Basics of fMRI Time-Series Analysis
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Basics of fMRI Time-Series Analysis
Douglas N. Greve
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fMRI Analysis Overview
Higher Level GLM
First Level GLM Analysis
First Level GLM Analysis
Subject 3
First Level GLM Analysis
Subject 4
First Level GLM Analysis
Subject 1
Subject 2
CX
CX
CX
CX
PreprocessingMC, STC, B0
SmoothingNormalization
PreprocessingMC, STC, B0
SmoothingNormalization
PreprocessingMC, STC, B0
SmoothingNormalization
PreprocessingMC, STC, B0
SmoothingNormalization
Raw Data
Raw Data
Raw Data
Raw Data
CX
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Overview• Neuroanatomy 101
• fMRI Contrast Mechanism
• Hemodynamic Response
• “Univariate” GLM Analysis
• Hypothesis Testing
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Neuroantomy
• Gray matter• White matter• Cerebrospinal Fluid
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Functional Anatomy/Brain Mapping
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Visual Activation Paradigm
Flickering Checkerboard
Visual, Auditory, Motor, Tactile, Pain, Perceptual,Recognition, Memory, Emotion, Reward/Punishment, Olfactory, Taste, Gastral, Gambling, Economic, Acupuncture,Meditation, The Pepsi Challenge, …
• Scientific• Clinical• Pharmaceutical
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MRI Scanner
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Magnetic Resonance Imaging
T1-weightedContrast
BOLD-weightedContrast
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Blood Oxygen Level Dependence (BOLD)
Neurons
Lungs
Oxygen CO2
OxygenatedHemoglobin(DiaMagnetic)
DeoxygenatedHemoglobin(ParaMagnetic)
Contrast Agent
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Functional MRI (fMRI)Localized
NeuralFiring
LocalizedIncreased
Blood FlowStimulus
LocalizedBOLD
Changes
Sample BOLD response in 4D Space (3D) – voxels (64x64x35, 3x3x5mm^3, ~50,000) Time (1D) – time points (100, 2 sec) – Movie
Time 1 Time 2 Time 3 …
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4D Volume
64x64x35 85x1
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Visual/Auditory/Motor Activation Paradigm
15 sec ‘ON’, 15 sec ‘OFF’ • Flickering Checkerboard• Auditory Tone• Finger Tapping
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Block Design: 15s Off, 15s On
Voxel 1
Voxel 2
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Contrasts and Inference
p = 10-11, sig=-log10(p) =11 p = .10, sig=-log10(p) =1
OFFin N Var, Mean,,,
ONin N Var, Mean,,,
)2()1()1(
2
2
2
22
OFFOFFOFF
ONONON
OFFON
OFFOFFONON
OFFON
N
N
NNNN
t
OFFON Contrast
2
22
)2(
)1()1(st)Var(Contra
OFFON
OFFOFFONON
NN
NN
ONOFF
2ON2
OFF
Voxel 1 Voxel 2
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Statistical Parametric Map (SPM)+3%
0%
-3%
Contrast AmplitudeON-OFF
ContrastAmplitudeVariance
(Error Bars)
Significance t-Map (p,z,F)(Thresholded
p<.01) “Massive Univariate Analysis” -- Analyze each voxel separately
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Statistical Parametric Map (SPM)
Signficance Map sig=-log10(p) Signed by contrast
“Massive Univariate Analysis” -- Analyze each voxel separately
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Hemodynamics
• Delay• Dispersion• Grouping by simple time point inaccurate
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Hemodynamic Response Function (HRF)
TR (~2sec)
Time-to-Peak (~6sec)
Dispersion
Undershoot
Equilibrium(~16-32sec)
Delay (~1-2sec)
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Convolution with HRF
• Shifts, rolls off; more accurate • Loose ability to simply group time points• More complicated analysis• General Linear Model (GLM)
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GLMData fomone voxel
= Task base+
Baseline Offset(Nuisance)Task
Task=onoff•Implicit Contrast•HRF Amplitude
base=off
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Matrix Model
y = X *
Task
base
Data fromone voxel
Design MatrixRegressors
=
Vector ofRegressionCoefficients(“Betas”)
Design Matrix
Obs
erva
tion
s
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Two Task Conditions
y = X *
Odd
Even
base
Data fromone voxel
Design MatrixRegressors
=
Design Matrix
Obs
erva
tion
s
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Working Memory Task (fBIRN)
Images Stick Figs
“Scrambled” Encode Distractor Probe
16s 16s 16s 16s
Stick Figs
0. “Scrambled” – low-level baseline, no response1. Encode – series of passively viewed stick figuresDistractor – respond if there is a face 2. Emotional 3. NeutralProbe – series of two stick figures (forced choice) 4. Following Emotional Distractor 5. Following Neutral Distractor
fBIRN: Functional Biomedical Research Network (www.nbirn.net)
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Five Task Conditions
Encode
EmotDist
NeutDist
EmotProbe
NeutProbe
=
y = X *
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GLM Solution
Encode
EmotDist
NeutDist
EmotProbe
NeutProbe
=
y = X * • Set of simultaneous equations • Each row of X is an equation• Each column of X is an unknown• s are unknown• 142 Time Points (Equations)• 5 unknowns
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Estimation of s
22
2
1
2
2
)ˆ( ,)ˆ( :Unbiased
Variance Residual ˆˆ
ˆ
Estimate) (Noise Residual ˆˆ
Estimate Signal ˆˆ
EstimatesParameter )(ˆ
and :Unknowns
),0(~ , ,
nnTrue
T
n
TT
n
n
EE
DOF
nn
syn
Xs
yXXX
NnnsynXy
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Estimates of the HRF Amplitude
Encode
EmotDist
NeutDist
EmotProbe
NeutProbe
=
Distractor Neutral following Probe toresponsein amplitude cHemodynamiˆ
Distractor Emotional following Probe toresponsein amplitude cHemodynamiˆ
Distractor Neutral toresponsein amplitude cHemodynamiˆ
Distractor Emotional toresponsein amplitude cHemodynamiˆ
Encode toresponsein amplitude cHemodynamiˆ
)(ˆ ,
NeuttProbe
EmotProbe
NeutDist
EmotDist
Encode
1
yXXXnXy TT
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Hypotheses and ContrastsWhich voxels respond more/less/differently to the Emotional Distractor than to the Neutral Distractor?
0,0,0ˆˆ
ˆˆ
ˆ
ˆˆ
NDistEDist
NDistEDist
NDistEDist
NDistEDist
MatirxContrast 00110
0c
0c
1c
1c
0c
ˆcˆcˆcˆcˆc
NProbe
EProbe
NDist
EDist
Encode
NProbeNProbeEProbeEProbeNDistNDistEDistEDistEncodeEncode
C
Contrast: Assign Weights to each Beta
EDist̂NDist̂
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Hypotheses
• Which voxels respond more to the Emotional Distractor than to the Neutral Distractor? • Which voxels respond to Encode (relative to baseline)?• Which voxels respond to the Emotional Distractor?• Which voxels respond to either Distractor?• Which voxels respond more to the Probe following the Emotional Distractor than to the Probe following the Neutral Distractor?
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Which voxels respond more to the Emotional Distractor than to the Neutral Distractor?
1. E
ncod
e2.
ED
ist
3. N
Dis
t4.
EP
robe
5. N
Pro
be
• Only interested in Emotional and Neutral Distractors• No statement about other conditions
Condition: 1 2 3 4 5Weight 0 +1 -1 0 0
Contrast Matrix C = [0 +1 -1 0 0]
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Which voxels respond to Encode (relative to baseline)?1.
Enc
ode
2. E
Dis
t3.
ND
ist
4. E
Pro
be5.
NP
robe
Only interested in Encode• No statement about other conditions
Condition: 1 2 3 4 5Weight +1 0 0 0 0
Contrast Matrix C = [+1 0 0 0 0]
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Which voxels respond to the Emotional Distractor (wrt baseline)?1.
Enc
ode
2. E
Dis
t3.
ND
ist
4. E
Pro
be5.
NP
robe
• Only interested in Emotional Distractor• No statement about other conditions
Condition: 1 2 3 4 5Weight 0 +1 0 0 0
Contrast Matrix C = [0 +1 0 0 0]
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Which voxels respond to either Distractor (wrt baseline)?1.
Enc
ode
2. E
Dis
t3.
ND
ist
4. E
Pro
be5.
NP
robe
• Only interested in Distractors• Average of two Distractors• No statement about other conditions
Condition: 1 2 3 4 5Weight 0 ½ ½ 0 0
Contrast Matrix C = [0 0.5 0.5 0 0]
• Don’t have so sum to 1, but usual• Could have used an F-test instead of average
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Which voxels respond more to the Probe following the Emotional Distractor than to the Probe following the Neutral Distractor?
1. E
ncod
e2.
ED
ist
3. N
Dis
t4.
EP
robe
5. N
Pro
be • Only interested in Probes• No statement about other conditions
Condition: 1 2 3 4 5Weight 0 0 0 +1 -1
Contrast Matrix C = [0 0 0 +1 -1]
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Contrasts and the Full Model
ate)(multivariTest -F ˆˆˆF
e)(univariatTest - tˆ)(
ˆ
ˆ
ˆt
Cin Rows J
Estimate VarianceContrast ˆ)(1ˆˆ
Contrast ˆˆ
ˆˆ Variance, Residual ˆˆ
ˆ
EstimatesParameter )(ˆ
),0(~ , ,
1JDOF,
21DOF
212
2
1
2
T
nTT
nTT
T
n
TT
n
CXXC
C
CXXCJ
C
XynDOF
nn
yXXX
NnnsynXy
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fMRI Analysis Overview
Higher Level GLM
First Level GLM Analysis
First Level GLM Analysis
Subject 3
First Level GLM Analysis
Subject 4
First Level GLM Analysis
Subject 1
Subject 2
CX
CX
CX
CX
PreprocessingMC, STC, B0
SmoothingNormalization
PreprocessingMC, STC, B0
SmoothingNormalization
PreprocessingMC, STC, B0
SmoothingNormalization
PreprocessingMC, STC, B0
SmoothingNormalization
Raw Data
Raw Data
Raw Data
Raw Data
CX
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Time Series Analysis Summary
• Correlational• Design Matrix (HRF shape)• Estimate HRF amplitude (Parameters)• Contrasts to test hypotheses• Results at each voxel:
• Contrast Value• Contrast Value Variance• p-value (Volume of Activation)
• Pass Contrast Value and Variance up to higher level analyses
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