1. Experimental Design Christian Ruff With slides from: Rik Henson
Daniel Glaser

2. Overview Parametric designs Categorical designs
Subtraction - Pure insertion, evoked / differential responses
Conjunction - Testing multiple hypotheses
Parametric designs
Linear - Adaptation, cognitive dimensions
Nonlinear - Polynomial expansions, neurometric functions
Factorial designs
Categorical - Interactions and pure insertion
Parametric - Linear and nonlinear interactions
- Psychophysiological Interactions

3. Cognitive Subtraction
Aim:
Neuronal structures underlying a single process P?
Procedure:
Contrast: [Task with P] – [control task without P ] = P
the critical assumption of „pure insertion“
 Neuronal structures computing face recognition?
Example:
Neuronal structures underlying face recognition?

4. Cognitive Subtraction: Baseline-problems
„Distant“ stimuli
-  Several components differ!
 P implicit in control task ?
„Queen!“ „Aunt Jenny?“
„Related“ stimuli
Name Person! Name Gender!
 Interaction of process and task ?
Same stimuli, different task

5. Differential event-related fMRI
Evoked responses
Differential event-related fMRI
SPM{F} testing for evoked responses
Parahippocampal responses to words
“Baseline” here corresponds to session mean
Estimation depends crucially on inclusion of null events or long SOAs
“Cognitive” interpretation hardly possible, but useful to define regions generally involved in the task
BOLD EPI fMRI at 2T, TR 3.2sec. Words presented every 16 secs; (i) studied words or (ii) new words

6. Differential event-related fMRI
Differential responses
Differential event-related fMRI
SPM{F} testing for evoked responses
Parahippocampal responses to words
SPM{F} testing for differences
studied words
new words
BOLD EPI fMRI at 2T, TR 3.2sec. Words presented every 16 secs; (i) studied words or (ii) new words
Peri-stimulus time {secs}

7. A categorical analysis
Experimental design
Word generation G
Word repetition R
R G R G R G R G R G R G
G - R = Intrinsic word generation
…under assumption of pure insertion

8. Overview Parametric designs Categorical designs
Subtraction - Pure insertion, evoked / differential responses
Conjunction - Testing multiple hypotheses
Parametric designs
Linear - Adaptation, cognitive dimensions
Nonlinear - Polynomial expansions, neurometric functions
Factorial designs
Categorical - Interactions and pure insertion
Parametric - Linear and nonlinear interactions
- Psychophysiological Interactions

9. Conjunctions
One way to minimise the baseline/pure insertion problem is to isolate the same process by two or more separate comparisons, and inspect the resulting simple effects for commonalities
A test for such activation common to several independent contrasts is called “Conjunction”
Conjunctions can be conducted across a whole variety of different contexts:
tasks
stimuli
senses (vision, audition)
etc.
But the contrasts entering a conjunction have to be truly independent!

10. Conjunctions Task (1/2) Stimuli (A/B)
Viewing Naming
Stimuli (A/B)
Objects Colours
Example: Which neural structures support object recognition, independent of task (naming vs viewing)? A1 A2 B2 B1
Visual Processing V
Object Recognition R
Phonological Retrieval P
Object viewing R,V
Colour viewing V
Object naming P,R,V
Colour naming P,V
(Object - Colour viewing) [ ]
&
(Object - Colour naming) [ ]
[ R,V - V ] & [ P,R,V - P,V ] = R & R = R
(assuming no interaction RxP; see later)
Common object
recognition response (R)
Price et al, 1997

11. Conjunctions

12. Two flavours of inference about conjunctions
SPM5 offers two general ways to test the significance of conjunctions:
Test of global null hypothesis: Significant set of consistent effects
 “which voxels show effects of similar direction (but not necessarily individual significance) across contrasts?”
Test of conjunction null hypothesis: Set of consistently significant effects
 “which voxels show, for each specified contrast, effects > threshold?”
Choice of test depends on hypothesis and congruence of contrasts; the global null test is more sensitive (i.e., when direction of effects hypothesised)
A1-A2
B1-B2
p(A1=A2)<p +
p(B1=B2)<p
Friston et al. (2005). Neuroimage, 25:661-7.
Nichols et al. (2005). Neuroimage, 25:

13. Parametric Designs: General Approach
Parametric designs approach the baseline problem by:
Varying the stimulus-parameter of interest on a continuum, in multiple (n>2) steps...
... and relating blood-flow to this parameter
Possible tests for such relations are manifold:
Linear
Nonlinear: Quadratic/cubic/etc.
„Data-driven“ (e.g., neurometric functions)

14. Overview Parametric designs Categorical designs
Subtraction - Pure insertion, evoked / differential responses
Conjunction - Testing multiple hypotheses
Parametric designs
Linear - Adaptation, cognitive dimensions
Nonlinear - Polynomial expansions, neurometric functions
Factorial designs
Categorical - Interactions and pure insertion
Parametric - Linear and nonlinear interactions
- Psychophysiological Interactions

15. A linear parametric contrast
Linear effect
of time

16. A nonlinear parametric contrast
The nonlinear effect of time
assessed with the SPM{T}

17. Nonlinear parametric design matrix
SPM{F}
E.g, F-contrast [0 1 0] on
Quadratic Parameter =>
Quadratic
Linear
Inverted ‘U’ response to
increasing word presentation
rate in the DLPFC
Polynomial expansion:
f(x) ~ b1 x + b2 x
…up to (N-1)th order for N levels
(SPM5 GUI offers polynomial expansion as option during creation of parametric modulation regressors)

18. Parametric Designs: Neurometric functions
versus
Rees, G., et al. (1997). Neuroimage, 6: 27-78
Inverted ‘U’ response to
increasing word presentation
rate in the DLPFC
Rees, G., et al. (1997). Neuroimage, 6: 27-78

19. Parametric Designs: Neurometric functions
Coding of tactile stimuli in Anterior Cingulate Cortex:
Stimulus (a) presence, (b) intensity, and (c) pain intensity
Variation of intensity of a heat stimulus applied to the right hand
(300, 400, 500, and 600 mJ)
Assumptions:
Büchel et al. (2002). The Journal of Neuroscience, 22: 970-6

20. Parametric Designs: Neurometric functions
 Stimulus intensity
 Stimulus presence
 Pain intensity
Büchel et al. (2002). The Journal of Neuroscience, 22: 970-6

21. Parametric Designs: Model-based regressors
Seymour, O‘Doherty, et al. (2004). Nature.

22. Overview Parametric designs Categorical designs
Subtraction - Pure insertion, evoked / differential responses
Conjunction - Testing multiple hypotheses
Parametric designs
Linear - Adaptation, cognitive dimensions
Nonlinear - Polynomial expansions, neurometric functions
Factorial designs
Categorical - Interactions and pure insertion
Parametric - Linear and nonlinear interactions
- Psychophysiological Interactions

23. Factorial designs: Main effects and InteractionsB2 B1
Task (1/2)
Viewing Naming
Stimuli (A/B)
Objects Colours
Main effect of task: (A1 + B1) – (A2 + B2)
Main effect of stimuli: (A1 + A2) – (B1 + B2)
Interaction of task and stimuli: Can show a failure of pure insertion
(A1 – B1) – (A2 – B2)
interaction effect
(Stimuli x Task)
Colours Objects Colours Objects
Viewing
Naming

24. Interactions and pure insertion
Components
Visual processing V
Object recognition R
Phonological retrieval P
Interaction RxP
Interaction
(name object - colour) - (view object - colour)
= (R + RxP) R = RxP
Object-naming-specific activations
adjusted rCBF
Interaction effects in the
left inferotemporal region
Context: no naming naming

25. Interactions and pure insertion
cross-over
and
simple
We can selectively inspect our data for one or the other by masking during inference

26. Overview Parametric designs Categorical designs
Subtraction - Pure insertion, evoked / differential responses
Conjunction - Testing multiple hypotheses
Parametric designs
Linear - Adaptation, cognitive dimensions
Nonlinear - Polynomial expansions, neurometric functions
Factorial designs
Categorical - Interactions and pure insertion
Parametric - Linear and nonlinear interactions
- Psychophysiological Interactions

27. Linear Parametric Interaction
A (Linear)
Time-by-Condition
Interaction
(“Generation strategy”?)
Contrast: [ ]  [-1 1]

28. Nonlinear Parametric Interaction
F-contrast tests for nonlinear
Generation-by-Time interaction
(including both linear and
Quadratic components)
Factorial Design with 2 factors:
Gen/Rep (Categorical, 2 levels)
Time (Parametric, 6 levels)
Time effects modelled with both linear and quadratic components…
G-R
Time
Lin
Time
Quad
G x T
Lin
G x T
Quad

29. Overview Parametric designs Categorical designs
Subtraction - Pure insertion, evoked / differential responses
Conjunction - Testing multiple hypotheses
Parametric designs
Linear - Adaptation, cognitive dimensions
Nonlinear - Polynomial expansions, neurometric functions
Factorial designs
Categorical - Interactions and pure insertion
Parametric - Linear and nonlinear interactions
- Psychophysiological Interactions

30. Psycho-physiological Interaction (PPI)
Parametric, factorial design, in which one factor is a psychological context …
...and the other is a physiological source (activity extracted from a brain region of interest)
Context
source
target X

31. Psycho-physiological Interaction (PPI)
Parametric, factorial design, in which one factor is a psychological context …
...and the other is a physiological source (activity extracted from a brain region of interest)
Set
Context-sensitive
connectivity
source
target
stimuli
Modulation of stimulus-specific responses
source
target

32. Psycho-physiological Interaction (PPI)
SPM{Z}
V1 activity
Attention
time V1
attention V5
V5 activity
no attention
Attentional modulation of
V1 - V5 contribution
V1 activity

33. Psycho-physiological Interaction (PPI)
SPM{Z}
V1 activity
time
attention
V5 activity
no attention V1
Att
V1 x Att
V1 activity

34. Psycho-physiological Interaction (PPI)
SPM{Z}
Stimuli:
Faces or objects
Faces
PPC IT
adjusted rCBF
Objects
medial parietal activity

35. Psycho-physiological Interaction (PPI)
PPIs tested by a GLM with form:
y = (V1A).b1 + V1.b2 + A.b3 + e c = [1 0 0]
However, the interaction term of interest, V1A, is the product of V1 activity and Attention block AFTER convolution with HRF
We are really interested in interaction at neural level, but:
(HRF  V1)  (HRF  A)  HRF  (V1  A)
(unless A low frequency, e.g., blocked; mainly problem for event-related PPIs)
SPM5 can effect a deconvolution of physiological regressors (V1), before calculating interaction term and reconvolving with the HRF – the “PPI button”

36. Overview Parametric designs “Bonus”: Mixed designs Categorical designs
Subtraction - Pure insertion, evoked / differential responses
Conjunction - Testing multiple hypotheses
Parametric designs
Linear - Adaptation, cognitive dimensions
Nonlinear - Polynomial expansions, neurometric functions
Factorial designs
Categorical - Interactions and pure insertion
Parametric - Linear and nonlinear interactions
- Psychophysiological Interactions
“Bonus”: Mixed designs

37. Mixed Designs
Recent interest in simultaneously measuring effects that are:
transient (“item- or event-related”)
sustained (“state- or epoch-related”)
What is the best design to estimate both…?
Sensitivity, or “efficiency”, e: e(c,X) = { cT (XTX)-1 c }-1
XTX represents covariance of regressors in design matrix; high covariance increases elements of (XTX)-1
 High correlation between regressors leads to low sensitivity to each regressor alone

38. Item effect only Efficiency = 565 (Item Effect)
Blocks = 40s, Fixed SOA = 4s
Design Matrix (X)
Efficiency = 565
(Item Effect)
OK…

39. Item and state effects Efficiency = 16 (Item Effect)
Blocks = 40s, Fixed SOA = 4s
Design Matrix (X)
Efficiency = 16
(Item Effect)
Correlation = .97
Not good…

40. Item and state effects Efficiency = 54 (Item Effect)
Blocks = 40s, Randomised SOAmin= 2s
Design Matrix (X)
Efficiency = 54
(Item Effect)
Correlation = .78
Better!

41. Mixed design example: Chawla et al. (1999)
Visual stimulus = dots periodically changing in colour or motion
Epochs of attention to: 1) motion, or 2) colour
Events are target stimuli differing in motion or colour
Randomised, long SOAs between events (targets) to decorrelate epoch and event-related covariates
Attention modulates BOTH:
1) baseline activity (state-effect, additive)
2) evoked response (item-effect, multiplicative)

42. Mixed design example: Chawla et al. (1999)
Mixed Designs (Chawla et al 1999)
V Motion change under attention to
motion (red) or color (blue)
Item
Effect
(Evoked)
State
Effect
(Baseline)
V Color change under attention to
motion (red) or color (blue)