1. Inferences with fMRI, Atlas Construction

2. A Big Thanks To Prof. Jason Bohland Quantitative Neuroscience Laboratory Boston University Istavan (Pisti) Morocz, Harvard, MNI Firdaus Janoos, OSU/Harvard,MIT/Exxon

3. Sources http://neufo.org/lecture_events

4. Classical fMRI Pipeline

5. SPM-type approach Time-domain linear models dominate fMRI analysis -Massively univariate approach -estimate model parameters at each voxel -Compute test statistic at each voxel -threshold, controlling for error rate -Yields statistical parametric maps (SPMs) across voxels Time-domain linear model: design matrix: encodes predicted response and covariates

6. Per Voxel Design Matrix Constructed contains explanatory variables / regressors (columns) –For each column, a regression coefficient (beta) is estimated Design matrix X - Regressors are convolved with anticipated HRF to better fit observed data - highly correlated or linearly dependent regressors will impact model estimability - one design matrix per voxel, usually identical

7. Convolution With HRF

8. Estimation Parameter estimation: –Assumes ε is independently and identically distributed ~ N(0,σ 2 I) –Regressors are linearly independent –Effects of interest are independent of random error Betas alone tell us very little without an estimate of error Residual error is computed at each voxel: ordinary least squares

9. Inference Contrasts: A contrast - a linear combination of the parameters based on a particular hypothesis – is used to infer effects of interest “Did some voxels show a larger effect for condition A than condition B” - use contrast vector c = [1 -1] Calculate one-tailed t-statistic (N-rank(X) d.o.f.) Ratio of to estimate of its standard error (based on residual sum of squared error) A (uncorrected) p-value is obtained at each voxel Also derive F test: does x i model anything?

10. Statistical Threshold Slide from Duke University course notes A BC t = 2.10, p < 0.05 (uncorrected)t = 3.60, p < 0.001 (uncorrected)t = 7.15, p < 0.05, Bonferroni Corrected Multiple comparisons

11. Multi-subject Studies MR images obtained from http://www.oasis-brains.org  Combining results across subjects is made difficult by individual brain variability

12. Multi-subject Studies Inter-subject averaging typically takes one of 2 forms: 1.Spatial normalization – warping of each (hi-resolution, T1- weighted anatomical) brain volume to a standard template –Attempts to align same areas across subject (to voxel level?) –Adds argument for utility of spatial smoothing –By far the most commonly used method 6 different brains registered using 12-parameter affine transformation with least squares cost function From Ashburner and Friston (2003) in Human Brain Function, Volume 2

13. Multi-subject Studies 2.Region of interest (ROI) analysis –Effects from voxels in pre-defined ROIs are collapsed to a small set of components (e.g. Fourier coefficients) –Comparison across subjects is at the region level –Sidesteps problems w/ spatial normalization –still assumes function follows anatomy Nieto-Castanon et al., 2002

14. Spatial Normalization One often wants to understand properties of a population: Approach: Register or spatially normalize the subjects such that they are in a common coordinate space (reduce individual variability) Typically warp each subject to a template image in stereotactic space The assumption here is that registering size, shape, voxel intensity, curvature profiles, etc. will bring the local effect of interest into alignment across subjects Approach 1 (landmark-based): Identify (perhaps manually) some set of corresponding features in each brain Scale individual brains in order to bring those landmarks into alignment Approach 2 (intensity-based / densitometric): Optimize the parameters of a registration model s.t. the intensities of a (template) target image and the transformed source image match well.

15. Talairach’ing User-defined landmarks (subjective) xy plane defined by the superior extent of the anterior commissure (AC) and the inferior extent of the posterior commissue (PC) yz plane defined by hemispheric midline Lateral, anterior, and posterior extents of brain Origin: intersection of AC-line, midsagittal plane, and AC-PC plane ACPC

16. Talairach’ing User-defined landmarks (subjective) xy plane defined by the superior extent of the anterior commissure (AC) and the inferior extent of the posterior commissue (PC) yz plane defined by hemispheric midline Lateral, anterior, and posterior extents of brain Origin: intersection of AC-line, midsagittal plane, and AC-PC plane

17. Surface-Based models Real geometry of cortex is essentially a 2-D sheet Volumetric approaches do not use this information! TOOLS: CARET, FREESURFER, BRAINVISA, SUMA From Fischl et al., 1999

18. Free Surfer Spherical Registration Following surface extraction, each hemisphere can be inflated to a unit sphere while: –Preserving topological structure (local connectedness) –Minimizing metric distortion –Maintaining average curvature indices Subjects are then aligned to an average in the spherical space s.t. mean squared convexity differences are minimized while also minimizing metric distortions. –Considers entire curvature profile (not specific gyri / sulci) –But emphasizes consistent curvature features “for free” Fischl et al., 1999

19. Multi-subject studies Group inference: Correct inferences about the population require a 2 nd level analysis (treat individuals as random variables) Perform statistical test across individual summary statistics (e.g. “contrast images” computed at 1 st level for each subject) Non-parametric tests may be preferred for low N Much weaker assumptions than SPM Permute condition labels Compute test statistic (e.g. mean effect) for each permutation Compare observed test statistic to random distribution see Nichols and Holmes (2002) and SnPM toolbox.

20. What else ? Atlases – Can we build Atlases for populations ? Network analysis – what does the correlation structure across brain space tell us? Analysis of spontaneous BOLD signals (“resting state”) Machine Learning – do evoked BOLD patterns predict stimulus, behavior, etc?

21. Brain Voyager http://gallantlab.org/semanticmovies/

22. Harvard Whole Brain Atlas http://www.med.harvard.edu/AANLIB/ “A bound collection of maps” In practice it tells you where you are  Provide a common reference frame  Unify multiple diverse data modalities  Allow for dimensionality reduction / clustering of data  Establish a language / taxonomy of brain parts  Usually created from a single studied brain  Often take the form of cartoon labels and arrows Human Brain Atlases

23. There are multiple bases for parcellating cortex, e.g. 1.Cytoarchitecture 2.Chemoarchitecture 3.Connectivity profiles 4.Folding patterns MRI is the vehicle for most modern neuroanatomy… which features are identifiable from typical T1-weighted structural MRI images? typically ~256x256x128 voxel volumes (~1mm resolution) Brain Parcellation

24. Colorized version of Brodmann (1909) http://spot.colorado.edu/~dubin/talks/brodmann/brodmann.html Adaptation of von Economo and Koskinas (1925) From Triarhou (2007) CytoArchitectonic Parcellations

25. http://www.brain-map.org

26. Template space brain atlases Examples: Automated anatomical labeling (Tzourio-Mazoyer, 2002); ICBM Template Deform individual anatomy to atlas (MNI-space) “read off” anatomical labels from a parcellation of a single subject in that space (assumes corresponding structures are aligned)

27. Probabilistic Brain Atlases LPBA40 56 structures manually outlined in 40 normal subjects, registered to ICBM452 space (with different methods) ANATOMY TOOLBOX Cytoarchitectonic regions determined from 10 post-mortem brains, non-linearly morphed into ICBM152 space Eickhoff et al. (2002). Image from Art Toga, LONI

28. Brain Atlas Concordance The nomenclature problem is long-standing in neuroscience  People tend to think (and report) in regions, not coordinates In fMRI, we have a chance to address this quantitatively by comparing different atlases delineated in a common template (MNI-305) space Bohland et al. (2009), PLoS ONE

29. Parcellations As Sets What is a parcellation system? - a partitioning of the brain into a finite set of disjoint “regions” where each region is itself a set of locations (e.g. voxels, vertices, triangles, etc.) cf. elementary micro-area (Stephan, Zilles, Kötter, 2000)

30. Compare with Reference Atlas Reference atlases here are “flat” parcellations with 12 or 94 regions Similarity index (S) ranges from 0-1 Overlap saturating at K > 30 Clusters for large K are subdivisions of those for low K

31. Comparison methods Multiple measures of region overlap may be defined: Non-symmetric: e.g. the proportion of region i from parcellation R contained in region j from parcellation R’ Symmetric: e.g. the spatial overlap relative to the geometric mean of the 2 region sizes Both measures are normalized and bounded ( between 0 and 1 ) i j

32. C ij ICBM: superior temporal gyrus (100%) T&G: aSTg (94%) T&G: pdSTs (88%) CYTO: TE-1.2 (87%) H-O: STG anterior division (86%) T&G: adSTs (83%) T&G: pSTg (82%) ICBM: superior temporal gyrus (100%) LPBA: superior temporal gyrus (72%) TALg: superior temporal gyrus (47%) AAL: middle temporal gyrus (36%) AAL: superior temporal gyrus (33%) AAL: temporal pole (22%) TALg: middle temporal gyrus (17%) Single example: “Superior Temporal” region from the ICBM atlas This matrix has non-zero entry for any pair of regions (from 8 atlases) that overlap Bohland et al. (2009). PLoS ONE

33. HARVARD OXFORD ATLAS LPBA40 ATLAS All connections Edges encode max(C ij, C ji )

34. HARVARD OXFORD ATLAS LPBA40 ATLAS E ij < 0.25 pruned After pruning

35. 1000 random pairs used in simulations Green values are similarity scores above 95 th percentile Global Atlas Similarity

36. subcortical cerebellum ○ AAL ○ TAL ○ T&G ○ ICBM ○ CYTO