Event-related fMRI Christian Ruff With thanks to: Rik Henson

RealignmentSmoothing Normalisation General linear model Statistical parametric map (SPM) Image time-series Parameter estimates Design matrix Template Kernel Gaussian field theory p <0.05 Statisticalinference

OverviewOverview 1. Block/epoch vs. event-related fMRI 2. (Dis)Advantages of efMRI 3. GLM: Convolution 4. BOLD impulse response 5. Temporal Basis Functions 6. Timing Issues 7. Design Optimisation – “Efficiency” 1. Block/epoch vs. event-related fMRI 2. (Dis)Advantages of efMRI 3. GLM: Convolution 4. BOLD impulse response 5. Temporal Basis Functions 6. Timing Issues 7. Design Optimisation – “Efficiency”

Designs: Block/epoch- vs event-related U1P1 U3 U2 P2 Data Model P = Pleasant U = Unpleasant Block/epoch designs examine responses to series of similar stimuli U1U2U3 P1P2P3 Event-related designs account for response to each single stimulus ~4s

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

Blocked designs may trigger expectations and cognitive sets … Pleasant (P) Unpleasant (U) Intermixed designs can minimise this by stimulus randomisation ……… … … eFMRI: Stimulus randomisation Unpleasant (U) Pleasant (P)

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 (Gonsalves & Paller 2000) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Gonsalves & Paller 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 (Gonsalves & Paller 2000) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Gonsalves & Paller 2000) Advantages of event-related fMRI

eFMRI: post-hoc classification of trials Gonsalves, P & Paller, K.A. (2000). Nature Neuroscience, 3 (12):  Items with wrong memory of picture („hat“) were associated with more occipital activity at encoding than items with correct rejection („brain“) „was shown as picture“ „was not shown as picture“ Participant response:

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 (Gonsalves & Paller 2000) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Gonsalves & Paller 2000) 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 (Gonsalves & Paller 2000) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Gonsalves & Paller 2000) 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

eFMRI: “on-line” event-definition

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 (Gonsalves & Paller 2000) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Gonsalves & Paller 2000) 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 due to stimulus context or interactions 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 (Gonsalves & Paller 2000) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Gonsalves & Paller 2000) 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 due to stimulus context or interactions e.g, “oddball” designs (Clark et al., 2000) Advantages of event-related fMRI

timeOddball … eFMRI: Stimulus context

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 (Gonsalves & Paller 2000) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Gonsalves & Paller 2000) 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 due to stimulus context or interactions 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 (Gonsalves & Paller 2000) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Gonsalves & Paller 2000) 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 due to stimulus context or interactions 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

P1P2P3 “Event” model may capture state-item interactions (with longer SOAs) U1U2U3 Blocked Design “Epoch” model assumes constant neural processes throughout block Data Model U1 U2U3 P1P2 P3 eFMRI: “Event” model of block-designs Data Model

Convolved with HRF => Series of events Delta functions Designs can be blocked or intermixed, Designs can be blocked or intermixed, BUT models for blocked designs can be BUT models for blocked designs can be epoch- or event-related 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) 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) In SPM8, all conditions are specified in terms of their 1) onsets and 2) durationsIn SPM8, all conditions are specified in terms of their 1) onsets and 2) durations … epochs: variable or constant duration … epochs: variable or constant duration … events: zero duration … events: zero duration Designs can be blocked or intermixed, Designs can be blocked or intermixed, BUT models for blocked designs can be BUT models for blocked designs can be epoch- or event-related 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) 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) In SPM8, all conditions are specified in terms of their 1) onsets and 2) durationsIn SPM8, all conditions are specified in terms of their 1) onsets and 2) durations … epochs: variable or constant duration … epochs: variable or constant duration … events: zero duration … events: zero duration “Classic” Boxcar function Sustained epoch Modeling block designs: epochs vs events

Blocks of trials can be modelled as boxcars or runs of eventsBlocks of trials can be modelled as boxcars or runs of events BUT: interpretation of the parameter estimates may differBUT: interpretation of the parameter estimates may differ 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 Blocks of trials can be modelled as boxcars or runs of eventsBlocks of trials can be modelled as boxcars or runs of events BUT: interpretation of the parameter estimates may differBUT: interpretation of the parameter estimates may differ 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 Epochs vs events

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 have to/may be better blocked (e.g., if difficult to switch between states, or to reduce surprise effects) 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 have to/may be better blocked (e.g., if difficult to switch between states, or to reduce surprise effects) Disadvantages of intermixed designs

OverviewOverview 1. Block/epoch vs. event-related fMRI 2. (Dis)advantages of efMRI 3. GLM: Convolution 1. Block/epoch vs. event-related fMRI 2. (Dis)advantages of efMRI 3. GLM: Convolution

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 possible differences across: other regions (Schacter et al 1997) individuals (Aguirre et al, 1998)… but possible 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 possible differences across: other regions (Schacter et al 1997) individuals (Aguirre et al, 1998)… but possible differences across: other regions (Schacter et al 1997) individuals (Aguirre et al, 1998) Brief Stimulus Undershoot Initial Undershoot Peak BOLD impulse response

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, overlap between successive responses at short SOAs can be accommodated if the BOLD response is explicitly modeled, particularly if responses are assumed to superpose linearlyHowever, overlap between successive responses at short SOAs can be accommodated if the BOLD response is explicitly modeled, particularly if responses are assumed to superpose linearly Short SOAs are more sensitive; see laterShort SOAs are more sensitive; see later 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, overlap between successive responses at short SOAs can be accommodated if the BOLD response is explicitly modeled, particularly if responses are assumed to superpose linearlyHowever, overlap between successive responses at short SOAs can be accommodated if the BOLD response is explicitly modeled, particularly if responses are assumed to superpose linearly Short SOAs are more sensitive; see laterShort SOAs are more sensitive; see later Brief Stimulus Undershoot Initial Undershoot Peak BOLD impulse response

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 (Convolution) Model

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) General Linear Model in SPM

OverviewOverview 1. Block/epoch vs. event-related fMRI 2. (Dis)advantages of efMRI 3. GLM: Convolution 4. Temporal Basis Functions 1. Block/epoch vs. event-related fMRI 2. (Dis)advantages of efMRI 3. GLM: Convolution 4. Temporal Basis Functions

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 Set / FIRFourier Set / FIR Any shape (up to frequency limit / bin width) Inference via F-test Gamma FunctionsGamma Functions Bounded, asymmetrical (like BOLD) Set of different lags Inference via F-test Fourier Set / FIRFourier Set / FIR Any shape (up to frequency limit / bin width) Inference via F-test Gamma FunctionsGamma Functions Bounded, asymmetrical (like BOLD) Set of different lags Inference via F-test Temporal basis functions

Fourier Set / FIRFourier Set / FIR Any shape (up to frequency limit / bin width) 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 responses Variability captured by Taylor expansion Variability captured by Taylor expansion “Magnitude” inferences via t-test…? “Magnitude” inferences via t-test…? Fourier Set / FIRFourier Set / FIR Any shape (up to frequency limit / bin width) 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 responses Variability captured by Taylor expansion Variability captured by Taylor expansion “Magnitude” inferences via t-test…? “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) “Magnitude” inferences via t-test on canonical parameters (providing canonical is a reasonable fit)“Magnitude” inferences via t-test on canonical parameters (providing canonical is a reasonable 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) “Magnitude” inferences via t-test on canonical parameters (providing canonical is a reasonable fit)“Magnitude” inferences via t-test on canonical parameters (providing canonical is a reasonable fit) 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) “Magnitude” inferences via t-test on canonical parameters (providing canonical is a reasonable fit)“Magnitude” inferences via t-test on canonical parameters (providing canonical is a reasonable fit) “Latency” inferences via tests on ratio of derivative : canonical parameters“Latency” inferences via tests on ratio of derivative : canonical parameters “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) “Magnitude” inferences via t-test on canonical parameters (providing canonical is a reasonable fit)“Magnitude” inferences via t-test on canonical parameters (providing canonical is a reasonable fit) “Latency” inferences via tests on ratio of derivative : canonical parameters“Latency” inferences via tests on ratio of derivative : canonical parameters Canonical Temporal Dispersion Temporal basis functions

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 often unbalanced, e.g. when events defined by subject Define HRF from pilot scan on each subject May capture inter-subject 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 Other approaches (e.g., outside SPM)

+ FIR+ Dispersion+ TemporalCanonical … canonical + temporal + dispersion derivatives appear sufficient to capture most activity … may not be true for more complex trials (e.g. stimulus-prolonged delay (>~2 s)-response) … but then such trials better modelled with separate neural components (i.e., activity no longer delta function) + constrained HRF (Zarahn, 1999) In this example (rapid motor response to faces, Henson et al, 2001)… Which temporal basis set?

OverviewOverview 1. Block/epoch vs. event-related fMRI 2. (Dis)advantages of efMRI 3. GLM: Convolution 4. BOLD impulse response 5. Temporal Basis Functions 6. Timing Issues 1. Block/epoch vs. event-related fMRI 2. (Dis)advantages of efMRI 3. GLM: Convolution 4. BOLD impulse response 5. Temporal Basis Functions 6. Timing Issues

Typical TR for 60 slice EPI at 3mm spacing is ~ 4sTypical TR for 60 slice EPI at 3mm spacing is ~ 4s Scans TR=4s Timing issues: Sampling

Typical TR for 60 slice EPI at 3mm spacing is ~ 4sTypical TR for 60 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signalSampling at [0,4,8,12…] post- stimulus may miss peak signal Typical TR for 60 slice EPI at 3mm spacing is ~ 4sTypical TR for 60 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signalSampling at [0,4,8,12…] post- stimulus may miss peak signal Stimulus (synchronous) Scans TR=4s SOA=8s Sampling rate=4s Timing issues: Sampling

Typical TR for 60 slice EPI at 3mm spacing is ~ 4sTypical TR for 60 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signalSampling at [0,4,8,12…] post- stimulus may miss peak signal Higher effective sampling by:Higher effective sampling by: 1. Asynchrony e.g., SOA=1.5TR Typical TR for 60 slice EPI at 3mm spacing is ~ 4sTypical TR for 60 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signalSampling at [0,4,8,12…] post- stimulus may miss peak signal Higher effective sampling by:Higher effective sampling by: 1. Asynchrony e.g., SOA=1.5TR Stimulus (asynchronous) SOA=6s Sampling rate=2s Timing issues: Sampling Scans TR=4s

Typical TR for 60 slice EPI at 3mm spacing is ~ 4sTypical TR for 60 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signalSampling at [0,4,8,12…] post- stimulus may miss peak signal Higher effective sampling by:Higher effective sampling by: 1. Asynchrony e.g., SOA=1.5TR 2. Random Jitter e,g., SOA=(2±0.5)TR Typical TR for 60 slice EPI at 3mm spacing is ~ 4sTypical TR for 60 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signalSampling at [0,4,8,12…] post- stimulus may miss peak signal Higher effective sampling by:Higher effective sampling by: 1. Asynchrony e.g., SOA=1.5TR 2. Random Jitter e,g., SOA=(2±0.5)TR Stimulus (random jitter) Sampling rate=2s Timing issues: Sampling Scans TR=4s

Typical TR for 60 slice EPI at 3mm spacing is ~ 4sTypical TR for 60 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signalSampling at [0,4,8,12…] post- stimulus may miss peak signal Higher effective sampling by:Higher effective sampling by: 1. Asynchrony e.g., SOA=1.5TR 2. Random Jitter e,g., SOA=(2±0.5)TR Better response characterisation (Miezin et al, 2000)Better response characterisation (Miezin et al, 2000) Typical TR for 60 slice EPI at 3mm spacing is ~ 4sTypical TR for 60 slice EPI at 3mm spacing is ~ 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signalSampling at [0,4,8,12…] post- stimulus may miss peak signal Higher effective sampling by:Higher effective sampling by: 1. Asynchrony e.g., SOA=1.5TR 2. Random Jitter e,g., SOA=(2±0.5)TR Better response characterisation (Miezin et al, 2000)Better response characterisation (Miezin et al, 2000) Stimulus (random jitter) Sampling rate=2s Timing issues: Sampling Scans TR=4s

x2x2 x3x3 T=16, TR=2s Scan 0 1 o T 0 =9 o T 0 =16 Timing issues: Slice-Timing T1 = 0 s T16 = 2 s

“Slice-timing Problem”:“Slice-timing Problem”: 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 (slightly less problematic if middle slice is selected as reference, and with short TRs) (slightly less problematic if middle slice is selected as reference, and with short TRs) 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 “Slice-timing Problem”:“Slice-timing Problem”: 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 (slightly less problematic if middle slice is selected as reference, and with short TRs) (slightly less problematic if middle slice is selected as reference, and with short TRs) 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 Timing issues: Slice-timing Bottom Slice Top Slice SPM{t} TR=3s Interpolated SPM{t} Derivative SPM{F}

OverviewOverview 1. Block/epoch vs. event-related fMRI 2. (Dis)advantages of efMRI 3. GLM: Convolution 4. BOLD impulse response 5. Temporal Basis Functions 6. Timing Issues 7. Design Optimisation – “Efficiency” 1. Block/epoch vs. event-related fMRI 2. (Dis)advantages of efMRI 3. GLM: Convolution 4. BOLD impulse response 5. Temporal Basis Functions 6. Timing Issues 7. Design Optimisation – “Efficiency”

HRF can be viewed as a filter (Josephs & Henson, 1999)HRF can be viewed as a filter (Josephs & Henson, 1999) We want to maximise the signal passed by this filterWe want to maximise the signal passed by this filter Dominant frequency of canonical HRF is ~0.04 HzDominant frequency of canonical HRF is ~0.04 Hz  The most efficient design is a sinusoidal modulation of neural activity with period ~24s (e.g., boxcar with 12s on/ 12s off)(e.g., boxcar with 12s on/ 12s off) HRF can be viewed as a filter (Josephs & Henson, 1999)HRF can be viewed as a filter (Josephs & Henson, 1999) We want to maximise the signal passed by this filterWe want to maximise the signal passed by this filter Dominant frequency of canonical HRF is ~0.04 HzDominant frequency of canonical HRF is ~0.04 Hz  The most efficient design is a sinusoidal modulation of neural activity with period ~24s (e.g., boxcar with 12s on/ 12s off)(e.g., boxcar with 12s on/ 12s off) Design Efficiency

 =  = A very “efficient” design! Stimulus (“Neural”)HRFPredicted Data Sinusoidal modulation, f = 1/33s

= = Blocked-epoch (with small SOA) quite “efficient”   HRFPredicted DataStimulus (“Neural”) Blocked, epoch = 20s

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

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

T-statistic for a given contrast: T = T-statistic for a given contrast: T = c T b / var(c T b) For maximum T, we want minimum standard error of contrast estimates (  maximum precision For maximum T, we want minimum standard error of contrast estimates (var(c T b))  maximum precision Var(c T b) = sqrt(  2 c T (X T X) -1 c) (i.i.d) If we assume that noise variance ( is unaffected by changes in X, then our precision for given parameters is proportional to the design efficiency: e(c,X) = { c T (X T X) -1 c } -1 If we assume that noise variance (  2 ) is unaffected by changes in X, then our precision for given parameters is proportional to the design efficiency: e(c,X) = { c T (X T X) -1 c } -1  We can influence e (a priori) by the spacing and sequencing of epochs/events in our design matrix  e is specific for a given contrast! T-statistic for a given contrast: T = T-statistic for a given contrast: T = c T b / var(c T b) For maximum T, we want minimum standard error of contrast estimates (  maximum precision For maximum T, we want minimum standard error of contrast estimates (var(c T b))  maximum precision Var(c T b) = sqrt(  2 c T (X T X) -1 c) (i.i.d) If we assume that noise variance ( is unaffected by changes in X, then our precision for given parameters is proportional to the design efficiency: e(c,X) = { c T (X T X) -1 c } -1 If we assume that noise variance (  2 ) is unaffected by changes in X, then our precision for given parameters is proportional to the design efficiency: e(c,X) = { c T (X T X) -1 c } -1  We can influence e (a priori) by the spacing and sequencing of epochs/events in our design matrix  e is specific for a given contrast! Design efficiency

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 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 Design efficiency: Trial spacing

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=nSOAminDeterministic p(t)=1 iff t=nSOAmin 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=nSOAminDeterministic p(t)=1 iff t=nSOAmin Design efficiency: Trial spacing

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=nSOAminDeterministic p(t)=1 iff t=nSOAmin Stationary stochastic p(t)=constant<1Stationary stochastic p(t)=constant<1 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=nSOAminDeterministic p(t)=1 iff t=nSOAmin Stationary stochastic p(t)=constant<1Stationary stochastic p(t)=constant<1 Design efficiency: Trial spacing

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=nSOAminDeterministic p(t)=1 iff t=nSOAmin Stationary stochastic p(t)=constantStationary stochastic p(t)=constant Dynamic stochasticDynamic stochastic p(t) varies (e.g., 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=nSOAminDeterministic p(t)=1 iff t=nSOAmin Stationary stochastic p(t)=constantStationary stochastic p(t)=constant Dynamic stochasticDynamic stochastic p(t) varies (e.g., blocked) Blocked designs most efficient! (with small SOAmin) Design efficiency: Trial spacing

However, block designs are often not advisable due to interpretative difficulties (see before)However, block designs are often not advisable due to interpretative difficulties (see before) Event trains may then be constructed by modulating the event probabilities in a dynamic stochastic fashionEvent trains may then be constructed by modulating the event probabilities in a dynamic stochastic fashion This can result in intermediate levels of efficiencyThis can result in intermediate levels of efficiency However, block designs are often not advisable due to interpretative difficulties (see before)However, block designs are often not advisable due to interpretative difficulties (see before) Event trains may then be constructed by modulating the event probabilities in a dynamic stochastic fashionEvent trains may then be constructed by modulating the event probabilities in a dynamic stochastic fashion This can result in intermediate levels of efficiencyThis can result in intermediate levels of efficiency Design efficiency: Trial spacing 3 sessions with 128 scans Faces, scrambled faces SOA always 2.97 s Cycle length 24 s e

4s smoothing; 1/60s highpass filtering 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 x n Transition MatrixWith n event-types p i (h) is a n x n Transition Matrix Example: Randomised ABExample: Randomised AB AB A AB A B => 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 x n Transition MatrixWith n event-types p i (h) is a n x n Transition Matrix Example: Randomised ABExample: Randomised AB AB A AB A B => ABBBABAABABAAA... Differential Effect (A-B) Common Effect (A+B) Design efficiency: Trial sequencing

4s smoothing; 1/60s highpass filtering Example: Alternating ABExample: Alternating AB AB A01 AB A01 B10 => ABABABABABAB... Example: Alternating ABExample: Alternating AB AB A01 AB A01 B10 => ABABABABABAB... Alternating (A-B) Permuted (A-B) Example: Permuted ABExample: Permuted AB AB AB AA0 1 AB BA BB1 0 => ABBAABABABBA... Design efficiency: Trial sequencing

4s smoothing; 1/60s highpass filtering Example: Null eventsExample: Null events AB AB A B => 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) Example: Null eventsExample: Null events AB AB A B => 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) Null Events (A+B) Null Events (A-B) Design efficiency: Trial sequencing

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, given optimal block length is not exceeded)Blocked designs generally most efficient (with short SOAs, given optimal block length is not exceeded) However, psychological efficiency often dictates intermixed designs, and often also sets limits on SOAsHowever, psychological efficiency often dictates intermixed designs, and often also sets limits on SOAs With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (>2 seconds, and 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 (>2 seconds, and 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 optimalIf order constrained, intermediate SOAs (5-20s) can be optimal If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity)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, given optimal block length is not exceeded)Blocked designs generally most efficient (with short SOAs, given optimal block length is not exceeded) However, psychological efficiency often dictates intermixed designs, and often also sets limits on SOAsHowever, psychological efficiency often dictates intermixed designs, and often also sets limits on SOAs With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (>2 seconds, and 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 (>2 seconds, and 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 optimalIf order constrained, intermediate SOAs (5-20s) can be optimal If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity)If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity) Design efficiency: Conclusions

End: Overview 1. Block/epoch vs. event-related fMRI 2. (Dis)Advantages of efMRI 3. GLM: Convolution 4. BOLD impulse response 5. Temporal Basis Functions 6. Timing Issues 7. Design Optimisation – “Efficiency” 1. Block/epoch vs. event-related fMRI 2. (Dis)Advantages of efMRI 3. GLM: Convolution 4. BOLD impulse response 5. Temporal Basis Functions 6. Timing Issues 7. Design Optimisation – “Efficiency”