication mod-els and SC. Binary navigation (median accuracy: 0.12)and weighted communicability (median accuracy: 0.10)followed as the second and third most predictive com-munication models. Crucially, we observed that major-ity of communication models yielded greater predictionaccuracy than SC (median accuracy: 0.03). This indi-cates that modeling polysynaptic signaling through thetransformation of SC into communication matrices im-proved the behavioral predictive utility of structural con-nectomes.

We performed repeated measures t-tests to assess pair-wise statistical differences in the predictive utility of com-munication models and connectivity measures (Materialsand Methods). Figure 3b shows the effect size matrix (Co-hen’s d; Bonferroni-corrected for 136 multiple compar-isons with significance threshold α = 3.67× 10−4) of dif-ferences between mean prediction accuracies, with warm-and cool-colored cells indicating model pairs for whicha significant difference was observed. As expected, FCoutperformed all other predictors (e.g., p = 1×10−26 be-tween FC and binary navigation), while there was no evi-dence for a difference in predictive utility between binarynavigation (2nd best predictor) and weighted communi-cability (3rd best predictor) following correction for mul-tiple comparisons (p = 0.002). The lack of colored cellsalong the main diagonal of the effective size matrix in-dicates that predictors of similar ranking seldom yieldedsignificantly different accuracy. Importantly, seven com-munication models (out of 15) significantly outperformedSC, including binary navigation; binary, weighted anddistance communicability; binary and distance shortestpaths; and weighted search information (all p < 10−4).This underscores the improvement in behavioral predic-tive utility gained from accounting for polysynaptic com-munication in structural connectomes, compared to pre-dictions that only account for direct structural connec-tions.

Next, we aimed to separate the effects of commu-nication model choice and connection weight definition

on prediction accuracy. To this end, prediction accu-racies were averaged over the three weight definitionsfor each communication model (Fig. 3c,d), or aver-aged over the 15 models for each weight definition (Fig.3e,f). Prediction accuracies for FC and SC remainedthe same. With respect to the effect of communica-tion model, we found that communicability significantlyoutperformed other communication models and SC (e.g.,p = 3 × 10−5, 2 × 10−11 for comparisons of communica-bility to navigation and SC, respectively), although FCremained the leading predictor. Navigation and shortestpaths featured in second and third positions, both per-forming better than SC (p = 3× 10−7, 3× 10−5, respec-tively) and with no statistical difference between them(p = 0.26).With respect to connection weight definitionbinary connectomes yielded significantly higher predic-tion accuracies, on average, compared to weighted anddistance connectomes (p = 0.009, 2×10−5, respectively),albeit with a weaker effect size than differences betweencommunication models. This suggests that the choice ofcommunication model may be more important to behav-ior predictions than the definition of connection weights.

In order to assess the robustness of these results, weexecuted additional analyses in which we (i) substitutedthe lasso prediction model with a regression model ap-plied to features identified by the NBS (Fig. S3) and(ii) considered predictions for the cognition and tobaccouse dimensions separately (Supplementary Note 1 ; Figs.S4, S5, S6, S7). The NBS prediction method largelyreticulated lasso results (as was indicated by Fig. 2e-i). FC remained the strongest predictor of behavior, al-though with a smaller margin of difference to navigationand communicability communication models. Examiningcognition and tobacco use independently reiterated theoverall good performance of navigation and communica-bility. Importantly, however, it also revealed the pres-ence of certain dimension-specific relationships betweencommunication and behavior. For instance, search infor-mation yielded top- and bottom-ranking predictions forcognition and tobacco use, respectively.

Taken together, the behavioral prediction analysesled to three key findings. First, behavioral predictionswere more accurate when performed based on functionalrather than structural attributes. Second, while navi-gation and communicability typically showed high pre-dictive utility, our results did not point towards a sin-gle communication model as the best predictor of hu-man behavior. This indicates that different communi-cation models may be better suited to predict differentbehavioral dimensions, possibly suggesting the presenceof behavior-specific signaling mechanisms in the humanbrain. Third, and most importantly, the transformationof SC (only direct connections) into communication ma-trices (models of polysynaptic interactions) led to an im-provement of structural-based predictions, bringing themcloser to the predictive utility of FC. Collectively, thesefindings indicate that connectome communication mod-els capture higher-order structural relations among brain



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FIG. 3. Comparison of the behavioral predictive utility of connectome communication models (Lasso regression, N = 360thresholded connectomes, average cognition and tobacco use prediction accuracies). Across panels, top and bottom edgesboxplots indicate, respectively, the 25th and 75th percentiles, while the central mark shows the distribution median. (a)Prediction accuracy distributions for 10 repetitions of 10-fold cross-validation. Communication models, SC and FC were sortedbased on their median prediction accuracy. (b) Effect size matrix of pairwise statistical comparisons between predictors.Warm- and cool-colored cells indicate predictor pairs with significantly different means, as assessed by a repeated-measurest-test (Bonferroni-corrected for 136 multiple comparisons with significance threshold α = 3.67 × 10−4). A warm-colored i, jmatrix entry indicates that predictor i yields significantly more accurate predictions than predictor j. (c) Prediction accuracydistributions of communication models averaged across connection weight definitions. SC and FC were not subjected to anyaveraging and accuracies remain the same as in panel (a). (d) Effect size matrix of pairwise repeated-measures t-tests betweendistributions in panel (c), with colored cells indicating significant differences in mean prediction accuracies (Bonferroni-correctedwith significance threshold α = 0.0024). (e) Prediction accuracy distributions of connectomes with different connection weightdefinitions averaged across communication models. (f) Same as panel (d), but Bonferroni-corrected with significance thresholdα = 0.0167.

regions that can better account for interindividual varia-tion in behavior than SC alone.

Communication models improve structure-functioncoupling

We next investigated whether accounting for networkcommunication in the structural connectome can improvethe strength of the relation between SC and FC, knownas structure-function coupling. Classically, associationshave been directly tested between structural and func-tional connections [24]. A growing body of work in-

dicates that accounting for higher-order regional inter-actions through models of polysynaptic signaling (i.e.,transforming structural connectomes into communica-tion matrices) can improve structure-function coupling[5, 6, 8, 25, 26]. For two regions that are not directlyconnected with an anatomical fiber, strong FC is con-jectured to indicate the presence of an efficient signalingpath that facilitates communication through the under-lying anatomical connections [3].

To test this hypothesis, we computed the associationbetween FC and communication matrices for each indi-vidual in our sample. Additionally, as a benchmark, wealso considered the association of FC to SC and to in-



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terregional Euclidean distance. Associations were com-puted as the Spearman correlation between upper trian-gular matrix entries. In addition to individual-level as-sociations, we also analyzed structure-function couplingderived from group-level SC and FC. Finally, associa-tions were derived for coarse- (N = 68 regions) andfine-grained (N = 360 regions) connectomes, which werethresholded prior to the computation of communicationmodels. FC matrices were not thresholded. Further de-tails on the computation of structure-function couplingare provided in the Materials and Methods.

As previously reported [6], communication matriceswere correlated with FC, irrespective of the particularcommunication model (Fig. 4). In other words, FC wasgenerally stronger between regional pairs interconnectedby more efficient communication pathways. Group-levelcorrelations (rG; black crosses) were universally strongerthan those obtained for the median individual (rI ; box-plots), supporting the notion that predicting population-level FC traits is less challenging than modeling idiosyn-cratic relationships between brain structure and function.

We found that parcellation resolution had a strong in-fluence on the strength of structure-function coupling.The link between structure and function weakened forhigh resolution connectomes, irrespective of the commu-nication model (Fig. 4a). Moreover, the ranking of com-munication models in terms of structure-function cou-pling differed between connectome resolutions (Spear-man rank correlation between low- and high-resolutionFC predictions p = 0.65). For N = 68 regions, weightedand distance diffusion yielded the strongest structure-function couplings (rI = 0.46 and rG = 0.53 for weighteddiffusion; Fig. 4b,c). This recapitulates previous work in-dicating the functional predictive utility of random walkmodels applied to connectomes comprising less than onehundred regions [25]. However, in sharp contrast, dif-fusion performed poorly for N = 360 regions, goingfrom yielding the most accurate estimates of FC in low-resolution but ranking as the worst overall predictor inhigh-resolution. Conversely, the coupling between Eu-clidean distance and FC showed the opposite relationshipto connectome resolution, with interregional distancesleading to weak and strong associations for coarse- andfine-grained parcellations, respectively.

Navigation and shortest paths resulted in consistentlyhigh-ranked FC predictions regardless of connectome res-olution. For N = 68 regions, weighted navigation andshortest paths showed comparable associations to thetop-ranking diffusion models (e.g., rI = 0.42 for weightedshortest paths). For N = 360 regions, distance naviga-tion was the top-ranking model (rI = 0.18 and rG = 0.22;Fig. 4d,e), followed by distance shortest paths in secondplace, both outperforming the Euclidean distance bench-mark in the third position.

Crucially, despite the effects of connectome resolution,modeling polysynaptic communication on top of struc-tural connectomes tightened structure-function coupling.This was the case for 8 and 9 out of the 15 communi-

cation models considered, for low- and high-resolutionconnectomes, respectively. For instance, for the me-dian individual, weighted diffusion in 68-region connec-tomes strengthened coupling by 46% compared to SC,while computing distance navigation in 360-region con-nectomes boosted FC predictions by 66% compared toSC.

Grouping couplings by communication models reit-erated functional predictive utility differences betweenlow- and high-resolution connectomes (Fig. 4f). Group-ing couplings by connection weight definitions showedthat, on average, communication models computed onweighted and distance connectomes led to stronger cou-plings for coarse- and fine-grained parcellations, respec-tively (Fig. 4g), suggesting that the established influenceof interregional distance in SC and FC [27, 28] may bestronger for connectomes derived at finer levels of arealgranularity.

In summary, we observed that structure-functioncoupling is affected by connectome resolution and bywhether associations are computed on individual or pop-ulation levels. Regardless of parcellation granularity,most connectome communication models contributed tostrengthening structure-function coupling. Moreover,navigation and shortest paths yielded the most accurateand reliable predictions of FC. While here we focused onthresholded connectomes, similar results were observedfor unthresholded networks (Fig. S8). Rankings of func-tional predictive utility also remained consistent whenstratifying analyses between structurally connected andunconnected region pairs, as well as for intrahemisphericstructure-function associations (Supplementary Note 2 ;Fig. S9). Together, these observations build on the be-havioral prediction findings, further supporting the no-tion that connectome communication models contributeto bridging the gap between brain structure and function.

Ranking communication models

Finally, we aimed to derive a single ranking of pre-dictive utility, as the average of behavioral and func-tional prediction accuracy rankings, for the 15 connec-tome communication models explored and SC (Materi-als and Methods). First, we focused on results obtainedfor thresholded connectomes comprising N = 360 re-gions. To this end, we averaged the rankings from threeanalyses: lasso behavioral predictions (Fig. 3), NBS be-havioral predictions (Fig. S3) and FC predictions (Fig.4a). We found that distance navigation showed the high-est combined behavioral and functional predictive util-ity (average ranking τ = 3.7; 5a), followed by a tiebetween distance shortest paths and weighted commu-nicability (τ = 4.7). SC featured in the 11th positionand was outranked by most navigation, communicabil-ity, shortest paths and search information models. Wealso found that navigation was the top ranking modelregardless of connection weight definitions (τ = 5.9; 5b),



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FIG. 4. Structure-function coupling across connectome communication models (N = 68, 360 thresholded connectomes). (a)Data points show individual-level correlation of FC to communication, SC and Euclidean distance matrices. Black crossesindicate correlations obtained for group-averaged matrices. Top and bottom edges boxplots indicate, respectively, the 25th and75th percentiles, while the central mark shows the distribution median. Communication models, SC and Euclidean distancewere ranked according to the median structure-function coupling strength across individuals. (b) Scatter plot depicting therelationship between FC and the top-ranked communication model for connectomes comprising N = 68 regions, for the medianindividual. For ease of visualization, communication matrix entries were resampled to normal distributions. Warm and coolcolors indicate high and low data point density, respectively. (c) Same as (b), but for group-average matrices. (d-e) Sameas (b-c), but for connectomes comprising N = 360 regions. (f) Structure-function coupling for communication models, SCand Euclidean distance, averaged across connection weight definitions. (g) Structure-function coupling obtained for binary,weighted and distance connectomes, averaged across communication models.

followed by communicability (τ = 6.3), shortest paths(τ = 7.7), SC (τ = 8.7), search information (τ = 9.1),and diffusion in the last position (τ = 13.6). More-over, connection weights defined in terms of streamlinecounts and Euclidean distance resulted in similar pre-dictive utility rankings (τ = 7.4, 7.5, respectively) whilebinary connectomes typically led to less accurate predic-tions (τ = 10.5).

Next, we computed rankings for the three alternativesets of connectomes considered in this study, namelyN = 360 unthresholded, N = 68 thresholded and N = 68unthresholded connectomes (Fig. S10). Contrasting

results across these scenarios revealed that sparse andfine-grained connectomes benefited more from modelsof polysynaptic communication than dense and coarse-grained connectomes. Intuitively, a densely connectednetwork requires few polysynaptic paths to propagate in-formation, since most regions can communicate via directconnections. Consequently, while navigation, communi-cability and shortest paths typically improved the pre-dictive utility of SC for N = 360, a markedly reducednumber of signaling strategies was beneficial to the per-formance of connectomes comprising N = 68 regions.Importantly, across all sets of SC reconstructions, nav-



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NE di

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Dis

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Weightsa b c

FIG. 5. Overall ranking of communication models (N = 360 thresholded connectomes). Communication models and SCwere ranked according to averaged behavioral and functional predictions. (a) Overall predictive utility ranking for N = 360thresholded connectomes. Ranking shown in (a) grouped by (b) communication models and (c) connection weight definitions.

.

igation was the only model that constantly featured asadvantageous to the predictive utility of the human con-nectome.

DISCUSSION

Human cognition and behavior arise from the or-chestrated activity of multiple brain regions [29, 30].Resisting-state FC is currently one of the most widelyused neuroimaging measures to quantify this concertedactivity [31–33]. It is thus unsurprising that statisticalmethods trained on functional brain networks led to themost accurate predictions of human behavior. Impor-tantly, the signaling processes that facilitate synchronousinterregional activity must unfold along structural con-nections forming direct or indirect (polysynaptic) com-munication paths. Therefore, brain structure, brain func-tion, neural communication, and human behavior aretightly intertwined. This is corroborated by the key con-clusion of the present study: accounting for polysynapticcommunication in SC matrices can substantially improvestructure-function coupling and the predictive utility ofSC. Transforming a SC matrix into a communication ma-trix can be achieved efficiently for most communicationmodels without the need for any sophisticated computa-tional processing. We recommend performing the trans-formation when evaluating structure-function coupling orusing SC to predict interindividual variation in behavior.While accounting for communication did not lead to SCoutperforming FC with respect to behavior prediction, itnarrowed that gap between the predictive utility of SCand FC.

As investigators tackle the longstanding challenge ofelucidating the relationship between brain structure andfunction [34–36], it has become increasingly clear thatFC arises from high-order regional interactions that can-not be explained by direct anatomical connections [5]. Inline with this notion, we found that taking polysynapticsignaling into account through network communication

models strengthened structure-function coupling. Thisobservation recapitulates earlier reports on the functionalpredictive utility of connectome communication models[6] and provides support to the notion that FC is fa-cilitated by communication pathways in the underlyingstructural connectome. Taken together, the behavioraland functional prediction analyses contribute empiricalevidence that connectome communication models act asa bridge between structural and functional conceptual-izations of brain networks [3, 37].

Importantly, brain structure-function relationships en-compass a rich and diverse field of research, with sev-eral alternative classes of higher-order models showingpromise in modeling function from structure. Examplesinclude biophysical models of neural activity [38–40], sta-tistical methods [41, 42], and other approaches centeredaround network communication that we did not explorein the present work [26, 43–45]. Likewise, relating neu-roimaging data to behavior is a central goal of neuro-science [46, 47]. Recent studies have explored neuralcorrelates of behavior and cognition by leveraging graphmeasures of brain organization [48, 49], dynamic patternsof FC fluctuations [50, 51], multivariate correlation meth-ods [52, 53] and machine learning techniques [54, 55]. Ouranalyses sought to complement these efforts from the per-spective of connectome communication. The goal of thispaper was not to show that network communication mod-els lead to more accurate predictions than alternative ap-proaches, nor that our prediction scheme and statisticalmethods are superior to previously adopted techniques.Rather, we were interested in comparing the predictiveutility of candidate models of connectome communica-tion, as well as connectivity and distance benchmarks, ina controlled and internally consistent manner.



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Comparisons between connectome communicationmodels

Communication matrices computed with the naviga-tion and communicability models typically led to thehighest-ranking behavioral predictions amongst the can-didate signaling strategies explored. It is important tonotice, however, that search information and shortestpaths also performed well in certain scenarios. There-fore, while our behavioral results strongly suggested thebenefits of modeling polysynaptic signaling, they did notprovide a clear answer to the question of which commu-nication models are most associated to human behavioraldimensions. Alternatively, our findings may indicate theinteresting possibility that large-scale information inte-gration in the brain is not facilitated by a unique signal-ing mechanism, and that different communication modelsmay find more utility in describing varied behavioral andcognitive processes.

Navigation and shortest paths led to the most reliableFC predictions, featuring as the best models for high-resolution connectomes and closely following behind bydiffusion for low-resolution connectomes. Navigation andshortest paths computed on distance connectomes led toFC predictions that surpassed those obtained from Eu-clidean distance, which exerts a well-documented influ-ence on both SC and FC [27, 28, 56]. This indicates thatcombining the contributions of brain network topologyand geometry might be helpful in modeling structure-function relationships. Furthermore, given the high effi-ciency of communication along navigation and shortestpaths, these findings suggest that FC is facilitated pri-marily by highly efficient signaling pathways. This ob-servation stands in contrast with previous work on thefunctional relevance of models that incorporate devia-tions from optimal routes, such as search information[6, 57]. We note, however, that navigation implements adecentralized identification of near-optimal paths [58, 59]that contributes to the understanding of how efficient sig-naling can be achieved in the absence of global knowledgeof network architecture [12, 60].

Combining communication model rankings from be-havioral and functional predictions revealed that naviga-tion was the model with the highest overall predictiveutility ranking. This finding provides initial evidencethat, out of the putative communication strategies ex-plored, navigation may most faithfully describe underly-ing neural signaling patterns supporting human behaviorand brain function. Our results contribute to the grow-ing body of work supporting the neuroscientific utility ofnetwork navigation [8, 12, 61–63].

In addition to investigating putative neural signalingstrategies, we also considered different connection weightdefinitions. Polysynaptic transmission of neural signalsentails metabolic expenditures related to the propaga-tion of action potential along axonal projections and thecrossing of synaptic junctions. Communication in thebrain is thought to be metabolically frugal [30, 66], but

what aspects of structural connectivity are relevant to en-ergy consumption in large-scale signaling remain unclear.We found that weighted and distance connectomes typi-cally led to communication matrices with higher predic-tive utility. This is initial evidence that neural signalingmay favor communication paths prioritizing the adoptionof physically short and high caliber connections, insteadof paths that reduce the number of synaptic crossings be-tween regions. Additionally, these observations warrantfurther investigation of the relatively unexplored distanceconnectome [67].

In accordance to previous reports [68, 69], we observedthat FC predictions were more accurate for low- ratherthan high-resolution connectomes, as well as for group-rather than individual-level analyses. This is not sur-prising since the number of functional connections growsquadratically with the number of regions and capturingidiosyncrasies in FC is more challenging than modelinggeneral principles of connectivity. Despite their simplic-ity, these observations are important to the validationof FC prediction methods, suggesting that models con-structed and evaluated on coarse and population-levelnetworks may not generalize to more challenging settings.

Limitations and future directions

Several methodological limitations of the present workshould be discussed. First, we reiterate that the mainfocus of our investigation was to perform an evaluationof candidate models of connectome communication. Al-though we explored multiple brain network reconstruc-tion pipelines, we were not primarily concerned withwhich mapping techniques produced connectomes withthe highest predictive utility. The choice of parcellationschemes [70] and whether or not to threshold structuralconnectomes [71, 72] are both complex open questionsthat fall outside the scope of this work. We also notethat white matter tractography algorithms are suscepti-ble to a number of known biases that could potentiallyimpact our results [73].

Further research is necessary to untangle the contri-butions of specific brain regions to the predictive util-ity of different communication models. This could beachieved by examining lasso regression weights and NBSconnected components. Alternatively, behavior and func-tional predictions could be performed based on region-wise communication efficiencies, rather than completecommunication matrices [74]. Efforts in these directionscould help elucidate how different communication mod-els utilize features of connectome topology to facilitateinformation transfer.

While we sought to evaluate a wide-range of commu-nication models, alternative network propagation strate-gies could provide valuable insight into mechanisms ofneural signaling and warrant further research. Theseinclude linear transmission models [26], biased randomwalks [4], cooperative learning [75], dynamic communi-



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cation models [76], and information-theoretic approaches[77].

In conclusion, we demonstrated that taking into ac-count polysynaptic signaling via models of network com-munication improves the behavioral and functional pre-dictive utility of the human structural connectome. Over-all, navigation ranked as the communication model withhighest predictive utility, indicating that it may faith-fully approximate underlying signaling pathways relatedto human behavior and brain function. These findingscontribute novel insights to researchers interested in char-acterizing information processing in nervous systems.

ACKNOWLEDGMENTS

We thank Olaf Sporns for valuable discussions. Humandata were provided by the Human Connectome Project,WUMinn Consortium (1U54MH091657; Principal Inves-tigators: David Van Essen and Kamil Ugurbil) funded bythe 16 National Institutes of Health (NIH) institutes andcenters that support the NIH Blueprint for NeuroscienceResearch; and by the McDonnell Center for Systems Neu-roscience at Washington University.

MATERIALS AND METHODS

Structural connectivity data

Minimally preprocessed high-resolution diffusionweighted magnetic resonance imaging (MRI) data wasobtained from the Human Connectome Project (HCP)[18]. Details about the acquisition and preprocessingof diffusion MRI data are found in [78, 79]. Analyseswere restricted to participants with complete HCP3T imaging protocol, yielding a total sample of 889healthy adults (age 22–35, 52.8% females). Whole-brainstructural connectomes were mapped using diffusiontensor imaging and deterministic white matter tractog-raphy pipeline implemented using MRtrix3 [80] (FACTtracking algorithm, 5× 106 streamlines, 0.5 mm trackingstep-size, 400 mm maximum streamline length and 0.1fractional anisotropy cutoff for termination of tracks).The connection weight between a pair of regions wasdefined as the total number of streamlines connectingthem, resulting in a N ×N weighted connectivity matrixfor each participant. Group-level structural connectomeswere computed by averaging the connectivity matricesof all subjects.

We used cortical parcellations containing N = 68, 360regions. The 68-region parcellation consists of theanatomically delineated cortical areas of the Desikan-Killiany atlas [81]. The 360-region parcellation is a mul-timodal atlas constructed from high-resolution structuraland functional data from HCP [20]. We also consideredthresholded and unthresholded connectomes. Followingconnection density thresholding, only the top 15% and

20% strongest connection (in terms of streamline counts)were kept in connectomes comprising 360 and 68 regions,respectively. A more lenient threshold was applied toconnectomes with 68 regions in order to avoid networkfragmentation. Unthresholded connectomes maintainedall connections identified in the structural connectivityreconstruction process.

Connection weight and length definitions

Structural connectomes can be defined in terms ofN × N adjacency matrices of connectivity weights (W )or lengths (L). Connection weights provide a measureof the strength and reliability of anatomical connectionsbetween regions pairs, while connection lengths quantifythe distance or travel cost between regions pairs. Dif-ferent network communication measures are computedbased on W (e.g., diffusion efficiency and communica-bility), L (e.g., shortest path efficiency and navigationefficiency) or a combination of both (e.g., search infor-mation).

We considered three definitions of W : weighted, bi-nary and distance. In the weighted case, Wwei(i, j) wasdefined as the total number of streamlines with one end-point in region i and the other in region j. The bi-nary adjacency matrix was defined as Wbin(i, j) = 1 ifWwei(i, j) > 0 and Wbin(i, j) = 0 otherwise. Distance-based connectivity was defined as Wdis(i, j) = 1/D(i, j)if Wwei(i, j) > 0 and Wdis(i, j) = 0 otherwise, where D isthe Euclidean distance matrix between region centroids.

Similarly, L was also defined in terms of binary,weighted and distance connection traversal costs. Inall three cases, L(i, j) = ∞ for ij region pairs thatdo not share a direct anatomical connection, ensuringthat communication is restrict to unfold through the con-nectome. Binary (Lbin) and distance-based (Ldis) con-nection lengths are straightforwardly defined from theirweight counterparts as Lbin(i, j) = 1 if Wbin(i, j) = 1and Lbin(i, j) = ∞ otherwise, and Ldis(i, j) = D(i, j) ifWdis(i, j) > 0 and Ldis(i, j) = ∞ otherwise. Lengthsbased on the streamline count between regions pairs aredefined by monotonic weight-to-length transformationsthat remap large connection weights into short connec-tion lengths. This way, white matter tracts conjec-tured to have high caliber and integrity are consideredfaster channels of communication than weak and unreli-able ones. We considered a logarithmic weight-to-lengthremapping such that Lwei = −log10(Wwei/max(Wwei) +1) (the unity addition to the denominator avoids theremapping of the maximum weight into zero length) [12],producing normally distributed lengths that attenuatethe important of extreme weights [82, 83].



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Network communication models

In this section, we provide details regarding the def-inition of the five network communication models eval-uated in this study. All computations were carried outusing freely available code provided in the Brain Con-nectivity Toolbox (https://sites.google.com/site/bctnet/) [84].

First, we note a subtle but important distinction be-tween network communication models and measures. ANetwork communication model (e.g., shortest path rout-ing) delineates a strategy or algorithm to transfer infor-mation between node pairs. In turn, a network commu-nication measure (e.g., shortest path efficiency) quantify,from a graph-theoretical standpoint, the efficiency of in-formation transfer achieved by a given communicationmodel. For simplicity, we used “model” throughout thispaper to refer to both network communication modelsand measures.

We also note that certain communication measures areinherently asymmetric, in that Casy(i, j) 6= Casy(j, i).While this asymmetry contains meaningful informationon signaling properties of nervous systems [8], in thepresent study we consider symmetric communication ma-trices given by C(i, j) = (Casy(i, j) + Casy(j, i))/2. Thissimplification allows us to take into account only the up-per triangle of C, substantially reducing the dimension-ality of our predictive models and contributing to thecomputational tractability of our analyses.

Shortest path efficiency

Shortest path routing proposes that neural signalingtakes place along optimally efficient paths that mini-mize the sum of connection lengths traversed betweennodes. Let Λ∗ ∈ RN×N denote the matrix of shortestpath lengths, where Λ∗(i, j) = L(i, u) + ... + L(v, j) andu, ..., v is the sequence of nodes visited along the short-est path between nodes i and j. Shortest path efficiencywas defined as SPE = 1/Λ∗ [9]. We computed binary(SPEbin), weighted (SPEwei), and distance (SPEdis)shortest path efficiency matrices based on the Lbin, Lwei,Ldis connection length matrices, respectively.

Navigation efficiency

Navigation routing identifies communication paths bygreedily propagating information based on a measureof node (dis)similarity [11]. Following previous stud-ies on brain network communication, we used the Eu-clidean distance between region centroids to guide nav-igation [8, 12]. Navigating from node i to node j in-volves progressing to i’s neighbor that is closest in dis-tance to j. This process is repeat until j is reached (suc-cessful navigation) or a node is revisited (failed naviga-tion). Successful navigation path lengths are defined as

Λ(i, j) = L(i, u) + ...+ L(v, j), where u, ..., v is the se-quence of nodes visited during the navigation from i toj. Failure to navigate from i to j yields Λ(i, j) = ∞.Navigation efficiency was defined as NE = 1/Λ. Binary(NEbin), weighted (NEwei), and distance (NEdis) nav-igation efficiency matrices were computed based on theLbin, Lwei, Ldis, respectively.

Diffusion efficiency

Diffusion efficiency models neural signaling in termsof random walks. Let T ∈ RN×N denote the transi-tion matrix of a Markov chain process unfolding on theconnection weight matrix W . The probability that anaive random walker at node i will progress to node j

is given by T (i, j) = W (i, j)/∑Nu=1W (i, u). The mean

first passage time H(i, j) quantifies the expected num-ber of intermediate regions visited in a random walkfrom i to j (details on the mathematical derivation ofH from T are given in [13, 85, 86]). Diffusion efficiencyis defined as DE = 1/H, thus capturing the efficiencyof neural communication under a diffusive propagationstrategy [13]. Binary (DEbin), weighted (DEwei), anddistance (DEdis) diffusion efficiency matrices were com-puted based on the Wbin, Wwei, Wdis, respectively.

Search Information

Search information is derived from the probability ofrandom walkers serendipitously traveling along the short-est paths between node pairs [14]. Let Ω(i, j) = u, ..., vbe the sequence of nodes along the shortest path fromnode i to node j computed from the connection lengthmatrix L. The probability of a random walker start-ing at i reaches j via Ω(i, j) is given by P (Ω(i, j)) =T (i, u) × ... × T (v, j), where T is the previously definedtransition probability matrix computed from W . We de-fined search information as SI(i, j) = log2(P (Ω(i, j)))[6, 8]. This definition quantifies how accessible shortestpaths are to naive random walkers, capturing the degreeto which efficient routes are hidden in network topology.Note that the computation of search information dependsboth on L—for the identification of shortest paths—andW—for the simulation of random walk processes. Weused Wwei combined with Lbin, Lwei, and Ldis to com-pute, respectively, binary, weighted, and distance ver-sions of search information.

Communicability

Communicability models neural signaling as a diffu-sive process unfolding simultaneously along all possi-ble walks in a network [15]. Communicability betweennodes i and j is defined as the weighted sum of thetotal number of walks between them, with each walk



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weighted by its length (i.e., number of connections tra-versed). In the binary case, this yields CMY (i, j) =∑∞n=0Wbin(i, j)n/n!. In the limit n→∞, this sum con-

verges to CMY (i, j) = eWbin(i,j). Non-binary connectionweight matrices are typically normalized as W ′wei(i, j) =

Wwei(i, j)/(√s(i)

√(s(j))) prior to the computation of

communicability to attenuate the influence of high

strength nodes [16], where s(i) =∑Nu=1Wwei(i, u) is the

total strength of node i. We used Wbin, W ′wei and W ′disto compute, respectively, binary, weighted and distance-based versions of communicability.

Functional connectivity data

Minimally preprocessed resting-state functional MRIdata from the same 889 individuals was also obtainedfrom the HCP. Participants were scanned twice (right-to-left and left-to-right phase encodings) on two separatedays, resulting in a total of four sessions per individual.In each session, functional MRI data was acquired fora period of 14m33s with 720ms TR. Further details onresting-state functional MRI data collection and prepro-cessing as described in [78, 87]. Functional activity ineach of N = 68, 360 regions was computed by averagingthe signal of all vertices comprised in the region. Pair-wise Pearson correlation matrices were computed fromthe regional time series of each session, resulting in fourmatrices per participant. For each participant, the fourmatrices were averaged to yield a final N × N FC ma-trix. Group-level functional connectomes were computedby averaging the FC matrices of all subjects.

Behavioral dimensions

Information on HCP behavioral protocols and proce-dures is described elsewhere [88]. A total of 109 variablesmeasuring alertness, cognition, emotion, sensory-motorfunction, personality, psychiatric symptoms, substanceuse and life function were selected from the HCP be-havioral dataset [19]. Selected items consisted of raw(age- and gender-unadjusted), total or subtotal assess-ment scores. The set of 109 measures was submitted toan independent component analysis (ICA) pipeline in or-der to derive latent dimensions summarizing orthogonaldimensions of behavioral information. This procedurecontributed to the computational tractability of our anal-yses by enabling behavioral inferences to be performedon a small set of data-driven components, rather thanrestricted to arbitrarily selected measures.

Behavioral dimensions were computed as follows. Arank-based inverse Gaussian transformation [89] wasused to normalize continuous behavioral variables (87 of109). Age and gender were regressed out from all behav-ioral items. ICA was performed on the resulting residu-als using the FastICA algorithm [90] implemented in the

icasso MALTLAB package [91]. Participants were sam-pled with replacement to generate a total of 500 boot-strap samples. ICA was independently performed oneach sample with randomly selected initial conditions.Agglomerative clustering with average linkage was usedto derive consensus clusters of independent componentsacross different bootstrap samples and initial conditions.This procedure, including bootstrapping and randomiza-tion of initial conditions, was repeated for 10 trials of aset of candidate ICA models ranging from 3 to 30 inde-pendent components. The best number of componentswas estimated based on the reproducibility across the 10trials by means of a cluster quality index. Clearly sep-arated clusters indicate independent components wereconsistently and reliably estimated, despite being com-puted based on different bootstrap samples and initialconditions. This criterion identified the five componentmodel as the most robust and parsimonious set of latentdimensions. The obtained components were visualizedas word clouds with font size proportional to the contri-bution of each original behavioral variable (see Fig. S14in [19]). This enabled the characterization of the five di-mensions as cognitive performance, illicit substance use,tobacco use, personality and emotion traits, and mentalhealth. Further details on the computation of the behav-ioral dimensions are provided in [19].

Behavioral prediction framework

Let y ∈ Rn×1 be a vector of response variables corre-sponding to a given behavioral dimension, where n = 899is the number of individuals in our sample. LetX ∈ Rn×pbe a matrix of p explanatory variables corresponding tothe upper triangle of vectorized communication matri-ces C ∈ RN×N , so that p = N(N − 1)/2. We appliedtwo independent statistical models to predict y from X:lasso regression and a regression model based on networkfeatures identified by the NBS. These models implementdifferent strategies of feature selection aimed at identify-ing a parsimonious set of variables in X to predict y.

The data was split into train and test sets to perform10-fold cross-validation. The family structured in theHCP dataset was taken into account by ensuring that in-dividuals of the same family were not separated betweentrain and test sets [54]. Sensitivity to particular train-test data splits was addressed by repeating the 10-foldcross-validation 10 times. The same train and test setswere used for lasso and NBS regressions. Model param-eter estimation was performed exclusively on train setswhile model performance was assessed exclusively on testsets.

Lasso regression

Let Xa, ya and Xe, ye denote a split of X, y intotrain and test sets, respectively. We used lasso regression



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[22] to compute β as

minβ∈Rp 1

n||ya −Xaβ||22 + λ||β||1,

where 0 ≤ λ ≤ 1 is a feature selection parameter con-trolling model complexity. We systematically evaluated100 logarithmically-spaced values of λ ranging from 0.001to 1. Model fit was evaluated as the Pearson correlationcoefficient between ye and ye, where ye = Xeβ. For eachvalue of λ, model performance was computed as the av-erage model fit over 100 pairs of train and test sets (10repetitions of 10-fold splits). To avoid trivial cases forwhich maximum performance is achieved for ||β||1 = 0,we selected the smallest λ leading to model performancewithin one standard deviation of the maximum perfor-mance.

Network-based statistics regression

The NBS identifies sets of connected components thatexplain significant interindividual variation in a responsevariable [23]. We used the NBS as a feature selectiontechnique to identify behaviorally relevant groups of con-nections. We then fit a regression model to the averageconnection weight of the selected connections in orderto predict behavior. Importantly, connected componentswere identified exclusively in training sets, while predic-tion accuracy were computed based on held-out test sets.

Let Xa, ya and Xe, ye denote a split of X, y intotrain and test sets, respectively. The cross-validated pre-dictive utility of NBS connected components was com-puted as follows. For each column of Xa (correspondingto the value of a connection in the upper triangle of acommunication matrix C(i, j) across subjects in the trainset), the inter-individual Pearson correlation betweenC(i, j) and ya was computed. Connections for which sta-tistical association strength exceeded a t-statistic thresh-old t > |3| were grouped into sets of positive (t > 3)and negative (t < −3) connected components. This pro-cedure was repeated for 1000 random permutations ofya, and the likelihood of observing positive and negativeconnected components as large as empirical ones was as-sessed using a non-parametric test. Further details onthe NBS are found in [23].

Let Γ+ and Γ− be, respectively, the largest positive andnegative connected components identified by the NBSbased on the train data Xa, ya. We computed g+,−

a ∈R|ya|×1 as the average weight of connections belonging tothe connected component Γ+,−:

g+,−a =

1

|Γ+,−|∑

u∈Γ+,−

Xa(., u),

where |Γ+,−| indicates the number of connections com-prising the connected component. We defined the matrixGa = [g+

a |g−a ]. Therefore, Ga ∈ R|ya|×2 contains the av-erage weight of connections identified as positively andnegatively associated with the behavioral dimension y forsubjects in the train set Xa, ya. Using a bivariate lin-ear regression model, we computed the coefficients β suchthat

minβ∈R2 1

n||ya −Gaβ||22.

Analogously, we computed the average weight of con-nected components in the test set

g+,−e =

1

|Γ+,−|∑

u∈Γ+,−

Xe(., u)

and Ge = [g+e |g−e ]. Finally, behavioral predictions were

computed as ye = Geβ and out-of-sample prediction ac-curacy was evaluated as the Pearson correlation coeffi-cient between ye and ye. This procedure was repeat for100 pairs of train and test sets (10 repetitions of 10-foldsplits). In cases where no significant component was iden-tified by the NBS (|Γ+,−| = 0), model performance wasset to 0.

Functional connectivity prediction framework

FC prediction utility was determined via Spearmancorrelation between empirical FC and analytically de-rived communication matrices. Therefore, none of themodels and measures used to infer FC required train-ing, statistical estimation of weights or parameter tuning(an advantage over other classes of high-order models).Hence, we oftentimes adopted the term FC “prediction”even though predictive utility was not assessed out-of-sample [6].

Overall predictive utility rankings

Overall ranking of communication model predictiveutility were computed by averaging rankings obtainedfor behavioral and functional analyses, which were givenequal weight on the averaging process. The overall rank-ing for thresholded N = 360 connectomes was com-puted as the weighted average of rankings for (i) lassobehavioral predictions (0.25 weight), (ii) NBS behav-ioral predictions (0.25 weight), and (iii) FC predictions(0.5 weight). Rankings for other connectome mappingpipelines were computed by averaging, with equal weight,lasso behavioral predictions and FC predictions.



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SUPPLEMENTARY INFORMATION

Note 1: Behavioral predictive utility for thecognition and tobacco use dimensions

We have characterized the predictive utility of con-nectivity measures and communication models by con-sidering a pooled prediction accuracy between the cog-nition and tobacco use dimensions. As we have seen,these behavioral dimensions led to the most accurate andconsistent predictions in our sample. Considering theaverage prediction accuracy across the two traits facili-tated the comparison of communication models by pro-viding us with a single score on which to evaluate pre-diction accuracy. However, this approach may poten-tially obscure nuanced phenotype-specific relationshipsbetween brain and behavior. Indeed, we observed no cor-relation between the prediction accuracies obtained forcognition and tobacco use (Spearman rank correlationp = 0.49, 0.69 for lasso and NBS, respectively). There-fore, in this section, we sought to separately examinebehavioral predictions for the cognition and tobacco usedimensions.

We observed that the outstanding performance of FCwas mostly due to the cognition dimension (Fig. S4 andS5; this can also be observed in Fig. 2c,d). This is in linewith several findings on the relationship between cogni-tive processes and the architecture of functional networks[46]. Interestingly, while FC still yielded top-ranking pre-dictions of tobacco use, several communication modelsshowed comparable predictive utility in this dimension(Fig. S6 and S7; again evident in Fig. 2c,d). For in-stance, navigation was the best predictor of tobacco use,with binary and distance navigation occupying the firstpositions under lasso and NBS, respectively. Althoughnone of the communication models statistically outper-form FC, this points towards a tighter margin of differ-ence between the utility of structural and functional mea-sures in predicting behavioral phenotypes not directly re-lated to cognition.

Another interesting observation was that weightedsearch information was the best communication modelin predicting cognition, but showed near bottom-rankingpredictive utility of tobacco use, which resulted in amoderate performance when combining predictions fromboth behavioral dimensions. Along similar lines, weobserved that rankings of connection weight definitionswere sensitive different behavioral dimensions and predic-tion methods, painting an unclear picture of what weight-ing schemes best contribute to predict human behaviorfrom structural connectomes.

Therefore, collectively, our results did not point to-wards a single communication model as the best predictorof human behavior. Despite the overall good performanceof communicability and navigation, our observations in-dicate that different communication models may be bet-ter suited to predict different behavioral dimensions, pos-sibly suggesting the presence of behavior-specific signal-



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ing mechanisms in the human brain. Importantly, acrossthe multiple analyses performed, our results consistentlysuggested that network communication models, in par-ticular communicability and navigation, improve the be-havioral predictive utility of the human connectome.

Note 2: Additional analyses of structure-functioncoupling

We further examined structure-function relationshipsby stratifying FC predictions across anatomically con-nected and unconnected regions pairs (Fig. S9a). Inaccordance to previous work [6, 12], associations toFC were stronger for connected regions. Despite thesechanges in association strength, rankings of communi-cation models in terms FC predictions were consistentacross the scenarios explored (Spearman rank correlationr = 0.90, 0.68, 0.85 and p = 8×10−7, 3×10−3, 0 betweenconnected and all, all and unconnected, and connectedand unconnected region pairs, respectively). Interest-

ingly, certain communication models outperformed SCfor connected regions, suggesting that indirected polysy-naptic signaling maybe relevant for communication evenin the presence of direct anatomical links.

Estimates of structure-function coupling depend on ac-curate reconstruction of structural connectomes. How-ever, white matter tractography is prone to a numberof known biases, of which the underestimation of inter-hemispheric connections is an important concern [73]. Toattenuate this issue, past studies have focused on intra-hemispheric characterization of structure-function cou-pling [41, 56]. Focusing on the right hemisphere, wefound that, for all communication models, FC associa-tions were stronger compared to whole-brain estimates(Fig. S9b). Importantly, the functional predictive utilityranking of communication models remained consistent(Spearman rank correlation r = 0.93 and p = 0 betweenwhole-brain and right hemisphere rankings). This sug-gests that our analyses may provide a meaningful rank-ing of signaling strategies despite shortcomings in con-nectome mapping techniques.



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-0.1 0 0.1 0.2 0.3 0.4Observed vs predicted Pearson correlation

0.84

0.86

0.88

0.9

0.92

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erve

d vs

pre

dict

ed M

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a) All behavioral dimensions

r=-0.39, p=2e-04

0 0.1 0.2 0.3 0.4Observed vs predicted Pearson correlation

0.9

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b) Cognition and Tobacco use average

r=-0.91, p=0e+00

FIG. S1. Comparison between behavioral prediction accuracies computed using Pearson correlation and mean square errorevaluated using Spearman rank correlation (Lasso regression, N = 360 thresholded connectomes). The least squares line isshown in black.

0 0.1 0.2 0.3N=360, thresholded

0

0.1

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N=3

60, u

nthr

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0 0.1 0.2 0.3N=360, thresholded

0

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8, th

resh

olde

d

r=0.48, p=4e-06

0 0.1 0.2 0.3N=360, unthresholded

0

0.1

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nthr

esho

lded

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0 0.1 0.2N=68, thresholded

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unt

hres

hold

ed

r=0.49, p=3e-06

0 0.1 0.2 0.3N=360, thresholded

0

0.1

0.2

0.3

N=3

60, u

nthr

esho

lded

r=0.67, p=2e-05

0 0.1 0.2 0.3N=360, thresholded

0

0.1

0.2

0.3

N=6

8, th

resh

olde

d

r=0.35, p=0.0406

0 0.1 0.2 0.3N=360, unthresholded

0

0.1

0.2

0.3

N=6

8, u

nthr

esho

lded

r=0.35, p=0.0460

0 0.1 0.2N=68, thresholded

0

0.1

0.2

N=6

8, u

nthr

esho

lded

r=0.28, p=0.1079

a c d

e f g h

b

Robustness of lasso prediction accucary: Cognition and Tobacco use dimensions

Robustness of lasso prediction accucary: All behavioral dimensions

FIG. S2. Comparison between behavioral prediction accuracies across multiple connectome mapping pipelines (Lasso regres-sion). Scatter plots show the least squares and x = y lines are shown in solid black and gray dashed traces, as well as theSpearman rank correlation coefficient and p-value.



https://doi.org/10.1101/2020.04.21.053702


21

FCN

E dis

CM

Yw

eiN

E bin

SCSI

wei

NE w

eiSP

E bin

CM

Ydi

sC

MY

bin

SPE di

sSI

dis

DE di

sD

E wei

DE bi

nSI

bin

SPE w

ei

-0.1

0

0.1

0.2

0.3

0.4

Beha

vior

al p

redi

ctio

n ac

cura

cy


FCN

E dis

CM

Yw

eiN

E bin

SCSI

wei

NE w

eiSP

E bin

CM

Ydi

sC

MY

bin

SPE di

sSI

dis

DE di

sD

E wei

DE bi

nSI

bin

SPE w

ei

FCNEdis

CMYweiNEbin

SCSIwei

NEweiSPEbin

CMYdisCMYbinSPEdis

SIdisDEdisDEweiDEbinSIbin

SPEwei

-1

-0.5

0

0.5

1

Cohens's d

FC NE

SC

CM

Y SI

SPE

DE

0

0.2

0.4

Beha

vior

al p

redi

ctio

n ac

cura


comparisons

FC NE

SCC

MY SI

SPE

DE

FCNESC

CMYSI

SPEDE -1

-0.5

0

0.5

1

Cohens's d

Dis Wei Bin

0

0.05

0.1

0.15

0.2

Beha

vior

al p

redi

ctio

n ac

cura

cy WeightsPairwise

comparisons

Dis Wei Bin

Dis

Wei

Bin -0.2

0

0.2 Cohens's d

a b

c d e f

FIG. S3. Comparison of the behavioral predictive utility of connectome communication models (NBS, N = 360 thresholdedconnectomes, average cognition and tobacco use prediction accuracies). It is worth noting that the NBS feature selectionprocess is better suited to sparse graphs [23], which could confer an advantage to sparse SC matrices over fully-connectedcommunication and FC matrices.

FCSI

wei

SIbi

nC

MY

wei

NE bi

nSP

E wei

CM

Ydi

sC

MY

bin

SC SIdi

sN

E wei

DE di

sSP

E bin

SPE di

sN

E dis

DE bi

nD

E wei

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Beha

vior

al p

redi

ctio

n ac

cura

cy


FCSI

wei

SIbi

nC

MY

wei

NE bi

nSP

E wei

CM

Ydi

sC

MY

bin

SC SIdi

sN

E wei

DE di

sSP

E bin

SPE di

sN

E dis

DE bi

nD

E wei

FCSIweiSIbin

CMYweiNEbin

SPEweiCMYdisCMYbin

SCSIdis

NEweiDEdis

SPEbinSPEdisNEdisDEbinDEwei

-3

-2

-1

0

1

2

3

Cohens's d

FC SIC

MY SC NE

SPE

DE

-0.2

0

0.2

0.4

0.6

Beha

vior

al p

redi

ctio

n ac

cura


comparisons

FC SIC

MY SC NE

SPE

DE

FCSI

CMYSCNE

SPEDE

-2

0

2 Cohens's d

Wei Bin Dis

-0.1

0

0.1

0.2

Beha

vior

al p

redi

ctio

n ac

cura

cy WeightsPairwise

comparisons

Wei Bin Dis

Wei

Bin

Dis-0.4

-0.2

0

0.2

0.4

Cohens's d

a b

c d e f

FIG. S4. Comparison of the behavioral predictive utility of connectome communication models (Lasso regression, N = 360thresholded connectomes, cognition prediction accuracy).



https://doi.org/10.1101/2020.04.21.053702


22

FCSI

wei

CM

Yw

ei

SCN

E bin

CM

Ydi

sN

E dis

CM

Ybi

nD

E dis

SPE bi

nSI

bin

NE w

eiSI

dis

SPE di

sD

E bin

SPE w

eiD

E wei

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Beha

vior

al p

redi

ctio

n ac

cura

cy


FCSI

wei

CM

Yw

ei SCN

E bin

CM

Ydi

sN

E dis

CM

Ybi

nD

E dis

SPE bi

nSI

bin

NE w

eiSI

dis

SPE di

sD

E bin

SPE w

eiD

E wei

FCSIwei

CMYweiSC

NEbinCMYdis

NEdisCMYbin

DEdisSPEbin

SIbinNEwei

SIdisSPEdisDEbin

SPEweiDEwei

-1.5

-1

-0.5

0

0.5

1

1.5

Cohens's d

FC SCC

MY SI NE

DE

SPE

-0.2

0

0.2

0.4

Beha

vior

al p

redi

ctio

n ac

cura


comparisons

FC SCC

MY SI NE

DE

SPE

FCSC

CMYSI

NEDE

SPE-1

-0.5

0

0.5

1 Cohens's d

Dis Bin Wei

-0.1

0

0.1

0.2

Beha

vior

al p

redi

ctio

n ac

cura

cy WeightsPairwise

comparisons

Dis Bin Wei

Dis

Bin

Wei -0.2

-0.1

0

0.1

0.2

Cohens's d

a b

c d e f

FIG. S5. Comparison of the behavioral predictive utility of connectome communication models (NBS, N = 360 thresholdedconnectomes, cognition prediction accuracy)

NE bi

n

FCSP

E dis

SPE bi

nC

MY

wei

DE w

eiC

MY

bin

CM

Ydi

sN

E dis

NE w

eiD

E dis

DE bi

nSI

bin

SIw

eiSI

dis

SCSP

E wei

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Beha

vior

al p

redi

ctio

n ac

cura

cy


NE bi

nFC

SPE di

sSP

E bin

CM

Yw

eiD

E wei

CM

Ybi

nC

MY

dis

NE di

sN

E wei

DE di

sD

E bin

SIbi

nSI

wei

SIdi

sSC

SPE w

ei

NEbinFC

SPEdisSPEbin

CMYweiDEwei

CMYbinCMYdis

NEdisNEweiDEdisDEbinSIbinSIweiSIdis

SCSPEwei -1.5

-1

-0.5

0

0.5

1

1.5

Cohens's d

FCC

MY

SPE

NE

DE

SC SI

-0.2

0

0.2

0.4

Beha

vior

al p

redi

ctio

n ac

cura


comparisons

FCC

MY

SPE

NE

DE

SC SI

FCCMYSPE

NEDESCSI

-1

-0.5

0

0.5

1 Cohens's d

Bin Dis Wei-0.1

0

0.1

0.2

Beha

vior

al p

redi

ctio

n ac

cura

cy WeightsPairwise

comparisons

Bin Dis Wei

Bin

Dis

Wei-0.5

0

0.5

Cohens's d

a b

c d e f

FIG. S6. Comparison of the behavioral predictive utility of connectome communication models (Lasso regression, N = 360thresholded connectomes, tobacco use prediction accuracy)



https://doi.org/10.1101/2020.04.21.053702


23

NE di

sN

E wei FC

NE bi

nSP

E bin

CM

Yw

eiD

E wei

SIdi

sC

MY

bin

CM

Ydi

s

SCSP

E dis

SPE w

eiD

E bin

SIw

eiSI

bin

DE di

s

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Beha

vior

al p

redi

ctio

n ac

cura

cy


NE di

sN

E wei FC

NE bi

nSP

E bin

CM

Yw

eiD

E wei

SIdi

sC

MY

bin

CM

Ydi

sSC

SPE di

sSP

E wei

DE bi

nSI

wei

SIbi

nD

E dis

NEdisNEwei

FCNEbin

SPEbinCMYwei

DEweiSIdis

CMYbinCMYdis

SCSPEdisSPEwei

DEbinSIweiSIbin

DEdis -1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cohens's d

NE

FCC

MY

SPE

SC DE SI

-0.1

0

0.1

0.2

0.3

Beha

vior

al p

redi

ctio

n ac

cura


comparisons

NE

FCC

MY

SPE

SC DE SI

NEFC

CMYSPESCDESI -1

-0.5

0

0.5

1

Cohens's d

Wei Dis Bin

-0.1

0

0.1

0.2

Beha

vior

al p

redi

ctio

n ac

cura

cy WeightsPairwise

comparisons

Wei Dis Bin

Wei

Dis

Bin-0.2

-0.1

0

0.1

0.2

Cohens's d

a b

c d e f

FIG. S7. Comparison of the behavioral predictive utility of connectome communication models (NBS, N = 360 thresholdedconnectomes, tobacco use prediction accuracy



https://doi.org/10.1101/2020.04.21.053702


24

FIG. S8. Structure-function coupling across connectome communication models (N = 68, 360 unthresholded connectomes).



https://doi.org/10.1101/2020.04.21.053702


25

Connected All UnconnectedNode pairs

-0.2

-0.1

0

0.1

0.2

0.3

0.4

FC c

orre

latio

n

a

All Intra-hemisphericNode pairs

-0.2

-0.1

0

0.1

0.2

0.3

0.4

FC c

orre

latio

n

b

FIG. S9. Stratification of structure-function coupling across connectome communication models (N = 360 thresholded connec-tomes). Markers indicate median (across subjects) Spearman correlation between FC and communication models. Squared,circular and triangular markers denote models computed on weighted, binary and distance connectomes, respectively. Markercolors denote different FC predictors. Teal: shortest paths, violet: navigation, red: diffusion, blue: search information, orange:communicability, pink: SC, and green: Euclidean distance. (a) Structure-function coupling anatomically connected (left),all (center) and anatomically unconnected (right) region pairs. (b) Structure-function coupling for whole-brain (left) andright-hemisphere (right) connectomes.



https://doi.org/10.1101/2020.04.21.053702


26

NE bi

nN

E wei

NE di

sC

MY bi

nC

MY w

eiSC

SPE bi

nSP

E wei

SPE di

sSI

bin

CM

Y dis

SIw

eiD

E wei

SIdi

sD

E dis

DE bi

n

2.5

7.5

12.5

17.5Av

erag

e ra

nkin

g N=360, unthresholded

NE

SCC

MY

SPE SI DE

2.5

7.5

12.5

N=360, unthresholded

Wei

Bin

Dis

2.5

7.5

N=360, unthresholded

DE di

sN

E bin

SCN

E wei

NE di

sSP

E dis

DE w

eiSP

E wei

SPE bi

nD

E bin

SIbi

nC

MY w

eiC

MY di

sSI

dis

CM

Y bin

SIw

ei

2.5

7.5

12.5

Aver

age

rank

ing N=68, thresholded

SC NE

DE

SPE

CM

Y SI

2.5

7.5

N=68, thresholded

Dis

Bin

Wei

2.5

7.5

N=68, thresholded

NE w

eiSC

SPE w

eiC

MY w

eiSI

wei

NE bi

nD

E wei

CM

Y dis

SPE bi

nSP

E dis

SIdi

sC

MY bi

nN

E dis

DE di

sSI

bin

DE bi

n

2.5

7.5

12.5

Aver

age

rank

ing N=68, unthresholded

SC NE

SPE

CM

Y SI DE

2.5

7.5

N=68, unthresholded

Wei Dis

Bin

2.5

7.5

N=68, unthresholded

a b c

d e f

g h i

FIG. S10. Overall ranking of communication models (multiple connectome mapping pipelines). Communication models and SCwere ranked according to averaged behavioral and functional predictions. (a,d,g) Overall predictive utility ranking. Rankingsshown in (a,d,g) grouped by (b,e,h) communication models and (c,f,i) connection weight definitions.



https://doi.org/10.1101/2020.04.21.053702


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