: To Block or Not to Block?

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

2. Experimental (A) - Control (B) What we want from a design • 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 • Power: Can I detect results?

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. estimate standard error Power in linear models • Power: probability of detecting a true effect • Function of statistical, psychological, and physical constraints • Powerful designs maximize test statistics where true effects are present: • 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. Reduce noise • Make design more efficient Design Efficiency • To minimize standard error: 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. Balanced: Max. x variance No x variance Low x variance data data data predicted predicted predicted Maximize variance of predictors • Maximize variation along x-axis of the plots below (Rescaling doesn’t count) • Principles: • Keep equal numbers in high and low predicted groups • Concentrate on extremes

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

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. Indicator functions (onsets) Assumed HRF (Basis function) Design Matrix (XT) Design Matrix (X) A B C D A A B B Time C C D D Time (s) Time (s) Convolution refresher • 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. predictors Block Event indicators Event-related Blocked vs. ER powerConsider Famous (red) vs. NonFamous (green)

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

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

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

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

16. 60 s HP filter 1/60 = .016 Hz High-pass filtering Frequency domain fMRI Noise: Time domain 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. Image of predictors Data & Fitted Canonical Single HRF HRF + derivatives Finite Impulse Response (FIR) Basis sets 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. 3 s picture viewing “I used to wear Batman underoos…” “What a cool movie!” Interpretability • Block designs do not inform about whether activity is related to specific psychological events • Case study: Face recognition; compare Famous-Nonfamous Recog: 250 ms “What was he in?” “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 “I used to wear Batman underoos…” Recog: 250 ms “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: greenyellowredblue • Experimental: redbluegreenyellow 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. Assuming Linear Responses 1% rest events41% rest events81% rest events Efficiency of contrast [1 -1] ISI in sec 2 4 6 10 14 ER design practical advice • What is the best inter-trial interval (ITI)? • “Jitter” (include rest events) or no jitter? 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 events41% rest events81% rest events I like at least 4 s between events; conservative on linearity Efficiency of contrast [1 -1] For A + B About 16-20 s, on average, between events (I.e., use jitter) 2 4 6 10 14 ISI in sec Wager & Nichols, 2003

35. Thank you! Download the Genetic Algorithm toolbox at: http://www.columbia.edu/cu/psychology/tor/

36. = * K * X = Z 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’ • 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