Variation in cortical connectivity profiles is typically modeled as having a coarse spatial scale parcellated into interconnected brain areas. We created a high-dimensional common model of the human connectome to search for fine-scale structure that is shared across brains. Projecting individual connectivity data into this new common model connectome accounts for substantially more variance in the human connectome than do previous models. This newly discovered shared structure is closely related to fine-scale distinctions in representations of information. These results reveal a shared fine-scale structure that is a major component of the human connectome that coexists with coarse-scale, areal structure. This shared fine-scale structure was not captured in previous models and was, therefore, inaccessible to analysis and study.
Resting state functional magnetic resonance imaging (rsfMRI) reveals patterns of functional connectivity that are used to investigate the human connectome [1–3] and parcellate the brain into interconnected areas that form brain systems and can be modeled as networks [4–11]. The connectivity of a single area is considered to be relatively homogeneous and typically is modeled as a mean connectivity profile. Cortical topography, however, has both a coarse scale of cortical areas and a finer scale of multiplexed topographies within areas [12–16]. Fine-scale within-area topographies are reflected in patterns of activity that can be measured with fMRI and decoded using multivariate pattern analysis (MVPA) [12,13,17]. Fine-scale variation in connectivity, however, has been overlooked due to poor anatomical alignment of this variation across individual brains. We ask here whether local variation in functional connectivity also has a fine-scale structure, similar to fine-scale response tuning topographies, and whether such variation can be captured in a common model with basis functions that are shared across brains. We developed a new algorithm, connectivity hyperalignment (CHA), to model local variation in connectivity profiles with shared basis functions for connectivity profiles across individuals and individual-specific local topographies of those connectivity basis functions (Fig 1). The resultant common model connectome consists of transformation matrices for each individual brain, which contain individual-specific topographic basis functions, and a common model connectome space, which contains shared connectivity profiles (Fig 2). Individual transformation matrices transform an individual brain’s connectome, in its native anatomical coordinate space, into the common model space [13,16]. The individual transformation matrices and common model connectivity matrix are derived iteratively from training data. Validity testing is done on connectivity profiles and other functional parameters from independent test data that are hyperaligned into the common model connectome space. The results show that CHA can derive these shared basis functions from functional connectivity derived from neural activity while watching an audiovisual movie and from neural activity in the resting state. The resultant common model connectome accounts for substantially more shared variance in functional connectivity derived from both movie fMRI data and resting state fMRI data than was accounted for by previous models. This shared variance resides in fine-scale local variations in connectivity. We show further that this local variability in functional connectivity profiles is meaningful in that it is closely related to local patterns of response that encode fine distinctions among representations. Our results indicate that shared fine-scale local variation, which was not evident in previous models, is a major component of the human connectome that coexists with shared coarse-scale areal structure. Our common model connectome makes this fine-scale local variation accessible for group-level study of its network properties.
CHA afforded large increases in ISCs of connectivity profile vectors in both the movie fMRI data and the rsfMRI data (Fig 3 and Fig 4). Increases in ISCs of functional connectivity derived from movie data were distributed across all of cortex (Fig 3). ISC at a cortical node is the correlation of the one subject’s connectivity profile with the mean of other subjects’ profiles, indexing how well other subjects’ connectivity profiles can predict an individual’s connectivity profiles. Fig 3A shows a cortical map of mean ISCs of connectivity profiles in the common model connectome space as compared to ISCs in anatomically-aligned data. Fig 3B is a scatterplot of mean ISCs for individuals after anatomical alignment and CHA, which shows that CHA increased ISC for each individual and preserved individual similarity or deviance from the group. We quantify the increases in 24 functional ROIs, identified using a meta-analytic database, NeuroSynth [21] (Fig 3C; S1 Table). Mean ISC of connectivity profiles across these ROIs was markedly higher in the common model connectome than in the anatomically-aligned data (0. 67 versus 0. 15; difference = 0. 52,95% confidence interval, CI = [0. 46,0. 56]). Increases in ISCs of resting state connectivity profiles were similarly distributed across all of cortex and replicated the findings based on ISCs of movie viewing connectivity profiles (Fig 4). Fig 4A shows a cortical map of mean ISCs of resting state connectivity profiles in the common model connectome space and in data aligned with the HCP’s MSM-All method (multimodal surface matching [22]). Fig 4B is a scatterplot of mean ISCs for individuals after MSM-All alignment and CHA, which shows that CHA of resting state data increased ISC for each individual and preserved individual similarity or deviance from the group. Fig 4C shows a cortical map of within-subject correlations between connectivity profiles from different resting state sessions. We quantify the increases in 26 functional ROIs, identified using a meta-analytic database, NeuroSynth [21] (Fig 4D; S6 Table). Mean ISC of connectivity profiles across these ROIs was markedly higher in the common model connectome than in the MSM-All-aligned data (0. 66 versus 0. 35; difference = 0. 31 [0. 30,0. 33]). ISCs of resting state connectivity profiles in the common model connectome space are slightly higher than within-subject correlations of resting state connectivity profiles (mean correlation = 0. 64; CI for difference = [0. 00,0. 05]) (Fig 4D). This latter result indicates that an individual’s connectome based on resting state functional connectivity is better predicted by the common model connectome, based on other subjects’ data, than by estimates based on a typical sample of that subject’s own rsfMRI data, due to the benefit of estimating connectivity profiles based on a large number of brains and the precision of CHA. The substantial increase in ISCs with hyperalignment is due in part to discovery of shared variance that was obscured by misalignment but also to suppression of unshared variance and amplification of shared variance mediated by filtering the data in the transformation step with smaller weights for nodes with unshared or noisy variance and larger weights for nodes with shared variance. To gauge the size of the effect of filtering independent of better information alignment, we calculated ISCs in data that are filtered by our algorithm but aligned based on anatomy or MSM-All (see methods). ROI mean ISCs of connectivity profiles in movie data filtered with CHA but aligned based on anatomy was 0. 22 (CHA versus filter-control difference = 0. 45 [0. 39 0. 49]) and for HCP resting state data filtered with CHA but aligned based on MSM-All was 0. 41 (CHA versus filter-control difference = 0. 25 [0. 23,0. 27]). These ISCs are larger than ISCs of unfiltered, anatomically and MSM-All-aligned data but, nonetheless, still markedly lower than ISCs of connectivity profiles in the common model connectome space, which is both filtered and re-aligned by CHA. We investigated the spatial specificity of the common model connectome by computing the intersubject spatial point spread functions (PSF) of ISCs of connectivity profiles [16]. The PSF of connectivity profiles was computed as the correlation of the connectivity profile in a cortical surface node for a given subject with the average connectivity profiles of other subjects in the same node and nodes at cortical distances ranging from 3 to 12 mm. We similarly calculated within-subject PSFs based on within-subject correlations (WSC) of connectivity profiles between two resting state sessions. Fig 5A shows the slopes of connectivity profile PSFs for movie data in 24 functionally-defined ROIs, and Fig 5B shows the mean PSF across these ROIs as a function of cortical distance in the common model connectome space and in anatomically-aligned data. CHA increased the average slope of PSF across these ROIs, relative to anatomical alignment, from 0. 013 to 0. 105 (difference = 0. 092 [0. 080,0. 099]). Fig 5C shows the slopes of connectivity profile PSFs for resting state connectivity profiles in the 26 functionally-defined ROIs, and Fig 5D shows the mean PSF across these ROIs (ISC or WSC as a function of cortical distance) in the common model connectome space, in MSM-All-aligned data, and within-subject. CHA increased the average slope of PSF across these ROIs, relative to MSM-All alignment, from 0. 012 to 0. 065 (difference = 0. 053 [0. 047,0. 055]). The intersubject PSF slopes in the common model connectome space and the PSF within-subject (slope = 0. 067) were not significantly different (difference = 0. 002 [-0. 002,0. 007]). This fine spatial granularity was ubiquitous in cortex, with steep PSFs in sensory-perceptual areas in occipital and temporal cortices as well as in higher-order cognitive areas in lateral and medial parietal and prefrontal cortices. The mean PSFs across ROIs (Fig 5B and 5D) clearly show that CHA captures fine-scale variations in connectivity profiles for neighboring cortical nodes across subjects that are not captured by anatomical alignment or MSM-All alignment. The ISCs of connectivity profiles for neighboring nodes in the common model connectome are substantially lower than ISCs for the same node (differences = 0. 21 [0. 18,0. 23] for movie data and 0. 09 [0. 08,0. 09] for resting state data). Similar fine spatial granularity is seen in the within-subject between-session PSFs for resting state connectivity profiles (0. 10 [0. 09,0. 10]). By contrast, ISCs for connectivity profiles in the anatomically-aligned and MSM-All aligned data barely differ for nodes spaced 0 versus 1 voxel/3 mm (differences = 0. 005, [0. 005,0. 005] and 0. 004, [0. 004,0. 015], respectively) and 2 voxels/6 mm (0. 01 [0. 01,0. 02] and 0. 02 [0. 01,0. 02], respectively) apart. Decrements for larger distances (ISCs of nodes spaced 3 voxels/9 mm: 0. 03 [0. 03,0. 03] and 0. 03 [0. 03,0. 03], respectively; and 4 voxels/12 mm: (0. 05 [0. 05,0. 06] and 0. 05 [0. 04,0. 05], respectively) were similarly small. Next we asked if this shared variance in fine-scale local variation in connectivity profiles carries meaning by testing whether it reflects fine-scale variations in response tuning topographies that carry fine-grained distinctions in representation. We tested whether projecting movie response data into the CHA-derived common connectome space afforded better alignment of representational geometry for movie time-points and better bsMVPC of movie time segments. Results show that shared fine-scale structure in the common model connectome is closely related to fine distinctions in representations. Fig 6A shows a cortical map of mean ISCs of local representational geometry after anatomical alignment and in the common model connectome. Representational geometry is the matrix of all pairwise similarities between patterns of response to different time-points in the movie, resulting in a matrix of more than 800,000 pairwise similarities (see methods). Fig 6B shows a cortical map of mean bsMVPC accuracies for 15 s movie time-segments in searchlights after anatomical alignment and CHA. CHA greatly increased both ISCs of representational geometry and bsMVPC accuracies. CHA significantly increased ISCs of representational geometry in all ROIs (ROI mean ISCs = 0. 308 and 0. 210 after CHA and anatomical alignment, respectively, difference = 0. 097 [0. 080,0. 110]). CHA also dramatically increased bsMVPC accuracies in all ROIs (ROI mean bsMVPC accuracies = 10. 37% and 1. 04% after CHA and anatomical alignment, respectively, difference = 9. 33% [7. 71%, 10. 54%]). We tested the generalization of the common model connectome derived from resting state fMRI by applying connectivity hyperalignment parameters derived from one session of resting state data to task maps provided by the HCP database comprised of 32 task activation maps and 14 task contrast maps (S2 Table). These task maps reflect simple operations and, thus, do not have the same fine-grained structure that is associated with activation by dynamic, naturalistic stimuli such as a movie. We calculated the ISC of these task maps between each subject and the average of others before and after hyperalignment. Hyperalignment improved correlations on average across all tasks and in all but two (Face-Shapes and Body-Average, labeled ns) task contrast maps (Fig 7). The average correlation across task maps increased from 0. 58 to 0. 65 (mean difference = 0. 07 [0. 06,0. 08]). Since CHA aligned fine-scale patterns of response tuning functions across subjects better than anatomy-based alignment, we asked how well it compares to our previously published response-based hyperalignment (RHA) [16]. Because RHA requires responses that are synchronized across subjects in time, it cannot be applied to resting state data. We compare CHA and RHA of movie viewing data on 1) ISC of connectivity profiles, 2) ISC of representational geometry, and 3) bsMVPC of 15 s movie segments. Results showed that both CHA and RHA increased ISCs and bsMVPC classification accuracies significantly over anatomy-based alignment, but each algorithm achieves better alignment for the information that it uses to derive a common model, namely connectivity profiles and patterns of response, respectively. ISCs of connectivity profiles are significantly higher in a common model based on CHA than in a common model based on RHA (ROI mean ISCs = 0. 67 and 0. 575, respectively; CHA-RHA difference = 0. 095 [0. 081,0. 112]) (S1 Fig). By contrast, RHA marginally but significantly outperforms CHA on some validations based on response tuning functions, namely ISCs of representational geometry (ROI means = 0. 322 and 0. 308, respectively; RHA-CHA difference = 0. 014 [0. 007,0. 019]) (S2 Fig), and bsMVPC of movie segments (ROI mean accuracies = 13. 65% and 10. 37%, respectively; RHA-CHA difference = 3. 28% [2. 76%, 3. 78%]) (S3 Fig).
These results show that fine-scale local variation in connectivity profile is a major component of the human connectome that can be modeled with shared connectivity basis functions. Each connectivity basis function has a connectivity profile that is shared across subjects and a different local connectivity topography in each individual brain. These basis functions are derived from multiple subject data in local cortical fields. An individual’s connectivity pattern in a cortical field is modeled as multiplexed or overlaid connectivity topographic basis functions, and the connectivity profile of each cortical node or voxel is modeled as a weighted mixture of local connectivity profile basis functions. Thus, the connectivity profile for each voxel or node is modeled as a high-dimensional vector of connectivity profile bases, capturing how it varies locally from its neighbors, rather than modeling the connectivity of a brain area as a single connectivity profile that is shared by all voxels or nodes. We show that these shared basis functions can be discovered with connectivity hyperalignment of data collected during viewing and listening to a rich naturalistic movie and during the resting state. These basis functions constitute a common model connectome. Shared fine-scale variation is a ubiquitous characteristic of all of human cortex and is a major component of the human connectome that coexists with shared coarse-scale areal variation. We show that patterns of connectivity exhibit fine-scale variation that is captured in the CHA-derived common model connectome. We define fine-scale structure as voxel-by-voxel or node-by-node variation in response and connectivity profiles, as compared to the coarse structure of parcels that consist of sets of voxels or surface nodes and are treated as a functional unit with a homogeneous functional profile. In Fig 8 we illustrate the fine scale structure that is captured in the common model connectome for connectivity patterns in a left lateral-occipital/inferior-temporal cortex cortical field. Quantitatively, we show that shared fine-scale structure is captured in the common model connectome with a direct measure of the spatial granularity of local variation in connectivity profiles—the intersubject point-spread function. The intersubject spatial point-spread function for variation in connectivity profiles is dramatically, six to eight-fold, steeper after data are transformed into the common model connectome than for data that are anatomically aligned. Next we show that capture of this fine-scale structure in functional connectivity generalizes to capture of fine-scale structure in neural representation. Transformation of movie data into the common model space, using matrices derived from functional connectivity in independent movie data, afford bsMVPC of time segments that are tenfold higher than for anatomically-aligned data. bsMVPC of movie time segments relies on fine-scale structure that is not well-aligned based on anatomy, nor on functional alignment using a “rubber-sheet” warping of cortical topographies, nor on hyperalignment based on responses to a limited variety of still images of visual categories [13,16,23–25]. ISCs of local representational geometries also are dramatically higher after CHA than after anatomical alignment. These local representational geometries reflect fine-scale structure that reveals how information spaces in different cortical fields vary, offering a window on how these spaces are transformed along processing pathways and reshaped by task demands [26–28]. Finally, we also show that transformations derived from rsfMRI improve alignment of topographies in task activation and task contrast maps in the HCP database. The existence and importance of fine-scale connectivity is well-recognized [29–31] but previously was not modeled in a common computational framework and, consequently, was largely overlooked. Attempts to model within-area topographies of connectivity either were limited mostly to within-subject analyses or coarser within-area topographies that could be captured with anatomy-based alignment of group data [31]. Consequently, when not simply overlooked, within-area variations in connectivity profiles were usually analyzed as gradients that have a single cycle in a cortical area, such as retinotopy or somatotopy [29–31]. Other models of shared structure in the human connectome have focused on the identification of shared functional networks that can be identified with cluster analysis (e. g. [5,32,33]) or independent components analysis (ICA; e. g. [19]). These methods do not attempt to align the fine-scale structure within areas in these networks. In some approaches, each voxel is assigned to one cluster or system and is, thereby, associated with the time-series tuning function that characterizes that cluster [5,8, 32,33]. Approaches that use ICA, or related componential analyses such as PCA or SVD, have the potential to capture node-by-node variation in connectivity profiles, but implementations of these approaches have not adapted them to analyze this fine-scale topographic structure. For example, dual regression could allow using group ICA as a common space for modeling each voxel in an individual as a weighted sum of independent components [34,35]. In practice, however, each voxel is characterized in ICA analyses by the network to which it belongs, not as a mixture of multiplexed functional topographies. Node-by-node local variation in connectivity topographies is blurred in group analyses because individual variation on independent components is projected into anatomically-aligned brains rather than into a single reference voxel space to reveal shared fine-scale structure, as we do here. A novel approach by Langs et al. [32,33] allows nodes to be assigned to different clusters in a common functional connectivity embedding space independently of anatomical location. The implementations of this method, however, do not attempt to discover shared fine-scale structure, and the low dimensionality of the embedding space and small number of clusters are probably insufficient to capture this level of detail. Cortical functional architecture has multiplexed topographies at multiple spatial scales. In primary visual cortex, retinotopy is multiplexed with ocular dominance columns, edge orientation, spatial frequency, motion direction, and motion velocity, among other low-level visual attributes [36,37]. Primary visual cortex sends coherent projections to other visual areas where these topographies are recapitulated and transformed, affording the emergence of more complex features, such as curvature, texture, shape, color constancy, and biological motion; and, subsequently, even higher-order attributes such as object categories, view-invariant face identity, and species-invariant attributes of animals such as action categories and dangerousness [12,15,26–28,38–40]. Similar transformations of multiplexed topographies characterize other sensory modalities and, undoubtedly, supramodal cognitive operations. Modeling inter-areal communication as a single value of connectivity strength sheds no light on how information is transformed along cortical processing pathways to allow high-order information to be disentangled from confounding attributes [41]. Multiplexed cortical topographies at multiple spatial scales can be modeled with individual-specific topographic basis functions that have shared tuning profiles [13,16] and shared connectivity profiles (as shown here). No previous model captured multiple spatial scales of connectivity topographies with connectivity profiles that are shared across brains. By capturing coarse- and fine-scale connectivity topographies with shared basis functions, the common model connectome casts a bright light on the dominant role of fine-scale connectivity patterns in the human connectome and opens new territory for investigation of the network properties of cortical connectivity at finer levels of detail. With this new perspective, inter-areal connectivity can be modeled as more than a simple replication of global activity, as is the assumption underlying existing approaches to modeling the connectome, but, instead, as information processing operations in which functional topographies are transformed by projections between areas.
All fMRI data collection at Dartmouth College was approved by the Dartmouth Committee for the Protection of Human Subjects. Resting state data from the Human Connectome Project was approved by the Institutional Review Boards associated with that project. We scanned 11 healthy young right-handed participants (4 females; Mean age: 24. 6+/-3. 7 years) during movie viewing. Participants had no history of neurological or psychiatric illness. All had normal or corrected-to-normal vision. Informed consent was collected in accordance with the procedures set by the local Committee for the Protection of Human Subjects. Participants were paid for their participation. These data also were used in a prior publication on whole cortex RHA [16]. In the HCP database [20], we found unrelated subjects of age < = 35 with at least four resting state scans, yielding a list of 64 subjects. We chose the first 20 of these subjects in the sorted order of subject IDs for our analysis. For each subject, we used their cortical surfaces and fMRI data aligned to the group using MSM-All [22] with 32K nodes in each hemisphere as provided by the HCP. We used data from one resting state session [19] (“rfMRI_REST1_LR”) to derive CHA parameters and validated it on a different resting state session (“rfMRI_REST2_LR”), and task fMRI sessions [18] (EMOTION, GAMBLING, LANGUAGE, MOTOR, RELATIONAL, SOCIAL, and WM). Resting state data were acquired for 1200 TRs with a TR of 0. 720 s in each session (total time = 14 min 33 s). The data used to derive the CHA parameters and common model and the resting state data used for validation tests used the same phase-encoding direction (LR). We used a single session of rsfMRI for alignment to mimic a typical resting state data acquisition which usually varies from 10–20 mins of scanning. See [19] for more details about the acquisition and preprocessing pipelines. We use CHA to derive a common model of the human connectome and the transformation matrices that project individual brains’ connectomes into the common model connectome space. The common model connectome is a high-dimensional information space. In the current implementation, the model space based on movie fMRI data has 54,034 dimensions, corresponding to the number of voxels in the gray matter mask, and the model space based on HCP resting state fMRI data has 59,412 dimensions, corresponding to the number of cortical nodes in those data. The derivation of this space starts with hyperalignment in local cortical fields, searchlights, which yields orthogonal transformation matrices for each subject in each field. These searchlights are aligned across subjects based on anatomy (movie data) or MSM-All (HCP resting state data); consequently, each locus within a searchlight is similarly aligned across subjects before CHA. Local transformation matrices for each searchlight map anatomically or MSM-All aligned cortical loci in a cortical field to CHA-aligned dimensions in the common model connectome. These local transformation matrices are then aggregated into a whole brain transformation matrix, which is not globally orthogonal. The whole brain transformation matrices are derived based on local hyperalignment in searchlights to constrain resampling of information to cortical neighborhoods defined by those searchlights.
Resting state fMRI has become a ubiquitous tool for measuring connectivity in normal and diseased brains. Current dominant models of connectivity are based on coarse-scale connectivity among brain regions, ignoring fine-scale structure within those regions. We developed a high-dimensional common model of the human connectome that captures both coarse and fine-scale structure of connectivity shared across brains. We showed that this shared fine-scale structure is related to fine-scale distinctions in representation of information, and our model accounts for substantially more shared variance of connectivity compared to previous models. Our model opens new territory—shared fine-scale structure, a dominant but mostly unexplored component of the human connectome—for analysis and study.
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imaging techniques
resting state functional magnetic resonance imaging
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A computational model of shared fine-scale structure in the human connectome