Spatial and Temporal Limits of fMRI

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Spatial and Temporal Limitsof fMRI
Jody Culham Department of Psychology University
of Western Ontario
http//www.fmri4newbies.com/
Last Update November 29, 2008 fMRI Course,
Louvain, Belgium
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Spatial Limits of fMRI
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fMRI in the Big Picture
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What Limits Spatial Resolution

• noise
• smaller voxels have lower SNR
• head motion
• the smaller your voxels, the more contamination
  head motion induces
• temporal resolution
• the smaller your voxels, the longer it takes to
  acquire the same volume
• 4 mm x 4 mm at 16 slices/sec
• OR 1 mm x 1 mm at 1 slice/sec
• vasculature
• depends on pulse sequences
• e.g., spin echo sequences reduce contributions
  from large vessels
• some preprocessing techniques may reduce
  contribution of large vessels (Menon, 2002, MRM)

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Ocular Dominance Columns

• Columns on the order of 0.5 mm have been
  observed with fMRI

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Submillimeter Resolution
vein
Stria of Gennari (Layer IV)
Gradient Echo Functional (superficial
activation includes vessels)
Spin Echo Functional (activation localized to
Layer IV)
Spin Echo Anatomical
Gradient Echo Anatomical

• Goenze, Zappe Logothetis, 2007, Magnetic
  Resonance Imaging
• anaesthetized monkey 4.7 T contrast agent
  (MION)
• 0.3 x 0.3 x 2 mm

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Temporal Limits of fMRIANDEvent-Related
Averaging
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Sampling Rate
Huettel, Song McCarthy, 2004, Functional
Magnetic Resonance Imaging
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BOLD Time Course
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Evolution of BOLD Response
Hu et al., 1997, MRM
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Event-Related Averaging
In this example an event is the start of a block
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Event-Related Averaging
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Event-Related Averaging
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Event-Related Averaging
Zero average signal intensity in first volume
of all 8 events
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Event-Related Averaging
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Event-related Averaging

• File-based
• 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

• Epoch-based
• 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 or your trial orders are
  counterbalanced)
• can give very different results from GLM stats

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Convolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown
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BOLD Summates
Neuronal Activity
BOLD Signal
Slide from Matt Brown
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BOLD Overlap and Jittering

• Closely-spaced haemodynamic impulses summate.
• Constant ITI causes tetanus.

Burock et al. 1998.
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Design Types
null trial (nothing happens)
trial of one type (e.g., face image)
trial of another type (e.g., place image)
Block Design
Slow ER Design
Rapid Counterbalanced ER Design
Rapid Jittered ER Design
Mixed Design
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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.

WRONG!!!!!
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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 OCraven Figure Rosen
et al., 1998, PNAS
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?
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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
0
0
4
8
12
Time (sec)
Definitions modified from Huettel, Song
McCarthy, 2004, Functional Magnetic Resonance
Imaging
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Block Designs Poor Estimation
Huettel, Song McCarthy, 2004, Functional
Magnetic Resonance Imaging
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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
• cant look at effects of single events (e.g.,
  correct vs. incorrect trials, remembered vs.
  forgotten items)
• becomes unmanagable with too many conditions (4
  conditions baseline is about the max I will use
  in one run)

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Slow Event-Related Designs
Slow ER Design
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Spaced Mixed Trial 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
Source Bandettini et al., 2000
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Optimal Constant ITI
Source Bandettini et al., 2000
Brief (lt 2 sec) stimuli optimal trial spacing
12 sec For longer stimuli optimal trial spacing
8 2stimulus duration Effective loss in
power of event related design -35 i.e., for 6
minutes of block design, run 9 min ER design
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Trial to Trial Variability
Huettel, Song McCarthy, 2004, Functional
Magnetic Resonance Imaging
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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

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Effect of Adding Trials
Huettel, Song McCarthy, 2004, Functional
Magnetic Resonance Imaging
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Pros Cons of Slow ER Designs

• Pros
• 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

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Can we go faster?!

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

Rapid Counterbalanced ER Design
Rapid Jittered ER Design
Mixed Design
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Linearity of BOLD response
Linearity Do things add up?
Not quite linear but good enough!
Source Dale Buckner, 1997
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Optimal Rapid ITI
Source Dale Buckner, 1997
Rapid Mixed Trial Designs Short ITIs (2 sec) are
best for detection power Do you know why?
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Design Types
trial of one type (e.g., face image)
trial of another type (e.g., place image)
Rapid Counterbalanced ER Design
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Detection with Rapid ER Designs
Figure Huettel, Song McCarthy, 2004

• 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

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Variability of HRF Between Subjects

• Aguirre, Zarahn DEsposito, 1998
• HRF shows considerable variability between
  subjects

different subjects

• Within subjects, responses are more consistent,
  although there is still some variability between
  sessions

same subject, same session
same subject, different session
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Variability of HRF Between Areas

• Possible caveat HRF may also vary between areas,
  not just subjects
• Buckner et al., 1996
• noted a delay of .5-1 sec between visual and
  prefrontal regions
• vasculature difference?
• processing latency?
• Bug or feature?
• Menon Kim mental chronometry

Buckner et al., 1996
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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
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The Problem of Trial History
Activation
Activation
WARNING This slide is confusing, needs to be
redone. Supposed to show that yellowgtredgtwhite,
not just because of trial summation
Time
Time
Event-related average is wonky because trial
types differ in the history of preceding trials

• Estimation does not work well if trial history
  differs between trial types
• Two options
• Control trial history by making it the same for
  all trial types
• Model the trial history by deconvolving the
  signal (requires jittered timing)

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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

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Analysis of Single Trials with Counterbalanced
Orders

• Approach used by Kourtzi Kanwisher (2001,
  Science) for pre-defined ROIs
• for each trial type, compute averaged time
  courses synced to trial onset then subtract
  differences

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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 cant exclude error trials and keep
  counterbalanced trial history
• you cant use this approach when you cant
  control trial status (e.g., items that are later
  remembered vs. forgotten)

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Design Types
trial of one type (e.g., face image)
trial of another type (e.g., place image)
Rapid Jittered ER Design
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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
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BOLD Overlap with Jittering
Neuronal activity from closely-spaced, jittered
events
BOLD activity from closely-spaced, jittered events
Slide from Matt Brown
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BOLD Overlap with Jittering
Neuronal activity from closely-spaced, jittered
events
BOLD activity from closely-spaced, jittered events
Slide from Matt Brown
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Fast fMRI Detection
Slide from Matt Brown
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Post Hoc Trial Sorting Example
Wagner et al., 1998, Science
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Fast fMRI Detection

• Pros
• Incorporates prior knowledge of BOLD signal form
• affords some protection against noise
• Easy to implement
• Can do post hoc sorting of trial type
• Cons
• Vulnerable to inaccurate hemodyamic model
• No time course produced independent of assumed
  haemodynamic shape

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Fast fMRI Estimation

• We can detect fMRI activation in rapid event
  related designs in the same way that we do for
  other designs (block design, slow event related
  design
• For any kind of event-related designs, it is very
  important to have a resonably accurate model of
  the HRF
• In addition, with rapid event related designs, we
  can also estimate time courses using a technique
  called deconvolution

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

• time course from 4 trials of two types (pink,
  blue) in a jittered design

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Summed Activation
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Single Stick Predictor

• single predictor for first volume of pink trial
  type

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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)

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Predictor Matrix

• Diagonal filled with 1s

. . .
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Predictors for the Blue Trial Type

• set of 12 predictors for subsequent volumes of
  blue trial type

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Linear Deconvolution
Miezen et al. 2000

• Jittering ITI also preserves linear independence
  among the hemodynamic components comprising the
  BOLD signal.

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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)

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Predictor x Beta Weights for Blue Trial Type

• height of beta weights indicates amplitude of
  response (higher betas larger response)

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Fast fMRI Estimation

• Pros
• Produces time course
• Does not assume specific shape for hemodynamic
  function
• Can use narrow jitter window
• Robust against trial history biases (though not
  immune to it)
• Compound trial types possible
• Cons
• Complicated
• Unrealistic assumptions about maintenance
  activity
• BOLD is non-linear with inter-event intervals lt 6
  sec.
• Nonlinearity becomes severe under 2 sec.
• Sensitive to noise

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

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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

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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

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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

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EXTRA SLIDES
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Voxel Size
non-isotropic
non-isotropic
isotropic
3 x 3 x 6 54 mm3 e.g., SNR 100
3 x 3 x 3 27 mm3 e.g., SNR 71
2.1 x 2.1 x 6 27 mm3 e.g., SNR 71
In general, larger voxels buy you more SNR.
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Partial Voluming

• The fMRI signal occurs in gray matter (where the
  synapses and dendrites are)
• If your voxel includes white matter (where the
  axons are), fluid, or space outside the brain,
  you effectively water down your signal

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Partial Voluming
Partial volume effects The combination, within a
single voxel, of signal contributions from two or
more distinct tissue types or functional regions
(Huettel, Song McCarthy, 2004)
This voxel contains mostly gray matter
This voxel contains mostly white matter
This voxel contains both gray and white matter.
Even if neurons within the voxel are strongly
activated, the signal may be washed out by the
absence of activation in white matter.
Partial voluming becomes more of a problem with
larger voxel sizes Worst case scenario A 22 cm
x 22 cm x 22 cm voxel would contain the whole
brain
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The Initial Dip

• The initial dip seems to have better spatial
  specificity
• However, its often called the elusive initial
  dip for a reason

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Initial Dip (Hypo-oxic Phase)

• Transient increase in oxygen consumption, before
  change in blood flow
• Menon et al., 1995 Hu, et al., 1997
• Smaller amplitude than main BOLD signal
• 10 of peak amplitude (e.g., 0.1 signal change)
• Potentially more spatially specific
• Oxygen utilization may be more closely associated
  with neuronal activity than positive response

Slide modified from Duke course
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Rise (Hyperoxic Phase)

• Results from vasodilation of arterioles,
  resulting in a large increase in cerebral blood
  flow
• Inflection point can be used to index onset of
  processing

Slide modified from Duke course
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Peak Overshoot

• Over-compensatory response
• More pronounced in BOLD signal measures than flow
  measures
• Overshoot found in blocked designs with extended
  intervals
• Signal saturates after 10s of stimulation

Slide modified from Duke course
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Sustained Response

• Blocked design analyses rest upon presence of
  sustained response
• Comparison of sustained activity vs. baseline
• Statistically simple, powerful
• Problems
• Difficulty in identifying magnitude of activation
• Little ability to describe form of hemodynamic
  response
• May require detrending of raw time course

Slide modified from Duke course
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Undershoot

• Cerebral blood flow more locked to stimuli than
  cerebral blood volume
• Increased blood volume with baseline flow leads
  to decrease in MR signal
• More frequently observed for longer-duration
  stimuli (gt10s)
• Short duration stimuli may not evidence
• May remain for 10s of seconds

Slide modified from Duke course
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Implications

• Aguirre, Zarahn DEsposito, 1998
• Generic HRF models (gamma functions) account for
  70 of variance
• Subject-specific models account for 92 of the
  variance (22 more!)
• Poor modelling reduces statistical power
• Less of a problem for block designs than
  event-related
• Biggest problem with delay tasks where an
  inappropriate estimate of the initial and final
  components contaminates the delay component

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Blocked vs. Event-related
Source Buckner 1998
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Advantages of Event-Related

• Flexibility and randomization
• eliminate predictability of block designs
• avoid practice effects
• Post hoc sorting
• (e.g., correct vs. incorrect, aware vs. unaware,
  remembered vs. forgotten items, fast vs. slow
  RTs)
• Can look at novelty and priming
• Rare or unpredictable events can be measured
• e.g., P300
• Can look at temporal dynamics of response
• Dissociation of motion artifacts from activation
• Dissociate components of delay tasks
• Mental chronometry

Source Buckner Braver, 1999
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Exponential Distribution of ITIs
Exponential Distribution
Flat Distribution
Frequency
Frequency
2
3
4
5
6
7
2
3
4
5
6
7
Intertrial Interval
Intertrial Interval

• An exponential distribution of ITIs is recommended

WARNING Ive been getting conflicting advice on
whether its better to have an exponential
distribtuion need to find out more
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NEW SLIDES