Experimental Design and Efficiency in fMRI
Heidi Bonnici and Sinéad Mullally
Methods for Dummies
13th January 2010
Overview
• Experimental Design
– Types of Experimental Design
– Timing parameters – Blocked and Event-Related Design
• Design Efficiency
– Response vs Baseline (signal-processing)
– Response 1 - Response 2 (statistics)
Overview
• Experimental Design
– Types of Experimental Design
– Timing parameters – Blocked and Event-Related Design
• Design Efficiency
– Response vs Baseline (signal-processing)
– Response 1 - Response 2 (statistics)
Main Take Home Point
of Experimental Design
Make sure you’ve chosen your analysis method and
contrasts before you start your experiment
Why is it so important to correctly design
your experiment?
• Main design goal: To test specific hypotheses
• We want to manipulate the subject’s experience and
behaviour in some way that is likely to produce a
functionally specific neurovascular response.
• What can we manipulate?
– Stimulus type and properties
– Stimulus timing
– Subject instructions
Overview
• Experimental Design
– Types of Experimental Design
– Timing parameters – Blocked and Event-Related Design
• Design Efficiency
– Response vs Baseline (signal-processing)
– Response 1 - Response 2 (statistics)
Types of Experimental Design
1. Categorical – comparing the activity from one task to
another task
2. Factorial - combining two or more factors within a task
and looking at the effect of one factor on the response to
other factor
•
Parametric – exploring systematic changes in the brain
responses according to some performance attributes of
task
Categorical Design: Subtraction
Assumption of pure insertion: One task does not affect the effect of another task.
Comparing the activity of one task to another task
considering the fact that the neural structures supporting cognitive and
behavioural processes combine in a simple additive manner
Can only test for one effect
Example:
Task: decide for each noun whether it refers to an animate or inanimate
object.
goat
bucket
Categorical Design: Conjunction
Tests multiple effects
A-B
Does not depend on pure insertion
– conjunction discounts
interaction terms
two or more distinct task pairs each
share a common processing
difference
common areas of activation for
each task pair
Task pairs independent
(AI-BI) & (AII-BII)
Factorial design
Combining two or more factors within a task and looking at the effect of one
factor upon the other/s.
MOTION
Load task
Rees, Frith &
Lavie (1997)
NO MOTION
LOW
A
B
HIGH
C
D
LOAD
•
•
•
•
A – Low attentional load, motion
B – Low attentional load, no motion
C – High attentional load, motion
D – High attentional load, no motion
MOTION
Terminology
LOW
• Simple main effects
• Main effects
• Interaction terms
NO MOTION
A
B
C
D
LOAD
HIGH
MOTION
SIMPLE MAIN EFFECTS
• A – B: Simple main effect of
motion (vs. no motion) in the
context of low load
• B – D: Simple main effect of
low load (vs. high load) in the
context of no motion
LOW
NO MOTION
A
B
C
D
LOAD
HIGH
• D – C: ?
• Simple main effect of no
motion (vs. motion) in the
context of high load
OR
The inverse simple
main effect of motion
(vs. no motion) in the
Context of high load
MOTION
MAIN EFFECTS
• (A + B) – (C + D):
• the main effect of low load (vs.
high load) irrelevant of motion
• Main effect of load
• (A + C) – (B + D): ?
• The main effect of motion (vs. no
motion) irrelevant of load
•  Main effect of motion
LOW
NO MOTION
A
B
C
D
LOAD
HIGH
MOTION
INTERACTION TERMS
• (A - B) – (C - D):
• the interaction effect of motion (vs.
no motion) greater under low (vs.
high) load
• (B - A) – (D - C): ?
• the interaction effect of no motion
(vs. motion) greater under low (vs.
high) load
LOW
NO MOTION
A
B
C
D
LOAD
HIGH
Factorial design in SPM
• How do we enter these effects in
SPM?
MOTION
LOW
NO MOTION
A
B
C
D
LOAD
HIGH
• Simple main effect of motion in
the context of low load:
• A vs. B or (A – B)
A
[1
B
-1
C
0
D
0]
Factorial design in SPM
• Main effect of low load:
• (A + B) – (C + D)
A
[1
• Interaction term of motion greater
under low load:
• (A – B) – (C – D)
A
[1
B
C
D
1
-1
-1]
B
C
D
-1
-1
1]
Parametric Design
exploring systematic changes in the brain responses according to some
performance attributes of task
• Linear
Cognitive components and
dimensions
• Nonlinear
Polynomial expansion
Assumption: as the task becomes more difficult blood flow to the regions specialised for
task analysis will increase
Overview
• Experimental Design
– Types of Experimental Design
– Timing parameters – Blocked and Event-Related Design
• Design Efficiency
– Response vs Baseline (signal-processing)
– Response 1 - Response 2 (statistics)
Timing Parameters – Blocked Design
• It involves presenting two conditions – an activation (A)
condition and a baseline (B) condition. Each condition is
presented for an identical epoch of time.
Task A
Task B
Task A
Task B
Task A
Task B
Task A
Task B
Task A
REST
Task B
REST
Task A
REST
Task B
REST
What baseline should you choose?
• Task A vs. Task B
– Example: Squeezing Right Hand vs. Left Hand
– Allows you to distinguish differential activation between
conditions
– Does not allow identification of activity common to both tasks
• Can control for uninteresting activity
• Task A vs. No-task
– Example: Squeezing Right Hand vs. Rest
– Shows you activity associated with task
– May introduce unwanted results
Choosing Length of Blocks
• Longer blocks allow for stability of extended patterns of
brain activation.
• Shorter blocks allow for more transitions between tasks.
– Task-related variability increases with increasing
numbers of transitions
Pros and Cons of Blocked Design
Pros:
• Avoid rapid task-switching (e.g. patients)
• Fast and easy to run;
• Good signal to noise ratio
Cons:
• Expectation
• Habituation
• Signal drift
• Poor choice of baseline may preclude meaningful conclusions
• Many tasks cannot be conducted repeatedly
Timing Parameters – Event-Related Design
• It allows different trials or stimuli to be presented
in arbitrary sequences.
• Jittering events can reduce possibility of
correlated regressors – increased efficiency
time
Pros and Cons of Event-Related Design
Pros:
•
Real world testing
•
Eliminate predictability of block designs (e.g. expectation);
•
Can look at novelty and priming;
•
Can look at temporal dynamics of response.
Cons:
•
•
Low statistical power (small signal change)
More complex design and analysis (esp. timing and baseline issues).
Overview
• Experimental Design
– Types of Experimental Design
– Timing parameters – Blocked and Event-Related Design
• Design Efficiency
– What is efficiency
– Signal Processing perspective
– General Advice
Efficiency is…
•
… a numerical value which reflects the ability of
your design to detect the effect of interest.
Efficiency is…
•
… a numerical value which reflects the ability of
your design to detect the effect of interest.
•
General Linear Model:
Y
Data
•
=
X
Design Matrix
.
β
Parameters
+
ε
error
Efficiency (e) is the ability to estimate β, given the design matrix X
Y=Xβ+ε
Efficiency is…
The inverse of the variance within the estimated β,
for this specific contrast
•
e (c, X) = inverse (σ2 cT Inverse(XTX) c)
•
e (c, X) is specific for a given contrast (c), given
the question that you are trying to answer (with your design X).
•
So, to optimise experimental design:
–
–
–
minimise the variance in the contrast i.e. minimise [cT (XTX)] by maximising [cT Inverse(XTX)]
we assume that noise variance (σ 2) is unaffected by changes in X.
All we can alter in this equation is X.
•
Therefore we minimise the variance (a priori) to maximise efficiency:
–
–
by the spacing and sequencing of epochs/events in our design matrix
ensuring that your regressors are not correlated (for more details see Rik Henson’s website)
Background: terminology
•
Trial - replications of a condition
•
A trial consists of one or more components, that may be:
– “events” or “impulses” - brief bursts of neural activity
– “epochs” - periods of sustained neural activity
•
SOA (Stimulus Onset Asynchrony) - time between the onsets of components. Also
referred to as the ITI (inter-trial interval).
•
ISI (Inter-Stimulus Interval) - time between offset of one component and onset of next
•
SOA = ISI + Stimulus Duration
•
For events: SOA = ISI (as events are assumed to have zero duration)
Signal Processing
•
Signal processing is the analysis, interpretation, and manipulation of signals.
•
Given that we can treat fMRI volumes as time series (for each voxel) it is useful to adopt a
signal-processing perspective.
•
Using a “linear convolution” model, the predicted fMRI series is obtained by convolving a
neural function (e.g. stimulus function) was an assumed IR.
The BOLD Impulse Response (IR)
•
A BOLD response to an impulse (brief burst) of activity typically has the
following characteristics:
–
–
A peak occurring at 4-6s
Followed by an undershoot from approximately 10-30s
Fixed SOA = 16s
Stimulus (“Neural”)
HRF

Not particularly efficient…
Predicted Data
=
Fixed SOA = 4s
Stimulus (“Neural”)
HRF

Predicted Data
=
Very Inefficient…
Randomised, SOAmin= 4s
Stimulus (“Neural”)
HRF

Predicted Data
=
More Efficient, despite using only half as many stimuli as previous…
Blocked, SOAmin= 4s
Stimulus (“Neural”)
HRF

Predicted Data
=
but this design is even more Efficient…
Background: terminology
•
The fourier transformation decomposes a function into the sum of a (potentially infinite)
number of sine wave frequency components.
•
A frequency domain graph shows how much of the signal lies within each given frequency
band over a range of frequencies
–
Here the sine wave that best matches the basic on-off alternation has a dominant frequency corresponding to its
‘fundamental’ frequency: F0 = 1/(20s+20s) = 0.025 Hz
–
Plus ‘harmonics’ – capture the sharper edges of the square-wave function relative to the fundamental sinusoid
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100
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Blocked, epoch = 20s
Stimulus (“Neural”)
HRF
Predicted Data

=

=
• A convolution in time is equivalent to a multiplication in frequency space
• In this way the transformed IR acts as a filter: passes low frequencies but attenuates higher frequencies.
Blocked, epoch = 20s
Stimulus (“Neural”)
HRF
Predicted Data

=

=
Efficient design as most of the signal is ‘passed’ by the IR filter
So what is the most efficiency
design of all…
Sinusoidal modulation, f = 1/33s
Stimulus (“Neural”)
HRF

Predicted Data
=
The most efficient design of all!
Highpass Filtering
•
fMRI noise tends to have two components:
–
Low frequency ‘1/f’ noise e.g. physical (scanner drifts);
physiological [cardiac (~1 Hz), respiratory (~0.25 Hz)]
–
Background white noise
•
Highpass filters aims to maximise the loss of noise but minimise the loss of signal.
•
We apply the highpass filter to the lowpass filter inherent in the IR to creast a single ‘bandpass’ filter (or ‘effective HRF’).
Blocked (80s), SOAmin=4s, highpass filter = 1/120s
Stimulus (“Neural”)
HRF

Predicted Data
=
“Effective HRF” (after highpass filtering) (Josephs & Henson, 1999)

=
Don’t have long (>60s) blocks!
Randomised, SOAmin=4s, highpass filter = 1/120s
Stimulus (“Neural”)
HRF
Predicted Data

=

=
(Randomised design spreads power over frequencies)
General Advice (Rik Henson)
1.
Scan for as long as possible (as increasing the number of volumes increasing
the degrees of freedom).
2.
For group studies increasing the number of participants adds more statistical
power that increasing the number of DF.
3.
Do not contrast conditions that are far apart in time (because of low-frequency
noise in the data).
4.
Randomize the order, or randomize the SOA, of conditions that are close in
time.
http://www.mrc-cbu.cam.ac.uk/Imaging/Common/fMRI-efficiency.shtml
Conclusions:
1.
2.
3.
4.
5.
6.
7.
Blocked designs generally most efficient (with short SOAs, given optimal block
length is not exceeded)
However, psychological efficiency often dictates intermixed designs, and often
also sets limits on SOAs
With randomised designs, optimal SOA for differential effect (A-B) is minimal
SOA (>2 seconds, and assuming no saturation), whereas optimal SOA for main
effect (A+B) is 16-20s
Inclusion of null events improves efficiency for main effect at short SOAs (at
cost of efficiency for differential effects)
If order constrained, intermediate SOAs (5-20s) can be optimal
If SOA constrained, pseudorandomised designs can be optimal (but may
introduce context-sensitivity)
Remember an optimal design for one contrast may not be optimal for another
http://www.mrc-cbu.cam.ac.uk/Imaging/Common/fMRI-efficiency.shtml
Useful links and thanks
• Antoinette Nicolle
• http://imaging.mrccbu.cam.ac.uk/imaging/DesignEfficiency
• Nick and Edoardo’s slides from MfD 2008