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

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

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): Method 2 (whole brain search)
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
Very simple to run
Very simple to understand
Easy to combine with other individual difference measures
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

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 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
Trial1
Trial2
Trial3
TrialN

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

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

25. Interpreting PPIs (do not make causal claims)
TPJ
DMPFC
Attribution
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
TPJ
DMPFC
Attribution

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. [ ] 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 Con’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 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?