Measuring Granger Causality between Cortical Regions from Voxelwise fMRI BOLD Signals with LASSO
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{"title"=>"Measuring granger causality between cortical regions from voxelwise fmRI BOLD signals with LASSO", "type"=>"journal", "authors"=>[{"first_name"=>"Wei", "last_name"=>"Tang", "scopus_author_id"=>"25422755400"}, {"first_name"=>"Steven L.", "last_name"=>"Bressler", "scopus_author_id"=>"55403619000"}, {"first_name"=>"Chad M.", "last_name"=>"Sylvester", "scopus_author_id"=>"14051150600"}, {"first_name"=>"Gordon L.", "last_name"=>"Shulman", "scopus_author_id"=>"7102613906"}, {"first_name"=>"Maurizio", "last_name"=>"Corbetta", "scopus_author_id"=>"7003824365"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"issn"=>"1553734X", "pui"=>"365220672", "doi"=>"10.1371/journal.pcbi.1002513", "sgr"=>"84863686049", "scopus"=>"2-s2.0-84863686049", "isbn"=>"1553-7358 (Electronic)\\n1553-734X (Linking)", "pmid"=>"22654651"}, "id"=>"1051f42d-f9fa-3e29-85ec-4367a8978b28", "abstract"=>"Functional brain network studies using the Blood Oxygen-Level Dependent (BOLD) signal from functional Magnetic Resonance Imaging (fMRI) are becoming increasingly prevalent in research on the neural basis of human cognition. An important problem in functional brain network analysis is to understand directed functional interactions between brain regions during cognitive performance. This problem has important implications for understanding top-down influences from frontal and parietal control regions to visual occipital cortex in visuospatial attention, the goal motivating the present study. A common approach to measuring directed functional interactions between two brain regions is to first create nodal signals by averaging the BOLD signals of all the voxels in each region, and to then measure directed functional interactions between the nodal signals. Another approach, that avoids averaging, is to measure directed functional interactions between all pairwise combinations of voxels in the two regions. Here we employ an alternative approach that avoids the drawbacks of both averaging and pairwise voxel measures. In this approach, we first use the Least Absolute Shrinkage Selection Operator (LASSO) to pre-select voxels for analysis, then compute a Multivariate Vector AutoRegressive (MVAR) model from the time series of the selected voxels, and finally compute summary Granger Causality (GC) statistics from the model to represent directed interregional interactions. We demonstrate the effectiveness of this approach on both simulated and empirical fMRI data. We also show that averaging regional BOLD activity to create a nodal signal may lead to biased GC estimation of directed interregional interactions. The approach presented here makes it feasible to compute GC between brain regions without the need for averaging. Our results suggest that in the analysis of functional brain networks, careful consideration must be given to the way that network nodes and edges are defined because those definitions may have important implications for the validity of the analysis.", "link"=>"http://www.mendeley.com/research/measuring-granger-causality-between-cortical-regions-voxelwise-fmri-bold-signals-lasso", "reader_count"=>68, "reader_count_by_academic_status"=>{"Unspecified"=>3, "Professor > Associate Professor"=>10, "Researcher"=>18, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>16, "Student > Postgraduate"=>1, "Student > Master"=>7, "Other"=>2, "Student > Bachelor"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>7}, "reader_count_by_user_role"=>{"Unspecified"=>3, "Professor > Associate Professor"=>10, "Researcher"=>18, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>16, "Student > Postgraduate"=>1, "Student > Master"=>7, "Other"=>2, "Student > Bachelor"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>7}, "reader_count_by_subject_area"=>{"Engineering"=>11, "Unspecified"=>7, "Biochemistry, Genetics and Molecular Biology"=>1, "Mathematics"=>4, "Agricultural and Biological Sciences"=>10, "Medicine and Dentistry"=>2, "Neuroscience"=>9, "Physics and Astronomy"=>5, "Psychology"=>13, "Computer Science"=>5, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>11}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>2}, "Neuroscience"=>{"Neuroscience"=>9}, "Physics and Astronomy"=>{"Physics and Astronomy"=>5}, "Psychology"=>{"Psychology"=>13}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>10}, "Computer Science"=>{"Computer Science"=>5}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Mathematics"=>{"Mathematics"=>4}, "Unspecified"=>{"Unspecified"=>7}}, "reader_count_by_country"=>{"Cuba"=>1, "United States"=>1, "Japan"=>1, "United Kingdom"=>1}, "group_count"=>3}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/632992"], "description"=>"<p>Red dots represent the voxels of ROI Y, green dots the voxels of ROI X, and arrows the significant <i>t</i>-scores between interregional voxel pairs. Positive values are colored orange and negative values are colored blue.</p>", "links"=>[], "tags"=>["computation", "hypothetical", "submatrix"], "article_id"=>303488, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002513.g008", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_illustration_of_the_computation_of_summary_statistics_f_and_W_for_hypothetical_submatrix_B_yx_/303488", "title"=>"Schematic illustration of the computation of summary statistics <i>f</i> and <i>W</i> for hypothetical submatrix B<sub>yx</sub>.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-24 00:58:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/633070"], "description"=>"<p>The fraction changed over the models from values of approximately 0.05 to values of approximately 0.29, increasing by approximately 0.04 every 8 models.</p>", "links"=>[], "tags"=>["non-zero", "coefficients", "submatrices", "56", "simulation"], "article_id"=>303558, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002513.t001", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_fraction_of_non_zero_coefficients_in_each_of_the_4_submatrices_for_each_of_the_56_simulation_models_/303558", "title"=>"The fraction of non-zero coefficients in each of the 4 submatrices for each of the 56 simulation models.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-05-24 00:59:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/632825"], "description"=>"<p>Patterns are shown for one exemplary ROI pair from one subject. The <i>t</i>-scores from LASSO-GC analysis were z-normalized. Green dots represent voxels from right VP and red dots represent voxels from right FEF. A) Estimated connectivity patterns with the LASSO-GC measure. Significant <i>t</i>-scores are shown as arrows, with the thickness representing the absolute magnitude of the <i>t</i>-scores, and the color representing the sign of the <i>t</i>-score (orange for positive, blue for negative). B) Estimated connectivity patterns with the correlation measure. Significant cross-correlation coefficients are shown as lines, with the thickness representing the absolute magnitude and the color representing the sign (orange for positive, blue for negative). C) Summary statistics for the patterns shown in the previous two panels. For the correlation measure, FEF→VP and VP→FEF have the same summary scores since the measure is non-directional.</p>", "links"=>[], "tags"=>["connectivity", "patterns", "lasso-gc"], "article_id"=>303313, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002513.g006", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_connectivity_patterns_with_LASSO_GC_and_correlation_measures_/303313", "title"=>"Comparison of connectivity patterns with LASSO-GC and correlation measures.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-24 00:55:13"}
  • {"files"=>["https://ndownloader.figshare.com/files/327626", "https://ndownloader.figshare.com/files/327663", "https://ndownloader.figshare.com/files/327713", "https://ndownloader.figshare.com/files/327757", "https://ndownloader.figshare.com/files/327806", "https://ndownloader.figshare.com/files/327836", "https://ndownloader.figshare.com/files/327880"], "description"=>"<div><p>Functional brain network studies using the Blood Oxygen-Level Dependent (BOLD) signal from functional Magnetic Resonance Imaging (fMRI) are becoming increasingly prevalent in research on the neural basis of human cognition. An important problem in functional brain network analysis is to understand directed functional interactions between brain regions during cognitive performance. This problem has important implications for understanding top-down influences from frontal and parietal control regions to visual occipital cortex in visuospatial attention, the goal motivating the present study. A common approach to measuring directed functional interactions between two brain regions is to first create nodal signals by averaging the BOLD signals of all the voxels in each region, and to then measure directed functional interactions between the nodal signals. Another approach, that avoids averaging, is to measure directed functional interactions between all pairwise combinations of voxels in the two regions. Here we employ an alternative approach that avoids the drawbacks of both averaging and pairwise voxel measures. In this approach, we first use the Least Absolute Shrinkage Selection Operator (LASSO) to pre-select voxels for analysis, then compute a Multivariate Vector AutoRegressive (MVAR) model from the time series of the selected voxels, and finally compute summary Granger Causality (GC) statistics from the model to represent directed interregional interactions. We demonstrate the effectiveness of this approach on both simulated and empirical fMRI data. We also show that averaging regional BOLD activity to create a nodal signal may lead to biased GC estimation of directed interregional interactions. The approach presented here makes it feasible to compute GC between brain regions without the need for averaging. Our results suggest that in the analysis of functional brain networks, careful consideration must be given to the way that network nodes and edges are defined because those definitions may have important implications for the validity of the analysis.</p> </div>", "links"=>[], "tags"=>["measuring", "granger", "causality", "cortical", "regions", "voxelwise", "fmri", "signals", "lasso"], "article_id"=>124674, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002513.s001", "https://dx.doi.org/10.1371/journal.pcbi.1002513.s002", "https://dx.doi.org/10.1371/journal.pcbi.1002513.s003", "https://dx.doi.org/10.1371/journal.pcbi.1002513.s004", "https://dx.doi.org/10.1371/journal.pcbi.1002513.s005", "https://dx.doi.org/10.1371/journal.pcbi.1002513.s006", "https://dx.doi.org/10.1371/journal.pcbi.1002513.s007"], "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Measuring_Granger_Causality_between_Cortical_Regions_from_Voxelwise_fMRI_BOLD_Signals_with_LASSO/124674", "title"=>"Measuring Granger Causality between Cortical Regions from Voxelwise fMRI BOLD Signals with LASSO", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2012-05-24 01:17:54"}
  • {"files"=>["https://ndownloader.figshare.com/files/632710"], "description"=>"<p>The GC strength (W summary statistic) in each submatrix, computed directly from the simulation model, is compared with the <i>W</i> statistic estimated by the LASSO-GC and pairwise-GC methods. The estimated LASSO-GC <i>W</i> statistic more closely matches the <i>W</i> statistic of the model across simulation models than does the estimated pairwise-GC <i>W</i> statistic. Since the estimated <i>W</i> statistic is based on <i>t</i>-scores and the <i>W</i> statistic computed directly from the simulation model is based on <i>b</i> coefficient values, both <i>b</i> and <i>t</i>-scores were normalized to standard <i>z</i>-scores before calculating <i>W</i>. The horizontal axis is arranged the same way as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002513#pcbi-1002513-g002\" target=\"_blank\">Figure 2</a>.</p>", "links"=>[], "tags"=>["lasso-gc", "pairwise-gc", "methods", "recovering"], "article_id"=>303197, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002513.g005", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_LASSO_GC_and_pairwise_GC_methods_in_recovering_the_W_summary_statistic_/303197", "title"=>"Comparison of LASSO-GC and pairwise-GC methods in recovering the <i>W</i> summary statistic.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-24 00:53:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/632483"], "description"=>"<p>The X voxels in A-C are represented by green dots and Y voxels by red dots. All the <i>t</i> and <i>b</i> values are <i>z</i>-normalized. A) Simulated connectivity pattern of the model for the four B matrices, with orange arrows representing positive <i>b</i> values and blue arrows negative <i>b</i> values. B) Estimated connectivity pattern with LASSO-GC method. Significant <i>t</i>-scores are shown as arrows, with the thickness representing the absolute magnitude of the <i>t</i>-scores, and the color representing the sign of the <i>t</i>-score (orange for positive, blue for negative). The pattern is similar to that in the model. C) Estimated connectivity pattern with pairwise-GC method, shown in the same manner as for the LASSO-GC result. The connectivity is much denser than the model pattern. D) Summary statistics <i>f</i> and <i>W</i> for the patterns shown in the previous three panels. LASSO-GC values match the model values more closely than do pairwise-GC values.</p>", "links"=>[], "tags"=>["estimation", "lasso-gc", "pairwise-gc", "methods", "simulation"], "article_id"=>302969, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002513.g003", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_model_estimation_by_LASSO_GC_and_pairwise_GC_methods_for_one_simulation_model_/302969", "title"=>"Comparison of model estimation by LASSO-GC and pairwise-GC methods for one simulation model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-24 00:49:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/632602"], "description"=>"<p>The fraction of significant <i>b</i> coefficients (<i>f</i> summary statistic) in each submatrix, computed directly from the simulation model, is compared with the <i>f</i> statistic estimated by the LASSO-GC and pairwise-GC methods. The estimated LASSO-GC <i>f</i> statistic more closely matches the <i>f</i> statistic of the model across simulation models than does the estimated pairwise-GC <i>f</i> statistic. The horizontal axis is arranged the same way as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002513#pcbi-1002513-g002\" target=\"_blank\">Figure 2</a>. The example shown in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002513#pcbi-1002513-g003\" target=\"_blank\">Figure 3</a> is from the 28th model.</p>", "links"=>[], "tags"=>["lasso-gc", "pairwise-gc", "methods", "recovering"], "article_id"=>303095, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002513.g004", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_LASSO_GC_and_pairwise_GC_methods_in_recovering_the_f_summary_statistic_/303095", "title"=>"Comparison of LASSO-GC and pairwise-GC methods in recovering the <i>f</i> summary statistic.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-24 00:51:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/632929"], "description"=>"<p>The <i>f</i> and <i>W</i> summary statistics were computed from LASSO-GC for each of 60 ROI pairs and 6 subjects, and then averaged over pairs and subjects. For each ROI pair, one ROI was in the Dorsal Attention Network (DAN) and the other was in Visual Occipital Cortex (VOC). The bars represent mean <i>f</i> and <i>W</i> summary statistics for VOC-to-VOC connectivity, DAN-to-DAN connectivity, DAN-to-VOC connectivity, and VOC-to-DAN connectivity. Error bars represent the standard error of the mean. Significant differences from paired-sample <i>t</i>-tests are marked (*: <i>p</i><0.05).</p>", "links"=>[], "tags"=>["connectivity", "dorsal", "occipital", "cortex", "spatial"], "article_id"=>303416, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002513.g007", "stats"=>{"downloads"=>1, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Functional_connectivity_analysis_of_Dorsal_Attention_Network_and_Visual_Occipital_Cortex_in_visual_spatial_attention_/303416", "title"=>"Functional connectivity analysis of Dorsal Attention Network and Visual Occipital Cortex in visual spatial attention.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-24 00:56:56"}
  • {"files"=>["https://ndownloader.figshare.com/files/632378"], "description"=>"<p>GC was computed from averaged voxel time series as <i>t</i><sub>yx</sub> and <i>t</i><sub>xy</sub>, and then normalized to <i>z</i>-scores, for a range of simulation models (top row). GC was also computed as voxel-based <i>W</i> (middle row) and <i>f</i> (bottom row) summary statistics computed directly from the parameters of the same simulation models (<i>b</i> values normalized to <i>z</i>-scores before computing <i>W</i>). The horizontal axis labels the 56 simulation models in the order of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002513#pcbi-1002513-t001\" target=\"_blank\">Table 1</a>, representing different connectivity parameter settings. The <i>t</i>-scores do not significantly correlate with either <i>W</i> or <i>f</i> across simulation models, demonstrating that GC computed from averaged voxel time series is not sensitive to true connectivity.</p>", "links"=>[], "tags"=>["causality", "patterns", "simulated"], "article_id"=>302867, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002513.g002", "stats"=>{"downloads"=>1, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Granger_Causality_patterns_between_simulated_ROIs_/302867", "title"=>"Granger Causality patterns between simulated ROIs.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-24 00:47:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/632325"], "description"=>"<p>A) Sequential driving pattern, where voxel <i>x</i> drives voxel <i>y</i>, which in turn drives voxel <i>z</i>. GC from <i>x</i> to <i>z</i> may be spuriously identified as being significant. B) Differentially delayed driving, where voxel x drives voxel <i>y</i> with shorter delay and <i>z</i> with longer delay. GC from <i>y</i> to <i>z</i> may be spuriously identified as being significant. Modified from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002513#pcbi.1002513-Chen1\" target=\"_blank\">[26]</a>.</p>", "links"=>[], "tags"=>["patterns", "spurious", "granger"], "article_id"=>302817, "categories"=>["Neuroscience"], "users"=>["Wei Tang", "Steven L. Bressler", "Chad M. Sylvester", "Gordon L. Shulman", "Maurizio Corbetta"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002513.g001", "stats"=>{"downloads"=>3, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simple_driving_patterns_that_can_lead_to_spurious_identification_of_significant_Granger_Causality_/302817", "title"=>"Simple driving patterns that can lead to spurious identification of significant Granger Causality.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-05-24 00:46:57"}

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Relative Metric

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