fMRI Methods

Lecture5 – Multi subject analyses

4 basic analyses

1. Correlation with an HRF convolved model

2. Regression with an HRF convolved model

3. Regression with an un-convolved model (deconvolution)

4. Trigger averaging

Can be applied voxel-by-voxel or to an ROI.

How do we combine these analyses across subjects?

Differences in anatomyNeed to create a common workspace for everyone

Co-registrationRemember that our fMRI data is in the functional scans, which have a different resolution than the anatomical scans

Functional-anatomical alignmentInterpolate fMRI low res to anatomy high res

Anatomical

Functional

Functional-anatomical alignmentInterpolate fMRI low res to anatomy high res

Overlaid

Edgedisplay

Talairach/MNIConform the subjects to a general coordinate frame

Talairach atlas: based on a single 60 year old female brain.

MNI atlas – based on the average anatomy of 250 brains.

Z

Y

X

40,67,12

Talairach/MNIStretch and squeeze individual brains to fit

Normalizes anatomical volume based on 8 points:AC,PC, and 6 sides of the cube.

Talairach/MNI

Talairach and MNI transformations do not normalize the sulci/gyri, so there’s still some anatomical variability:

Cortical based alignment

More advanced techniques try and warp the anatomy so as to normalize the sulci locations across brains.

Alignments

1. Functional to anatomical co-registration within each subject

2. Anatomical normalization across subjects.

Now we know that extracting a time-course from voxel 29,10,32 (x,y,z) will give us brain activity from a similar

brain location in all of our subjects.

Spatial smoothingSome anatomical variability will always remain, so smooth

the data across space and pray for overlap…

8mm

Multi-subject analyses

Now that our brains are all in the same coordinate frame how do we combine the statistical analyses?

Subject 1 Subject 2 Subject 3

Fixed effects analysis

Combine the data across subjects (as if it came from a single subject) and solve one GLM to determine whether there was

a significant “effect”.

Assumes inter-subject homogeneity – that the response is identical in all subject.

Fixed effects analysisCommonly done by building a long GLM; stacking the data

= * + errora1 a2

Fixed effects analysis

Two problems:

1. Effects are not necessarily evident in majority of subjects (a strong effect in one subject could generate significant results).

2. Explosion in degrees of freedom

Random effects analysis

Solve for each subject separately and test whether the effect was consistent across subjects – “two stage analysis”

Takes inter-subject variability into account

Random effects analysisSolve standard GLM for each subject

= * + errora1 a2

Diff1.11.1-0.3

20.51.2

Random effects analysisWhen comparing responses in the same subjects, perform

paired “repeated measure” t-test on beta values

Beta 21.21.40.42.20.81

Beta 10.10.30.70.20.3-0.2

Random effects analysisWhen comparing responses across different subjects,

perform regular “two sample” t-test on beta values

Group 21.21.40.42.20.81

Group 10.10.30.70.20.3-0.2

Multi-subject mapsConvert t-values to p-values (d.o.f = # of subjects)

1. Do it for every voxel

2. Apply multiple comparisons correction

3. Project onto the anatomy of an exemplar subject for display

Multi-subject ROI analyses

There are two ways to select an ROI:

2. Across the group such that the exact same talairach coordinates will apply to all.

Subject 1

Subject 2

Subject 3

Subject 4

Multi-subject ROI analyses

2. In each subject separately, slightly different talairach coordinates for each.

Subject 1 Subject 2 Subject 3 Subject 4

Requires clear anatomical/functional criteria for ROI selection

Cool displaysA picture is worth a thousand words

Extract the brain

Segmentation

Segmentation

Decide at what signal intensity to threshold gray-white matter boundary.

Different thresholds in different slices?

Segmentation

Determine white matter and gray matter volumes

Hollow cortical surface

Beauty-accuracy tradeoff

Experimental designs

The choice of experimental design (block or event related design) depends on whether you want to decompose

temporal components or not.

Block designs are commonly used to assess whether a cortical area has preference for a particular stimulus type.

e.g. mapping the somatosensory homunculus

Experimental designs

Example of separating temporal components

Perceptual memory

What brain area encodes short term memory in a visual task?

Two things happen during the presentation of the first stimulus. Visual response and “ignition” of memory trace.

Temporal components of the task need to be separated…

Perceptual memory

Build a model that extracts delay period activity

Cue Delay Test

Cue Delay Test

Cue Delay Test

Perceptual memory

We can now estimate working memory responses in V1 during the different delay lengths.

It’s the beta value associated with d

StatisticsSo far we’ve used t-tests to compare beta values.A t-test is a “parametric” statistic that assumes the data are normally distributed.

What if our beta values are not normally distributed?

Bootstraping

Bootstrapping is a method for characterizing a variable’s distribution by re-sampling with replacement.

We assume that the urn represents the world population. By re-sampling with replacement we characterize it.

b1

b2b3

b4

b1

b1b1b2

b2 b2

b2 b4

b4

b4

b3b3

mean1

mean2

mean3

Bootstraping

Compute a histogram of 10,000 random samples:

Define the 5th and 95th percentiles of our betas’ distribution.

Perform “non-parametric” statistical tests…

Measure response of an autistic individual, does it fall beyond the confidence interval?

95th

Randomization

On the same lines one can generate several useful distributions for testing statistical significance…

1.Randomizing the design matrix:

Actual design

Shuffled design

Randomization

Shuffle the design matrix 10,000 different ways.

For every shuffle convolve with an HRF and solve GLM to compute beta values.

Compute the distribution of random beta values (hopefully centered on 0).

Determine whether the actual beta values fall above/below 5th and 95th percentiles.

Randomization

2. Randomizing condition identity without replacement:

c1

c2c2

c1

c1

c1

c2

c2

Condition 1

Condition 2

Compute difference between randomly assigned conditions.

Randomization

Always think about the null hypothesis…

Extract 10,000 randomly assigned condition pairs and compute the difference in each.

Compute the randomized differences distribution.

Determine whether the actual difference falls above/below the 5th/95th percentile of the distribution

Randomization

3. Randomizing subject identity:

g1

g2g2

g1

g1

g1

g2

g2

Group 1

Group 2

Compute difference between randomly assigned groups.

RandomizationExtract 10,000 randomly assigned group pairs and compute the difference in each.

Determine whether the actual group difference is larger than the 95th percentile of the randomized difference distribution.

Scanning this week

Who wants to scan and who is authorized to scan?

Split into groups.

Each group needs a volunteer to go in the scanner and an experienced user to guide the scan.

Decide on an experiment and create stimulus (visual or auditory).

Decide on a time slot for the group.

To the lab!