1. Basics of Experimental Design for fMRI: Event-Related Designs
Jody Culham
Brain and Mind Institute
Department of Psychology
Western University
Basics of Experimental Design for fMRI: Event-Related Designs
Last Update: October 27, 2014
Last Course: Psychology 9223, F2014, Western University

2. Event-Related Averaging
(can be used for block or event-related designs) 2

3. 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

4. Event-Related Averaging
Second, we compute an event related average for the gray condition

5. Event-Related Averaging
Third, we can plot the average ERA for the blue and gray conditions on the same graph

6. 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

7. But what if the curves don’t have the same starting point?
But what if the data looked like this?
…or this?
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

8. 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

9. File-based vs. Epoch-based Averaging
time courses may start at different points because different event histories or noise
Epoch-based Averaging
each curve starts at zero
can be risky with noisy data
only use it if trial histories are counterbalanced or ITI is very long
can yield very different conclusions than GLM stats
e.g., set EACH curve such that at time=0, %BSC=0
File-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

10. The Problem of Trial History: Cartoon Example
Hypothetical Data
HRF Model for Event 1
HRF Model for Event 2
What β weights would result?

11. The Problem of Trial History: Cartoon Example
Hypothetical Data
HRF Model for Event 1
HRF Model for Event 2
What β weights would result?

12. The Problem of Trial History: Cartoon Example
Hypothetical Data
HRF x β=2 for Event 1
HRF x β=-0 for Event 2

13. But remember the HRF may not fit our data well
Handwerker et al., 2004, Neuroimage
HRF model may not match individual subject’s HRF
errors are particularly problematic in undershoot phase

14. The Problem of Trial History: Cartoon Example
Hypothetical Data
HRF Model for Event 1
HRF Model for Event 2
What β weights would result?

15. The Problem of Trial History: Cartoon Example
Hypothetical Data
HRF x β=2 for Event 1
HRF x β=-0.5 for Event 2

16. The Problem of Trial History: Cartoon Example
Hypothetical Data
HRF Model for Event 1
HRF Model for Event 2
What β weights would result?

17. The Problem of Trial History: Cartoon Example
Hypothetical Data
HRF x β=1.9 for Event 1
HRF x β=0 for Event 2
What β weights would result?

18. The Problem of Trial or Block History
β estimates can be distorted because of imperfect HRF models
This problem is worse when events occur in close succession
The problem is affected by trial or block history

19. Solutions to the Problem of Trial History
use widely spaced events to allow activation to return to baseline between events
use perfectly counterbalanced orders of events to avoid systematic differences in trial history between conditions
remember conditions need to precede themselves too
use subject-specific HRF models
may still be imperfect
use solutions that don’t assume an HRF  deconvolution

20. Basics of Event-Related Designs20

21. 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
Initial Dip
Overshoot
Post-stimulus Undershoot 1 2 3
BOLD Response (% signal change)
Time
Stimulus
WRONG!!!!!
Jody

22. 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
Jody
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?

23. Predictor Height Depends on Stimulus Duration

24. Design Types Block Design Slow ER Design Rapid Jittered ER Design
= trial of one type
(e.g., face image)
Design Types
= trial of another type
(e.g., place image)
Block
Design
Slow ER
Design
Rapid
Jittered ER
Design
Jody
Mixed
Design

25. Detection vs. Estimation
detection: determination of whether activity of a given voxel (or region) changes in response to the experimental manipulation 1
estimation: measurement of the time course within an active voxel in response to the experimental manipulation
% Signal Change
Jody 4 8 12
Time (sec)
Definitions modified from: Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

26. Block Designs: Poor Estimation
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

27. Pros & Cons of Block Designs
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)
Jody

28. Slow Event-Related Designs
Slow ER
Design
Jody

29. Convolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown

30. BOLD Summates Neuronal Activity BOLD Signal
Slide adapted from Matt Brown

31. Terminology Trial 2 Trial 1 SD = stimulus duration
ITI = intertrial interval – time from offset of one trial to onset of the next
SOA = stimulus onset asynchrony = time from onset of one trial to the next

32. Slow Event-Related Design: Constant ITI
Bandettini et al. (2000)
What is the optimal trial spacing (duration + intertrial interval, ITI) for a Spaced Mixed Trial design with constant stimulus duration?
2 s stim
vary ISI
Block
Event-related average
Jody
Source: Bandettini et al., 2000

33. Optimal Constant ITI Brief (< 2 sec) stimuli:
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 slow event-related design:
= -35%
i.e., for 6 minutes of block design, run ~9 min slow ER design
Jody

34. Trial to Trial Variability
Huettel, Song & McCarthy, 2004,
Functional Magnetic Resonance Imaging

35. 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

36. Effect of Adding Trials
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

37. Pros & Cons of Slow ER Designs
excellent estimation
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
Example: Delayed Hand Actions
(Singhal et al., 2013)
Visual Response
Delay
Action
Execution
Grasp Go (G)
Reach Go (R)
Grasp Stop (GS)
Reach Stop (RS)
Action-related artifact
Really long delay: 18 s
Effect of this design on our subject
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
Jody

38. Pros & Cons of Slow ER Designs
excellent estimation
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
Example: Delayed Hand Actions
(Culham, 2004 vs. Singhal et al., 2013)
10-s delay
18-s delay
Effect of this design on our subject
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
Jody

39. “Do You Wanna Go Faster?”
Rapid
Jittered ER
Design
Tzvi
Yes, but we have to test assumptions regarding linearity of BOLD signal first

40. Linearity of BOLD response
“Do things add up?”
red = 2 - 1
green = 3 - 2
Sync each trial response to start of trial
Tzvi
Not quite linear
but good enough!
Source: Dale & Buckner, 1997

41. Linearity is okay for events every ~4+ s

42. Why isn’t BOLD totally linear?
In part because neurons aren’t totally linear either
“Phasic” (or “transient”) neural responses
Adaptation or habituation… stay tuned
May depend on factors like stimulus duration and stimulus intensity
Spikes/ms
Ganmor et al., 2010, Neuron
Time (ms)

43. Optimal Rapid ITI Rapid Mixed Trial Designs
Source: Dale & Buckner, 1997
Tzvi
Rapid Mixed Trial Designs
Short ITIs (~2 sec) are best for detection power
Do you know why?

44. Efficiency (Power) For more recommendations, see:

45. Two Approaches Detection – find the blobs
Business as usual
Model predicted activation using square-wave predictor functions convolved with assumed HRF
Extract beta weights for each condition; Contrast betas
Drawback: Because trials are packed so closely together, any misestimates of the HRF will lead to imperfect GLM predictors and betas
Estimation – find the time course
make a model that can estimate the volume-by-volume time courses through a deconvolution of the signal

46. 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

47. BOLD Overlap with Jittering
Neuronal activity from closely-spaced, jittered events
BOLD activity from closely-spaced, jittered events
Slide from Matt Brown

48. BOLD Overlap with Jittering
Neuronal activity from closely-spaced, jittered events
BOLD activity from closely-spaced, jittered events
Slide from Matt Brown

49. 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

50. Why jitter? Yields larger fluctuations in signal
When pink is on, yellow is off
 pink and yellow are anticorrelated
Includes cases when both pink and yellow are off  less anticorrelation
Without jittering predictors from different trial types are strongly anticorrelated
As we know, the GLM doesn’t do so well when predictors are correlated (or anticorrelated)

51. GLM: Tutorial data
Just as in the GLM for a block design, we have one predictor for each condition other than the baseline

52. GLM: Output
Faces > Baseline

53. Vary Intertrial Interval (ITI)
How to Jitter
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
TD = 2 s
ITI = 0 s
SOA = 2 s
TD = 2 s
ITI = 4 s
SOA = 6 s
Vary Intertrial Interval (ITI)
Stimulus Onset Asynchrony (SOA) = ITI + Trial Duration
may want to make TD (e.g., 2 s) and ITI durations (e.g., 0, 2, 4, 6 s) an integer multiple of TR (e.g., 2 s) for ease of creating protocol files
Frequency of ITIs
in Each Condition 2 4 6
ITI (s)
Flat Distribution
Exponential Distribution
Another way to think about it…
Include “Null” Trials
= null trial
(nothing happens)
Can randomize or counterbalance distribution of three trial types
Outcome may be similar to varying ISI

54. Assumption of HRF is More Problematic for Event-Related Designs
We know that the standard two-gamma HRF is a mediocre approximation for individual Ss’ HRFs
Handwerker et al., 2004, Neuroimage
We know this isn’t such a big deal for block designs but it is a bigger issue for rapid event-related designs.

55. 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

56. Algorithms for Picking Efficient Designs Optseq2

57. Algorithms for Picking Efficient Designs Genetic Algorithms

58. You Can’t Always Counterbalance
You may be interested in variables for which you can not control trial sequence
e.g., subject errors can mess up your counterbalancing
e.g., memory experiments: remembered vs. forgotten items
e.g., decision-making: choice 1 vs. choice 2
e.g., correlations with behavioral ratings

59. Post Hoc Trial Sorting Example
Wagner et al., 1998, Science

60. Pros & Cons of Applying Standard GLM to Rapid-ER Designs
high detection power
trials can be put in unpredictable order
subjects don’t get so bored
Cons and Caveats
reduced detection compared to block designs
requires stronger assumptions about linearity
BOLD is non-linear with inter-event intervals < 6 sec.
Nonlinearity becomes severe under 2 sec.
errors in HRF model can introduce errors in activation estimates

61. Design Types Mixed Design = trial of one type (e.g., face image)
= trial of another type
(e.g., place image)
Mixed
Design

62. 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

63. Pros and Cons of Mixed Designs
allow researchers to distinguish between state-related and item-related activation
Cons
sensitive to errors in HRF modelling

64. Deconvolution of Event-Related Designs Using the GLM

65. Two Approaches Detection – find the blobs
Business as usual
Model predicted activation using square-wave predictor functions convolved with assumed HRF
Extract beta weights for each condition; Contrast betas
Drawback: Because trials are packed so closely together, any misestimates of the HRF will lead to imperfect GLM predictors and betas
Estimation – find the time course
make a model that can estimate the volume-by-volume time courses through a deconvolution of the signal

66. Convolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown

67. 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

68. DEconvolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown

69. Deconvolution Example
time course from 4 trials of two types (pink, blue) in a “jittered” design

70. Summed Activation

71. Single Stick Predictor (stick predictors are also called finite impulse response (FIR) functions)
single predictor for first volume of pink trial type

72. Predictors for Pink Trial Type
set of 12 predictors for subsequent volumes of pink trial type
need enough predictors to cover unfolding of HRF (depends on TR)

73. Predictor Matrix
Diagonal filled with 1’s .

74. Predictors for Pink Trial Type

75. Predictors for the Blue Trial Type

76. Predictor x Beta Weights for Pink Trial Type
sequence of beta weights for one trial type yields an estimate of the average activation (including HRF)

77. Predictor x Beta Weights for Blue Trial Type
height of beta weights indicates amplitude of response (higher betas = larger response)

78. Overview

79. A Little Math Problem
x + y + z = 9 What are x and y and z?

80. Another Little Math Problem
x + y = 6 x + z = 7 z + y = 5 What are x and y and z?

81. Solution to Another Little Math Problem
x + y = 6 x + z = 7 z + y = 5 What are x and y and z? y = 6 - x z = 7 - x (7-x) + (6-x) = 5 13 – 2x = 5 2x = 13 – 5 = 8 x = 4 y = 6 – x = 6 – 4 = 2 z = 7 – x = 7 – 4 = 3

82. Comparisons of Two Problems
x + y + z = 9
x + y = 6
x + z = 7
z + y = 5
three unknowns
one equation
unsolvable!
three unknowns
three equations
solvable!

83. Why Jitter? Solvable Deconvolution
Miezen et al. 2000

84. Decon GLM
To find areas that respond to all stims, we could fill the contrast column with +’s
14 predictors (time points) for Cues
14 predictors (time points) for Face trials
…but that would be kind of dumb because we don’t expect all time points to be highly positive, just the ones at the peak of the HRF
14 predictors (time points) for House trials
14 predictors (time points) for Object trials

85. Contrasts on Peak Volumes
We can search for areas that show activation at the peak (e.g., 3-5 s after stimulus onset

86. Results: Peaks > Baseline

87. Graph beta weights for spike predictors  Get deconvolution time course
Why go to all this bother? Why not just generate an event-related average? …

88. Pros and Cons of Deconvolution
Produces time course that dissociates activation from trial history
Does not assume specific shape for hemodynamic function
Robust against trial history biases (though not immune to it)
Compound trial types possible (e.g., stimulus-delay-response)
may wish to include “half-trials” (stimulus without response)
Cons:
Complicated
Quite sensitive to noise
Contrasts don’t take HRF fully into account, they just examine peaks

89. Not Mutually Exclusive
Convolution and deconvolution GLMs are not mutually exclusive
Example
use convolution GLM to detect blobs, use deconvolution to estimate time courses

90. Design Types Block Design Slow ER Design Rapid Jittered ER Design
= trial of one type
(e.g., face image)
Design Types
= trial of another type
(e.g., place image)
Block
Design
Slow ER
Design
Rapid
Jittered ER
Design
Jody
Mixed
Design

91. Take-home message Block designs Slow ER designs Fast ER designs
Great detection, poor estimation
Slow ER designs
Poor detection, great estimation
Fast ER designs
Good detection, very good estimation
Excellent choice for designs where predictability is undesirable or where you want to factor in subject’s behavior