1. Surface-based Exploratory Group Analysis in FreeSurfer

2. Outline Processing Stages Command-line Stream Assemble Data
Design/Contrast (GLM Theory)
Analyze
Visualize
Interactive/Automated GUI (QDEC)
Correction for multiple comparisons

3. Aging Exploratory Analysis
In which areas does thickness change with age?
Cortical Thickness vs Aging
Salat, et al, 2004, Cerebral Cortex

4. N=40 (all in fsaverage space)
Aging Thickness Study
N=40 (all in fsaverage space)
Positive Age Correlation
Negative Age Correlation
p<.01

5. Surface-based Measures
Morphometric (eg, thickness)
Functional
PET
MEG/EEG
Diffusion (?) sampled just under the surface
For group morphometric analysis, the observed data is comprised of a set of surface measures (such as cortical thickness) at each vertex in a surface model, for each subject in the group. This data can be organized as a set of vectors, each associated with a different vertex in the surface model, and containing a surface measurement for every subject in the group at the corresponding vertex.

6. Processing Stages Specify Subjects and Surface measures Assemble Data:
Resample into Common Space
Smooth
Concatenate into one file
Model and Contrasts (GLM)
Fit Model (Estimate)
Correct for multiple comparisons
Visualize

7. The General Linear Model (GLM)
Is Thickness correlated with Age?
Thickness x1 x2 y2 y1
Dependent
Variable,
Measurement
Subject 1
Subject 2
HRF Amplitude
IQ, Height, Weight
Linear modeling describes the observed data as a linear combination of explanatory factors plus noise, and determines how well that description explains the data being analyzed.
Age
Of course, you’d
need more then two
subjects …
Independent Variable

8. System of Linear Equations
Linear Model
Intercept: b
Slope: m
Thickness
Age x1 x2 y2 y1
System of Linear Equations
y1 = 1*b + x1*m
y2 = 1*b + x2*m y1 y2
1 x1
1 x2 b m = *
Matrix Formulation
Intercept = Offset
X = Design Matrix
 = Regression Coefficients
= Parameter estimates
= “betas”
= Intercepts and Slopes
= beta.mgh (mri_glmfit)
First, a linear model must be designed to include all explanatory variables (EVs) that may account for each vector's values. A simple linear model is given by y=a*x+b+e, where the observed data y is a one-dimensional vector of surface measures -- one measurement per subject at a vertex; x is a one-dimensional vector containing a variable, such as age, describing each subject; a is the parameter estimate (PE) for x, for instance the value that a subject's age must be multiplied by to fit the data in y; b is a constant, and in this example, would correspond to the baseline measurement present in the data; and e is the error in the model fitting. If an additional explanatory variable is added to explain the observed data, the model would be given as y=a1*x1+a2*x2+b+e, containing two different model waveforms, a1*x1 and a2*x2, corresponding to two variables, such as age and gender, describing all subjects in the study.
2.1 Estimation overview
Once the model is specified, an estimation step follows, in which the model is fit to each vertex's vector separately; no interactions between vertices are taken into account in the examples presented here. This step generates the estimate of the "goodness of fit" of each of the explanatory variables to each vector of surface measurements. Thus if a particular vertex responds strongly to the explanatory variable x1, a large value for a1 will be produced by model-fitting; if the data appears unrelated to x2 then a2 will have a very small value.
This kind of linear modeling is commonly expressed in matrix notation, where the the matrix X contains all the explanatory variables (designed effects and confounds) in the model, and the matrix A contains all the PEs. The matrix X is also commonly called the design matrix and it can be user-specified in FreeSurfer in the form of an FSGD (FreeSurfer Group Descriptor) file, as the exercises below illustrate. Each column of X corresponds to a different explanatory variable (also called a regressor or a covariate). As typically formulated and solved, the estimation step produces a set of estimates of the PEs, which in turn are used in hypothesis testing. b m 
Y = X*
mri_glmfit output: beta.mgh

9. Hypotheses and Contrasts
Is Thickness correlated with Age?
Does m = 0?
Null Hypothesis: H0: m=0 y1 y2
1 x1
1 x2 b m = *
m= [0 1]* b m
Intercept: b
Slope: m
Thickness
Age x1 x2 y2 y1 b m 
 = C* ?
2.2 Inference overview
Estimates of the PEs can be converted into statistical parametric maps, which are commonly visualized as a color-coded surface overlay. The overlay assigns each vertex a value based on the likelihood that the null hypothesis is false at that vertex. A linear combination of estimates of PEs is used to encode the particular hypothesis of interest. This encoding is accomplished with a user-specified ''contrast vector'', which assigns a contrast weight to each column of the design matrix. A simple example of a contrast vector that tests the null hypothesis for the explanatory variable associated with the first design matrix column would be[ ]. To compute this particular contrast at each vertex, the PE value associated with the first design matrix column at that vertex is divided by the error in its estimate, yielding a t-value. The t-value provides a good measure of confidence in the estimate of the PE value, and can be converted into a probability (P) or Z statistic at that vertex via a standard statistical transformation. T, P and Z values all convey the same information about how significantly the observed data is related to a given explanatory variable.
C=[0 1]: Contrast Matrix
mri_glmfit output: gamma.mgh

10. More than Two Data Points
Thickness
Intercept: b y1 y2 y3 y4
1 x1
1 x2
1 x3
1 x4 b m = *
Slope: m
Age
Y = X*
y1 = 1*b + x1*m
y2 = 1*b + x2*m
y3 = 1*b + x3*m
y4 = 1*b + x4*m
No matter how many data points you have, there is still only one slope and one intercept.
rvar.mgh = residual error variance
Model Error
Noise
Uncertainty
rvar.mgh

11. t-Test and p-values  = C* Y = X* p-value/significance
value between 0 and 1
closer to 0 means more significant
FreeSurfer stores p-values as –log10(p):
0.1=10-1sig=1, 0.01=10-2sig=2
sig.mgh files
Signed by sign of 
p-value is for an unsigned test
p-value
sig =
1.0
0.05 =
1.3
0.01 =
2.0
0.001=
3.0
A t-value map can be produced for each explanatory variable of interest. Each map indicates how strongly vertices on the surface are related to one explanatory variable. Parameter estimates can also be compared to see if one explanatory variable is more strongly related to the data than another. To encode this kind of hypothesis, one PE is subtracted from another using a "contrast" vector such as [ ], a combined standard error is computed, and a new t-map is generated. In a similar fashion, to test for a more complicated collection of effects, a matrix of contrast weights can be specified. A more rigorous description of single and multiple linear regression and GLM, types of analyses, estimation and hypothesis testing is available at

12. Two Groups Do groups differ in Intercept? Do groups differ in Slope?
Intercept: b1
Slope: m1
Thickness
Age
Intercept: b2
Slope: m2
Is average slope different than 0? …

13. Two Groups Y = X* * = y11 = 1*b1 + 0*b2 + x11*m1 + 0*m2
Intercept: b1
Slope: m1
Thickness
Age
Intercept: b2
Slope: m2
y11
y12
y21
y22
x11 0
x12 0
x21
x22 b1 b2 m1 m2 = *
Y = X*
y11 = 1*b1 + 0*b2 + x11*m *m2
y12 = 1*b1 + 0*b2 + x12*m *m2
y21 = 0*b1 + 1*b *m1 + x21*m2
y22 = 0*b1 + 1*b *m1 + x22*m2

14. Two Groups Y = X*  * = y11 1 0 x11 0 y12 1 0 x12 0 y21 0 1 0 x21b1 b2 m1 m2
y11
y12
y21
y22
x11 0
x12 0
x21
x22 *
Do groups differ in Intercept?
Does b1=b2?
Does b1-b2 = 0?
C = [ ],  = C* =
Do groups differ in Slope?
Does m1=m2?
Does m1-m2=0?
C = [ ],  = C* b1 b2 m1 m2
Y = X*

Intercept: b1
Slope: m1
Thickness
Age
Intercept: b2
Slope: m2
Is average slope different than 0?
Does (m1+m2)/2 = 0?
C = [ ],  = C*

15. Surface-based Group Analysis in FreeSurfer
Create your own design matrix and contrast matrices
Create an FSGD File
FreeSurfer creates design matrix
You still have to specify contrasts
QDEC
Limited to 2 discrete variables, 2 levels max
Limited to 2 continuous variables

16. Command-line Processing Stages
Assemble Data (mris_preproc)
Resample into Common Space
Smooth
Concatenate into one file
Model and Contrasts (GLM) (FSGD)
Fit Model (Estimate) (mri_glmfit)
Correct for multiple comparisons
Visualize (tksurfer) }
recon-all -qcache
-qcache is a way to run preprocessing (resampling and smoothing) on each individual subject. The results are then stored in the subject's folder. These two steps take the longest when doing a group analysis. When this is done for a bunch of subjects, it allows for fast group analysis and allows the user to change the subject selection and re-run without having to wait along time. It make it possible to do these things more interactively, especially when running QDEC.

17. Specifying Subjects $SUBJECTS_DIR fred jenny margaret … bert
Subject ID
$SUBJECTS_DIR
fred
jenny
margaret …
bert
Set SUBJECTS_DIR, issue a command (mksubjdirs) to create directory structure. Convert (using mri_convert) data to COR format and store in mri/RRR, run recon-all. Typically, we acquire 3 high-quality T1 volumes to use as input to reconstruction (128-slice sagital, 1 mm in-plane resolution).

18. FreeSurfer Directory Tree
bert
bem stats morph mri rgb scripts surf tiff label
orig T1 brain wm aseg
Subject ID
lh.aparc_annnot
rh.aparc_annnot
Set SUBJECTS_DIR, issue a command (mksubjdirs) to create directory structure. Convert (using mri_convert) data to COR format and store in mri/RRR, run recon-all. Typically, we acquire 3 high-quality T1 volumes to use as input to reconstruction (128-slice sagital, 1 mm in-plane resolution).
lh.white
rh.white
lh.thickness
rh.thickness
lh.sphere.reg
rh.sphere.reg
SUBJECTS_DIR environment variable

19. Example: Thickness Study
$SUBJECTS_DIR/bert/surf/lh.thickness
$SUBJECTS_DIR/fred/surf/lh.thickness
$SUBJECTS_DIR/jenny/surf/lh.thickness
$SUBJECTS_DIR/margaret/surf/lh.thickness …

20. FreeSurfer Group Descriptor (FSGD) File
Simple text file
List of all subjects in the study
Accompanying demographics
Like a spreadsheet
Automatic design matrix creation
You must still specify the contrast matrices
Integrated with tksurfer
Note: Can specify design matrix explicitly with --design

21. FSGD Format GroupDescriptorFile 1 Class Male Class Female
Variables Age Weight IQ
Input bert Male
Input fred Male
Input jenny Female
Input margaret Female
One Discrete Factor (Gender) with Two Levels (M&F)
Three Continuous Variables: Age, Weight, IQ
Class = Group
Note: Can specify design matrix explicitly with --design

22. } FSGDF  X (Automatic) } X = C = [-1 1 0 0 0 0 0 0]
X =
Male Group
Female Group
Female Age
Male Age
Weight
Age IQ
C = [ ] }
Tests for the difference in intercept/offset between groups
C = [ ] }
Tests for the difference in age slope between groups
DODS – Different Offset, Different Slope

23. Another FSGD Example Two Discrete Factors One Continuous Variable: Age
Gender: Two Levels (M&F)
Handedness: Two Levels (L&R)
One Continuous Variable: Age
GroupDescriptorFile 1
Class MaleRight
Class MaleLeft
Class FemaleRight
Class FemaleLeft
Variables Age
Input bert MaleLeft
Input fred MaleRight
Input jenny FemaleRight
Input margaret FemaleLeft
Class = Group

24. Interaction Contrast  3-1)- 4-2) 1+2+ 3-4
Two Discrete Factors (no continuous, for now)
Gender: Two Levels (M&F)
Handedness: Two Levels (L&R)
Four Regressors (Offsets)
MR (1), ML (2), FR (3), FL (4) M F R L 1 4 3 2  
GroupDescriptorFile 1
Class MaleRight
Class MaleLeft
Class FemaleRight
Class FemaleLeft
Input bert MaleLeft
Input fred MaleRight
Input jenny FemaleRight
Input margaret FemaleLeft

3-1)- 4-2)
1+2+ 3-4
C = [ ] 
This is a different example with two discrete factors each with two levels.

25. } Number of Regressors } C = [-1 1 0 0 0 0 0 0]
Each Group/Class:
Has its own Intercept
Has its own Slope for each continuous variable
DODS = Different offset, different slope
NRegressors = NClasses*(NVariables+1)
NRegressors
C = [ ] }
Tests for the difference in intercept/offset between groups
C = [ ] }
Tests for the difference in age slope between groups

26. Factors, Levels, Groups, Classes
Factors can be Discrete or Continuous:
Continuous Variables: Age, IQ, Volume, etc
Discrete Factors: Gender, Handedness, Diagnosis
Discrete Factors have Levels:
Gender: Male and Female
Handedness: Left and Right
Diagnosis: Normal, MCI, AD
Group or Class: Specification of All Discrete Factors:
Left-handed Male MCI
Right-handed Female Normal

27. Assemble Data: mris_preproc
mris_preproc --help
--fsgd FSGDFile : Specify subjects thru FSGD File
--hemi lh : Process left hemisphere
--meas thickness : $SUBJECTS_DIR/subjectid/surf/hemi.thickness
--target fsaverage : common space is subject fsaverage
--o lh.thickness.mgh : output “volume-encoded surface file”
Lots of other options!
lh.thickness.mgh – file with thickness maps for all subjects  Input to Smoother or GLM

28. Surface Smoothing mri_surf2surf --help Loads lh.thickness.mgh
2D surface-based smoothing
Specify FWHM (eg, fwhm = 10 mm)
Saves lh.thickness.sm10.mgh
Can be slow (~10-60min)
recon-all -qcache

29. mri_glmfit Reads in FSGD File and constructs X
Reads in your contrasts (C1, C2, etc)
Loads data (lh.thickness.sm10.mgh)
Fits GLM (ie, computes )
Computes contrasts (=C*)
t or F ratios, significances
Significance -log10(p) (.01  2, .001  3)

30. mri_glmfit mri_glmfit --y lh.thickness.sm10.mgh --fsgd gender_age.txt
--C age.mtx –C gender.mtx
--surf fsaverage lh
--cortex
--glmdir lh.gender_age.glmdir
mri_glmfit --help

31. mri_glmfit mri_glmfit --y lh.thickness.sm10.mgh --fsgd gender_age.txt
--C age.mtx –C gender.mtx
--surf fsaverage lh
--cortex
--glmdir lh.gender_age.glmdir
Input file (output from smoothing).
Stack of subjects, one frame per subject

32. mri_glmfit mri_glmfit --y lh.thickness.sm10.mgh --fsgd gender_age.txt
--C age.mtx –C gender.mtx
--surf fsaverage lh
--cortex
--glmdir lh.gender_age.glmdir
FreeSurfer Group Descriptor File (FSGD)
Group membership
Covariates

33. mri_glmfit mri_glmfit --y lh.thickness.sm10.mgh --fsgd gender_age.txt
--C age.mtx –C gender.mtx
--surf fsaverage lh
--cortex
--glmdir lh.gender_age.glmdir
Contrast Matrices
Simple text/ASCII files
Test hypotheses

34. mri_glmfit mri_glmfit --y lh.thickness.sm10.mgh --fsgd gender_age.txt
--C age.mtx –C gender.mtx
--surf fsaverage lh
--cortex
--glmdir lh.gender_age.glmdir
Perform analysis on left hemisphere of fsaverage subject
Masks by fsaverage cortex.label
Computes FWHM in 2D

35. mri_glmfit Output directory: lh.gender_age.glmdir/ mri_glmfit
beta.mgh – parameter estimates
rvar.mgh – residual error variance
etc …
age/
sig.mgh – -log10(p), uncorrected
gamma.mgh, F.mgh
gender/
sig.mgh – -log10(p)
mri_glmfit
--y lh.thickness.sm10.mgh
--fsgd gender_age.txt
--C age.mtx –C gender.mtx
--surf fsaverage lh
--cortex
--glmdir lh.gender_age.glmdir

36. Visualization with tksurfer
Saturation:
-log10(p),
Eg, 5=.00001
Threshold:
-log10(p),
Eg, 2=.01
uncorrected
False
Dicovery
Rate
Eg, .01
View->Configure->Overlay
File->LoadOverlay

37. Visualization with tksurfer
File->
Load Group Descriptor File …

38. Problem of Multiple Comparisons
p value is probability that a voxel is falsely activated
Threshold too liberal: many false positives
Threshold too restrictive: lose activation (false negatives)

39. Clusters True signal tends to be clustered
p<.10
p<.01
p<10-7
True signal tends to be clustered
False Positives tend to be randomly distributed in space
Cluster – set of spatially contiguous voxels that are above a given threshold.

40. Cluster-forming Threshold
p<.00001
sig<5
p<.0001
sig<4
Unthresholded
p<.001
sig<3
As threshold lowers, clusters may expand or merge and new clusters can form. No way to say what the threshold should be.

41. Cluster Table, Uncorrected
p<.0001
sig<4
38 clusters
ClusterNo Area(mm2) X Y Z Structure
Cluster superiorfrontal
Cluster insula
Cluster superiorparietal
Cluster precentral
Cluster supramarginal …
How likely is it to get a cluster of a certain size under the null hypothesis?

42. Correction for Multiple Comparisons
Cluster-based
Monte Carlo simulation
Permutation Tests
False Discovery Rate (FDR) – built into tksurfer and QDEC. (Genovese, et al, NI 2002)

43. Cluster-based Corr. for Multiple Comparisons
Simulate data under Null Hypothesis:
Synthesize Gaussian noise and then smooth (Monte Carlo)
Permute rows of design matrix (Permutation, orthog)
Analyze, threshold, cluster, max cluster size
Repeat 10,000 times
Analyze real data, get cluster sizes
P(cluster) = #MaxClusterSize > ClusterSize/10000
mri_glmfit-sim

44. Cluster Table, Corrected
p<.0001
sig<4
22 clusters out of 38 have cluster p-value < .05
ClusterNo Area(mm2) X Y Z Structure Cluster P
Cluster superiorfrontal
Cluster insula
Cluster superiorparietal
Cluster precentral
Cluster supramarginal …
Note the difference between the Cluster Forming Threshold (p<.0001) and the Cluster p-value.

45. Surface-based Corr. for Multiple Comparisons
2D Cluster-based Correction at p < .05
mri_glmfit-sim
--glmdir lh.gender_age.glmdir
--cache pos 2
--cwpvalthresh .05
--2spaces

46. Surface-based Corr. for Multiple Comparisons
2D Cluster-based Correction at p < .05
Original mri_glmfit command:
mri_glmfit
--y lh.thickness.sm10.mgh
--fsgd gender_age.txt
--C age.mtx –C gender.mtx
--surf fsaverage lh
--cortex
--glmdir lh.gender_age.glmdir
mri_glmfit-sim
--glmdir lh.gender_age.glmdir
--cache pos 2
--cwpvalthresh .05
--2spaces
lh.gender_age.glmdir/
beta.mgh – parameter estimates
rvar.mgh – residual error variance
etc …
age/
sig.mgh – -log10(p), uncorrected
gamma.mgh, F.mgh
gender/
sig.mgh – -log10(p)

47. Surface-based Corr. for Multiple Comparisons
2D Cluster-based Correction at p < .05
mri_glmfit-sim
--glmdir lh.gender_age.glmdir
--cache pos 2
--cwpvalthresh .05
--2spaces
Use pre-cached simulation results
positive contrast
voxelwise threshold = 2 (p<.01)
Can use another simulation or permutation

48. Surface-based Corr. for Multiple Comparisons
2D Cluster-based Correction at p < .05
mri_glmfit-sim
--glmdir lh.gender_age.glmdir
--cache pos 2
--cwpvalthresh .05
--2spaces
Cluster-wise threshold p<.05

49. Surface-based Corr. for Multiple Comparisons49
Surface-based Corr. for Multiple Comparisons
2D Cluster-based Correction at p < .05
mri_glmfit-sim
--glmdir lh.gender_age.glmdir
--cache pos 2
--cwpvalthresh .05
--2spaces
Bonferroni correct over two hemispheres

50. Correction for Multiple Comparisons Output
mri_glmfit-sim
--glmdir lh.gender_age.glmdir
--cache pos 2
--cwpvalthresh .05
--2spaces
lh.gender_age.glmdir
age
gender
sig.mgh – pre-existing uncorrected p-values
cache.th20.pos.sig.cluster.mgh – map of significance of clusters
cache.th20.pos.sig.ocn.annot – annotation of significant clusters
cache.th20.pos.sig.cluster.summary – text file of cluster table (clusters, sizes, MNI305 XYZ, and their significances)
Only shows clusters p<.05

51. Tutorial Command-line Stream QDEC – same data set
Create an FSGD File for a thickness study
Age and Gender
Run
mris_preproc
mri_surf2surf
mri_glmfit
mri_glmfit-sim
tksurfer
QDEC – same data set

52. QDEC GUI Load QDEC Table File List of Subjects
List of Factors (Discrete and Cont)
Choose Factors
Choose Input (cached):
Hemisphere
Measure (eg, thickness)
Smoothing Level
“Analyze”
Builds Design Matrix
Builds Contrast Matrices
Constructs Human-Readable Questions
Analyzes
Displays Results