Basics of Experimental Design for fMRI: Event-Related Designs Last Update: January 18, 2012 Last Course: Psychology 9223,

Basics of Experimental Designfor fMRI:

Event-Related Designs

http://www.fmri4newbies.com/

Last Update: January 18, 2012Last Course: Psychology 9223, W2010, University of Western Ontario

Jody CulhamBrain and Mind Institute

Department of PsychologyUniversity of Western Ontario

Part III

Choosing an Event-Related Design

Convolution of Single Trials

Neuronal Activity

Haemodynamic Function

BOLD Signal

Time

Time

Slide from Matt Brown

BOLD Summates

Neuronal Activity BOLD Signal

Slide from Matt Brown

BOLD Overlap and Jittering

• Closely-spaced haemodynamic impulses summate.

• Constant ITI causes tetanus.

Burock et al. 1998.

Design TypesBlock

Design

Slow ERDesign

RapidCounterbalanced

ER Design

RapidJittered ER

Design

MixedDesign

= null trial (nothing happens)

= trial of one type (e.g., face image)

= trial of another type (e.g., place image)

Block Designs

Early Assumption: Because the hemodynamic response delays and blurs the response to activation, the temporal resolution of fMRI is limited.

= trial of one type (e.g., face image)

= trial of another type (e.g., place image)

WRONG!!!!!

BlockDesign

Positive BOLD response

InitialDip

OvershootPost-stimulusUndershoot

0

1

2

3

BO

LD R

espo

nse

(% s

igna

l cha

nge)

Time

Stimulus

What are the temporal limits?What is the briefest stimulus that fMRI can detect?

Blamire et al. (1992): 2 secBandettini (1993): 0.5 secSavoy et al (1995): 34 msec

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?

Data: Blamire et al., 1992, PNASFigure: Huettel, Song & McCarthy, 2004

2 s stimulisingle events

Data: Robert Savoy & Kathy O’CravenFigure: Rosen et al., 1998, PNAS

Detection vs. Estimation

• detection: determination of whether activity of a given voxel (or region) changes in response to the experimental manipulation

Definitions modified from: Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

% S

ign

al C

ha

ng

e

0

Time (sec)

0 4 8 12

1

• estimation: measurement of the time course within an active voxel in response to the experimental manipulation

Block Designs: Poor Estimation

Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

Pros & Cons of Block Designs

Pros• 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)

Slow Event-Related Designs

Slow ERDesign

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?

Block

2 s stimvary ISI

Sync with trial onset and average

Source: Bandettini et al., 2000

Optimal Constant ITI

Brief (< 2 sec) stimuli:optimal trial spacing = 12 sec

For longer stimuli:optimal trial spacing = 8 + 2*stimulus duration

Effective loss in power of event related design:= -35%i.e., for 6 minutes of block design, run ~9 min ER design

Source: Bandettini et al., 2000

Trial to Trial Variability

Huettel, Song & McCarthy, 2004,Functional Magnetic Resonance Imaging

How Many Trials Do You Need?

• 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

Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

Effect of Adding Trials

Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

Pros & Cons of Slow ER DesignsPros• good estimation power• allows accurate estimate of baseline activation

and deviations from it• 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

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

Hand motionartifact

% s

igna

l cha

nge

Time

Activation

“Do You Wanna Go Faster?”

• Yes, but we have to test assumptions regarding linearity of BOLD signal first

RapidJittered ER

Design

MixedDesign

RapidCounterbalanced

ER Design

Linearity of BOLD response

Source: Dale & Buckner, 1997

Linearity:“Do things add up?”

red = 2 - 1

green = 3 - 2

Sync each trial response to start of trial

Not quite linear but good enough!

Optimal Rapid ITI

Rapid Mixed Trial DesignsShort ITIs (~2 sec) are best for detection power

Do you know why?

Source: Dale & Buckner, 1997

Efficiency (Power)

Design Types= trial of one type (e.g., face image)

= trial of another type (e.g., place image)

RapidCounterbalanced

ER Design

Detection with Rapid ER Designs

• To detect activation differences between conditions in a rapid ER design, you can create HRF-convolved reference time courses

• You can perform contrasts between beta weights as usual

Figure: Huettel, Song & McCarthy, 2004

Variability Between Subjects/Areas

• greater variability between subjects than between regions

• deviations from canonical HRF cause false negatives (Type II errors)

• Consider including a run to establish subject-specific HRFs from robust area like M1

Handwerker et al., 2004, Neuroimage

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

Event-Related Averaging

Second, we compute an event related average for the gray condition

Event-Related Averaging

Third, we can plot the average ERA for the blue and gray conditions on the same graph

Event-Related Averaging in BV

Define which subjects/runs to include

Define which conditions to average (usually exclude baseline)

Set time window

Determine how you want to define the y-axis values, including zero

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.

But what if the curves don’t have the same starting point?

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

But what if the data looked like this?

…or this?

Epoch-based averaging

In the latter two cases, we could simply shift the curves so they all start from the same (zero) baseline

FILE-BASED AVERAGING: zero baseline determined across all conditions (for 0 to 0: points in red circles)

EPOCH-BASED AVERAGING: zero baselines are specific to each epoch

File-based vs. Epoch-based Averaging

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

time courses may start at different points because different event histories or noise

0

Epoch-based Averaging• each curve starts at zero

• can be risky with noisy data

• only use it if you are fairly certain your pre-stim baselines are valid (e.g., you have a long ITI and/or your trial orders are counterbalanced)

• can yield very different conclusions than GLM stats

e.g., set EACH curve such that at time=0, %BSC=0

0

0

What if…?• This design has the benefit that each condition epoch is preceded

by a baseline, which is nice for making event-related averages

• However, we might decide that this design takes too much time because we are spending over half of the time on the baseline.

• Perhaps we should use the following paradigm instead…?

• This regular triad sequence has some nice features, but it can make ERAs more complicated to understand.

Regular Ordering and ERAs• We might have a time course that looks like this

Example of ERA Problems• If you make an ERA the usual way, you might get something that

looks like this:

• Initially some people can be confused how to interpret this ERA because the pre-event activation looks wonky.

Intact

Scrambled

Fixation

One common newbie mistake is to make

ERAs for all conditions, including

the baseline (Fixation).

This situation will illustrate some of the confusion with that

File-Based (Pre=2, Post=10, baseline 0 to 0)

Example of ERA Problems

• If you make the ERA over a longer time window, the situation becomes clearer. • You have three curves that are merely shifted in time with respect to one

another.

File-Based (Pre=2, Post=10, baseline 0 to 0) File-Based (Pre=8, Post=18, baseline 0 to 0)

Example of ERA Problems

• Now you should realize that the different pre-epoch baselines result from the fact that each condition has different preceding conditions– Intact is always preceded by Fixation– Scrambled is always preceded by Intact– Fixation is always preceded by Scrambled

Intact

Scrambled

Fixation

End ofIntact

End of Scrambled

End of Fixation

File-Based (Pre=2, Post=10, baseline 0 to 0)

Example of ERA Problems

• Because of the different histories, changes with respect to baseline are hard to interpret. Nevertheless, ERAs can show you how much the conditions differed once the BOLD response stabilized

– This period shows, rightly so, Intact > Scrambled > Fixation

Intact

Scrambled

Fixation

File-Based (Pre=2, Post=10, baseline 0 to 0)

Example of ERA Problems

• Because the pre-epoch baselines are so different (due to differences in preceding conditions), here it would be really stupid to do epoch-based averaging (e.g., with x=-2 as the y=0 baseline)

• In fact, it would lead us to conclude (falsely!) that there was more activation for Fixation than for Scrambled

Epoch-Based (Pre=2, Post=10, baseline -2 to -2)

Example of ERA Problems• In a situation with a regular sequence like this, instead of making an ERA with a short time window and

curves for all conditions, you can make one single time window long enough to show the series of conditions (and here you can also pick a sensible y= 0 based on x=-2)

Intact Scrambled FixationFile-Based average for Intact condition only (Pre=2, Post23, baseline -2 to -2)

Partial confounding

• We can also run into problems (less obvious but with the same ERA issues) if the histories of conditions are partially confounded (e.g., quasi-random orders)

• In the case we just considered, the histories for various conditions were completely confounded

– Intact was always preceded by Fixation– Scrambled was always preceded by Intact– Fixation was always preceded by Scrambled

• Intact is preceded by Scrambled 3X and by Fixation 3X• Scrambled is preceded by Intact 4X and Fixation 1X• Fixation is preceded by Intact 2X, by Scrambled 2X and

by nothing 1X• No condition is ever preceded by itself

The Problem of Trial/Block History

This problem also occurs for single trial designs.

This problem also occurs even if the history is only partially confounded (e.g., if Condition A is preceded by Condition X twice as often as Condition B is preceded by Condition X).

If we knew with certainty what a given subject’s HRF looked like, we could model it (but that’s rarely the case).

Thus we have only two solutions: 1) Counterbalance trial history so that each curve should start with the

same baseline2) Jitter the intertrial intervals so that we can estimate the HRF

• more on this in analysis when we talk about deconvolution

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

Analysis of Single Trials with Counterbalanced Orders

Approach used by Kourtzi & Kanwisher (2001, Science) for pre-defined ROI’s:

• for each trial type, compute averaged time courses synced to trial onset; then subtract differences

…

Raw dataEvent-related average

with control period factored out

A signal change = (A – F)/F

B signal change = (B – F)/F

Event-related average

sync to trial onset

A

B

F

Pros & Cons of Counterbalanced Rapid ER Designs

Pros

• high detection power with advantages of ER designs (e.g., can have many trial types in an unpredictable order)

Cons and Caveats

• reduced detection compared to block designs

• estimation power is better than block designs but not great

• accurate detection requires accurate HRF modelling

• counterbalancing only considers one or two trials preceding each stimulus; have to assume that higher-order history is random enough not to matter

• what do you do with the trials at the beginning of the run… just throw them out?

• you can’t exclude error trials and keep counterbalanced trial history

• you can’t use this approach when you can’t control trial status (e.g., items that are later remembered vs. forgotten)

Design Types

RapidJittered ER

Design

= trial of one type (e.g., face image)

= trial of another type (e.g., place image)

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

BOLD Overlap with Jittering

Neuronal activity from closely-spaced, jittered events

BOLD activity from closely-spaced, jittered events

Slide from Matt Brown

BOLD Overlap with Jittering

Neuronal activity from closely-spaced, jittered events

BOLD activity from closely-spaced, jittered events

Slide from Matt Brown

Fast fMRI DetectionA) BOLD Signal

B) Individual Haemodynamic Components

C) 2 Predictor Curves for use with GLM (summation of B)

Slide from Matt Brown

Post Hoc Trial Sorting Example

Wagner et al., 1998, Science

Algorithms for Picking Efficient DesignsOptseq2

Algorithms for Picking Efficient DesignsGenetic Algorithms

Design Types

MixedDesign

= trial of one type (e.g., face image)

= trial of another type (e.g., place image)

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

Pros and Cons of Mixed Designs

Pros• allow researchers to distinguish between state-

related and item-related activation

Cons• sensitive to errors in HRF modelling

EXTRA SLIDES

A Variant of Mixed Designs: Semirandom Designs

• a type of event-related design in which the probability of an event will occur within a given time interval changes systematically over the course of an experiment

First period:P of event: 25%

Middle period:P of event: 75%

Last period:P of event: 25%

• probability as a function of time can be sinusoidal rather than square wave

Pros and Cons of Semirandom Designs

Pros• good tradeoff between detection and estimation• simulations by Liu et al. (2001) suggest that semirandom

designs have slightly less detection power than block designs but much better estimation power

Cons• relies on assumptions of linearity• complex analysis• “However, if the process of interest differs across ISIs, then the

basic assumption of the semirandom design is violated. Known causes of ISI-related differences include hemodynamic refractory effects, especially at very short intervals, and changes in cognitive processes based on rate of presentation (i.e., a task may be simpler at slow rates than at fast rates).”

-- Huettel, Song & McCarthy, 2004