Event-related fMRI Rik Henson With thanks to: Karl Friston, Oliver Josephs Event-related fMRI Rik Henson With thanks to: Karl Friston, Oliver Josephs.

Event-related fMRI Rik Henson With thanks to: Karl Friston, Oliver Josephs Event-related fMRI Rik Henson With thanks to: Karl Friston, Oliver Josephs

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

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

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)

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, S1…Similar 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, S1…Similar 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

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 accommodated…However, 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 sensitive…Short 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 accommodated…However, 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 sensitive…Short SOAs are more sensitive… BOLD Impulse Response Brief Stimulus Undershoot Initial Undershoot Peak

General Linear (Convolution) Model GLM for a single voxel: y(t) = u(t)  h(  ) +  (t) u(t) = neural causes (stimulus train) u(t) =   (t - nT) h(  ) = hemodynamic (BOLD) response h(  ) =  ß i f i (  ) f i (  ) = temporal basis functions y(t) =   ß i f i (t - nT) +  (t) y = X ß + ε GLM for a single voxel: y(t) = u(t)  h(  ) +  (t) u(t) = neural causes (stimulus train) u(t) =   (t - nT) h(  ) = hemodynamic (BOLD) response h(  ) =  ß i f i (  ) f i (  ) = temporal basis functions y(t) =   ß i f i (t - nT) +  (t) y = X ß + ε Design Matrix convolution T 2T 3T... u(t) h(  )=  ß i f i (  ) sampled each scan

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)  ƒ 1 (  ) | x(t)  ƒ 2 (  ) |...] … Gamma functions ƒ i (  ) of peristimulus time  (Orthogonalised)

x2x2 x3x3 A word about down-sampling T=16, TR=2s Scan 0 1 o T 0 =9 o T 0 =16

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

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

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

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 Set“Informed” 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 Set“Informed” Basis Set Best guess of canonical BOLD response Variability captured by Taylor expansion “Magnitude” inferences via t-test…?

Temporal Basis Functions

“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

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

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 gamma functions) plus Multivariate Taylor expansion in: plus Multivariate Taylor expansion in: time (Temporal Derivative) width (Dispersion Derivative) Canonical Temporal Dispersion

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) F-tests allow for any “canonical-like” responsesF-tests allow for any “canonical-like” responses “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) F-tests allow for any “canonical-like” responsesF-tests allow for any “canonical-like” responses Canonical Temporal Dispersion

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) F-tests allow for any “canonical-like” responsesF-tests allow for any “canonical-like” responses T-tests on canonical HRF alone (at 1 st level) can be improved by derivatives reducing residual error, and can be interpreted as “amplitude” differences, assuming canonical HRF is good fit …T-tests on canonical HRF alone (at 1 st level) can be improved by derivatives reducing residual error, and can be interpreted as “amplitude” differences, assuming canonical HRF is good fit … “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) F-tests allow for any “canonical-like” responsesF-tests allow for any “canonical-like” responses T-tests on canonical HRF alone (at 1 st level) can be improved by derivatives reducing residual error, and can be interpreted as “amplitude” differences, assuming canonical HRF is good fit …T-tests on canonical HRF alone (at 1 st level) can be improved by derivatives reducing residual error, and can be interpreted as “amplitude” differences, assuming canonical HRF is good fit … Canonical Temporal Dispersion

(Other Approaches) Long Stimulus Onset Asychrony (SOA) Can ignore overlap between responses (Cohen et al 1997) … but long SOAs are less sensitive Fully counterbalanced designs Assume response overlap cancels (Saykin et al 1999) Include fixation trials to “selectively average” response even at short SOA (Dale & Buckner, 1997) … but unbalanced when events defined by subject Define HRF from pilot scan on each subject May capture intersubject variability (Zarahn et al, 1997) … but not interregional variability Numerical fitting of highly parametrised response functions Separate estimate of magnitude, latency, duration (Kruggel et al 1999) … but computationally expensive for every voxel

Temporal Basis Sets: Which One? + FIR+ Dispersion+ TemporalCanonical …canonical + temporal + dispersion derivatives appear sufficient …may not be for more complex trials (eg stimulus-delay-response) …but then such trials better modelled with separate neural components (ie activity no longer delta function) + constrained HRF (Zarahn, 1999) In this example (rapid motor response to faces, Henson et al, 2001)…

Timing Issues : Practical Typical TR for 48 slice EPI at 3mm spacing is ~ 4sTypical TR for 48 slice EPI at 3mm spacing is ~ 4s Scans TR=4s

Timing Issues : Practical Typical TR for 48 slice EPI at 3mm spacing is ~ 4sTypical TR for 48 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] poststimulus may miss peak signalSampling at [0,4,8,12…] poststimulus may miss peak signal Typical TR for 48 slice EPI at 3mm spacing is ~ 4sTypical TR for 48 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] poststimulus may miss peak signalSampling at [0,4,8,12…] poststimulus may miss peak signal Scans Stimulus (synchronous) TR=4s SOA=8s Sampling rate=4s

Timing Issues : Practical Typical TR for 48 slice EPI at 3mm spacing is ~ 4sTypical TR for 48 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] poststimulus may miss peak signalSampling at [0,4,8,12…] poststimulus may miss peak signal Higher effective sampling by: 1. Asynchrony eg SOA=1.5TRHigher effective sampling by: 1. Asynchrony eg SOA=1.5TR Typical TR for 48 slice EPI at 3mm spacing is ~ 4sTypical TR for 48 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] poststimulus may miss peak signalSampling at [0,4,8,12…] poststimulus may miss peak signal Higher effective sampling by: 1. Asynchrony eg SOA=1.5TRHigher effective sampling by: 1. Asynchrony eg SOA=1.5TR Stimulus (asynchronous) Scans TR=4s SOA=6s Sampling rate=2s

Timing Issues : Practical Typical TR for 48 slice EPI at 3mm spacing is ~ 4sTypical TR for 48 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] poststimulus may miss peak signalSampling at [0,4,8,12…] poststimulus may miss peak signal Higher effective sampling by: 1. Asynchrony eg SOA=1.5TR 2. Random Jitter eg SOA=(2±0.5)TRHigher effective sampling by: 1. Asynchrony eg SOA=1.5TR 2. Random Jitter eg SOA=(2±0.5)TR Typical TR for 48 slice EPI at 3mm spacing is ~ 4sTypical TR for 48 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] poststimulus may miss peak signalSampling at [0,4,8,12…] poststimulus may miss peak signal Higher effective sampling by: 1. Asynchrony eg SOA=1.5TR 2. Random Jitter eg SOA=(2±0.5)TRHigher effective sampling by: 1. Asynchrony eg SOA=1.5TR 2. Random Jitter eg SOA=(2±0.5)TR Stimulus (random jitter) Scans TR=4s Sampling rate=2s

Timing Issues : Practical Typical TR for 48 slice EPI at 3mm spacing is ~ 4sTypical TR for 48 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] poststimulus may miss peak signalSampling at [0,4,8,12…] poststimulus may miss peak signal Higher effective sampling by: 1. Asynchrony eg SOA=1.5TR 2. Random Jitter eg SOA=(2±0.5)TRHigher effective sampling by: 1. Asynchrony eg SOA=1.5TR 2. Random Jitter eg SOA=(2±0.5)TR Better response characterisation (Miezin et al, 2000)Better response characterisation (Miezin et al, 2000) Typical TR for 48 slice EPI at 3mm spacing is ~ 4sTypical TR for 48 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] poststimulus may miss peak signalSampling at [0,4,8,12…] poststimulus may miss peak signal Higher effective sampling by: 1. Asynchrony eg SOA=1.5TR 2. Random Jitter eg SOA=(2±0.5)TRHigher effective sampling by: 1. Asynchrony eg SOA=1.5TR 2. Random Jitter eg SOA=(2±0.5)TR Better response characterisation (Miezin et al, 2000)Better response characterisation (Miezin et al, 2000) Stimulus (random jitter) Scans TR=4s Sampling rate=2s

Timing Issues : Practical …but “Slice-timing Problem”…but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices Slices acquired at different times, yet model is the same for all slices …but “Slice-timing Problem”…but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices Slices acquired at different times, yet model is the same for all slices

Timing Issues : Practical …but “Slice-timing Problem”…but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices …but “Slice-timing Problem”…but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices Bottom Slice Top Slice SPM{t} TR=3s

Timing Issues : Practical …but “Slice-timing Problem”…but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices Solutions:Solutions: 1. Temporal interpolation of data … but less good for longer TRs …but “Slice-timing Problem”…but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices Solutions:Solutions: 1. Temporal interpolation of data … but less good for longer TRs Interpolated SPM{t} Bottom Slice Top Slice SPM{t} TR=3s

Timing Issues : Practical …but “Slice-timing Problem”…but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices Solutions:Solutions: 1. Temporal interpolation of data … but less good for longer TRs 2. More general basis set (e.g., with temporal derivatives) … but inferences via F-test …but “Slice-timing Problem”…but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices Solutions:Solutions: 1. Temporal interpolation of data … but less good for longer TRs 2. More general basis set (e.g., with temporal derivatives) … but inferences via F-test Derivative SPM{F} Interpolated SPM{t} Bottom Slice Top Slice SPM{t} TR=3s

 = Fixed SOA = 16s Not particularly efficient… Stimulus (“Neural”)HRFPredicted Data

 = Fixed SOA = 4s Very Inefficient… Stimulus (“Neural”)HRFPredicted Data

 = Randomised, SOA min = 4s More Efficient… Stimulus (“Neural”)HRFPredicted Data

 = Blocked, SOA min = 4s Even more Efficient… Stimulus (“Neural”)HRFPredicted Data

 =  Blocked, epoch = 20s = Blocked-epoch (with small SOA) and Time-Freq equivalences Stimulus (“Neural”)HRFPredicted Data

 = Sinusoidal modulation, f = 1/33s  = The most efficient design of all! Stimulus (“Neural”)HRFPredicted Data

 =  “Effective HRF” (after highpass filtering) (Josephs & Henson, 1999) Blocked (80s), SOA min =4s, highpass filter = 1/120s Don’t have long (>60s) blocks! = Stimulus (“Neural”)HRFPredicted Data

Randomised, SOA min =4s, highpass filter = 1/120s  =  = (Randomised design spreads power over frequencies) Stimulus (“Neural”)HRFPredicted Data

Design Efficiency T = T = c T  / var(c T  ) Var(c T  ) = sqrt(  2 c T (X T X) -1 c) (i.i.d) For max. T, want min. contrast variability (Friston et al, 1999)For max. T, want min. contrast variability (Friston et al, 1999) If assume that noise variance ( is unaffected by changes in X…If assume that noise variance (  2 ) is unaffected by changes in X… …then want maximal efficiency, e:…then want maximal efficiency, e: e(c,X) = { c T (X T X) -1 c } -1 e(c,X) = { c T (X T X) -1 c } -1 = maximal bandpassed signal energy (Josephs & Henson, 1999)= maximal bandpassed signal energy (Josephs & Henson, 1999) T = T = c T  / var(c T  ) Var(c T  ) = sqrt(  2 c T (X T X) -1 c) (i.i.d) For max. T, want min. contrast variability (Friston et al, 1999)For max. T, want min. contrast variability (Friston et al, 1999) If assume that noise variance ( is unaffected by changes in X…If assume that noise variance (  2 ) is unaffected by changes in X… …then want maximal efficiency, e:…then want maximal efficiency, e: e(c,X) = { c T (X T X) -1 c } -1 e(c,X) = { c T (X T X) -1 c } -1 = maximal bandpassed signal energy (Josephs & Henson, 1999)= maximal bandpassed signal energy (Josephs & Henson, 1999) Events (A-B)

4s smoothing; 1/60s highpass filtering Efficiency - Multiple Event-types Design parametrised by:Design parametrised by: SOA min Minimum SOA p i (h) Probability of event-type i given history h of last m events With n event-types p i (h) is a n m  n Transition MatrixWith n event-types p i (h) is a n m  n Transition Matrix Example: Randomised ABExample: Randomised AB AB A0.50.5 AB A0.50.5 B0.50.5 => ABBBABAABABAAA... Design parametrised by:Design parametrised by: SOA min Minimum SOA p i (h) Probability of event-type i given history h of last m events With n event-types p i (h) is a n m  n Transition MatrixWith n event-types p i (h) is a n m  n Transition Matrix Example: Randomised ABExample: Randomised AB AB A0.50.5 AB A0.50.5 B0.50.5 => ABBBABAABABAAA... Differential Effect (A-B) Common Effect (A+B)

4s smoothing; 1/60s highpass filtering Efficiency - Multiple Event-types Example: Alternating ABExample: Alternating AB AB A01 AB A01 B10 => ABABABABABAB... Example: Alternating ABExample: Alternating AB AB A01 AB A01 B10B10B10B10 => ABABABABABAB... Alternating (A-B) Permuted (A-B) Example: Permuted ABExample: Permuted AB AB AB AA0 1 AB0.50.5 BA0.50.5 BB1 0 => ABBAABABABBA...

4s smoothing; 1/60s highpass filtering Efficiency - Multiple Event-types Example: Null eventsExample: Null events AB AB A0.330.33 B0.330.33 => AB-BAA--B---ABB... Efficient for differential and main effects at short SOAEfficient for differential and main effects at short SOA Equivalent to stochastic SOA (Null Event like third unmodelled event-type)Equivalent to stochastic SOA (Null Event like third unmodelled event-type) Selective averaging of data (Dale & Buckner 1997)Selective averaging of data (Dale & Buckner 1997) Example: Null eventsExample: Null events AB AB A0.330.33 B0.330.33 => AB-BAA--B---ABB... Efficient for differential and main effects at short SOAEfficient for differential and main effects at short SOA Equivalent to stochastic SOA (Null Event like third unmodelled event-type)Equivalent to stochastic SOA (Null Event like third unmodelled event-type) Selective averaging of data (Dale & Buckner 1997)Selective averaging of data (Dale & Buckner 1997) Null Events (A+B) Null Events (A-B)

Efficiency - Conclusions Optimal design for one contrast may not be optimal for anotherOptimal design for one contrast may not be optimal for another Blocked designs generally most efficient with short SOAs (but earlier restrictions and problems of interpretation…)Blocked designs generally most efficient with short SOAs (but earlier restrictions and problems of interpretation…) With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20sWith randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20s Inclusion of null events improves efficiency for main effect at short SOAs (at cost of efficiency for differential effects)Inclusion of null events improves efficiency for main effect at short SOAs (at cost of efficiency for differential effects) If order constrained, intermediate SOAs (5-20s) can be optimal; If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity)If order constrained, intermediate SOAs (5-20s) can be optimal; If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity) Optimal design for one contrast may not be optimal for anotherOptimal design for one contrast may not be optimal for another Blocked designs generally most efficient with short SOAs (but earlier restrictions and problems of interpretation…)Blocked designs generally most efficient with short SOAs (but earlier restrictions and problems of interpretation…) With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20sWith randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20s Inclusion of null events improves efficiency for main effect at short SOAs (at cost of efficiency for differential effects)Inclusion of null events improves efficiency for main effect at short SOAs (at cost of efficiency for differential effects) If order constrained, intermediate SOAs (5-20s) can be optimal; If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity)If order constrained, intermediate SOAs (5-20s) can be optimal; If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity)

Volterra series - a general nonlinear input-output model y(t) = 1 [u(t)] + 2 [u(t)] +.... + n [u(t)] +.... y(t) =  1 [u(t)] +  2 [u(t)] +.... +  n [u(t)] +.... n [u(t)] = ....  h n (t 1,..., t n )u(t - t 1 ).... u(t - t n )dt 1.... dt n  n [u(t)] = ....  h n (t 1,..., t n )u(t - t 1 ).... u(t - t n )dt 1.... dt n Volterra series - a general nonlinear input-output model y(t) = 1 [u(t)] + 2 [u(t)] +.... + n [u(t)] +.... y(t) =  1 [u(t)] +  2 [u(t)] +.... +  n [u(t)] +.... n [u(t)] = ....  h n (t 1,..., t n )u(t - t 1 ).... u(t - t n )dt 1.... dt n  n [u(t)] = ....  h n (t 1,..., t n )u(t - t 1 ).... u(t - t n )dt 1.... dt n Nonlinear Model  [u(t)] response y(t) input u(t) Stimulus function kernels (h) estimate

Nonlinear Model Friston et al (1997) SPM{F} testing H 0 : kernel coefficients, h = 0 kernel coefficients - h SPM{F} p < 0.001

Nonlinear Model Friston et al (1997) SPM{F} testing H 0 : kernel coefficients, h = 0 Significant nonlinearities at SOAs 0-10s: (e.g., underadditivity from 0-5s) (e.g., underadditivity from 0-5s) kernel coefficients - h SPM{F} p < 0.001

Nonlinear Effects Underadditivity at short SOAs Linear Prediction Volterra Prediction

Nonlinear Effects Underadditivity at short SOAs Linear Prediction Volterra Prediction Implications for Efficiency

Example 1: Intermixed Trials (Henson et al 2000) Short SOA, fully randomised, with 1/3 null eventsShort SOA, fully randomised, with 1/3 null events Faces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4sFaces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4s Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2)Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2) Short SOA, fully randomised, with 1/3 null eventsShort SOA, fully randomised, with 1/3 null events Faces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4sFaces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4s Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2)Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2)

Lag=3 FamousNonfamous(Target)...

Example 1: Intermixed Trials (Henson et al 2000) Short SOA, fully randomised, with 1/3 null eventsShort SOA, fully randomised, with 1/3 null events Faces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4sFaces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4s Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2)Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2) Interaction (F1-F2)-(N1-N2) masked by main effect (F+N)Interaction (F1-F2)-(N1-N2) masked by main effect (F+N) Right fusiform interaction of repetition priming and familiarityRight fusiform interaction of repetition priming and familiarity Short SOA, fully randomised, with 1/3 null eventsShort SOA, fully randomised, with 1/3 null events Faces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4sFaces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4s Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2)Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2) Interaction (F1-F2)-(N1-N2) masked by main effect (F+N)Interaction (F1-F2)-(N1-N2) masked by main effect (F+N) Right fusiform interaction of repetition priming and familiarityRight fusiform interaction of repetition priming and familiarity

Example 2: Post hoc classification (Henson et al 1999) Subjects indicate whether studied (Old) words:Subjects indicate whether studied (Old) words: i) evoke recollection of prior occurrence (R) i) evoke recollection of prior occurrence (R) ii) feeling of familiarity without recollection (K) ii) feeling of familiarity without recollection (K) iii) no memory (N) iii) no memory (N) Random Effects analysis on canonical parameter estimate for event-typesRandom Effects analysis on canonical parameter estimate for event-types Fixed SOA of 8s => sensitive to differential but not main effect (de/activations arbitrary)Fixed SOA of 8s => sensitive to differential but not main effect (de/activations arbitrary) Subjects indicate whether studied (Old) words:Subjects indicate whether studied (Old) words: i) evoke recollection of prior occurrence (R) i) evoke recollection of prior occurrence (R) ii) feeling of familiarity without recollection (K) ii) feeling of familiarity without recollection (K) iii) no memory (N) iii) no memory (N) Random Effects analysis on canonical parameter estimate for event-typesRandom Effects analysis on canonical parameter estimate for event-types Fixed SOA of 8s => sensitive to differential but not main effect (de/activations arbitrary)Fixed SOA of 8s => sensitive to differential but not main effect (de/activations arbitrary) SPM{t} SPM{t} R-K SPM{t} SPM{t} K-R

Example 3: Subject-defined events (Portas et al 1999) Subjects respond when “pop-out” of 3D percept from 2D stereogramSubjects respond when “pop-out” of 3D percept from 2D stereogram

Example 3: Subject-defined events (Portas et al 1999) Subjects respond when “pop-out” of 3D percept from 2D stereogramSubjects respond when “pop-out” of 3D percept from 2D stereogram Popout response also produces tonePopout response also produces tone Control event is response to tone during 3D perceptControl event is response to tone during 3D percept Subjects respond when “pop-out” of 3D percept from 2D stereogramSubjects respond when “pop-out” of 3D percept from 2D stereogram Popout response also produces tonePopout response also produces tone Control event is response to tone during 3D perceptControl event is response to tone during 3D percept Temporo-occipital differential activation Pop-out Control

Example 4: Oddball Paradigm (Strange et al, 2000) 16 same-category words every 3 secs, plus …16 same-category words every 3 secs, plus … … 1 perceptual, 1 semantic, and 1 emotional oddball… 1 perceptual, 1 semantic, and 1 emotional oddball 16 same-category words every 3 secs, plus …16 same-category words every 3 secs, plus … … 1 perceptual, 1 semantic, and 1 emotional oddball… 1 perceptual, 1 semantic, and 1 emotional oddball

WHEAT BARLEY OATS HOPS RYE … ~3s CORN Perceptual Oddball PLUG Semantic Oddball RAPE Emotional Oddball

Example 4: Oddball Paradigm (Strange et al, 2000) 16 same-category words every 3 secs, plus …16 same-category words every 3 secs, plus … … 1 perceptual, 1 semantic, and 1 emotional oddball… 1 perceptual, 1 semantic, and 1 emotional oddball 16 same-category words every 3 secs, plus …16 same-category words every 3 secs, plus … … 1 perceptual, 1 semantic, and 1 emotional oddball… 1 perceptual, 1 semantic, and 1 emotional oddball Right Prefrontal Cortex Parameter Estimates Controls Oddballs 3 nonoddballs randomly matched as controls3 nonoddballs randomly matched as controls Conjunction of oddball vs. control contrast images: generic deviance detectorConjunction of oddball vs. control contrast images: generic deviance detector

Epochs of attention to: 1) motion, or 2) colourEpochs of attention to: 1) motion, or 2) colour Events are target stimuli differing in motion or colourEvents are target stimuli differing in motion or colour Randomised, long SOAs to decorrelate epoch and event- related covariatesRandomised, long SOAs to decorrelate epoch and event- related covariates Interaction between epoch (attention) and event (stimulus) in V4 and V5Interaction between epoch (attention) and event (stimulus) in V4 and V5 Epochs of attention to: 1) motion, or 2) colourEpochs of attention to: 1) motion, or 2) colour Events are target stimuli differing in motion or colourEvents are target stimuli differing in motion or colour Randomised, long SOAs to decorrelate epoch and event- related covariatesRandomised, long SOAs to decorrelate epoch and event- related covariates Interaction between epoch (attention) and event (stimulus) in V4 and V5Interaction between epoch (attention) and event (stimulus) in V4 and V5 Example 5: Epoch/Event Interactions (Chawla et al 1999) attention to motion attention to colour Interaction between attention and stimulus motion change in V5

THE END

Randomised O1N1 O3 O2 N2 Data Model O = Old Words N = New Words Blocked O1O2O3 N1N2N3

(LOW–HIGH) x (OLD-NEW) Right Anterior Prefrontal (BA 10)Left Dorsal Prefrontal (BA 9/46) OLD – NEW (Collapse Ratio) Left Inferior Parietal (BA 7/40)Medial Parietal (BA 18/31) Confounds of blocking (Herron et al, 2004) PET studies of “memory retrieval” compared blocks (scans) with different ratios of old:new items…PET studies of “memory retrieval” compared blocks (scans) with different ratios of old:new items… However, the ratio actually affects the difference between old and new itemsHowever, the ratio actually affects the difference between old and new items PET studies of “memory retrieval” compared blocks (scans) with different ratios of old:new items…PET studies of “memory retrieval” compared blocks (scans) with different ratios of old:new items… However, the ratio actually affects the difference between old and new itemsHowever, the ratio actually affects the difference between old and new items

RR R F F R = Words Later Remembered F = Words Later Forgotten Event-Related ~4s Data Model

Time … “Oddball”

N1N2N3 “Event” model O1O2O3 Blocked Design “Epoch” model Data Model O1O2O3 N1N2N3

Epoch vs Events Convolved with HRF => Series of events Delta functions Epochs are periods of sustained stimulation (e.g, box-car functions)Epochs are periods of sustained stimulation (e.g, box-car functions) Events are impulses (delta-functions)Events are impulses (delta-functions) In SPM99, epochs and events are distinct (eg, in choice of basis functions)In SPM99, epochs and events are distinct (eg, in choice of basis functions) In SPM2, all conditions are specified in terms of their 1) onsets and 2) durations…In SPM2, all conditions are specified in terms of their 1) onsets and 2) durations… … events simply have zero duration … events simply have zero duration Near-identical regressors can be created by 1) sustained epochs, 2) rapid series of events (SOAs<~3s)Near-identical regressors can be created by 1) sustained epochs, 2) rapid series of events (SOAs<~3s) i.e, designs can be blocked or intermixedi.e, designs can be blocked or intermixed … models can be epoch or event-related … models can be epoch or event-related Epochs are periods of sustained stimulation (e.g, box-car functions)Epochs are periods of sustained stimulation (e.g, box-car functions) Events are impulses (delta-functions)Events are impulses (delta-functions) In SPM99, epochs and events are distinct (eg, in choice of basis functions)In SPM99, epochs and events are distinct (eg, in choice of basis functions) In SPM2, all conditions are specified in terms of their 1) onsets and 2) durations…In SPM2, all conditions are specified in terms of their 1) onsets and 2) durations… … events simply have zero duration … events simply have zero duration Near-identical regressors can be created by 1) sustained epochs, 2) rapid series of events (SOAs<~3s)Near-identical regressors can be created by 1) sustained epochs, 2) rapid series of events (SOAs<~3s) i.e, designs can be blocked or intermixedi.e, designs can be blocked or intermixed … models can be epoch or event-related … models can be epoch or event-related Boxcar function Sustained epoch

Epoch vs Events Though blocks of trials can be modelled as boxcars or runs of events…Though blocks of trials can be modelled as boxcars or runs of events… … interpretation of the parameter estimates differs… Consider an experiment presenting words at different rates in different blocks:Consider an experiment presenting words at different rates in different blocks: An “epoch” model will estimate parameter that increases with rate, because the parameter reflects response per blockAn “epoch” model will estimate parameter that increases with rate, because the parameter reflects response per block An “event” model may estimate parameter that decreases with rate, because the parameter reflects response per wordAn “event” model may estimate parameter that decreases with rate, because the parameter reflects response per word Though blocks of trials can be modelled as boxcars or runs of events…Though blocks of trials can be modelled as boxcars or runs of events… … interpretation of the parameter estimates differs… Consider an experiment presenting words at different rates in different blocks:Consider an experiment presenting words at different rates in different blocks: An “epoch” model will estimate parameter that increases with rate, because the parameter reflects response per blockAn “epoch” model will estimate parameter that increases with rate, because the parameter reflects response per block An “event” model may estimate parameter that decreases with rate, because the parameter reflects response per wordAn “event” model may estimate parameter that decreases with rate, because the parameter reflects response per word  =3  =5  =9  =11 Rate = 1/4sRate = 1/2s

Note on Epoch Durations As duration of epochs increases from 0 to ~2s, shape of convolved response changes little (mainly amplitude of response changes)As duration of epochs increases from 0 to ~2s, shape of convolved response changes little (mainly amplitude of response changes) Since it is the “amplitude” that is effectively estimated by the GLM, the results for epochs of constant duration <2s will be very similar to those for events (at typical SNRs)Since it is the “amplitude” that is effectively estimated by the GLM, the results for epochs of constant duration <2s will be very similar to those for events (at typical SNRs) If however the epochs vary in duration from trial-to-trial (e.g, to match RT), then epoch and event models will give different resultsIf however the epochs vary in duration from trial-to-trial (e.g, to match RT), then epoch and event models will give different results However, while RT-related duration may be appropriate for “motor” regions, it may not be appropriate for all regions (e.g, “visual”)However, while RT-related duration may be appropriate for “motor” regions, it may not be appropriate for all regions (e.g, “visual”) Thus a “parametric modulation” of events by RT may be a better model in such situationsThus a “parametric modulation” of events by RT may be a better model in such situations As duration of epochs increases from 0 to ~2s, shape of convolved response changes little (mainly amplitude of response changes)As duration of epochs increases from 0 to ~2s, shape of convolved response changes little (mainly amplitude of response changes) Since it is the “amplitude” that is effectively estimated by the GLM, the results for epochs of constant duration <2s will be very similar to those for events (at typical SNRs)Since it is the “amplitude” that is effectively estimated by the GLM, the results for epochs of constant duration <2s will be very similar to those for events (at typical SNRs) If however the epochs vary in duration from trial-to-trial (e.g, to match RT), then epoch and event models will give different resultsIf however the epochs vary in duration from trial-to-trial (e.g, to match RT), then epoch and event models will give different results However, while RT-related duration may be appropriate for “motor” regions, it may not be appropriate for all regions (e.g, “visual”)However, while RT-related duration may be appropriate for “motor” regions, it may not be appropriate for all regions (e.g, “visual”) Thus a “parametric modulation” of events by RT may be a better model in such situationsThus a “parametric modulation” of events by RT may be a better model in such situations

Timing Issues : Latency Assume the real response, r(t), is a scaled (by  ) version of the canonical, f(t), but delayed by a small amount dt: r(t) =  f(t+dt) ~  f(t) +  f ´(t) dt 1 st -order Taylor R(t) = ß 1 f(t) + ß 2 f ´(t) GLM fit If the fitted response, R(t), is modelled by canonical+temporal derivative: Then if want to reduce estimate of BOLD impulse response to one composite value, with some robustness to latency issues (e.g, real, or induced by slice-timing):  = sqrt(ß 1 2 + ß 2 2 ) (Calhoun et al, 2004) (similar logic applicable to other partial derivatives)

Timing Issues : Latency Assume the real response, r(t), is a scaled (by  ) version of the canonical, f(t), but delayed by a small amount dt: r(t) =  f(t+dt) ~  f(t) +  f ´(t) dt 1 st -order Taylor R(t) = ß 1 f(t) + ß 2 f ´(t) GLM fit   = ß 1 dt = ß 2 / ß 1 ie, Latency can be approximated by the ratio of derivative-to-canonical parameter estimates (within limits of first-order approximation, +/-1s) (Henson et al, 2002) (Liao et al, 2002) If the fitted response, R(t), is modelled by the canonical + temporal derivative: Then canonical and derivative parameter estimates, ß 1 and ß 2, are such that :

Timing Issues : Latency Delayed Responses (green/ yellow) Canonical ß 2 /ß 1 Actual latency, dt, vs. ß 2 / ß 1 Canonical Derivative Basis Functions Face repetition reduces latency as well as magnitude of fusiform response ß1ß1 ß1ß1 ß1ß1 ß2ß2 ß2ß2 ß2ß2 Parameter Estimates

A. Decreased B. Advanced C. Shortened (same integrated) D. Shortened (same maximum) A. Smaller Peak B. Earlier Onset C. Earlier Peak D. Smaller Peak and earlier Peak Timing Issues : Latency NeuralBOLD

BOLD Response Latency (Iterative) Numerical fitting of explicitly parameterised canonical HRF (Henson et al, 2001)Numerical fitting of explicitly parameterised canonical HRF (Henson et al, 2001) Distinguishes between Onset and Peak latency…Distinguishes between Onset and Peak latency… …unlike temporal derivative… …unlike temporal derivative… …and which may be important for interpreting neural changes (see previous slide) …and which may be important for interpreting neural changes (see previous slide) Distribution of parameters tested nonparametrically (Wilcoxon’s T over subjects)Distribution of parameters tested nonparametrically (Wilcoxon’s T over subjects) Numerical fitting of explicitly parameterised canonical HRF (Henson et al, 2001)Numerical fitting of explicitly parameterised canonical HRF (Henson et al, 2001) Distinguishes between Onset and Peak latency…Distinguishes between Onset and Peak latency… …unlike temporal derivative… …unlike temporal derivative… …and which may be important for interpreting neural changes (see previous slide) …and which may be important for interpreting neural changes (see previous slide) Distribution of parameters tested nonparametrically (Wilcoxon’s T over subjects)Distribution of parameters tested nonparametrically (Wilcoxon’s T over subjects) Height Peak Delay Onset Delay

BOLD Response Latency (Iterative) No difference in Onset Delay, wT(11)=35 240ms Peak Delay wT(11)=14, p<.05 0.34% Height Change wT(11)=5, p<.001 Most parsimonious account is that repetition reduces duration of neural activity… D. Shortened (same maximum) Neural D. Smaller Peak and earlier Peak BOLD

Temporal Basis Sets: Inferences How can inferences be made in hierarchical models (eg, “Random Effects” analyses over, for example, subjects)? 1. Univariate T-tests on canonical parameter alone? may miss significant experimental variability canonical parameter estimate not appropriate index of “magnitude” if real responses are non-canonical (see later) 2. Univariate F-tests on parameters from multiple basis functions? need appropriate corrections for nonsphericity (Glaser et al, 2001) 3. Multivariate tests (eg Wilks Lambda, Henson et al, 2000) not powerful unless ~10 times as many subjects as parameters

Efficiency - Single Event-type Design parametrised by:Design parametrised by: SOA min Minimum SOA p(t) Probability of event at each SOA min p(t) Probability of event at each SOA min Deterministic p(t)=1 iff t=nTDeterministic p(t)=1 iff t=nT Stationary stochastic p(t)=constantStationary stochastic p(t)=constant Dynamic stochasticDynamic stochastic p(t) varies (eg blocked) Design parametrised by:Design parametrised by: SOA min Minimum SOA p(t) Probability of event at each SOA min p(t) Probability of event at each SOA min Deterministic p(t)=1 iff t=nTDeterministic p(t)=1 iff t=nT Stationary stochastic p(t)=constantStationary stochastic p(t)=constant Dynamic stochasticDynamic stochastic p(t) varies (eg blocked) Blocked designs most efficient! (with small SOAmin)

Efficiency – Detection vs Estimation “Detection power” vs “Estimation efficiency” (Liu et al, 2001)“Detection power” vs “Estimation efficiency” (Liu et al, 2001) Detect response, or characterise shape of response?Detect response, or characterise shape of response? Maximal detection power in blocked designs;Maximal detection power in blocked designs; Maximal estimation efficiency in randomised designs => simply corresponds to choice of basis functions: detection = canonical HRF detection = canonical HRF estimation = FIR estimation = FIR “Detection power” vs “Estimation efficiency” (Liu et al, 2001)“Detection power” vs “Estimation efficiency” (Liu et al, 2001) Detect response, or characterise shape of response?Detect response, or characterise shape of response? Maximal detection power in blocked designs;Maximal detection power in blocked designs; Maximal estimation efficiency in randomised designs => simply corresponds to choice of basis functions: detection = canonical HRF detection = canonical HRF estimation = FIR estimation = FIR

Event-related fMRI Rik Henson With thanks to: Karl Friston, Oliver Josephs Event-related fMRI Rik Henson With thanks to: Karl Friston, Oliver Josephs.

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Event-related fMRI Rik Henson With thanks to: Karl Friston, Oliver Josephs Event-related fMRI Rik Henson With thanks to: Karl Friston, Oliver Josephs.

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