Normalized Cut Group Clustering of Resting-State fMRI Data
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{"title"=>"Normalized cut group clustering of resting-state fMRI data", "type"=>"journal", "authors"=>[{"first_name"=>"Martijn", "last_name"=>"van den Heuvel", "scopus_author_id"=>"24333539900"}, {"first_name"=>"Rene", "last_name"=>"Mandl", "scopus_author_id"=>"6603866400"}, {"first_name"=>"Hilleke Hulshoff", "last_name"=>"Pol", "scopus_author_id"=>"6602660664"}], "year"=>2008, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"352015931", "isbn"=>"1932-6203", "issn"=>"19326203", "doi"=>"10.1371/journal.pone.0002001", "scopus"=>"2-s2.0-44349149239", "pmid"=>"18431486", "sgr"=>"44349149239"}, "id"=>"6feb263d-0ec9-39e2-8e94-7d426b3a5a22", "abstract"=>"BACKGROUND: Functional brain imaging studies have indicated that distinct anatomical brain regions can show coherent spontaneous neuronal activity during rest. Regions that show such correlated behavior are said to form resting-state networks (RSNs). RSNs have been investigated using seed-dependent functional connectivity maps and by using a number of model-free methods. However, examining RSNs across a group of subjects is still a complex task and often involves human input in selecting meaningful networks.\\n\\nMETHODOLOGY/PRINCIPAL FINDINGS: We report on a voxel based model-free normalized cut graph clustering approach with whole brain coverage for group analysis of resting-state data, in which the number of RSNs is computed as an optimal clustering fit of the data. Inter-voxel correlations of time-series are grouped at the individual level and the consistency of the resulting networks across subjects is clustered at the group level, defining the group RSNs. We scanned a group of 26 subjects at rest with a fast BOLD sensitive fMRI scanning protocol on a 3 Tesla MR scanner.\\n\\nCONCLUSIONS/SIGNIFICANCE: An optimal group clustering fit revealed 7 RSNs. The 7 RSNs included motor/visual, auditory and attention networks and the frequently reported default mode network. The found RSNs showed large overlap with recently reported resting-state results and support the idea of the formation of spatially distinct RSNs during rest in the human brain.", "link"=>"http://www.mendeley.com/research/normalized-cut-group-clustering-restingstate-fmri-data", "reader_count"=>319, "reader_count_by_academic_status"=>{"Unspecified"=>5, "Professor > Associate Professor"=>30, "Researcher"=>76, "Student > Doctoral Student"=>16, "Student > Ph. D. Student"=>86, "Student > Postgraduate"=>16, "Student > Master"=>54, "Other"=>4, "Student > Bachelor"=>13, "Lecturer"=>5, "Lecturer > Senior Lecturer"=>2, "Professor"=>12}, "reader_count_by_user_role"=>{"Unspecified"=>5, "Professor > Associate Professor"=>30, "Researcher"=>76, "Student > Doctoral Student"=>16, "Student > Ph. D. Student"=>86, "Student > Postgraduate"=>16, "Student > Master"=>54, "Other"=>4, "Student > Bachelor"=>13, "Lecturer"=>5, "Lecturer > Senior Lecturer"=>2, "Professor"=>12}, "reader_count_by_subject_area"=>{"Engineering"=>38, "Unspecified"=>26, "Mathematics"=>9, "Agricultural and Biological Sciences"=>44, "Medicine and Dentistry"=>50, "Neuroscience"=>30, "Arts and Humanities"=>1, "Physics and Astronomy"=>16, "Chemical Engineering"=>1, "Psychology"=>52, "Computer Science"=>51, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>38}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>50}, "Neuroscience"=>{"Neuroscience"=>30}, "Physics and Astronomy"=>{"Physics and Astronomy"=>16}, "Psychology"=>{"Psychology"=>52}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>44}, "Computer Science"=>{"Computer Science"=>51}, "Mathematics"=>{"Mathematics"=>9}, "Unspecified"=>{"Unspecified"=>26}, "Chemical Engineering"=>{"Chemical Engineering"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>1}}, "reader_count_by_country"=>{"United States"=>10, "United Kingdom"=>7, "Malaysia"=>1, "Russia"=>1, "Netherlands"=>3, "Austria"=>1, "Turkey"=>2, "Korea (South)"=>1, "Belgium"=>1, "China"=>5, "Poland"=>1, "Denmark"=>1, "Brazil"=>1, "Italy"=>5, "Australia"=>1, "Chile"=>1, "Germany"=>3}, "group_count"=>19}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/932943"], "description"=>"<p><i>Step A1 Graph formation</i>. An individual graph was constructed, consisting of M cortical voxels and (M<sup>2</sup> -M)/2 edges connecting all voxel pairs. The weight <i>w</i>(<i>i,j</i>) of edge <i>e</i>(<i>i,j</i>) connecting voxel <i>i</i> and voxel <i>j</i> was computed as the correlation between the filtered time-series of voxel <i>i</i> and voxel <i>j</i>, reflecting the level of functional connectivity between the two voxels. <i>Step A2 Clustering</i>. Prior to the clustering, a cut-off threshold of 0.4 was applied to reduce the complexity of the graph and lower the computational load, setting all weights to zero that did not reach this threshold. Normalized cut clustering was used to partition the graph in a fixed number of 20 networks, grouping voxels that showed a high level of functional connectivity into networks, resulting in an individual clustermap.</p>", "links"=>[], "tags"=>["clustering"], "article_id"=>603390, "categories"=>["Medicine", "Neuroscience"], "users"=>["Martijn van den Heuvel", "Rene Mandl", "Hilleke Hulshoff Pol"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0002001.g005", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Individual_clustering_stage_/603390", "title"=>"Individual clustering stage.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2008-04-23 00:56:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/932793"], "description"=>"<p>To verify that the optimization procedure considering the selection of the group graph complexity cut-off threshold resulted in a stable clustering, the group clustering was repeated with multiple settings of the graph complexity cut-off threshold. The group clustering stage (stage B) was repeated (using the individual clustermaps consisting of 20 clusters) with different settings for the group cut-off threshold varying around the found optimum of 9 (ranging from 7 to 11). The number of clusters was set to the found optimum of 7 (see main text). Next, for each of the 7 clusters, the 5 group cluster solutions were summated, creating an overlap map with voxels ranging up to a maximum of 5. The maximum of 5 indicated the overlap of all 5 clustering solutions. Figure shows large overlap between the 5 group clusterings, for all of the 7 clusters. This large overlap demonstrates that varying the cut-off threshold around the found optimum only minor influenced the group results, indicating that the automatic parameter setting procedure resulted in a stable clustering solution.</p>", "links"=>[], "tags"=>["clusterings", "varying", "graph", "cut-off"], "article_id"=>603240, "categories"=>["Medicine", "Neuroscience"], "users"=>["Martijn van den Heuvel", "Rene Mandl", "Hilleke Hulshoff Pol"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0002001.g004", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Overlap_of_multiple_group_clusterings_with_varying_group_graph_complexity_cut_off_thresholds_/603240", "title"=>"Overlap of multiple group clusterings with varying group graph complexity cut-off thresholds.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2008-04-23 00:54:00"}
  • {"files"=>["https://ndownloader.figshare.com/files/933029"], "description"=>"<p><i>Step B1 Formation of a group graph</i>. A group graph was constructed, consisting of the cortical voxels that resulted from the group averaged cortical segmentation map and edges connecting all possible voxel pairs. The weight <i>W</i>(<i>i,j</i>) of the edge connecting voxel <i>i</i> and voxel <i>j</i> reflected the cluster consistency across the group of subjects and was computed as follows. For each individual clustermap, the individual cluster-similarity between voxel <i>i</i> and <i>j</i> was defined as 1 if in the individual clustermap voxel <i>i</i> and voxel <i>j</i> were grouped in the same cluster and 0 otherwise. Figure box shows the clustermaps of subject 1 and 2 and the last subject (subject S). In subject 1 the voxels <i>i</i> and <i>j</i> were not clustered in the same cluster, hence the cluster-similarity between voxel <i>i</i> and voxel <i>j</i> was set to 0. In contrast, in subject 2 and in subject S voxel <i>i</i> and <i>j</i> were clustered in the same cluster and therefore the cluster-similarity values between these voxels in these subjects were set to 1. At the group level, <i>W</i>(<i>i,j</i>) was computed as the summation of the cluster-similarities between voxel <i>i</i> and voxel <i>j</i> over the group of S subjects. <i>Step B2 Setting cluster parameters</i>. The group graph was clustered with increasing number of clusters P and increasing graph complexity cut-off thresholds Q. An optimal fit was computed as the clustering fit with the first minimum normalized cut cost value in descending direction of the number of P clusters, to maximize the number of meaningful clustered RSNs. <i>Step B3 Computing group clustermap.</i> The cortical voxels were labeled according to the optimal clustering fit, resulting in the group clustermap. The group clustermap represents networks of voxels that were consistently clustered into the same resting-state network across the group of subjects.</p>", "links"=>[], "tags"=>["clustering"], "article_id"=>603485, "categories"=>["Medicine", "Neuroscience"], "users"=>["Martijn van den Heuvel", "Rene Mandl", "Hilleke Hulshoff Pol"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0002001.g006", "stats"=>{"downloads"=>3, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Group_clustering_stage_/603485", "title"=>"Group clustering stage.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2008-04-23 00:58:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/932667"], "description"=>"<p>To test the assumed minor effect of overclustering at the individual level on the group clustering results, the individual clustering (Stage A) was repeated with varying overclustering settings (i.e., the number of clusters) and analyzed at the group level (Stage B). For each individual dataset, the individual clustering (stage A) was repeated with varying number of clusters (assumed to result in overclustering), ranging from 15 to 35 (with steps of 5). This resulted in 5 clustermaps per individual dataset. Next, the group clustering (stage B) was repeated with the 5 sets of individual clustermaps (graph complexity threshold set to 9; number of RSNs set to 7). For each of the 7 resulting group clusters, the 5 cluster solutions were summated, creating an overlap map (cluster <i>a</i>–<i>g</i>) with voxel values ranging up to a maximum of 5. The maximum of 5 indicated an overlap off all 5 cluster solutions. Figure shows highly similar cluster results over the 5 different group clusterings, as suggested by the large overlap for each of the 7 clusters. As expected, the results demonstrated that the overclustering at the individual level did not change the nature of the group clustering.</p>", "links"=>[], "tags"=>["clusterings", "sets", "varying"], "article_id"=>603118, "categories"=>["Medicine", "Neuroscience"], "users"=>["Martijn van den Heuvel", "Rene Mandl", "Hilleke Hulshoff Pol"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0002001.g003", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Overlap_of_multiple_group_clusterings_of_different_sets_of_individual_clustermaps_varying_on_the_level_of_individual_overclustering_/603118", "title"=>"Overlap of multiple group clusterings of different sets of individual clustermaps, varying on the level of individual overclustering.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2008-04-23 00:51:58"}
  • {"files"=>["https://ndownloader.figshare.com/files/459706"], "description"=>"<div><h3>Background</h3><p>Functional brain imaging studies have indicated that distinct anatomical brain regions can show coherent spontaneous neuronal activity during rest. Regions that show such correlated behavior are said to form resting-state networks (RSNs). RSNs have been investigated using seed-dependent functional connectivity maps and by using a number of model-free methods. However, examining RSNs across a group of subjects is still a complex task and often involves human input in selecting meaningful networks.</p><h3>Methodology/Principal Findings</h3><p>We report on a voxel based model-free normalized cut graph clustering approach with whole brain coverage for group analysis of resting-state data, in which the number of RSNs is computed as an optimal clustering fit of the data. Inter-voxel correlations of time-series are grouped at the individual level and the consistency of the resulting networks across subjects is clustered at the group level, defining the group RSNs. We scanned a group of 26 subjects at rest with a fast BOLD sensitive fMRI scanning protocol on a 3 Tesla MR scanner.</p><h3>Conclusions/Significance</h3><p>An optimal group clustering fit revealed 7 RSNs. The 7 RSNs included motor/visual, auditory and attention networks and the frequently reported default mode network. The found RSNs showed large overlap with recently reported resting-state results and support the idea of the formation of spatially distinct RSNs during rest in the human brain.</p></div>", "links"=>[], "tags"=>["normalized", "clustering", "resting-state", "fmri"], "article_id"=>150571, "categories"=>["Medicine", "Neuroscience"], "users"=>["Martijn van den Heuvel", "Rene Mandl", "Hilleke Hulshoff Pol"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0002001", "stats"=>{"downloads"=>2, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Normalized_Cut_Group_Clustering_of_Resting_State_fMRI_Data/150571", "title"=>"Normalized Cut Group Clustering of Resting-State fMRI Data", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2008-04-23 00:09:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/932558"], "description"=>"<p>At the individual clustering stage, the constructed individual connectivity graph was threshold with the set individual graph cut-off threshold <i>rc</i> before clustering. To examine the effect of <i>rc</i> on the final group clustering, the individual clustering procedure was repeated with 3 settings of <i>rc</i>, being 0.3, 0.4 and 0.5. The overclustering parameter was kept fixed on 20. Group clustering (graph complexity threshold set to 9; number of RSNs set to 7) was repeated with the 3 sets of individual clustering results, resulting in 3 group clusterings. For all of the 7 group clusters the overlap of these clustering solutions was computed. Figure clearly shows large overlap for all of the 7 group clusters, indicating that the setting of <i>rc</i> did not affect the final group clustering. However, when <i>rc</i> was increased to 0.6 and up, more and more paths were removed from the individual graph. This clearly affected the individual clustering and the group clustering, changing the spatially layout of the clusters (data not shown).</p>", "links"=>[], "tags"=>["clusterings", "sets", "varying", "cut-off"], "article_id"=>603004, "categories"=>["Medicine", "Neuroscience"], "users"=>["Martijn van den Heuvel", "Rene Mandl", "Hilleke Hulshoff Pol"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0002001.g002", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Overlap_of_multiple_group_clusterings_of_different_sets_of_individual_clustermaps_varying_on_the_individual_cut_off_threshold_/603004", "title"=>"Overlap of multiple group clusterings of different sets of individual clustermaps, varying on the individual cut-off threshold.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2008-04-23 00:50:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/932466"], "description"=>"<p>Group clustering of 3 Tesla resting-state fMRI data of a group of 26 subjects revealed 7 resting-state networks (RSNs). 1a shows a functional connected network consisting of the posterior cingulate/precuneus, medial frontal regions and bilateral parietal/temporal regions, a RSN known as the default mode network. 1b and 1c show lateralized parietal-frontal networks, networks that are often reported in attention and memory processing. 1d shows a joint network of both sensorimotor and visual networks. Iteratively clustering partitioned this cluster in 3 sub-clusters, shown in clustermap d'. The results showed separate clusters for primary visual regions (cluster <i>d</i>'<i>-1</i>), primary sensorimotor regions (cluster <i>d</i>'<i>-2</i>) and extra-striate visual regions (cluster <i>d</i>'<i>-3</i>). 1e shows a network of bilateral insular regions and posterior cingulate cortex. 1f and 1g represent singular clusters consisting of, respectively, a posterior part of Brodmann Area 7 and an anterior part of the cingulate cortex. The clustered networks show resemblance with previous reported RSNs.</p>", "links"=>[], "tags"=>["clustered", "resting-state"], "article_id"=>602911, "categories"=>["Medicine", "Neuroscience"], "users"=>["Martijn van den Heuvel", "Rene Mandl", "Hilleke Hulshoff Pol"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0002001.g001", "stats"=>{"downloads"=>1, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Group_clustered_resting_state_networks_/602911", "title"=>"Group clustered resting-state networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2008-04-23 00:48:31"}

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  • {"unique-ip"=>"16", "full-text"=>"16", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2018", "month"=>"5"}
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  • {"unique-ip"=>"10", "full-text"=>"9", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"3", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2018", "month"=>"7"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"8"}
  • {"unique-ip"=>"9", "full-text"=>"8", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"10"}
  • {"unique-ip"=>"15", "full-text"=>"11", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"6", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2018", "month"=>"11"}
  • {"unique-ip"=>"9", "full-text"=>"9", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"9"}
  • {"unique-ip"=>"12", "full-text"=>"13", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"12"}
  • {"unique-ip"=>"19", "full-text"=>"16", "pdf"=>"6", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"2"}
  • {"unique-ip"=>"8", "full-text"=>"10", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"3"}
  • {"unique-ip"=>"5", "full-text"=>"4", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
  • {"unique-ip"=>"13", "full-text"=>"15", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2019", "month"=>"5"}
  • {"unique-ip"=>"11", "full-text"=>"12", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2019", "month"=>"8"}
  • {"unique-ip"=>"12", "full-text"=>"14", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2019", "month"=>"9"}

Relative Metric

{"start_date"=>"2008-01-01T00:00:00Z", "end_date"=>"2008-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences", "average_usage"=>[324, 674, 863, 1015, 1146, 1259, 1360, 1452, 1540, 1621, 1704, 1776, 1843, 1905, 1968, 2029, 2097, 2162, 2233, 2289, 2352, 2412, 2476, 2538, 2601, 2655, 2714, 2777, 2841, 2894, 2946, 2998, 3047, 3103, 3151, 3201, 3258, 3317, 3369, 3424, 3471, 3521, 3583, 3625, 3687, 3743, 3788, 3838, 3896, 3953, 4015, 4075, 4148, 4201, 4275, 4347, 4420, 4486, 4535, 4592, 4660, 4731, 4792, 4845, 4901, 4971, 5027, 5089, 5148, 5200, 5261, 5318, 5374]}, {"subject_area"=>"/Computer and information sciences", "average_usage"=>[339, 724, 899, 1082, 1207, 1287, 1387, 1492, 1620, 1704, 1778, 1868, 1917, 1973, 2046, 2095, 2185, 2232, 2275, 2327, 2363, 2404, 2469, 2530, 2615, 2652, 2721, 2770, 2845, 2897, 2939, 2975, 3033, 3084, 3137, 3194, 3256, 3322, 3364, 3419, 3462, 3512, 3586, 3639, 3696, 3760, 3830, 3897, 3962, 4036, 4086, 4124, 4170, 4220, 4272, 4331, 4406, 4478, 4536, 4577, 4639, 4707, 4750, 4795, 4850, 4935, 5033, 5113, 5169, 5210, 5264, 5315, 5356, 5403]}, {"subject_area"=>"/Computer and information sciences/Neural networks", "average_usage"=>[372, 657, 846, 1068, 1166, 1238, 1308, 1348, 1384, 1478, 1546, 1610, 1665, 1707, 1744, 1812, 1859, 1901, 1943, 2037, 2084, 2137, 2189, 2255, 2304, 2364, 2410, 2448, 2480, 2512, 2545, 2571, 2615, 2649, 2694, 2751, 2834, 2877, 2946, 3025, 3074, 3122, 3178, 3253, 3344, 3440, 3476, 3495, 3520, 3540, 3571, 3633, 3698, 3727, 4030, 4059, 4090, 4122, 4171, 4363, 4393, 4431, 4477, 4538, 4573, 4607, 4646, 4704, 4731, 4765, 4831, 4872, 4923, 4995]}, {"subject_area"=>"/Medicine and health sciences", "average_usage"=>[303, 661, 845, 1003, 1135, 1248, 1352, 1439, 1532, 1618, 1691, 1765, 1831, 1902, 1969, 2028, 2098, 2159, 2234, 2294, 2356, 2423, 2483, 2548, 2615, 2682, 2743, 2796, 2853, 2907, 2970, 3025, 3078, 3138, 3197, 3243, 3307, 3351, 3420, 3468, 3519, 3569, 3625, 3688, 3739, 3799, 3850, 3911, 3961, 4009, 4075, 4137, 4194, 4263, 4329, 4393, 4449, 4501, 4566, 4638, 4706, 4761, 4828, 4898, 4948, 4999, 5040, 5107, 5170, 5226, 5292, 5352, 5434]}]}
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