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fMRI design and analysis
Advanced designs
(Epoch) fMRI example…(Epoch) fMRI example…
box-car function
= 1 + (t)
voxel timeseries
2+
baseline (mean)
(box-car unconvolved)
(Epoch) fMRI example…(Epoch) fMRI example…
y
data
vecto
r
(
voxe
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e se
ries)
=
= X
desig
n m
atrix
1
2
para
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+
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r vec
tor
(Epoch) fMRI example……fitted and adjusted data(Epoch) fMRI example…
…fitted and adjusted data
Raw fMRI timeseries
Residuals highpass filtered (and scaled)
fitted high-pass filter
Adjusted data
fitted box-car
Convolution with HRF
Boxcar function convolved with HRF
=
hæmodynamic response
Residuals Unconvolved fit
Convolved fit Residuals (less structure)
Fixed vs. Random Effects
Fixed vs. Random EffectsFixed vs. Random Effects
Subject 1
• Subjects can be Fixed or Random variables
• If subjects are a Fixed variable in a single design matrix (SPM “sessions”), the error term conflates within- and between-subject variance
– But in fMRI (unlike PET) the between-scan variance is normally much smaller than the between-subject variance
• If one wishes to make an inference from a subject sample to the population, one needs to treat subjects as a Random variable, and needs a proper mixture of within- and between-subject variance
• In SPM, this is achieved by a two-stage procedure:1) (Contrasts of) parameters are estimated
from a (Fixed Effect) model for each subject2) Images of these contrasts become the data
for a second design matrix (usually simple t-test or ANOVA)
• Subjects can be Fixed or Random variables
• If subjects are a Fixed variable in a single design matrix (SPM “sessions”), the error term conflates within- and between-subject variance
– But in fMRI (unlike PET) the between-scan variance is normally much smaller than the between-subject variance
• If one wishes to make an inference from a subject sample to the population, one needs to treat subjects as a Random variable, and needs a proper mixture of within- and between-subject variance
• In SPM, this is achieved by a two-stage procedure:1) (Contrasts of) parameters are estimated
from a (Fixed Effect) model for each subject2) Images of these contrasts become the data
for a second design matrix (usually simple t-test or ANOVA)
Subject 2
Subject 3
Subject 4
Subject 6
Multi-subject Fixed Effect model
error df ~ 300
Subject 5
WHEN special case of n independent observations per
subject:
var(pop) = 2b + 2
w / Nn
Two-stage “Summary Statistic” approachTwo-stage “Summary Statistic” approach
p < 0.001 (uncorrected)
SPM{t}
1st-level (within-subject) 2nd-level (between-subject)
con
tra
st im
age
s o
f c i
1^
2^
3^
4^
5^
6^
N=6 subjects(error df =5)
One-sample t-test
po
p
^
^
1)^
wwithin-subject error^
2)
3)^
4)^
5)^
6)
Statistical inference
Types of Errors
Slide modified from Duke course
Is the region truly active?
Doe
s ou
r st
at t
est
indi
cate
th
at t
he r
egio
n is
act
ive?
Yes
No
Yes No
HIT Type I Error
Type II Error
Correct Rejection
p value:probability of a Type I error
e.g., p <.05
“There is less than a 5% probability that a voxel our stats have declared as “active” is in reality NOT active
• If n=100,000 voxels tested with pu=0.05 of falsely rejecting Ho...
…then approx n pu (eg 5,000) will do so by chance (false positives, or “type I” errors)
• Therefore need to “correct” p-values for number of comparisons
• A severe correction would be a Bonferroni, where pc = pu /n…
…but this is only appropriate when the n tests independent…
… SPMs are smooth, meaning that nearby voxels are correlated
=> Random Field Theory...
• If n=100,000 voxels tested with pu=0.05 of falsely rejecting Ho...
…then approx n pu (eg 5,000) will do so by chance (false positives, or “type I” errors)
• Therefore need to “correct” p-values for number of comparisons
• A severe correction would be a Bonferroni, where pc = pu /n…
…but this is only appropriate when the n tests independent…
… SPMs are smooth, meaning that nearby voxels are correlated
=> Random Field Theory...
Multiple comparisons…Multiple comparisons…
Gaussian10mm FWHM(2mm pixels)
pu = 0.05
SPM{t} Eg random noise
Random Field Theory (RFT)
Consider SPM as lattice representation of continuous random field
“Euler characteristic”: a topological measure (# “components” - # “holes”)
Euler depends on smoothness
Smoothness estimated by covariance of partial derivatives of residuals (expressed as “resels” or FWHM)
Smoothness does not have to be stationary (for height thresholding): estimated locally as “resels-per-voxel” (RPV)
DESIGNS
= trial of another type (e.g., place image)
= trial of one type (e.g., face image) = null trial
(nothing happens)Design Types
BlockDesign
Slow ERDesign
RapidCounterbalanced
ER Design
RapidJittered ER
Design
MixedDesign
Parametric designs
An Example
Culham et al., 1998, J. Neuorphysiol.
Analysis of Parametric Designs
parametric variant:
passive viewing and tracking of 1, 2, 3, 4 or 5 balls
Factorial Designs
Factorial Designs
Example: Sugiura et al. (2005, JOCN) showed subjects pictures of objects and places. The objects and places were either familiar (e.g., the subject’s office or the subject’s bag) or unfamiliar (e.g., a stranger’s office or a stranger’s bag)
This is a “2 x 2 factorial design” (2 stimuli x 2 familiarity levels)
Statistical Approaches
In a 2 x 2 design, you can make up to six comparisons between pairs of conditions (A1 vs. A2, B1 vs. B2, A1 vs. B1, A2 vs. B2, A1 vs. B2, A2 vs. B1). This is a lot of comparisons (and if you do six comparisons with p < .05, your overall p value is .05 x 6 = .3 which is high). How do you decide which to perform?
Factorial Designs
Main effectsDifference between columns
Difference between rows
InteractionsDifference between columns depending on status of row (or vice versa)
Main Effect of Stimuli
In LO, there is a greater activation to Objects than Places
In the PPA, there is greater activation to Places than Objects
Main Effect of Familiarity
In the precuneus, familiar objects generated more activation than unfamiliar objects
Interaction of Stimuli and Familiarity
In the posterior cingulate, familiarity made a difference for places but not objects
fMR Adaptation
Using fMR Adaptation to Study Coding
Example: We know that neurons in the brain can be tuned for individual faces
“Jennifer Aniston” neuron in human medial temporal lobeQuiroga et al., 2005, Nature
Using fMR Adaptation to Study TuningA
ctiv
atio
n
Act
iva
tion
Act
iva
tion
Act
iva
tion
Neuron 1likes
Jennifer Aniston
Neuron 2likes
Julia Roberts
Neuron 3likes
Brad Pitt Even though there are neurons tuned to each object, the population as a whole shows no preference
• fMRI resolution is typically around 3 x 3 x 6 mm so each sample comes from millions of neurons
fMR Adaptation
If you show a stimulus twice in a row, you get a reduced response the second time
Repeated
FaceTrial
Unrepeated
FaceTrial
Time
Hypothetical Activity inFace-Selective Area (e.g., FFA)
Act
ivat
ion
500-1000 msec
fMRI Adaptation
Slide modified from Russell Epstein
“different” trial:
“same” trial:
LO pFs (~=FFA)
Viewpoint dependence in LOC
Source: Kalanit Grill-Spector
Belin & Zatorre (2003) Neuroreport
- fMRI adaptation -14 subjects, passive listening-12 ‘adapt-Syllable’ blocs
(1 syllable, 12 speakers)-12 ‘adapt-Speaker’ blocs
(1 speaker, 12 words)- Same 144 stimuli in the two
conditions
Adaptation to speaker identity
Von Kriegstein et al (2003) Cognitive Brain Research
Belin & Zatorre (2003) Neuroreport
Petkov et al (2008) Nat Neurosci
Adaptation to speaker identity
Problems
The basis for effect is not well-understoodthis is seen in the many terms used to describe itfMR adaptation (fMR-A)primingrepetition suppression
The effect could be due to many factors such as:repeated stimuli are processed more “efficiently”more quickly?with fewer action potentials?with fewer neurons involved?
repeated stimuli draw less attention
repeated stimuli may not have to be encoded into memory
repeated stimuli affect other levels of processing with input to area demonstrating adaptation (data from Vogels et al.)
subjects may come to expect repetitions and their predictions may be violated by novel stimuli (Summerfield et al., 2008, Nat. Neurosci.)
Multivoxel Pattern Analyses
Multivariate statistics
Traditional fMRI analyses use a ‘massive univariate approach’
-> Information on the sensitivity of brain regions to sensory stimulation or cognitive tasks
But they miss the potentially rich information contained in the pattern of distributed activity over a number of voxels.
Data-Driven Approaches
Data Driven Analyses
Hasson et al. (2004, Science) showed subjects clips from a movie and found voxels which showed significant time correlations between subjects
Reverse correlation
They went back to the movie clips to find the common feature that may have been driving the intersubject consistency
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