(Epoch and) Event-related fMRI Karl Friston Rik Henson Oliver Josephs Wellcome Department of Cognitive Neurology & Institute of Cognitive Neuroscience.

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(Epoch and) Event-related fMRI Karl Friston Rik Henson Oliver Josephs Wellcome Department of Cognitive Neurology & Institute of Cognitive Neuroscience University College London UK Slide 2 Epoch vs Event-related fMRI PET Blocked conception (scans assigned to conditions) Boxcar function ABAB Condition A Scans 21-30Scans 1-10 Condition B Scans 11-20 fMRI Epoch conception (scans treated as timeseries) Convolved with HRF => fMRI Event-related conception Delta functions Design Matrix Slide 3 OverviewOverview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications Slide 4 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) Advantages of Event-related fMRI Slide 5 Randomised O1N1 O3 O2 N2 Data Model O = Old Words N = New Words Blocked O1O2O3 N1N2N3 Slide 6 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) Advantages of Event-related fMRI Slide 7 RR R F F R = Words Later Remembered F = Words Later Forgotten Event-Related ~4s Data Model Slide 8 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) Advantages of Event-related fMRI Slide 9 Slide 10 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 4. Some trials cannot be blocked e.g, oddball designs (Clark et al., 2000) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 4. Some trials cannot be blocked e.g, oddball designs (Clark et al., 2000) Advantages of Event-related fMRI Slide 11 Time Oddball Slide 12 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 4. Some trials cannot be blocked e.g, oddball designs (Clark et al., 2000) 5. More accurate models even for blocked designs? e.g, state-item interactions (Chawla et al, 1999) 5. More accurate models even for blocked designs? e.g, state-item interactions (Chawla et al, 1999) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 4. Some trials cannot be blocked e.g, oddball designs (Clark et al., 2000) 5. More accurate models even for blocked designs? e.g, state-item interactions (Chawla et al, 1999) 5. More accurate models even for blocked designs? e.g, state-item interactions (Chawla et al, 1999) Advantages of Event-related fMRI Slide 13 N1N2N3 Event model O1O2O3 Blocked Design Epoch model Data Model O1O2O3 N1N2N3 Slide 14 1. Less efficient for detecting effects than are blocked designs (see later) 1. Less efficient for detecting effects than are blocked designs (see later) 2. Some psychological processes may be better blocked (eg task-switching, attentional instructions) 1. Less efficient for detecting effects than are blocked designs (see later) 1. Less efficient for detecting effects than are blocked designs (see later) 2. Some psychological processes may be better blocked (eg task-switching, attentional instructions) (Disadvantages of Randomised Designs) Slide 15 OverviewOverview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications Slide 16 Function of blood oxygenation, flow, volume (Buxton et al, 1998)Function of blood oxygenation, flow, volume (Buxton et al, 1998) Peak (max. oxygenation) 4-6s poststimulus; baseline after 20-30sPeak (max. oxygenation) 4-6s poststimulus; baseline after 20-30s Initial undershoot can be observed (Malonek & Grinvald, 1996)Initial undershoot can be observed (Malonek & Grinvald, 1996) Similar across V1, A1, S1Similar across V1, A1, S1 but differences across: other regions (Schacter et al 1997) individuals (Aguirre et al, 1998) but differences across: other regions (Schacter et al 1997) individuals (Aguirre et al, 1998) Function of blood oxygenation, flow, volume (Buxton et al, 1998)Function of blood oxygenation, flow, volume (Buxton et al, 1998) Peak (max. oxygenation) 4-6s poststimulus; baseline after 20-30sPeak (max. oxygenation) 4-6s poststimulus; baseline after 20-30s Initial undershoot can be observed (Malonek & Grinvald, 1996)Initial undershoot can be observed (Malonek & Grinvald, 1996) Similar across V1, A1, S1Similar across V1, A1, S1 but differences across: other regions (Schacter et al 1997) individuals (Aguirre et al, 1998) but differences across: other regions (Schacter et al 1997) individuals (Aguirre et al, 1998) BOLD Impulse Response Brief Stimulus Undershoot Initial Undershoot Peak Slide 17 Early event-related fMRI studies used a long Stimulus Onset Asynchrony (SOA) to allow BOLD response to return to baselineEarly event-related fMRI studies used a long Stimulus Onset Asynchrony (SOA) to allow BOLD response to return to baseline However, if the BOLD response is explicitly modelled, overlap between successive responses at short SOAs can be accommodatedHowever, if the BOLD response is explicitly modelled, overlap between successive responses at short SOAs can be accommodated particularly if responses are assumed to superpose linearly particularly if responses are assumed to superpose linearly Short SOAs are more sensitiveShort SOAs are more sensitive Early event-related fMRI studies used a long Stimulus Onset Asynchrony (SOA) to allow BOLD response to return to baselineEarly event-related fMRI studies used a long Stimulus Onset Asynchrony (SOA) to allow BOLD response to return to baseline However, if the BOLD response is explicitly modelled, overlap between successive responses at short SOAs can be accommodatedHowever, if the BOLD response is explicitly modelled, overlap between successive responses at short SOAs can be accommodated particularly if responses are assumed to superpose linearly particularly if responses are assumed to superpose linearly Short SOAs are more sensitiveShort SOAs are more sensitive BOLD Impulse Response Brief Stimulus Undershoot Initial Undershoot Peak Slide 18 OverviewOverview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications Slide 19 General Linear (Convolution) Model GLM for a single voxel: Y(t) = x(t) h(t) + x(t) = stimulus train (delta functions) x(t) = (t - nT) h(t) = hemodynamic (BOLD) response h(t) = i f i (t) f i (t) = temporal basis functions Y(t) = i f i (t - nT) + GLM for a single voxel: Y(t) = x(t) h(t) + x(t) = stimulus train (delta functions) x(t) = (t - nT) h(t) = hemodynamic (BOLD) response h(t) = i f i (t) f i (t) = temporal basis functions Y(t) = i f i (t - nT) + Design Matrix convolution T 2T 3T... x(t) h(t)= i f i (t) sampled each scan Slide 20 General Linear Model (in SPM) Auditory words every 20s SPM{F} 0 time {secs} 30 Sampled every TR = 1.7s Design matrix, X [x(t) 1 ( ) | x(t) 2 ( ) |...] Gamma functions i ( ) of peristimulus time (Orthogonalised) Slide 21 OverviewOverview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications Slide 22 Temporal Basis Functions Fourier SetFourier Set Windowed sines & cosines Any shape (up to frequency limit) Inference via F-test Fourier SetFourier Set Windowed sines & cosines Any shape (up to frequency limit) Inference via F-test Slide 23 Temporal Basis Functions Finite Impulse ResponseFinite Impulse Response Mini timebins (selective averaging) Any shape (up to bin-width) Inference via F-test Finite Impulse ResponseFinite Impulse Response Mini timebins (selective averaging) Any shape (up to bin-width) Inference via F-test Slide 24 Temporal Basis Functions Fourier SetFourier Set Windowed sines & cosines Any shape (up to frequency limit) Inference via F-test Gamma FunctionsGamma Functions Bounded, asymmetrical (like BOLD) Set of different lags Inference via F-test Fourier SetFourier Set Windowed sines & cosines Any shape (up to frequency limit) Inference via F-test Gamma FunctionsGamma Functions Bounded, asymmetrical (like BOLD) Set of different lags Inference via F-test Slide 25 Temporal Basis Functions Fourier SetFourier Set Windowed sines & cosines Any shape (up to frequency limit) Inference via F-test Gamma FunctionsGamma Functions Bounded, asymmetrical (like BOLD) Set of different lags Inference via F-test Informed Basis SetInformed Basis Set Best guess of canonical BOLD response Variability captured by Taylor expansion Magnitude inferences via t-test? Fourier SetFourier Set Windowed sines & cosines Any shape (up to frequency limit) Inference via F-test Gamma FunctionsGamma Functions Bounded, asymmetrical (like BOLD) Set of different lags Inference via F-test Informed Basis SetInformed Basis Set Best guess of canonical BOLD response Variability captured by Taylor expansion Magnitude inferences via t-test? Slide 26 Temporal Basis Functions Slide 27 Informed Basis Set (Friston et al. 1998) (Friston et al. 1998) Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions) Informed Basis Set (Friston et al. 1998) (Friston et al. 1998) Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions) Canonical Slide 28 Temporal Basis Functions Informed Basis Set (Friston et al. 1998) (Friston et al. 1998) Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions) plus Multivariate Taylor expansion in: plus Multivariate Taylor expansion in: time (Temporal Derivative) Informed Basis Set (Friston et al. 1998) (Friston et al. 1998) Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions) plus Multivariate Taylor expansion in: plus Multivariate Taylor expansion in: time (Temporal Derivative) Canonical Temporal Slide 29 Temporal Basis Functions Informed Basis Set (Friston et al. 1998) (Friston et al. 1998) Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions) plus Multivariate Taylor expansion in: plus Multivariate Taylor expansion in: time (Temporal Derivative) width (Dispersion Derivative) Informed Basis Set (Friston et al. 1998) (Friston et al. 1998) Canonical HRF (2 gamma functions)Canonical HRF (2...