Functional Connectivity: PPI and
beta Series
With thanks to Derek Nee & Bob
Spunt
1
Localization vs integration
• Localization
• Integration
– What areas of the
brain respond to
experimental
manipulation?
– How do regions of the
brain influence each
other?
– How is this influence
affected by experimental
manipulation?
– Localize functions to
distinct regions of
the brain
– Mechanize functions to
brain interactions
2
Basic Idea
3
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?
4
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?
5
Example
6
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
7
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)
8
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
9
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
10
Example
• What brain regions is DMPFC working with
during attribution?
– i.e., “why” in the how/why task
11
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
12
Beta series GLM
• Beta series method assumes that individual trial variation is
meaningful
• For a given seed region, what other regions show similar trial-bytrial 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
13
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
14
Beta series correlation
Take beta series from seed region
= 1.1
why2 = 1.3
why3 = 0.7
…
whyN = 1.8
why1
Yields a correlation map
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)
15
Beta series correlation
Repeat process for a different event
= 0.6
2 = 1.1
3 = 0.3
…
N = 1.4
1
Yields a correlation map
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)
16
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
17
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 ttest
18
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
19
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
20
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?
21
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
22
PPI GLM
Y = β0 + (why – how)β1 + DMPFCβ2 + (why - how)*DMPFCβ3 + ε
• Hypothesis:
Physiological variable
TPJ Activation
Psychological variable
– H0: β3 = 0, there is no interaction
– Ha: β3 > 0, positive interaction
Interaction
why
how
DMPFC Activation
23
PPI deconvolution
DMPFC BOLD
• Accomplished by
Deconvolve
– Taking BOLD signal
– Deconvolving to putative
neuronal inputs
– Computing interactions at
neural input level
– Convolving with HRF to
predict BOLD signal
why – how
DMPFC Neural
X
Reconvolve
Gitelman et al., 2003, NeuroImage
24
Interpreting PPIs
(do not make causal claims)
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
DMP
FC
Attributi
on
– 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
DMP
FC
TPJ
25
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”)
26
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_whyhow1.mat”)
27
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)
28
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
29
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
30
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
31
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
32
Questions?
33