1. The statistical analysis of fMRI data using FMRISTAT and MINC

3. PCA_IMAGE: PCA of time  space:20 40 60 80
100
120 4 3 2 1
Component
Frame
Temporal components (sd, % variance explained)
105.7, 77.8%
26.1, 4.8%
15.8, 1.7%
14.8, 1.5%
Slice
Spatial components 6 8 10
1: exclude
first frames
2: drift
3: long-range
correlation
or anatomical
effect: remove
by converting
to % of brain
4: signal?

5. FMRIDESIGN example: pain perception50
100
150
200
250
300
350 -1 1 2
Alternating hot and warm stimuli separated by rest (9 seconds each).
hot
warm
-0.2
0.2
0.4
Hemodynamic response function: difference of two gamma densities
Responses = stimuli * HRF, sampled every 3 seconds
Time, seconds

7. FMRILM: fits a linear model for fMRI time series with AR(p) errors
? ?
Yt = (stimulust * HRF) b + driftt c + errort
AR(p) errors:
? ? ?
errort = a1 errort-1 + … + ap errort-p + s WNt
unknown parameters

8. Hot - warm effect, % Sd of effect, % T = effect / sd, 110 df 1 0.5
-0.5 -1
0.25
0.2
0.15
Sd of effect, %
0.1
0.05 6 4 2
T = effect / sd, 110 df -2 -4 -6

10. Results from 4 runs on the same subject

11. MULTISTAT: mixed effects linear model for combining effects from different runs/sessions/subjects:
Ei = effect for run/session/subject i
Si = standard error of effect
Mixed effects model:
Ei = covariatesi c + Si WNiF +  WNiR
}from
FMRILM ? ?
Usually 1, but
could add group,
treatment, age,
sex, ...
‘Fixed effects’ error,
due to variability
within the same run
Random effect,
due to variability
from run to run

12. Target 100 effective df, so use 19mm smoothing:
Run 1
Run 2
Run 3
Run 4
Effect, E i
Sd, S
T stat,
/ S -1 1
MULTISTAT
0.1
0.2 -5 5
Target 100 effective df, so use 19mm smoothing:

14. STAT_THRESHOLD: thresholds and P-values
T, F, Hotelling’s T2, Roy’s maximum root (maximum canonical correlation)
Conjunctions of all these
Arbitrary number of dimensions (supply the resels)
Thresholds and P-values for
Local maxima (takes the best of Bonferroni, random field theory)
Cluster spatial extent (mm3 or resels) allowing for randomness in estimating local FWHM

15. STAT_SUMMARY: SPM-style summary of local maxima and clusters, and their P- and Q-values
Analyses T, F, Hotelling’s T2, Roy’s maximum root (maximum canonical correlation) volumes, and conjunctions of all these
Mask volume and mask threshold can be supplied
Supports isotropic (supply FWHM scalar) or non-isotropic (supply FWHM volume, from FMRILM or MULTISTAT) to calculate resels
Finds all local maxima and clusters above a threshold
Uses resels to calculate P- and Q-values for
Local maxima: uses better of Bonferroni or random field theory
Clusters: allows for randomness in estimating FWHM volume

16. Estimating the delay of the response
Delay or latency to the peak of the HRF is approximated by a linear combination of two optimally chosen basis functions:
delay -5 5 10 15 20 25
-0.4
-0.2
0.2
0.4
0.6
t (seconds)
basis1
basis2
HRF
shift
HRF(t + shift) ~ basis1(t) w1(shift) + basis2(t) w2(shift)
Convolve bases with the stimulus, then add to the linear model

17. Shift of the hot stimulus
T stat for magnitude T stat for shift
Shift (secs) Sd of shift (secs)

18. Shift of the hot stimulus
T stat for magnitude T stat for shift
T>4
T~2
Shift (secs) Sd of shift (secs)
~1 sec
+/- 0.5 sec

19. Combining shifts of the hot stimulus
(Contours are T stat for magnitude > 4)
Run 1
Run 2
Run 3
Run 4
Effect, E i
Sd, S
T stat,
/ S -4 -2 2 4
MULTISTAT 1 -5 5

20. Shift of the hot stimulus
Shift (secs)
T stat for
magnitude > 4.93

21. References http://www.math.mcgill.ca/keith/fmristat
Worsley et al. (2002). A general statistical analysis for fMRI data. NeuroImage, 15:1-15.
Liao et al. (2002). Estimating the delay of the response in fMRI data. NeuroImage, 16:

22. I/O of MINC in FMRISTAT
I/O is written by Roger Gunn and John Aston, based on EMMA
d=FMRIS_READ_IMAGE(‘file.mnc’, slice, frame) reads minc file into MATLAB structure e.g. d.dim=[ ], d.data= array of data read in, etc.
FMRIS_WRITE_IMAGE(d, slice, frame) reverses this, supply d.file_name = ‘file_out.mnc’ and d.parent_file for ‘like’ option of minc tools

23. Limitations of EMMA (1993)
EMMA flips an array if the step is negative, so voxel coordinates do not agree with e.g. register
There’s a lot of stuff in EMMA for PET data analysis that FMRISTAT never uses
EMMA limits the amount of data that can be I/O in one shot – limit is now too low!
Can modify MINC file dimensions, but not step or start
EMMA cannot read vector data e.g. non-linear warps – must use Louis’ def_to_vol to break up a vector into separate x, y, z volumes … waste of space!
Some parts of EMMA use obsolete commands that do not exist in MATLAB 6.2, e.g. table
Need e.g. Frank to create a new EMMA for Windows with every new version of Windows or MATLAB

24. Work-arounds
Need to store 3 x 3 symmetric matrices at every voxel, so write them as 6 ‘frames’
Local FWHM volumes use 2 frames, 1 for local FWHM and 1 for local resels
PYTHON? Jonathan Taylor (Stanford) has translated FMRISTAT into PYTHON, and it can I/O MINC, ANALYZE and AFNI
FMRISTAT can I/O ANALYZE (not well tested) but not yet AFNI …

25. A ‘stat’ file type? MULTISTAT takes as input, and produces as output:
Effect volume
Sd volume
FWHM scalar or volume
DF scalar
Can we combine these into a single ‘stat’ file using EMMA (or a replacement)?