A Population-Based Atlas of the Macroscale Structural Connectome in the Human Brain

A comprehensive map of the structural connectome in the human brain has been a coveted resource for understanding how brain networks function under normal and pathological conditions. Here we report an expert-vetted, population-based atlas of the structural connectome derived from diffusion MRI data (N=842). This was achieved by creating a high-resolution template of diffusion patterns averaged across individual subjects and using tractography to generate 550,000 trajectories of representative white matter fascicles. The trajectories were clustered and labeled by a team of experienced neuroanatomists. Multi-level network topology was illustrated by connectograms of the whole brain, subdivisions in the association, projection, and commissural pathways, and individual fiber bundles. This atlas of the structural connectome represents normative neuroanatomical organization of human brain white matter, complimentary to traditional histologically-derived and voxel-based white matter atlases, allowing for better modeling and simulation of brain connectivity for future connectomic studies as well as clinical and educational applications.


Introduction
The organization of structural connectivity in the human brain determines how neural networks communicate, thereby serving as a critical constraint on brain functionality and providing potential etiology for clinical pathology 1,2 . Characterizing this structural organization has relied on either histological slides or neuroanatomically-validated atlases based on individual subjects 3,4 ; however, a population-based 3-dimensional (3D) structural connectome at the macroscale level has yet to be constructed. A population-based connectome is critical for demonstrating representative topological interconnectivity in the general population, a stated objective of the national investment in the Human Connectome Project 5,6 . If achieved, such a map of the structural connectome could augment existing histological and single-subject atlases, thus allowing for robust modeling and simulation in both empirical and theoretical studies.
To date, diffusion MRI is the only non-invasive tool for mapping the 3D trajectories of human macroscopic white matter pathways 7,8 . This is realized by resolving local fiber orientations at the voxel level and delineating entire axonal trajectories by implementing a stepwise tracking algorithm 9 .
Nonetheless, caveats of diffusion MRI fiber tracking include false tracts and suboptimal white matter coverage 10,11 . The validity of tractography can range from 3.75% to 92% due to differences in reconstruction methods and algorithms 12 . An optimized tracking approach is required for achieving the highest validity. To further reduce false fibers, image acquisition should utilize a contemporary high-angular-resolution modality 13 , and any collection of tracked pathways should undergo examination by expert neuroanatomists.
Here we constructed a population-based structural connectome by a template-based and expert-vetted approach. We employed high-angular-resolution diffusion MRI data (n=842) from healthy subjects in the Human Connectome Project (HCP) database 14 and aggregated them into an averaged template of diffusion distributions that can inform the orientations of underlying fiber architectures. The averaged diffusion pattern of the entire sample is thus representative of normative, non-pathological structural characteristics within healthy subjects. Based on this template, a total of 550,000 tracks (density around 1 track per voxel) were generated using a tracking method that was shown to achieve the highest number of valid connections in an open competition 12 . Generated tracks were subsequently clustered and then labeled by a team of clinical neuroanatomists, capitalizing on their previous experience in both cadaveric white-matter and comparative tractography techniques 15,16 . Furthermore, the tracks were categorized into the projection, association, commissural, cerebellar, brainstem, and cranial nerve pathways to generate multi-level connectograms illustrating network topology at the macroscopic level.
The strategy of this approach allowed us to compile a comprehensive atlas of the structural connectome in the human brain at the population level, allowing for taxonomical identification of pathways that together comprise the full macroscopic structural connectome.

A high spatial and angular resolution diffusion template of the human brain
Diffusion MRI data from 842 participants was reconstructed in a standard space to calculate the spin distribution function (SDF) 17,18 within each voxel (Fig. 1a). An SDF is an empirical distribution of the density of diffusing water orientations, calculated for each voxel to reveal the underlying fiber architectures (Fig. 2a). The SDFs of all subjects were averaged to build an SDF template, heretofore called the HCP-842, which represents an average diffusion pattern within a normal population (Fig. 1b).
As shown in Fig. 2, the magnitude of the peaks (Fig. 2b) and their orientations (Fig. 2c) derived from the SDF template reliably reflect the coverage of white matter structures and inform their local fiber orientations (red: left-right, green: anterior-posterior, blue: inferior-superior). The peaks on an SDF suggest the local orientations of underlying fiber bundles, whereas the magnitudes measured at the peaks provide quantitative measurements for connectivity. These offer the necessary information for a fiber-tracking algorithm to delineate long-distance white matter trajectories.
Qualitatively, the HCP-842 appears to resolve underlying neuroanatomical architecture with high fidelity: Comparing a coronal slice of the HCP-842 (1-mm resolution, Fig. 2d) with a similar section from the BigBrain histology image (the 200-micron resolution version, Fig. 2e), we see that HCP-842 clearly delineates subcortical structures such as the hippocampus (HIP), substantia nigra (SN), red nucleus (RN), and thalamus (TH). The high spatial resolution of the orientation map is even more apparent at the anterior commissure (AC) (Fig. 2f), a small left-right connecting pathway clamped by the pre-commissural (PreC) and post-commissural (PostC) branches of fornix that run in the vertical direction (color-coded by blue). The clamping structure formed between AC and fornix is a benchmark for examining the spatial resolution of the template. Fig. 2f resolves AC from the PreC and PostC branches, whereas Fig. 2g shows the averaged SDFs at the same region depicting the structural characteristics of AC with the PreC and PostC branches of the fornix. The ability to resolve branches of fornix from AC reveals the intricate sensitivity of the HCP-842 to map detailed brain connections.

Supervised labeling and segmentation of major pathways
We applied whole-brain fiber tracking to the HCP-842, producing a total of 550,000 fiber trajectories in the standard space to achieve an average density of 1 track per voxel (Fig. 1c). A white matter mask was used to remove tracks that have premature terminations in the core white matter. The remaining whole-brain tracks were then automatically clustered by a single-linkage clustering algorithm, generating unique clusters of fiber bundles (Fig. 1d). The trajectories that were proximally close to one another were grouped. Each cluster could subsequently contain a different number of trajectories based on the anatomical proximity of the tracks. Suppl. Fig. S1 shows the largest 40 clusters as an example. A team of clinical neuroanatomists examined and labeled the clusters according to neuroanatomical nomenclature. Suppl. Table S1 lists all labels used in naming the clusters and the relevant neuroanatomy literature used for examination. Label "X" indicates a false tract, which may arise due to false continuations (Suppl. Fig. S2a) or premature termination (Suppl. Fig. S2b). Only the 550 largest clusters were used because the false rate (either false continuation or premature termination) increased substantially in clusters with a smaller size (Suppl. Fig. S2c).
The labeled clusters were subsequently merged according to their neuroanatomy label, and missing components of the large fiber bundles were tracked separately and merged to ensure completeness as per the literature (Fig. 1e). The high-angular-resolution can be appreciated in the corticospinal tracts generated from HCP842 (Suppl. Fig. S3a Fig. S3b), as the anatomical evidence (Suppl. Fig. S3c, modified from Gray's Anatomy) indicates its missing lateral parts.

A population-based atlas of macroscopic structural connectome
The full atlas of the structural connectome is shown in Fig. 3 (abbreviation listed in Suppl. Table S1) and includes the most comprehensive map of white matter pathways yet reported. This includes the projection pathways that connect cortical areas with subcortical nuclei, brain stem nuclei, and brainstem.
Acoustic radiation has not been previously reported in tractography due to the complicated crossing pattern involved with the pathway. The association pathways connect disparate cortical areas, including a set of U-fibers (U) which have not previously been comprehensively tracked or presented in the standard space. The commissural pathways connect the two hemispheres and include the corpus callosum, anterior commissure, and posterior commissure. The cerebellar pathways include the cerebellar tracts (CB) and peduncles (SCP, MCP, ICP), and they provide the major input, output, and internal connectivity of the cerebellum. We were even able to resolve several brainstem pathways, such as central tegmental tract (CTT), dorsal longitudinal fasciculus (DLF), lateral lemniscus (LL). Finally, we discovered a limit of the current spatial resolution, where a set of cranial nerves including CN III, CN VII, and CN VIII were successfully identified, but CN I, IV, VI, and IX could not be identified due to insufficient spatial resolution. The detailed connective routes of the structural connectome atlas are presented in Supporting Information, including projection pathways (Suppl. Fig. S4), association pathways (Suppl. Fig. S5), commissural pathways (Suppl. Fig. S6), cerebellar pathways (Suppl. Fig. S7), brainstem pathways (Suppl. Fig. S8), and cranial nerves (Suppl. Fig. S9). The atlas data, including the track trajectories and connectograms, are available at http://brain.labsolver.org.

Neuroanatomical constraints on connective topology
The atlas of the structural connectome from the HCP-842 addresses a critical need in connectivity estimates that suffer from a high false positive error rate 11,12 : the atlas enables estimation of normative region-to-region connectivity that is anatomically constrained. Figure 4 shows region-to-region connectivity matrix weighted by the SDF magnitude along the fiber pathways, segmented into the projection, association, and commissural pathways. The abbreviations for brain region are listed in Suppl. Table S2. Higher intensity (white) indicates greater SDF magnitude along the pathway. This anatomically-constrained view of structural connectivity between gray matter targets highlights how specific classes of white matter pathways define unique connective topologies. For example, commissural pathways have a generally symmetrical topology of connections between the hemispheres, with greater homotopic connectivity than heterotopic connectivity, whereas the association pathways are more uniform in their intra-cortical connections.
Finally, the connectograms of the structural connectome are illustrated in a multi-level approach (Fig. 5).
The connectogram of the whole brain pathways illustrates the first level of the gross network topology ( Fig. 5a, the high-resolution version shown in Suppl. Fig. S10). The overall figure shows a dense network topology, and its network characteristics cannot be readily visualized due to the high complexity of the brain network at this level. The connectograms of the projection, association, and commissural pathways in Fig. 5b, 5c, and 5d depict the second level of the network topology (high-resolution details in Suppl. Fig. S11), and within this level, the connectograms start to reveal important network features.
The projection pathway in Fig. 5b indicates hub structures at thalamus, putamen, and brainstem, illustrating the role of these regions in integrative sensorimotor function between the cerebral cortex and corresponding peripheral systems. The association pathway, as shown in Fig

Discussion
Having an accurate, high-resolution and normative map of both the trajectories of macroscopic white matter pathways and their connectivity diagram has remained an unmet challenge in human neuroscience. Here we present the first complete atlas of the structural connectome that delineates fiber pathways within the cerebrum, cerebellum, brainstem, and a subset of cranial nerves. The fiber trajectories were generated from a group-averaged template of 842 subjects using a fiber tracking algorithm that has been shown to minimize tracking errors relative to other methods 19 . Using an automated clustering approach, tracks were grouped into small bundles and subsequently labeled by a team of clinical neuroanatomists and vetted according to their neuroanatomic nomenclature. This combination of optimizing strategies allowed us to construct a high-quality, group-averaged structural connectome atlas of the human brain, and this HCP-842 atlas and it associated data set will be made publicly available (http://brain.labsolver.org) to promote future connectomic studies and assist neuroscientists to gain insight into the structural topology of the human brain.
We should note that several white matter atlases have been released before, and these mainly consisted of voxel segmentation on individual subjects labeling the core of major pathways using a low angular resolution approach [20][21][22][23] . Several tractography atlases [24][25][26][27] were also developed using diffusion tensor imaging 28 , which was known to have lower angular resolution and cannot resolve crossing patterns 29,30 . Our atlas, by contrast, is the first population-based atlas from 842 individuals using high angular and high spatial resolution data, allowing for the resolution of multiple fiber populations within a white matter region to delineate the intertwining architecture of human white matter. The population-based map of the structural connectome reflects both the 3D trajectories of white matter fascicles and delineates how gray matter regions are physically connected. This comprehensive atlas covers all white matter regions within the cerebrum, cerebellum, and brainstem. The atlas offers structural detail of both large and small pathways, including the clamping structure between the fornix and the anterior commissure, which cannot be discerned from individual studies due to lower resolution and signal-to-noise ratio of conventional diffusion MRI.
While overcoming many challenges, our current approach still has its limitations. Several cranial nerves that are smaller than 1-mm resolution were missed. These can only be tracked using images acquired at a much higher resolution. In addition, the expert examination may have its own errors, especially for identifying minor pathways and branches. It is also possible that the branching patterns of the white matter pathways differ person from person. Unfortunately, the representative pathways provided by our population-based atlas cannot address individual differences. Finally, the atlas reveals only three levels of the network topology, as more recent studies have focused on subcomponents of the fiber bundles (e.g. SLF I, II, and III) 15,16 . Although the spatial resolution of the atlas can be improved, it provides a macroscopic framework for future connectomic studies to explore microscopic connections under its categorical system.
Despite these limitations, a vetted atlas of the structural connectome has many benefits for clinical, scientific, and educational applications. It can be used to confirm or explore potential cortical connections, and the atlas can be used to derive a normative pattern of network measures to assist graph theoretical analysis of clusters and hubs in the brain connectome. In cognitive neuroscience, the atlas can augment functional-structural correlative inferences. In clinical research, the 3D trajectories of major fiber pathways can aid researchers in localizing white matter structures of interest (e.g., electrode placement during deep brain stimulation surgery). Such investigators can use this atlas as an interactive roadmap as they evaluate individual-subject connectomic data. This, for example, may enable future investigations into the correlation of white-matter lesions with known gross-white matter structures.
Another advantage of the current atlas is that it includes a normative template of diffusion distribution across the brain. This may allow for future efforts comparing normal diffusion patterns with those from the neurological or psychiatric pathologies. Finally, in science education, the atlas is a novel resource superseding conventional 2D slice-based histological atlases. The trajectory information provides panoramic views on the relative location of each white matter bundle, allowing for an in-depth understanding of the white matter structure. The diffusion data were reconstructed in the ICBM-152 space (ICBM: International Consortium for Brain Mapping) using the q-space diffeomorphic reconstruction (QSDR) 18 , a method that conserved the diffusible spins after nonlinear transformation and could be applied to DTI, DSI, and multishell data.
QSDR calculated the spin distribution function (SDF), , an orientation distribution function defined as the density of spins that have diffusion displacement oriented at direction during the diffusion time: is a diffeomorphic mapping function that maps standard space coordinates r to the subject's space.
is the Jacobian matrix of the mapping function, whereas is the Jacobian determinant.
are the diffusion signals acquired at . b i is the b-value, and is the direction of the diffusion sensitization gradient. is the diffusion sampling ratio controlling the detection range of the diffusing spins. D is the diffusivity of water, and Z 0 is the constant estimated by the diffusion signals of free water diffusion in the brain ventricle 18 . The nonlinearity of diffusion gradients was corrected using the nonlinear terms of the magnetic field obtained from gradient coils. The HCP dataset includes a 3-by-3 gradient deviation matrix for each voxel to estimate the effective gradient direction and strength.
This matrix was applied to the diffusion sensitization gradient, in Eq. (1) to correct the effect of gradient nonlinearity.
To achieve super-resolution reconstruction, we modified a nonlinear registration algorithm that used Fourier basis as the deformation function 31 to boost the registration accuracy. The original setting used a set of 7-by-9-by-7 Fourier basis at x-y-z directions for 2-mm resolution, and the computation and memory bottleneck was at the inverse step of a 1327-by-1327 matrix (not a sparse matrix). We increased the resolution of the Fourier basis by 4-fold to 0.5-mm resolution (i.e. 28-by-36-by-28 Fourier basis), which required solving an 84676-by-84676 matrix for each optimization iteration.
Here instead of solving the large matrix using a standard Gauss-Jordan method (a complexity of O(n 3 )), which would increase the computation time by a factor of (4x4x4) 3 =262,144, we used the Jacobi method that allowed for parallel processing and could utilize solutions from the previous iteration to speed up the processing. This greatly reduced the computation complexity to O(n) and only increased the computation time by a factor of 4x4x4=64. The parallel processing further reduced the computation time, allowing us to reconstruct the data using multi-thread resources. The registration accuracy was We used a deterministic fiber tracking algorithm that used the SDF information to achieve higher accuracy 32 . Each of the tracks generated was automatically screened for its termination location. A white matter mask created by 0.6 Otsu's threshold was used to eliminate tracks with premature termination in the white matter region. The total number of tracks was set to achieve an average seeding density around 1 track per voxel. Specifically, the fiber tracking was conducted using angular thresholds of 40, 50, 60, 70, and 80 degrees. Each angular threshold generated 100,000 tracks, and a total of 500,000 tracks were obtained. Since the white matter mask also removed tracks connecting to/from the spinal cord, an additional set of whole brain tracking was conducted to allow tracks terminates at the lowest section of the brainstem. The fiber tracking was also conducted using angular thresholds of 40, 50, 60, 70, and 80 degrees. Each angular threshold generated 10,000 tracks, and a total of 50,000 tracks were obtained. the Euclidian distance between two coordinates x and y, and the d H (X,Y) calculates the Hausdorff distance between set X and Y. The first set of whole brain tracks was clustered using 2 mm as the single linkage threshold, and we only selected 500 largest clusters because the rest of smaller clusters contained less than 0.01% of the total tracks (i.e. < 50 tracks). This selection was further justified in our expert examination, in which we found that the probability of a smaller cluster being recognized as false tracks was higher (Fig. 4c). The same cluster selection strategy was applied to our second set of the tracks (i.e. the tracks connecting to/from spinal cords). A single linkage clustering was conducted using 2 mm as the threshold, and the first 50 largest clusters were collected. The resulting clusters contain unique trajectories without repeated tracks, and the largest 550 clusters were selected whereas the other smaller clusters were discarded. Since each cluster may contain tracks with repeated trajectories, we removed redundant trajectories that are substantially close to the one another using a Hausdorff distance of 1mm. A weighted connectivity matrix was quantified using a cortical parcellation was based on regions derived from the AAL atlas (Table S2). It is noteworthy that our tractography atlas can be readily applied to any cortical parcellation atlas, and currently there is no consensus on how network nodes should be defined.
Here we used only one of the most popular parcellation from the AAL atlas to illustrate the network characteristics.
The average of along-track SDF values was used as the connectivity value. The connectograms of each fiber bundle and whole brain tracks were generated using CIRCOS  The processing pipeline (DSI Studio), SDF data of all 842 subjects, and HCP-842 template are available at http://dsi-studio.labsolver.org. The SDF template can be reproduced using the HCP data and documentations on the website. The atlas data, including the track trajectories and connectograms, are available at http://brain.labsolver.org.     connectogram corresponds to the right hemisphere. The connectogram of the human brain shows a dense network topology between the brain regions, forming a complicated architecture.