Basics of fMRI Time-Series Analysis

Basics of fMRI Time-Series Analysis

Douglas N. Greve

2

fMRI Analysis Overview

Higher Level GLM

First Level GLM Analysis


Subject 3


Subject 4


Subject 1

Subject 2

CX

CX

CX

CX

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



Subject 3


Subject 4


Subject 1

Subject 2

CX

CX

CX

CX









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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Documents

Basics of fMRI Time-Series Analysis