1. : To Block or Not to Block?
Basic fMRI Design
: To Block or Not to Block?
Tor D. Wager
Columbia University
With help from:

2. What we want from a design
Power: Can I detect results?
Interpretability: Can I relate brain data to specific psychological events?
Memory retrieval and comparison processes associated with recognition
Robust to errors in model specification
Timing, hemodynamic response (HRF) shape
Experimental (A) Control (B)

3. Types of designs: Blocked and event-related
Block design: Similar events are grouped
Event-related design: Events are mixed
If these were reaction time (RT) data, they would be equally statistically good. (The only concerns would be psychological).
But for fMRI designs, they are very different!

4. Power in linear models estimate standard error
Power: probability of detecting a true effect
Function of statistical, psychological, and physical constraints
Powerful designs maximize test statistics where true effects are present:
estimate
standard error
Psychological: Maximize true effect
Physical: Reduce error by reducing noise
Statistical: minimize estimation uncertainty due to design; maximize efficiency
See work by Dale, Henson, Liu, Friston, others

5. Design Efficiency To minimize standard error: Reduce noise
Make design more efficient
Efficient designs:
Maximize variance of predictors
Minimize covariance among predictors
In fMRI designs:
Formula is more complex, principle is the same
Factor in contrasts, filtering and autocorrelation
What is it?
A-optimality

6. Maximize variance of predictors
Maximize variation along x-axis of the plots below (Rescaling doesn’t count)
predicted
data
Balanced:
Max. x variance
predicted
data
No x variance
predicted
data
Low x variance
Principles:
Keep equal numbers in high and low predicted groups
Concentrate on extremes

7. Minimize covariance among predictors
Avoid confounds and partial confounds
Fully confounded
Fame
Sex Y N F M
Partial (low power)
Fame
Sex Y N F M
Orthogonal
Fame Y N
Sex F M

8. fMRI Data Hemodynamic response (HRF) is delayed and prolonged in time
Stimuli are often convolved with an HRF
Data is typically autocorrelated: low-frequency drift
Data and predictors are low-pass filtered
These two kinds of filtering operations make order and timing of stimuli critically important

9. Efficient (powerful) fMRI designs
Depends on what you’re trying to measure
Main effect (Task vs. implicit baseline)
Difference between conditions
Assumed HRF shape or estimates of shape
Can test different designs with efficiency metric
First discuss assumed shapes, then talk about estimating shape

10. Convolution refresher
Time (s) A B C D
Indicator functions
(onsets)
Assumed HRF
(Basis function)
Design Matrix (XT) A B C D
Time (s)
Time
Design Matrix (X) A B C D
Convolving with this HRF blurs high frequencies
Changes variance & covariance of predictors
Assumed “neural” event duration+shape, HRF shape, linear summation of responses to events

11. Blocked vs. ER power Consider Famous (red) vs. NonFamous (green)
predictors
Event
indicators
Block
Event-related

12. Blocked vs. ER power: higher contrast variance = higher power
Red-Green:
[1 -1] contrast
HIGH POWER
Red+Green
[1 1] “contrast”
LOW POWER
Block
Red-Green:
OK POWER
Event-related
Red+Green
OK POWER

13. Summary so far Block designs are efficient…if
Balance time on expt’l and control conditions, including rest

14. fMRI designs: Block length matters
Rise and fall:
High predictor variance means efficient design
2 sec blocks:
Too fast!
Signal is blurred away by convolution
50 sec blocks:
About the same

15. High-pass filtering Reduces noise Reduces efficiency
Removing low frequencies from design and data
Often done using nuisance covariates
Tradeoff in precision:
Reduces noise
Reduces efficiency

16. High-pass filtering fMRI Noise: Time domain Frequency domain
HP filter
1/60 =
.016 Hz
Unfiltered
Filtered

17. Efficiency in block designs
18 s blocks, 80 s filter
Filtering reduces efficiency…
(But you’re removing noise, too)
Best design depends on noise structure (and HRF)
Low autocorrelation: 18 s block, 80 s HP filter
Higher + autocorrelation: Shorter blocks (12 s) and 60 s filter

18. Summary so far Block designs are efficient…if
Balance time on expt’l and control conditions, including rest
Choose appropriate block length and filtering options

19. HRFs vary across regions
Checkerboard, n = 10
Thermal pain, n = 23
HRF shape depends on:
vasculature
time course of neural activity
Stimulus On
Aversive picture, n = 30
Aversive anticipation
See Schacter et al.
Aguirre et al.

20. How robust are blocked and ER designs to variation in HRF?
Depends on how HRF is modeled
ER designs can flexibly estimate HRF shapes, making them robust
First look at power when the predicted and actual HRFs don’t match
Then look at basis functions, which allow flexible estimation

21. HRF mismatch in blocked and ER designs
What happens when the true HRF does not match the assumed one?
Simple case: mis-specification of onsets

22. HRF mismatch in blocked and ER designs

23. Basis sets Image of predictors Data & Fitted Canonical Single HRF
HRF + derivatives
Finite Impulse Response (FIR)
Time (s)

24. Comparing efficiency for different design types
Block best for detection
M-sequence best for shape (Buracas et al.)
Event-related designs so-so on both
Optimized designs good tradeoff
Greve, OptSeq
Wager, Genetic Algorithm
Liu
Block,
16 s on/off
Theoretical limit
Optimized (GA)
Contrast detection power
Event-related
m-sequences
HRF shape estimation power

25. Summary so far Block designs are efficient…if
Balance time on expt’l and control conditions, including rest
Choose appropriate block length and filtering options
Get the HRF shape right for the brain area of interest
Event related designs are good for…
Flexible modeling of HRF shapes (both + and - for power)
Mixed/hybrid designs are good for…
Balancing power and shape estimation

26. Interpretability
Block designs do not inform about whether activity is related to specific psychological events
Case study: Face recognition; compare Famous-Nonfamous
3 s picture viewing
Recog: 250 ms
“I used to wear Batman underoos…”
“What was he in?”
“What a cool movie!”
“Get back on task”

27. Interpretability
Differences between famous and nonfamous faces in any of these processes could show up in block contrast
More face viewing time does not equal more power! Need time on task of interest
Recog: 250 ms
“I used to wear Batman underoos…”
“What was he in?”
“Get back on task”
“What a cool movie!”

28. Interpretability Blocking trials may change subjects’ strategy
Stroop task: “name the color of the print”
Control block: green yellow red blue
Experimental: red blue green yellow
Block: more word reading in control
Go-no go task: “press fast, but withhold if X” N P R S X X X X
Many tasks cannot be blocked

29. Interpretability
Block design power and interpretability depends on actual time on task (duty cycle)
Subjects should be doing the mental operation you want them to during the whole block
Case study: Error detection / correction
Researchers develop interference task with up to 25% errors
Researchers want power: “Let’s use a block design”
20 s blocks, 6 trials per block
Compare high error blocks (25%) vs. low (5%)

30. Interpretability: Case study
Block predictions would look like this:
But the true response in an error-selective brain region might look more like this:
The block design has high efficiency, but low power because it makes inaccurate predictions (r = 0.42)

31. Summary Block designs are efficient…if
Balance time on expt’l and control conditions, including rest
Choose appropriate block length and filtering options
Get the HRF shape right for the brain area of interest
Task performance & strategy are not context-sensitive
Event related designs are good for…
Flexible modeling of HRF shapes (both + and - for power)
Better identification of activity related to specific events
When unpredictability is important
Mixed designs are good for…
Balancing power and shape estimation

32. ER design practical advice
What is the best inter-trial interval (ITI)?
“Jitter” (include rest events) or no jitter?
1% rest events 41% rest events 81% rest events
ISI in sec
Efficiency of contrast [1 -1]
Assuming Linear Responses 2 4 6 10 14
Randomize order, present as fast as you can, no rest

33. fMRI data nonlinear at short ISIs
Meizin et al. (2000): 10% nonlinear saturation at 5 s ISI
Design
1,2,5,6,10 or 11 visual flashes, 1s ISI, then 30s rest
Note actual vs. predicted relative magnitude
Wager et al., 2005

34. ER design practical advice
Nonlinear response model
For A - B
About 5 s, on average, between reps of the same event, no rest
1% rest events 41% rest events 81% rest events
I like at least 4 s between events; conservative on linearity
Efficiency of contrast [1 -1]
For A + B
About s, on average, between events (I.e., use jitter) 2 4 6 10 14
ISI in sec
Wager & Nichols, 2003

35. Download the Genetic Algorithm toolbox at:
Thank you!
Download the Genetic Algorithm toolbox at:

36. Design efficiency in fMRI
Formula is more complex, principle is the same
Factor in contrasts, filtering and autocorrelation
Define: filtering matrix = K, autocorrelation matrix = V
Matrix whose rows contain a set of contrasts = C
filtered design matrix = Z
Z-: pseudoinverse of Z = inv(Z’Z)Z’ K * X = Z
Not equal to power, but can be converted to power given effect sizes
See Friston et al., 2000; Zarahn, 2001

37. Nonlinearity in BOLD signal

38. Pros and cons of blocking
+ High power, if parameters chosen correctly
+ Simple to implement
+ Relatively robust to changes in HRF shape
- Predictable events may change task strategy and activity patterns
- Cannot infer activity related to specific psychological events
- Power limited if Ss are not doing cognitive operation of interest throughout blocks