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
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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
BOLD-weighted Contrast
T1-weighted Contrast
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Blood Oxygen Level Dependence (BOLD)
Neurons
Deoxygenated Hemoglobin (ParaMagnetic)
Oxygenated Hemoglobin (DiaMagnetic)
Lungs
Contrast Agent
Oxygen
CO2
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Functional MRI (fMRI)
Sample BOLD response in 4D Space (3D) voxels
(64x64x35, 3x3x5mm3, 50,000) Time (1D) time
points (100, 2 sec) Movie
Time 3
Time 1
Time 2
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4D Volume
85x1
64x64x35
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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
Voxel 1
Voxel 2
p 10-11, sig-log10(p) 11
p .10, sig-log10(p) 1
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Statistical Parametric Map (SPM)
Significance t-Map (p,z,F) (Thresholded plt.01)
Contrast Amplitude bON-bOFF
Contrast Amplitude Variance (Error Bars)
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)
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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GLM
Data fom one voxel
Baseline Offset (Nuisance)
Task

bTask
bbase

bbaseboff

• bTaskbon-boff
• Implicit Contrast
• HRF Amplitude

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Matrix Model
y X b
bTask bbase

Observations
Vector of Regression Coefficients (Betas)
Design Matrix
Design Matrix Regressors
Data from one voxel
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Two Task Conditions
y X b
bOdd bEven bbase

Observations
Design Matrix
Design Matrix Regressors
Data from one voxel
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Working Memory Task (fBIRN)
0. Scrambled low-level baseline, no
response 1. Encode series of passively viewed
stick figures Distractor respond if there is a
face 2. Emotional 3. Neutral Probe
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
y X b
bEncode bEmotDist bNeutDist bEmotProbe bNeutProbe

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GLM Solution
y X b

• Set of simultaneous equations
• Each row of X is an equation
• Each column of X is an unknown
• bs are unknown
• 142 Time Points (Equations)
• 5 unknowns

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Estimation of bs
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Estimates of the HRF Amplitude

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Hypotheses and Contrasts
Which voxels respond more/less/differently to the
Emotional Distractor than to the Neutral
Distractor?
Contrast Assign Weights to each Beta
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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?

• Only interested in Emotional and Neutral
  Distractors
• 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
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Which voxels respond to Encode (relative to
baseline)?

• Only interested in Encode
• No statement about other conditions

Condition 1 2 3 4 5 Weight 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)?

• Only interested in Emotional Distractor
• No statement about other conditions

Condition 1 2 3 4 5 Weight 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)?

• Only interested in Distractors
• Average of two Distractors
• No statement about other conditions

Condition 1 2 3 4 5 Weight 0 ½ ½ 0 0
Contrast Matrix C 0 0.5 0.5 0 0

• Dont 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?

• Only interested in Probes
• No statement about other conditions

Condition 1 2 3 4 5 Weight 0 0 0 1 -1
Contrast Matrix C 0 0 0 1 -1
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Contrasts and the Full Model
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fMRI Analysis Overview
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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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