1. Rapid-Presentation Event-Related Design for fMRI
Douglas N. Greve
Copywrite Douglas N. Greve, 2002.

2. Outline What is Event-Related Design? Fixed-Interval Event-Related
Rapid-Presentation (Jittered) Event-Related
Efficiency and Event Scheduling
Mathematical Basis
optseq – a tool for RPER design (
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

3. Dispersion
Dispersion is the spreading out of the response over time, usually far beyond the end of the stimulus
How closely can one event follow another?
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

4. Event-Related fMRI Estimate response from a single event type
cf Blocked Design (Habituation, Expectation, Set, Power)
Randomize Schedule (Order and Timing)
Post-Hoc Event Sorting
Multimodal Integration (EEG/MEG,Behavioral)
Fixed Interval and Rapid Presentation (Jittered/Stochastic)
Results from a single voxel in visual cortex to a 3 second stimulus (shown in green). Not like EEG/MEG where response is finished after a few hundred ms. How closely can trials/events be placed and still be able to differentiate their responses? This data is the average of 212 responses.
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

5. Event vs Event Type Three Event Types (yellow, red, green)
Number of Events (Repetitions) per Event Type
Yellow: 2
Red: 2
Green: 3
Two events belong to the same Event Type if, by hypothesis, they have the same response (violations are treated as noise).
Event Type = Condition = Trial Type = Explanatory Variable
Event = Stimulus = Trial
An event is a single presentation of a stimulus (also called a trial or presentation). An Event Type is a hypothetical construct. Events are classified as certain event types, either a priori or depend upon the subject response (post hoc event sorting). All events classified as a given event type are assumed to have the same hemodynamic response, and differences are treated as noise.
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

6. Event Schedule Description of which event is presented when
time code duration label
yellow
red
red
green
Time is the accumulated time since onset of scanning run
Code unique numeric id
Output of optseq
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

7. Fixed-Interval Event-Related
12-20s
Push trials apart enough to prevent overlap.
Interval fixed at minimum is most efficient.
Random Sequence (Counter-balanced)
Allows Post-Hoc Stimulus Definition
Mitigates Habituation, Expectation (?), and Set
Inflexible/Inefficient/Boring
Good if limited by number of stimuli (not scanning time)
Blue bar is length of typical block from blocked design. Raw signal still interpretable. Assumption: time-invariant response. Not very many presentations. Most efficient without overlap is fixed at minimum time needed to prevent overlap.
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

8. Rapid-Presentation Event-Related
Closely Spaced Trials (Overlap!)
Raw signal uninterpretable
Random Sequence and Schedule
Highly resistant to habituation, set, and expectation
Jitter = “Random” Inter-Stimulus Interval (ISI/SOA)
It is possible to present stimuli so close to each other that they overlap and still distinguish between average hemodynamic responses. Must observe all levels of overlap. Raw signal uninterpretable.
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

9. Scheduling and Efficiency
B: N=10
C: N=10
Efficiency is statistical power/SNR/CNR per acquisition
Efficiency increases with N (number of observations)
Efficiency decreases with overlap
Efficiency increases with differential overlap
Choose schedule with optimum efficiency before scanning
Why is rapid-presentation more efficient than fixed-interval? Three designs: A, B, and C all within a fixed scanning interval. A has no overlap but only N=5. B has N=10 but no differential overlap. C has N=10 and differential overlap. Larger the N, the lower the ISI.
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

10. Mathematical Concepts
Forward Model
(X = design matrix)
Inverse Model
Y is the Ntp-by-1 observable, X is the Ntp-by-Nbeta design matrix (the schedule is imbedded in X), beta is the Nbeta-by-1 vector of estimates relating to the model of the hemodynamic response.
Residual Error
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

11. Contrast, Contrast Vector
(or Matrix), Contrast Effect Size, COPE (FSL)
t-Ratio
Efficiency
C is the contrast vector/matrix (number of columns equals the number of elements in beta), gamma is the (scalar) contrast effect size. The efficiency and variance reduction factor (VRF) are related. The VRF of the ith component directly relates to the ability to detect a difference between the ith component of beta and baseline. For the ith component, the VRF is can be computed from 1/C*inv(XtX)Ct, where C is a vector of zeros except at the ith component. The VRF is the factor by which the residual error variance is reduced in the t-ratio. For a contrast vector, the efficiency and VRF are the same. If a contrast matrix is used, then the efficiency/VRF are essentially a weighted combination of all contrast vectors. Basic Idea: Try to make columns of X (ie, regressors) as orthogonal as possible.
Variance Reduction Factor
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

12. Where does jitter come from? (What’s a Null Condition?)
“Null” condition – fixation cross or dot
By hypothesis, no response to null
Insert random amounts of null between task conditions
Differential ISI = Differential Overlap A + B A + A B A + + B + B A
The null condition is not a condition. Conditions A and B with fixation (+). Yellow bars indicate the ISI between A trials. Red bars indicate ISI between B trials. Green bars indicate ISI from A to B. Differential overlap can come from non-adjacent presentations. Zero ISI. No bars between null and A or B because null is not a condition.
Time
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

13. Design Parameters (optseq)
TR – time between volume acquisition (temporal resolution).
Ntp – number of time points (TRs, frames, volumes, …)
Nc – number of event types (conditions)
Npc – number of events/repetitions of each event type (can vary across event types)
Tpc – duration of each event type (can vary across event types)
Schedule – event onset time and identity
Event Response Model – FIR Post-Stimulus Delay Window (needed for optimization)
All these parameters need to be set in order to actually run an experiment. These parameters are interrelated. Several constraints are described on the following slides.
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

14. Time Constraints
Total Scan Time = Ntp * TR A B C +
Ta = Na*Tpa
Tb = Nb*Tpb
Tc = Nc*Tpc
Null Time
Total Stimulation Time
Three task conditions (A,B,C) plus a null condition. The colored bars show the total amount of time allocated to each event type (ie, they do not represent single presentations). There are two points to be made here. First, the total amount of stimulation time cannot exceed the total scan time (the Time Constraint). Second, the amount of time not allocated to task-related stimulation is given to the Null Stimulus. The Null Stimulus time will be randomly chopped up and inserted between the task stimuli. Thus, the amount of Null Time affects/dictates the average interval between task stimuli. The design efficiency will be affected by the amount of Null Time; the Null Time resulting in the maximum efficiency is unknown, but will roughly occur when the Null Time is equal to average stimulation time of the task-related conditions.
Total Stimulation Time Cannot Exceed Total Scan Time
How much Null Time is needed? Rule of thumb: same as any other task condition (or the average of the task conditions).
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

15. Event Response Model (FIR)
PSD=0
PSDMin
PSDMax
dPSD
PSD: Post-Stimulus Delay (PSD = 0 = Stimulus Onset)
PSDMin: Response is zero for PSD < PSDMin
PSDMax: Response is zero for PSD > PSDMax
PSD Window should be long enough to capture response
Response can be anything in between (FIR model)
dPSD: sets basic temporal resolution for schedule
DOF Constraint: Nbeta = nPSD*Nc < Ntp
The DOF constraint requires that the number of estimates (Nbeta) be less than the number of observations. Why use an FIR?
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

16. Other optseq Parameters/Options
Getting help: optseq2 --help
Search termination criteria: nsearch/tsearch
Output files (and format)
Optimizing over number of repetitions
Nuisance variables (polynomial drift terms)
Cost Functions
First-Order Counter-Balancing Pre-optimization
To come: contrasts and non-FIR
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve

17. Rapid-Presentation Properties
Efficient (not as efficient as blocked)
Can distinguish responses despite overlap
Highly resistant to habituation, set, and expectation
Flexible timing (Behavioral, EEG, MEG)
Linear overlap assumption
Analysis: Selective Averaging/Deconvolution (GLM)
Schedule Optimization Tool (optseq)
Rapid-Presenation Event-related Design for fMRI -- Douglas N. Greve