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**Statistical Signal Processing for fMRI**

Douglas N. Greve Mark Vangel Anastasia Yendiki

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**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

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**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

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**Challenges 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

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**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

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**Hemodynamic Response (BOLD)**

Time-to-Peak (~6sec) Dispersion TR (~2sec) Equilibrium (~16-32sec) Undershoot Delay (~1-2sec) HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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**fMRI Noise Synthetic data.**

HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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**Averaging Synthetic data.**

HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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**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

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**Preprocessing Slice-Timing Correction (?) Motion Correction**

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

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**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

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**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

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**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

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**HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve**

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**Hemodynamic Response Model**

Time-to-Peak (~6sec) Dispersion TR (~2sec) Equilibrium (~16-32sec) Undershoot Delay (~1-2sec) HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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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 HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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**Blood Oxygen Level Dependence (BOLD)**

Neurons Deoxygenated Hemoglobin (ParaMagnetic) Oxygenated Hemoglobin (DiaMagnetic) Lungs Oxygen CO2 HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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**Functional MRI (fMRI) Sample BOLD response in 4D**

Localized Neural Firing Increased Blood Flow Stimulus BOLD Changes Sample BOLD response in 4D Space (3D) – voxels (64x64x35, 3x3x5mm^3) Time (1D) – time points (100, 2 sec) Time 3 … Time 1 Time 2 HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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**} Analysis Goals Given: raw fMRI time course and**

stimulus presentation times Compute: Hemodynamic Response (HRF) Amplitude HRF Confidence Interval P-Value Noise Amplitude } Quantify Uncertainty HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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**Final Results: Maps Assign values to each voxel**

Display as pseudo-color images Threshold? HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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**Final Results: Tables List of active regions Cluster Number TalX (mm)**

TalY TalZ Volume (mm^3) Sig (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

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**Final Results: Waveforms**

Average raw data over time and space HST583: Statistical Signal Processing for fMRI -- Douglas N. Greve

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