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... In either each ROI or each ROI pair, brain regions and their associated streamlines are aligned to a template Zhang et al. (2018) . Thus, the WM integrity measures (e.g., FA, MD) can be directly calculated and statistical analyzed according to the following three main scientific questions: ...

... Specifically, both ROIs in each ROI pair are either tumor-related, language-related, or hand motor-related. In each ROI pair, FADTTS was applied to the fiber bundles of FA and MD values Zhang et al. (2018) . At the global and local levels, we conducted the hypothesis testing in both (5) and (6) . ...

... The key parameters of our GBM DTI data set are similar to those of the BRATS 2017 data set, so we follow the same pre-processing steps Menze et al. (2015b) to homogenize our GBM DTI dataset. In Zhang et al. (2018) , the T1 or T1c images were needed for segmenting different types of tissues to provide the soft criterion for guiding the growth and termination of streamlines. Since our GBM DTI dataset does not have all MRI modalities, we trained different combinations of MRI modalities to address this issue based on the BRATS 2017 data set. ...

Glioblastoma (GBM) brain tumor is the most aggressive white matter (WM) invasive cerebral primary neoplasm. Due to its inherently heterogeneous appearance and shape, previous studies pursued either the segmentation precision of the tumors or qualitative analysis of the impact of brain tumors on WM integrity with manual delineation of tumors. This paper aims to develop a comprehensive analytical pipeline, called (TS)2WM, to integrate both the superior performance of brain tumor segmentation and the impact of GBM tumors on the WM integrity via tumor segmentation and tract statistics using the diffusion tensor imaging (DTI) technique. The (TS)2WM consists of three components: (i) A dilated densely connected convolutional network (D2C2N) for automatically segment GBM tumors. (ii) A modified structural connectome processing pipeline to characterize the connectivity pattern of WM bundles. (iii) A multivariate analysis to delineate the local and global associations between different DTI-related measurements and clinical variables on both brain tumors and language-related regions of interest. Among those, the proposed D2C2N model achieves competitive tumor segmentation accuracy compared with many state-of-the-art tumor segmentation methods. Significant differences in various DTI-related measurements at the streamline, weighted network, and binary network levels (e.g., diffusion properties along major fiber bundles) were found in tumor-related, language-related, and hand motor-related brain regions in 62 GBM patients as compared to healthy subjects from the Human Connectome Project.

... Diffusion MRI data are now collected in almost all major cohort-based neuroimaging studies, e.g., the Human Connectome Project [Van Essen et al., 2013], the UK Biobank [Miller et al., 2016] and the Adolescent Brain Cognitive Development (ABCD) Study [Casey et al., 2018]. Structural connectivity (SC) analysis is among the most important applications of dMRI [Park and Friston, 2013;Zhao et al., 2015;Yeh et al., 2016;Zhang et al., 2018], where individual-level microstructural brain networks are constructed to delineate anatomical connections between brain regions. Figure 1 illustrates the pipeline we used for extracting SC [Zhang et al., 2018] (Figure 1a) and an SC matrix extracted from one subject in the ABCD data ( Figure 1b). ...

... Structural connectivity (SC) analysis is among the most important applications of dMRI [Park and Friston, 2013;Zhao et al., 2015;Yeh et al., 2016;Zhang et al., 2018], where individual-level microstructural brain networks are constructed to delineate anatomical connections between brain regions. Figure 1 illustrates the pipeline we used for extracting SC [Zhang et al., 2018] (Figure 1a) and an SC matrix extracted from one subject in the ABCD data ( Figure 1b). Brain network classification and identification of predictive subnetworks are probably among the most important applications of SC into the mechanistic understanding of neuroscience phenomena. ...

... To obtain structural connectome, we used a state-of-the art dMRI data preprocessing framework named population-based connectome mapping (PSC) [Zhang et al., 2018]. PSC uses a reproducible probabilistic tractography algorithm [Girard et al., 2014;Maier-Hein et al., 2017] to generate the wholebrain tractography. ...

Structural brain networks constructed from diffusion MRI are important biomarkers for understanding human brain and its relation to cognitive functioning. There is increasing interest in learning differences in structural brain networks between groups of subjects in neuroimaging studies, leading to a variable selection problem in network classification. Traditional methods often use independent edgewise tests or unstructured generalized linear model (GLM) with regularization on vectorized networks to select edges distinguishing the groups, which ignore the network structure and make the results hard to interpret. In this paper, we develop a symmetric bilinear logistic regression (SBLR) with elastic-net penalty to identify a set of small clique subgraphs in network classification. Clique subgraphs, consisting of all the interconnections among a subset of brain regions, have appealing neurological interpretations as they may correspond to some anatomical circuits in the brain related to the outcome. We apply this method to study the differences in structural connectome between adolescents with high and low crystallized cognitive ability, using the crystallized cognition composite score and picture vocabulary and oral reading recognition tests from NIH Toolbox. A few clique subgraphs containing several small sets of brain regions are identified between different levels of functioning, indicating their importance in crystallized cognition.

... Diffusion MRI data are now collected in almost all major cohort-based neuroimaging studies, e.g., the Human Connectome Project ( Van Essen et al., 2013 ), the UK Biobank ( Miller et al., 2016 ) and the Adolescent Brain Cognitive Development (ABCD) Study ( Casey et al., 2018 ). Structural connectivity (SC) analysis is among the most important applications of dMRI ( Park and Friston, 2013;Yeh et al., 2016;Zhang et al., 2018;Zhao et al., 2015 ), where individual-level microstructural brain networks are constructed to delineate anatomical connections between brain regions. Fig. 1 il-Fig. ...

... To obtain structural connectome, we used a state-of-the art dMRI data preprocessing framework named population-based structural connectome (PSC) mapping ( Zhang et al., 2018 ). PSC uses a reproducible probabilistic tractography algorithm ( Girard et al., 2014;Maier-Hein et al., 2017 ) to generate the whole-brain tractography. ...

... In this process several procedures were used to increase the reproducibility: (1) each gray matter ROI is dilated to include a small portion of white matter region, (2) streamlines connecting multiple ROIs are cut into pieces so that we can extract the correct and complete pathway and (3) apparent outlier streamlines are removed. Extensive experiments have illustrated that these procedures can significantly improve the reproducibility of the extracted weighted networks, and readers can refer to Zhang et al. (2018) for more details. To analyze the brain as a network, a scalar number is usually extracted to summarize each connection. ...

Structural brain networks constructed from diffusion MRI are important biomarkers for understanding human brain structure and its relation to cognitive functioning. There is increasing interest in learning differences in structural brain networks between groups of subjects in neuroimaging studies, leading to a variable selection problem in network classification. Traditional methods often use independent edgewise tests or unstructured generalized linear model (GLM) with regularization on vectorized networks to select edges distinguishing the groups, which ignore the network structure and make the results hard to interpret. In this paper, we develop a symmetric bilinear logistic regression (SBLR) with elastic-net penalty to identify a set of small clique subgraphs in network classification. Clique subgraphs, consisting of all the interconnections among a subset of brain regions, have appealing neurological interpretations as they may correspond to some anatomical circuits in the brain related to the outcome. We apply this method to study differences in the structural connectome between adolescents with high and low crystallized cognitive ability, using the crystallized cognition composite score, picture vocabulary and oral reading recognition tests from NIH Toolbox. A few clique subgraphs containing several small sets of brain regions are identified between different levels of functioning, indicating their importance in crystallized cognition.

... Here, applying a state-of-the-art diffusion imaging processing pipeline (Zhang et al 2018), we examined the structural connectome in cognitively superior older adults (Supernormals, SN) that we previously identified in the ADNI cohort (Lin et al 2017a, Lin et al 2017b over a 2year period. This longitudinal design enabled us to test whether Supernormals maintain a unique structural connectome that remains stable over time. ...

... To extract brain connectome, we employed an established population-based structural connectome processing pipeline (Zhang et al 2018). First, we applied reproducible probabilistic tractography algorithm (Girard et al 2014, Maier-Hein et al 2017 to DWI data to generate streamlines across the whole brain. ...

... Then, we extracted 2 diffusion metrics from the streamlines to describe the connection: the mean of MD (mean diffusivity) and the mean of FA (fractional anisotropy). Another feature we extracted is CSA (connected surface area) which was proposed to reflect the amount of neurons connecting two regions (Zhang et al 2018). To calculate CSA, at each intersection between the surface of an ROI and a streamline, a small circle with fixed radius is drawn, and the total number of voxels covered by these circles is the CSA. ...

Studying older adults with excellent cognitive capacities (Supernormals) provides a unique opportunity for identifying factors related to cognitive success – a critical topic across lifespan. There is a limited understanding of Supernormals’ neural substrates, especially whether any of them attends shaping and supporting superior cognitive function or confer resistance to age-related neurodegeneration such as Alzheimer’s disease (AD). Here, applying a state-of-the-art diffusion imaging processing pipeline and finite mixture modelling, we longitudinally examine the structural connectome of Supernormals. We find a unique structural connectome, containing the connections between frontal, cingulate, parietal, temporal, and subcortical regions in the same hemisphere that remains stable over time in Supernormals, relatively to typical agers. The connectome significantly classifies positive vs. negative AD pathology at 72% accuracy in a new sample mixing Supernormals, typical agers, and AD risk [amnestic mild cognitive impairment (aMCI)] subjects. Among this connectome, the mean diffusivity of the connection between right isthmus cingulate cortex and right precuneus most robustly contributes to predicting AD pathology across samples. The mean diffusivity of this connection links negatively to global cognition in those Supernormals with positive AD pathology. But this relationship does not exist in typical agers or aMCI. Our data suggest the presence of a structural connectome supporting cognitive success. Cingulate to precuneus white matter integrity may be useful as a structural marker for monitoring neurodegeneration and may provide critical information for understanding how some older adults maintain or excel cognitively in light of significant AD pathology.

... The key steps in Connectoflow are: -Decompose: This step performs the parcel-to-parcel decomposition of the tractogram. It includes streamline-cutting operations [13] to maximize the number of streamlines with terminations in the provided atlas. Moreover, connection-wise cleaning processes that remove loops, discard spurious streamlines and discard incoherent curvatures are used to remove as many false positives as possible [13]. ...

... It includes streamline-cutting operations [13] to maximize the number of streamlines with terminations in the provided atlas. Moreover, connection-wise cleaning processes that remove loops, discard spurious streamlines and discard incoherent curvatures are used to remove as many false positives as possible [13]. ...

Tractography involves complicated processing and connectomics include even more complexity. To facilitate structural connectome reconstructionwe present: Connectoflow. Connectoflow requires simple inputs, has simple options and provides simple outputs, all with cutting-edge processing.By leveraging the simplicity of Nextflow and Docker/Singularity, Connectoflow is robust and efficient. By combining Tractoflow with Connectoflow,one can go from raw DW-images to structural connectomes in a few simplified steps. The proposed pipeline innovates by including connection-wisecleaning/filtering, provides connection weights that go beyond streamline count (COMMIT) as well as advanced connection-wise metrics (similarityand AFD)

... (d) We also used graph theoretical analysis to investigate the topological changes by comparing the SC and FC for HIV+ subjects with HC subjects motion corrected using a 6-degrees of freedom rigid-body registration and field maps were used to correct the susceptibility induced distortion, using FUGUE in FSL (Jenkinson, 2003). DTI processing and structural connectome construction were then performed using the population-based structural connectome pipeline (Zhang et al., 2018). A reproducible probabilistic whole-brain tractography algorithm (Girard, Whittingstall, Deriche, & Descoteaux, 2014;Maier-Hein et al., 2017) was used to reconstruct streamlines. ...

... This single shell scheme may introduce errors for tractography due to fiber-crossing issue (Sotiropoulos et al., 2013). In our study, we have adopted a reliable tractography and SC reconstruction pipeline (Zhang et al., 2018) to mitigate to some extent. ...

MRI-based neuroimaging techniques have been used to investigate brain injury associated with HIV-infection. Whole-brain cortical mean-field dynamic modeling provides a way to integrate structural and functional imaging outcomes, allowing investigation of microscale brain dynamics. In this study, we adopted the relaxed mean-field dynamic modeling to investigate structural and functional connectivity in 42 HIV-infected subjects before and after 12-week of combination antiretroviral therapy (cART) and compared them with 46 age-matched healthy subjects. Microscale brain dynamics were modeled by a set of parameters including two region-specific microscale brain properties, recurrent connection strengths, and subcortical inputs. We also analyzed the relationship between the model parameters (i.e., the recurrent connection and subcortical inputs) and functional network topological characterizations, including smallworldness, clustering coefficient, and network efficiency. The results show that untreated HIV-infected individuals have disrupted local brain dynamics that in part correlate with network topological measurements. Notably, after 12 weeks of cART, both the microscale brain dynamics and the network topological measurements improved and were closer to those in the healthy brain. This was also associated with improved cognitive performance, suggesting that improvement in local brain dynamics translates into clinical improvement.

... Hence, V in both FC and SC networks correspond to N = 68 cortical surface regions, with 34 nodes in each hemisphere. Based on the data-processing pipeline in [53], [54], the SC network A of each subject is extracted from the dMRI and structural MRI data. Brain functional activities on each RoI are given by the restingstate BOLD time courses measured using fMRI [55]. ...

... To mitigate such data imbalance problem, we discard all functional edges with negative weights and restrict ourselves to entries Σ ij ∈ [0, 1], as it is customarily done in prior FC studies [56], [57]. For additional details about the data, preprocessing, and network construction steps, refer to [53], [54] and http://www.humanconnectome.org/. ...

Recent advances in neuroimaging along with algorithmic innovations in statistical learning from network data offer a unique pathway to integrate brain structure and function, and thus facilitate revealing some of the brain's organizing principles at the system level. In this direction, we develop a supervised graph representation learning framework to model the relationship between brain structural connectivity (SC) and functional connectivity (FC) via a graph encoder-decoder system, where the SC is used as input to predict empirical FC. A trainable graph convolutional encoder captures direct and indirect interactions between brain regions-of-interest that mimic actual neural communications, as well as to integrate information from both the structural network topology and nodal (i.e., region-specific) attributes. The encoder learns node-level SC embeddings which are combined to generate (whole brain) graph-level representations for reconstructing empirical FC networks. The proposed end-to-end model utilizes a multi-objective loss function to jointly reconstruct FC networks and learn discriminative graph representations of the SC-to-FC mapping for downstream subject (i.e., graph-level) classification. Comprehensive experiments demonstrate that the learnt representations of said relationship capture valuable information from the intrinsic properties of the subject's brain networks and lead to improved accuracy in classifying a large population of heavy drinkers and non-drinkers from the Human Connectome Project. Our work offers new insights on the relationship between brain networks that support the promising prospect of using graph representation learning to discover more about human brain activity and function.

... Using state-of-the-art connectome extraction pipeline (Zhang et al., 2018), we can extract structural brain networks from diffusion MRI (dMRI) data. The structural brain network for an individual corresponds to a set of white matter connections among predefined brain regions. ...

... The dataset contains dMRI data over a 5-year span for 40 supernormals and 45 cognitively normal controls. A state-of-the-art DTI processing pipeline (Zhang et al., 2018) was applied to extract structural brain networks of subjects. More specifically, we first used a reproducible probabilistic tractography algorithm (Girard et al., 2014;Maier-Hein et al., 2017) to generate the whole-brain tractography data for each dMRI scan in the dataset. ...

Modern neuroimaging technologies, combined with state-of-the-art data processing pipelines, have made it possible to collect longitudinal observations of an individual's brain connectome at different ages. It is of substantial scientific interest to study how brain connectivity varies over time in relation to human cognitive traits. In brain connectomics, the structural brain network for an individual corresponds to a set of interconnections among brain regions. We propose a symmetric bilinear logistic regression to learn a set of small subgraphs relevant to a binary outcome from longitudinal brain networks as well as estimating the time effects of the subgraphs. We enforce the extracted signal subgraphs to have clique structure which has appealing interpretations as they can be related to neurological circuits. The time effect of each signal subgraph reflects how its predictive effect on the outcome varies over time, which may improve our understanding of interactions between the aging of brain structure and neurological disorders. Application of this method on longitudinal brain connectomics and cognitive capacity data shows interesting discovery of relevant interconnections among a small set of brain regions in frontal and temporal lobes with better predictive performance than competitors.

... This single shell scheme may introduce errors for tractography due to fiber-crossing issue (Sotiropoulos et al., 2013). In our study, we have adopted a reliable tractography and SC reconstruction pipeline (Zhang et al., 2018) to mitigate to some extent. Second, we could only derive a population-based whole-brain dynamic model using averaged FC and SC. ...

... Briefly, the b0 images and diffusion-weighted images were motion corrected using a six-degrees of freedom (DOF) rigid-body registration and field maps were used to correct the susceptibility induced distortion, using FUGUE in FSL (Jenkinson, 2003). DTI processing and structural connectome construction were then performed using the population-based structural connectome pipeline (PSC) (Zhang et al., 2018). A reproducible probabilistic whole-brain tractography algorithm (Girard, Whittingstall, Deriche, & Descoteaux, 2014;Maier-Hein et al., 2017) was used to reconstruct streamlines. ...

In this study, we adopted the relaxed mean-field dynamic modeling to investigate structural and functional connectivity in forty-two HIV-infected subjects before and after 12-week of combination antiretroviral therapy (cART) and compared them with forty-six age-matched healthy subjects. Microscale brain dynamics were modeled by a set of parameters including two region-specific microscale brain properties, recurrent connection strengths, and subcortical inputs. We also analyzed the relationship between the model parameters (i.e. the recurrent connection and subcortical inputs) and functional network topological characterizations. The results show that untreated HIV-infected individuals have disrupted local brain dynamics that in part correlate with network topological measurements. Notably, after 12 weeks of cART, both the microscale brain dynamics and the network topological measurements improved and were closer to those in the healthy brain. This was also associated with improved cognitive performance, suggesting that improvement in local brain dynamics translates into clinical improvement.

... DTI data were first corrected for eddy current-induced distortion, motion, and susceptibility-induced distortion. Corrected data were then processed using the population-based structural connectome pipeline, which has been described in detail previously (Zhang et al. 2018). Briefly, this pipeline performs HARDI tractography with anatomical priors, then registers this data to parcellated T1 data for the same subject and groups each tractography dataset into bundles connecting specified regions of interest. ...

... Here, we primarily focused on total number of connections, which represents the number of streamlines connecting two regions, because connectomes of the number of connections have been shown to have greater within-subject reproducibility than connectomes of anisotropy or diffusivity (Zhang et al. 2018), suggesting that these connectome matrices provide fingerprints of a subject's white matter structure while summarizing tract properties between ROIs. We will subsequently refer to the number of connections as connectivity. ...

Making reasonable decisions related to financial and health scenarios is a crucial capacity that can be difficult for older adults to maintain as they age, yet few studies examine neurocognitive factors that are generalizable to different types of everyday decision-making capacity. Here we propose an innovative approach, based on individual risk-taking preference, to identify neural profiles that may help predict older adults’ everyday decision-making capacity. Using performance and cognitive arousal information from two gambling tasks, we identified three decision-making preference groups: ambiguity problem-solvers (A), risk-seekers (R), and a control group without strong risk-taking preferences (C). Comparisons of the number of connections within white matter tracts between A vs. C and R vs. C groups resulted in features consistent with the theory of dual neural functional systems involved in decision-making. Unique tracts from the A vs. C contrast were primarily centered in dorsal frontal regions/reflective system; unique tracts from the R vs. C contrast were centered in the ventral frontal regions/impulsive system; and shared tracts from both contrasts were centered in the basal ganglia, coordinating the switch between the two types of decision-making preference. Number of connections from the tracts differentiating A vs. C significantly predicted financial and health/safety decision-making capacity, and the association remained significant after controlling for multiple socioeconomic and cognitive factors. The connectome identified may provide insight into a generic white matter mechanism related to everyday decision-making capacity in older age.

... DTI data were processed using the population-based structural connectome pipeline (see Fig. 2), which has been described previously (Zhang et al. 2018c). Briefly, this pipeline performs high angular resolution diffusion (HARDI) tractography with anatomical priors, registers this data to parcellated T1 data for the same subject, and groups each tractography dataset into bundles connecting specified regions of interest (see Fig. 2, second panel). ...

... This indicates that the breadth of connection of streamlines in particular brain regions may be more important than the anisotropy or diffusivity along these streamlines. We have previously shown that endpoint-related features, particularly connected surface area, are more robust and reproducible across scans of the same subject, compared to diffusion-related features (Zhang et al. 2018c). The most prominent tracts identified are within the left frontal, parietal, and basal ganglia regions. ...

Cumulative evidence suggests the existence of common processes underlying subjective experience of cognitive and physical fatigue. However, mechanistic understanding of the brain structural connections underlying the experience of fatigue in general, without the influence of clinical conditions, is limited. The purpose of the study was to examine the relationship between structural connectivity and perceived state fatigue in older adults. We enrolled cognitively and physically healthy older individuals (n = 52) and categorized them into three groups (low cognitive/low physical fatigue; low cognitive/high physical fatigue; high cognitive/low physical fatigue; no subjects had high cognitive/high physical fatigue) based on perceived fatigue from cognitive and physical fatigue manipulation tasks. Using sophisticated diffusion tensor imaging processing techniques, we extracted connectome matrices for six different characteristics of whole-brain structural connections for each subject. Tensor network principal component analysis was used to examine group differences in these connectome matrices, and extract principal brain networks for each group. Connected surface area of principal brain networks differentiated the two high fatigue groups from the low cognitive/physical fatigue group (high vs. low physical fatigue, p = 0.046; high vs. low cognitive fatigue, p = 0.036). Greater connected surface area within striatal-frontal-parietal networks was correlated with lower cognitive and physical fatigue, and was predictive of perceived physical and cognitive fatigue measures not used for group categorization (Pittsburgh fatigability physical subscale, R² = 0.70, p < 0.0001; difference in self-report fatigue before and after gambling tasks, R² = 0.54, p < 0.0001). There are potentially structural connectomes resilient to both cognitive and physical fatigue in older adults.

... Based on the selected atlas, we may build the connectivity matrix by counting the number of fiber bundles passing between each pair of Regions Of Interest (ROIs) after fiber tracking. This connectivity matrix can then be used as a matrix-valued predictor in statistical analyses studying relationships with human traits (Zhang et al., 2018;Wang et al., 2019;Lin et al., 2020;de Reus and Van den Heuvel, 2013). ...

... In addition to the endpoints, the length and shape of the fibers may contain useful information (Zhang et al., 2018), which can be incorporated in clustering analyses. Module (iii) ...

Our understanding of the structure of the brain and its relationships with human traits is largely determined by how we represent the structural connectome. Standard practice divides the brain into regions of interest (ROIs) and represents the connectome as an adjacency matrix having cells measuring connectivity between pairs of ROIs. Statistical analyses are then heavily driven by the (largely arbitrary) choice of ROIs. In this article, we propose a novel tractography-based representation of brain connectomes, which clusters fiber endpoints to define a data adaptive parcellation targeted to explain variation among individuals and predict human traits. This representation leads to Principal Parcellation Analysis (PPA), representing individual brain connectomes by compositional vectors building on a basis system of fiber bundles that captures the connectivity at the population level. PPA reduces subjectivity and facilitates statistical analyses. We illustrate the proposed approach through applications to data from the Human Connectome Project (HCP) and show that PPA connectomes improve power in predicting human traits over state-of-the-art methods based on classical connectomes, while dramatically improving parsimony and maintaining interpretability. Our PPA package is publicly available on GitHub, and can be implemented routinely for diffusion tensor image data.

... Recently, mapping the brain imaging data [13] to networks involved different types of signals across spatial and temporal scales; consequently, a variety of structural and functional networks have been obtained [14,15,16,17]. This network mapping enabled getting a new insight into the functional organisation of the brain [18,19], in particular, based on the standard and deep graph theoretic methods [20,21,22] and the algebraic topology of graphs [1,23]. ...

Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human connectome can be crucial for the brain complex dynamics. In this context, the best-connected brain areas, designated as hub nodes, play a central role in supporting integrated brain function. Here, we study the structure of simplicial complexes attached to eight global hubs in the female and male connectomes and identify the core networks among the affected brain regions. These eight hubs (Putamen, Caudate, Hippocampus and Thalamus-Proper in the left and right cerebral hemisphere) are the highest-ranking according to their topological dimension, defined as the number of simplexes of all orders in which the node participates. Furthermore, we analyse the weight-dependent heterogeneity of simplexes. We demonstrate changes in the structure of identified core networks and topological entropy when the threshold weight is gradually increased. These results highlight the role of higher-order interactions in human brain networks and provide additional evidence for (dis)similarity between the female and male connectomes.

... Other recent studies have detected significant global heritability of FA, AD and RD in human populations [6,51] . And studies have demonstrated heritability of specific regions of connectivity, in human [52,53]. However, the work described here is the first to bring together a robust study of heritability of all these metrics (volume, FA, AD, RD, connection strength) in the mouse. ...

Genome-wide association studies have demonstrated significant links between human brain structure and common DNA variants. Similar studies with rodents have been challenging because of smaller brain volumes. Using high field MRI (9.4T) and compressed sensing, we have achieved microscopic resolution and sufficiently high throughput for rodent population studies. We generated whole brain structural MRI and diffusion connectomes for four diverse isogenic lines of mice (C57BL/6J, DBA/2J, CAST/EiJ, and BTBR) at spatial resolution 20,000 times higher than human connectomes. We measured narrow sense heritability (h²) I.e. the fraction of variance explained by strains in a simple ANOVA model for volumes and scalar diffusion metrics, and estimates of residual technical error for 166 regions in each hemisphere and connectivity between the regions. Volumes of discrete brain regions had the highest mean heritability (0.71 ± 0.23 SD, n = 332), followed by fractional anisotropy (0.54 ± 0.26), radial diffusivity (0.34 ± 0.022), and axial diffusivity (0.28 ± 0.19). Connection profiles were statistically different in 280 of 322 nodes across all four strains. Nearly 150 of the connection profiles were statistically different between the C57BL/6J, DBA/2J, and CAST/EiJ lines. Microscopic whole brain MRI/DTI has allowed us to identify significant heritable phenotypes in brain volume, scalar DTI metrics, and quantitative connectomes.

... To extract brain connectome, we employed an established structural connectome processing pipeline (for details see Zhang et al., 2018). ...

A major challenge in the cognitive training field is inducing broad, far-transfer training effects. Thus far, little is known about the neural mechanisms underlying broad training effects. Here we tested a set of competitive hypotheses regarding the role of brain integration vs. segregation underlying the broad training effect. We retrospectively analyzed data from a randomized controlled trial comparing neurocognitive effects of vision-based speed of processing training (VSOP) and an active control consisting of mental leisure activities (MLA) in older adults with MCI. We classified a subset of participants in the VSOP as learners, who showed improvement in executive function and episodic memory. The other participants in the VSOP (i.e., VSOP non-learners) and a subset of participants in the MLA (i.e., MLA non-learners) served as controls. Structural brain networks were constructed from diffusion tensor imaging. Clustering coefficients (CCs) and characteristic path lengths were computed as measures of segregation and integration, respectively. Learners showed significantly greater global CCs after intervention than controls. Nodal CCs were selectively enhanced in cingulate cortex, parietal regions, striatum, and thalamus. Among VSOP learners, those with more severe baseline neurodegeneration had greater improvement in segregation after training. Our findings suggest broad training effects are related to enhanced segregation in selective brain networks, providing insight into cognitive training related neuroplasticity.

... The deep nuclei provide another challenge for streamlines termination. Their complex structure often renders dMRI tractography uninterpretable within a nucleus [Zhang et al., 2018], despite well-organized underlying WM pathways passing through the surrounding regions and along the surface. Short connections between nuclei are also very hard to interpret. ...

The human brain is a complex and organized network, where the connection between regions is not achieved with single neurons crisscrossing each other but rather millions of densely packed and well-ordered neurons. Reconstruction from diffusion MRI tractography is only an attempt to capture the full complexity of this network, at the macroscale. This review provides an overview of the misconceptions, biases and pitfalls present in structural white matter bundle and connectome reconstruction using tractography. The goal is not to discourage readers, but rather to inform them of the limitations present in the methods used by researchers in the field in order to focus on what they can do and promote proper interpretations of their results. It also provides a list of open problems that could be solved in future research projects for the next generation of PhD students.

... We use the data for two consensus connectomes that we have generated in 1 at the Budapest connectome server 3.0 40,41 based on the diffusion MRI data from Human Connectome Project (HCP) for 500 individuals 25 . The server uses brain mapping tools for for parcellation, tractography, and graph construction 13,42,43 to map the experimental data of each individual. Then the consensus connectome is determined as a set of edges that are common to a selected group of individuals. ...

Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human connectome can be crucial for the brain complex dynamics. In this context, the best-connected brain areas, designated as hub nodes, play a central role in supporting integrated brain function. Here, we study the structure of simplicial complexes attached to eight global hubs in the female and male connectomes and identify the core networks among the affected brain regions. These eight hubs (Putamen, Caudate, Hippocampus and Thalamus-Proper in the left and right cerebral hemisphere) are the highest-ranking according to their topological dimension, defined as the number of simplexes of all orders in which the node participates. Furthermore, we analyse the weight-dependent heterogeneity of simplexes. We demonstrate changes in the structure of identified core networks and topological entropy when the threshold weight is gradually increased. These results highlight the role of higher-order interactions in human brain networks and provide additional evidence for (dis)similarity between the female and male connectomes.

... The strength of structural connectivity between the brain regions is determined by the number of fibers passing through them [17,18]. The structural brain network is expected to exhibit sparse topology without many loops or cycles ( Figure 1) [19,17,20]. On the other hand, functional connectivity obtained from the resting-state functional MRI (fMRI) is often computed as the Pearson correlation coefficient between brain regions [21,22,23,24]. ...

This paper proposes a novel topological learning framework that can integrate networks of different sizes and topology through persistent homology. This is possible through the introduction of a new topological loss function that enables such challenging task. The use of the proposed loss function bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations with ground truth to assess the effectiveness of the topological loss in discriminating networks with different topology. The method is further applied to a twin brain imaging study in determining if the brain network is genetically heritable. The challenge is in overlaying the topologically different functional brain networks obtained from the resting-state functional magnetic resonance imaging (fMRI) onto the template structural brain network obtained through the diffusion tensor imaging (DTI).

... After diffusion preprocessing, the eddy corrected diffusion weighted images are postprocessed using MRtrix3 (www.mrtrix.org), Advanced Normalization Tools (ANTs) (80), and the Sherbrooke Connectivity Imaging Lab toolbox in python (Scilpy) as part of the population-based SC (PSC) pipeline (81). The b0 reference image is extracted, skull stripped, bias-field corrected, cropped, intensity normalized, and resampled to 1 mm isotropic resolution. ...

Rationale: We provide an in-depth description of a comprehensive clinical, immunological, and neuroimaging study that includes a full image processing pipeline. This approach, although implemented in HIV infected individuals, can be used in the general population to assess cerebrovascular health.
Aims: In this longitudinal study, we seek to determine the effects of neuroinflammation due to HIV-1 infection on the pathomechanisms of cerebral small vessel disease (CSVD). The study focuses on the interaction of activated platelets, pro-inflammatory monocytes and endothelial cells and their impact on the neurovascular unit. The effects on the neurovascular unit are evaluated by a novel combination of imaging biomarkers.
Sample Size: We will enroll 110 HIV-infected individuals on stable combination anti-retroviral therapy for at least three months and an equal number of age-matched controls. We anticipate a drop-out rate of 20%.
Methods and Design: Subjects are followed for three years and evaluated by flow cytometric analysis of whole blood (to measure platelet activation, platelet monocyte complexes, and markers of monocyte activation), neuropsychological testing, and brain MRI at the baseline, 18- and 36-month time points. MRI imaging follows the recommended clinical small vessel imaging standards and adds several advanced sequences to obtain quantitative assessments of brain tissues including white matter microstructure, tissue susceptibility, and blood perfusion.
Discussion: The study provides further understanding of the underlying mechanisms of CSVD in chronic inflammatory disorders such as HIV infection. The longitudinal study design and comprehensive approach allows the investigation of quantitative changes in imaging metrics and their impact on cognitive performance.

... The consensus connectomes that we study are generated at the Budapest Reference Connectome Server v3.0 12 using data from the Human Connectome Project (HCP) for 500 individuals 2 . As it is described in 13 , the server produces the connectomes for each anonymised individual based on its diffusion MRI data of HCP and by applying the brain mapping tools 11,55,56 for parcellation, tractography, and graph construction. From these individual graphs, the consensus connectome with the edges that are common for a specified group of individuals is generated, corresponding to the settings of a variety of parameters 13 . ...

Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and edges indicate the occurrence of fiber tracts between them, has enabled an objective graph-theoretic analysis of human connectomes. However, the latent structure on higher-order interactions remains unexplored, where many brain regions act in synergy to perform complex functions. Here we use the simplicial complexes description of human connectome, where the shared simplexes encode higher-order relationships between groups of nodes. We study consensus connectome of 100 female (F-connectome) and of 100 male (M-connectome) subjects that we generated from the Budapest Reference Connectome Server v3.0 based on data from the Human Connectome Project. Our analysis reveals that the functional geometry of the common F&M-connectome coincides with the M-connectome and is characterized by a complex architecture of simplexes to the 14th order, which is built in six anatomical communities, and linked by short cycles. The F-connectome has additional edges that involve different brain regions, thereby increasing the size of simplexes and introducing new cycles. Both connectomes contain characteristic subjacent graphs that make them 3/2-hyperbolic. These results shed new light on the functional architecture of the brain, suggesting that insightful differences among connectomes are hidden in their higher-order connectivity.

... To extract brain connectome, we employed an established structural connectome processing pipeline (for details, see Zhang et al., 2018). First, we applied a reproducible probabilistic tractography algorithm (Girard et al., 2014) to diffusion MRI data to generate streamlines across the whole brain. ...

The relationship between AD pathology and cognitive decline is an important topic in the aging research field. Recent studies suggest that memory deficits are more susceptible to phosphorylated tau (Ptau), than amyloid-beta. However, little is known regarding the neurocognitive mechanisms linking Ptau and memory related decline. Here, we extracted data from ADNI participants with CSF (cerebrospinal fluid) Ptau collected at baseline, diffusion tensor imaging measure twice, two-year apart, and longitudinal memory data over five years. We defined three age- and education-matched groups: Ptau negative cognitively unimpaired, Ptau positive cognitively unimpaired, and Ptau positive individuals with mild cognitive impairment. We found the presence of CSF Ptau at baseline was related to a loss of structural stability in medial temporal lobe connectivity in a way that matched proposed disease progression, and this loss of stability in connections known to be important for memory moderated the relationship between Ptau accumulation and memory decline.

... Secondly, the streamlines from the WM bundle C k,i,j considered as outliers (streamlines taking anatomically implausible paths) were automatically removed from the final bundle C k,i,j using an algorithm that identifies streamlines creating loops (i.e., winding more than 360 degrees). Outliers are then detected using a hierarchical clustering approach based on QuickBundles 57,59 with a tree-length threshold of 0.2 60 . ...

The human brain is a complex system that can be efficiently represented as a network of structural connectivity. Many imaging studies would benefit from such network information, which is not always available. In this work, we present a whole-brain multi-scale structural connectome atlas. This tool has been derived from a cohort of 66 healthy subjects imaged with optimal technology in the setting of the Human Connectome Project. From these data we created, using extensively validated diffusion-data processing, tractography and gray-matter parcellation tools, a multi-scale probabilistic atlas of the human connectome. In addition, we provide user-friendly and accessible code to match this atlas to individual brain imaging data to extract connection-specific quantitative information. This can be used to associate individual imaging findings, such as focal white-matter lesions or regional alterations, to specific connections and brain circuits. Accordingly, network-level consequences of regional changes can be analyzed even in absence of diffusion and tractography data. This method is expected to broaden the accessibility and lower the yield for connectome research.

... For each budget and both reconstruction methods, within-and between-subject L 2 errors were computed for the scan-2 fODFs using the complete data scan-1 fODFs as ground truth. The reproducibility at each voxel was summarized using the dICC: dICC v "d 2 v,bs {pd 2 v,bs`d 2 v,ws q [33], whered v,bs andd v,ws are the mean between-and withinsubject errors at voxel v, respectively. dICC takes values ranging from 0 to 1, where a higher value indicates better reproducibility, i.e., large inter-subject variance and small intra-subject variance. ...

High angular resolution diffusion imaging (HARDI), a type of diffusion magnetic resonance imaging (dMRI) that measures diffusion signals on a sphere in q-space, is widely used in data acquisition for human brain structural connectome analysis. Accurate estimation of the local diffusion, and thus the structural connectome, typically requires dense sampling in HARDI, resulting in long acquisition times and logistical challenges. We propose a method to select an optimal set of q-space directions for recovery of the local diffusion under a sparsity constraint on the sampling budget. Relevant historical dMRI data is leveraged to estimate a prior distribution of the local diffusion in a template space using reduced rank Gaussian process models. For a new subject to be scanned, the priors are mapped into the subject-specific coordinate and used to guide an optimized q-space sampling which minimizes the expected integrated squared error of a diffusion function estimator from sparse samples. The optimized sampling locations are inferred by an efficient greedy algorithm with theoretical bounds approximating the global optimum. Simulation studies and a real data application using the Human Connectome Project data demonstrate that our proposed method provides substantial advantages over its competitors.

... For each budget and both reconstruction methods, within-and between-subject L 2 errors were computed for the scan-2 fODFs using the complete data scan-1 fODFs as ground truth. The reproducibility at each voxel was summarized using the dICC: dICC v "d 2 v,bs {pd 2 v,bs`d 2 v,ws q [33], whered v,bs andd v,ws are the mean between-and withinsubject errors at voxel v, respectively. dICC takes values ranging from 0 to 1, where a higher value indicates better reproducibility, i.e., large inter-subject variance and small intra-subject variance. ...

High angular resolution diffusion imaging (HARDI) is a type of diffusion magnetic resonance imaging (dMRI) that measures diffusion signals on a sphere in q-space. It has been widely used in data acquisition for human brain structural connectome analysis. To more accurately estimate the structural connectome, dense samples in q-space are often acquired, potentially resulting in long scanning times and logistical challenges. This paper proposes a statistical method to select q-space directions optimally and estimate the local diffusion function from sparse observations. The proposed approach leverages relevant historical dMRI data to calculate a prior distribution to characterize local diffusion variability in each voxel in a template space. For a new subject to be scanned, the priors are mapped into the subject-specific coordinate and used to help select the best q-space samples. Simulation studies demonstrate big advantages over the existing HARDI sampling and analysis framework. We also applied the proposed method to the Human Connectome Project data and a dataset of aging adults with mild cognitive impairment. The results indicate that with very few q-space samples (e.g., 15 or 20), we can recover structural brain networks comparable to the ones estimated from 60 or more diffusion directions with the existing methods.

... When choosing a method to perform parcellation of the entire white matter, the previously described points related to reproducibility and consistency of anatomical tract identification across different populations and acquisitions (as described in Section 4.1) are also important facts to consider [417,54,539,545]. ...

Diffusion magnetic resonance imaging (dMRI) tractography is an advanced imaging technique that enables in vivo mapping of the brain's white matter connections at macro scale. Over the last two decades, the study of brain connectivity using dMRI tractography has played a prominent role in the neuroimaging research landscape. In this paper, we provide a high-level overview of how tractography is used to enable quantitative analysis of the brain's structural connectivity in health and disease. We first provide a review of methodology involved in three main processing steps that are common across most approaches for quantitative analysis of tractography, including methods for tractography correction, segmentation and quantification. For each step, we aim to describe methodological choices, their popularity, and potential pros and cons. We then review studies that have used quantitative tractography approaches to study the brain's white matter, focusing on applications in neurodevelopment, aging, neurological disorders, mental disorders, and neurosurgery. We conclude that, while there have been considerable advancements in methodological technologies and breadth of applications, there nevertheless remains no consensus about the "best" methodology in quantitative analysis of tractography, and researchers should remain cautious when interpreting results in research and clinical applications.

... Next, cluster labeling identifies the pair of regions connected by 830 each inter-subject cluster and discards duplicate centroids. Finally, the third clustering stage aims to regroup centroids into a small number of clusters for each connection using QuickBundles with the MDF distance, an algorithm that has also been successfully used in numerous methods (Cousineau et al., 2017;Garyfallidis et al., 2018;Zhang et al., 2018b). The method was applied to 835 probabilistic tractography from 100 subjects of the HCP dataset, obtaining a multi-subject atlas composed of 525 bundles. ...

The study of short association fibers is still an incomplete task due to their higher inter-subject variability and the smaller size of this kind of fibers in comparison to known long association bundles. However, their description is essential to understand human brain dysfunction and better characterize the human brain connectome. In this work, we present a multi-subject atlas of short association fibers, which was computed using a superficial white matter bundle identification method based on fiber clustering. To create the atlas, we used probabilistic tractography from one hundred subjects from the HCP database, aligned with non-linear registration. The method starts with an intra-subject clustering of short fibers (30-85 mm). Based on a cortical atlas, the intra-subject cluster centroids from all subjects are segmented to identify the centroids connecting each region of interest (ROI) of the atlas. To reduce computational load, the centroids from each ROI group are randomly separated into ten subgroups. Then, an inter-subject hierarchical clustering is applied to each centroid subgroup, followed by a second level of clustering to select the most-reproducible clusters across subjects for each ROI group. Finally, the clusters are labeled according to the regions that they connect, and clustered to create the final bundle atlas.
The resulting atlas is composed of 525 bundles of superficial short association fibers along the whole brain, with 384 bundles connecting pairs of different ROIs and 141 bundles connecting portions of the same ROI. The reproducibility of the bundles was verified using automatic segmentation on three different tractogram databases. Results for deterministic and probabilistic tractography data show high reproducibility, especially for probabilistic tractography in HCP data. In comparison to previous work, our atlas features a higher number of bundles and greater cortical surface coverage.

... where corr(Á, Á) represents the Pearson correlation and SC(E, Á) and FC (E, Á) represent the structural and functional connections between ROI E and all other ROIs respectively. Zhang et al., 2018), which is a generalization of the intraclass correlation coefficient (ICC) (Shrout & Fleiss, 1979), with values in the range (0, 1). d 2 bs and d 2 ws represent the average distance squared between subjects and within multiple scans of a subject respectively. ...

There has been increasing interest in jointly studying structural connectivity (SC) and functional connectivity (FC) derived from diffusion and functional MRI. Previous connectome integration studies almost exclusively required predefined atlases. However, there are many potential atlases to choose from and this choice heavily affects all subsequent analyses. To avoid such an arbitrary choice, we propose a novel atlas-free approach, named Surface-Based Connectivity Integration (SBCI), to more accurately study the relationships between SC and FC throughout the intra-cortical gray matter. SBCI represents both SC and FC in a continuous manner on the white surface, avoiding the need for prespecified atlases. The continuous SC is represented as a probability density function and is smoothed for better facilitation of its integration with FC. To infer the relationship between SC and FC, three novel sets of SC-FC coupling (SFC) measures are derived. Using data from the Human Connectome Project, we introduce the high-quality SFC measures produced by SBCI and demonstrate the use of these measures to study sex differences in a cohort of young adults. Compared with atlas-based methods, this atlas-free framework produces more reproducible SFC features and shows greater predictive power in distinguishing biological sex. This opens promising new directions for all connectomics studies.

... . In total, about 20 connectome descriptors (adjacency matrices) describing different aspects of white matter fiber tract connections were generated (seeZhang et al. (2018) for more information on the extracted descriptors). Each adjacency matrix has a dimension of 68 × 68, representing R = 68 regions' connection pattern. ...

Statistical methods relating tensor predictors to scalar outcomes in a regression model generally vectorize the tensor predictor and estimate the coefficients of its entries employing some form of regularization, use summaries of the tensor covariate, or use a low dimensional approximation of the coefficient tensor. However, low rank approximations of the coefficient tensor can suffer if the true rank is not small. We propose a tensor regression framework which assumes a soft version of the parallel factors (PARAFAC) approximation. In contrast to classic PARAFAC where each entry of the coefficient tensor is the sum of products of row-specific contributions across the tensor modes, the soft tensor regression (Softer) framework allows the row-specific contributions to vary around an overall mean. We follow a Bayesian approach to inference, and show that softening the PARAFAC increases model flexibility, leads to improved estimation of coefficient tensors, more accurate identification of important predictor entries, and more precise predictions, even for a low approximation rank. From a theoretical perspective, we show that employing Softer leads to a weakly consistent posterior distribution of the coefficient tensor, irrespective of the true or approximation tensor rank, a result that is not true when employing the classic PARAFAC for tensor regression. In the context of our motivating application, we adapt Softer to symmetric and semi-symmetric tensor predictors and analyze the relationship between brain network characteristics and human traits.

... 11,12 T1weighted MRI has distinct advantages compared to DTI in terms of reliability in constructing brain networks and standardizing pulse sequences across scanner types. 30,31 Unlike fMRI, T1 MRI is more routinely prescribed as presurgical, standard of care. T1 MRI has greater resistance to artifact over other imaging modalities and requires less resource to preprocess and analyze than other acquisitions. ...

Diffuse gliomas are incurable brain tumors, yet there is signi cant heterogeneity in patient survival. Advanced computational techniques such as radiomics show potential for presurgical prediction of survival and other outcomes from neuroimaging. However, these techniques ignore non-lesioned brain features that could be essential for improving prediction accuracy. Whole-brain network (connectome) features were retrospectively identi ed from 305 adult patients diagnosed with diffuse glioma. These features were entered into a Cox proportional hazards model to predict overall survival with 10-folds cross-validation. The mean time-dependent area under the curve (AUC) of the connectome model was compared with the mean AUCs of clinical and radiomic models using a pairwise t-test with Bonferroni correction. One clinical model included only features that are known presurgery (clinical) and another included an advantaged set of features that are not typically known presurgery (clinical+). The median survival time for all patients was 134.2 months. The connectome model (AUC 0.88 +/-0.01) demonstrated superior performance (P < 0.001, corrected) compared to the clinical (AUC 0.61 +/-0.02), clinical+ (AUC 0.79 +/-0.01) and radiomic models (AUC 0.75 +/-0.02). These ndings indicate that the connectome is a feasible and reliable early biomarker for predicting survival in patients with diffuse glioma. Connectome models could be valuable tools for precision medicine by informing patient risk strati cation and treatment decision-making.

... • HCP (Wang et al., 2019): This is a 68 × 68 × 212 binary tensor consisting of structural connectivity patterns among 68 brain regions for 212 individuals from Human Connectome Project (HCP). All the individual images were preprocessed following a standard pipeline (Zhang et al., 2018), and the brain was parcellated to 68 regions-of-interest following the Desikan atlas (Desikan et al., 2006). The tensor entries encode the presence or absence of fiber connections between those 68 brain regions for each of the 212 individuals. ...

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a multilinear Bernoulli model, develop a rank-constrained likelihood-based estimation method, and obtain the theoretical accuracy guarantees. In contrast to continuous-valued problems, the binary tensor problem exhibits an interesting phase transition phenomenon according to the signal-to-noise ratio. The error bound for the parameter tensor estimation is established, and we show that the obtained rate is minimax optimal under the considered model. Furthermore, we develop an alternating optimization algorithm with convergence guarantees. The efficacy of our approach is demonstrated through both simulations and analyses of multiple data sets on the tasks of tensor completion and clustering.

... In this article, instead of being concerned with small measurement errors that are difficult to distinguish from actual biological variation, we focus on identifying outlying brain networks that are almost certainly attributable to measurement errors in reconstructing the connectome. Such gross errors can potentially arise due to problems during the data collection phase; for example, due to non-negligible movement of the patient in the scanner [Baum et al., 2018] or mistakes in preprocessing large of amounts of data using complex structural connectome reconstruction pipelines [Zhang et al., 2018]. ...

It has become routine in neuroscience studies to measure brain networks for different individuals using neuroimaging. These networks are typically expressed as adjacency matrices, with each cell containing a summary of connectivity between a pair of brain regions. There is an emerging statistical literature describing methods for the analysis of such multi-network data in which nodes are common across networks but the edges vary. However, there has been essentially no consideration of the important problem of outlier detection. In particular, for certain subjects, the neuroimaging data are so poor quality that the network cannot be reliably reconstructed. For such subjects, the resulting adjacency matrix may be mostly zero or exhibit a bizarre pattern not consistent with a functioning brain. These outlying networks may serve as influential points, contaminating subsequent statistical analyses. We propose a simple Outlier DetectIon for Networks (ODIN) method relying on an influence measure under a hierarchical generalized linear model for the adjacency matrices. An efficient computational algorithm is described, and ODIN is illustrated through simulations and an application to data from the UK Biobank. ODIN was successful in identifying moderate to extreme outliers. Removing such outliers can significantly change inferences in downstream applications.

Motivation:
It has become routine in neuroscience studies to measure brain networks for different individuals using neuroimaging. These networks are typically expressed as adjacency matrices, with each cell containing a summary of connectivity between a pair of brain regions. There is an emerging statistical literature describing methods for the analysis of such multi-network data in which nodes are common across networks but the edges vary. However, there has been essentially no consideration of the important problem of outlier detection. In particular, for certain subjects, the neuroimaging data are so poor quality that the network cannot be reliably reconstructed. For such subjects, the resulting adjacency matrix may be mostly zero or exhibit a bizarre pattern not consistent with a functioning brain. These outlying networks may serve as influential points, contaminating subsequent statistical analyses. We propose a simple Outlier DetectIon for Networks (ODIN) method relying on an influence measure under a hierarchical generalized linear model for the adjacency matrices. An efficient computational algorithm is described, and ODIN is illustrated through simulations and an application to data from the UK Biobank.
Results:
ODIN was successful in identifying moderate to extreme outliers. Removing such outliers can significantly change inferences in downstream applications.
Availability:
ODIN has been implemented in both Python and R and these implementations along with other code are publicly available at github.com/pritamdey/ODIN-python and github.com/pritamdey/ODIN-r respectively.
Supplementary information:
Supplementary data are available at Bioinformatics online.

Statistical methods relating tensor predictors to scalar outcomes in a regression model generally vectorize the tensor predictor and estimate the coefficients of its entries employing some form of regularization, use summaries of the tensor covariate, or use a low dimensional approximation of the coefficient tensor. However, low rank approximations of the coefficient tensor can suffer if the true rank is not small. We propose a tensor regression framework which assumes a soft version of the parallel factors (PARAFAC) approximation. In contrast to classic PARAFAC, where each entry of the coefficient tensor is the sum of products of row-specific contributions across the tensor modes, the soft tensor regression (Softer) framework allows the row-specific contributions to vary around an overall mean. We follow a Bayesian approach to inference, and show that softening the PARAFAC increases model flexibility, leads to more precise predictions, improved estimation of coefficient tensors, and more accurate identification of important predictor entries, even for a low approximation rank. From a theoretical perspective, we show that the posterior distribution of the coefficient tensor based on Softer is weakly consistent irrespective of the true tensor or approximation rank. In the context of our motivating application, we adapt Softer to symmetric and semi-symmetric tensor predictors and analyze the relationship between brain network characteristics and human traits.

Brain hubs are best connected central nodes in the human connectome that play a critical role in integrated brain dynamics. How the hubs perform their function vs different dynamical processes and the role of their higher-order connections involving different brain regions remains elusive. Here we simulate the phase synchronisation processes on the human connectome core network consisting of the eight brain hubs and all attached simplexes of different sizes. The leading pairwise interactions among neighbouring nodes are assumed, taking into account the natural weights of edges. Our results reveal that increasing the positive pairwise couplings promotes a continuous synchronisation while a weak partial synchronisation occurs for a wide range of negative couplings. The weights of edges stabilise the synchronisation process supporting the absence of hysteresis. Furthermore, the time evolution of the order parameter shows cyclic fluctuations induced by the concurrent evolution of phases associated with different groups of nodes. We show that these oscillations exhibit long-range temporal correlations and multifractality. The asymmetrical singularity spectra are determined, which vary with the time scale and depend on the weights of edges. These findings suggest a possible way that the brain functional geometry maintains a desirable low-level synchrony through complex patterns of phase fluctuations.

The recent developments in resonance imaging technologies have allowed growing access to a wide variety of complex information on brain functioning. Regardless of the several types of data modalities which are now available, a fundamental interest in the neurosciences is in conducting inference on brain networks. In this article, we discuss statistical methods for brain networks with a specific focus on the Bayesian approach. Due to its ability to allow careful uncertainty quantification, borrowing of information, and inclusion of experts knowledge, the Bayesian paradigm can provide a particularly effective tool in the neuroscience studies.

Aphasia is a prevalent cognitive syndrome caused by stroke. The rarity of premorbid imaging and heterogeneity of lesion obscures the links between the local effects of the lesion, global anatomical network organization, and aphasia symptoms. We applied a simulated attack approach in humans to examine the effects of 39 stroke lesions (16 females) on anatomical network topology by simulating their effects in a control sample of 36 healthy (15 females) brain networks. We focused on measures of global network organization thought to support overall brain function and resilience in the whole brain and within the left hemisphere. After removing lesion volume from the network topology measures and behavioral scores (the Western Aphasia Battery Aphasia Quotient; WAB-AQ, four behavioral factor scores obtained from a neuropsychological battery, and a factor sum), we compared the behavioral variance accounted for by simulated post-stroke connectomes to that observed in the randomly permuted data. Global measures of anatomical network topology in the whole brain and left hemisphere accounted for 10% variance or more of the WAB-AQ and the lexical factor score beyond lesion volume and null permutations. Streamline networks provided more reliable point estimates than FA networks. Edge weights and network efficiency were weighted most highly in predicting the WAB-AQ for FA networks. Overall, our results suggest that global network measures provide modest statistical value beyond lesion volume when predicting overall aphasia severity, but less value in predicting specific behaviors. Variability in estimates could be induced by premorbid ability, deafferentation and diaschisis, and neuroplasticity following stroke.Significance StatementPost-stroke, the remaining neuroanatomy maintains cognition and supports recovery. However, studies often utilize small, cross-sectional samples that cannot fully model the interactions between lesions and other variables that affect networks in stroke. Alternate methods are required to account for these effects. "Simulated attack" models are computational approaches that apply virtual damage to the brain and measure their putative consequences. Using a simulated attack model, we estimated how simulated damage to anatomical networks could account for language performance. Overall, our results reveal that global network measures can provide modest statistical value predicting overall aphasia severity, but less value in predicting specific behaviors. These findings suggest that more theoretically precise network models could be necessary to robustly predict individual outcomes in aphasia.

Automated methods that can identify white matter bundles from large tractography datasets have several applications in neuroscience research. In these applications, clustering algorithms have shown to play an important role in the analysis and visualization of white matter structure, generating useful data which can be the basis for further studies. This work proposes FFClust, an efficient fiber clustering method for large tractography datasets containing millions of fibers. Resulting clusters describe the whole set of main white matter fascicles present on an individual brain. The method aims to identify compact and homogeneous clusters, which enables several applications. In individuals, the clusters can be used to study the local connectivity in pathological brains, while at population level, the processing and analysis of reproducible bundles, and other post-processing algorithms can be carried out to study the brain connectivity and create new white matter bundle atlases. The proposed method was evaluated in terms of quality and execution time performance versus the state-of-the-art clustering techniques used in the area. Results show that FFClust is effective in the creation of compact clusters, with a low intra-cluster distance, while keeping a good quality Davies–Bouldin index, which is a metric that quantifies the quality of clustering approaches. Furthermore, it is about 8.6 times faster than the most efficient state-of-the-art method for one million fibers dataset. In addition, we show that FFClust is able to correctly identify atlas bundles connecting different brain regions, as an example of application and the utility of compact clusters.

Background
Perceived fatigue is among the most common complaints in older adults and is substantially influenced by diminished resources or impaired structure of widespread cortical and subcortical regions. Alzheimer’s disease and its preclinical stage – mild cognitive impairment (MCI) – is considered a brain network disease. It is unknown, however, whether those with MCI will therefore perceive worse fatigue, and whether an impaired global brain network will worsen their experience of fatigue.
Methods
In this pilot case-control study of age-, sex-, and education-matched MCI and their cognitively healthy counterparts (HC), perceived fatigue was measured using Multidimensional Fatigue Inventory, and diffusion tensor imaging (DTI) tractography data was analyzed using graph theory methods to explore small-worldness properties: segregation and integration.
Results
Perceived fatigue was more severe in MCI than HC. Despite a trend for greater network alterations in MCI, there were no significant group differences in integration or segregation. Greater perceived fatigue was related to higher segregation across groups; more perceived fatigue was related to higher segregation and lower integration in MCI but not HC.
Conclusions
Findings of the present study support the notion that altered whole-brain small-worldness properties in brain aging or neurodegeneration may underpin perceived fatigue.

Fiber clustering is a popular strategy for automated white matter parcellation using diffusion MRI
tractography. However, there has been no investigation to assess fiber clustering parcellation test-retest reproducibility, i.e. whether white matter parcellations could be reliably reproduced in repeated scans. This work presents the first study of fiber clustering white matter parcellation test-retest reproducibility. We perform evaluation on a large test-retest dataset, including a total of 255 subjects from multiple independently acquired datasets. Our results in general indicate that the fiber clustering method produced more reproducible white matter parcellations than a popular cortical-parcellation-based method.

The data science of networks is a rapidly developing field with myriad applications. In neuroscience, the brain is commonly modeled as a connectome, a network of nodes connected by edges. While there have been thousands of papers on connectomics, the statistics of networks remains limited and poorly understood. Here, we provide an overview from the perspective of statistical network science of the kinds of models, assumptions, problems, and applications that are theoretically and empirically justified for analysis of connectome data. We hope this review spurs further development and application of statistically grounded methods in connectomics.

Diffusion magnetic resonance imaging (dMRI) tractography is an advanced imaging technique that enables in vivo reconstruction of the brain’s white matter connections at macro scale. It provides an important tool for quantitative mapping of the brain’s structural connectivity using measures of connectivity or tissue microstructure. Over the last two decades, the study of brain connectivity using dMRI tractography has played a prominent role in the neuroimaging research landscape. In this paper, we provide a high-level overview of how tractography is used to enable quantitative analysis of the brain’s structural connectivity in health and disease. We focus on two types of quantitative analyses of tractography, including: 1) tract-specific analysis that refers to research that is typically hypothesis-driven and studies particular anatomical fiber tracts, and 2) connectome-based analysis that refers to research that is more data-driven and generally studies the structural connectivity of the entire brain. We first provide a review of methodology involved in three main processing steps that are common across most approaches for quantitative analysis of tractography, including methods for tractography correction, segmentation and quantification. For each step, we aim to describe methodological choices, their popularity, and potential pros and cons. We then review studies that have used quantitative tractography approaches to study the brain’s white matter, focusing on applications in neurodevelopment, aging, neurological disorders, mental disorders, and neurosurgery. We conclude that, while there have been considerable advancements in methodological technologies and breadth of applications, there nevertheless remains no consensus about the “best” methodology in quantitative analysis of tractography, and researchers should remain cautious when interpreting results in research and clinical applications.

There has been a huge interest in studying human brain connectomes inferred from different imaging modalities and exploring their relationships with human traits, such as cognition. Brain connectomes are usually represented as networks, with nodes corresponding to different regions of interest (ROIs) and edges to connection strengths between ROIs. Due to the high-dimensionality and non-Euclidean nature of networks, it is challenging to depict their population distribution and relate them to human traits. Current approaches focus on summarizing the network using either pre-specified topological features or principal components analysis (PCA). In this paper, building on recent advances in deep learning, we develop a nonlinear latent factor model to characterize the population distribution of brain graphs and infer their relationships to human traits. We refer to our method as Graph AuTo-Encoding (GATE). We applied GATE to two large-scale brain imaging datasets, the Adolescent Brain Cognitive Development (ABCD) study and the Human Connectome Project (HCP) for adults, to study the structural brain connectome and its relationship with cognition. Numerical results demonstrate huge advantages of GATE over competitors in terms of prediction accuracy, statistical inference, and computing efficiency. We found that the structural connectome has a stronger association with a wide range of human cognitive traits than was apparent using previous approaches.

Temporal changes in medical images are often evaluated along a parametrized function that represents a structure of interest (e.g. white matter tracts). By attributing samples along these functions with distributions of image properties in the local neighborhood, we create distribution-valued signatures for these functions. We propose a novel, comprehensive framework which models their temporal evolution trajectories. This is achieved under the unifying scheme of Wasserstein distance metric. The regression problem is formulated as a constrained optimization problem and solved using an alternating projection algorithm. The solution simultaneously preserves the functional characteristics of the curve, models the temporal change in distribution profiles and forces the estimated distributions to be valid. Hypothesis testing is applied in two ways using Wasserstein based test statistics. Validation is presented on synthetic data. Estimation of a population trajectory is shown using diffusion properties along DTI tracts from a healthy population of infants. Detection of delayed growth is shown using a case study.

Diffusion MRI tractography is the most widely used macroscale method for mapping connectomes in vivo. However, tractography is prone to various errors and biases, and thus tractography-derived connectomes require careful validation. Here, we critically review studies that have developed or utilized phantoms and tracer maps to validate tractography-derived connectomes, either quantitatively or qualitatively. We identify key factors impacting connectome reconstruction accuracy, including streamline seeding, propagation and filtering methods, and consider the strengths and limitations of state-of-the-art connectome phantoms and associated validation studies. These studies demonstrate the inherent limitations of current fiber orientation models and tractography algorithms and their impact on connectome reconstruction accuracy. Reconstructing connectomes with both high sensitivity and high specificity is challenging, given that some tractography methods can generate an abundance of spurious connections, while others can overlook genuine fiber bundles. We argue that streamline filtering can minimize spurious connections and potentially improve the biological plausibility of connectomes derived from tractography. We find that algorithmic choices such as the tractography seeding methodology, angular threshold, and streamline propagation method can substantially impact connectome reconstruction accuracy. Hence, careful application of tractography is necessary to reconstruct accurate connectomes. Improvements in diffusion MRI acquisition techniques will not necessarily overcome current tractography limitations without accompanying modeling and algorithmic advances.

This paper studies the problem of classifying longitudinal structural brain networks to identify meaningful substructures and their time‐varying effects. The problem is motivated by a subpopulation of healthy older adults who can maintain excellent cognitive functions across time, while others usually have cognitive decline in aging. It is of substantial scientific interest to study neurological mechanisms behind this successful aging phenomena; however, existing statistical tools for longitudinal networks are very limited. We propose a structured classification method that could identify a set of small outcome‐relevant subgraphs and estimate the age effect of each signal subgraph from the longitudinal network predictors, as well as an efficient algorithm for model estimation. Application of this method to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data identifies a small set of brain regions whose connectivity strengths are predictive of successful cognitive aging, which has more appealing interpretation and better predictive performance compared to unstructured classification method.

Background:
Mapping diffusion MRI tractography streamlines to the cortical surface facilitates the integration of white matter features onto gray matter, especially for connectivity analysis.
Method:
In this work, we present methods that combine cortical surface meshes with tractography reconstruction to improve endpoint precision and coverage. This cortical mapping also enables the study of structural measures from tractography along the cortex and subcortical structures. In addition to structural connectivity analysis, novel adaptive and dynamic surface seeding methods are proposed. These improvements are made by incorporating cortical maps such as endpoint density.
Results:
The proposed dynamic surface seeding increases the cortical coverage and reduces endpoint location biases. Our results suggest that the use of cortical and subcortical meshes together with a proper seeding strategy can reduce the variability in structural connectivity analysis.
Conclusion:
The proposed adaptive and dynamic seeding utilize cortical maps to better distribute tractography interconnections, thus increasing cortical coverage and reducing endpoint bias. This also facilitates the analysis of white matter & diffusion MRI features along the cortex, combined with cortical measures or functional activation. Impact statement This research presents an overview of surface mapping methods for tractography to reduce structural connectivity variability. The proposed adaptive and dynamic seeding utilize cortical maps to better distribute tractography interconnections, thus increasing cortical coverage and reducing end-point bias. This also facilitates the analysis of white matter and diffusion magnetic resonance imaging features along the cortex, combined with cortical measures or functional activation.

The rise of network data in many different domains has offered researchers new insight into the problem of modeling complex systems and propelled the development of numerous innovative statistical methodologies and computational tools. In this paper, we primarily focus on two types of biological networks, gene networks and brain networks, where statistical network modeling has found both fruitful and challenging applications. Unlike other network examples such as social networks where network edges can be directly observed, both gene and brain networks require careful estimation of edges using covariates as a first step. We provide a discussion on existing statistical and computational methods for edge esitimation and subsequent statistical inference problems in these two types of biological networks.

Tractography combined with regions of interest (ROIs) has been used to non-invasively study the structural connectivity of the cortex as well as to assess the reliability of these connections. However, the subcortical connectome (subcortex to subcortex) has not been comprehensively examined, in part due to the difficulty of performing tractography in this complex and compact region. In this study, we performed an in vivo investigation using tractography to assess the feasibility and reliability of mapping known connections between structures of the subcortex using the test-retest dataset from the Human Connectome Project (HCP). We further validated our observations using a separate unrelated subjects dataset from the HCP. Quantitative assessment was performed by computing tract densities and spatial overlap of identified connections between subcortical ROIs. Further, known connections between structures of the basal ganglia and thalamus were identified and visually inspected, comparing tractography reconstructed trajectories with descriptions from tract-tracing studies. Our observations demonstrate both the feasibility and reliability of using a data-driven tractography-based approach to map the subcortical connectome in vivo.

We conduct an imaging genetics study to explore how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer's disease and mild cognitive impairment. We develop an analysis of longitudinal resting-state functional magnetic resonance imaging (rs-fMRI) and genetic data obtained from a sample of 111 subjects with a total of 319 rs-fMRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. A Dynamic Causal Model (DCM) is fit to the rs-fMRI scans to estimate effective brain connectivity within the DMN and related to a set of single nucleotide polymorphisms (SNPs) contained in an empirical disease-constrained set which is obtained out-of-sample from 663 ADNI subjects having only genome-wide data. We relate longitudinal effective brain connectivity estimated using spectral DCM to SNPs using both linear mixed effect (LME) models as well as function-on-scalar regression (FSR). In both cases we implement a parametric bootstrap for testing SNP coefficients and make comparisons with p-values obtained from asymptotic null distributions. In both networks at an initial q-value threshold of 0.1 no effects are found. We report on exploratory patterns of associations with relatively high ranks that exhibit stability to the differing assumptions made by both FSR and LME.

The aim of this paper is to develop a novel class of functional structural equation models (FSEMs) for dissecting functional genetic and environmental effects on twin functional data, while characterizing the varying association between functional data and covariates of interest. We propose a three-stage estimation procedure to estimate varying coefficient functions for various covariates (e.g., gender) as well as three covariance operators for the genetic and environmental effects. We develop an inference procedure based on weighted likelihood ratio statistics to test the genetic/environmental effect at either a fixed location or a compact region. We also systematically carry out the theoretical analysis of the estimated varying functions, the weighted likelihood ratio statistics, and the estimated covariance operators. We conduct extensive Monte Carlo simulations to examine the finite-sample performance of the estimation and inference procedures. We apply the proposed FSEM to quantify the degree of genetic and environmental effects on twin white-matter tracts obtained from the UNC early brain development study.

In this work, we propose a diffusion MRI protocol for mining Parkinson’s disease diffusion MRI datasets and recover robust disease-specific biomarkers. Using advanced high angular resolution diffusion imaging (HARDI) crossing fiber modeling and tractography robust to partial volume effects, we automatically dissected 50 white matter (WM) fascicles. These fascicles connect deep nuclei (thalamus, putamen, pallidum) to different cortical functional areas (associative, motor, sensorimotor, limbic), basal forebrain and substantia nigra. Then, among these 50 candidate WM fascicles, only the ones that passed a test-retest reproducibility procedure qualified for further tractometry analysis. Leveraging the unique 2-timepoints test-retest Parkinson’s Progression Markers Initiative (PPMI) dataset of over 600 subjects, we found statistically significant differences in tract profiles along the subcortico-cortical pathways between Parkinson’s disease patients and healthy controls. In particular, significant increases in FA, apparent fiber density, tract-density and generalized FA were detected in some locations of the nigro-subthalamo-putaminal-thalamo-cortical pathway. This connection is one of the major motor circuits balancing the coordination of motor output. Detailed and quantifiable knowledge on WM fascicles in these areas is thus essential to improve the quality and outcome of Deep Brain Stimulation, and to target new WM locations for investigation.

Tractograms are mathematical representations of the main paths of axons within the white matter of the brain, from diffusion MRI data. Such representations are in the form of polylines, called streamlines, and one streamline approximates the common path of tens of thousands of axons. The analysis of tractograms is a task of interest in multiple fields, like neurosurgery and neurology. A basic building block of many pipelines of analysis is the definition of a distance function between streamlines. Multiple distance functions have been proposed in the literature, and different authors use different distances, usually without a specific reason other than invoking the "common practice". To this end, in this work we want to test such common practices, in order to obtain factual reasons for choosing one distance over another. For these reasons, in this work we compare many streamline distance functions available in the literature. We focus on the common task of automatic bundle segmentation and we adopt the recent approach of supervised segmentation from expert-based examples. Using the HCP dataset, we compare several distances obtaining guidelines on the choice of which distance function one should use for supervised bundle segmentation.

In studying structural inter-connections in the human brain, it is common to first estimate fiber bundles connecting different regions of the brain relying on diffusion MRI. These fiber bundles act as highways for neural activity and communication, snaking through the brain and connecting different regions. Current statistical methods for analyzing these fibers reduce the rich information into an adjacency matrix, with the elements containing a count of the number of fibers or a mean diffusion feature (such as fractional anisotropy) along the fibers. The goal of this article is to avoid discarding the rich functional data on the shape, size and orientation of fibers, developing flexible models for characterizing the population distribution of fibers between brain regions of interest within and across different individuals. We start by decomposing each fiber in each individual's brain into a corresponding rotation matrix, shape and translation from a global reference curve. These components can be viewed as data lying on a product space composed of different Euclidean spaces and manifolds. To non-parametrically model the distribution within and across individuals, we rely on a hierarchical mixture of product kernels specific to the component spaces. Taking a Bayesian approach to inference, we develop an efficient method for posterior sampling. The approach automatically produces clusters of fibers within and across individuals, and yields interesting new insights into variation in fiber curves, while providing a useful starting point for more elaborate models relating fibers to covariates and neuropsychiatric traits.

Diffusion MRI (dMRI) provides rich information on the white matter of the human brain, enabling insight into neurological disease, normal aging, and neuroplasticity. We present BundleMAP, an approach to extracting features from dMRI data that can be used for supervised classification, regression, and hypothesis testing. Our features are based on aggregating measurements along nerve fiber bundles, enabling visualization and anatomical interpretation. The main idea behind BundleMAP is to use the ISOMAP manifold learning technique to jointly parametrize nerve fiber bundles. We combine this idea with mechanisms for outlier removal and feature selection to obtain a practical machine learning pipeline. We demonstrate that it increases accuracy of disease detection and estimation of disease activity, and that it improves the power of statistical tests.

Recent progress in diffusion MRI and tractography algorithms as well as the launch of the Human Connectome Project (HCP)1 have provided brain research with an abundance of structural connectivity data. In this work, we describe and evaluate a method that can infer the structural brain network that interconnects a given set of Regions of Interest (ROIs) from probabilistic tractography data. The proposed method, referred to as Minimum Asymmetry Network Inference Algorithm (MANIA), does not determine the connectivity between two ROIs based on an arbitrary connectivity threshold. Instead, we exploit a basic limitation of the tractography process: the observed streamlines from a source to a target do not provide any information about the polarity of the underlying white matter, and so if there are some fibers connecting two voxels (or two ROIs) X and Y, tractography should be able in principle to follow this connection in both directions, from X to Y and from Y to X. We leverage this limitation to formulate the network inference process as an optimization problem that minimizes the (appropriately normalized) asymmetry of the observed network. We evaluate the proposed method using both the FiberCup dataset and based on a noise model that randomly corrupts the observed connectivity of synthetic networks. As a case-study, we apply MANIA on diffusion MRI data from 28 healthy subjects to infer the structural network between 18 corticolimbic ROIs that are associated with various neuropsychiatric conditions including depression, anxiety and addiction.

Network data are increasingly measured along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring a brain connectivity network for each individual along with their membership in an low or high creative reasoning group. It is of paramount importance to develop statistical methods for testing of global and local changes in the structural interconnections among brain regions across groups. We develop a general Bayesian procedure for inference and testing on group differences in the network structure, which relies on a nonparametric representation for the conditional probability mass function associated with a network-valued random variable. By leveraging on mixtures of low-rank factorizations, we allow simple global and local hypothesis testing adjusting for multiplicity. An efficient Gibbs sampler is defined for posterior computation. We provide theoretical results on the flexibility of the model and assess testing performance in simulations. The approach is applied to provide novel results showing relationships between human brain networks and creativity.

Diffusion MRI tractography has emerged as a useful and popular tool for mapping connections between brain regions. In this study, we examined the performance of quantitative anisotropy (QA) in facilitating deterministic fiber tracking. Two phantom studies were conducted. The first phantom study examined the susceptibility of fractional anisotropy (FA), generalized factional anisotropy (GFA), and QA to various partial volume effects. The second phantom study examined the spatial resolution of the FA-aided, GFA-aided, and QA-aided tractographies. An in vivo study was conducted to track the arcuate fasciculus, and two neurosurgeons blind to the acquisition and analysis settings were invited to identify false tracks. The performance of QA in assisting fiber tracking was compared with FA, GFA, and anatomical information from T1-weighted images. Our first phantom study showed that QA is less sensitive to the partial volume effects of crossing fibers and free water, suggesting that it is a robust index. The second phantom study showed that the QA-aided tractography has better resolution than the FA-aided and GFA-aided tractography. Our in vivo study further showed that the QA-aided tractography outperforms the FA-aided, GFA-aided, and anatomy-aided tractographies. In the shell scheme (HARDI), the FA-aided, GFA-aided, and anatomy-aided tractographies have 30.7%, 32.6%, and 24.45% of the false tracks, respectively, while the QA-aided tractography has 16.2%. In the grid scheme (DSI), the FA-aided, GFA-aided, and anatomy-aided tractographies have 12.3%, 9.0%, and 10.93% of the false tracks, respectively, while the QA-aided tractography has 4.43%. The QA-aided deterministic fiber tracking may assist fiber tracking studies and facilitate the advancement of human connectomics.

Diffusion magnetic resonance imaging (dMRI) offers a unique approach to study the structural connectivity of the brain. DMRI allows to reconstruct the 3D pathways of axons within the white matter as a set of polylines (streamlines), called the tractogram. Tractograms of different brains need to be aligned in a common representation space for various purposes, such as group-analysis, segmentation or atlas construction. Typically, such alignment is obtained with affine registration, through which tractograms are globally transformed, with the limit of not reconciling local differences. In this paper, we propose to improve registration-based alignment by what we call mapping. The goal of mapping is to find the correspondence between streamlines across brains, i.e. to find the map of which streamline in one tractogram correspond to which streamline in the other tractogram. We frame the mapping problem as a rectangular linear assignment problem (RLAP), a cornerstone of combinatorial optimization. We adopt a variant of the famous Hungarian method to get the optimal solution of the RLAP. We validate the proposed method with a tract alignment application, where we register two tractograms and, given one anatomical tract, we segment the corresponding one in the other tractogram. On dMRI data from the Human Connectome Project, we provide experimental evidence that mapping, implemented as a RLAP, can vastly improve both the true positive rate and false discovery rate of registration-based alignment, establishing a strong argument in favor of what we propose. We conclude by discussing the limitations of the current approach, which gives perspective for future work.

In elastic shape analysis, a representation of a shape is invariant to translation, scaling, rotation, and reparameterization, and important problems such as computing the distance and geodesic between two curves, the mean of a set of curves, and other statistical analyses require finding a best rotation and reparameterization between two curves. In this paper, we focus on this key subproblem and study different tools for optimizations on the joint group of rotations and reparameterizations. We develop and analyze a novel Riemannian optimization approach and evaluate its use in shape distance computation and classification using two public datasets. Experiments show significant advantages in computational time and reliability in performance compared to the current state-of-the-art method. A brief version of this paper can be found in Huang et al. (Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems 2014).

In vivo tractography based on diffusion magnetic resonance imaging (dMRI) has opened new doors to study structure-function relationships in the human brain. Initially developed to map the trajectory of major white matter tracts, dMRI is used increasingly to infer long-range anatomical connections of the cortex. Because axonal projections originate and terminate in the gray matter but travel mainly through the deep white matter, the success of tractography hinges on the capacity to follow fibers across this transition. Here we demonstrate that the complex arrangement of white matter fibers residing just under the cortical sheet poses severe challenges for long-range tractography over roughly half of the brain. We investigate this issue by comparing dMRI from very-high-resolution ex vivo macaque brain specimens with histological analysis of the same tissue. Using probabilistic tracking from pure gray and white matter seeds, we found that ∼50% of the cortical surface was effectively inaccessible for long-range diffusion tracking because of dense white matter zones just beneath the infragranular layers of the cortex. Analysis of the corresponding myelin-stained sections revealed that these zones colocalized with dense and uniform sheets of axons running mostly parallel to the cortical surface, most often in sulcal regions but also in many gyral crowns. Tracer injection into the sulcal cortex demonstrated that at least some axonal fibers pass directly through these fiber systems. Current and future high-resolution dMRI studies of the human brain will need to develop methods to overcome the challenges posed by superficial white matter systems to determine long-range anatomical connections accurately.

The multiband EPI sequence has been developed for the human connectome project to accelerate MRI data acquisition. However, no study has yet investigated the test-retest (TRT) reliability of the graph metrics of white matter (WM) structural brain networks constructed from this new sequence. Here, we employed a multiband diffusion MRI (dMRI) dataset with repeated scanning sessions and constructed both low- and high-resolution WM networks by volume- and surface-based parcellation methods. The reproducibility of network metrics and its dependence on type of construction procedures was assessed by the intra-class correlation coefficient (ICC). We observed conserved topological architecture of WM structural networks constructed from the multiband dMRI data as previous findings from conventional dMRI. For the global network properties, the first order metrics were more reliable than second order metrics. Between two parcellation methods, networks with volume-based parcellation showed better reliability than surface-based parcellation, especially for the global metrics. Between different resolutions, the high-resolution network exhibited higher TRT performance than the low-resolution in terms of the global metrics with a large effect size, whereas the low-resolution performs better in terms of local (region and connection) properties with a relatively low effect size. Moreover, we identified that the association and primary cortices showed higher reproducibility than the paralimbic/limbic regions. The important hub regions and rich-club connections are more reliable than the non-hub regions and connections. Finally, we found WM networks from the multiband dMRI showed higher reproducibility compared with those from the conventional dMRI. Together, our results demonstrated the fair to good reliability of the WM structural brain networks from the multiband EPI sequence, suggesting its potential utility for exploring individual differences and for clinical applications.

This systematic review aimed to assess the reproducibility of graph-theoretic brain network metrics. Primary research studies of test-retest reliability conducted on healthy human subjects were included that quantified test-retest reliability using either the intra-class correlation coefficient (ICC) or the coefficient of variance (CV). The MEDLINE, Web of Knowledge, Google Scholar and OpenGrey databases were searched up to February 2014. Risk of bias was assessed with 10 criteria, weighted toward methodological quality. Twenty-three studies were included in the review (n = 499 subjects) and evaluated for various characteristics including sample size (5 - 45), retest interval (<1 hour - >1 year), acquisition method and test-retest reliability scores. For at least one metric, ICCs reached the "fair" range (ICC 0.40 - 0.59) in 1 study, the "good" range (ICC 0.60 - 0.74) in 5 studies and the "excellent" range (ICC > 0.74) in 16 studies. Heterogeneity of methods prevented further quantitative analysis. Reproducibility was good overall. For the metrics having 3 or more ICCs reported for both functional and structural networks, 6 of 7 were higher in structural networks, indicating that structural networks may be more reliable over time. We were also able to highlight and discuss a number of methodological factors affecting reproducibility.

Tractography based on diffusion-weighted MRI (DWI) is widely used
for mapping the structural connections of the human brain. Its
accuracy is known to be limited by technical factors affecting in vivo
data acquisition, such as noise, artifacts, and data undersampling
resulting from scan time constraints. It generally is assumed that
improvements in data quality and implementation of sophisticated
tractography methods will lead to increasingly accurate maps of
human anatomical connections. However, assessing the anatomical
accuracy of DWI tractography is difficult because of the lack of independent
knowledge of the true anatomical connections in
humans. Here we investigate the future prospects of DWI-based
connectional imaging by applying advanced tractography methods
to an ex vivo DWI dataset of the macaque brain. The results
of different tractography methods were compared with maps of
known axonal projections from previous tracer studies in the
macaque. Despite the exceptional quality of the DWI data, none
of the methods demonstrated high anatomical accuracy. The
methods that showed the highest sensitivity showed the lowest
specificity, and vice versa. Additionally, anatomical accuracy was
highly dependent upon parameters of the tractography algorithm,
with different optimal values for mapping different pathways.
These results suggest that there is an inherent limitation in determining
long-range anatomical projections based on voxel-averaged
estimates of local fiber orientation obtained from DWI
data that is unlikely to be overcome by improvements in data
acquisition and analysis alone.

Collections of networks are available in many research fields. In connectomic
applications, inter-connections among brain regions are collected from each
patient, with interest focusing on studying shared structure and the population
distribution of deviations across individuals. Current methods focus on
reducing network data to features prior to statistical analysis, while we
propose a fully generative Bayesian nonparametric approach for modeling the
population distribution of network-valued data. The joint distribution of the
edges follows a multivariate Bernoulli distribution, with transformed edge
probability vectors expressed as the sum of a shared similarity vector and a
class-specific deviation modeled via flexible low-rank factorization exploiting
the network structure. The formulation is provably flexible, leads to a simple
and computationally efficient Gibbs sampler, and provides a framework for
clustering graph-valued data, while inferring a cluster-specific rank. We
discuss theoretical properties and illustrate the performance in simulations
and application to human brain network data.

Tract-Based Spatial Statistics (TBSS) is a popular software pipeline to coregister sets of diffusion tensor Fractional Anisotropy (FA) images for performing voxel-wise comparisons. It is primarily defined by its skeleton projection step intended to reduce effects of local misregistration. A white matter "skeleton" is computed by morphological thinning of the inter-subject mean FA, and then all voxels are projected to the nearest location on this skeleton. Here we investigate several enhancements to the TBSS pipeline based on recent advances in registration for other modalities, principally based on groupwise registration with the ANTS-SyN algorithm. We validate these enhancements using simulation experiments with synthetically-modified images. When used with these enhancements, we discover that TBSS's skeleton projection step actually reduces algorithm accuracy, as the improved registration leaves fewer errors to warrant correction, and the effects of this projection's compromises become stronger than those of its benefits. In our experiments, our proposed pipeline without skeleton projection is more sensitive for detecting true changes and has greater specificity in resisting false positives from misregistration. We also present comparative results of the proposed and traditional methods, both with and without the skeleton projection step, on three real-life datasets: two comparing differing populations of Alzheimer's disease patients to matched controls, and one comparing progressive supranuclear palsy patients to matched controls. The proposed pipeline produces more plausible results according to each disease's pathophysiology.

Diffusion MRI tractography has emerged as a useful and popular tool for mapping connections between brain regions. In this study, we examined the performance of quantitative anisotropy (QA) in facilitating deterministic fiber tracking. Two phantom studies were conducted. The first phantom study examined the susceptibility of fractional anisotropy (FA), generalized factional anisotropy (GFA), and QA to various partial volume effects. The second phantom study examined the spatial resolution of the FA-aided, GFA-aided, and QA-aided tractographies. An in vivo study was conducted to track the arcuate fasciculus, and two neurosurgeons blind to the acquisition and analysis settings were invited to identify false tracks. The performance of QA in assisting fiber tracking was compared with FA, GFA, and anatomical information from T1-weighted images. Our first phantom study showed that QA is less sensitive to the partial volume effects of crossing fibers and free water, suggesting that it is a robust index. The second phantom study showed that the QA-aided tractography has better resolution than the FA-aided and GFA-aided tractography. Our in vivo study further showed that the QA-aided tractography outperforms the FA-aided, GFA-aided, and anatomy-aided tractographies. In the shell scheme (HARDI), the FA-aided, GFA-aided, and anatomy-aided tractographies have 30.7%, 32.6%, and 24.45% of the false tracks, respectively, while the QA-aided tractography has 16.2%. In the grid scheme (DSI), the FA-aided, GFA-aided, and anatomy-aided tractographies have 12.3%, 9.0%, and 10.93% of the false tracks, respectively, while the QA-aided tractography has 4.43%. The QA-aided deterministic fiber tracking may assist fiber tracking studies and facilitate the advancement of human connectomics.

Currently, connectomes (e.g., functional or structural brain graphs) can be
estimated in humans at $\approx 1~mm^3$ scale using a combination of diffusion
weighted magnetic resonance imaging, functional magnetic resonance imaging and
structural magnetic resonance imaging scans. This manuscript summarizes a
novel, scalable implementation of open-source algorithms to rapidly estimate
magnetic resonance connectomes, using both anatomical regions of interest
(ROIs) and voxel-size vertices. To assess the reliability of our pipeline, we
develop a novel nonparametric non-Euclidean reliability metric. Here we provide
an overview of the methods used, demonstrate our implementation, and discuss
available user extensions. We conclude with results showing the efficacy and
reliability of the pipeline over previous state-of-the-art.

Diusion Tensor MRI has become the preferred imaging modality to explore white matter structure and brain connectivity in vivo. Conventional region of interest analysis and voxel-based comparison does not make use of the geometric properties of fiber tracts. This pa- per explores shape modelling of major fiber bundles. We describe tracts, represented as clustered sets of curves of similar shape, by a shape proto- type swept along a space trajectory. This approach can naturally describe white matter structures observed either as bundles dispersing towards the cortex or tracts defined as dense patterns of parallel fibers. Sets of stream- line curves obtained from tractography are clustered, parametrized and aligned with a similarity transform. An average curve and eigenmodes of shape variation describe a compact statistical shape model. Reconstruc- tion by sweeping the template along the trajectory results in a simplified model of a tract. Feasibility is demonstrated by modelling callosal and cortico-spinal fasciculi of two dierent subjects.

Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We develop several statistical inference procedures for MVCM and systematically study their theoretical properties. We first establish the weak convergence of the local linear estimate of coefficient functions, as well as its asymptotic bias and variance, and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate. We establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions. We propose a global test for linear hypotheses of varying coefficient functions, and derive its asymptotic distribution under the null hypothesis. We also propose a simultaneous confidence band for each individual effect curve. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply MVCM to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment.

We compare two strategies for modeling the connections of the brain's white matter: fiber clustering and the parcellation-based connectome. Both methods analyze diffusion magnetic resonance imaging fiber tractography to produce a quantitative description of the brain's connections. Fiber clustering is designed to reconstruct anatomically-defined white matter tracts, while the parcellation-based white matter segmentation enables the study of the brain as a network. From the perspective of white matter segmentation, we compare and contrast the goals and methods of the parcellation-based and clustering approaches, with special focus on reviewing the field of fiber clustering. We also propose a third category of new hybrid methods that combine aspects of parcellation and clustering, for joint analysis of connection structure and anatomy or function. We conclude that these different approaches for segmentation and modeling of the white matter can advance the neuroscientific study of the brain's connectivity in complementary ways.

Motivated by recent work studying massive imaging data in the neuroimaging
literature, we propose multivariate varying coefficient models (MVCM) for
modeling the relation between multiple functional responses and a set of
covariates. We develop several statistical inference procedures for MVCM and
systematically study their theoretical properties. We first establish the weak
convergence of the local linear estimate of coefficient functions, as well as
its asymptotic bias and variance, and then we derive asymptotic bias and mean
integrated squared error of smoothed individual functions and their uniform
convergence rate. We establish the uniform convergence rate of the estimated
covariance function of the individual functions and its associated eigenvalue
and eigenfunctions. We propose a global test for linear hypotheses of varying
coefficient functions, and derive its asymptotic distribution under the null
hypothesis. We also propose a simultaneous confidence band for each individual
effect curve. We conduct Monte Carlo simulation to examine the finite-sample
performance of the proposed procedures. We apply MVCM to investigate the
development of white matter diffusivities along the genu tract of the corpus
callosum in a clinical study of neurodevelopment.

Diffusion MR data sets produce large numbers of streamlines which are hard to visualize, interact with, and interpret in a clinically acceptable time scale, despite numerous proposed approaches. As a solution we present a simple, compact, tailor-made clustering algorithm, QuickBundles (QB), that overcomes the complexity of these large data sets and provides informative clusters in seconds. Each QB cluster can be represented by a single centroid streamline; collectively these centroid streamlines can be taken as an effective representation of the tractography. We provide a number of tests to show how the QB reduction has good consistency and robustness. We show how the QB reduction can help in the search for similarities across several subjects.

Tractography based on diffusion weighted imaging (DWI) data is a method for identifying the major white matter fascicles (tracts) in the living human brain. The health of these tracts is an important factor underlying many cognitive and neurological disorders. In vivo, tissue properties may vary systematically along each tract for several reasons: different populations of axons enter and exit the tract, and disease can strike at local positions within the tract. Hence quantifying and understanding diffusion measures along each fiber tract (Tract Profile) may reveal new insights into white matter development, function, and disease that are not obvious from mean measures of that tract. We demonstrate several novel findings related to Tract Profiles in the brains of typically developing children and children at risk for white matter injury secondary to preterm birth. First, fractional anisotropy (FA) values vary substantially within a tract but the Tract FA Profile is consistent across subjects. Thus, Tract Profiles contain far more information than mean diffusion measures. Second, developmental changes in FA occur at specific positions within the Tract Profile, rather than along the entire tract. Third, Tract Profiles can be used to compare white matter properties of individual patients to standardized Tract Profiles of a healthy population to elucidate unique features of that patient's clinical condition. Fourth, Tract Profiles can be used to evaluate the association between white matter properties and behavioral outcomes. Specifically, in the preterm group reading ability is positively correlated with FA measured at specific locations on the left arcuate and left superior longitudinal fasciculus and the magnitude of the correlation varies significantly along the Tract Profiles. We introduce open source software for automated fiber-tract quantification (AFQ) that measures Tract Profiles of MRI parameters for 18 white matter tracts. With further validation, AFQ Tract Profiles have potential for informing clinical management and decision-making.