fMRI Methods Lecture5 – Multi subject analyses

1. fMRI MethodsLecture5 – Multi subject analyses

2. 4 basic analyses Correlation with an HRF convolved model Regression with an HRF convolved model Regression with an un-convolved model (deconvolution) Trigger averaging Can be applied voxel-by-voxel or to an ROI. How do we combine these analyses across subjects?

3. Differences in anatomy Need to create a common workspace for everyone

4. Co-registration Remember that our fMRI data is in the functional scans, which have a different resolution than the anatomical scans

5. Functional-anatomical alignment Interpolate fMRI low res to anatomy high res Anatomical Functional

6. Functional-anatomical alignment Interpolate fMRI low res to anatomy high res Overlaid Edge display

7. Talairach/MNI Conform the subjects to a general coordinate frame Z 40,67,12 Talairach atlas: based on a single 60 year old female brain. MNI atlas – based on the average anatomy of 250 brains. Y X

8. Talairach/MNI Stretch and squeeze individual brains to fit Normalizes anatomical volume based on 8 points: AC,PC, and 6 sides of the cube.

9. Talairach/MNI Talairach and MNI transformations do not normalize the sulci/gyri, so there’s still some anatomical variability:

10. Cortical based alignment More advanced techniques try and warp the anatomy so as to normalize the sulci locations across brains.

11. Alignments Functional to anatomical co-registration within each subject Anatomical normalization across subjects. Now we know that extracting a time-course from voxel 29,10,32 (x,y,z) will give us brain activity from a similar brain location in all of our subjects.

12. Spatial smoothing Some anatomical variability will always remain, so smooth the data across space and pray for overlap… 8mm

13. Multi-subject analyses Subject 1 Subject 2 Subject 3 Now that our brains are all in the same coordinate frame how do we combine the statistical analyses?

14. Fixed effects analysis Combine the data across subjects (as if it came from a single subject) and solve one GLM to determine whether there was a significant “effect”. Assumes inter-subject homogeneity – that the response is identical in all subject.

15. Fixed effects analysis Commonly done by building a long GLM; stacking the data = * + a1 a2 error

16. Fixed effects analysis Two problems: Effects are not necessarily evident in majority of subjects (a strong effect in one subject could generate significant results). Explosion in degrees of freedom

17. Random effects analysis Solve for each subject separately and test whether the effect was consistent across subjects – “two stage analysis” Takes inter-subject variability into account

18. Random effects analysis Solve standard GLM for each subject * + a1 a2 error =

19. Random effects analysis When comparing responses in the same subjects, perform paired “repeated measure” t-test on beta values Beta 1 0.1 0.3 0.7 0.2 0.3 -0.2 Beta 2 1.2 1.4 0.4 2.2 0.8 1 Diff 1.1 1.1 -0.3 2 0.5 1.2

20. Random effects analysis When comparing responses across different subjects, perform regular “two sample” t-test on beta values Group 1 0.1 0.3 0.7 0.2 0.3 -0.2 Group 2 1.2 1.4 0.4 2.2 0.8 1

21. Multi-subject maps Convert t-values to p-values (d.o.f = # of subjects) Do it for every voxel Apply multiple comparisons correction Project onto the anatomy of an exemplar subject for display

22. Multi-subject ROI analyses There are two ways to select an ROI: Across the group such that the exact same talairach coordinates will apply to all. Subject 1 Subject 2 Subject 3 Subject 4

23. Multi-subject ROI analyses In each subject separately, slightly different talairach coordinates for each. Subject 1 Subject 2 Subject 3 Subject 4 Requires clear anatomical/functional criteria for ROI selection

24. Cool displays A picture is worth a thousand words

25. Extract the brain

26. Segmentation

27. Segmentation Decide at what signal intensity to threshold gray-white matter boundary. Different thresholds in different slices?

28. Segmentation Determine white matter and gray matter volumes

29. Hollow cortical surface Beauty-accuracy tradeoff

30. Experimental designs The choice of experimental design (block or event related design) depends on whether you want to decompose temporal components or not. Block designs are commonly used to assess whether a cortical area has preference for a particular stimulus type. e.g. mapping the somatosensory homunculus

31. Experimental designs Example of separating temporal components

32. Perceptual memory What brain area encodes short term memory in a visual task? Two things happen during the presentation of the first stimulus. Visual response and “ignition” of memory trace. Temporal components of the task need to be separated…

33. Perceptual memory Build a model that extracts delay period activity Delay Cue Test Delay Cue Test Delay Cue Test

34. Perceptual memory We can now estimate working memory responses in V1 during the different delay lengths. It’s the beta value associated with d

35. Statistics So far we’ve used t-tests to compare beta values. A t-test is a “parametric” statistic that assumes the data are normally distributed. What if our beta values are not normally distributed?

36. Bootstraping Bootstrapping is a method for characterizing a variable’s distribution by re-sampling with replacement. b2 b4 mean1 b2 b1 b4 b2 b1 b1 b4 mean2 b1 b3 b2 mean3 b4 b3 b2 b3 We assume that the urn represents the world population. By re-sampling with replacement we characterize it.

37. Bootstraping Compute a histogram of 10,000 random samples: Define the 5th and 95th percentiles of our betas’ distribution. Perform “non-parametric” statistical tests… Measure response of an autistic individual, does it fall beyond the confidence interval? 95th

38. Randomization On the same lines one can generate several useful distributions for testing statistical significance… Randomizing the design matrix: Actual design Shuffled design

39. Randomization Shuffle the design matrix 10,000 different ways. For every shuffle convolve with an HRF and solve GLM to compute beta values. Compute the distribution of random beta values (hopefully centered on 0). Determine whether the actual beta values fall above/below 5th and 95th percentiles.

40. Randomization Randomizing condition identity without replacement: Condition 1 c1 c1 c2 c2 c1 Condition 2 c1 c2 c2 Compute difference between randomly assigned conditions.

41. Randomization Extract 10,000 randomly assigned condition pairs and compute the difference in each. Compute the randomized differences distribution. Determine whether the actual difference falls above/below the 5th/95th percentile of the distribution Always think about the null hypothesis…

42. Randomization Randomizing subject identity: Group 1 g1 g1 g2 g2 g1 Group 2 g1 g2 g2 Compute difference between randomly assigned groups.

43. Randomization Extract 10,000 randomly assigned group pairs and compute the difference in each. Determine whether the actual group difference is larger than the 95th percentile of the randomized difference distribution.

44. Scanning this week Who wants to scan and who is authorized to scan? Split into groups. Each group needs a volunteer to go in the scanner and an experienced user to guide the scan. Decide on an experiment and create stimulus (visual or auditory). Decide on a time slot for the group.

45. To the lab!