The Brain’s First “Traffic Map” through Unified Structural and Functional Connectivity (USFC) Modeling

The brain’s white matter connections are thought to provide the structural basis for its functional connections between distant brain regions but how our brain selects the best structural routes for effective functional communications remains poorly understood. In this study, we propose a Unified Structural and Functional Connectivity (USFC) model and use an “economical assumption” to create the brain’s first “traffic map” reflecting how frequently each structural connection segment of the brain is used to achieve the global functional communication system. The resulting USFC map highlights regions in the subcortical, default-mode, and salience networks as the most heavily traversed nodes and a midline frontal-caudate-thalamus-posterior cingulate-visual cortex corridor as the backbone of the whole brain connectivity system. Our results further revealed a striking negative association between structural and functional connectivity strengths in routes supporting negative functional connections as well as much higher efficiency metrics in the USFC connectome when compared to structural and functional ones alone. Overall, the proposed USFC model opens up a new window for effective brain connectome modeling and provides a considerable leap forward in brain mapping efforts for a better understanding of the brain’s fundamental communication mechanisms.


Introduction
As of now, the two main non-invasive imaging approaches for characterizing the brain's connectome are: structural diffusion-weighted MRI 1 and resting state functional MRI (rs-fMRI) 2 .Structurally, diffusionweighted MRI-based tractography approach offers a global view of how distant brain regions are connected through white matter ber tracts 3 .The human brain's structural connectome is remarkable for its highly organized and modular architecture, facilitating e cient communication and functional specialization 4,5 .Functionally, the resting-state fMRI approach offers a way of measuring "functional connectivity (FC)" by quantifying the degree of blood oxygen level dependent (BOLD) signal uctuation synchronizations across distant brain regions 6,7 .Based on the "neurons ring together wiring together" principle 8 , FC measures enable the characterization of the human brain functional connectome 9 , which is typically organized into distinct networks including the somatomotor 6 , visual 10 , auditory 11 , default mode network (DMN) 12,13 , salience 14 , and executive control ones 15 .These functional networks are generally believed to directly underlie various primary, cognitive, and socioemotional functions 16,17 .Both the structural and functional connectome feature a small-world network topology, characterized by densely locally interconnected clusters of brain regions and critical long-distance "short cuts" and hubs that bridge inter-cluster communication 18,19 , providing supports for both segregated and integrated information processing, essential for complex cognitive processes 20 .
There are ongoing efforts to unveil the relationships between structural and functional connectomes based on the idea that structural white matter ber bundles form the foundation for FC or communication [21][22][23][24][25][26][27][28] .Most studies are correlational in nature and their ndings support a moderate positive relationship between structural and functional connections (via global modules max (R 2 ) ≈ 0.1, via local modules R 2 ranging between − 0.01 to 0.42) 24,29,30 .However, it is generally accepted that there is not a one-to-one correspondence between these two types of connections since many functional connections exist between brain regions without direct structural connections 31 .Instead, FC could be mediated by multiple segments of structural connections.Given the interconnected nature of the structural connectome, it is likely that there are multiple structural pathways linking these pairs of regions with signi cant FC without a direct structural link.However, it remains unclear how our brain selects the best structural route for a speci c functional connection.New insights into this structural-functional coupling mechanism would shed important light on how our brain works in health and disease.
In this study, we liken the brain to a country with different brain regions being different cities, the brain's structural connectome corresponding to the road system, and the functional connectome re ecting the amount of people traveling among different cities.Given that there are different routes from one city to another, how people choose their routes will determine the "tra c map" (i.e., the load of each road segment) of the road system.Under this new framework, the goal of this work is to characterize the "tra c map" and reveal the most heavily used structural segments of the brain, which may bear signi cant implications for better understanding of both normal brain functioning and diseased conditions.To achieve this, we make one important economical assumption that distance and road condition (translating to anatomical distance and structural connectivity (SC) strength in the brain) are the two most important factors for route selection.Based on this principle, we aim to build the brain's rst uni ed structural and functional connectome (USFC) to uncover its effective "tra c map".Employing the model, we identi ed an asymmetric network of brain tra c, characterized by a predominance of pathways originating from the subcortical, default-mode, and salience networks as well as a midline frontal-caudate-thalamus-posterior cingulate-visual cortex corridor that acts as the backbone of the global brain communication system.Our results also accentuate the critical role of stronger structural connections in underpinning signi cant negative FC, offering fresh perspectives on their functional relevance.Finally, the USFC map exhibits much elevated levels of e ciency, modularity, and betweenness centrality in comparison to conventional structural and FC maps, supporting its superiority in modeling the brain's superb e ciency in communication.Overall, the USFC model provides a novel framework for modeling the brain's effective connectivity system and potentially opens up a new window uncovering the brain's working principles.

Materials and Methods
This study involved 394 subjects from the Human Connectome Project − 1200 Subjects Release (S1200) including behavioral and 3T MRI data.These subjects were randomly selected from the shu ed dataset, constituting one-third of the total sample.We downloaded minimally processed diffusion tensor imaging, T1-MPRAGE and rs-fMRI data to perform structural and FC analysis.Details of the minimal image processing are provided in Glasser et al. 32 .

Structural connectivity
Individual structural networks were constructed through the utilization of whole brain probabilistic ber tracking with MRtrix3 (www.mrtrix.org)within the subject's space as described in Has Silemek et al. 33 .To generate fractional anisotropy (FA) and mean diffusivity maps, we initially applied diffusion tensor tting to diffusion tensor imaging data, accounting for head motion and eddy currents, and performed skull stripping procedures using FSL's diffusion toolbox 34 .
To obtain a precise estimation of the ber orientation distribution (FOD) during constrained spherical deconvolution, we determined the multi-shell, multi-tissue response functions based on FOD values exceeding 0.7 for white matter and lower that 0.2 for gray matter and cerebrospinal uid 35 .Subsequently, for ber construction, we employed probabilistic tractography algorithms, which generated a total of 150,000 bers, with a minimum length threshold set at 20 mm.Default parameters included a step size of 0.2 mm, a minimum radius of curvature of 1 mm, and an FOD cut-off of 0.1.Seeds for tractography were speci ed using all voxels from 1 mm dilated white matter masks.The tracking of these seeds was con ned by the mask's boundaries and prede ned FA or FOD thresholds.Streamlines were mapped onto structural image which was labeled based on the AAL atlas (2009).Following this, we computed the average FA for each ber after estimating the FA values at each point along the ber's trajectory as an index of the SC strength for this ber tract.For each pair of nodes, the mean FA of the bers that intersect both nodes was calculated, ensuring that the number of bers in the selected vectors of the nodes matched the number of bers in the tract structure.

Functional connectivity
The preprocessing steps for FC involved several key procedures, including skull stripping using FSL, segmentation of white matter, gray matter, and cerebral spinal uid via FSL FAST and motion correction with AFNI (participants with framework displacement > 0.3 mm and < 900 volumes were excluded), bandpass ltering in the frequency range of 0.01 to 0.1 Hz using AFNI, and spatial smoothing via a Gaussian kernel with a full width at half-maximum of 6 mm, non-linear registration of rs-fMRI images to the Montreal Neurological Institute atlas using ANTs.Following preprocessing, global signal regression was applied to remove the mean gray matter signal.Subsequently, FC was computed by measuring the correlation between the average signals of each pair of 90 regions in the AAL atlas (p < 0.05, falsediscovery rate (fdr) 36 corrected).

Uni ed Structural and Functional Connectome (USFC) Construction
Construction of USFC was performed by a custom MATLAB script including the following procedures:

Template Distance Calculation
First, we de ned a standard distance map based on the AAL template extracting the anatomical coordinates for designated brain regions, which were sequentially labeled from 1 to 90.Then, the Euclidean distance between the center of mass of each of the 90 region pairs was determined.

Identifying the most "e cient" pathway
The cost function was de ned as the Euclidean distance of AAL atlas divided by the strength of direct SC between a pair of regions along all potential routes (up to 4 steps were searched).The most "e cient" pathway for each FC in each subject was identi ed by summing the cost of each "step" and choosing the one with the least "cost" as follows: where EP is the most e cient pathway, D denotes the Euclidian distance and SC re ects the structural connectivity between each pair of AAL connection.Schematic demonstration of the most "e cient" pathway is visualized in Fig. 1.

Uni ed structural and functional connectivity (USFC) value calculation
A USFC value for each "road segment"/direct SC was then calculated as the sum of all FC values that use this segment in their respective routes, essentially quantifying the amount of "tra c" on this "road segment" for each subject (i.e., weighted by both the number and degree of "tra c") (Fig. 1).After calculating the mean USFC by averaging the values in each pair of connections across the group, onesample t-test and fdr correction at a threshold p lower than 0.05 were applied.

Structural-functional relationships across all USFC routes:
To better understand the relationships between SC and FC along the de ned USFC routes, we performed functional-structural strength correlation analysis at the group level across all routes in four subgroups based the number of steps of the corresponding route, focusing on those that are consistent in over 50% of the subjects.The SC for each step was calculated by averaging the SC values for every pair of nodes within the respective route.Spearman correlation was performed to test the relationship between the SC and FC at each step and p < 0.05 was accepted as signi cant.

Graph-theoretical metrics:
To examine the information transferring e ciency of the newly derived USFC connectome, we utilized three principal graph-theoretical metrics calculating via Networkx package in Python 37 to assess weighted network characteristics: e ciency 38-40 , modularity 41 , and betweenness centrality 42 .E ciency denotes the network's capacity for swift and economical propagation of information.Modularity quanti es the degree to which the network is partitioned into cohesive communities or clusters with dense intra-cluster connections.Betweenness centrality measures the nodes' role in facilitating information ow, thus re ecting their capacity to integrate data across disparate functional regions.These metrics were computed for each individual across various metrics, namely FC, SC, and USFC, and statistical comparisons were made using the t-test.

Results
The brain's rst "Tra c Map" The USFC map, characterizing the accumulative "functional load" of each structural connection accounting for the distance (Fig. 1 & Supplementary Fig. 1a), is visualized in the rst column of Fig. 2a while the SC and FC maps were presented in the rst columns of Fig. 2b, and c, respectively.To better quantify the global distribution of USFC, SC, and FC weights in each brain region, we calculated the overall regional load of each connectivity type and showed their distribution in middle column of Fig. 2. It is immediately clear that USFC featured a long right tail with a set of regions showing much higher values that the rest of the brain (second column of Fig. 2a and Supplementary Table 1).Based on the interquartile range (IQR) calculation 43 , we detected 11 outlier regions (out of the range between the 25th and 75th percentile) with much higher regional USFC values than the rest of the brain, indicating their heaviest involvement in all USFC routes.These regions include the bilateral posterior cingulate gyrus (PCG) in the DMN, thalamus/caudate/pallidum in the subcortical network, dorsolateral cingulate gyrus in the salience network, and left Heschl gyrus [median (IQR): USFC = 48.6 (21.07)] (second column of Fig. 2a & Supplementary Table 1).Two of these outliers (bilateral thalamus) were also highlighted by SC [median (IQR): SC = 19.3(8.24)] (second column of Fig. 2b), while no outlier was found in FC [median (IQR): FC = 6.69 (4.06)] (second column of Fig. 2c).Consistent with the regional loadings, when examined at network level, the subcortical, the salience and the default-mode network ranked as the top three with highest network-level USFC values (third column of Fig. 2a).
The ten most heavily used structural pathways based on USFC were shown in Fig. 3. Strikingly, the two hubs of the DMN (i.e., the right PCG and orbital part of the superior medial frontal cortex), were involved in 7 out of the top-10 most heavily used USFC pathways (Fig. 3 & Supplementary Table 2).The bilateral caudate and thalamus were involved in 6 out these top 10 pathways.Together with three connections between the PCG and visual regions (i.e., left calcarine, superior occipital gyrus and cuneus), one connection between the caudate and left superior orbital frontal cortex, and another one between the right calcarine and inferior occipital gyrus, the top 10 most heavily USFC pathways feature a clearly de ned, along-the-middle-line, anterior-to-posterior backbone corridor connecting medial frontal to caudate to thalamus and to visual regions (Fig. 3 & Supplementary Table 2).

Relationships between SC and FC strengths along the de ned USFC routes
To better understand the relationships between SC and FC strengths along the de ned USFC routes, correlation analysis was done for USFCs at each step for negative ( rst column of Fig. 4) and positive FCs (third column of Fig. 4) separately.There are 890/769/3 1-/2-/3-step USFCs supporting positive FCs and 546/1334/42 1-/2-/3-step USFCs supporting negative FCs, as shown in the middle column of Fig. 4, with images from top to bottom corresponding to the 1-step, 2-step, and 3-step USFCs, respectively.No common patterns (i.e., shared by > 50% of subjects) emerged for 4-step connections so they were not evaluated.For positive FCs, signi cantly positive (for 1-step routes) (Fig. 4a, third column) or nonsigni cant correlations (for 2 and 3-step routes) (Fig. 4b & Fig. 4c, third column) were observed for routes, which is consistent with previous ndings 24 .Intriguingly, more signi cant and stronger negative associations were identi ed for routes underlying negative FCs for all routes raging from 1 to 3 steps (Fig. 4, rst column), indicating that stronger negative FC are supported by USFC routes with overall stronger SC.

Information Transferring E ciency of USFC:
To examine the information transferring property of the USFC map, three graph-theoretical metrics, namely global e ciency, betweenness centrality, and modularity were calculated and compared between SC, FC, and USFC maps.As shown in Fig. 4, USFC demonstrated superior performances across all three measures, as evidenced by signi cantly higher global e ciency (p < 0.001) (Fig. 4a), betweenness centrality (p < 0.001) (Fig. 4b) and modularity (p < 0.001) (Fig. 4c).In line with the global measures, signi cantly superior local e ciency was observed across the entire brain in USFC compared to SC and FC alone (Fig. 4d) (p < 0.001).Higher regional betweenness centrality was observed in regions primarily involved in the DMN, as well as in salience, frontoparietal, dorsal attention, limbic, visual and somatomotor networks (Fig. 4e) (p < 0.001).Higher local modularity was located in salience, frontoparietal, limbic and subcortical networks (Fig. 4f) in USFC compared to FC and SC (p < 0.001).

Discussion
Based on an economical assumption, our new Uni ed Structural and Functional Connectivity (USFC) modeling represents the rst effort to build a brain's effective "tra c map" highlighting the brain's major structural pathways that are most heavily used for e cient functional signal transferring.Based on this model, we revealed a highly skewed brain tra c system featuring the subcortical, the default-mode, and the salience network housing some of the brain's most traversed nodes and a medial frontal-caudatethalamus-posterior cingulate-visual cortex midline "backbone" corridor as the mostly heavily used structural pathways.Moreover, the nding that stronger structural connections are underlying stronger negative functional connections further supports the functional roles of negative FC and provides a fresh perspective on the dynamic interactions among brain regions.Finally, the signi cantly higher e ciency, modularity, and betweenness centrality demonstrated in the USFC map when compared with structural and functional connectomes may support the superiority of this "tra c map" in potentially revealing the true working mechanism of the human brain.Overall, the proposed USFC model opens a new window for brain connectome modeling and provides a considerable leap forward in brain mapping efforts by offering a more intricate depiction of the brain's connectivity landscape.
The heavily skewed "tra c map" that features the central role of the DMN in USFC.
Our analysis uncovered an striking pattern within the brain's USFC blueprint: the DMN regions collectively possess the third highest nodal USFC values while more strikingly, seven of the top ten most heavily tra cked pathways involve either the PCG or medial prefrontal cortex, the two hub regions of the DMN 44 .Centrally located and occupy a large portion of the brain, the DMN is known for being "active" during rest and its versatile roles in self-reference, social cognition, episodic and autobiographical memory, language, sematic memory, among others [45][46][47] .All these functions involve complex communications within and between DMN and other brain regions which likely underlies our nding of its central role in the newly de ned USFC system.Speci cally, the prominent inter-network connections between the DMN hubs and subcortical/visual regions as shown in the top ten USFC pathways likely underscore the DMN's potential integrative role across different domains, which is highly in line with ndings demonstrating DMN's active and dynamic reorganization of its connectivity patterns across a range of cognitive and socioemotional tasks [48][49][50][51] .This nding provides another critical piece of evidence from a global brain "tra c map" perspective that the DMN's role likely goes beyond a passive default state but rather globally contributes to the brain's e cient signal processing across task domains 49,50 .Overall, our nding of the central role of the DMN in the newly de ned USFC system provides new support/explanation for its established importance in development 50,52 , normal adult functioning 48-51,53−55 , aging 56,57 and various brain disorders [58][59][60][61] .
The importance of subcortical/salience networks in USFC and midline "backbone" corridor Beyond DMN connections, six of the top-ten most heavily tra cked segments involve the thalamus/caudate while at a network level, the subcortical and salience network regions collectively rank as the two mostly traversed networks in the whole brain "tra c map" ranking (Fig. 2).Regarding the salience network, although not highlighted in the top ten mostly heavily used pathways, its regions collectively rank second in the whole brain tra c map system and the middle cingulate cortex was detected as one of the "outliers" with the highest USFC loadings.These ndings are consistent with its reported role of lying on the apex of the brain's global coordination system by performing a "switching" role among large scale functional networks, especially between the DMN and dorsal attention networks 48,51,62,63 .
The subcortical regions, in particular the thalamus's prominence in this tra c system is consistent with not only its known role as an "relay center" connecting peripheral neural system with the brain cortices but also its versatile involvement in modulating and re ning sensory data, shaping consciousness, and enhancing cognitive functions [64][65][66] .Its highly utilized connectivity with the PCG may be particularly indicative of a sophisticated mechanism that merges external sensory inputs with internal states, an essential process for coherent cognitive function 67 .Similarly, the caudate nucleus not only plays a critical role in movement planning and execution but also serves in a multitude of essential brain functions, including learning, memory, reward, motivation, emotional regulation, and aspects of romantic interaction 68,69 .Structurally, frontal regions are known to be connected to the caudate, which in turn is connected to the thalamus, and subsequently projecting to PCG, providing SC support for the observed medial frontal-caudate-thalamus-posterior cingulate -visual pathway that leads the most heavily USFC segments.The nding of a clearly de ned midline corridor connecting frontal to caudate to thalamus to posterior cingulate and nally to visual cortices supporting the most "tra c" in the brain through USFC modeling is striking and opens up new windows for better understanding of the "backbone" structure of the brain's global communication system.Consistent with our ndings, Hagman et al have previously delineated the SC hubs of the human brain and similarly detected a midline "structural core" linking precuneus to posterior, middle, anterior cingulate cortex and nally to medial orbital frontal cortices 4 .However, their examinations exclude subcortical areas so the potential "bridging"/ "disseminating" (e.g., the thalamus) role of subcortical regions were not counted for.With combined consideration of both functional and SC and including both cortical and subcortical regions, the midline corridor delineated in this study featuring frontal-subcortical-parietal-occipital links may have better captured the "backbone" of the brain's global communication system and deserves more attention in future search of its relevance in health and disease.
The intriguing nding of strong structural underpinnings of negative FCs.
The nding of moderate but signi cant positive correlations between SC and FC strengths associated with positive FCs is in line with previous reports 24,70 .However, the nding that routes underpinning negative FCs show a robust negative relationship between SC and FC strengths across one-to-three step connections is more intriguing.Ongoing debate regarding global signal regression and the consequent observation of negative correlations (anti-correlations), underscores the lack of consensus on a singular method for processing resting state data to uncover the 'true' nature of brain functionality 71 .Contrary to the notion of negative FC as a mere byproduct of signal processing, emerging research posits it as a salient aspect of the brain's functional architecture de ning modularity of the resting-state fMRI connectome, deeply linked with its structural framework 12,[72][73][74][75][76][77] .Our ndings add to the evidence supporting the functional signi cance of negative FCs after global signal regression and suggest that the brain utilizes a delicate tra c system to choose the best routes (i.e., composed of segments with stronger SC) for negative interactions across different brain regions.Notably, Skudlarski et al. indicated that regions with negative functional FC are not necessarily disconnected structurally 78 .Instead, there is an implication of a complex relationship where structurally close regions can exhibit negative FC, suggesting an intricate coordination of brain dynamics.However, we have to point out that the "one-step" route delineated in this study should not be confused with "direct SC" or "connected by a single white matter bundle" give the limitation of diffusion-weighted imaging-based tractography.In other words, the one-step SC used in this study was derived based on probabilistic tractography and as long as there is a "connected structural route" connecting two brain regions, we de ne these two regions are "structurally connected" and treat them as "one-step" connections.It is possible that multiple white matter ber bundles are underlying each of these "one-step" structural connection and the accumulated phase lag across the multiple structural connections may have contributed to the observed negative FC 79 .Compared with the relationships associated with negative FCs, where all three step groups (i.e., 1-3) show signi cant negative correlations, the relationships associated with positive FCs only show positive relationships for 1-step route.One potential explanation could be that choices for multiple-step positive FCs are more abundant than those for negative FCs and SC is not necessarily a limiting factor, and the choices are not as tightly regulated, resulting in weaker SC-FC correlations.Regardless, the nding that stronger structural routes are underlying stronger negative FCs provides further support for the importance of negative FCs in the brain's e cient/effective communication and functioning.
The USFC-based connectome demonstrates signi cantly higher performance than both the FC and SC systems.
For all three measures of the brain system communication effectiveness, namely global e ciency, modularity, and betweenness centrality, the USFC-based connectome demonstrates signi cantly higher performance than both the FC and SC systems.These ndings support the potential superiority of the USFC system in depicting the brain's signal transferring e ciency.Essentially, only looking at the "road system" (i.e., equivalent to the brain's SC system) or the nal "number of people traveling between any two cities" (i.e., equivalent to the brain's FC system) could not provide a clear picture of the brain's "tra c patterns" while it is this tra c pattern that directly unveils how the road system effectively work to support the between-city travelling (i.e., signal transferring).The much higher global e ciency and betweenness centrality is likely supported by the highlighted most heavily utilized routes between major functional works while the higher modularity may result from the more densely connected local systems within USFC.
Although this work provides a new perspective on brain connectome modeling, there are several major limitations associated with the current version of USFC that deserve future improvements.First, we made the economic assumption (i.e., shorter distance and stronger SC) for route selection but the "real-time tra c" is not considered in this formula.In other words, future improvement could further consider the current "tra c" along each route (i.e., real-time modeling of the "dynamic" FC 80 ) in determining the optimal route between two brain regions.Second, as mentioned above, direct structural connection in this study might not represent one single ber bundle the 1-step routes may consist of multiple white matter ber bundles, which bears critical implications on the understanding of SC-FC relationships, particular those with the negative FCs.Finally, we used average FA along the tracts to index SC strength but there are other metrics too (e.g., number of bers) worth further consideration.
Overall, the USFC model presents a compelling new framework to model the brains "effective connectome" and opens a new window for future research aimed at deciphering the enigmatic principles that govern the brain's e cient communication system.By highlighting the "most-heavily-used brain pathways/networks" in its current version and pursuing continued efforts to re ne/navigate this complex "tra c" in both normal and diseased populations, the implications from this new model may reach far into the realms of neuroscience, with the potential to transform both theoretical models and clinical/intervention approaches.

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