event-related fmri (er-fmri) methods & models for fmri data analysis 05 november 2008 klaas enno...
Post on 19-Dec-2015
224 views
TRANSCRIPT
![Page 1: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/1.jpg)
Event-related fMRI (er-fMRI)
Methods & models for fMRI data analysis05 November 2008
Klaas Enno Stephan
Laboratory for Social and Neural Systems ResearchInstitute for Empirical Research in EconomicsUniversity of Zurich
Functional Imaging Laboratory (FIL)Wellcome Trust Centre for NeuroimagingUniversity College London
With many thanks for slides & images to:
FIL Methods group, particularly Rik Henson and Christian Ruff
![Page 2: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/2.jpg)
Overview of SPM
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
![Page 3: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/3.jpg)
Overview
1. Advantages of er-fMRI
2. BOLD impulse response
3. General Linear Model
4. Temporal basis functions
5. Timing issues
6. Design optimisation
7. Nonlinearities at short SOAa
![Page 4: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/4.jpg)
Advantages of er-fMRI
1. Randomised trial orderc.f. confounds of blocked designs
![Page 5: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/5.jpg)
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
…… …… ………………
er-fMRI: Stimulus randomisation
Unpleasant (U) Unpleasant (U) Unpleasant (U)Pleasant (P)
Pleasant (P)
![Page 6: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/6.jpg)
Advantages of er-fMRI
1. Randomised trial orderc.f. confounds of blocked designs
2. Post hoc classification of trialse.g. according to performance or subsequent memory
![Page 7: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/7.jpg)
er-fMRI: post-hoc classification of trials
Gonsalves & Paller (2000) Gonsalves & Paller (2000) Nature NeuroscienceNature Neuroscience
Items with wrongItems with wrong memory of picture („hat“) were associated with memory of picture („hat“) were associated with more occipital activity more occipital activity at encodingat encoding than items with correct rejection than items with correct rejection („brain“)(„brain“)
„„was shown as was shown as picture“picture“
„„was was notnot shown shown as picture“as picture“
Participant Participant response:response:
![Page 8: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/8.jpg)
Advantages of er-fMRI
1. Randomised trial orderc.f. confounds of blocked designs
2. Post hoc classification of trialse.g. according to performance or subsequent memory
3. Some events can only be indicated by subjecte.g. spontaneous perceptual changes
![Page 9: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/9.jpg)
eFMRI: “on-line” event-definition
Bistable percepts
Binocular rivalry
![Page 10: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/10.jpg)
Advantages of er-fMRI
1. Randomised trial orderc.f. confounds of blocked designs
2. Post hoc classification of trialse.g. according to performance or subsequent memory
3. Some events can only be indicated by subjecte.g. spontaneous perceptual changes
4. Some trials cannot be blockede.g. “oddball” designs
![Page 11: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/11.jpg)
time
…
er-fMRI: “oddball” designs
![Page 12: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/12.jpg)
Advantages of er-fMRI
1. Randomised trial orderc.f. confounds of blocked designs
2. Post hoc classification of trialse.g. according to performance or subsequent memory
3. Some events can only be indicated by subjecte.g. spontaneous perceptual changes
4. Some trials cannot be blockede.g. “oddball” designs
5. More accurate models even for blocked designs?“state-item” interactions
![Page 13: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/13.jpg)
P1 P2 P3
“Event” model may capture state-item interactions
U1 U2 U3
“Epoch” model assumes constant neural processes throughout block
U1 U2 U3 P1 P2 P3
er-fMRI: “event-based” model of block-designs
Data
Model
![Page 14: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/14.jpg)
Convolved with HRF
=>
Series of eventsDelta
functions
• DesignsDesigns can be blocked or intermixed, can be blocked or intermixed, BUTBUT models models for blocked designs can be for blocked designs can be
epoch- or event-relatedepoch- or event-related
• Epochs are periods of sustained Epochs are periods of sustained stimulation (e.g, box-car functions)stimulation (e.g, box-car functions)
• Events are impulses (delta-functions)Events are impulses (delta-functions)
• Near-identical regressors can be Near-identical regressors can be created by 1) sustained epochs, 2) created by 1) sustained epochs, 2) rapid series of events (SOAs<~3s)rapid series of events (SOAs<~3s)
• In SPM5, all conditions are specified in In SPM5, all conditions are specified in terms of their 1) onsets and 2) durationsterms of their 1) onsets and 2) durations
… … epochs: variable or constant epochs: variable or constant durationduration
… … events: zero durationevents: zero duration
“Classic” Boxcar function
Sustained epoch
Modeling block designs: epochs vs events
![Page 15: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/15.jpg)
• Blocks of trials can be modelled as Blocks of trials can be modelled as boxcars or runs of eventsboxcars or runs of events
• BUT: interpretation of the parameter BUT: interpretation of the parameter estimates may differestimates may differ
• Consider an experiment presenting Consider an experiment presenting words at different rates in different words at different rates in different blocks:blocks:
• An “epoch” model will estimate An “epoch” model will estimate parameter that parameter that increases with increases with raterate, because the parameter , because the parameter reflects reflects response per blockresponse per block
• An “event” model may estimate An “event” model may estimate parameter that parameter that decreases with decreases with raterate, because the parameter , because the parameter reflects reflects response per wordresponse per word
=3 =5
=9=11
Rate = 1/4s Rate = 1/2s
Epochs vs events
![Page 16: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/16.jpg)
Disadvantages of er-fMRI
1. Less efficient for detecting effects than blocked designs.
2. Some psychological processes may be better blocked (e.g. task-switching, attentional instructions).
![Page 17: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/17.jpg)
• Function of blood oxygenation, flow, volume (Buxton et al. 1998)
• Peak (max. oxygenation) 4-6s post-stimulus; return to baseline after 20-30s
• initial undershoot sometimes observed (Malonek & Grinvald, 1996)
• Similar across V1, A1, S1…
• … but differences across other regions (Schacter et al. 1997) and individuals (Aguirre et al. 1998)
BOLD impulse response
BriefStimulus
Undershoot
InitialUndershoot
Peak
![Page 18: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/18.jpg)
• Early er-fMRI studies used a long Stimulus Onset Asynchrony (SOA) to allow BOLD response to return to baseline.
• However, if the BOLD response is explicitly modelled, overlap between successive responses at short SOAs can be accommodated…
• … particularly if responses are assumed to superpose linearly.
• Short SOAs can give a more efficient design (see below).
BOLD impulse response
BriefStimulus
Undershoot
InitialUndershoot
Peak
![Page 19: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/19.jpg)
General Linear (Convolution) Model
GLM for a single voxel:
y(t) = u(t) h() + (t)
u(t) = neural causes (stimulus train)
u(t) = (t - nT)
h(t) = BOLD) response
h() = ßi fi ()
fi(t) = 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
![Page 20: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/20.jpg)
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)
![Page 21: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/21.jpg)
Temporal basis functions
Finite Impulse Response (FIR) model Fourier basis set
Gamma functions set Informed basis set
![Page 22: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/22.jpg)
Informed basis set
• Canonical HRF (2 gamma functions)
plus Multivariate Taylor expansion in:time (Temporal Derivative)
width (Dispersion Derivative)
• F-tests allow for any “canonical-like” responses
• T-tests on canonical HRF alone (at 1st
level) can be improved by derivatives reducing residual error, and can be interpreted as “amplitude” differences, assuming canonical HRF is a reasonable fit…
CanonicalTemporalDispersion
Friston et al. 1998, NeuroImage
![Page 23: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/23.jpg)
Temporal basis sets: Which one?
+ FIR+ Dispersion+ TemporalCanonical
• canonical + temporal + dispersion derivatives appear sufficient
• may not be for more complex trials (e.g. stimulus-delay-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)…
![Page 24: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/24.jpg)
Penny et al. 2007, Hum. Brain Mapp.
right occipital cortexleft occipital cortex
![Page 25: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/25.jpg)
Timing Issues : Practical
• Assume TR is 4s
• Sampling at [0,4,8,12…] post- stimulus may miss peak signal
Scans TR=4s
Stimulus (synchronous)
Sampling rate=4s
![Page 26: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/26.jpg)
Timing Issues : Practical
• Assume TR is 4s
• Sampling at [0,4,8,12…] post- stimulus may miss peak signal
• Higher effective sampling by:
– 1. Asynchrony, e.g. SOA = 1.5TR
Scans TR=4s
Stimulus (asynchronous)
Sampling rate=2s
![Page 27: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/27.jpg)
Timing Issues : Practical
• Assume TR is 4s
• Sampling at [0,4,8,12…] post- stimulus may miss peak signal
• Higher effective sampling by:
– 1. Asynchrony, e.g. SOA = 1.5TR
– 2. Random jitter, e.g. SOA = (2 ± 0.5)TR
• Better response characterisation (Miezin et al, 2000)
Scans TR=4s
Stimulus (random jitter)
Sampling rate=2s
![Page 28: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/28.jpg)
Slice-timing
T=16, TR=2s
Scan0 1
o
T0=9 oT0=16
![Page 29: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/29.jpg)
Slice-timing
• Slices acquired at different times, yet model is the same for all slices
=> different results (using canonical HRF) for different reference slices
• Solutions:
1. Temporal interpolation of data… but less good for longer
TRs
2. More general basis set (e.g. with temporal derivatives)
… but inference via F-testDerivative
SPM{F}
Interpolated
SPM{t}
Bottom sliceTop slice
SPM{t} SPM{t}
TR=3s
Henson et al. 1999
![Page 30: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/30.jpg)
Design efficiency
1122 ))(ˆ(),,ˆ( cXXcXc TT 1122 ))(ˆ(),,ˆ( cXXcXc TT
)ˆvar(
ˆ
T
T
c
cT
)ˆvar(
ˆ
T
T
c
cT
• The aim is to minimize the standard error of a t-contrast (i.e. the denominator of a t-statistic).
cXXcc TTT 12 )(ˆ)ˆvar( cXXcc TTT 12 )(ˆ)ˆvar(
• This is equivalent to maximizing the efficiency ε:
Noise variance Design variance
• If we assume that the noise variance is independent of the specific design:
11 ))((),( cXXcXc TT 11 ))((),( cXXcXc TT
• This is a relative measure: all we can say is that one design is more efficient than another (for a given contrast).
NB: efficiency depends on design
matrix and the chosen contrast !
![Page 31: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/31.jpg)
Another perspective on efficiency
efficiency = bandpassed signal energy
Hemodynamic transfer function (based on canonical HRF):neural activity (Hz) → BOLD
Highpass-filtered
Josephs & Henson 1999, Phil Trans B
![Page 32: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/32.jpg)
=
Fixed SOA = 16s
Not particularly efficient…
Stimulus (“Neural”) HRF Predicted Data
![Page 33: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/33.jpg)
=
Fixed SOA = 4s
Very inefficient…
Stimulus (“Neural”) HRF Predicted Data
![Page 34: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/34.jpg)
=
Randomised, SOAmin= 4s
More efficient …
Stimulus (“Neural”) HRF Predicted Data
![Page 35: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/35.jpg)
=
Blocked, SOAmin= 4s
Even more efficient…
Stimulus (“Neural”) HRF Predicted Data
![Page 36: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/36.jpg)
=
Blocked, epoch = 20s
=
Blocked-epoch (with short SOA)
Stimulus (“Neural”) HRF Predicted Data
![Page 37: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/37.jpg)
=
Sinusoidal modulation, f = 1/33s
=
The most efficient design of all!
Stimulus (“Neural”) HRF Predicted Data
![Page 38: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/38.jpg)
=
Blocked (80s), SOAmin=4s, highpass filter = 1/120s
Don’t use long (>60s) blocks!
=
Stimulus (“Neural”) HRFPredicted data(incl. HP filtering!)
![Page 39: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/39.jpg)
Randomised, SOAmin=4s, highpass filter = 1/120s
=
=
Randomised design spreads power over frequencies.
Stimulus (“Neural”) HRF Predicted Data
![Page 40: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/40.jpg)
4s smoothing; 1/60s highpass 4s smoothing; 1/60s highpass
filteringfiltering
Efficiency: Multiple event types• Design parametrised by:
SOAmin Minimum SOA
pi(h) Probability of event-type i given history h of last m events
• With n event-types pi(h) is a nm n Transition Matrix
• Example: Randomised AB
A B A0.5 0.5
B 0.5 0.5
=> ABBBABAABABAAA...
Differential Effect (A-B)
Common Effect (A+B)
![Page 41: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/41.jpg)
4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering
• Example: Alternating AB
A BA 0
1
B 1 0
=> ABABABABABAB...Alternating (A-B)
Permuted (A-B)
Efficiency: Multiple event types
• Example: Permuted AB
A B
AA 0 1
AB 0.5 0.5
BA 0.5 0.5
BB 1 0
=> ABBAABABABBA...
![Page 42: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/42.jpg)
4s smoothing; 1/60s highpass filtering4s smoothing; 1/60s highpass filtering
• Example: Null events A B
A 0.33 0.33
B 0.33 0.33
=> AB-BAA--B---ABB...
• Efficient for differential and main effects at short SOA
• Equivalent to stochastic SOA (Null Event like third unmodelled event-type)
Null Events (A+B)
Null Events (A-B)
Efficiency: Multiple event types
![Page 43: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/43.jpg)
Efficiency - Conclusions
• Optimal design for one contrast may not be optimal for another.
• Blocked designs generally most efficient with short SOAs.
• With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20s.
• Inclusion of null events gives good efficiency for both common and differential effects at short SOAs.
• If order constrained, intermediate SOAs (5-20s) can be optimal; if SOA constrained, pseudorandomised designs can be optimal (but may introduce context-sensitivity).
![Page 44: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/44.jpg)
But beware: Nonlinearities at short SOAs
Friston et al. 2000, NeuroImage Friston et al. 1998, Magn. Res. Med.
![Page 45: Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis 05 November 2008 Klaas Enno Stephan Laboratory for Social and Neural Systems Research](https://reader033.vdocuments.mx/reader033/viewer/2022051315/56649d3e5503460f94a16e4c/html5/thumbnails/45.jpg)
Thank you