Basics of fMRI Time-Series Analysis

Douglas N. Greve

fMRI Analysis Overview

Higher Level GLM

First Level GLM Analysis

Subject 3

Subject 4

Subject 1

Subject 2

PreprocessingMC, STC, B0

SmoothingNormalization

Raw Data

Overview• Neuroanatomy 101

• fMRI Contrast Mechanism

• Hemodynamic Response

• “Univariate” GLM Analysis

• Hypothesis Testing

Neuroantomy

• Gray matter• White matter• Cerebrospinal Fluid

Functional Anatomy/Brain Mapping

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

MRI Scanner

Magnetic Resonance Imaging

T1-weightedContrast

BOLD-weightedContrast

Blood Oxygen Level Dependence (BOLD)

Neurons

Oxygen CO2

OxygenatedHemoglobin(DiaMagnetic)

DeoxygenatedHemoglobin(ParaMagnetic)

Contrast Agent

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 …

4D Volume

64x64x35 85x1

Visual/Auditory/Motor Activation Paradigm

15 sec ‘ON’, 15 sec ‘OFF’ • Flickering Checkerboard• Auditory Tone• Finger Tapping

Block Design: 15s Off, 15s On

Voxel 1

Voxel 2

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(

OFFOFFOFF

ONONON

OFFOFFONON

OFFON Contrast

)1()1(st)Var(Contra

OFFOFFONON

Voxel 1 Voxel 2

Statistical Parametric Map (SPM)+3%

Contrast AmplitudeON-OFF

ContrastAmplitudeVariance

(Error Bars)

Significance t-Map (p,z,F)(Thresholded

p<.01) “Massive Univariate Analysis” -- Analyze each voxel separately

Statistical Parametric Map (SPM)

Signficance Map sig=-log10(p) Signed by contrast

“Massive Univariate Analysis” -- Analyze each voxel separately

Hemodynamics

• Delay• Dispersion• Grouping by simple time point inaccurate

Hemodynamic Response Function (HRF)

TR (~2sec)

Time-to-Peak (~6sec)

Dispersion

Undershoot

Equilibrium(~16-32sec)

Delay (~1-2sec)

Convolution with HRF

• Shifts, rolls off; more accurate • Loose ability to simply group time points• More complicated analysis• General Linear Model (GLM)

GLMData fomone voxel

= Task base+

Baseline Offset(Nuisance)Task

Task=onoff•Implicit Contrast•HRF Amplitude

base=off

Matrix Model

y = X *

Data fromone voxel

Design MatrixRegressors

Vector ofRegressionCoefficients(“Betas”)

Design Matrix

Two Task Conditions

y = X *

Data fromone voxel

Design MatrixRegressors

Design Matrix

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)

Five Task Conditions

Encode

EmotDist

NeutDist

EmotProbe

NeutProbe

y = X *

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

Estimation of s

)ˆ( ,)ˆ( :Unbiased

Variance Residual ˆˆ

Estimate) (Noise Residual ˆˆ

Estimate Signal ˆˆ

EstimatesParameter )(ˆ

and :Unknowns

),0(~ , ,

nnTrue

NnnsynXy

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

yXXXnXy TT

Hypotheses and ContrastsWhich voxels respond more/less/differently to the Emotional Distractor than to the Neutral Distractor?

0,0,0ˆˆ

NDistEDist

MatirxContrast 00110

ˆcˆcˆcˆcˆc

NProbe

EProbe

Encode

NProbeNProbeEProbeEProbeNDistNDistEDistEDistEncodeEncode

Contrast: Assign Weights to each Beta

EDist̂NDist̂

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?

Which voxels respond more to the Emotional Distractor than to the Neutral Distractor?

• 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]

Which voxels respond to Encode (relative to baseline)?1.

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]

Which voxels respond to the Emotional Distractor (wrt baseline)?1.

• 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]

Which voxels respond to either Distractor (wrt baseline)?1.

• 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

Which voxels respond more to the Probe following the Emotional Distractor than to the Probe following the Neutral Distractor?

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]

Contrasts and the Full Model

ate)(multivariTest -F ˆˆˆF

e)(univariatTest - tˆ)(

Cin Rows J

Estimate VarianceContrast ˆ)(1ˆˆ

Contrast ˆˆ

ˆˆ Variance, Residual ˆˆ

EstimatesParameter )(ˆ

),0(~ , ,

1JDOF,

XynDOF

NnnsynXy

fMRI Analysis Overview

Higher Level GLM

Subject 3

Subject 4

Subject 1

Subject 2

Raw Data

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

Basics of fMRI Time-Series Analysis

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