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Basics of fMRI Time-Series Analysis

Basics of fMRI Time-Series Analysis. Douglas N. Greve. fMRI Analysis Overview. Subject 1. Preprocessing MC, STC, B0 Smoothing Normalization. Preprocessing MC, STC, B0 Smoothing Normalization. Preprocessing MC, STC, B0 Smoothing Normalization. Preprocessing MC, STC, B0 Smoothing

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Basics of fMRI Time-Series Analysis

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  1. Basics of fMRI Time-Series Analysis Douglas N. Greve

  2. fMRI Analysis Overview Subject 1 Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization First Level GLM Analysis X X X X X C C C C C Raw Data Subject 2 First Level GLM Analysis Raw Data Higher Level GLM Subject 3 First Level GLM Analysis Raw Data Subject 4 First Level GLM Analysis Raw Data

  3. Overview • Neuroanatomy 101 • fMRI Contrast Mechanism • Hemodynamic Response • “Univariate” GLM Analysis • Hypothesis Testing

  4. Neuroantomy • Gray matter • White matter • Cerebrospinal Fluid

  5. Functional Anatomy/Brain Mapping

  6. 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

  7. MRI Scanner

  8. Magnetic Resonance Imaging BOLD-weighted Contrast T1-weighted Contrast

  9. Blood Oxygen Level Dependence (BOLD) Neurons Deoxygenated Hemoglobin (ParaMagnetic) Oxygenated Hemoglobin (DiaMagnetic) Lungs Contrast Agent Oxygen CO2

  10. Localized Neural Firing Localized Increased Blood Flow Localized BOLD Changes Stimulus Functional MRI (fMRI) Sample BOLD response in 4D Space (3D) – voxels (64x64x35, 3x3x5mm^3, ~50,000) Time (1D) – time points (100, 2 sec) – Movie Time 3 … Time 1 Time 2

  11. 4D Volume 85x1 64x64x35

  12. Visual/Auditory/Motor Activation Paradigm • 15 sec ‘ON’, 15 sec ‘OFF’ • Flickering Checkerboard • Auditory Tone • Finger Tapping

  13. Block Design: 15s Off, 15s On Voxel 1 Voxel 2

  14. Contrasts and Inference Voxel 1 Voxel 2 p = 10-11, sig=-log10(p) =11 p = .10, sig=-log10(p) =1

  15. +3% 0% -3% Statistical Parametric Map (SPM) Significance t-Map (p,z,F) (Thresholded p<.01) Contrast Amplitude bON-bOFF Contrast Amplitude Variance (Error Bars) “Massive Univariate Analysis” -- Analyze each voxel separately

  16. Statistical Parametric Map (SPM) Signficance Map sig=-log10(p) Signed by contrast “Massive Univariate Analysis” -- Analyze each voxel separately

  17. Hemodynamics • Delay • Dispersion • Grouping by simple time point inaccurate

  18. Time-to-Peak (~6sec) Dispersion Undershoot Hemodynamic Response Function (HRF) TR (~2sec) Equilibrium (~16-32sec) Delay (~1-2sec)

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

  20. GLM Data fom one voxel Baseline Offset (Nuisance) Task = bTask + bbase bbase=boff • bTask=bon-boff • Implicit Contrast • HRF Amplitude

  21. Matrix Model y = X * b bTask bbase = Observations Vector of Regression Coefficients (“Betas”) Design Matrix Design Matrix Regressors Data from one voxel

  22. Two Task Conditions y = X * b bOdd bEven bbase = Observations Design Matrix Design Matrix Regressors Data from one voxel

  23. “Scrambled” Encode Distractor Probe Images Stick Figs Stick Figs 16s 16s 16s 16s 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)

  24. Five Task Conditions y = X * b bEncode bEmotDist bNeutDist bEmotProbe bNeutProbe =

  25. bEncode bEmotDist bNeutDist bEmotProbe bNeutProbe 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 =

  26. Estimation of bs

  27. bEncode bEmotDist bNeutDist bEmotProbe bNeutProbe Estimates of the HRF Amplitude =

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

  29. 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?

  30. 5. NProbe 1. Encode 4. EProbe 3. NDist 2. EDist 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]

  31. 5. NProbe 1. Encode 4. EProbe 3. NDist 2. EDist 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]

  32. 5. NProbe 1. Encode 4. EProbe 3. NDist 2. EDist 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]

  33. 5. NProbe 1. Encode 4. EProbe 3. NDist 2. EDist 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] • Don’t have so sum to 1, but usual • Could have used an F-test instead of average

  34. 5. NProbe 1. Encode 4. EProbe 3. NDist 2. EDist 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]

  35. Contrasts and the Full Model

  36. fMRI Analysis Overview Subject 1 Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization Preprocessing MC, STC, B0 Smoothing Normalization First Level GLM Analysis X X X X X C C C C C Raw Data Subject 2 First Level GLM Analysis Raw Data Higher Level GLM Subject 3 First Level GLM Analysis Raw Data Subject 4 First Level GLM Analysis Raw Data

  37. 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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