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

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

Basic Idea

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?

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?

Example

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

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)

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

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

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

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

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

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

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)

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)

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

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

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

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

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?

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

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

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

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

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”)

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”)

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)

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

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 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

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

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

Questions?