FILFIL
Event-related Event-related fMRIfMRI
Rik HensonRik Henson
With thanks to: Karl Friston, Oliver Josephs
Event-related Event-related fMRIfMRI
Rik HensonRik Henson
With thanks to: Karl Friston, Oliver Josephs
FILFIL
OverviewOverviewOverviewOverview
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
FILFIL
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 (Wagner et al 1998)e.g, according to subsequent memory (Wagner et al 1998)
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 blocked4. Some trials cannot be blockede.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 (Wagner et al 1998)e.g, according to subsequent memory (Wagner et al 1998)
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 blocked4. Some trials cannot be blockede.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 ofAdvantages of Event-related fMRIEvent-related fMRIAdvantages ofAdvantages of Event-related fMRIEvent-related fMRI
FILFIL
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 may be better blocked 2. Some psychological processes may be better blocked (eg task-switching, attentional instructions)(eg task-switching, attentional instructions)
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 may be better blocked 2. Some psychological processes may be better blocked (eg task-switching, attentional instructions)(eg task-switching, attentional instructions)
(Disa(Disadvantages of dvantages of Randomised Designs)Randomised Designs)(Disa(Disadvantages of dvantages of Randomised Designs)Randomised Designs)
FILFIL
OverviewOverviewOverviewOverview
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
FILFIL
• 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 differences across:but 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 differences across:but differences across: other regions (Schacter et al 1997) other regions (Schacter et al 1997)
individuals (Aguirre et al, 1998)individuals (Aguirre et al, 1998)
BOLD Impulse ResponseBOLD Impulse ResponseBOLD Impulse ResponseBOLD Impulse Response
BriefStimulus
Undershoot
InitialUndershoot
Peak
FILFIL
• 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, if the BOLD response is However, if the BOLD response is explicitly modelled, overlap between explicitly modelled, overlap between successive responses at short SOAs successive responses at short SOAs can be accommodatedcan be accommodated……
• … … particularly if responses are particularly if responses are assumed to superpose linearlyassumed to superpose linearly
• Short SOAs are more sensitive…Short SOAs are more sensitive…
• 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, if the BOLD response is However, if the BOLD response is explicitly modelled, overlap between explicitly modelled, overlap between successive responses at short SOAs successive responses at short SOAs can be accommodatedcan be accommodated……
• … … particularly if responses are particularly if responses are assumed to superpose linearlyassumed to superpose linearly
• Short SOAs are more sensitive…Short SOAs are more sensitive…
BOLD Impulse ResponseBOLD Impulse ResponseBOLD Impulse ResponseBOLD Impulse Response
BriefStimulus
Undershoot
InitialUndershoot
Peak
FILFIL
OverviewOverviewOverviewOverview
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
FILFIL
General General Linear Linear (Convolution) (Convolution) ModelModelGeneral General Linear Linear (Convolution) (Convolution) ModelModel
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
FILFIL
General Linear Model (in SPM)General Linear Model (in SPM)General Linear Model (in SPM)General Linear Model (in SPM)
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)
FILFIL
x2 x3
A word about down-samplingA word about down-samplingA word about down-samplingA word about down-sampling
T=16, TR=2s
Scan0 1
o
T0=9 oT0=16
FILFIL
OverviewOverviewOverviewOverview
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
FILFIL
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
FILFIL
Temporal Basis FunctionsTemporal Basis FunctionsTemporal Basis FunctionsTemporal Basis Functions
• Finite Impulse ResponseFinite Impulse ResponseMini “timebins” (selective Mini “timebins” (selective
averaging)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 Mini “timebins” (selective
averaging)averaging)AAny shapeny shape (up to bin-width (up to bin-width))Inference via F-testInference via F-test
FILFIL
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
• Gamma FunctionsGamma FunctionsBounded, asymmetrical (like Bounded, asymmetrical (like
BOLD)BOLD)Set of different lagsSet of different lagsInference 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
• Gamma FunctionsGamma FunctionsBounded, asymmetrical (like Bounded, asymmetrical (like
BOLD)BOLD)Set of different lagsSet of different lagsInference via F-testInference via F-test
FILFIL
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
• 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 Variability captured by Taylor
expansion expansion “Magnitude” inferences via t-“Magnitude” inferences via t-testtest…?…?
• 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
• 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 Variability captured by Taylor
expansion expansion “Magnitude” inferences via t-“Magnitude” inferences via t-testtest…?…?
FILFIL
Temporal Basis FunctionsTemporal Basis FunctionsTemporal Basis FunctionsTemporal Basis Functions
FILFIL
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
FILFIL
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
FILFIL
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
FILFIL
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))
• F-tests allow for any “canonical-like” F-tests allow for any “canonical-like” responsesresponses
““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))
• F-tests allow for any “canonical-like” F-tests allow for any “canonical-like” responsesresponses
CanonicalTemporalDispersion
FILFIL
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))
• F-tests allow for any “canonical-like” F-tests allow for any “canonical-like” responsesresponses
• T-tests on canonical HRF alone (at 1T-tests on canonical HRF alone (at 1st st level) level) can be improved by derivatives reducing can be improved by derivatives reducing residual error, and can be interpreted as residual error, and can be interpreted as “amplitude” differences, “amplitude” differences, assumingassuming canonical canonical HRFHRF is good fit is good 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))
• F-tests allow for any “canonical-like” F-tests allow for any “canonical-like” responsesresponses
• T-tests on canonical HRF alone (at 1T-tests on canonical HRF alone (at 1st st level) level) can be improved by derivatives reducing can be improved by derivatives reducing residual error, and can be interpreted as residual error, and can be interpreted as “amplitude” differences, “amplitude” differences, assumingassuming canonical canonical HRFHRF is good fit is good fit……
CanonicalTemporalDispersion
FILFIL
(Other Approaches)(Other Approaches)(Other Approaches)(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
FILFIL
Temporal Basis Sets: Which One?Temporal Basis Sets: Which One?Temporal Basis Sets: Which One?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)…
FILFIL
OverviewOverviewOverviewOverview
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
FILFIL
Timing Issues : PracticalTiming Issues : PracticalTiming Issues : PracticalTiming Issues : Practical
• Typical TR for 48 slice EPI at Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing is ~ 4s
• Typical TR for 48 slice EPI at Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing is ~ 4s
Scans TR=4s
FILFIL
Timing Issues : PracticalTiming Issues : PracticalTiming Issues : PracticalTiming Issues : Practical
• Typical TR for 48 slice EPI at Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing 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 Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing 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
Scans
Stimulus (synchronous)
TR=4s
SOA=8s
Sampling rate=4s
FILFIL
Timing Issues : PracticalTiming Issues : PracticalTiming Issues : PracticalTiming Issues : Practical
• Typical TR for 48 slice EPI at Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing 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: 1. Higher effective sampling by: 1. AsynchronyAsynchrony eg eg SOA=1.5TRSOA=1.5TR
• Typical TR for 48 slice EPI at Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing 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: 1. Higher effective sampling by: 1. AsynchronyAsynchrony eg eg SOA=1.5TRSOA=1.5TR
Stimulus (asynchronous)
Scans TR=4s
SOA=6s
Sampling rate=2s
FILFIL
Timing Issues : PracticalTiming Issues : PracticalTiming Issues : PracticalTiming Issues : Practical
• Typical TR for 48 slice EPI at Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing 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. 1. AsynchronyAsynchrony eg eg SOA=1.5TRSOA=1.5TR 2. Random 2. Random Jitter Jitter eg eg SOA=(2±0.5)TRSOA=(2±0.5)TR
• Typical TR for 48 slice EPI at Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing 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. 1. AsynchronyAsynchrony eg eg SOA=1.5TRSOA=1.5TR 2. Random 2. Random Jitter Jitter eg eg SOA=(2±0.5)TRSOA=(2±0.5)TR
Stimulus (random jitter)
Scans TR=4s
Sampling rate=2s
FILFIL
Timing Issues : PracticalTiming Issues : PracticalTiming Issues : PracticalTiming Issues : Practical
• Typical TR for 48 slice EPI at Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing 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. 1. AsynchronyAsynchrony eg eg SOA=1.5TRSOA=1.5TR 2. Random 2. Random Jitter Jitter eg eg 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 Typical TR for 48 slice EPI at 3mm spacing is ~ 4s3mm spacing 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. 1. AsynchronyAsynchrony eg eg SOA=1.5TRSOA=1.5TR 2. Random 2. Random Jitter Jitter eg eg 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)
Scans TR=4s
Sampling rate=2s
FILFIL
Timing Issues : PracticalTiming Issues : PracticalTiming Issues : PracticalTiming Issues : Practical
• ……but “Slice-timing Problem”but “Slice-timing Problem”(Henson et al, 1999)(Henson et al, 1999)
Slices acquired at different times, Slices acquired at different times, yet model is the same for all slicesyet model is the same for all slices
• ……but “Slice-timing Problem”but “Slice-timing Problem”(Henson et al, 1999)(Henson et al, 1999)
Slices acquired at different times, Slices acquired at different times, yet model is the same for all slicesyet model is the same for all slices
FILFIL
Timing Issues : PracticalTiming Issues : PracticalTiming Issues : PracticalTiming Issues : Practical
• ……but “Slice-timing Problem”but “Slice-timing Problem”(Henson et al, 1999)(Henson et al, 1999)
Slices acquired at different times, Slices acquired at different times, yet model is the same for all slicesyet model is the same for all slices
=> different results (using canonical => different results (using canonical HRF) for different reference slicesHRF) for different reference slices
• ……but “Slice-timing Problem”but “Slice-timing Problem”(Henson et al, 1999)(Henson et al, 1999)
Slices acquired at different times, Slices acquired at different times, yet model is the same for all slicesyet model is the same for all slices
=> different results (using canonical => different results (using canonical HRF) for different reference slicesHRF) for different reference slices
Bottom SliceTop Slice
SPM{t} SPM{t}
TR=3s
FILFIL
Timing Issues : PracticalTiming Issues : PracticalTiming Issues : PracticalTiming Issues : Practical
• ……but “Slice-timing Problem”but “Slice-timing Problem”(Henson et al, 1999)(Henson et al, 1999)
Slices acquired at different times, Slices acquired at different times, yet model is the same for all slicesyet model is the same for all slices
=> different results (using canonical => different results (using canonical HRF) for different reference slicesHRF) for different reference slices
• Solutions:Solutions:
1. Temporal interpolation of data1. Temporal interpolation of data… but less good for longer … but less good for longer
TRsTRs
• ……but “Slice-timing Problem”but “Slice-timing Problem”(Henson et al, 1999)(Henson et al, 1999)
Slices acquired at different times, Slices acquired at different times, yet model is the same for all slicesyet model is the same for all slices
=> different results (using canonical => different results (using canonical HRF) for different reference slicesHRF) for different reference slices
• Solutions:Solutions:
1. Temporal interpolation of data1. Temporal interpolation of data… but less good for longer … but less good for longer
TRsTRs
Interpolated
SPM{t}
Bottom SliceTop Slice
SPM{t} SPM{t}
TR=3s
FILFIL
Timing Issues : PracticalTiming Issues : PracticalTiming Issues : PracticalTiming Issues : Practical
• ……but “Slice-timing Problem”but “Slice-timing Problem”(Henson et al, 1999)(Henson et al, 1999)
Slices acquired at different times, Slices acquired at different times, yet model is the same for all slicesyet model is the same for all slices=> different results (using canonical => different results (using canonical HRF) for different reference slicesHRF) for different reference slices
• Solutions:Solutions:
1. Temporal interpolation of data1. Temporal interpolation of data… but less good for longer … but less good for longer
TRsTRs2. 2. More general basis set (e.g., with More general basis set (e.g., with
temporal derivatives)temporal derivatives)… but inferences via F-test… but inferences via F-test
• ……but “Slice-timing Problem”but “Slice-timing Problem”(Henson et al, 1999)(Henson et al, 1999)
Slices acquired at different times, Slices acquired at different times, yet model is the same for all slicesyet model is the same for all slices=> different results (using canonical => different results (using canonical HRF) for different reference slicesHRF) for different reference slices
• Solutions:Solutions:
1. Temporal interpolation of data1. Temporal interpolation of data… but less good for longer … but less good for longer
TRsTRs2. 2. More general basis set (e.g., with More general basis set (e.g., with
temporal derivatives)temporal derivatives)… but inferences via F-test… but inferences via F-test
Derivative
SPM{F}
Interpolated
SPM{t}
Bottom SliceTop Slice
SPM{t} SPM{t}
TR=3s
FILFIL
OverviewOverviewOverviewOverview
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
FILFIL
=
Fixed SOA = 16s
Not particularly efficient…
Stimulus (“Neural”) HRF Predicted Data
FILFIL
=
Fixed SOA = 4s
Very Inefficient…
Stimulus (“Neural”) HRF Predicted Data
FILFIL
=
Randomised, SOAmin= 4s
More Efficient…
Stimulus (“Neural”) HRF Predicted Data
FILFIL
=
Blocked, SOAmin= 4s
Even more Efficient…
Stimulus (“Neural”) HRF Predicted Data
FILFIL
=
Blocked, epoch = 20s
=
Blocked-epoch (with small SOA) and Time-Freq equivalences
Stimulus (“Neural”) HRF Predicted Data
FILFIL
=
Sinusoidal modulation, f = 1/33s
=
The most efficient design of all!
Stimulus (“Neural”) HRF Predicted Data
FILFIL
=
“Effective HRF” (after highpass filtering)(Josephs & Henson, 1999)
Blocked (80s), SOAmin=4s, highpass filter = 1/120s
Don’t have long (>60s) blocks!
=
Stimulus (“Neural”) HRF Predicted Data
FILFIL
Randomised, SOAmin=4s, highpass filter = 1/120s
=
=
(Randomised design spreads power over frequencies)
Stimulus (“Neural”) HRF Predicted Data
FILFIL
Design EfficiencyDesign EfficiencyDesign EfficiencyDesign Efficiency
T = T = cT / var(cT)
Var(cT) = sqrt(2cT(XTX)-1c) (i.i.d)
• For max. T, want min. contrast For max. T, want min. contrast variability (Friston et al, 1999)variability (Friston et al, 1999)
• If assume that noise variance (If assume that noise variance (2) is is unaffected by changes in X…unaffected by changes in X…
• ……then want maximal efficiency, e:then want maximal efficiency, e:
e(c,X) = e(c,X) = { { ccT T ((XXTTXX))-1 -1 cc } }-1-1
• = maximal bandpassed signal energy = maximal bandpassed signal energy (Josephs & Henson, 1999)(Josephs & Henson, 1999)
T = T = cT / var(cT)
Var(cT) = sqrt(2cT(XTX)-1c) (i.i.d)
• For max. T, want min. contrast For max. T, want min. contrast variability (Friston et al, 1999)variability (Friston et al, 1999)
• If assume that noise variance (If assume that noise variance (2) is is unaffected by changes in X…unaffected by changes in X…
• ……then want maximal efficiency, e:then want maximal efficiency, e:
e(c,X) = e(c,X) = { { ccT T ((XXTTXX))-1 -1 cc } }-1-1
• = maximal bandpassed signal energy = maximal bandpassed signal energy (Josephs & Henson, 1999)(Josephs & Henson, 1999)
Events (A-B)
FILFIL
4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering
Efficiency - Multiple Event-typesEfficiency - Multiple Event-typesEfficiency - Multiple Event-typesEfficiency - Multiple Event-types
• 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
nnmm n 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
nnmm n 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)
FILFIL
4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering
Efficiency - Multiple Event-typesEfficiency - Multiple Event-typesEfficiency - Multiple Event-typesEfficiency - Multiple Event-types
• 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...
FILFIL
4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering
Efficiency - Multiple Event-typesEfficiency - Multiple Event-typesEfficiency - Multiple Event-typesEfficiency - Multiple Event-types
• 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 effects at short SOAmain effects at short SOA
• Equivalent to stochastic SOA Equivalent to stochastic SOA (Null Event like third (Null Event like third unmodelled event-type) unmodelled event-type)
• Selective averaging of data Selective averaging of data (Dale & Buckner 1997)(Dale & Buckner 1997)
• 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 effects at short SOAmain effects at short SOA
• Equivalent to stochastic SOA Equivalent to stochastic SOA (Null Event like third (Null Event like third unmodelled event-type) unmodelled event-type)
• Selective averaging of data Selective averaging of data (Dale & Buckner 1997)(Dale & Buckner 1997)
Null Events (A+B)
Null Events (A-B)
FILFIL
Efficiency - ConclusionsEfficiency - ConclusionsEfficiency - ConclusionsEfficiency - Conclusions
• 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 Blocked designs generally most efficient with short SOAs (but earlier restrictions and problems of interpretation…)(but earlier restrictions and problems of interpretation…)
• With randomised designs, optimal SOA for differential effect With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20soptimal SOA for main effect (A+B) is 16-20s
• Inclusion of null events improves efficiency for main effect at Inclusion of null events improves efficiency for main effect at short SOAs (at cost of efficiency for differential effects)short SOAs (at 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 If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity)optimal (but may 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 Blocked designs generally most efficient with short SOAs (but earlier restrictions and problems of interpretation…)(but earlier restrictions and problems of interpretation…)
• With randomised designs, optimal SOA for differential effect With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20soptimal SOA for main effect (A+B) is 16-20s
• Inclusion of null events improves efficiency for main effect at Inclusion of null events improves efficiency for main effect at short SOAs (at cost of efficiency for differential effects)short SOAs (at 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 If SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity)optimal (but may introduce context-sensitivity)
FILFIL
OverviewOverviewOverviewOverview
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
FILFIL
Volterra series Volterra series - a general nonlinear input-output model- a general nonlinear input-output model
y(t) = y(t) = 11[u(t)] + [u(t)] + 22[u(t)] + .... + [u(t)] + .... + nn[u(t)] + ....[u(t)] + ....
nn[u(t)] = [u(t)] = .... .... h hnn(t(t11,..., t,..., tnn)u(t - t)u(t - t11) .... u(t - t) .... u(t - tnn)dt)dt1 1 .... dt.... dtnn
Volterra series Volterra series - a general nonlinear input-output model- a general nonlinear input-output model
y(t) = y(t) = 11[u(t)] + [u(t)] + 22[u(t)] + .... + [u(t)] + .... + nn[u(t)] + ....[u(t)] + ....
nn[u(t)] = [u(t)] = .... .... h hnn(t(t11,..., t,..., tnn)u(t - t)u(t - t11) .... u(t - t) .... u(t - tnn)dt)dt1 1 .... dt.... dtnn
Nonlinear ModelNonlinear ModelNonlinear ModelNonlinear Model
[u(t)][u(t)] response y(t)response y(t)input u(t)input u(t)
Stimulus functionStimulus function
kernels (h)kernels (h) estimateestimate
FILFIL
Nonlinear ModelNonlinear ModelNonlinear ModelNonlinear Model
Friston et al (1997)Friston et al (1997)
Friston et al (1997)Friston et al (1997)
SPM{F} testing HSPM{F} testing H00: kernel coefficients, h = 0: kernel coefficients, h = 0
kernel coefficients - hkernel coefficients - h
SPM{F}SPM{F}p < 0.001p < 0.001
FILFIL
Nonlinear ModelNonlinear ModelNonlinear ModelNonlinear Model
Friston et al (1997)Friston et al (1997)
Friston et al (1997)Friston et al (1997)
SPM{F} testing HSPM{F} testing H00: kernel coefficients, h = 0: kernel coefficients, h = 0
Significant nonlinearities at SOAs 0-10s:Significant nonlinearities at SOAs 0-10s: (e.g., underadditivity from 0-5s)(e.g., underadditivity from 0-5s)
kernel coefficients - hkernel coefficients - h
SPM{F}SPM{F}p < 0.001p < 0.001
FILFIL
Nonlinear EffectsNonlinear EffectsNonlinear EffectsNonlinear Effects
Underadditivity at short SOAsUnderadditivity at short SOAsLinearPrediction
VolterraPrediction
FILFIL
Nonlinear EffectsNonlinear EffectsNonlinear EffectsNonlinear Effects
Underadditivity at short SOAsUnderadditivity at short SOAsLinearPrediction
VolterraPrediction
FILFIL
Nonlinear EffectsNonlinear EffectsNonlinear EffectsNonlinear Effects
Underadditivity at short SOAsUnderadditivity at short SOAsLinearPrediction
VolterraPrediction
Implicationsfor Efficiency
FILFIL
OverviewOverviewOverviewOverview
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
1. Advantages of efMRI1. Advantages of efMRI
2. BOLD impulse response2. BOLD impulse response
3. General Linear Model3. General Linear Model
4. Temporal Basis Functions4. Temporal Basis Functions
5. Timing Issues5. Timing Issues
6. Design Optimisation6. Design Optimisation
7. Nonlinear Models7. Nonlinear Models
8. Example Applications8. Example Applications
FILFIL
Example 1: Intermixed Trials (Henson et al 2000)Example 1: Intermixed Trials (Henson et al 2000)Example 1: Intermixed Trials (Henson et al 2000)Example 1: Intermixed Trials (Henson et al 2000)
• Short SOA, fully randomised, Short SOA, fully randomised, with 1/3 null eventswith 1/3 null events
• Faces presented for 0.5s against Faces presented for 0.5s against chequerboard baseline, chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4sSOA=(2 ± 0.5)s, TR=1.4s
• Factorial event-types:Factorial event-types: 1. 1. Famous/Nonfamous (F/N)Famous/Nonfamous (F/N) 2. 2. 1st/2nd Presentation (1/2)1st/2nd Presentation (1/2)
• Short SOA, fully randomised, Short SOA, fully randomised, with 1/3 null eventswith 1/3 null events
• Faces presented for 0.5s against Faces presented for 0.5s against chequerboard baseline, chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4sSOA=(2 ± 0.5)s, TR=1.4s
• Factorial event-types:Factorial event-types: 1. 1. Famous/Nonfamous (F/N)Famous/Nonfamous (F/N) 2. 2. 1st/2nd Presentation (1/2)1st/2nd Presentation (1/2)
FILFIL
Lag=3Lag=3
Famous Nonfamous (Target)
. . .
FILFIL
Example 1: Intermixed Trials (Henson et al 2000)Example 1: Intermixed Trials (Henson et al 2000)Example 1: Intermixed Trials (Henson et al 2000)Example 1: Intermixed Trials (Henson et al 2000)
• Short SOA, fully randomised, Short SOA, fully randomised, with 1/3 null eventswith 1/3 null events
• Faces presented for 0.5s against Faces presented for 0.5s against chequerboard baseline, chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4sSOA=(2 ± 0.5)s, TR=1.4s
• Factorial event-types:Factorial event-types: 1. 1. Famous/Nonfamous (F/N)Famous/Nonfamous (F/N) 2. 2. 1st/2nd Presentation (1/2)1st/2nd Presentation (1/2)
• Interaction (F1-F2)-(N1-N2) Interaction (F1-F2)-(N1-N2) masked by main effect (F+N)masked by main effect (F+N)
• Right fusiform interaction of Right fusiform interaction of repetition priming and familiarityrepetition priming and familiarity
• Short SOA, fully randomised, Short SOA, fully randomised, with 1/3 null eventswith 1/3 null events
• Faces presented for 0.5s against Faces presented for 0.5s against chequerboard baseline, chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4sSOA=(2 ± 0.5)s, TR=1.4s
• Factorial event-types:Factorial event-types: 1. 1. Famous/Nonfamous (F/N)Famous/Nonfamous (F/N) 2. 2. 1st/2nd Presentation (1/2)1st/2nd Presentation (1/2)
• Interaction (F1-F2)-(N1-N2) Interaction (F1-F2)-(N1-N2) masked by main effect (F+N)masked by main effect (F+N)
• Right fusiform interaction of Right fusiform interaction of repetition priming and familiarityrepetition priming and familiarity
FILFIL
Example 2: Post hoc classification (Henson et al 1999)Example 2: Post hoc classification (Henson et al 1999)Example 2: Post hoc classification (Henson et al 1999)Example 2: Post hoc classification (Henson et al 1999)
• Subjects indicate whether Subjects indicate whether studied (Old) words: studied (Old) words:
i) evoke recollection of i) evoke recollection of prior occurrence (R) prior occurrence (R)
ii) feeling of familiarity ii) feeling of familiarity without recollection (K)without recollection (K)
iii) no memory (N)iii) no memory (N)
• Random Effects analysis Random Effects analysis on canonical parameter on canonical parameter estimate for event-typesestimate for event-types
• Fixed SOA of 8s => sensitive to Fixed SOA of 8s => sensitive to differential but not main effect differential but not main effect (de/activations arbitrary)(de/activations arbitrary)
• Subjects indicate whether Subjects indicate whether studied (Old) words: studied (Old) words:
i) evoke recollection of i) evoke recollection of prior occurrence (R) prior occurrence (R)
ii) feeling of familiarity ii) feeling of familiarity without recollection (K)without recollection (K)
iii) no memory (N)iii) no memory (N)
• Random Effects analysis Random Effects analysis on canonical parameter on canonical parameter estimate for event-typesestimate for event-types
• Fixed SOA of 8s => sensitive to Fixed SOA of 8s => sensitive to differential but not main effect differential but not main effect (de/activations arbitrary)(de/activations arbitrary)
SPM{t} SPM{t} R-K
SPM{t} SPM{t} K-R
FILFIL
Example 3: Subject-defined events (Portas et al 1999)Example 3: Subject-defined events (Portas et al 1999)Example 3: Subject-defined events (Portas et al 1999)Example 3: Subject-defined events (Portas et al 1999)
• Subjects respond when Subjects respond when “pop-out” of 3D percept “pop-out” of 3D percept from 2D stereogramfrom 2D stereogram
• Subjects respond when Subjects respond when “pop-out” of 3D percept “pop-out” of 3D percept from 2D stereogramfrom 2D stereogram
FILFIL
FILFIL
Example 3: Subject-defined events (Portas et al 1999)Example 3: Subject-defined events (Portas et al 1999)Example 3: Subject-defined events (Portas et al 1999)Example 3: Subject-defined events (Portas et al 1999)
• Subjects respond when Subjects respond when “pop-out” of 3D percept “pop-out” of 3D percept from 2D stereogramfrom 2D stereogram
• Popout response also Popout response also produces toneproduces tone
• Control event is response to Control event is response to tone during 3D percepttone during 3D percept
• Subjects respond when Subjects respond when “pop-out” of 3D percept “pop-out” of 3D percept from 2D stereogramfrom 2D stereogram
• Popout response also Popout response also produces toneproduces tone
• Control event is response to Control event is response to tone during 3D percepttone during 3D percept
Temporo-occipital differential activation
Pop-out
Control
FILFIL
Example 4: Oddball Paradigm (Strange et al, 2000)Example 4: Oddball Paradigm (Strange et al, 2000)Example 4: Oddball Paradigm (Strange et al, 2000)Example 4: Oddball Paradigm (Strange et al, 2000)
• 16 same-category words 16 same-category words every 3 secs, plus … every 3 secs, plus …
• … … 1 perceptual, 1 semantic, 1 perceptual, 1 semantic, and 1 emotional oddballand 1 emotional oddball
• 16 same-category words 16 same-category words every 3 secs, plus … every 3 secs, plus …
• … … 1 perceptual, 1 semantic, 1 perceptual, 1 semantic, and 1 emotional oddballand 1 emotional oddball
FILFIL
WHEAT
BARLEY
OATS
HOPS
RYE
…
~3s
CORN
Perceptual Oddball
PLUG
Semantic Oddball
RAPE
Emotional Oddball
FILFIL
Example 4: Oddball Paradigm (Strange et al, 2000)Example 4: Oddball Paradigm (Strange et al, 2000)Example 4: Oddball Paradigm (Strange et al, 2000)Example 4: Oddball Paradigm (Strange et al, 2000)
• 16 same-category words 16 same-category words every 3 secs, plus … every 3 secs, plus …
• … … 1 perceptual, 1 semantic, 1 perceptual, 1 semantic, and 1 emotional oddballand 1 emotional oddball
• 16 same-category words 16 same-category words every 3 secs, plus … every 3 secs, plus …
• … … 1 perceptual, 1 semantic, 1 perceptual, 1 semantic, and 1 emotional oddballand 1 emotional oddball
Right Prefrontal Cortex
Par
amet
er E
stim
ates
Controls
Oddballs
•3 nonoddballs randomly 3 nonoddballs randomly matched as controlsmatched as controls
•Conjunction of oddball vs. Conjunction of oddball vs. control contrast images: control contrast images: generic deviance detectorgeneric deviance detector
FILFIL
• Epochs of attention to: Epochs of attention to: 1) motion, or 2) 1) motion, or 2)
colourcolour
• Events are target stimuli Events are target stimuli differing in motion or colourdiffering in motion or colour
• Randomised, long SOAs to Randomised, long SOAs to decorrelate epoch and event-decorrelate epoch and event-related covariatesrelated covariates
• Interaction between epoch Interaction between epoch (attention) and event (attention) and event (stimulus) in V4 and V5(stimulus) in V4 and V5
• Epochs of attention to: Epochs of attention to: 1) motion, or 2) 1) motion, or 2)
colourcolour
• Events are target stimuli Events are target stimuli differing in motion or colourdiffering in motion or colour
• Randomised, long SOAs to Randomised, long SOAs to decorrelate epoch and event-decorrelate epoch and event-related covariatesrelated covariates
• Interaction between epoch Interaction between epoch (attention) and event (attention) and event (stimulus) in V4 and V5(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
FILFIL
THE END
FILFIL
Randomised
O1 N1 O3O2 N2
Data
ModelO = Old WordsN = New WordsBlocked
O1 O2 O3 N1 N2 N3
FILFIL
(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)Confounds of blocking (Herron et al, 2004)Confounds of blocking (Herron et al, 2004)Confounds of blocking (Herron et al, 2004)
• PET studies of “memory retrieval” compared blocks (scans) with different PET studies of “memory retrieval” compared blocks (scans) with different ratios of old:new items…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 PET studies of “memory retrieval” compared blocks (scans) with different ratios of old:new items…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
FILFIL
R R RF F
R = Words Later Remembered
F = Words Later Forgotten
Event-Related ~4s
Data
Model
FILFIL
FILFIL
Time…
“Oddball”
FILFIL
N1 N2 N3
“Event” model
O1 O2 O3
Blocked Design
“Epoch” model
Data
Model
O1 O2 O3 N1 N2 N3
FILFIL
Epoch vsEpoch vs EventsEventsEpoch vsEpoch vs EventsEvents
Convolved with HRF
=>
Series of eventsDelta
functions
• 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)
• In SPM99, epochs and events are distinct In SPM99, epochs and events are distinct (eg, in choice of basis functions)(eg, in choice of basis functions)
• In SPM2, all conditions are specified in In SPM2, all conditions are specified in terms of their 1) terms of their 1) onsetsonsets and 2) and 2) durations…durations…
… … events simply have zero durationevents simply have zero duration
• 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)
• i.e, i.e, designsdesigns can be can be blockedblocked or or intermixedintermixed
• … … modelsmodels can be 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)
• In SPM99, epochs and events are distinct In SPM99, epochs and events are distinct (eg, in choice of basis functions)(eg, in choice of basis functions)
• In SPM2, all conditions are specified in In SPM2, all conditions are specified in terms of their 1) terms of their 1) onsetsonsets and 2) and 2) durations…durations…
… … events simply have zero durationevents simply have zero duration
• 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)
• i.e, i.e, designsdesigns can be can be blockedblocked or or intermixedintermixed
• … … modelsmodels can be can be epochepoch or or eventevent-related-related
Boxcar function
Sustained epoch
FILFIL
Epoch vsEpoch vs EventsEventsEpoch vsEpoch vs EventsEvents
• Though blocks of trials can be modelled as Though blocks of trials can be modelled as boxcars or runs of events…boxcars or runs of events…
… … interpretation of the parameter interpretation of the parameter estimates differs…estimates differs…
• 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
• Though blocks of trials can be modelled as Though blocks of trials can be modelled as boxcars or runs of events…boxcars or runs of events…
… … interpretation of the parameter interpretation of the parameter estimates differs…estimates differs…
• 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
FILFIL
Note on Epoch DurationsNote on Epoch DurationsNote on Epoch DurationsNote on Epoch Durations
• As duration of epochs increases from 0 to ~2s, As duration of epochs increases from 0 to ~2s, shape of convolved response changes little shape of convolved response changes little (mainly amplitude of response changes)(mainly amplitude of response changes)
• Since it is the “amplitude” that is effectively Since it is the “amplitude” that is effectively estimated by the GLM, the results for epochs of estimated by the GLM, the results for epochs of constantconstant duration <2s will be very similar to duration <2s will be very similar to those for events (at typical SNRs)those for events (at typical SNRs)
• If however the epochs vary in duration from If however the epochs vary in duration from trial-to-trial (e.g, to match RT), then epoch and trial-to-trial (e.g, to match RT), then epoch and event models will give different resultsevent models will give different results
• However, while RT-related duration may be However, while RT-related duration may be appropriate for “motor” regions, it may not be appropriate for “motor” regions, it may not be appropriate for all regions (e.g, “visual”)appropriate for all regions (e.g, “visual”)
• Thus a “parametric modulation” of events by RT Thus a “parametric modulation” of events by RT may be a better model in such situationsmay be a better model in such situations
• As duration of epochs increases from 0 to ~2s, As duration of epochs increases from 0 to ~2s, shape of convolved response changes little shape of convolved response changes little (mainly amplitude of response changes)(mainly amplitude of response changes)
• Since it is the “amplitude” that is effectively Since it is the “amplitude” that is effectively estimated by the GLM, the results for epochs of estimated by the GLM, the results for epochs of constantconstant duration <2s will be very similar to duration <2s will be very similar to those for events (at typical SNRs)those for events (at typical SNRs)
• If however the epochs vary in duration from If however the epochs vary in duration from trial-to-trial (e.g, to match RT), then epoch and trial-to-trial (e.g, to match RT), then epoch and event models will give different resultsevent models will give different results
• However, while RT-related duration may be However, while RT-related duration may be appropriate for “motor” regions, it may not be appropriate for “motor” regions, it may not be appropriate for all regions (e.g, “visual”)appropriate for all regions (e.g, “visual”)
• Thus a “parametric modulation” of events by RT Thus a “parametric modulation” of events by RT may be a better model in such situationsmay be a better model in such situations
FILFIL
Timing Issues : LatencyTiming Issues : LatencyTiming Issues : LatencyTiming 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 1st-order Taylor
R(t) = ß1 f(t) + ß2 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(ß12 + ß2
2) (Calhoun et al, 2004)
(similar logic applicable to other partial derivatives)
FILFIL
Timing Issues : LatencyTiming Issues : LatencyTiming Issues : LatencyTiming 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 1st-order Taylor
R(t) = ß1 f(t) + ß2 f ´(t) GLM fit
= ß1 dt = ß2 / ß1
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, ß1 and ß2, are such that :
FILFIL
Timing Issues : LatencyTiming Issues : Latency
DelayedResponses
(green/ yellow)
Canonical
ß2 /ß1
Actuallatency, dt,vs. ß2 / ß1
CanonicalDerivative
Basis Functions
Face repetition reduces latency as well as magnitude of fusiform response
ß1 ß1 ß1 ß2ß2ß2
ParameterEstimates
FILFIL
A. Decreased
B. Advanced
C. Shortened (same integrated)
D. Shortened (same maximum)
A. Smaller Peak
B. Earlier Onset
C. Earlier Peak
D. Smaller Peakand earlier Peak
Timing Issues : LatencyTiming Issues : Latency
Neural BOLD
FILFIL
BOLDBOLD Response Latency (Iterative) Response Latency (Iterative)BOLDBOLD Response Latency (Iterative) Response Latency (Iterative)
• Numerical fitting of explicitly Numerical fitting of explicitly parameterised canonical HRF parameterised canonical HRF (Henson et al, 2001)(Henson et al, 2001)
• Distinguishes between Distinguishes between OnsetOnset and and PeakPeak latency… latency…
……unlike temporal derivative…unlike temporal derivative…
… …and which may be important for and which may be important for interpreting neural changes interpreting neural changes (see previous slide)(see previous slide)
• Distribution of parameters Distribution of parameters tested nonparametrically tested nonparametrically (Wilcoxon’s T over subjects)(Wilcoxon’s T over subjects)
• Numerical fitting of explicitly Numerical fitting of explicitly parameterised canonical HRF parameterised canonical HRF (Henson et al, 2001)(Henson et al, 2001)
• Distinguishes between Distinguishes between OnsetOnset and and PeakPeak latency… latency…
……unlike temporal derivative…unlike temporal derivative…
… …and which may be important for and which may be important for interpreting neural changes interpreting neural changes (see previous slide)(see previous slide)
• Distribution of parameters Distribution of parameters tested nonparametrically tested nonparametrically (Wilcoxon’s T over subjects)(Wilcoxon’s T over subjects)
Height
Peak Delay
Onset Delay
FILFIL
BOLDBOLD Response Latency (Iterative) Response Latency (Iterative)BOLDBOLD Response Latency (Iterative) Response Latency (Iterative)
No difference in Onset Delay, wT(11)=35
240ms Peak DelaywT(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 Peakand earlier Peak
BOLD
FILFIL
Temporal Basis Sets: InferencesTemporal Basis Sets: InferencesTemporal Basis Sets: InferencesTemporal 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 variabilitycanonical 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
FILFIL
Efficiency - Single Event-typeEfficiency - Single Event-typeEfficiency - Single Event-typeEfficiency - Single Event-type
• 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=nTp(t)=1 iff t=nT
• Stationary stochastic Stationary stochastic p(t)=constantp(t)=constant
• Dynamic stochasticDynamic stochasticp(t) varies (eg p(t) varies (eg
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=nTp(t)=1 iff t=nT
• Stationary stochastic Stationary stochastic p(t)=constantp(t)=constant
• Dynamic stochasticDynamic stochasticp(t) varies (eg p(t) varies (eg
blocked)blocked) Blocked designs most efficient! (with small SOAmin)
FILFIL
Efficiency – Efficiency – Detection vs EstimationDetection vs EstimationEfficiency – Efficiency – Detection vs EstimationDetection vs Estimation
• ““Detection power” vs Detection power” vs “Estimation efficiency” “Estimation efficiency”
(Liu et al, (Liu et al, 2001)2001)
• Detect response, or characterise Detect response, or characterise shape of response?shape of response?
• Maximal detection power in Maximal detection power in blocked designs;blocked designs;Maximal estimation efficiency Maximal estimation efficiency in randomised designsin randomised designs
=> simply corresponds to choice => simply corresponds to choice of basis functions: of basis functions:
detection = canonical HRFdetection = canonical HRF estimation = FIRestimation = FIR
• ““Detection power” vs Detection power” vs “Estimation efficiency” “Estimation efficiency”
(Liu et al, (Liu et al, 2001)2001)
• Detect response, or characterise Detect response, or characterise shape of response?shape of response?
• Maximal detection power in Maximal detection power in blocked designs;blocked designs;Maximal estimation efficiency Maximal estimation efficiency in randomised designsin randomised designs
=> simply corresponds to choice => simply corresponds to choice of basis functions: of basis functions:
detection = canonical HRFdetection = canonical HRF estimation = FIRestimation = FIR