fMRI design and analysis Advanced designs

(Epoch) fMRI example… box-car function = 11 +  (t) voxel timeseries 22 + baseline (mean) (box-car unconvolved)

(Epoch) fMRI example… y data vector (voxel time series) = =X design matrix 11 22  parameters   +  + error vector

(Epoch) fMRI example… …fitted and adjusted data Raw fMRI timeseries Residualshighpass filtered (and scaled) fitted high-pass filter Adjusted data fitted box-car

Convolution with HRF Boxcar function convolved with HRF = hæmodynamic response  ResidualsUnconvolved fit Convolved fit Residuals (less structure)

Fixed 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 subject 2) 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 subject 2) 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 ) =  2 b   +  2 w / Nn Two-stage “Summary Statistic” approach       p < (uncorrected) SPM{t} 1 st -level (within-subject)2 nd -level (between-subject) contrast images of c  i 11 ^ 22 ^ 33 ^ 44 ^ 55 ^ 66 ^ N=6 subjects (error df =5) One-sample t-test ^  pop  ^ ^   1 ) ^   w   within-subject error ^   2 )   3 ) ^   4 ) ^   5 ) ^   6 )

Statistical inference

Types of Errors Slide modified from Duke course Is the region truly active? Does our stat test indicate that the region is active? Yes No YesNo 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 p u =0.05 of falsely rejecting H o... …then approx n  p u (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 p c = p u /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 p u =0.05 of falsely rejecting H o... …then approx n  p u (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 p c = p u /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… Gaussian 10mm FWHM (2mm pixels) p u = 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 Block Design Slow ER Design Rapid Counterbalanced ER Design Rapid Jittered ER Design Mixed Design

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

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 Activation Neuron 1 likes Jennifer Aniston Neuron 2 likes Julia Roberts Neuron 3 likes 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 Face Trial  Unrepeated Face Trial Time Hypothetical Activity in Face-Selective Area (e.g., FFA) Activation

msec fMRI Adaptation Slide modified from Russell Epstein “different” trial: “same” trial:

And more… We could use this technique to determine the selectivity of face- selective areas to many other dimensions Repeated Individual, Different Expression Repeated Expression, Different Individual

Why is adaptation useful? Now we can ask what it takes for stimulus to be considered the “same” in an area For example, do face-selective areas care about viewpoint? Time Activation  Repeated Individual, Different Viewpoint Viewpoint invariance: area codes the face as the same despite the viewpoint change Viewpoint selectivity: area codes the face as different when viewpoint changes

= = viewpoint-specific viewpoint-invariant Are scene representations in FFA viewpoint-invariant or viewpoint-specific?

LOpFs (~=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-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