Basics of Experimental Design for fMRI: Event-Related Designs Jody Culham Brain and Mind Institute Department of Psychology Western University http://www.fmri4newbies.com/ Basics of Experimental Design for fMRI: Event-Related Designs Last Update: October 27, 2014 Last Course: Psychology 9223, F2014, Western University

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

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 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

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

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

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

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

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

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

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

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

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

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

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?

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

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

Basics of Event-Related Designs 20

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

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?

Predictor Height Depends on Stimulus Duration

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

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

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

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

Slow Event-Related Designs Slow ER Design Jody

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

BOLD Summates Neuronal Activity BOLD Signal Slide adapted from Matt Brown

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

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

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

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

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

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

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

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

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

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

Linearity is okay for events every ~4+ s

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)

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?

Efficiency (Power) For more recommendations, see: http://imaging.mrc-cbu.cam.ac.uk/imaging/DesignEfficiency

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

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 Detection A) BOLD Signal B) Individual Haemodynamic Components C) 2 Predictor Curves for use with GLM (summation of B) Slide from Matt Brown

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)

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

GLM: Output Faces > Baseline

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

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.

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

Algorithms for Picking Efficient Designs Optseq2

Algorithms for Picking Efficient Designs Genetic Algorithms

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

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

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

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

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 allow researchers to distinguish between state-related and item-related activation Cons sensitive to errors in HRF modelling

Deconvolution of Event-Related Designs Using the GLM

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

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

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

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

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

Summed Activation

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

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)

Predictor Matrix Diagonal filled with 1’s .

Predictors for Pink Trial Type

Predictors for the Blue Trial Type

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)

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

Overview

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

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

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

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!

Why Jitter? Solvable Deconvolution Miezen et al. 2000

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

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

Results: Peaks > Baseline

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

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

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

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

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