Get documents about "Slide 1 - Wellcome Trust Centre for Neuroimaging_ UCL20114432122
Document Sample
Study Design and Efficiency
Margarita Sarri
Hugo Spiers
We will talk about:
What kinds of designs are out there? -
Blocked vs event-related designs
How can I order my events?
What is estimation efficiency?
Which designs are more efficient?
Spacing of events
Sampling issues
Filtering issues
Event related vs Blocked designs
Blocked / Epoch/ Box design
Types of trials are ‘blocked’ together e.g. AAAAA BBBBB
AAAAA.
Event related design
Types of trials are interleaved and each trial is modelled separately as
an ‘event’ e.g. AABABBAB
Blocked design
typically used in experiments where the detection of activation is the primary
goal.
e.g localise a specific brain region showing a differential response to one type
of stimulus (e.g. faces vs houses)
In general 2 blocks more efficient than 4.
Ideal modulation frequency being approximately 16sec
but you may not be able to test certain things with such a design…
So you may want to go for an event related design…
Why should I use efMRI ?
Flexibility and randomization
eliminate predictability of block designs
avoid practice effects/strategy use
Post hoc sorting
e.g. classification of correct vs. incorrect, subjective perception:
aware vs. unaware, remembered vs. forgotten items, parametric
scores: e.g. fast vs. slow RTs
P
Measuring novelty: Rare or unpredictable events L
e.g. oddball designs. H
A
K
Allows to look at events on a shorter time scale.
But you can also combine block and efMRI…
A block can be treated as a continuous train of event-trials
E.g Otten, Henson & Rugg, Nature Neuroscience 2002
‘Subsequent memory’ experiment separating transient (events) and
sustained (blocks) neural activity.
At the beginning of each trial a cue instructed subjects to make an
phonological or semantic judgement.
83sec rest 83sec
Hmmm I think I like efMRI.
But how do I order my
trials?
efMRI: Sequencing of events
Deterministic Stochastic
10
20
designs: 30
designs:
40
50
the occurrence of events 60 the occurrence of
is pre-determined e.g. a 70 an event depends
blocked design or on a a specified
probability e.g.
80
alternating design (all the random or
1 2 3 4 5 6 7 8
probabilities are zero or one ) permuted design
Blocked Stochastic designs
can be stationary or
dynamic
Alternating
Random
Permuted
How do I do I create a permuted order of
events?
ensure mini-runs of same stimuli…
i.e. modulate the probability of different event-types over experimental time
Permutation methods continued…
So what is
Efficiency?
Efficiency is…
Efficiency is a numerical value
which reflects the ability of your design to detect the effect of
interest
General Linear Model:
Y = X . β + e
Data Design Matrix Parameters error
Efficiency is the ability to estimate β, given the design matrix X
Efficiency can be calculated because the variance of β is proportional
to the variance of X
What is variance?
Variance = Standard Deviation 2
Standard Standard
Deviation Deviation
High Variance
Low Variance
Testing a Hypothesis
T- Test for the difference between 2 conditions
Standard Standard
Deviation Deviation
Higher ability to detect a difference
Lower ability to detect a difference
• By reducing the variance in the design we can maximize our T values
How do we calculate it?
Efficiency Inverse( Var(β) )
Inverse( Var(β) ) Var(X)
T
Var(X) Inverse( X X )
T
X . X T
= X X
A B C D A 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 B 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A B C D
1 0 0 0
1 0 0 0
C
D
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
A 5 0 0 0
1 0 0 0 B 0 5 0 0
1 0 0 0
0 1 0 0 C 0 0 5 4
0 1 0 0 D 0 0 4 5
0 1 0 0
0 1 0 0
0 1 0 0
0 0 0 0
0 0 0 0
0 0 1 0
0 0 1 1
0 0 1 1
0 0 1 1
0
0
0
0
1
0
1
1 Non-
0
0
0
0
0
0
0
0 overlapping
conditions
Overlapping
conditions
T
T inverse (X X)
X X
A B C D A B C D
A 5 0 0 0 A 0.2 0 0 0
B 0 5 0 0 B 0 0.2 0 0
C 0 0 5 4 C 0 0 0.6 -0.4
D 0 0 4 5 D 0 0 -0.4 0.6
The efficiency is related to the specific
contrast you are interested in
Efficiency = inverse(σ2 cT Inverse(XTX) c)
Where c = contrast
σ2 = noise variance
But if we assume that noise variance σ2 is constant then:
Efficiency = inverse (cT Inverse (XTX) c)
Efficiency = Inverse( cT Inverse(XTX) c)
When c is Simple Effect,
e.g. main effect of A c = [1 0 0 0]
T
CT inverse(X X) C
1 A B C D 1000
0 A 0.2 0 0 0
B 0 0.2 0 0
0 C 0 0 0.6 -0.4
0 D 0 0 -0.4 0.6
A, B: Efficiency = 1 / 0.2 = 5
C, D: Efficiency = 1 / 0.6 = 1.7
Efficiency = Inverse( cT Inverse(XTX) c)
When c is contrast difference,
e.g. For A – B c = [1 -1 0 0]
T
CT inverse(X X) C
1 A B C D 1 -1 0 0
-1 A 0.2 0 0 0
B 0 0.2 0 0
0 C 0 0 0.6 -0.4
0 D 0 0 -0.4 0.6
A-B: Efficiency = 1 / 0.4 = 2.5
C-D: Efficiency = 1 / 2 = 0.5
Variable No. of Trials
T
X inv(X X)
0.5
100
1
200
1.5
300
2
400
500 2.5
600
3
700
3.5
800
4
900
0.5 1 1.5 2 2.5 3 3.5 4 4.5 4.5
0.5 1 1.5 2 2.5 3 3.5 4 4.5
Random: Random: 2.1 4.2
Events = Events =
25 Relative Efficiency
50
How does trial order effect
Efficiency?
Example
Different Designs – Boxcar Events
T
X inv(X X)
A B C D E F
1 0 0 0 0 0 A B C D E F
1 0 1 0 0 1
1 0 0 0 0 1 A 0.2488 0.0377 -0.0297 -0.0396 -0.0012 -0.0873
1 0 0 1 0 0 B 0.0377 0.2862 -0.0941 -0.0421 -0.0873 -0.0263
1 0 0 0 0 0 C -0.0297 -0.0941 0.2871 0.0495 -0.0297 -0.0941
0 1 1 0 0 0 D -0.0396 -0.0421 0.0495 0.2327 -0.0396 -0.0421
0 1 0 0 0 0
0 1 0 1 1 0 E -0.0012 -0.0873 -0.0297 -0.0396 0.2488 0.0377
0 1 0 0 1 0 F -0.0873 -0.0263 -0.0941 -0.0421 0.0377 0.2862
0 1 1 0 0 1
0 0 0 0 0 0
0 0 0 1 0 1
0 0 0 0 1 0 1
0 0 1 0 1 0
0 0 0 0 0 0
0 0 0 1 0 0
2
0 0 0 0 1 0
0 0 1 0 0 0 3
0 0 0 0 0 1
0 0 0 1 0 0
4
5
Blocked
6
1 2 3 4 5 6
Fixed
Interleaved
Random
Different Designs
T
inv(X X)
X
1
10
2
20
3
30
4
40
50 5
60 6
70 7
80
8
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Blocked
5
Fixed
Interleaved 1.5
Random-
Uniform 2.8
Random-
Sinusoidal 3.5
Different Designs
T
inv(X X)
X
1
10
2
20
3
30
4
40
50 5
60 6
70 7
80 8
1 2 3 4 5 6 7 8
Blocked
1
0.8
0.6
0.4
0.2
5
0
-0.2
1.5
-0.4
-0.6
-0.8
-1
0 5 10 15 20 25 30 35 40
1
0.8
0.6
0.4
2.8
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0 5 10 15 20 25 30 35 40
1
0.8
0.6
3.5
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0 5 10 15 20 25 30 35 40
Sequencing of events
Stochastic designs: at each
point at which an event could
occur there is a specified
probability of that event
occurring. The timing of when
the events occur is specified.
Non-occurrence = null event.
Deterministic designs: the
occurrence of events is pre-
determined.
The variable deterministic
design i.e. a blocked design,
is the most efficient.
Joel’s example of different stimulus presentations
Tasks
AB C
Blocked
Efficiency calculation
design
100
90
80
70
60
50
Fully 40
30
randomised 20
10
0
Block Dynamic Randomised
stochastic
Dynamic
stochastic
{
minimum SOA (inter-stimulus interval)
different designs
probability of occurrence
How fast can I present my
trials?
max. The absolute minimum…
oxygenation: 4-
6s post-stimulus
Early event-related fMRI studies used a long Stimulus
Onset Asynchrony (SOA) to allow BOLD response to
return to baseline (20-30s).
Peak However, if the BOLD response is explicitly modelled,
overlap between successive responses at short SOAs can
be accommodated… (assuming that successive responses
Brief add up in a linear fashion)
Stimulus
Undershoot The lower limit on SOAs is dictated by nonlinear interactions
among events that can be though of as saturation phenomena or
‘‘refractoriness’’ at a neuronal or hemodynamic level.
But, very short SOAs (< 1s) are not advisable as the
Initial predicted additive effects upon the HRF of two closely
Undershoot occurring stimuli break down.
So you can have events occurring even every 1-2 sec!
But think of psychological validity!
And how should my events
be spaced? optimal SOA
Choosing the best SOA
Optimal SOA depends on:
Probability of occurrence (design)
Whether one is looking for evoked responses per
se or differences in evoked responses.
Generally SOAs that are small and randomly distributed are the most efficient.
Random SOAs ensure
Rapid presentation rates allow for the that preparatory or
maintenance of a particular cognitive or anticipatory
attentional set, decrease the latitude that the factors do not confound
subject has for engaging alternative event-related responses
strategies, or incidental processing. and ensure a uniform
context in which events
are presented.
Stationary Stochastic designs Main effect
Differential responses
ONE TRIAL TYPE TWO TRIAL TYPES
Probability
SOA
the most efficient SOA for differential responses is very small.
longer SOAs of around 16 s are necessary to estimate the responses themselves.
What should I do if I am interested in
the main effects (‘evoked responses’)?
to identify areas that are activated by both event types
You can use long SOA’s (around 16 secs!).
But behaviourally this may be inefficient
So you can introduce ‘null’ events and
keep your SOA short.
These null events now provide a baseline
against which the response to either trial
type 1 or 2 can be estimated even using a
very small SOA. (p=0.5 0.3)
Here is what happens when you add null events…
Random
Note that although null events increase efficiency for main effects (at
short SOA’s), they slightly decrease efficiency for differential effects
What should I do if I am interested in the differential effects?
For very short SOA’s use a randomised design
But for medium SOA’s a permuted (4-6sec) or an alternating (8sec) design is better
To sum up: Remember that…
Blocked designs generally more efficient
Some random event-related designs are much
better than others.
Different design is appropriate depending on
what you want to optimize.
Critical properties to optimize
Ordering of trials
spacing between stimuli
Timing of the SOAs in relation to the TR
If the TR (Repetition Time of slice collection) is divisible by the SOA then data
collected for each event will be from the same slices, at the same points along the
HRF.
Scans TR = 4s
Stimulus (synchronous) SOA=8s
Stimulus (asynchronous) SOA=6s
Stimulus (random jitter)
Therefore, either choose a TR and SOA that are not divisible or introduce a ‘jitter’
such that the SOA is randomly shifted.
Temporal Filtering: The High Pass Filter
A temporal filter is used in fMRI to get rid
of noise, thus increasing the efficiency of
the data.
Non-neuronal noise tends to be of low-
frequency, including ‘scanner drift’ and
physiological phenomenon.
Applying a high pass filter means that
parameters that occur at a slow rate are
removed from the analysis.
The default high pass filter in SPM is 128s,
thus if you have experimental events
occurring less frequently than once every
128s then the associated signal will be
removed by the filter!!
Sources
Summary
Blocked designs are generally the most efficient, but blocked
designs have restrictions.
For event-related designs, dynamic stochastic presentation of stimuli
is most efficient.
However, the most optimal design for your data depends on the
SOA that you use. The general rule is the smaller your SOA the
better, but sometimes a small SOA may not be possible.
Also, the most optimal design for one contrast may not be optimal
for another e.g. the inclusion of null events improves the efficiency
of main effects at short SOAs, at the cost of efficiency for
differential effects.
Finally, there is no point scanning two tasks to look for differences
between them if they are too different or too similar.
