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Event-related Event-related fMRIfMRIEvent-related Event-related fMRIfMRI
Christian RuffChristian Ruff
With thanks to: Rik Henson
RealignmentRealignment SmoothingSmoothing
NormalisationNormalisation
General linear modelGeneral linear model
Statistical parametric map (SPM)Statistical parametric map (SPM)Image time-seriesImage time-series
Parameter estimatesParameter estimates
Design matrixDesign matrix
TemplateTemplate
KernelKernel
Gaussian Gaussian field theoryfield theory
p <0.05p <0.05
StatisticalStatisticalinferenceinference
OverviewOverviewOverviewOverview
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)Advantages of efMRI2. (Dis)Advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. BOLD impulse response4. BOLD impulse response
5. Temporal Basis Functions5. Temporal Basis Functions
6. Timing Issues6. Timing Issues
7. Design Optimisation 7. Design Optimisation – “Efficiency”– “Efficiency”
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)Advantages of efMRI2. (Dis)Advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. BOLD impulse response4. BOLD impulse response
5. Temporal Basis Functions5. Temporal Basis Functions
6. Timing Issues6. Timing Issues
7. Design Optimisation 7. Design Optimisation – “Efficiency”– “Efficiency”
Designs: Block/epoch- vs event-Designs: Block/epoch- vs event-relatedrelated
Designs: Block/epoch- vs event-Designs: Block/epoch- vs event-relatedrelated
U1 P1 U3U2 P2
Data
Model
P = PleasantU = Unpleasant
Block/epoch designs examine responses to series of similar stimuli
U1 U2 U3 P1 P2 P3
Event-related designs account for response to each single stimulus
~4s
1. Randomised1. Randomised trialtrial order orderc.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
1. Randomised1. Randomised trialtrial order orderc.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
Advantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRI
Blocked designs may trigger expectations and cognitive setsBlocked designs may trigger expectations and cognitive sets
……
Pleasant (P)Unpleasant (U)
Intermixed designs can minimise this by stimulus randomisationIntermixed designs can minimise this by stimulus randomisation
…… …… ………………
eFMRI: Stimulus randomisationeFMRI: Stimulus randomisationeFMRI: Stimulus randomisationeFMRI: Stimulus randomisation
Unpleasant (U) Unpleasant (U) Unpleasant (U)Pleasant (P) Pleasant (P)
1. Randomised trial order 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
2. Post hoc / subjective classification of trials2. Post hoc / subjective classification of trialse.g, according to subsequent memory (Gonsalves & Paller 2000)e.g, according to subsequent memory (Gonsalves & Paller 2000)
1. Randomised trial order 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
2. Post hoc / subjective classification of trials2. Post hoc / subjective classification of trialse.g, according to subsequent memory (Gonsalves & Paller 2000)e.g, according to subsequent memory (Gonsalves & Paller 2000)
Advantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRI
eFMRI: post-hoc classification of eFMRI: post-hoc classification of trialstrials
eFMRI: post-hoc classification of eFMRI: post-hoc classification of trialstrials
Gonsalves, P & Paller, K.A. (2000). Gonsalves, P & Paller, K.A. (2000). Nature Neuroscience, 3Nature Neuroscience, 3 (12):1316-21 (12):1316-21
Items with wrongItems with wrong memory of picture („hat“) were associated with more memory of picture („hat“) were associated with more occipital activity occipital activity at encodingat encoding than items with correct rejection („brain“) than items with correct rejection („brain“)
„„was shown as was shown as picture“picture“
„„was was notnot shown shown as picture“as picture“
Participant response:Participant response:
1. Randomised trial order 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
2. Post hoc / subjective classification of trials2. Post hoc / subjective classification of trialse.g, according to subsequent memory (Gonsalves & Paller 2000)e.g, according to subsequent memory (Gonsalves & Paller 2000)
3. Some events can only be indicated by subject (in time)3. Some events can only be indicated by subject (in time)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)
1. Randomised trial order 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
2. Post hoc / subjective classification of trials2. Post hoc / subjective classification of trialse.g, according to subsequent memory (Gonsalves & Paller 2000)e.g, according to subsequent memory (Gonsalves & Paller 2000)
3. Some events can only be indicated by subject (in time)3. Some events can only be indicated by subject (in time)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)
Advantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRI
eFMRI: “on-line” event-definitioneFMRI: “on-line” event-definitioneFMRI: “on-line” event-definitioneFMRI: “on-line” event-definition
1. Randomised trial order 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
2. Post hoc / subjective classification of trials2. Post hoc / subjective classification of trialse.g, according to subsequent memory (Gonsalves & Paller 2000)e.g, according to subsequent memory (Gonsalves & Paller 2000)
3. Some events can only be indicated by subject (in time)3. Some events can only be indicated by subject (in time)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)
4. Some trials cannot be blocked due to stimulus context or interactions4. Some trials cannot be blocked due to stimulus context or interactionse.g, “oddball” designs (Clark et al., 2000)e.g, “oddball” designs (Clark et al., 2000)
1. Randomised trial order 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
2. Post hoc / subjective classification of trials2. Post hoc / subjective classification of trialse.g, according to subsequent memory (Gonsalves & Paller 2000)e.g, according to subsequent memory (Gonsalves & Paller 2000)
3. Some events can only be indicated by subject (in time)3. Some events can only be indicated by subject (in time)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)
4. Some trials cannot be blocked due to stimulus context or interactions4. Some trials cannot be blocked due to stimulus context or interactionse.g, “oddball” designs (Clark et al., 2000)e.g, “oddball” designs (Clark et al., 2000)
Advantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRI
time
OddballOddball
…
eFMRI: Stimulus contexteFMRI: Stimulus contexteFMRI: Stimulus contexteFMRI: Stimulus context
1. Randomised trial order 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
2. Post hoc / subjective classification of trials2. Post hoc / subjective classification of trialse.g, according to subsequent memory (Gonsalves & Paller 2000)e.g, according to subsequent memory (Gonsalves & Paller 2000)
3. Some events can only be indicated by subject (in time)3. Some events can only be indicated by subject (in time)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)
4. Some trials cannot be blocked due to stimulus context or interactions4. Some trials cannot be blocked due to stimulus context or interactionse.g, “oddball” designs (Clark et al., 2000)e.g, “oddball” designs (Clark et al., 2000)
5. More accurate models even for blocked designs?5. More accurate models even for blocked designs?e.g., “state-item” interactions (Chawla et al, 1999)e.g., “state-item” interactions (Chawla et al, 1999)
1. Randomised trial order 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997)c.f. confounds of blocked designs (Johnson et al 1997)
2. Post hoc / subjective classification of trials2. Post hoc / subjective classification of trialse.g, according to subsequent memory (Gonsalves & Paller 2000)e.g, according to subsequent memory (Gonsalves & Paller 2000)
3. Some events can only be indicated by subject (in time)3. Some events can only be indicated by subject (in time)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)
4. Some trials cannot be blocked due to stimulus context or interactions4. Some trials cannot be blocked due to stimulus context or interactionse.g, “oddball” designs (Clark et al., 2000)e.g, “oddball” designs (Clark et al., 2000)
5. More accurate models even for blocked designs?5. More accurate models even for blocked designs?e.g., “state-item” interactions (Chawla et al, 1999)e.g., “state-item” interactions (Chawla et al, 1999)
Advantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRIAdvantages of event-related fMRI
P1 P2 P3
“Event” model may capture state-item interactions (with longer SOAs)
U1 U2 U3
Blocked Design
“Epoch” model assumes constant neural processes throughout block
Data
Model
U1 U2 U3 P1 P2 P3
eFMRI: “Event” model of block-eFMRI: “Event” model of block-designs designs
eFMRI: “Event” model of block-eFMRI: “Event” model of block-designs designs
Data
Model
Convolved with HRF
=>
Series of eventsDelta
functions
• DesignsDesigns can be can be blockedblocked or or intermixed, intermixed, BUTBUT models models for blocked designs can be for blocked designs can be epochepoch- or - or eventevent-related-related
• EpochsEpochs are periods of sustained stimulation are periods of sustained stimulation (e.g, box-car functions)(e.g, box-car functions)
• EventsEvents are impulses (delta-functions) are impulses (delta-functions)
• Near-identical regressors can be created by Near-identical regressors can be created by 1) sustained epochs, 2) rapid series of 1) sustained epochs, 2) rapid series of events (SOAs<~3s)events (SOAs<~3s)
• In SPM8, all conditions are specified in In SPM8, all conditions are specified in terms of their 1) terms of their 1) onsetsonsets and 2) and 2) durationsdurations
… … epochs: variable or constant durationepochs: variable or constant duration … … events: zero durationevents: zero duration
• DesignsDesigns can be can be blockedblocked or or intermixed, intermixed, BUTBUT models models for blocked designs can be for blocked designs can be epochepoch- or - or eventevent-related-related
• EpochsEpochs are periods of sustained stimulation are periods of sustained stimulation (e.g, box-car functions)(e.g, box-car functions)
• EventsEvents are impulses (delta-functions) are impulses (delta-functions)
• Near-identical regressors can be created by Near-identical regressors can be created by 1) sustained epochs, 2) rapid series of 1) sustained epochs, 2) rapid series of events (SOAs<~3s)events (SOAs<~3s)
• In SPM8, all conditions are specified in In SPM8, all conditions are specified in terms of their 1) terms of their 1) onsetsonsets and 2) and 2) durationsdurations
… … epochs: variable or constant durationepochs: variable or constant duration … … events: zero durationevents: zero duration
“Classic” Boxcar function
Sustained epoch
Modeling block designs: epochs vs Modeling block designs: epochs vs eventsevents
Modeling block designs: epochs vs Modeling block designs: epochs vs eventsevents
• Blocks of trials can be modelled as boxcars Blocks of trials can be modelled as boxcars or runs of eventsor runs of events
• BUT: interpretation of the parameter BUT: interpretation of the parameter estimates may differestimates may differ
• Consider an experiment presenting words Consider an experiment presenting words at different rates in different blocks:at different rates in different blocks:
• An “epoch” model will estimate An “epoch” model will estimate parameter that increases with rate, parameter that increases with rate, because the parameter reflects because the parameter reflects response per blockresponse per block
• An “event” model may estimate An “event” model may estimate parameter that parameter that decreasesdecreases with rate, with rate, because the parameter reflects because the parameter reflects response per wordresponse per word
• Blocks of trials can be modelled as boxcars Blocks of trials can be modelled as boxcars or runs of eventsor runs of events
• BUT: interpretation of the parameter BUT: interpretation of the parameter estimates may differestimates may differ
• Consider an experiment presenting words Consider an experiment presenting words at different rates in different blocks:at different rates in different blocks:
• An “epoch” model will estimate An “epoch” model will estimate parameter that increases with rate, parameter that increases with rate, because the parameter reflects because the parameter reflects response per blockresponse per block
• An “event” model may estimate An “event” model may estimate parameter that parameter that decreasesdecreases with rate, with rate, because the parameter reflects because the parameter reflects response per wordresponse per word
=3 =5
=9=11
Rate = 1/4s Rate = 1/2s
Epochs vs eventsEpochs vs eventsEpochs vs eventsEpochs vs events
1. 1. Less efficient for detecting effects than are blocked designs Less efficient for detecting effects than are blocked designs (see later…) (see later…)
2. Some psychological processes have to/may be better blocked 2. Some psychological processes have to/may be better blocked (e.g., if difficult to switch between states, or to reduce surprise effects)(e.g., if difficult to switch between states, or to reduce surprise effects)
1. 1. Less efficient for detecting effects than are blocked designs Less efficient for detecting effects than are blocked designs (see later…) (see later…)
2. Some psychological processes have to/may be better blocked 2. Some psychological processes have to/may be better blocked (e.g., if difficult to switch between states, or to reduce surprise effects)(e.g., if difficult to switch between states, or to reduce surprise effects)
Disadvantages of intermixed designsDisadvantages of intermixed designsDisadvantages of intermixed designsDisadvantages of intermixed designs
OverviewOverviewOverviewOverview
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)advantages of efMRI2. (Dis)advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)advantages of efMRI2. (Dis)advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
• Function of blood oxygenation, flow, Function of blood oxygenation, flow, volume (Buxton et al, 1998)volume (Buxton et al, 1998)
• Peak (max. oxygenation) 4-6s Peak (max. oxygenation) 4-6s poststimulus; baseline after 20-30spoststimulus; baseline after 20-30s
• Initial undershoot can be observed Initial undershoot can be observed (Malonek & Grinvald, 1996)(Malonek & Grinvald, 1996)
• Similar across V1, A1, S1…Similar across V1, A1, S1…
• … … but possible differences across:but possible differences across: other regions (Schacter et al 1997) other regions (Schacter et al 1997)
individuals (Aguirre et al, 1998)individuals (Aguirre et al, 1998)
• Function of blood oxygenation, flow, Function of blood oxygenation, flow, volume (Buxton et al, 1998)volume (Buxton et al, 1998)
• Peak (max. oxygenation) 4-6s Peak (max. oxygenation) 4-6s poststimulus; baseline after 20-30spoststimulus; baseline after 20-30s
• Initial undershoot can be observed Initial undershoot can be observed (Malonek & Grinvald, 1996)(Malonek & Grinvald, 1996)
• Similar across V1, A1, S1…Similar across V1, A1, S1…
• … … but possible differences across:but possible differences across: other regions (Schacter et al 1997) other regions (Schacter et al 1997)
individuals (Aguirre et al, 1998)individuals (Aguirre et al, 1998)
BriefStimulus
Undershoot
InitialUndershoot
Peak
BOLD impulse responseBOLD impulse responseBOLD impulse responseBOLD impulse response
• Early event-related fMRI studies Early event-related fMRI studies used a long Stimulus Onset used a long Stimulus Onset Asynchrony (SOA) to allow BOLD Asynchrony (SOA) to allow BOLD response to return to baselineresponse to return to baseline
• However, overlap between However, overlap between successive responses at short SOAs successive responses at short SOAs can be accommodated if the BOLD can be accommodated if the BOLD response is explicitly modeled, response is explicitly modeled, particularly if responses are assumed particularly if responses are assumed to superpose linearlyto superpose linearly
• Short SOAs are more sensitive; see Short SOAs are more sensitive; see laterlater
• Early event-related fMRI studies Early event-related fMRI studies used a long Stimulus Onset used a long Stimulus Onset Asynchrony (SOA) to allow BOLD Asynchrony (SOA) to allow BOLD response to return to baselineresponse to return to baseline
• However, overlap between However, overlap between successive responses at short SOAs successive responses at short SOAs can be accommodated if the BOLD can be accommodated if the BOLD response is explicitly modeled, response is explicitly modeled, particularly if responses are assumed particularly if responses are assumed to superpose linearlyto superpose linearly
• Short SOAs are more sensitive; see Short SOAs are more sensitive; see laterlater
BriefStimulus
Undershoot
InitialUndershoot
Peak
BOLD impulse responseBOLD impulse responseBOLD impulse responseBOLD 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() = ßi fi ()
fi() = temporal basis functions
y(t) = ßi fi (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() = ßi fi ()
fi() = temporal basis functions
y(t) = ßi fi (t - nT) + (t)
y = X ß + ε
Design Matrix
convolution
T 2T 3T ...
u(t) h()= ßi fi ()
sampled each scan
General General Linear Linear (Convolution) (Convolution) ModelModelGeneral General Linear Linear (Convolution) (Convolution) ModelModel
Auditory words
every 20s
SPM{F}SPM{F}
0 time {secs} 300 time {secs} 30
Sampled every TR = 1.7s
Design matrix, Design matrix, XX
[x(t)[x(t)ƒƒ11(() | x(t)) | x(t)ƒƒ22(() |...]) |...]…
Gamma functions ƒGamma functions ƒii(() of ) of
peristimulus time peristimulus time (Orthogonalised)(Orthogonalised)
General General Linear Model in SPMLinear Model in SPMGeneral General Linear Model in SPMLinear Model in SPM
OverviewOverviewOverviewOverview
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)advantages of efMRI2. (Dis)advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. Temporal Basis Functions4. Temporal Basis Functions
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)advantages of efMRI2. (Dis)advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. Temporal Basis Functions4. Temporal Basis Functions
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal basis functions
• Fourier SetFourier SetWindowed sines & cosinesWindowed sines & cosinesAny shape (up to frequency limit)Any shape (up to frequency limit)Inference via F-testInference via F-test
• Fourier SetFourier SetWindowed sines & cosinesWindowed sines & cosinesAny shape (up to frequency limit)Any shape (up to frequency limit)Inference via F-testInference via F-test
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal basis functions
• Finite Impulse ResponseFinite Impulse ResponseMini “timebins” (selective averaging)Mini “timebins” (selective averaging)AAny shapeny shape (up to bin-width (up to bin-width))Inference via F-testInference via F-test
• Finite Impulse ResponseFinite Impulse ResponseMini “timebins” (selective averaging)Mini “timebins” (selective averaging)AAny shapeny shape (up to bin-width (up to bin-width))Inference via F-testInference via F-test
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal basis functions
• Fourier Set / FIRFourier Set / FIRAny shape (up to frequency limit / bin Any shape (up to frequency limit / bin
width)width)Inference via F-testInference via F-test
• Gamma FunctionsGamma FunctionsBounded, asymmetrical (like BOLD)Bounded, asymmetrical (like BOLD)Set of different lagsSet of different lagsInference via F-testInference via F-test
• Fourier Set / FIRFourier Set / FIRAny shape (up to frequency limit / bin Any shape (up to frequency limit / bin
width)width)Inference via F-testInference via F-test
• Gamma FunctionsGamma FunctionsBounded, asymmetrical (like BOLD)Bounded, asymmetrical (like BOLD)Set of different lagsSet of different lagsInference via F-testInference via F-test
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal basis functions
• Fourier Set / FIRFourier Set / FIRAny shape (up to frequency limit / bin width)Any shape (up to frequency limit / bin width)Inference via F-testInference via F-test
• Gamma FunctionsGamma FunctionsBounded, asymmetrical (like BOLD)Bounded, asymmetrical (like BOLD)Set of different lagsSet of different lagsInference via F-testInference via F-test
• ““Informed” Basis SetInformed” Basis SetBest guess of canonical BOLD responseBest guess of canonical BOLD responseVariability captured by Taylor expansion Variability captured by Taylor expansion “Magnitude” inferences via t-test“Magnitude” inferences via t-test…?…?
• Fourier Set / FIRFourier Set / FIRAny shape (up to frequency limit / bin width)Any shape (up to frequency limit / bin width)Inference via F-testInference via F-test
• Gamma FunctionsGamma FunctionsBounded, asymmetrical (like BOLD)Bounded, asymmetrical (like BOLD)Set of different lagsSet of different lagsInference via F-testInference via F-test
• ““Informed” Basis SetInformed” Basis SetBest guess of canonical BOLD responseBest guess of canonical BOLD responseVariability captured by Taylor expansion Variability captured by Taylor expansion “Magnitude” inferences via t-test“Magnitude” inferences via t-test…?…?
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal basis functions
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
Canonical
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal basis functions
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
plusplus Multivariate Taylor expansion in: Multivariate Taylor expansion in:
time (time (Temporal DerivativeTemporal Derivative))
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
plusplus Multivariate Taylor expansion in: Multivariate Taylor expansion in:
time (time (Temporal DerivativeTemporal Derivative))
CanonicalTemporal
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal basis functions
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
plusplus Multivariate Taylor expansion in: Multivariate Taylor expansion in:
time (time (Temporal DerivativeTemporal Derivative))
width (width (Dispersion DerivativeDispersion Derivative))
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
plusplus Multivariate Taylor expansion in: Multivariate Taylor expansion in:
time (time (Temporal DerivativeTemporal Derivative))
width (width (Dispersion DerivativeDispersion Derivative))
CanonicalTemporalDispersion
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal basis functions
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
plusplus Multivariate Taylor expansion in: Multivariate Taylor expansion in:
time (time (Temporal DerivativeTemporal Derivative))
width (width (Dispersion DerivativeDispersion Derivative))
• ““Magnitude” inferences via t-test on Magnitude” inferences via t-test on canonical parameterscanonical parameters (providing (providing canonical is a reasonable fit)canonical is a reasonable fit)
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
plusplus Multivariate Taylor expansion in: Multivariate Taylor expansion in:
time (time (Temporal DerivativeTemporal Derivative))
width (width (Dispersion DerivativeDispersion Derivative))
• ““Magnitude” inferences via t-test on Magnitude” inferences via t-test on canonical parameterscanonical parameters (providing (providing canonical is a reasonable fit)canonical is a reasonable fit)
CanonicalTemporalDispersion
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal basis functions
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
plusplus Multivariate Taylor expansion in: Multivariate Taylor expansion in:
time (time (Temporal DerivativeTemporal Derivative))
width (width (Dispersion DerivativeDispersion Derivative))
• ““Magnitude” inferences via t-test on Magnitude” inferences via t-test on canonical parameterscanonical parameters (providing (providing canonical is a reasonable fit)canonical is a reasonable fit)
• ““Latency” inferences via testLatency” inferences via testss on on ratioratio of of derivativederivative : : canonical parameterscanonical parameters
““Informed” Basis SetInformed” Basis Set (Friston et al. 1998)(Friston et al. 1998)
• Canonical HRF (2 gamma functions)Canonical HRF (2 gamma functions)
plusplus Multivariate Taylor expansion in: Multivariate Taylor expansion in:
time (time (Temporal DerivativeTemporal Derivative))
width (width (Dispersion DerivativeDispersion Derivative))
• ““Magnitude” inferences via t-test on Magnitude” inferences via t-test on canonical parameterscanonical parameters (providing (providing canonical is a reasonable fit)canonical is a reasonable fit)
• ““Latency” inferences via testLatency” inferences via testss on on ratioratio of of derivativederivative : : canonical parameterscanonical parameters
CanonicalTemporalDispersion
Temporal basis functionsTemporal basis functionsTemporal basis functionsTemporal 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)Other approaches (e.g., outside SPM)Other approaches (e.g., outside SPM)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?Which temporal basis set?Which temporal basis set?Which temporal basis set?
OverviewOverviewOverviewOverview
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)advantages of efMRI2. (Dis)advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. BOLD impulse response4. BOLD impulse response
5. Temporal Basis Functions5. Temporal Basis Functions
6. Timing Issues6. Timing Issues
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)advantages of efMRI2. (Dis)advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. BOLD impulse response4. BOLD impulse response
5. Temporal Basis Functions5. Temporal Basis Functions
6. Timing Issues6. Timing Issues
• Typical TR for 60 slice EPI at 3mm Typical TR for 60 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
• Typical TR for 60 slice EPI at 3mm Typical TR for 60 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
Scans TR=4s
Timing issues: SamplingTiming issues: SamplingTiming issues: SamplingTiming issues: Sampling
• Typical TR for 48 slice EPI at 3mm Typical TR for 48 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
• Sampling at [0,4,8,12…] post- Sampling at [0,4,8,12…] post- stimulus may miss peak signalstimulus may miss peak signal
• Typical TR for 48 slice EPI at 3mm Typical TR for 48 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
• Sampling at [0,4,8,12…] post- Sampling at [0,4,8,12…] post- stimulus may miss peak signalstimulus may miss peak signal Stimulus (synchronous)
Scans TR=4s
SOA=8s
Sampling rate=4s
Timing issues: SamplingTiming issues: SamplingTiming issues: SamplingTiming issues: Sampling
• Typical TR for 48 slice EPI at 3mm Typical TR for 48 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
• Sampling at [0,4,8,1Sampling at [0,4,8,122…] post- …] post- stimulus may miss peak signalstimulus may miss peak signal
• Higher effective sampling by: Higher effective sampling by:
1. Asynchrony1. Asynchronye.g.,e.g., SOA=1.5TR SOA=1.5TR
• Typical TR for 48 slice EPI at 3mm Typical TR for 48 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
• Sampling at [0,4,8,1Sampling at [0,4,8,122…] post- …] post- stimulus may miss peak signalstimulus may miss peak signal
• Higher effective sampling by: Higher effective sampling by:
1. Asynchrony1. Asynchronye.g.,e.g., SOA=1.5TR SOA=1.5TR
Stimulus (asynchronous) SOA=6s
Sampling rate=2s
Timing issues: SamplingTiming issues: SamplingTiming issues: SamplingTiming issues: Sampling
Scans TR=4s
• Typical TR for 48 slice EPI at 3mm Typical TR for 48 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
• Sampling at [0,4,8,1Sampling at [0,4,8,122…] post- …] post- stimulus may miss peak signalstimulus may miss peak signal
• Higher effective sampling by: Higher effective sampling by:
1. Asynchrony1. Asynchronye.g.,e.g., SOA=1.5TR SOA=1.5TR 2. Random Jitter 2. Random Jitter
e,g., e,g., SOA=(2±0.5)TRSOA=(2±0.5)TR
• Typical TR for 48 slice EPI at 3mm Typical TR for 48 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
• Sampling at [0,4,8,1Sampling at [0,4,8,122…] post- …] post- stimulus may miss peak signalstimulus may miss peak signal
• Higher effective sampling by: Higher effective sampling by:
1. Asynchrony1. Asynchronye.g.,e.g., SOA=1.5TR SOA=1.5TR 2. Random Jitter 2. Random Jitter
e,g., e,g., SOA=(2±0.5)TRSOA=(2±0.5)TR
Stimulus (random jitter)
Sampling rate=2s
Timing issues: SamplingTiming issues: SamplingTiming issues: SamplingTiming issues: Sampling
Scans TR=4s
• Typical TR for 48 slice EPI at 3mm Typical TR for 48 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
• Sampling at [0,4,8,1Sampling at [0,4,8,122…] post- …] post- stimulus may miss peak signalstimulus may miss peak signal
• Higher effective sampling by: Higher effective sampling by:
1. Asynchrony1. Asynchronye.g.,e.g., SOA=1.5TR SOA=1.5TR 2. Random Jitter 2. Random Jitter
e,g., e,g., SOA=(2±0.5)TRSOA=(2±0.5)TR
• Better response characterisation Better response characterisation (Miezin et al, 2000)(Miezin et al, 2000)
• Typical TR for 48 slice EPI at 3mm Typical TR for 48 slice EPI at 3mm spacing is ~ 4sspacing is ~ 4s
• Sampling at [0,4,8,1Sampling at [0,4,8,122…] post- …] post- stimulus may miss peak signalstimulus may miss peak signal
• Higher effective sampling by: Higher effective sampling by:
1. Asynchrony1. Asynchronye.g.,e.g., SOA=1.5TR SOA=1.5TR 2. Random Jitter 2. Random Jitter
e,g., e,g., SOA=(2±0.5)TRSOA=(2±0.5)TR
• Better response characterisation Better response characterisation (Miezin et al, 2000)(Miezin et al, 2000)
Stimulus (random jitter)
Sampling rate=2s
Timing issues: SamplingTiming issues: SamplingTiming issues: SamplingTiming issues: Sampling
Scans TR=4s
x2 x3
T=16, TR=2s
Scan0 1
o
T0=9 oT0=16
Timing issues: Slice-TimingTiming issues: Slice-TimingTiming issues: Slice-TimingTiming issues: Slice-Timing
T1 = 0 s
T16 = 2 s
• ““Slice-timing Problem”:Slice-timing Problem”: Slices acquired at different times, yet model Slices acquired at different times, yet model
is the same for all slicesis the same for all slices different results (using canonical HRF) for different results (using canonical HRF) for
different reference slices different reference slices (slightly less problematic if middle slice is (slightly less problematic if middle slice is
selected as reference, and with short TRs)selected as reference, and with short TRs)
• Solutions:Solutions:
1. Temporal interpolation of data1. Temporal interpolation of data… but less good for longer TRs… but less good for longer TRs
2. 2. More general basis set (e.g., withMore general basis set (e.g., withtemporal derivatives)temporal derivatives)
… but inferences via F-test… but inferences via F-test
• ““Slice-timing Problem”:Slice-timing Problem”: Slices acquired at different times, yet model Slices acquired at different times, yet model
is the same for all slicesis the same for all slices different results (using canonical HRF) for different results (using canonical HRF) for
different reference slices different reference slices (slightly less problematic if middle slice is (slightly less problematic if middle slice is
selected as reference, and with short TRs)selected as reference, and with short TRs)
• Solutions:Solutions:
1. Temporal interpolation of data1. Temporal interpolation of data… but less good for longer TRs… but less good for longer TRs
2. 2. More general basis set (e.g., withMore general basis set (e.g., withtemporal derivatives)temporal derivatives)
… but inferences via F-test… but inferences via F-test
Timing issues: Slice-timingTiming issues: Slice-timingTiming issues: Slice-timingTiming issues: Slice-timing
Bottom SliceTop Slice
SPM{t} SPM{t}
TR=3s
Interpolated
SPM{t}
Derivative
SPM{F}
OverviewOverviewOverviewOverview
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)advantages of efMRI2. (Dis)advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. BOLD impulse response4. BOLD impulse response
5. Temporal Basis Functions5. Temporal Basis Functions
6. Timing Issues6. Timing Issues
7. Design Optimisation – “Efficiency”7. Design Optimisation – “Efficiency”
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)advantages of efMRI2. (Dis)advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. BOLD impulse response4. BOLD impulse response
5. Temporal Basis Functions5. Temporal Basis Functions
6. Timing Issues6. Timing Issues
7. Design Optimisation – “Efficiency”7. Design Optimisation – “Efficiency”
• HRF can be viewed as a filter HRF can be viewed as a filter (Josephs & Henson, 1999)(Josephs & Henson, 1999)
• We want to maximise the signal We want to maximise the signal passed by this filterpassed by this filter
• Dominant frequency of canonical Dominant frequency of canonical HRF is ~0.04 HzHRF is ~0.04 Hz
The most efficient design is a The most efficient design is a sinusoidal modulation of neural sinusoidal modulation of neural activity with period ~24sactivity 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 HRF can be viewed as a filter (Josephs & Henson, 1999)(Josephs & Henson, 1999)
• We want to maximise the signal We want to maximise the signal passed by this filterpassed by this filter
• Dominant frequency of canonical Dominant frequency of canonical HRF is ~0.04 HzHRF is ~0.04 Hz
The most efficient design is a The most efficient design is a sinusoidal modulation of neural sinusoidal modulation of neural activity with period ~24sactivity with period ~24s
• (e.g., boxcar with 12s on/ 12s off)(e.g., boxcar with 12s on/ 12s off)
Design EfficiencyDesign EfficiencyDesign EfficiencyDesign Efficiency
=
=
A very “efficient” design!
Stimulus (“Neural”) HRF Predicted Data
Sinusoidal modulation, f = 1/33sSinusoidal modulation, f = 1/33s
=
=
Blocked-epoch (with small SOA) quite “efficient”
HRF Predicted DataStimulus (“Neural”)
Blocked, epoch = 20sBlocked, epoch = 20sBlocked, epoch = 20sBlocked, epoch = 20s
=
“Effective HRF” (after highpass filtering)(Josephs & Henson, 1999)
Very ineffective: Don’t have long (>60s) blocks!
=
Stimulus (“Neural”) HRF Predicted Data
Blocked (80s), SOAmin=4s, highpass filter = 1/120s
Blocked (80s), SOAmin=4s, highpass filter = 1/120s
=
=
Randomised design spreads power over frequencies
Stimulus (“Neural”) HRF Predicted Data
Randomised, SOAmin=4s, highpass filter = 1/120sRandomised, SOAmin=4s, highpass filter = 1/120s
• T-statistic for a given contrast: T-statistic for a given contrast: T = T = cTb / var(cTb)
• For maximum T, we want minimum standard error of For maximum T, we want minimum standard error of contrast estimates ( contrast estimates (var(cTb)) maximum precision maximum precision
• Var(cTb) = sqrt(2cT(XTX)-1c) (i.i.d)
• If we assume that noise variance (If we assume that noise variance (2) is unaffected by changes in is unaffected by changes in X, t X, then our precision for given parameters is proportional to the hen our precision for given parameters is proportional to the design efficiency: design efficiency: e(c,X) = e(c,X) = { { ccT T ((XXTTXX))-1 -1 cc } }-1-1
We can We can influence influence ee (a priori) by the spacing and sequencing of (a priori) by the spacing and sequencing of epochs/events in our design matrix epochs/events in our design matrix
e e is specific for a given contrast!is specific for a given contrast!
• T-statistic for a given contrast: T-statistic for a given contrast: T = T = cTb / var(cTb)
• For maximum T, we want minimum standard error of For maximum T, we want minimum standard error of contrast estimates ( contrast estimates (var(cTb)) maximum precision maximum precision
• Var(cTb) = sqrt(2cT(XTX)-1c) (i.i.d)
• If we assume that noise variance (If we assume that noise variance (2) is unaffected by changes in is unaffected by changes in X, t X, then our precision for given parameters is proportional to the hen our precision for given parameters is proportional to the design efficiency: design efficiency: e(c,X) = e(c,X) = { { ccT T ((XXTTXX))-1 -1 cc } }-1-1
We can We can influence influence ee (a priori) by the spacing and sequencing of (a priori) by the spacing and sequencing of epochs/events in our design matrix epochs/events in our design matrix
e e is specific for a given contrast!is specific for a given contrast!
Design efficiencyDesign efficiency
• Design parametrised by:Design parametrised by:
SOASOAminmin Minimum SOA Minimum SOA
p(t)p(t) Probability of event Probability of event
at each at each SOASOAminmin
• Design parametrised by:Design parametrised by:
SOASOAminmin Minimum SOA Minimum SOA
p(t)p(t) Probability of event Probability of event
at each at each SOASOAminmin
Design efficiency: Trial spacingDesign efficiency: Trial spacing
• Design parametrised by:Design parametrised by:
SOASOAminmin Minimum SOA Minimum SOA
p(t)p(t) Probability of event Probability of event
at each at each SOASOAminmin
• DeterministicDeterministicp(t)=1 iff t=nSOAminp(t)=1 iff t=nSOAmin
• Design parametrised by:Design parametrised by:
SOASOAminmin Minimum SOA Minimum SOA
p(t)p(t) Probability of event Probability of event
at each at each SOASOAminmin
• DeterministicDeterministicp(t)=1 iff t=nSOAminp(t)=1 iff t=nSOAmin
Design efficiency: Trial spacingDesign efficiency: Trial spacing
• Design parametrised by:Design parametrised by:
SOASOAminmin Minimum SOA Minimum SOA
p(t)p(t) Probability of event Probability of event
at each at each SOASOAminmin
• DeterministicDeterministicp(t)=1 iff t=nSOAminp(t)=1 iff t=nSOAmin
• Stationary stochastic Stationary stochastic p(t)=constant<1p(t)=constant<1
• Design parametrised by:Design parametrised by:
SOASOAminmin Minimum SOA Minimum SOA
p(t)p(t) Probability of event Probability of event
at each at each SOASOAminmin
• DeterministicDeterministicp(t)=1 iff t=nSOAminp(t)=1 iff t=nSOAmin
• Stationary stochastic Stationary stochastic p(t)=constant<1p(t)=constant<1
Design efficiency: Trial spacingDesign efficiency: Trial spacing
• Design parametrised by:Design parametrised by:
SOASOAminmin Minimum SOA Minimum SOA
p(t)p(t) Probability of event Probability of event
at each at each SOASOAminmin
• DeterministicDeterministicp(t)=1 iff t=nSOAminp(t)=1 iff t=nSOAmin
• Stationary stochastic Stationary stochastic p(t)=constantp(t)=constant
• Dynamic stochasticDynamic stochasticp(t) varies (e.g., p(t) varies (e.g.,
blocked)blocked)
• Design parametrised by:Design parametrised by:
SOASOAminmin Minimum SOA Minimum SOA
p(t)p(t) Probability of event Probability of event
at each at each SOASOAminmin
• DeterministicDeterministicp(t)=1 iff t=nSOAminp(t)=1 iff t=nSOAmin
• Stationary stochastic Stationary stochastic p(t)=constantp(t)=constant
• Dynamic stochasticDynamic stochasticp(t) varies (e.g., p(t) varies (e.g.,
blocked)blocked)
Blocked designs most efficient! (with small SOAmin)
Design efficiency: Trial spacingDesign efficiency: Trial spacing
• However, block designs are often However, block designs are often not advisable due to interpretative not advisable due to interpretative difficulties (see before)difficulties (see before)
• Event trains may then be Event trains may then be constructed by modulating the constructed by modulating the event probabilities in a dynamic event probabilities in a dynamic stochastic fashionstochastic fashion
• This can result in intermediate This can result in intermediate levels of efficiencylevels of efficiency
• However, block designs are often However, block designs are often not advisable due to interpretative not advisable due to interpretative difficulties (see before)difficulties (see before)
• Event trains may then be Event trains may then be constructed by modulating the constructed by modulating the event probabilities in a dynamic event probabilities in a dynamic stochastic fashionstochastic fashion
• This can result in intermediate This can result in intermediate levels of efficiencylevels of efficiency
Design efficiency: Trial spacingDesign efficiency: Trial spacing
3 sessions with 128 scansFaces, scrambled facesSOA always 2.97 sCycle length 24 s
e
4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering
• Design parametrised by:Design parametrised by:SOASOAminmin Minimum SOA Minimum SOA
ppii((hh)) Probability of event-type Probability of event-type i i
given history given history hh of last of last mm events events
• With With nn event-types event-types ppii((hh)) is a is a n x nn x n
Transition MatrixTransition Matrix
• Example: Randomised ABExample: Randomised AB
AA BBAA 0.50.5
0.5 0.5
BB 0.50.5 0.50.5
=> => ABBBABAABABAAA...ABBBABAABABAAA...
• Design parametrised by:Design parametrised by:SOASOAminmin Minimum SOA Minimum SOA
ppii((hh)) Probability of event-type Probability of event-type i i
given history given history hh of last of last mm events events
• With With nn event-types event-types ppii((hh)) is a is a n x nn x n
Transition MatrixTransition Matrix
• Example: Randomised ABExample: Randomised AB
AA BBAA 0.50.5
0.5 0.5
BB 0.50.5 0.50.5
=> => ABBBABAABABAAA...ABBBABAABABAAA...
Differential Effect (A-B)
Common Effect (A+B)
Design efficiency: Trial sequencingDesign efficiency: Trial sequencing
4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering
• Example: Alternating ABExample: Alternating AB AA BB
AA 001 1 BB 11 00
=> => ABABABABABAB...ABABABABABAB...
• Example: Alternating ABExample: Alternating AB AA BB
AA 001 1 BB 11 00
=> => ABABABABABAB...ABABABABABAB... Alternating (A-B)
Permuted (A-B)
• Example: Permuted ABExample: Permuted AB
AA BB
AAAA 0 0 11
ABAB 0.50.5 0.5 0.5
BABA 0.50.5 0.50.5
BBBB 1 1 00
=> => ABBAABABABBA...ABBAABABABBA...
Design efficiency: Trial sequencingDesign efficiency: Trial sequencing
4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering
• Example: Null eventsExample: Null events
AA BB
AA 0.330.330.330.33
BB 0.330.33 0.330.33
=> => AB-BAA--B---ABB...AB-BAA--B---ABB...
• Efficient for differential Efficient for differential andand main main effects at short SOAeffects at short SOA
• Equivalent to stochastic SOA (Null Equivalent to stochastic SOA (Null Event like third unmodelled event-Event like third unmodelled event-type) type)
• Example: Null eventsExample: Null events
AA BB
AA 0.330.330.330.33
BB 0.330.33 0.330.33
=> => AB-BAA--B---ABB...AB-BAA--B---ABB...
• Efficient for differential Efficient for differential andand main main effects at short SOAeffects at short SOA
• Equivalent to stochastic SOA (Null Equivalent to stochastic SOA (Null Event like third unmodelled event-Event like third unmodelled event-type) type)
Null Events (A+B)
Null Events (A-B)
Design efficiency: Trial sequencingDesign efficiency: Trial sequencing
• Optimal design for one contrast may not be optimal for another Optimal design for one contrast may not be optimal for another
• Blocked designs generally most efficient (with short SOAs, given optimal Blocked designs generally most efficient (with short SOAs, given optimal block length is not exceeded)block length is not exceeded)
• However, However, psychological efficiencypsychological efficiency often dictates intermixed designs, and often dictates intermixed designs, and often also sets limits on SOAsoften also sets limits on SOAs
• With randomised designs, optimal SOA for differential effect (A-B) is With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (>2 seconds, and assuming no saturation), whereas optimal minimal SOA (>2 seconds, and assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20sSOA for main effect (A+B) is 16-20s
• Inclusion of null events improves efficiency for main effect at short SOAs (at Inclusion of null events improves efficiency for main effect at short SOAs (at cost of efficiency for differential effects)cost of efficiency for differential effects)
• If order constrained, intermediate SOAs (5-20s) can be optimal If order constrained, intermediate SOAs (5-20s) can be optimal
• If SOA constrained, pseudorandomised designs can be optimal (but may If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity)introduce context-sensitivity)
• Optimal design for one contrast may not be optimal for another Optimal design for one contrast may not be optimal for another
• Blocked designs generally most efficient (with short SOAs, given optimal Blocked designs generally most efficient (with short SOAs, given optimal block length is not exceeded)block length is not exceeded)
• However, However, psychological efficiencypsychological efficiency often dictates intermixed designs, and often dictates intermixed designs, and often also sets limits on SOAsoften also sets limits on SOAs
• With randomised designs, optimal SOA for differential effect (A-B) is With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (>2 seconds, and assuming no saturation), whereas optimal minimal SOA (>2 seconds, and assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20sSOA for main effect (A+B) is 16-20s
• Inclusion of null events improves efficiency for main effect at short SOAs (at Inclusion of null events improves efficiency for main effect at short SOAs (at cost of efficiency for differential effects)cost of efficiency for differential effects)
• If order constrained, intermediate SOAs (5-20s) can be optimal If order constrained, intermediate SOAs (5-20s) can be optimal
• If SOA constrained, pseudorandomised designs can be optimal (but may If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity)introduce context-sensitivity)
Design efficiency: ConclusionsDesign efficiency: Conclusions
End: OverviewEnd: OverviewEnd: OverviewEnd: Overview
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)Advantages of efMRI2. (Dis)Advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. BOLD impulse response4. BOLD impulse response
5. Temporal Basis Functions5. Temporal Basis Functions
6. Timing Issues6. Timing Issues
7. Design Optimisation 7. Design Optimisation – “Efficiency”– “Efficiency”
1. Block/epoch vs. event-related fMRI1. Block/epoch vs. event-related fMRI
2. (Dis)Advantages of efMRI2. (Dis)Advantages of efMRI
3. GLM: Convolution3. GLM: Convolution
4. BOLD impulse response4. BOLD impulse response
5. Temporal Basis Functions5. Temporal Basis Functions
6. Timing Issues6. Timing Issues
7. Design Optimisation 7. Design Optimisation – “Efficiency”– “Efficiency”
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