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```Overview of fMRI Analysis
Andy James
fMRI Methods Journal Club
Tuesday, February 8, 2005
Experiment Steps
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Hypothesis formation
In practice, data
Subject selection
analysis will dictate
all other steps,
Data collection
including what
hypotheses can
Data preprocessing
Data Analysis
Publication
Classifying statistical approaches
By response / dependent variable
• qualitative (accuracy, keypress)
• quantitative (RT, BOLD)
By model dependence
• Model dependent (t-test, GLM, Fourier)
• Model independent (ICA, correlational)
Model-dependent: t-test
Question: By how many standard deviations
do response samples for two tasks differ?
x-y
t= s
xy
(Huettel, 2004)
Statistical Parametric Map (SPM)
Each voxel represents
a statistical value or
probability (i.e. a
t-score).
Map is color coded
(Peterson et al., 1990)
Model-dependent: General
Linear Model (GLM)
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Made popular by SPM (Friston, 1995)
GLM is a linear regression in which
a) Model is constructed from stimulus paradigm
b) Data is fitted to model
c) Goodness of Fit is evaluated
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With fMRI, typically univariate
(just one dependent variable: BOLD activity)
Assumption: Relationships are LINEAR and ADDITIVE
Understanding GLM Equations
y(t) = b * x(t) + c + e(t)
y(t) : Dependent / Response Variable
x(t) : Independent / Predictor Variable
e(t): error
b: beta weight relating x(t) to y(t).
c: constant (baseline activity)
Understanding GLM Equations
Time
y(t) = b * x(t) + c + e(t)
300
312
298
305 = b*
452
465
445
0
0
0
0
1
1
1
+ 300
+ 300
+ 300
+ 300
+ 300
+ 300
+ 300
+ 0
+ 12
+ (-2)
+ 5
+ 2
+ 15
+ (-5)
Understanding GLM Equations
y(t) = b * x(t) + c + e(t)
What value
of b best
fits these
equations?
(Least Sum
of Squares)
300
312
298
305
452
465
445
=
=
=
=
=
=
=
0
0
0
0
b
b
b
+ 300
+ 300
+ 300
+ 300
+ 300
+ 300
+ 300
+ 0
+ 12
+ (-2)
+ 5
+ 2
+ 15
+ (-5)
Note:
Still
univariate
Graphical Model representation
Graphical model for
two independent variables:
x1(t) = visual stimulation
x2(t) = auditory stimulation
Test yourself:
Univariate or multivariate?
Time
y(t) = b1*x1(t) + b2*x2(t)
+ c + e(t)
x1(t)
x2(t)
y(t) = b1*x1(t) + b2*x2(t)
+ b3*[x1(t)*x2(t)]
+ c + e(t)
Interaction effects:
“is the whole greater than
the sum of the parts?”
ex: thalamic response
to simultaneous visual
and auditory stimuli
Time
Modeling Interaction Effects
x1(t)
x2(t)
x1(t)*x2(t)
Modeling the Whole Brain
• BrainVoyager software calculates a separate
GLM for each voxel
• Is SPM software’s GLM multivariate?
• EPI: 128 x 128 x 36 voxels = ~80,000 voxels
• With a = .05; expect 4,000 false positives!
How can we control for this false positive rate?
Controlling for False Positives
• Bonferonni correction: a / # comparisons
.05 / 80,000  a = .0000006! Too conservative!
• Spatial smoothing:
Clump voxels into groups (ex: cubes of 27
voxels) to reduce # comparisons (80,0003,000)
• Clustering
Only include significantly active voxels that are
adjacent to N significantly active voxels
Multicollinearity
• b value assess how well predictor
individually predicts response.
• What if two IVs are correlated?
(i.e. leg length)
• Can GLM handle
multicollinearity?
GLM: The Model is Everything!
• Trash in, trash out
– bad model = meaningless findings
• A “good” GLM is one that can…
…model interaction effects
…test viability of additional predictors (“F-drop”)
…assess correlations among independent variables
• Can BrainVoyager and SPM do this?
Multiple Subjects Statistics
• Requires standardization of brains (MNI)
• Fixed-effects analyses
– Only examines within-session variance
• Mixed or Random-effects analyses
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Incorporate within- and across-session variance
More conservative
Requires large N. (“large” > 10)
Non-GLM approaches
• Structural equation modeling
– Make assumptions of directionality of
influences (i.e. frontal  SMA  Motor strip)
– Test strength of directional influences
– BUT bound by model!
• Fourier analysis
– Model brain response by stimulus frequency
Fourier analysis
(Huettel, 2004)
Next session: Temporally
Invariant Techniques
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Factor Analysis
Independent Component Analysis (ICA)
Temporal Clustering Analysis (TCA)
Connectivity Analysis (“correlational”)
– within-condition interregional covariate
analysis (WICA)
– all other correlational approaches are subset
References
• Huettel SA, Song AW & McCarthy G. (2004).
Functional Magnetic Resonance Imaging. Sinauer
Associates Inc; Sunderland, Massachusetts USA.
• Peterson SE, Fox PT, Snyder AZ & Raichle ME.
(1990). Activation of the extrastriate and frontal
cortical areas by visual words and word-like
stimuli. Science, 249(4972), 1041-1044.
• SPM software: http://www.fil.ion.ucl.ac.uk/spm/
```
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