Jody Culham
Brain and Mind Institute
Department of Psychology
University of Western Ontario
http://www.fmri4newbies.com/
Basics of Experimental Design
for fMRI:
Event-Related Designs
Last Update: January 18, 2012
Last Course: Psychology 9223, W2010, University of Western Ontario
Part III
Choosing an Event-Related Design
Convolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown
BOLD Summates
Neuronal Activity
Slide from Matt Brown
BOLD Signal
BOLD Overlap and Jittering
• Closely-spaced
haemodynamic impulses
summate.
• Constant ITI causes tetanus.
Burock et al. 1998.
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
Block
Design
Slow ER
Design
Rapid
Counterbalanced
ER Design
Rapid
Jittered ER
Design
Mixed
Design
Design Types
= null trial
(nothing happens)
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?
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
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?
Sync with trial onset and 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
• good estimation power
• allows accurate estimate of baseline activation
and deviations from it
• 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
% signal change
Pros & Cons of Slow ER Designs
Activation


Hand motion
artifact
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
Time
“Do You Wanna Go Faster?”
• Yes, but we have to test assumptions regarding
linearity of BOLD signal first
Rapid
Counterbalanced
ER Design
Rapid
Jittered ER
Design
Mixed
Design
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
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)
Design Types
Rapid
Counterbalanced
ER Design
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
Detection with Rapid ER Designs
Figure: Huettel, Song & McCarthy, 2004
• To detect activation differences between conditions in
a rapid ER design, you can create HRF-convolved
reference time courses
• You can perform contrasts between beta weights as
usual
Variability Between Subjects/Areas
• greater variability
between subjects
than between
regions
• deviations from
canonical HRF
cause false
negatives (Type II
errors)
• Consider including
a run to establish
subject-specific
HRFs from robust
area like M1
Handwerker et al., 2004, Neuroimage
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)
• 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
The Problem of Trial/Block History
This problem also occurs for single trial designs.
This problem also occurs even if the history is only partially confounded
(e.g., if Condition A is preceded by Condition X twice as often as
Condition B is preceded by Condition X).
If we knew with certainty what a given subject’s HRF looked like, we
could model it (but that’s rarely the case).
Thus we have only two solutions:
1)
Counterbalance trial history so that each curve should start with the
same baseline
2)
Jitter the intertrial intervals so that we can estimate the HRF
•
more on this in analysis when we talk about deconvolution
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
Analysis of Single Trials with
Counterbalanced Orders
Approach used by Kourtzi & Kanwisher (2001, Science) for pre-defined ROI’s:
•
for each trial type, compute averaged time courses synced to trial onset; then subtract
differences
Event-related average
Raw data
Event-related average
with control period factored out
A signal change = (A – F)/F
A
…
B
B signal change = (B – F)/F
F
sync to trial onset
Pros & Cons of Counterbalanced Rapid
ER Designs
Pros
• high detection power with advantages of ER designs (e.g., can have
many trial types in an unpredictable order)
Cons and Caveats
• reduced detection compared to block designs
• estimation power is better than block designs but not great
• accurate detection requires accurate HRF modelling
• counterbalancing only considers one or two trials preceding each
stimulus; have to assume that higher-order history is random enough
not to matter
• what do you do with the trials at the beginning of the run… just throw
them out?
• you can’t exclude error trials and keep counterbalanced trial history
• you can’t use this approach when you can’t control trial status (e.g.,
items that are later remembered vs. forgotten)
Design Types
Rapid
Jittered ER
Design
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
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
Post Hoc Trial Sorting Example
Wagner et al., 1998, Science
Algorithms for Picking Efficient Designs
Optseq2
Algorithms for Picking Efficient Designs
Genetic Algorithms
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
EXTRA SLIDES
A Variant of Mixed Designs: Semirandom
Designs
• a type of event-related design in which the probability
of an event will occur within a given time interval
changes systematically over the course of an
experiment
First period:
P of event: 25%
Middle period:
P of event: 75%
Last period:
P of event: 25%
• probability as a function of time can be sinusoidal
rather than square wave
Pros and Cons of Semirandom Designs
Pros
• good tradeoff between detection and estimation
• simulations by Liu et al. (2001) suggest that semirandom
designs have slightly less detection power than block designs
but much better estimation power
Cons
• relies on assumptions of linearity
• complex analysis
• “However, if the process of interest differs across ISIs, then the
basic assumption of the semirandom design is violated. Known
causes of ISI-related differences include hemodynamic
refractory effects, especially at very short intervals, and changes
in cognitive processes based on rate of presentation (i.e., a task
may be simpler at slow rates than at fast rates).”
-- Huettel, Song & McCarthy, 2004