Connectivity Modeling

1. Connectivity Modeling Anthony Randal McIntosh Department of Psychology University of Toronto

2. Overview • Theoretical issues and basis for analytic approach • Structural equation modeling • Integrating anatomy and function • Partial Least Squares • Identification of distributed systems • Applications • Sensory learning • Working memory

3. Theoretical focus • All behavioural and cognitive operations in the brain come about through the the action of distributed networks • In order to assess this, need methods that can measure the whole brain and analyses that look at more than one region at a time • Ideally, we would like to analyze spatial and temporal patterns of brain function at the same time

4. Causal patterns in brain research Brain Behaviour Design/Task

5. Response Stimulus Causal patterns in brain research

6. Response Stimulus Causal patterns in brain research

7. Theory to Analysis • Examine the influences between brain areas • Interregional correlation (Horwitz, et al, 1984) • Structural equation modeling (McIntosh & Gonzalez-Lima, 1991, Buchel & Friston, 1997) • Multiple regression and extensions (e.g., Kalman filters, Buchel & Friston, 1998) • Bayes networks (Dynamic Causal Modeling, Friston, Penny, et al, 2003) • Identification of interacting regions • Partial Least Squares (McIntosh, Bookstein, et al, 1996) • Canonical Variates Analysis (Strother et al, 1995) • Independent Components Analysis - 32 flavours (McKeown et al, 1998, Calhoun et al, 2001, Beckmann, Smith, et al., 2002)

8. Functional and Effective Connectivity

9. Structural Equation Modeling • Multivariate multiple regression • Combines interregional covariances with anatomical framework • Provides means to assess whether effective connections are modified by task-demands or differ between groups • Is not meant to be a model test in the coventional sense • Goodness of fit not as relevant

10. Structural Equation Modeling

11. McIntosh et al, J. Neurosci, 1994 Dorsal vs. Ventral Cortical Visual Streams

12. What inferences does Structual Equation Modeling allow? Space Object

13. What inferences does Structual Equation Modeling allow? Space Object

14. Partial Least Squares • “Least-squares” decomposition of “part” of a covariance matrix • PLS is optimized to explain the relation between two or more blocks of data • what pattern in one block most strongly covaries with a pattern in another block? • Ignores the relation among items within data blocks • Statistical assessment through resampling algorithms • Permutation test and bootstrap estimation of standard error McIntosh, Bookstein, et al, Neuroimage, 1996

15. Task PLS Compute matrix Mdevwhich is n*k by m n is the number of subjects or repetitions, k is the number of scans, m is the number of voxels. Each voxel is centered relative to the grand mean. • Compute matrix X, a matrix of scan means expressed as deviations from the grand mean. Alternative: project (correlate) set of orthonormal contrasts (design matrix) on to the data matrix Matrix X now the covariance of image activity with the experimental design.

16. Task PLS • Perform asingular value decomposition (SVD) on X to define the latent variables (LV): SVD(X) = [U,S,V] where: X = U*S*VT U is the k by m orthonormal matrix containing voxel weights (singular or eigen image). S is a diagonal matrix of k singular (“eigen”) values. (The kth singular value is zero because we use deviation values in X, i.e., we eliminate the grand mean to create X). VT is the transpose of matrix V, a k by k orthonormal matrix of scan weights. • Project singular image on to original data to obtain “brain scores” Index of how well each subject shows the effect

17. Task PLS

18. Behavior PLS • Compute matrix Mwhich is n*k by m n is the number of subjects/repetitions, k is the number of scans, m is the number of voxels. • Create vector B, whichis an n* k by 1 vector of performance measures for each scan. • Create matrix Y, which contains the scan-specific correlations of voxel activity (Yk) and behavior (Bk).

19. Behavior PLS • Perform asingular value decomposition (SVD) on Y to define the latent variables (LV): SVD(X) = [U,S,V] where: X = U*S*VT U is the k by m orthonormal matrix containing voxel weights (singular or eigen image). S is a diagonal matrix of k singular (“eigen”) values. VT is the transpose of matrix V, a k by k orthonormal matrix of scan weights.

20. Behavior PLS

21. Statistical Assessment • Assessment of omnibus/latent variable structure through permutation tests • Is the latent variable significantly different from “noise”? • Assessment of the precision of estimates derived from PLS through bootstrap estimation of standard errors • How reliable is the answer? • Procrustes rotation to original solution space used to correct for axis rotation and reflection during resampling Milan & Whittaker, 1995, Royal Stat Society J

22. Permutation Bootstrap Est Standard Error ANOVA Singular Vector Weight Why use bootstrap? • Estimation of standard errors is a direct assessment of the stability of your data • A signal can be significantly different from noise (e.g., P<0.01), but not be reliable

23. Response Stimulus Causal patterns in brain research

24. Multiblock PLS

25. Multiblock PLS

26. McIntosh, Cabeza & Lobaugh, J Neurophys 1998 How do we use this?

27. Sensory Associative Learning • Identify system(s) that respond to change in significance of the tone • Identify system(s) that relate to (effect) a change in behavior as a result of learning • Identify the overlap between 1 and 2

28. Task PLS

29. Behaviour PLS

30. Multiblock PLS

31. Explaining regional activation

32. Seed voxel PLS

33. Structural Equation Model

34. ERP/MEG/fMRI Data Sets Occasions, Trials, Subjects, Groups TIME SPACE Voxels, detectors, electrodes

35. Occasions,Trials, Subjects, Groups Time and Space ERP/MEG/fMRI DataFlatten the matrix Occasions,Trials, Subjects, Groups Time Space: Voxels/Channels

36. Task PLS

37. Temporal Brain Scores Spatiotemporal PLS- fMRI Voxel Saliences How strongly does the brain differentiate tasks at each timepoint??? McIntosh, Protzner & Chau, Neuroimage, in press

38. N-back Task VariantMotivation • Working memory may be conceived as the interplay of sustained attention and memory • For a given WM task - is there a dissociation that would reflect the relative contribution of an attentional component v.s. recruitment of memory retrieval? Lenartowicz & McIntosh, submitted

39. N-Back Task Variant 2-back (standard - Std) 0-back (detection) 1-back 2-back (Cued) Time

40. Task PLS

41. Task PLS

42. Task PLS

43. Task PLS

44. Task PLS • Dominant effect on anterior cingulate activity • What is the functional connectivity of the anterior cingulate? • Does it change between the 2-back tasks? • Is the pattern of functional connectivity related to behavior?

45. Behaviour/Seed PLS

46. Behaviour/Seed PLS

47. Summary & Implications • Anterior cingulate activity differentiates tasks based on attentional demands • Functional connectivity varies with attentional demand • Relation of functional connectivity patterns to performance also varies with attentional demand • Behavioural relevance of a region to a cognitive operation depends on its pattern of functional connectivity • Neural Context - McIntosh, Neural Networks 2001

48. Evaluating the analytic tools:How do we know when the math is right? • Neurobiological interpretation • Identification of new principles • Psychological interpretation • What is the level of nervous system operation that best relates to the cognitive operation? • What is the question? • Level of the answer • Does the experimental design require a certain analytic tool? • Is causality necessary or will correlation suffice?

49. Thank You Acknowledgements: Collaborators: NJ Lobaugh, MN Rajah, CL Grady Funding: CIHR, NSERC, JS McDonnell Fnd http://www.rotman-baycrest.on.ca

50. What inferences does Structual Equation Modeling allow?