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

l tim

e se

ries)

=

= X

desig

n m

atrix

1

2

para

met

ers

+

+

erro

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