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Spatial and Temporal Limitsof fMRI
Jody CulhamDepartment of Psychology
University of Western Ontario
Last Update: November 29, 2008fMRI Course, Louvain, Belgium
http://www.fmri4newbies.com/
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)
Ocular Dominance Columns
• Columns on the order of ~0.5 mm have been observed with fMRI
Submillimeter Resolution
Goenze, Zappe & Logothetis, 2007, Magnetic Resonance Imaging• anaesthetized monkey; 4.7 T; contrast agent (MION)• ~0.3 x 0.3 x 2 mm
Gradient EchoFunctional
(superficial activationincludes vessels)
Spin EchoFunctional(activation
localized to Layer IV)
Spin EchoAnatomical
Gradient EchoAnatomical
vein
Stria of Gennari(Layer IV)
Sampling Rate
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging
Event-Related Averaging
“Zero” = average signal intensity in first volume of all 8 events
Event-Related AveragingRAW
Not particularly usefulNo baseline, just averaged valuesError bars may be huge (esp. if multiple runs)
FILE-BASED
Zero = average across all events at specified volume(s)Safest procedure to useMost similar to GLM stats
EPOCH-BASED
Zero = starting point of each curve at specified volume(s)Sometimes useful if well-justifiedMay look very different than GLM stats
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
Convolution of Single Trials
Neuronal Activity
Haemodynamic Function
BOLD Signal
Time
Time
Slide from Matt Brown
BOLD Overlap and Jittering
• Closely-spaced haemodynamic impulses summate.
• Constant ITI causes tetanus.
Burock et al. 1998.
Design Types
BlockDesign
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
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 (4 conditions +
baseline is about the max I will use in one run)
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?
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
Can we 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
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 of HRF Between SubjectsAguirre, Zarahn & D’Esposito, 1998• HRF shows considerable variability between subjects
• Within subjects, responses are more consistent, although there is still some variability between sessions
different subjects
same subject, same session same subject, different session
Variability of HRF Between AreasPossible 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
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
The Problem of Trial History
• Estimation does not work well if trial history differs between trial types• Two options
1. Control trial history by making it the same for all trial types
2. Model the trial history by deconvolving the signal (requires jittered timing)
Event-related average is wonky because trial types differ in the history of preceding trials
Time
Act
iva
tion
Time
Act
iva
tion
WARNING: This slide is confusing, needs to be redone. Supposed to show that yellow>red>white, not just because of trial summation
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
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
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
Convolution of Single Trials
Neuronal Activity
Haemodynamic Function
BOLD Signal
Time
Time
Slide from Matt Brown
DEconvolution of Single Trials
Neuronal Activity
Haemodynamic Function
BOLD Signal
Time
Time
Slide from Matt Brown
Deconvolution Example• time course from 4 trials of two types (pink, blue) in a “jittered” design
Single Stick Predictor
QuickTime™ and a decompressor
are needed to see this picture.
• 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)
Predictors for the Blue Trial Type
• set of 12 predictors for subsequent volumes of blue trial type
Linear Deconvolution
• Jittering ITI also preserves linear independence among the hemodynamic components comprising the BOLD signal.
Miezen et al.2000
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)
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 < 6 sec.– Nonlinearity becomes severe under 2 sec.
• Sensitive to noise
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
EXCEPT when the activated region does not fill the voxel (partial voluming)
Voxel Size
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
isotropic
non-isotropic
non-isotropic
In general, larger voxels buy you more SNR.
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
fMRI for Dummies
Partial Voluming
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
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)
The Initial Dip
• The initial dip seems to have better spatial specificity• However, it’s often called the “elusive initial dip” for a reason
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
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
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
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
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 (>10s)– Short duration stimuli may not evidence– May remain for 10s of seconds
Slide modified from Duke course
ImplicationsAguirre, Zarahn & D’Esposito, 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
Advantages of Event-Related 1) Flexibility and randomization
• eliminate predictability of block designs• avoid practice effects
2) Post hoc sorting • (e.g., correct vs. incorrect, aware vs. unaware, remembered
vs. forgotten items, fast vs. slow RTs)
3) Can look at novelty and priming
4) Rare or unpredictable events can be measured• e.g., P300
5) Can look at temporal dynamics of response• Dissociation of motion artifacts from activation• Dissociate components of delay tasks• Mental chronometry
Source: Buckner & Braver, 1999
Exponential Distribution of ITIs
• An exponential distribution of ITIs is recommended
2 3 4 5 6 7 2 3 4 5 6 7Intertrial Interval Intertrial Interval
Fre
quen
cy
Fre
quen
cy
Flat Distribution ExponentialDistribution
WARNING: I’ve been getting conflicting advice on whether it’s better to have an exponential distribtuion… need to find out more
