Transcript Statistical Signal Processing for fMRI Douglas N. Greve Mark Vangel Anastasia Yendiki Overview • First-Level Univariate Analysis • Signal Modeling • Nuisance Modeling • Noise Modeling • Hypothesis Testing •

Statistical Signal Processing
for fMRI
Douglas N. Greve
Mark Vangel
Anastasia Yendiki
Overview
• First-Level Univariate Analysis
• Signal Modeling
• Nuisance Modeling
• Noise Modeling
• Hypothesis Testing
• Correction for Multiple Comparisons
• Cross-Subject/Higher Level Analysis
• Lab
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Analysis Goals
• Quantify Neural Correlates in fMRI
• Amplitude of Hemodynamic Response
• Delay/Shape of Hemodynamic Response
• Extent/Size of Activation
• Localization of function
• Quantify Uncertainty
• Cross-subject (within group)
• Cross-group – eg, Normals, Clinical Populations
• Within-subject – EEG/MEG/Optical/Surgical Planning
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Challenges
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Large Noise – thermal, physiological, motion
Small Signal – delay, dispersion
Structural/Functional Alignment – within subject
Intersubject Alignment
Copious amounts of data – eg, 20 subjects, 5 runs per
subject, 100 time points per run, 64x64x30 volume = 1.2G
data points
• More spatial voxels than time points (multiple comparisons
problem).
• Model Validation
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Method
• Correlational – synchronized stimulus and acquistion
• Linear/Gaussian Assumptions
• GLM – “General” Linear Model
• MSE – Minimum Square Error
• LMS – Least Mean Squares
• “Massively Univariate”
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Hemodynamic Response (BOLD)
Time-to-Peak (~6sec)
Dispersion
TR (~2sec)
Undershoot
Delay (~1-2sec)
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Equilibrium
(~16-32sec)
fMRI Noise
Synthetic data.
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Averaging
Synthetic data.
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Typical Analysis Stream
• Preprocessing
• “Univariate” First-Level GLM Analysis
• “Univariate” Higher-Level GLM Analysis
• “Multivariate” Analysis
• Packages:
• SPM – Statistical Parametric Mapping
• AFNI – Analysis of Functional NeuroImages
• FSL – fMRI Software Library
• FS-FAST – FreeSurfer Functional Analysis STream
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Preprocessing
• k-Space reconstruction
• Slice-Timing Correction (?)
• Motion Correction
• Spatial Filtering (Smoothing - FWHM)
• Intensity Normalization
• Temporal Filtering (or in analysis)
• Per-run, within subject
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Univariate First-Level Analysis
• Per-voxel, per-subject
• Postulate model of the observable (ie raw time course)
• Signal model (eg, hemodynamic response)
• Noise model (eg, autocorrelation function)
• Drift (eg, mean offset, linear, quadratic)
• General Linear Model (GLM)
• Parameterized
• Linear (superposition)
• Least-mean-square estimation of parameters
• Hypothesis Test = Contrast of Parameters
• Assemble into a map
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Univariate High-level Analysis
• Per-voxel, Cross-subject
• Requires intersubject registration
• Dave Kennedy
• Uses information from First/Lower Levels
• GLM to describe relationship
• Random Effects
• Fixed Effects
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Multivariate Statistics
• Cross-voxel (within map)
• Thresholding and multiple comparisons problem
• Gaussian Random Fields (GRF)
• Principal Component Analysis (PCA/SVD)
• Independent Component Analysis
• Region-of-Interest
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Hemodynamic Response Model
Time-to-Peak (~6sec)
Dispersion
TR (~2sec)
Undershoot
Delay (~1-2sec)
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Equilibrium
(~16-32sec)
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, …
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
• Scientific
• Clinical
• Pharmaceutical
Blood Oxygen Level Dependence (BOLD)
Oxygenated
Hemoglobin
(DiaMagnetic)
Neurons
Lungs
Oxygen
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
CO2
Deoxygenated
Hemoglobin
(ParaMagnetic)
Functional MRI (fMRI)
Stimulus
Localized
Neural
Firing
Localized
Increased
Blood Flow
Localized
BOLD
Changes
Sample BOLD response in 4D
Space (3D) – voxels (64x64x35, 3x3x5mm^3)
Time (1D) – time points (100, 2 sec)
Time 1
Time 2
Time 3 …
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Analysis Goals
Given:
• raw fMRI time course and
• stimulus presentation times
Compute:
• Hemodynamic Response (HRF) Amplitude
• HRF Confidence Interval
Quantify Uncertainty
• P-Value
• Noise Amplitude
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HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Final Results: Maps
• Assign values to each voxel
• Display as pseudo-color images
• Threshold?
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Final Results: Tables
• List of active regions
Cluster TalX
TalY
TalZ
Volume Sig
Number (mm)
(mm)
(mm)
(mm^3) (log10)
1
-30.5
13.2
0.2
125.6
5.7
2
4.5
9.7
-20.2
878.1
4.1
3
2.9
-18.0
17.7
400.3
3.2
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve
Final Results: Waveforms
• Average raw data over time and space
HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve