Transcript MSc_fMRI_Advanced design and analysis

fMRI design and analysis
Advanced designs
(Epoch) fMRI example…
= b1
+ b2
+ (t)
(box-car
unconvolved)
voxel timeseries
box-car function
baseline (mean)
(Epoch) fMRI example…
b1

=
+
b2
y
=
X

b
+

(Epoch) fMRI example…
…fitted and adjusted data
Raw fMRI timeseries
Adjusted data
fitted box-car
highpass filtered (and
scaled)
fitted high-pass filter
Residuals
Convolution with HRF
Unconvolved fit
Residuals

Boxcar function
Convolved fit
=
hæmodynamic response
convolved with HRF
Residuals (less structure)
Fixed vs. Random Effects
Fixed vs. Random Effects
• 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 subject
2) Images of these contrasts become the data
for
a second design matrix (usually simple ttest
or ANOVA)
Multi-subject Fixed Effect model
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
Subject 6
error df ~ 300
Two-stage “Summary Statistic” approach
2nd-level (between-subject)
b^1
(^1)

b^2
(^2)

b^3
(^3)

b^4
(^4)

b^5
(^5)

b^6
(^6)

contrast images of cbi
1st-level (within-subject)
^ = within-subject error
w
One-sample
t-test

N=6 subjects
(error df =5)
p < 0.001 (uncorrected)
SPM{t}
^b
pop
WHEN special case of n
independent observations per
subject:
var(bpop) = 2b / N + 2w / Nn
Statistical inference
Types of Errors
Is the region truly active?
Yes
No
Does our stat test indicate
that the region is active?
Yes
HIT
Type II
Error
No
Type I
Error
Correct
Rejection
Slide modified from Duke course
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
Multiple comparisons…
• 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)
SPM{t}
Eg random noise
• Therefore need to “correct” pvalues for number of comparisons
• A severe correction would be a
Bonferroni, where pc = pu /n…
Gaussian
…but this is only appropriate when
10mm FWHM
the n tests independent…
(2mm pixels)
… SPMs are smooth, meaning that
nearby voxels are correlated
=> Random Field Theory...
pu = 0.05
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 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
= null trial
(nothing happens)
Design Types
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 effects
Difference between columns
Difference between rows
Interactions
Difference 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 lobe
Quiroga et al., 2005, Nature
Using fMR Adaptation to Study Tuning
• fMRI resolution is typically around 3 x 3 x 6 mm so each sample comes from
millions of neurons
Even though there are
neurons tuned to each
object, the population as
a whole shows no
preference
Activation
Neuron 3
likes
Brad Pitt
Activation
Neuron 2
likes
Julia Roberts
Activation
Activation
Neuron 1
likes
Jennifer Aniston
fMR Adaptation
If you show a stimulus twice in a row, you get a reduced
response the second time
Unrepeated
Face
Trial

Repeated
Face
Trial

Activation
Hypothetical Activity in
Face-Selective Area (e.g., FFA)
Time
fMRI Adaptation
“different” trial:
500-1000 msec
“same” trial:
Slide modified from
Russell Epstein
Viewpoint dependence in LOC
LO
Source: Kalanit Grill-Spector
pFs (~=FFA)
Adaptation to speaker identity
- 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
Belin & Zatorre (2003) Neuroreport
Adaptation to speaker identity
Belin & Zatorre (2003) Neuroreport
Von Kriegstein et al (2003) Cognitive Brain Research
Petkov et al (2008) Nat Neurosci
Problems
The basis for effect is not well-understood
this is seen in the many terms used to describe it
 fMR
adaptation (fMR-A)
 priming
 repetition 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