Functional Connectivity: PPI and beta Series

1. Functional Connectivity: PPI and beta Series With thanks to Derek Nee & Bob Spunt

2. Localization vs integration • Integration • How do regions of the brain influence each other? • How is this influence affected by experimental manipulation? • Mechanize functions to brain interactions • Localization • What areas of the brain respond to experimental manipulation? • Localize functions to distinct regions of the brain

3. Basic Idea

4. Some common approaches • Between subjects functional connectivity • Time series correlations • Beta Series • Look for changes in correlation as a function of condition • Are X and Y more tightly coupled in condition A compared to condition B? • Psychophysiological Interaction (PPI) • Look for changes in the regression slope as a function of condition • Does more X activation produce more Y activation in condition A compared to condition B?

5. Between subjects correlation • Do participants who tend to show increased brain activity in region X also tend to show increased brain activity in region Y for a specific contrast?

6. Example

7. Why/ How Example • Do people who show more activity in DMPFC also show more activity in other regions associated with mentalizing? • As opposed to the appearance of a “network” coming from multiple different people activating sub regions • Slightly stronger evidence

8. How to do it • Method 1 (ROI method): • Extract parameter estimates at group level from a priori hypothesized ROIs • Examine their correlations with one another • Method 2 (whole brain search) • Extract PEs at group level from an a priori hypothesized ROI or peak voxel in a theoretically relevant cluster • Regress onto brain activity in whole brain analysis at group level • Variants (see yesterday’s lecture)

9. Between subjects connectivity Strengths Limits Throws out a lot of temporal information Does not actually get at whether regions are coactive during the task (only individual differences across people) No ability to make causal inference • Very simple to run • Very simple to understand • Easy to combine with other individual difference measures

10. Within subject approaches • For a given seed region • Find areas that show changes in their relationship with the seed region • Within conditions • As a function of different task conditions • Beta series– takes advantage of within trial variation • PPI– treats within trail variability as noise in a more traditional interaction analysis

11. Example • What brain regions is DMPFC working with during attribution? • i.e., “why” in the how/why task

12. Standard GLM Trial3 Trial2 Trial1 TrialN • Typical GLM for our experiment: Y = β0 + Xwhyβwhy + Xhowβhow + ε Xwhy is predictor for ‘why’ condition Xhow is predictor for ‘how’ condition • Trials are combined into a single predictor • Individual trial variation considered noise

13. Beta series GLM • Beta series method assumes that individual trial variation is meaningful • For a given seed region, what other regions show similar trial-by-trial variability? • i.e. simple correlation • To examine between-trial variability, need a separate predictor for each trial Y = β0 + Xwhy1βwhy1+ Xwhy2βwhy2+ Xwhy3βwhy3+ … + XwhyNβwhyN+ Xhow1βhow1+ Xhow2βhow2 + Xhow3βhow3 + … + XhowNβhowN + ε

14. Beta series Each predictor is now replaced with a series of predictors When fit to the GLM, this will yield a series of betas why1 = 1.1 why2 = 1.3 why2 = 0.7

15. Beta series correlation Take beta series from seed region Yields a correlation map why1 = 1.1 why2= 1.3 why3= 0.7 … whyN= 1.8 Correlate the seed beta series with the beta series at every other voxel of the brain Map of correlations during why events (note: not real data for this task)

16. Beta series correlation Repeat process for a different event Yields a correlation map 1= 0.6 2= 1.1 3= 0.3 … N= 1.4 Correlate the seed beta series with the beta series at every other voxel of the brain Map of correlations during attend how events (note: not real data for this task)

17. Note • Can learn descriptive information about what regions co-vary during specific task conditions • But, to figure out what is specific to our condition of interest… • Logic similar to subtraction analysis in standard GLM analysis

18. Beta series Comparison Examine changes in correlations as a function of condition through simple subtraction _ = Note: important to first normalize the correlation maps, so that t-statistics can be performed Send normalized correlation diff maps (1 per subject) to 2nd level for simple one-sample t-test

19. Selected other examples • Persistence of emotional memories (Ritchey et al., Cerebral Cortex 2008) • Increased connectivity between amygdala and hippocampus during encoding predicts increased temporal durability of emotional memories • Emotional regulation in depression (Heller et al., PNAS 2010) • Decreased NAcc activity in depressed individuals is related to diminished connectivity between NAcc and PFC • Individual differences in financial risk-taking (Samanez-Larkin et al., J Neurosci 2010) • Individuals with reduced connectivity between the NAcc and PFC made more risk-seeking mistakes

20. Beta series evaluation • Pro’s • Allows flexible modeling • Good for multi-event per trial designs • Tease apart sub parts of psychological process • After 1st level GLM is estimated, can repeat correlations on any number of seeds and conditions • Relatively more powerful for event related designs • Con’s • No directionality of inference • Individual beta estimates are noisy • Massive 1st level model • All the beta images take a lot of harddrive space • No precooked SPM implementation • Relatively less powerful for block designs

21. Within subject approaches • Beta Series • Look for changes in correlation as a function of condition • Are X and Y more tightly coupled in condition A compared to condition B? • Psychophysiological Interaction (PPI) • Look for changes in the regression slope as a function of condition • Does more X activation produce more Y activation in condition A compared to condition B?

22. PsychoPhysiological Interaction (PPI) • Specifies the GLM with 3 predictors of interest • 1) Psychological term • Contrast of interest • E.g. why – how • 2) Physiological term • Time series from seed region • E.g. DMPFC • 3) Interaction term • Psych X Phys • Interaction of the seed time series with the psychological contrast of interest

23. PPI GLM Physiological variable Interaction Psychological variable Interaction why TPJ Activation how DMPFC Activation Y = β0 + (why – how)β1 + DMPFCβ2 + (why - how)*DMPFCβ3 + ε • Hypothesis: • H0: β3 = 0, there is no interaction • Ha: β3> 0, positive interaction

24. PPI deconvolution DMPFC BOLD Deconvolve why – how DMPFC Neural X Reconvolve Gitelman et al., 2003, NeuroImage • Accomplished by • Taking BOLD signal • Deconvolving to putative neuronal inputs • Computing interactions at neural input level • Convolving with HRF to predict BOLD signal

25. Interpreting PPIs (do not make causal claims) Attribution DMPFC TPJ Attribution TPJ DMPFC • 2 possible interpretations: • 1) Contribution of the source area to the seed area response (or vice versa) depends upon experimental context • E.g. DMPFC input to TPJ is modulated by attribution • 2) Seed response to experimental context depends on activation in the source area (or vice versa) • E.g. Effect of attribution on TPJ is modulated by DMPFC

26. PPI in SPM • First, must perform standard GLM analysis • 1) Create a volume of interest (VOI) • Examine results, go to seed and click “Eigenvariate” • Will need to name the VOI (e.g. DMPFC_1) • Specify session (e.g. 1) • Define VOI shape (e.g. sphere, box, cluster) • Repeat for each session • Each VOI will be saved (e.g. “VOI_DMPFC_1.mat”)

27. PPI In SPM • 2) click “PPIs” in the main menu • Select the standard GLM’s “SPM.mat” • Select “psychophysiological interaction” • SPM will go through each predictor in the standard GLM and ask if you want to include it as part of the Psychological variable • If included, set a weight (i.e. 1 for why, -1 for how) • Name the PPI (e.g. DMPFC_why-how1) • Repeat for each session • Each PPI will be saved (e.g. “PPI_DMPFC_why-how1.mat”)

28. PPI IN SPM • 3) Specify a new GLM: a GLM for PPI • Each of the saved PPI_.mat files contains the 3 regressors of interest • PPI.ppi – the interaction • PPI.P – the psychological term • PPI.Y – the physiological term • For each session, load the appropriate PPI_.mat file in MATLAB and type the above variables in as regressors • Include any other nuisance regressors you normally would (e.g. motion regressors)

29. PPI In SPM 4) After estimating, the contrast is simply a 1 for the interaction term (e.g. [1 0 0 0] for the design to the right) 5) Submit the interaction contrasts from each subject to second-level one-sample t-test For more precise details on each step and a tutorial data set, consult the SPM8 manual

30. PPI Pros and Cons • Pro’s • Model-based with an approximated neuronal input structure • Implemented in SPM • Con’s • New model for each seed • New model for each psychological contrast • Optimized for simple (e.g. 2-condition) designs, but may not be suitable for more complex designs • See http://www.nitrc.org/projects/gppi/ for a potential solution to this • Claims to be “effective connectivity”, but still is not much more than a simple correlation

31. Comparison of PPI and beta series • gPPI and beta series produced bigger effects than sPPI • Modeling each condition separately may produce better effects that treating the contrast in one step • A comparison of statistical methods for detecting context-modulated functional connectivity in fMRI • Cisler, Bush & Steele, 2014, Neuroimage

32. Selected shortcomings • Both beta series and PPI require a task • Scott will talk about task-free/resting-state connectivity • Both beta series and PPI requires specification of seeds • Places strong constraints on revealed networks • May prefer a data driven approach • Neither beta series nor PPI specify direction of influence • May want methods to examine effective connectivity • Scott and Luis will cover methods that are well-suited to address these shortcomings

33. Questions?