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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)