Connectomics: Parcellations and Network Analysis Methods

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Simple tutorial on methods for functional connectome analysis: learning regions, extracting functional signal, inferring the network structure, and comparing it across subjects.

Connectomics: Parcellations and Network Analysis Methods

  1. 1. Connectomics: Parcellation & Network Analysis MethodsGa¨el Varoquaux INRIA, Parietal – NeurospinLearning objectivesChosing regions forconnectivity analysisExtraction of thenetwork structureInter-subject comparisonof network structuresVaroquaux & CraddockNeuroImage 2013
  2. 2. Declaration of RelevantFinancial Interests or RelationshipsSpeaker Name: Gaël VaroquauxI have no relevant financial interest or relationship to disclosewith regard to the subject matter of this presentation.ISMRM20thANNUAL MEETING & EXHIBITION“Adapting MR in a Changing World”
  3. 3. Functional connectivity and connectomicsFluctuations in functional imagingsignals capture brain interactionsMany pathologies are expressedby modified brain interactionsNeed quantitative tools to developbiomarkersConnectome based on regions toreduce number of connections studiedG Varoquaux 3
  4. 4. Connectomics: Problem setting and vocabularyInfer and compareconnections betweena set of regionsGraph: set of nodes and connectionsWeighted or not.Directed or not.Can be represented by anadjacency matrix.G Varoquaux 4
  5. 5. Connectomics: an outline1 Functional parcellations2 Signal extraction3 Connectivity graphs4 Comparing connectomesG Varoquaux 5
  6. 6. 1 Functional parcellationsDefining regions for connectomicsG Varoquaux 6
  7. 7. 1 Need for functional parcellationsAnatomical atlases do not resolve functional structuresHarvard Oxford AALG Varoquaux 7
  8. 8. 1 ClusteringGroup together voxels with similar time courses... ... ...... ...Considerations– Spatial constraints – Number of regions – Running timeG Varoquaux 8
  9. 9. 1 ClusteringNormalized cutsDownloadable atlasWith many parcelsbecomes a regular pavingWard clusteringGood with many parcelsVery fastPython implementationhttp://nisl.github.ioG Varoquaux 9
  10. 10. 1 Linear decomposition modelsCognitive networks are present at restTime coursesG Varoquaux 10
  11. 11. 1 Linear decomposition modelsCognitive networks are present at restTime coursesLanguageG Varoquaux 10
  12. 12. 1 Linear decomposition modelsCognitive networks are present at restTime coursesAudioG Varoquaux 10
  13. 13. 1 Linear decomposition modelsCognitive networks are present at restTime coursesVisualG Varoquaux 10
  14. 14. 1 Linear decomposition modelsCognitive networks are present at restTime coursesDorsal Att.G Varoquaux 10
  15. 15. 1 Linear decomposition modelsCognitive networks are present at restTime coursesMotorG Varoquaux 10
  16. 16. 1 Linear decomposition modelsCognitive networks are present at restTime coursesSalienceG Varoquaux 10
  17. 17. 1 Linear decomposition modelsCognitive networks are present at restTime coursesVentral Att.G Varoquaux 10
  18. 18. 1 Linear decomposition modelsCognitive networks are present at restTime coursesParietalG Varoquaux 10
  19. 19. 1 Linear decomposition modelsCognitive networks are present at restTime coursesObserve a mixtureNeed to unmix networksG Varoquaux 10
  20. 20. 1 Linear decomposition modelsIndependent Component AnalysisExtracts networksDownloadable atlas[Smith 2009]Sparse dictionary learningNetworks outlined cleanlyBleeding edgeAtlas on requestG Varoquaux 11
  21. 21. 1 Linear decomposition modelsIndependent Component AnalysisExtracts networksDownloadable atlas[Smith 2009]Sparse dictionary learningNetworks outlined cleanlyBleeding edgeAtlas on requestG Varoquaux 11
  22. 22. 2 Signal extractionEnforce specificity to neural signalG Varoquaux 12
  23. 23. 2 Choice of regionsToo many regions givesharder statistical problem:⇒ ∼ 30 ROIs forgroup-difference analysisNearly-overlapping regionswill mix signalsAvoid too small regions ⇒ ∼ 10mm radiusCapture different functional networksAutomatic parcellation do not solve everythingG Varoquaux 13
  24. 24. 2 Time-series extractionExtract ROI-average signal:weighted-mean with weightsgiven by grey-matter probabilityRegress out confounds:- movement parameters- CSF and white matter signals- Compcorr: data-driven noise identification[Behzadi 2007]- Global mean... overhyped discussion (see later)G Varoquaux 14
  25. 25. 3 Connectivity graphsFrom correlations to connectionsFunctional connectivity:correlation-based statisticsG Varoquaux 15
  26. 26. 3 Correlation, covariance1For x and y centered:covariance: cov(x, y) =1n ixiyicorrelation: cor(x, y) =cov(x, y)std(x) std(y)Correlation is normalized: cor(x, y) ∈ [−1, 1]Quantify linear dependence between x and yCorrelation matrixfunctional connectivity graphs[Bullmore1996, Achard2006...]G Varoquaux 16
  27. 27. 3 Partial correlationRemove the effect of z by regressing it outx/z = residuals of regression of x on zIn a set of p signals,partial correlation: cor(xi/Z, xj/Z), Z = {xk, k = i, j}partial variance: var(xi/Z), Z = {xk, k = i}Partial correlation matrix[Marrelec2006, Fransson2008, ...]G Varoquaux 17
  28. 28. 3 Inverse covarianceK = Matrix inverse of the covariance matrixOn the diagonal: partial varianceOff diagonal: scaled partial correlationKi,j = −cor(xi/Z, xj/Z) std(xi/Z) std(xj/Z)Inverse covariance matrix[Smith 2011, Varoquaux NIPS 2010, ...]G Varoquaux 18
  29. 29. 3 Summary: observations and indirect effectsObservationsCorrelation01234Covariance:scaled by varianceDirect connectionsPartial correlation01234Inverse covariance:scaled by partial varianceG Varoquaux 19
  30. 30. 3 Summary: observations and indirect effectsObservationsCorrelationDirect connectionsPartial correlationG Varoquaux 19
  31. 31. 3 Summary: observations and indirect effectsObservationsCorrelationDirect connectionsPartial correlationGlobal signal regressionMatters less on partial correlationsBut unspecific, and can make thecovariance matrix ill-conditionedG Varoquaux 19
  32. 32. 3 Inverse covariance and graphical modelGaussian graphical modelsZeros in inverse covariance giveconditional independenceΣ−1i,j = 0 ⇔xi, xj independentconditionally on {xk, k = i, j}Robust to the Gaussian assumptionG Varoquaux 20
  33. 33. 3 Partial correlation matrix estimationp nodes, n observations (e.g. fMRI volumes)If not n p2,ambiguities:(multicolinearity)021021 021021? ?Thresholding partial correlations does not recoverground truth independence structureG Varoquaux 21
  34. 34. 3 Inverse covariance matrix estimationSparse Inverse Covariance estimators: Independence betweennodes makes estimation of partial correlation easier01234Independencestructure+ 01234ConnectivityvaluesJoint estimationG Varoquaux 22
  35. 35. 3 Inverse covariance matrix estimationSparse Inverse Covariance estimators: Independence betweennodes makes estimation of partial correlation easier01234Independencestructure+ 01234ConnectivityvaluesJoint estimationGroup-sparse inverse covariance: learn different connectomeswith same independence structure[Varoquaux, NIPS 2010]G Varoquaux 22
  36. 36. 4 Comparing connectomesDetecting and localizing differencesEdge-level tests Network-level testsG Varoquaux 23
  37. 37. 4 Comparing connectomesDetecting and localizing differencesEdge-level testsG Varoquaux 23
  38. 38. 4 Pair-wise tests on correlationsCorrelations ∈ [−1, 1]⇒ cannot apply Gaussianstatistics, e.g. T testsZ-transform:Z = arctanh cor =12ln1 + cor1 − corZ(cor) is normaly-distributed:For n observations, Z(cor) = NZ(cor),1√nG Varoquaux 24
  39. 39. 4 Indirect effects: to partial or not to partial?0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025Large lesionCorrelation matrices0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025Large lesionPartial correlation matricesSpread-out variability in correlation matricesNoise in partial-correlationsStrong dependence between coefficients[Varoquaux MICCAI 2010]G Varoquaux 25
  40. 40. 4 Indirect effects versus noise: a trade off0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025Large lesionCorrelation matrices0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025Large lesionPartial correlation matrices0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025 Control0 5 10 15 20 250510152025Large lesionTangent-space residuals[Varoquaux MICCAI 2010]G Varoquaux 26
  41. 41. 0 5 10 15 20 2505101520250 5 10 15 20 2505101520250 5 10 15 20 250510152025Edge-level tests Localization is hard (non-localeffects)Multiple testing kills performanceG Varoquaux 27
  42. 42. 0 5 10 15 20 2505101520250 5 10 15 20 2505101520250 5 10 15 20 250510152025Network-level tests Nodes clustertogether toform networksG Varoquaux 27
  43. 43. 4 Network-level metricsNetwork-wide activityQuantify amount of signal in ΣnetworkDeterminant: |Σnetwork|= generalized varianceNetwork integration: = log |ΣA|Cross-talk between network A and BMutual information= log |ΣAB| − log |ΣA| − log |ΣB|[Marrelec 2008, Varoquaux NIPS 2010]G Varoquaux 28
  44. 44. 4 Pitfalls when comparing connectomesMissing nodesVery correlated nodes:e.g. nearly-overlapping regionsHub nodes give more noisy partialcorrelationsG Varoquaux 29
  45. 45. Practical connectomics: take home messagesNeed to choosefunctionally-relevent regionsRegress confounds out from signalsPartial correlations to isolatedirect effectsNetworks are interesting unitsfor comparisonhttp://gael-varoquaux.info [NeuroImage 2013]
  46. 46. References (not exhaustive)[Achard 2006] A resilient, low-frequency, small-world human brain functional networkwith highly connected association cortical hubs, J Neurosci[Behzadi 2007] A component based noise correction method (CompCor) for BOLDand perfusion based fMRI, NeuroImage[Bullmore 2009] Complex brain networks: graph theoretical analysis of structuraland functional systems, Nat Rev Neurosci[Craddock 2011] A Whole Brain fMRI Atlas Generated via Spatially ConstrainedSpectral Clustering, Hum Brain Mapp[Frasson 2008] The precuneus/posterior cingulate cortex plays a pivotal role in thedefault mode network: Evidence from a partial correlation network analysis,NeuroImage[Marrelec 2006] Partial correlation for functional brain interactivity investigation infunctional MRI, NeuroImage[Marrelec 2008] Regions, systems, and the brain: hierarchical measures of functionalintegration in fMRI, Med Im Analys
  47. 47. References (not exhaustive)[Smith 2010] Network Modelling Methods for fMRI, NeuroImage[Smith 2009] Correspondence of the brain’s functional architecture during activationand rest, PNAS[Varoquaux MICCAI 2010] Detection of brain functional-connectivity difference inpost-stroke patients using group-level covariance modeling, Med Imag Proc CompAided Intervention[Varoquaux NIPS 2010] Brain covariance selection: better individual functionalconnectivity models using population prior, Neural Inf Proc Sys[Varoquaux 2011] Multi-subject dictionary learning to segment an atlas of brainspontaneous activity, IPMI[Varoquaux 2012] Markov models for fMRI correlation structure: is brain functionalconnectivity small world, or decomposable into networks?, J Physio Paris[Varoquaux 2013] Learning and comparing functional connectomes across subjects,NeuroImage

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