Jody Culham
Brain and Mind Institute
Department of Psychology
Western University
http://www.fmri4newbies.com/
Basics of Experimental Design
for fMRI:
Event-Related Designs
Last Update: February 22, 2013
Last Course: Psychology 9223, W2013, Western University
Event-Related Averaging
(can be used for block or event-related designs)
Event-Related Averaging
In this example an “event”
is the start of a block
In single-trial designs, an
event may be the start of a
single trial
First, we compute an event related average for the blue condition
• Define a time window before (2 volumes) and after (15 volumes)
the event
• Extract the time course for every event (here there are four events
in one run)
• Average the time courses across all the events
Event-Related Averaging
Second, we compute an event
related average for the gray
condition
Event-Related Averaging
Third, we can plot the average
ERA for the blue and gray
conditions on the same graph
Event-Related Averaging in BV
Define which subjects/runs to include
Set time window
Define which
conditions to
average (usually
exclude baseline)
We can tell BV where to put the
y=0 baseline. Here it’s the
average of the two circled data
points at x=0.
Determine how you want to define
the y-axis values, including zero
But what if the curves don’t have the
same starting point?
In the data shown, the
curves started at the same
level, as we expect they
should because both
conditions were always
preceded by a resting
baseline period
But what if the data looked
like this?
…or this?
Epoch-based averaging
FILE-BASED AVERAGING: zero baseline determined across all conditions (for 0 to 0: points in red circles)
In the latter two cases, we could simply shift the curves so they all start from the same (zero) baseline
EPOCH-BASED AVERAGING: zero baselines are specific to each epoch
File-based vs. Epoch-based Averaging
time courses may start at different
points because different event
histories or noise
e.g., set EACH curve
such that at time=0,
%BSC=0
0
0
0
File-based Averaging
Epoch-based Averaging
•
•
•
•
•
•
zero is based on average starting point
of all curves
works best when low frequencies have
been filtered out of your data
similar to what your GLM stats are
testing
•
each curve starts at zero
can be risky with noisy data
only use it if you are fairly certain
your pre-stim baselines are valid
(e.g., you have a long ITI and/or
your trial orders are
counterbalanced)
can yield very different conclusions
than GLM stats
What if…?
• This design has the benefit that each condition epoch is preceded
by a baseline, which is nice for making event-related averages
• However, we might decide that this design takes too much time
because we are spending over half of the time on the baseline.
• Perhaps we should use the following paradigm instead…?
• This regular triad sequence has some nice features, but it can
make ERAs more complicated to understand.
Regular Ordering and ERAs
• We might have a time course that looks like this
Example of ERA Problems
• If you make an ERA the usual way, you might get something that
looks like this:
File-Based (Pre=2, Post=10, baseline 0 to 0)
Intact
Scrambled
One common newbie
mistake is to make
ERAs for all
conditions, including
the baseline (Fixation).
This situation will
illustrate some of the
confusion with that
Fixation
• Initially some people can be confused how to interpret this ERA
because the pre-event activation looks wonky.
Example of ERA Problems
File-Based (Pre=2, Post=10, baseline 0 to 0)
File-Based (Pre=8, Post=18, baseline 0 to 0)
Intact
Scrambled
Fixation
• If you make the ERA over a longer
time window, the situation becomes
clearer.
• You have three curves that are merely
shifted in time with respect to one
another.
Example of ERA Problems
File-Based (Pre=2, Post=10, baseline 0 to 0)
Intact
End of
Intact
Scrambled
End of
Scrambled
End of
Fixation
Fixation
• Now you should realize that the different pre-epoch baselines result
from the fact that each condition has different preceding conditions
– Intact is always preceded by Fixation
– Scrambled is always preceded by Intact
– Fixation is always preceded by Scrambled
Example of ERA Problems
File-Based (Pre=2, Post=10, baseline 0 to 0)
Intact
Scrambled
Fixation
• Because of the different histories, changes with respect to baseline are
hard to interpret. Nevertheless, ERAs can show you how much the
conditions differed once the BOLD response stabilized
– This period shows, rightly so, Intact > Scrambled > Fixation
Example of ERA Problems
Epoch-Based (Pre=2, Post=10, baseline -2 to -2)
• Because the pre-epoch baselines are so different (due to differences in
preceding conditions), here it would be really stupid to do epoch-based
averaging (e.g., with x=-2 as the y=0 baseline)
• In fact, it would lead us to conclude (falsely!) that there was more
activation for Fixation than for Scrambled
Example of ERA Problems
• In a situation with a regular sequence like this, instead of making an
ERA with a short time window and curves for all conditions, you can
make one single time window long enough to show the series of
conditions (and here you can also pick a sensible y= 0 based on x=-2)
File-Based average for Intact condition only (Pre=2, Post23, baseline -2 to -2)
Intact
Scrambled
Fixation
Partial confounding
• In the case we just considered, the histories for various
conditions were completely confounded
– Intact was always preceded by Fixation
– Scrambled was always preceded by Intact
– Fixation was always preceded by Scrambled
• We can also run into problems (less obvious but with the same ERA
issues) if the histories of conditions are partially confounded (e.g.,
quasi-random orders)
• Intact is preceded by Scrambled 3X and by Fixation 3X
• Scrambled is preceded by Intact 4X and Fixation 1X
• Fixation is preceded by Intact 2X, by Scrambled 2X and
by nothing 1X
• No condition is ever preceded by itself
ERAs: Take-home messages
• ERAs can be a valuable way to look at activation
over time
• BUT
– you have to carefully select the baseline (file-based vs.
epoch-based; which time points to take as baseline)
– you have to know whether the history of your conditions is
counterbalanced
• if it’s not counterbalanced, ERAs can be misleading
• This problem of “history” will come up again…
Basics of Event-Related Designs
Block Designs
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
Block
Design
Early Assumption: Because the hemodynamic response delays and blurs
the response to activation, the temporal resolution of fMRI is limited.
Positive BOLD response
BOLD Response
(% signal change)
WRONG!!!!!
3
2
Overshoot
1
Initial
Dip
0
Post-stimulus
Undershoot
Time
Stimulus
What are the temporal limits?
What is the briefest stimulus that fMRI can detect?
Blamire et al. (1992): 2 sec
Bandettini (1993): 0.5 sec
Savoy et al (1995): 34 msec
2 s stimuli
single events
Data: Blamire et al., 1992, PNAS
Figure: Huettel, Song & McCarthy, 2004
Data: Robert Savoy & Kathy O’Craven
Figure: Rosen et al., 1998, PNAS
Although the shape of the HRF delayed and blurred, it is predictable.
Event-related potentials (ERPs) are based on averaging small
responses over many trials.
Can we do the same thing with fMRI?
Predictor Height Depends on Stimulus
Duration
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
Block
Design
Slow ER
Design
Rapid
Jittered ER
Design
Mixed
Design
Design Types
Detection vs. Estimation
% Signal Change
• detection: determination of whether
activity of a given voxel (or region)
changes in response to the
experimental manipulation
1
0
0
4
8
12
• estimation: measurement of the time
course within an active voxel in
response to the experimental
manipulation
Time (sec)
Definitions modified from: Huettel, Song & McCarthy, 2004,
Functional Magnetic Resonance Imaging
Block Designs: Poor Estimation
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging
Pros & Cons of Block Designs
Pros
• high detection power
• has been the most widely used approach for fMRI studies
• accurate estimation of hemodynamic response function is not as
critical as with event-related designs
Cons
• poor estimation power
• subjects get into a mental set for a block
• very predictable for subject
• can’t look at effects of single events (e.g., correct vs. incorrect
trials, remembered vs. forgotten items)
• becomes unmanagable with too many conditions (e.g., more
than 4 conditions + baseline)
Slow Event-Related Designs
Slow ER
Design
Convolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown
BOLD Summates
Neuronal Activity
Slide adapted from Matt Brown
BOLD Signal
Slow Event-Related Design: Constant ITI
Block
2 s stim
vary ISI
Bandettini et al. (2000)
What is the optimal trial spacing (duration +
intertrial interval, ITI) for a Spaced Mixed
Trial design with constant stimulus
duration?
Event-related average
Source: Bandettini et al., 2000
Optimal Constant ITI
Source: Bandettini et al., 2000
Brief (< 2 sec) stimuli:
optimal trial spacing = 12 sec
For longer stimuli:
optimal trial spacing = 8 + 2*stimulus duration
Effective loss in power of event related design:
= -35%
i.e., for 6 minutes of block design, run ~9 min ER design
Trial to Trial Variability
Huettel, Song & McCarthy, 2004,
Functional Magnetic Resonance Imaging
How Many Trials Do You Need?
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging
•
•
•
standard error of the mean varies with square root of number of trials
Number of trials needed will vary with effect size
Function begins to asymptote around 15 trials
Effect of Adding Trials
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging
Pros & Cons of Slow ER Designs
Pros
• excellent estimation
• useful for studies with delay
periods
• very useful for designs with
motion artifacts (grasping,
swallowing, speech)
because you can tease out
artifacts
• analysis is straightforward
Example: Delayed Hand Actions
(Singhal et al., under revision)
Visual Delay
Action
Response
Execution
Grasp Go (G)
Reach Go (R)
Grasp Stop (GS)
Reach Stop (RS)
Actionrelated
artifact
Really long delay:
18 s
Cons
• poor detection power because you get very few trials
per condition by spending most of your sampling
power on estimating the baseline
• subjects can get VERY bored and sleepy with long
inter-trial intervals
Effect of this design
on our subject
“Do You Wanna Go Faster?”
Rapid
Jittered ER
Design
• Yes, but we have to test assumptions regarding
linearity of BOLD signal first
Linearity of BOLD response
Linearity:
“Do things add up?”
red = 2 - 1
green = 3 - 2
Sync each trial response
to start of trial
Not quite linear
but good enough!
Source: Dale & Buckner, 1997
Linearity is okay for events every ~4+ s
Why isn’t BOLD totally linear?
In part because neurons aren’t totally linear either
•“Phasic” (or “transient”) neural responses
•Adaptation or habituation… stay tuned
Spikes/ms
– May depend on factors like stimulus duration and stimulus intensity
Time (ms)
Ganmor et al., 2010, Neuron
Optimal Rapid ITI
Source: Dale & Buckner, 1997
Rapid Mixed Trial Designs
Short ITIs (~2 sec) are best for detection power
Do you know why?
Efficiency (Power)
Two Approaches
• Detection – find the blobs
– Business as usual
– Model predicted activation using square-wave predictor
functions convolved with assumed HRF
– Extract beta weights for each condition; Contrast betas
– Drawback: Because trials are packed so closely together,
any misestimates of the HRF will lead to imperfect GLM
predictors and betas
• Estimation – find the time course
– make a model that can estimate the volume-by-volume time
courses through a deconvolution of the signal
BOLD Overlap With Regular Trial Spacing
Neuronal activity from TWO event types with constant ITI
Partial tetanus BOLD activity from two event types
Slide from Matt Brown
BOLD Overlap with Jittering
Neuronal activity from closely-spaced, jittered events
BOLD activity from closely-spaced, jittered events
Slide from Matt Brown
BOLD Overlap with Jittering
Neuronal activity from closely-spaced, jittered events
BOLD activity from closely-spaced, jittered events
Slide from Matt Brown
Fast fMRI Detection
A) BOLD Signal
B) Individual Haemodynamic Components
C) 2 Predictor Curves for use with GLM (summation of B)
Slide from Matt Brown
Why jitter?
• Yields larger fluctuations in signal
When pink is on, yellow is off
 pink and yellow are anticorrelated
Includes cases when both pink and yellow are off
 less anticorrelation
• Without jittering predictors from different trial types
are strongly anticorrelated
– As we know, the GLM doesn’t do so well when predictors
are correlated (or anticorrelated)
GLM: Tutorial data
• Just as in the GLM for a block design, we have one
predictor for each condition other than the baseline
GLM: Output
Faces > Baseline
How to Jitter
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
TD = 2 s
ITI = 0 s
SOA = 2 s
TD = 2 s
ITI = 4 s
SOA = 6 s
Vary Intertrial Interval (ITI)
•
•
Stimulus Onset Asynchrony (SOA) = ITI + Trial Duration
may want to make TD (e.g., 2 s) and ITI durations (e.g., 0, 2, 4, 6 s) an integer multiple
of TR (e.g., 2 s) for ease of creating protocol files
Flat Distribution
Frequency
of ITIs
in Each
Condition
Another way to think about it…
Exponential Distribution
Frequency
of ITIs
in Each
Condition
0 2 4 6
0 2 4 6
ITI (s)
ITI (s)
Include “Null” Trials
= null trial
(nothing happens)
•
•
Can randomize or counterbalance distribution of three trial types
Outcome may be similar to varying ISI
Assumption of HRF is More Problematic for
Event-Related Designs
We know that the standard two-gamma HRF
is a mediocre approximation for individual Ss’
HRFs
Handwerker et al., 2004, Neuroimage
We know this isn’t such a big deal for block
designs but it is a bigger issue for rapid
event-related designs.
One Approach to Estimation:
Counterbalanced Trial Orders
•
Each condition must have the same history for preceding trials so that trial
history subtracts out in comparisons
•
For example if you have a sequence of Face, Place and Object trials (e.g.,
FPFOPPOF…), with 30 trials for each condition, you could make sure that the
breakdown of trials (yellow) with respect to the preceding trial (blue) was as
follows:
•
•
•
…Face  Face x 10
…Place  Face x 10
…Object  Face x 10
•
•
•
…Face  Place x 10
…Place  Place x 10
…Object  Place x 10
•
•
•
…Face  Object x 10
…Place  Object x 10
…Object  Object x 10
•
Most counterbalancing algorithms do not control for trial history beyond the
preceding one or two items
Algorithms for Picking Efficient Designs
Optseq2
Algorithms for Picking Efficient Designs
Genetic Algorithms
You Can’t Always Counterbalance
You may be interested in variables for which you can not control trial
sequence
e.g., subject errors can mess up your counterbalancing
e.g., memory experiments: remembered vs. forgotten items
e.g., decision-making: choice 1 vs. choice 2
e.g., correlations with behavioral ratings
Post Hoc Trial Sorting Example
Wagner et al., 1998, Science
Pros & Cons of Applying Standard GLM
to Rapid-ER Designs
Pros
• high detection power
• trials can be put in unpredictable order
• subjects don’t get so bored
Cons and Caveats
• reduced detection compared to block designs
• requires stronger assumptions about linearity
– BOLD is non-linear with inter-event intervals < 6 sec.
– Nonlinearity becomes severe under 2 sec.
• errors in HRF model can introduce errors in activation estimates
Design Types
Mixed
Design
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
Example of Mixed Design
Otten, Henson, & Rugg, 2002, Nature Neuroscience
• used short task blocks in which subjects encoded words
into memory
• In some areas, mean level of activity for a block
predicted retrieval success
Pros and Cons of Mixed Designs
Pros
• allow researchers to distinguish between staterelated and item-related activation
Cons
• sensitive to errors in HRF modelling
Deconvolution of Event-Related Designs
Using the GLM
Two Approaches
• Detection – find the blobs
– Business as usual
– Model predicted activation using square-wave predictor
functions convolved with assumed HRF
– Extract beta weights for each condition; Contrast betas
– Drawback: Because trials are packed so closely together,
any misestimates of the HRF will lead to imperfect GLM
predictors and betas
• Estimation – find the time course
– make a model that can estimate the volume-by-volume time
courses through a deconvolution of the signal
Convolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown
Fast fMRI Detection
A) BOLD Signal
B) Individual Haemodynamic Components
C) 2 Predictor Curves for use with GLM (summation of B)
Slide from Matt Brown
DEconvolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown
Deconvolution Example
• time course from 4 trials of two types (pink, blue) in a “jittered” design
Summed Activation
Single Stick Predictor
(stick predictors are also called finite impulse response (FIR) functions)
• single predictor for first volume of pink trial type
Predictors for Pink Trial Type
• set of 12 predictors for subsequent volumes of pink trial type
• need enough predictors to cover unfolding of HRF (depends on TR)
Predictor Matrix
• Diagonal filled with 1’s
.
.
.
Predictors for Pink Trial Type
Predictors for the Blue Trial Type
Predictor x Beta Weights for Pink Trial Type
• sequence of beta weights for one trial type yields an estimate of
the average activation (including HRF)
Predictor x Beta Weights for Blue Trial Type
• height of beta weights indicates amplitude of response (higher
betas = larger response)
Linear Deconvolution
Miezen et al.
2000
•
Jittering ITI also preserves linear independence among the hemodynamic
components comprising the BOLD signal.
Decon GLM
To find areas
that respond to
all stims, we
could fill the
contrast column
with +’s
…but that would
be kind of dumb
because we
don’t expect all
time points to be
highly positive,
just the ones at
the peak of the
HRF
14 predictors (time points)
for Cues
14 predictors (time points)
for Face trials
14 predictors (time points)
for House trials
14 predictors (time points)
for Object trials
Contrasts on Peak Volumes
We can search
for areas that
show activation
at the peak (e.g.,
3-5 s after
stimulus onset
Results: Peaks > Baseline
Graph beta weights
for spike predictors 
Get deconvolution
time course
Why go to all this
bother? Why not just
generate an eventrelated average?
…
Pros and Cons of Deconvolution
Pros:
• Produces time course that dissociates activation from trial history
• Does not assume specific shape for hemodynamic function
• Robust against trial history biases (though not immune to it)
• Compound trial types possible (e.g., stimulus-delay-response)
– may wish to include “half-trials” (stimulus without response)
Cons:
• Complicated
• Quite sensitive to noise
• Contrasts don’t take HRF fully into account, they just examine peaks
Not Mutually Exclusive
• Convolution and deconvolution GLMs are not
mutually exclusive
• Example
– use convolution GLM to detect blobs, use deconvolution to
estimate time courses
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
Block
Design
Slow ER
Design
Rapid
Jittered ER
Design
Mixed
Design
Design Types
Take-home message
• Block designs
– Great detection, poor estimation
• Slow ER designs
– Poor detection, great estimation
• Fast ER designs
– Good detection, very good estimation
– Excellent choice for designs where predictability is
undesirable or where you want to factor in subject’s behavior