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Overview of fMRI Analysis
Andy James
fMRI Methods Journal Club
Tuesday, February 8, 2005
Experiment Steps
•
•
•
•
•
•
•
Hypothesis formation
In practice, data
Subject selection
analysis will dictate
Paradigm design
all other steps,
Data collection
including what
hypotheses can
Data preprocessing
feasibly be answered!
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
for ease of reading.
(Peterson et al., 1990)
Model-dependent: General
Linear Model (GLM)
•
•
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
•
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
–
–
–
–
Incorporate within- and across-session variance
Allows broader generalization to population
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
•
•
•
•
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/