Mapping Topographic Structure in White Matter Pathways with Level Set Trees
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{"title"=>"Mapping topographic structure in white matter pathways with level set trees", "type"=>"journal", "authors"=>[{"first_name"=>"Brian P.", "last_name"=>"Kent", "scopus_author_id"=>"37037656200"}, {"first_name"=>"Alessandro", "last_name"=>"Rinaldo", "scopus_author_id"=>"10641935600"}, {"first_name"=>"Fang Cheng", "last_name"=>"Yeh", "scopus_author_id"=>"57093275200"}, {"first_name"=>"Timothy", "last_name"=>"Verstynen", "scopus_author_id"=>"6507219295"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"arxiv"=>"1311.5312", "sgr"=>"84899505151", "pmid"=>"24714673", "pui"=>"372971552", "issn"=>"19326203", "scopus"=>"2-s2.0-84899505151", "doi"=>"10.1371/journal.pone.0093344"}, "id"=>"5673ccaf-0637-3786-afea-772fb4ffa053", "abstract"=>"Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees---which provide a concise representation of the hierarchical mode structure of probability density functions---offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N=30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber tracks and an efficient segmentation of the tracks that has empirical accuracy comparable to standard nonparametric clustering methods. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output.", "link"=>"http://www.mendeley.com/research/mapping-topographic-structure-white-matter-pathways-level-set-trees", "reader_count"=>29, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>2, "Researcher"=>13, "Student > Ph. D. Student"=>11, "Other"=>1, "Student > Bachelor"=>1, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>2, "Researcher"=>13, "Student > Ph. D. Student"=>11, "Other"=>1, "Student > Bachelor"=>1, "Professor"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>1, "Mathematics"=>3, "Medicine and Dentistry"=>4, "Agricultural and Biological Sciences"=>2, "Neuroscience"=>7, "Physics and Astronomy"=>1, "Psychology"=>7, "Computer Science"=>2}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>4}, "Neuroscience"=>{"Neuroscience"=>7}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Psychology"=>{"Psychology"=>7}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>2}, "Computer Science"=>{"Computer Science"=>2}, "Mathematics"=>{"Mathematics"=>3}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"United States"=>3, "Italy"=>1, "United Kingdom"=>1}, "group_count"=>2}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1454519"], "description"=>"<p><b>Algorithm 1.</b> Conceptual level set tree estimation procedure.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "conceptual", "estimation"], "article_id"=>990814, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.t002", "stats"=>{"downloads"=>1, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Algorithm_1_Conceptual_level_set_tree_estimation_procedure_/990814", "title"=>"<b>Algorithm 1.</b> Conceptual level set tree estimation procedure.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454516"], "description"=>"<p><b>Algorithm 2.</b> Compute.knn.density. Compute the k-nearest neighbor density estimate at a sample point.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "compute", "k-nearest"], "article_id"=>990811, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.t004", "stats"=>{"downloads"=>6, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Algorithm_2_Compute_knn_density_Compute_the_k_nearest_neighbor_density_estimate_at_a_sample_point_/990811", "title"=>"<b>Algorithm 2.</b> Compute.knn.density. Compute the k-nearest neighbor density estimate at a sample point.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454515"], "description"=>"<p><b>Algorithm 4.</b> Prune.tree. Remove small leaf nodes from the level set tree.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "nodes"], "article_id"=>990810, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.t005", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Algorithm_4_Prune_tree_Remove_small_leaf_nodes_from_the_level_set_tree_/990810", "title"=>"<b>Algorithm 4.</b> Prune.tree. Remove small leaf nodes from the level set tree.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454510"], "description"=>"<p>A, C, E) Example draws from each of three simulation scenarios (Gaussians, arcs & Gaussians, and resampled striatal endpoints, from the top), with observations colored by true group label. B, D, E) Error rate for each type of simulation over several degrees of clustering difficulty, created by contracting the groups toward the grand mean by various amounts. For each type of simulation and each degree of difficulty, the mean and standard deviation of classification error are reported for 8 clustering methods: DBSCAN (dbscan), level set tree clustering (density), diffusion maps (diffuse), Gaussian mixture models (gmm), K-means++ (kmeans), hierarchical clustering with single linkage (s.link), spectral clustering (spectral), and hierarchical clustering with linkage by the Ward criterion (ward).</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "clustering"], "article_id"=>990805, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.g005", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_clustering_method_accuracy_in_simulations_/990805", "title"=>"Comparison of clustering method accuracy in simulations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454509"], "description"=>"<p>A, C, E) Striatal endpoints colored by cluster assignment for three different cluster labeling methods. Gray points are unassigned because their estimated density is too low. Cluster colors match the tree node colors in the panels below. B) Tree nodes corresponding to clusters in panel A. These nodes are selected by cutting across the tree at a desired density or mass level. D) Tree nodes corresponding to clusters in panel C. Each leaf of the tree produces a cluster. F) Tree nodes corresponding to clusters in panel E. The tree is traversed upward from the root (or roots) until the desired number of clusters first appears.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods"], "article_id"=>990804, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.g004", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Clustering_with_a_level_set_tree_/990804", "title"=>"Clustering with a level set tree.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454506"], "description"=>"<p>A) Striatal endpoints from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093344#pone-0093344-g002\" target=\"_blank\">Figure 2</a>. Red points are members of a selected node of the level set tree, shown in red in panel B. C) Striatal endpoints belonging to a different mode of the level set tree, shown in panel D.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "subsets"], "article_id"=>990801, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.g003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Exploring_data_subsets_with_a_level_set_tree_/990801", "title"=>"Exploring data subsets with a level set tree.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454518"], "description"=>"<p><b>Algorithm 3.</b> Compute.knn.graph. Construct a k-nearest neighbor similarity graph.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "k-nearest"], "article_id"=>990813, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.t003", "stats"=>{"downloads"=>6, "page_views"=>23, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Algorithm_3_Compute_knn_graph_Construct_a_k_nearest_neighbor_similarity_graph_/990813", "title"=>"<b>Algorithm 3.</b> Compute.knn.graph. Construct a k-nearest neighbor similarity graph.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454503"], "description"=>"<p>A) 10,000 streamlines (yellow) mapped from the lateral frontal cortex (middle frontal gyrus) to the striatal nuclei (caudate nucleus, putamen and nucleus accumbens) shown as a gray region of interest (ROI). Data taken from a representative subject. B) Endpoint locations (in millimeters) of the streamlines shown in panel A, colored by estimated density (red is high). C) The corresponding level set tree, which indicates a complex cluster structure in these data. A major split occurs when 10% of the data are excluded from the density upper level set, and each branch of the split has relevant sub-clusters at various resolutions. Note the lack of information in the density level index on this plot, which is a typical outcome.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "corticostriatal", "endpoint"], "article_id"=>990798, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.g002", "stats"=>{"downloads"=>4, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Level_set_tree_for_corticostriatal_fiber_endpoint_locations_/990798", "title"=>"Level set tree for corticostriatal fiber endpoint locations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454500"], "description"=>"<p>A) The true pdf is a mixture of three Gaussians (black curve). For each of four example density levels (dotted lines), the high-density clusters are indicated by solid line segments. B) Population level set tree for the density in panel A. The high-density clusters of panel A are found at the intersections of the selected levels (dashed lines) with the tree. C) Estimated density (black curve) based on 2,000 data points sampled from the pdf in panel A. High-density points belonging to the leaves of the sample level set tree in panel D are shown on the horizontal axis and on the estimated density function. D) Level set tree estimate based on the sample in panel C. Leaves are colored to match corresponding points in the sample. For illustration, the trees in this figure are indexed by density levels while all other trees in this article are plotted on the mass scale.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods"], "article_id"=>990795, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.g001", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_population_and_sample_level_set_trees_/990795", "title"=>"Illustration of population and sample level set trees.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454517"], "description"=>"<p>Estimated level set tree information for a simple data simulation.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods"], "article_id"=>990812, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.t001", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Estimated_level_set_tree_information_for_a_simple_data_simulation_/990812", "title"=>"Estimated level set tree information for a simple data simulation.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454514"], "description"=>"<p>Colored streamlines show clusters that were consistently observed at both scan times. Gray streamlines show clusters detected at only one time point. Panels A, C, E, and G show results from the initial scan session. Panels B, D, F, and H show results from the second scanning session six months later.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "comparisons", "tested", "months"], "article_id"=>990809, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.g009", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Test_retest_comparisons_for_four_subjects_tested_six_months_apart_/990809", "title"=>"Test-retest comparisons for four subjects, tested six months apart.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454512"], "description"=>"<p>A, B) High-density fiber pathway clusters from the level set tree all-mode method for middle frontal gyrus fibers in two subjects. C, D) Single linkage hierarchical clustering results for the same fiber pathways, with the dendrogram cut to match the same number of clusters in the level set tree result. E, F) K-means clustering results for the sample fiber pathways.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "methods", "whole-fiber"], "article_id"=>990807, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.g007", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_methods_for_whole_fiber_segmentation_/990807", "title"=>"Comparison of methods for whole-fiber segmentation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454513"], "description"=>"<p>For the middle frontal gyrus ROI, 28 random subsamples of 15,000 fibers were drawn from the total of 51,126 fibers, while 1,500 fibers were drawn for 23 subsamples from the 3,038 total fibers in the rectus. A) All 28 level set trees plotted on the same canvas, illustrating the high degree of similarity between the data structure in the subsamples. B) Histograms of the mass levels of the splits over the whole set of subsample trees. Split mass levels are matched across subsamples by rank order. C) All 28 mode functions plotted together, illustrating that there is little variation in the number of clusters at each mass level. D) All 23 level set trees plotted together. E) Distribution of mass values for splits, matched across subsamples by rank within each sample’s tree. F) All 23 mode functions overlaid.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "30"], "article_id"=>990808, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.g008", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Repeat_reliability_for_level_set_tree_results_for_the_30_subject_template_/990808", "title"=>"Repeat reliability for level set tree results for the 30 subject template.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-08 03:33:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/1454511"], "description"=>"<p><b>A</b>) Foreground fibers for the seven selected clusters from the 30 subject template data set for streamlines tracked between the middle frontal gyrus and striatum, shown in both a sagittal and coronal view. Clusters are colored according to an all-mode clustering of the tree. B) The level set tree for data in panel A. Tree leaves are matched to fiber clusters by color. C) Same analysis as shown in A, but for a set of streamlines from the orbitofrontal cortex. Inset shows closeup of fiber streamlines in the striatal ROI mask. D) Level set tree for data shown in panel C. The branch colors of trees in panels B and D match the clusters shown in the streamlines of panels A and C respectively.</p>", "links"=>[], "tags"=>["anatomy", "nervous system", "neuroanatomy", "Connectomics", "neuroscience", "neuroimaging", "Computing methods", "Mathematical computing", "signal processing", "Image processing", "neurology", "mathematics", "Applied mathematics", "algorithms", "Statistics (mathematics)", "Statistical methods", "clustering"], "article_id"=>990806, "categories"=>["Biological Sciences"], "users"=>["Brian P. Kent", "Alessandro Rinaldo", "Fang-Cheng Yeh", "Timothy Verstynen"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0093344.g006", "stats"=>{"downloads"=>0, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Level_set_tree_clustering_for_whole_fiber_streamlines_/990806", "title"=>"Level set tree clustering for whole fiber streamlines.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-08 03:33:51"}

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