Surface-Based Coordinate System• Inter-subject alignment of cortical folding patterns• Establish a 2-D coordinate system on cortical surface- Every point in cortex should have a (unique) coordinate- Every coordinate should refer to a point in cortex• Improve alignment of functional areasSurface-Based Coordinate Systems:what ‘space’ to use?• Flat maps (Van Essen and Drury).+ simple computationally- cuts in coordinate system- nonconvex2. Ellipsoids (Sereno, et al).+ closed surface (no cuts)+ minimal distortion in mapping from cortex- difficult space to work in computationally.3. Spheres (Fischl, et al; Thompson and Toga)+ closed surface (no cuts)+ tractable computationally- a bit more distortion required in mapping. (but less than cross-subject variability)Surface-Based Coordinate Systems• Manually define corresponding points across subjects, force them to align, and interpolate every where else (Van Essen and Drury, Thompson and Toga). Two Different Approaches• Automatically align entire folding pattern acrosssubjects (Fischl, Sereno, Tootell and Dale).A Surface-Based Coordinate SystemSpherical Transformation:EquationsJd: Metric Distortion (macroscopic distances)JT: Topology preservation (oriented area)Energy Functional: Jd+λTJTTransformed SurfaceInflated SurfaceMaximally Isometric Spherical MappingSpherical Morphing: EquationsJc: Correlation error (aligns folding patterns)Jd: Metric distortion (constrains allowable shape differences)Energy Functional: Jc+λdJd+λTJTHow does one pick value of d?JT: Topology term (forces mapping to be invertible)Spherical Morphing: Equations),(1),(1==NiiCNC2)),(),(1(11),(2CNiCNi−=−=21)))(),(()))(),(((*(21=−=VvvcvvvvCCGVJAverage Folding Pattern:Variance of FoldingMaximum Likelihood Term:ddTTcJJJJ++=Complete Energy Functional:Average (Target)Individual SubjectInter-Subject MorphingSurface-Based AveragingAverage surface created from 30 subjectsApplications• Increased statistical power for inter-subject averaging• Automatic functional/anatomical labeling• Statistical analysis of morphometric properties– aging– neurodegenerative diseases– longitudinal studies of structural changes– hemispheric asymmetry• Inter-subject averaging of morphometric propertiesApplications• Increased statistical power for inter-subject averaging• Automatic functional/anatomical labeling• Statistical analysis of morphometric properties– aging– neurodegenerative diseases– longitudinal studies of structural changes– hemispheric asymmetry• Inter-subject averaging of morphometric propertiesTalairach Average Spherical AverageInter-Subject Averaging ofActivationsApplications• Increased statistical power for inter-subject averaging• Automatic functional/anatomical labeling• Statistical analysis of morphometric properties– aging– neurodegenerative diseases– longitudinal studies of structural changes– hemispheric asymmetry• Inter-subject averaging of morphometric propertiesApplications• Increased statistical power for inter-subject averaging• Automatic functional/anatomical labeling• Statistical analysis of morphometric properties– aging– neurodegenerative diseases– longitudinal studies of structural changes– hemispheric asymmetry• Inter-subject averaging of morphometric propertiesCortical Parcellation: Manual vs. Automated (1) Automatic ParcellationManual ParcellationThanks to Christophe Destrieux for this slide.Applications• Increased statistical power for inter-subject averaging• Automatic functional/anatomical labeling• Inter-subject averaging of morphometric properties• Statistical analysis of morphometric properties– aging– neurodegenerative diseases– longitudinal studies of structural changes– hemispheric asymmetryApplications• Increased statistical power for inter-subject averaging• Automatic functional/anatomical labeling• Statistical analysis of morphometric properties– aging– neurodegenerative diseases– longitudinal studies of structural changes– hemispheric asymmetry• Inter-subject averaging of morphometric propertiesStatistical Map of Cortical Thinning:AgingThanks to Drs. Randy Buckner and David Salat for supplying this slide.p < 10-6Cortical Thickness AD vs. ControlsThanks to Drs. Anders Dale, Randy Buckner and David Salat for supplying this slide.Cortical Thinning with Aging and ADData Courtesy of Randy Buckner, WUSTLThanks to Anders Dale for this slide.Multi-Modality IntegrationHow to infer the distribution of currents in the brain thatgave rise to a measured electromagnetic field (EEG orMEG)?Problem: measuring hundreds of variables and trying tosolve for potentially millions – ill-posed (need constraints).One solution (Dale and Sereno, 1993) – assume majorityof signal comes from pyramidal neurons in cortex. If onehas a cortical model, then position and orientation ofsources is known and the problem becomes linear.Multi-Modality IntegrationThanks to Drs. Anders Dale and Arthur Liu for supplying the next 3 slidesActivation to Word ReadingAnatomically Constrained MEG (aMEG)Sequence of Activation to Word Repetition:Anatomically and fMRI (fMEG) Constrained MEGThanks to Drs. Anders Dale, Eric Halgren and Arthur Liu for supplying this slideTalk Outline• The Spatial Structure of Retinotopic Cortex.• Cortical Analysis.• Subcortical Analysis.Talk Outline• The Spatial Structure of Retinotopic Cortex.• Cortical Analysis.• Subcortical Analysis.Whole-Brain SegmentationGoal: Segment T1-weighted MRI into anatomically andsemantically meaningful structures (e.g. caudate,putamen, etc…).Requirements:• Insensitive to pathology.• Insensitive to varying pulse sequences.Prerequisite: registration with anatomically meaningfulspace (e.g. Talairach)Why Segmentation is Hard!0 20 40 60 80 100 1200246810WMGMlVThCaPuPaHpAmSome Definitions Revisitedp(I|C) is called the likelihood of the image given theclassification. Since p(I|C) is frequently assumed to beGaussian in form, the log of the likelihood is commonly used.The classification C that maximizes p(C|I) is called themaximum a posteriori (MAP) estimate of C.The classification C that maximizes p(I|C) is called themaximum likelihood estimate (MLE) of C.How can we compute the MAP estimate of C?Bayes RuleWhat is the most likely classification C of an image I, givensome prior information we have about what kinds ofclassifications are allowable (p(C)) and a model for how animage is formed?