Day 2: Event-related fMRI experiment example.

1. SPM 12 practical course
by Volodymyr B. Bogdanov
vlabogd@yahoo.com
Kyiv 2015
Day 2: Event-related design first
(individual) level statistical
analysis and second (group)
level analysis
Model specification, Factor design and Review, Estimation,
Inference

2. Formula:
Y =Y = αα ++ ββ11 XX11 + …+ … ββnn XXnn ++ εε
Y – data
X – function (predictor, regressor)X – function (predictor, regressor)
αα – intercept (baseline)
ββ – parameter (slope)– parameter (slope)
εε – error (residuals)– error (residuals)
What is GLM?
Generalized Liner Model

3. data = response + noise + drift
+ +
X
Y
=
Matalb syntaxis:
glmfit( [X; drift; noise]’, Y)
ans =
-0.0000 (αα)
1.0000 (ββ for X)
1.0000 (ββ for drift)
1.0000 (ββ for noise)
drift noise

4. εε – error (residuals)– error (residuals)
Y – data X – function (predictor, regressor)X – function (predictor, regressor)
α – intercept (baseline)
ββ–parameter(slope)–parameter(slope)
glmfit(X, Y)
ans =
1.0093 (α)
1.0899 (β)
X
Y

5. εε – error (residuals)– error (residuals) X – function (predictor, regressor)X – function (predictor, regressor)
X
εε

6. Chapter 32
Face group fMRI data
Chapter 31
Face fMRI data
SPM12 Manual
C:spm12man
Functional images
Contrast images
(one individual)
Contrast images
(many individuals)
First level;
Fixed effects -
locally relevant
Second level;
Radom effects -
population relevant
Contrast images
(one group)

7. Briefly, this is a 2 factorial study with factors “fame”
and “repetition” where famous and non-famous faces were
presented twice against a checkerboard baselin.
The subject was asked to make fame judgements by making
key presses.

8. There are thus four event-types of interest; first and second
presentations of famous and non-famous faces, which we
denote N1, N2, F1 and F2.
Two independent factors:
“N”
Non-famous
“F”
Famous
“1” first
presentation
“2” second
presentation

9. Non-famous, first presentation: N1
Non-famous, second presentation: N2
Famous, first presentation: F1
Famous, second presentation: F2

10. Categorical 2 factor design Parametric 2 factor designCategorical 2 factor design Parametric 2 factor design

11. Preprocessing, event related design
(Chapter 31, Face fMRI data):
1. Reorientation
2. Realignment
3. Slice timing correction
4. Coregistration
5. Segmentation
6. Normalisation of functional images
7. Normalisation of the structural image
8. Smoothing

12. N=24 axial slices acquired with a TR=2s (time between the onset of the first slice of
one volume and the first slice of next volume).
TA is the time between the onset of the first and last slice of one volume
(i.e. TA = TR - TR/N) The most superior slice was sampled first.
But in the file the first slice (slice number 1) is the most inferior slice, making the slice
acquisition order [24 23 22 ... 1].
Slice timing correction: rationale
2 sec. delay!

13. After preprocessing is finished, it is time for statistical analysis.
I will try to cover following questions:
Categorical and parametric designs
Design matrix – how to read and understand it
Basis hemodynamic response function (HRF) and its time and
dispersion derivatives.
T and F contrast matrices
Two-factor factorial design specification. (from the SPM Manual)
Statistical inferences
Statistical table – how to read and understand it
Event-related peristimulus histogram (PSTH). (from the SPM Manual)
How to set different contrasts manually.
Parametric design model specification and plotting parametric
response. (from the SPM Manual)

14. Categorical design: what is it:
Modeling different features of the
stimuli as separate conditions, e.g. non-
famous and famous faces, or first and
second presentation of the same
image.

16. Category TD
Category UD
Category UE
Category TE

17. Categorical 2 factor design: resulting design matrix

18. N1 condition
Red – stimuli onsets
Blue – expected BOLD response
How to read design matrix?
The modeled responses to
different conditions are
arranged in columns.
Raws represent scans (2 sec
each in our case)

19. Scans (“images”), 2 seconds each.
Red – stimuli onsets
Blue – expected BOLD response

20. Expected BOLD responses to
two conditions
Blue – N1 condition
Red – F1 stimuli onsets

21. N1 t d Modeling time and dispersion derivatives of N1

22. Modeling time and dispersion derivatives of N1
What is time and dispersion derivatives and why
it is useful to include them in the model?

24. Combinations of canonical hemodynamic response function
(HRF) and its time derivative (t), correction for delay of response
HRF-tHRF+t

25. HRF-d
HRF+d
Combinations of canonical hemodynamic response function
(HRF) and its dispersion derivative (d), correction for
duration of response.

26. N1 t d N2 t d F1 t d F2 t d
motion parameters

27. What is T and F teststs?
T-test – one-directional effects (increase, decrease).
F-test – non-directional effects (either increase or decrease).
How to combine or compare different conditions (repressors,
predictors)?
T or F contrasts
Examples:
T-contrast [1]:
Condition has positive effect
F-contrast [1]:
Condition has positive or
negative effect
T-contrast [1 1]:
I total two conditions have
positive effect
F-contrast [1 1]:
In total two conditions have
positive or negative effect

28. T-contrast [1 0 0]:
First condition has positive effect

29. F-contrast [1 0 0]:
Condition has positive or negative effect

30. T-contrast [1 1 0]:
The first and second
conditions have positive
effect, controlled for any
effects of the third.
F-contrast [1 0 0; 0 1 0]:
Either first, or the second or both
conditions have either positive or
negative effect controlled for effect of
the third. If the first has positive and
the second has negative effect it still
works.

31. T-contrast [1 1 0]:
In total two conditions have positive effect,
controlled for the effect of the third

32. F-contrast [1 0 0; 0 1 0]

33. T-contrast [1 -1 0]:
First condition has greater
has positive effect than
the second, controlled for
effect of the third
F-contrast [1 -1 0]:
First condition has
somehow different effect,
than the second, controlled
for effect of the third
T-contrast [1 -0.5 -0.5]:
First condition has greater
has positive effect than two
other conditions.
F-contrast [1 -1 0; 0 1 -1]:
There is a difference of
effects between 3 conditions

34. F-contrast [1 -1 0]:
First condition has somehow different effect, than the
second, controlled for effect of the third

35. T-contrast [1 -1 0]:
First condition has greater has positive effect than the
second, controlled for effect of the third

36. What is factorial design?
It is a set of contrasts for complete combination of all levels of
all factors (2 factors in this case, factor “fame” and factor
“repetition”).
It can be set manually at the stage of contrast manager, but if
indicated in model specification proper contrasts are
generated automatically.
In current example Factorial design allows to estimate:
Effect of fame (controlled for repetition)
Effect of repetition (controlled for fame)
Interaction of two effects.

37. Category TD Category UD Category UECategory TE
Category TD Category UD Category UECategory TE
Effect of “easiness”:
vs
vs
Effect of “tastiness”:
Interaction of the two:
Category TD Category UE
Category UD Category TE
vs

38. Category TD Category UD Category UECategory TE
Effect of “easiness”:
vs
Consumption at the party
UD
UE
TD
TE

39. Preference among children
UD
UE
TD
TE
Category TD Category UD Category UECategory TE vs
Effect of “tastiness”:

40. Interaction of the two:
Category TD Category UE
Category UD Category TE
vs
For example Craving can be higher
for untasty difficult and tasty easy,
then for others.
UD
UE
TD
TE

41. The order of naming these factors is important - the factor to be
specified first is the one that “changes slowest”
In the list of conditions (1) N1, (2) N2, (3) F1, (4) F2 the factor
“repetition” changes every condition and the
factor “fame” changes every other condition.
So “Fame” changes slowest and is entered first.
Factor 1
(2 levels)
Fame
Factor 2
(2 levels)
Repetition
N1 0 0
N2 0 1
F1 1 0
F2 1 1
Always remeber the order of
conditions!
Important for settings of the
statistical contrasts.

42. Factor 1
(2 levels)
Repetition
Factor 2
(2 levels)
Fame
N1 0 0
F1 0 1
N2 1 0
F2 1 1
If the list of conditions is different (1) N1, (2) F1, (3) N2, (4) F2
the factor “Fame” changes every condition and the
factor “Repetition” changes every other condition.
So “Repetition” changes slowest and is entered first.

43. MIP – maximum
intensity projections
over glass-brain
Current contrast
(T-contrast)
[1 0 0 1 0 0 1 0 0 1]
Design matrix
Peak-level statistical threshold
Statistical results:

44. x, y, z (mm): coordinates in MNI space for each maximum.
Statistical results (table):

45. Peak-level: the chance (p) of finding (under the null hypothesis) a peak
with this or a greater height (T-statistic), uncorrected for search volume.

46. Peak-level: the chance (p) of finding (under the null hypothesis) a peak with
this or a greater height (T-statistic), corrected (FWE – familywise error)
(GOOD!)

47. Cluster is a number of voxels that reach the threshold, size of the
cluster (in voxels)

48. Cluster is a number of voxels that reach the threshold, size of the
cluster (in voxels)

49. Cluster-level: the chance (p) of finding a cluster with this many (ke) or a
greater number of voxels, corrected (FWE or FDR) / uncorrected for
search volume

50. Parametric design: what is it?
Modeling a feature of a condition as
continuous variable, e.g. the
interval between the first and the
second occurrence of the
presentation of the same face.

51. Parametric modulator –
weight of one unit
500 g
3000 g
200 g
100 g …
150 g
300 g

52. Parametric 2 factor design

53. Second level statistics – effect of faces in general (pulled
across conditions)
1. One canonical HRF
2. Informed set – canonical + 3 derivatives
3. Finite impulse response
Chapter 32
Face group fMRI data