Basics of fMRI Time-Series Analysis Douglas N. Greve

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

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 T1-weighted Contrast BOLD-weighted Contrast

9 Blood Oxygen Level Dependence (BOLD) Neurons Lungs OxygenCO2 Oxygenated Hemoglobin (DiaMagnetic) Deoxygenated Hemoglobin (ParaMagnetic) Contrast Agent

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

11 4D Volume 64x64x35 85x1

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 p = , sig=-log10(p) =11 p =.10, sig=-log10(p) =1 Voxel 1Voxel 2

15 Statistical Parametric Map (SPM) +3% 0% -3% Contrast Amplitude  ON -  OFF Contrast Amplitude Variance (Error Bars) Significance t-Map (p,z,F) (Thresholded p<.01) “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 Hemodynamic Response Function (HRF) TR (~2sec) Time-to-Peak (~6sec) Dispersion Undershoot 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 =  Task  base + Baseline Offset (Nuisance) Task  Task =  on  off Implicit Contrast HRF Amplitude  base =  off

21 Matrix Model y = X *   Task  base Data from one voxel Design Matrix Regressors = Vector of Regression Coefficients (“Betas”) Design Matrix Observations

22 Two Task Conditions y = X *   Odd  Even  base Data from one voxel Design Matrix Regressors = Design Matrix Observations

23 Working Memory Task (fBIRN) ImagesStick Figs “Scrambled”EncodeDistractorProbe 16s Stick Figs 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 (

24 Five Task Conditions  Encode  EmotDist  NeutDist  EmotProbe  NeutProbe = y = X * 

25 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

26 Estimation of  s

27 Estimates of the HRF Amplitude  Encode  EmotDist  NeutDist  EmotProbe  NeutProbe =

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 Which voxels respond more to the Emotional Distractor than to the Neutral Distractor? 1. Encode2. EDist3. NDist 4. EProbe5. NProbe Only interested in Emotional and Neutral Distractors No statement about other conditions Condition: Weight Contrast Matrix C = [ ]

31 Which voxels respond to Encode (relative to baseline)? 1. Encode2. EDist3. NDist 4. EProbe5. NProbe Only interested in Encode No statement about other conditions Condition: Weight Contrast Matrix C = [ ]

32 Which voxels respond to the Emotional Distractor (wrt baseline)? 1. Encode2. EDist3. NDist 4. EProbe5. NProbe Only interested in Emotional Distractor No statement about other conditions Condition: Weight Contrast Matrix C = [ ]

33 Which voxels respond to either Distractor (wrt baseline)? 1. Encode2. EDist3. NDist 4. EProbe5. NProbe Only interested in Distractors Average of two Distractors No statement about other conditions Condition: Weight 0 ½ ½ 0 0 Contrast Matrix C = [ ] Don’t have so sum to 1, but usual Could have used an F-test instead of average

34 Which voxels respond more to the Probe following the Emotional Distractor than to the Probe following the Neutral Distractor? 1. Encode2. EDist3. NDist 4. EProbe5. NProbe Only interested in Probes No statement about other conditions Condition: Weight Contrast Matrix C = [ ]

35 Contrasts and the Full Model

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

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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