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With thanks to Derek Nee & Bob Spunt

Functional Connectivity: PPI and beta Series

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• Localization– 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

Localization vs integration

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Basic Idea

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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?

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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?

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Example

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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

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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)

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Between subjects connectivity

Strengths• Very simple to run• Very simple to understand• Easy to combine with other

individual difference measures

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

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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

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Example

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

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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

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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

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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

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Beta series correlation

why1 = 1.1

why2 = 1.3

why3 = 0.7…whyN = 1.8

Take beta series from seed region

Correlate the seed beta series with the beta series at every other voxel of the brain

Yields a correlation map

Map of correlations during why events (note: not real

data for this task)

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Beta series correlation

1 = 0.6

2 = 1.1

3 = 0.3…N = 1.4

Repeat process for a different event

Correlate the seed beta series with the beta series at every other voxel of the brain

Yields a correlation map

Map of correlations during attend how events (note: not real data for this task)

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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

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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

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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

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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

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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?

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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

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PPI GLM

Y = β0 + (why – how)β1 + DMPFCβ2 + (why - how)*DMPFCβ3 + ε

• Hypothesis:– H0: β3 = 0, there is no interaction

– Ha: β3 > 0, positive interaction

Psychological variable Physiological variable Interaction

how

why

DMPFC ActivationTP

J Acti

vatio

n

Interaction

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PPI deconvolution

• Accomplished by– Taking BOLD signal– Deconvolving to putative

neuronal inputs– Computing interactions at

neural input level– Convolving with HRF to

predict BOLD signal

DMPFC BOLD

Deconvolve

DMPFC Neuralwhy – how

X

Reconvolve

Gitelman et al., 2003, NeuroImage

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Interpreting PPIs (do not make causal claims)

• 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

TPJDMP

FC

Attribution

TPJDMPFC

Attribution

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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”)

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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”)

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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)

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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

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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

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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

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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

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Questions?