fmri intro
TRANSCRIPT
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Basics of fMRI Analysis:
Preprocessing, First-Level Analysis, and
Group Analysis
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Overview
Neuroanatomy 101 and fMRI Contrast Mechanism Preprocessing
Hemodynamic Response
Univariate GLM Analysis Hypothesis Testing
Group Analysis (Random, Mixed, Fixed)
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Neuroanatomy
Gray matter
White matter
Cerebrospinal Fluid
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Functional Anatomy/Brain Mapping
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Visual Activation Paradigm
FlickeringCheckerboard
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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Magnetic Resonance Imaging
T1-weighted
Contrast
BOLD-weighted
Contrast
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Blood Oxygen Level Dependent (BOLD)
Neurons
Lungs
Oxygen CO2
Oxygenated
Hemoglobin
(DiaMagnetic)
Deoxygenated
Hemoglobin
(ParaMagnetic
Contrast Agen
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Functional MRI (fMRI)
Localized
Neural
Firing
Localized
Increased
Blood Flow
Stimulus
Localized
BOLD
Changes
Sample BOLD response in 4D
Space (3D)voxels (646435, 335 mm3, ~50,000)
Time (1D)time points (100, 2 sec)Movie
Time 1 Time 2 Time 3
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4D Volume
646435 851
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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
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
Raw Data
Raw Data
Raw Data
Raw Data
CX
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Preprocessing
Assures that assumptions of the analysis are met Time course comes from a single location
Uniformly spaced in time
Spatial smoothness
Analysisseparating signal from noise
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Preprocessing
Start with a 4D data set
1. Motion Correction2. Slice-Timing Correction
3. B0 Distortion Correction
4. Spatial Normalization
5. Spatial Smoothing
End with a 4D data set
Can be done in other orders Not everything is always done
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Motion
Analysis assumes that time course represents a
value from a single location
Subjects move
Shifts can cause noise, uncertainty
Edge of the brain and tissue boundaries
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Motion and Motion Correction
Motion correction reduces motion
Not perfect
Raw Corrected
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Motion Correction
Motion correction parameters
Six for each time point
Sometimes used as nuisance regressors
How much motion is too much?
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Slice Timing
Ascending Interleaved
Volume not acquired all at one time
Acquired slice-by-slice Each slice has a different delay
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Volume = 30 slices TR = 2 sec
Time for each slice = 2/30 = 66.7 ms
0s
2s
Effect of Slice Delay on Time Course
Sli Ti i C ti
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Slice Timing Correction
Temporal interpolation of adjacent time points
Usually sinc interpolation
Each slice gets a different interpolation
Some slices might not have any interpolation Can also be done in the GLM
You must know the slice order!
X
TR1 TR2 TR3
Slice
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B0 Distortion
Metric (stretching or compressing)
Intensity Dropout
A result of a long readout needed to get an entire slice in asingle shot.
Caused by B0 Inhomogeneity
Stretch
Dropout
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B0 Map
Echo 2TE2
Magnitude
Echo 1
TE1
Phase
Voxel Shift Map
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Voxel Shift Map
Units are voxels (3.5 mm)
Shift is in-plane
Blue = PA, Red AP
Regions affected near air/tissue boundaries
sinuses
B Distortion Correction
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B0 Distortion Correction
Can only fix metric distortion Dropout is lost forever
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B0 Distortion Correction
Can only fix metric distortion
Dropout is lost forever Interpolation
Need:
Echo spacing readout time
Phase encode direction
More important for surface than for volume
Important when combining from different scanners
S i l N li i
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Spatial Normalization
Transform volume into another volume
Re-slicing, re-gridding New volume is an atlas space
Align brains of different subjects so that a given
voxel represents the same location.
Similar to motion correction
Preparation for comparing across subjects
Volume-based
Surface-based
Combined Volume-surface-based (CVS)
Spatial Normalization: Volume
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Spatial Normalization: Volume
Subject 1
Subject 2
Subject 1
Subject 2
MNI305
MNI152
Native Space MNI305 Space
Affine (12 DOF) Registration
Spatial Normalization: Surface
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Subject 1 Subject 2 (Before)
Subject 2 (After)
Spatial Normalization: Surface
Shift, Rotate, Stretch
High dimensional (~500k)
Preserve metric properties
Take variance into account Common space for group
analysis (like Talairach)
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Spatial Smoothing
Replace voxel value with a weighted average of nearby voxel
(spatial convolution) Weighting is usually Gaussian
3D (volume)
2D (surface)
Do after all interpolation, before computing a standarddeviation
Similar to interpolation
Improves SNR
Improves intersubject registration
Can have a dramatic effect on your results
S ti l S thi
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Spatial Smoothing
Full-Width/Half-max
Spatially convolve image with Gaussian kernel.
Kernel sums to 1 Full-Width/Half-max:FWHM = s/sqrt(log(256))
s = standard deviation of the Gaussian
0 FWHM 5 FWHM 10 FWHM
2mm FWHM
10mm FWHM
5mm FWHM
Full Max
Half Max
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Spatial Smoothing
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Effect of Smoothing on Activation
Working memory paradigm FWHM: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 mm
V l S f b d S thi
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Volume- vs Surface-based Smoothing
5 mm apart in 3D
25 mm apart on surface
Averaging with other tissue
types (WM, CSF)
Averaging with other
functional areas
14mm FWHM
P i
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Preprocessing
Start with a 4D data set
1. Motion Correction - Interpolation2. Slice-Timing Correction
3. B0 Distortion Correction - Interpolation
4. Spatial Normalization - Interpolation
5. Spatial SmoothingInterpolation-like
End with a 4D data set
Can be done in other orders Not all are done
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fMRI Time-Series Analysis
fMRI Analysis Overview
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a y v v w
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
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
Raw Data
Raw Data
Raw Data
Raw Data
CX
Visual/Auditory/Motor Activation Paradigm
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Visual/Auditory/Motor Activation Paradigm
15 sec ON, 15 sec OFF Flickering Checkerboard
Auditory Tone
Finger Tapping
Block Design: 15s Off, 15s On
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g 5 O , 5 O
Voxel 1
Voxel 2
Stimulus Schedule
Paradigm File
Contrasts and Inference
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Contrasts and Inference
p = 1011, sig = log10(p) =11 p= 0.10, sig = log10(p) =1
OFFinNVar,Mean,,,
ONinNVar,Mean,,,
)2(
)1()1(
2
2
2
22
OFFOFFOFF
ONONON
OFFON
OFFOFFONON
OFFON
N
N
NN
NNt
s
s
ss
OFFON Contrast
2
2
)2(
)1()1(st)Var(Contra
OFFON
OFFONON
NN
NN ss
ON
OFF
2
ONs2
OFFs
Voxel 1 Voxel 2
Note:z, t, Fmonotonic withp
Statistical Parametric Map (SPM)
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Statistical Parametric Map (SPM)
+3%
0%
-3%
Contrast AmplitudeCON, COPE, CES
Contrast Amplitude
Variance
(Error Bars)VARCOPE, CESVAR
Significance
t-Map (p,z,F)
(Thresholdedp
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Hemodynamics
Delay
Dispersion
Grouping by simpletime point inaccurate
C l i i h HRF
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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)
GLM
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GLM
Data fom
one voxel
= Task
base
+
Baseline Offset
(Nuisance)Task
Task=onoffImplicit Contrast
HRF Amplitude
base=off
Matrix Model
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Matrix Model
y = X *
Taskbase
Data from
one voxel
Design Matrix
Regressors
=
Vector of
Regression
Coefficients
(Betas)
Design Matrix
Observa
tions
Two Task Conditions
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Two Task Conditions
y = X *
OddEven
base
Data from
one voxel
Design Matrix
Regressors
=
Design Matrix
Observa
tions
Working Memory Task (fBIRN)
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g y ( )
Images Stick Figs
Scrambled Encode Distractor Probe
16s 16s 16s 16s
Stick Figs
0. Scrambled low-level baseline, no response
1. Encodeseries of passively viewed stick figures,
Distractorrespond if there is a face
2. Emotional
3. Neutral
Probeseries of two stick figures (forced choice)
4. following Emotional Distractor
5. following Neutral Distractor
fBIRN: Functional Biomedical Research Network (www.nbirn.net)
Five Task Conditions
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Five Task Conditions
EncodeEmotDistNeutDist
EmotProbeNeutProbe
=
y = X *
GLM Solution
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GLM Solution
EncodeEmotDistNeutDistEmotProbeNeutProbe
=
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
)( 1 yXXX TT
Estimates of the HRF Amplitude
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st ates o t e p tude
EncodeEmotDistNeutDistEmotProbeNeutProbe
=
yXXXnXy TT 1)(,
DistractorNeutralfollowingProbetoresponseinamplitudechemodynami
DistractoEmotionalfollowingProbetoresponseinamplitudechemodynami
DistractorNeutraltoresponseinamplitudechemodynami
DistractorEmotionaltoresponseinamplitudechemodynami
Encodetoresponseinamplitudechemodynami
NeutProbe
EmotProbe
NeutDist
EmotDist
Encode
Hypotheses and Contrasts
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ypWhich voxels respond more/less/differently to the Emotional
Distractor than to the Neutral Distractor?
0,0,0
NDistEDist
NDistEDist
NDistEDist
NDistEDist
MatirxContrast00110
0c
0c
1c
1c
0c
ccccc
NProbe
EProbe
NDist
EDist
Encode
NProbeNProbeEProbeEProbeNDistNDistEDistEDistEncodeEncode
C
Contrast: Assign Weights to each Beta
EDist
NDist
Hypotheses
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yp
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 theNeutral Distractor?
Which voxels respond more to the Emotional Distractor than to
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the Neutral Distractor?
1.
Encod
e
2.
EDist
3.
NDist
4.
EProb
e
5.
NProbe
Only interested in Emotional and Neutral Distract
No statement about other conditions
Condition: 1 2 3 4 5
Weight 0 +1 -1 0 0
Contrast Matrix
C = [0 +1 -1 0 0]
Contrasts and the Full Model
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First Level GLM Outputs
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p
+3%
0%
-3%
Contrast AmplitudeCON, COPE, CES
Contrast Amplitude
Variance
(Error Bars)VARCOPE, CESVAR
Significance
t-Map (p,z,F)
(Thresholdedp
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y y
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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fMRI Group Analysis
fMRI Analysis Overview
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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
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
PreprocessingMC, STC, B0
Smoothing
Normalization
Raw Data
Raw Data
Raw Data
Raw Data
CX
Overview
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Goal of Group Analysis
Types of Group Analysis
Random Effects, Mixed Effects, Fixed Effects
Multi-Level General Linear Model (GLM)
Spatial Normalization, Atlas Space
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Subject 1
Subject 2
Subject 1
Subject 2
MNI305
Native Space MNI305 Space
Affine (12 DOF) Registration
Inter-Subject AveragingS h i l
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58
Subjec
t1
Subject2
NativeSpherical Spherical
Surface-to-Surface
Surface-t
Surface
GLM
Demographics
(cf. Talairach)
Is Pattern Repeatable Across Subject?
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Subject 1 Subject 2 Subject 3 Subject 4 Subject 5
Group Analysis
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Does not have to
be all positive!
Contrast Amplitudes
Contrast Amplitudes Variances
(Error Bars)
Random Effects (RFx) Analysis
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G
Gs
1
1
,
22
2
2
G
G
iG
G
G
GG
NDOF
N
Nt
G
G
s
ss
s
RFx
Random Effects (RFx) Analysis
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G
Gs
RFx
Model Subjects as a Random Effect
Variance comes from a single source:variance across subjects Mean at the population mean
Variance of the population variance
Does not take first-level noise into account(assumes 0)
Ordinary Least Squares (OLS)
Usually less activation than individuals
Mixed Effects (MFx) Analysis
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MFx
RFx
Down-weight each subject based on variance.
Weighted Least Squares (vs. Ordinary LS)
Mixed Effects (MFx) Analysis Down-weight each subject based on variance
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MFx
Down-weight each subject based on variance.
Weighted Least Squares (vs. Ordinary LS)
Protects against unequal variances across group or
groups (heteroskedasticity)
May increase or decrease significance with respect to
simple Random Effects
More complicated to compute
Pseudo-MFx simply weight by first-level
variance (easier to compute)
Fixed Effects (FFx) Analysis
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FFx
RFx
i
G
i
G
DOFDOF
N
t
G
G
2
2
2
2
ss
s
2
is
Fixed Effects (FFx) Analysis
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FFx
G
i
G
DDOF
N
t
G
G
2
2
2
2
ss
s
As if all subjects treated as a single subject (fixed effect)
Small error bars (with respect to RFx) Large DOF
Same mean as RFx
Huge areas of activation
Not generalizable beyond sample.
fMRI Analysis OverviewSubject 1
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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
C1X1
C1X1
C1X1
C1X1
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
Preprocessing
MC, STC, B0
Smoothing
Normalization
PreprocessingMC, STC, B0
Smoothing
Normalization
Raw Data
Raw Data
Raw Data
Raw Data
CGXG
Higher Level GLM Analysisy = X *
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G
Gs
=
11
1
11
G
y = X
Data fromone voxel
Design Matrix
(Regressors)
Vector of
Regression
Coefficients
(Betas)
Observations
(Low-LevelContrasts
)
Contrast Matrix:
C = [1]
Contrast = C* = G
One-Sample Group Mean (OSGM)
Summary
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PreprocessingMC, STC, B0, Normalize, Smooth
First Level GLM AnalysisDesign matrix, HRF,
Nuisance
Contrasts, Hypothesis Testingcontrast matrix
Group AnalysisRandom, Mixed, Fixed
Multi-level GLM (Design and Contrast Matrices)