1. Experimental Design and Efficiency in fMRI
Heidi Bonnici and Sinéad Mullally
Methods for Dummies
13th January 2010

2. Overview Experimental Design Design Efficiency
Types of Experimental Design
Timing parameters – Blocked and Event-Related Design
Design Efficiency
Response vs Baseline (signal-processing)
Response 1 - Response 2 (statistics)

3. Overview Experimental Design Design Efficiency
Types of Experimental Design
Timing parameters – Blocked and Event-Related Design
Design Efficiency
Response vs Baseline (signal-processing)
Response 1 - Response 2 (statistics)

4. Main Take Home Point of Experimental Design
Make sure you’ve chosen your analysis method and contrasts before you start your experiment

5. 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

6. Overview Experimental Design Design Efficiency
Types of Experimental Design
Timing parameters – Blocked and Event-Related Design
Design Efficiency
Response vs Baseline (signal-processing)
Response 1 - Response 2 (statistics)

7. Types of Experimental Design
Categorical – comparing the activity from one task to another task
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

8. 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

9. Categorical Design: Conjunction
A-B
Tests multiple effects
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)

10. A B C D Factorial design LOW LOAD HIGH
Combining two or more factors within a task and looking at the effect of one factor upon the other/s.
Load task
MOTION NO MOTION
Rees, Frith & Lavie (1997)
A B
C D
LOW
LOAD
HIGH
A – Low attentional load, motion
B – Low attentional load, no motion
C – High attentional load, motion
D – High attentional load, no motion

11. A B C D Simple main effects Main effects Interaction terms Terminology
MOTION NO MOTION
Terminology
A B
C D
Simple main effects
Main effects
Interaction terms
LOW
LOAD
HIGH

12. A B C D SIMPLE MAIN EFFECTS
MOTION NO MOTION
SIMPLE MAIN EFFECTS
A B
C D
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
D – C: ?
Simple main effect of no motion (vs. motion) in the context of high load
LOW
LOAD
HIGH
The inverse simple
main effect of motion
(vs. no motion) in the
Context of high load OR

13. A B C D MAIN EFFECTS MAIN EFFECTS (A + B) – (C + D):
MOTION NO MOTION
MAIN EFFECTS
MAIN EFFECTS
A B
C D
(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
LOAD
HIGH

14. A B C D INTERACTION TERMS INTERACTION TERMS (A - B) – (C - D):
MOTION NO MOTION
INTERACTION TERMS
INTERACTION TERMS
A B
C D
(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
LOAD
HIGH

15. Factorial design in SPM
MOTION NO MOTION
A B
C D
How do we enter these effects in SPM?
Simple main effect of motion in the context of low load:
A vs. B or (A – B)
LOW
LOAD
HIGH
A B C D
[ ]

16. Factorial design in SPM
Main effect of low load:
(A + B) – (C + D)
Interaction term of motion greater under low load:
(A – B) – (C – D)
A B C D
[ ]
A B C D
[ ]

17. Parametric Design Linear Nonlinear Cognitive components and dimensions
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

18. Overview Experimental Design Design Efficiency
Types of Experimental Design
Timing parameters – Blocked and Event-Related Design
Design Efficiency
Response vs Baseline (signal-processing)
Response 1 - Response 2 (statistics)

19. 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

20. 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

21. 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

22. Pros and Cons of Blocked Design
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

23. 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

24. Pros and Cons of Event-Related Design
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).

25. Overview Experimental Design Design Efficiency
Types of Experimental Design
Timing parameters – Blocked and Event-Related Design
Design Efficiency
What is efficiency
Signal Processing perspective
General Advice

26. Efficiency is…
… a numerical value which reflects the ability of your design to detect the effect of interest.

27. Efficiency is…
… a numerical value which reflects the ability of your design to detect the effect of interest.
General Linear Model:
Y = X β ε
Data Design Matrix Parameters error
Efficiency (e) is the ability to estimate β, given the design matrix X

28. Efficiency is… Y = X β + ε e (c, X) = inverse (σ2 cT Inverse(XTX) c)
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)
The inverse of the variance is essentially minimising the variance, increases the information – and thus the efficiency. 28

29. 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)

30. 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.

31. 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

32. Fixed SOA = 16s  = Not particularly efficient… Stimulus (“Neural”)
HRF
Predicted Data  =
Consider the ability to detect the BOLD response to a single event-type versus baseline. This slide shows the results of convolution using the IR.
The basic idea behind maximising efficiency is to maximise the ‘energy’ of the predicted fMRI timeseries (i.e. the sum of the squared signal values at each scan – this is proportional of the variance of the signal).
In order to best be abot to detect the signal in the presence of background noise, we want to maximise the variability of that signal – signal that varies little will be difficult to detect.
Not particularly efficient… 32

33. Fixed SOA = 4s  = Very Inefficient… Stimulus (“Neural”) HRF
Predicted Data  =
Successive events overlap considerably -> end up with an initial build up followed by small oscillations around a raised baseline.
Signal high but variance is low – majority of stimulus energy lost after highpass filtering.
Very Inefficient… 33

34. Randomised, SOAmin= 4s  =
Stimulus (“Neural”)
HRF
Predicted Data  =
Vary the SOA randomly. SOAmin = 4s but only a 50% probability of an event every 4s. This a an example of a stochastic design.
More efficient as larger variability in the signal.
More Efficient, despite using only half as many stimuli as previous… 34

35. Blocked, SOAmin= 4s  = but this design is even more Efficient…
Stimulus (“Neural”)
HRF
Predicted Data  =
Varies the SOA is a more systematic fashion – runs of null events followed by runs of events – corresponds to a blocked design i.e. v similar to what wld be obtained if neural activity were sustained throughout the block (only true with short SOA of 4s or less).
To understand why this is a more efficient design we need to consider the fourier transform of these time series.
but this design is even more Efficient… 35

36. 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) = Hz
Plus ‘harmonics’ – capture the sharper edges of the square-wave function relative to the fundamental sinusoid
a time-domain graph The ‘spectrum’ of frequency components is the frequency domain representation of the signal.
shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies.
Now if we take the Fourier transform of each function in the top row - plot amplitude (magnitude) as a function of frequency as shown in the bottom row.
The amplitude spectra (square-root of the "power spectra") of the square-wave neural function has a dominant frequency corresponding to its "fundamental" frequency (Fo = 1/(20s+20s) = Hz), plus a series of "harmonics" (3Fo, 5Fo, ... etc) of progressively decreasing amplitude.
The fundamental frequency corresponds to the frequency of a sinusoidal that best matches the basic on-off alternation; the harmonics can be thought of as capturing the "sharper" edges of the square-wave function relative to this fundamental sinusoid. 36

38. Blocked, epoch = 20s  =  = Stimulus (“Neural”) HRF Predicted Data
The fourier tranform does not change the data or the conclusions. But in this way, we can regard the neural activity as our original data and the IR as a "filter".
You can see immediately from the shape of the Fourier transform of the IR (second panel of the bottom row) that this filter will "pass" low frequencies, but attenuate higher frequencies (which is why it is sometimes called a "lowpass filter" or "temporal smoothing kernel").
This property is why much high-frequency information was lost in the fixed SOA=4s design in Fig 3. In the present epoch example, the result of multiplying the amplitude spectrum of the neural data by that of the filter is that some of the higher-frequency harmonics are attenuated, but the amplitude of the fundamental frequency is attenuated little. In other words, the majority of the signal is "passed" by the IR filter.  =
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. 38

39. Blocked, epoch = 20s
Stimulus (“Neural”)
HRF
Predicted Data  =
The fourier tranform does not change the data or the conclusions. But in this way, we can regard the neural activity as our original data and the IR as a "filter".
You can see immediately from the shape of the Fourier transform of the IR (second panel of the bottom row) that this filter will "pass" low frequencies, but attenuate higher frequencies (which is why it is sometimes called a "lowpass filter" or "temporal smoothing kernel").
This property is why much high-frequency information was lost in the fixed SOA=4s design in Fig 3. In the present epoch example, the result of multiplying the amplitude spectrum of the neural data by that of the filter is that some of the higher-frequency harmonics are attenuated, but the amplitude of the fundamental frequency is attenuated little. In other words, the majority of the signal is "passed" by the IR filter.  =
Efficient design as most of the signal is ‘passed’ by the IR filter 39

40. So what is the most efficiency design of all…

41. Sinusoidal modulation, f = 1/33s
Stimulus (“Neural”)
HRF
Predicted Data
Well, assuming we had a limited amount of total "stimulus energy", the optimal design would be to modulate the neural activity in a sinusoidal fashion (e.g, sinusoidally varying the luminance of a visual stimulus), with a frequency that matches the peak of the amplitude spectrum of the IR filter. With the assumed IR shape used here, this would be ~0.03Hz (1/30s). The sinusoidal modulation places all the stimulus energy at this single frequency, shown by the single line in frequency space.  =
The most efficient design of all! 41

42. 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 ‘band-pass’ filter (or ‘effective HRF’). 42

43.  =  = 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! 43

44. Randomised, SOAmin=4s, highpass filter = 1/120s
Stimulus (“Neural”)
HRF
Predicted Data  =  =
(Randomised design spreads power over frequencies)

45. General Advice (Rik Henson)
Scan for as long as possible (as increasing the number of volumes increasing the degrees of freedom).
For group studies increasing the number of participants adds more statistical power that increasing the number of DF.
Do not contrast conditions that are far apart in time (because of low-frequency noise in the data).
Randomize the order, or randomize the SOA, of conditions that are close in time.

46. Conclusions:
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

47. Useful links and thanks
Antoinette Nicolle
Nick and Edoardo’s slides from MfD 2008