Experimental Design

Experimental DesignExperimental Design

Christian RuffChristian Ruff

With slides from: Rik Henson

Daniel Glaser

OverviewOverview

• Categorical designsCategorical designsSubtraction Subtraction - Pure insertion, evoked / differential - Pure insertion, evoked / differential

responsesresponsesConjunction Conjunction - Testing multiple hypotheses- Testing multiple hypotheses

• Parametric designsParametric designsLinear Linear - Adaptation, cognitive dimensions- Adaptation, cognitive dimensionsNonlinearNonlinear - Polynomial expansions, neurometric - Polynomial expansions, neurometric

functionsfunctions • Factorial designsFactorial designs

CategoricalCategorical - Interactions and pure insertion- Interactions and pure insertionParametricParametric - Linear and nonlinear interactions- Linear and nonlinear interactions

- Psychophysiological Interactions- Psychophysiological Interactions

• Aim: Aim: – Neuronal structures underlying a Neuronal structures underlying a singlesingle process process PP? ?

• Procedure: Procedure: – Contrast: [Task with Contrast: [Task with PP] – [control task without ] – [control task without P P ] = ] = PP the critical assumption of „pure insertion“the critical assumption of „pure insertion“

Cognitive SubtractionCognitive Subtraction

- - Neuronal structures Neuronal structures computing face recognition? computing face recognition?

• ExampleExample: : – Neuronal structures underlying Neuronal structures underlying face recognitionface recognition? ?

Cognitive Subtraction: Baseline-Cognitive Subtraction: Baseline-problemsproblems

-- PP implicit in control task ? implicit in control task ?

„ „Queen!“ „Aunt Jenny?“Queen!“ „Aunt Jenny?“

• „ „Related“ stimuliRelated“ stimuli

-- Several components differ!Several components differ!

• „ „Distant“ stimuli Distant“ stimuli

Name Person! Name Gender!Name Person! Name Gender!

-- Interaction of process and taskInteraction of process and task ??

• Same stimuli, different taskSame stimuli, different task

Differential event-related fMRIDifferential event-related fMRI

Parahippocampal responses to words

BOLD EPI fMRI at 2T, BOLD EPI fMRI at 2T, TR 3.2sec. Words TR 3.2sec. Words

presented every 16 presented every 16 secs; (i) studied words secs; (i) studied words

or (ii) new wordsor (ii) new words

SPM{F} testing for SPM{F} testing for evoked responsesevoked responses

Evoked responsesEvoked responses

• “ “Baseline” here corresponds to session meanBaseline” here corresponds to session mean

• Estimation depends crucially on inclusion of null events Estimation depends crucially on inclusion of null events

or long SOAs or long SOAs

• “ “Cognitive” interpretation hardly possible, but useful to Cognitive” interpretation hardly possible, but useful to define regions generally involved in the task define regions generally involved in the task

Differential event-related fMRIDifferential event-related fMRI

Parahippocampal responses to words

BOLD EPI fMRI at 2T, BOLD EPI fMRI at 2T, TR 3.2sec. Words TR 3.2sec. Words

presented every 16 presented every 16 secs; (i) studied words secs; (i) studied words

or (ii) new wordsor (ii) new words

SPM{F} testing for SPM{F} testing for evoked responsesevoked responses

Differential responsesDifferential responses

Peri-stimulus time {secs}Peri-stimulus time {secs}

SPM{F} testing SPM{F} testing for differencesfor differences

studied wordsstudied words

new wordsnew words

Experimental designExperimental design

Word generationWord generation GGWord repetitionWord repetition RR

R G R G R G R G R G R GR G R G R G R G R G R G

G - R = Intrinsic word generationG - R = Intrinsic word generation

……under assumption of under assumption of pure insertionpure insertion

A categorical analysisA categorical analysis

OverviewOverview







• One way to minimise the baseline/pure insertion problem is to isolate the One way to minimise the baseline/pure insertion problem is to isolate the same process by two or more separate comparisons, and inspect the same process by two or more separate comparisons, and inspect the resulting simple effects for commonalitiesresulting simple effects for commonalities

• A test for such activation common to several independent contrasts is A test for such activation common to several independent contrasts is called “called “Conjunction”Conjunction”

• Conjunctions can be conducted across a whole variety of different Conjunctions can be conducted across a whole variety of different contexts:contexts:

• taskstasks• stimulistimuli• senses (vision, audition)senses (vision, audition)• etc.etc.

• But the contrasts entering a conjunction have to be truly independent!But the contrasts entering a conjunction have to be truly independent!

ConjunctionsConjunctions

Example: Which neural structures support object recognition, Example: Which neural structures support object recognition, independent of task (naming vs viewing)?independent of task (naming vs viewing)?

A1A1 A2A2

B2B2B1B1

Task (1/2)Task (1/2)ViewingViewing Naming Naming

Stim

uli (

A/B

)S

timul

i (A

/B)

Obj

ects

C

olou

rsO

bjec

ts

Col

ours

Visual ProcessingVisual Processing V V Object Recognition Object Recognition RRPhonological RetrievalPhonological Retrieval PP

Object viewingObject viewing R,VR,VColour viewingColour viewing VVObject namingObject naming P,R,VP,R,VColour namingColour naming P,VP,V

(Object - Colour viewing) [1 -1 0 0] (Object - Colour viewing) [1 -1 0 0] &&

(Object - Colour naming) [0 0 1 -1](Object - Colour naming) [0 0 1 -1]

[ R,V - V ] & [ P,R,V - P,V ] = R & R = R[ R,V - V ] & [ P,R,V - P,V ] = R & R = R

(assuming no interaction (assuming no interaction RxPRxP; see later); see later)


Price et al, 1997Common object Common object

recognition response (Rrecognition response (R))

SPM5 offers two general ways to test the SPM5 offers two general ways to test the significance of conjunctions: significance of conjunctions:

• Test of global null hypothesis: Test of global null hypothesis: Significant set of consistent effectsSignificant set of consistent effects

“ “which voxels show effects of similar which voxels show effects of similar direction (but not necessarily direction (but not necessarily individual significance) across contrasts?” individual significance) across contrasts?”

• Test of conjunction null hypothesis: Test of conjunction null hypothesis: Set of consistently significant effectsSet of consistently significant effects

“ “which voxels show, for each specified which voxels show, for each specified contrast, effects > threshold?” contrast, effects > threshold?”

• Choice of test depends on hypothesis and Choice of test depends on hypothesis and congruence of contrasts; the global null test congruence of contrasts; the global null test is more sensitive (i.e., when direction of is more sensitive (i.e., when direction of effects hypothesised)effects hypothesised)

Two flavours of inference about Two flavours of inference about conjunctionsconjunctions

A1-A2

B

1-B

2 p(A1=A2)<p

+p(B1=B2)<p

+

Friston et al.Friston et al. (2005). Neuroimage, Neuroimage, 25:661-7.25:661-7.

Nichols et al. (2005). Nichols et al. (2005). Neuroimage, Neuroimage, 25:653-60.25:653-60.

http://www.ncbi.nlm.nih.gov/entrez/utils/fref.fcgi?itool=AbstractPlus-def&PrId=3048&uid=15808966&db=pubmed&url=http://linkinghub.elsevier.com/retrieve/pii/S1053-8119%2804%2900750-5

OverviewOverview







Parametric Designs: General Parametric Designs: General ApproachApproach

• 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)

Linear effect Linear effect of time of time

A linear parametric contrastA linear parametric contrast

The nonlinear effect of time The nonlinear effect of time assessed with the SPM{T}assessed with the SPM{T}

A nonlinear parametric contrastA nonlinear parametric contrast

Inverted ‘U’ response toInverted ‘U’ response toincreasing word presentationincreasing word presentation

rate in the DLPFCrate in the DLPFCSPM{F}SPM{F}

Polynomial expansion:Polynomial expansion:f(x) ~ f(x) ~ b1 x + b2 x2 + ...

…up to (N-1)th order for N levels

Line

ar

Qua

dra t

icE.g, F-contrast [0 1 0] on E.g, F-contrast [0 1 0] on Quadratic Parameter =>Quadratic Parameter =>

Nonlinear parametric design matrixNonlinear parametric design matrix

(SPM5 GUI offers polynomial (SPM5 GUI offers polynomial expansion as option during creation expansion as option during creation of parametric modulation regressors)of parametric modulation regressors)

Parametric Designs: Neurometric Parametric Designs: Neurometric functionsfunctions

Rees, G., et al. (1997). Rees, G., et al. (1997). Neuroimage, 6Neuroimage, 6: 27-78: 27-78

versusversus

Inverted ‘U’ response toInverted ‘U’ response toincreasing word presentationincreasing word presentation

rate in the DLPFCrate in the DLPFCRees, G., et al. (1997). Rees, G., et al. (1997). Neuroimage, 6Neuroimage, 6: 27-78: 27-78


Coding of tactile stimuli in Anterior Cingulate Cortex:Coding of tactile stimuli in Anterior Cingulate Cortex:Stimulus (a) presence, (b) intensity, and (c) pain intensityStimulus (a) presence, (b) intensity, and (c) pain intensity

– Variation of intensity of a heat stimulus applied to the right handVariation of intensity of a heat stimulus applied to the right hand(300, 400, 500, and 600 mJ)(300, 400, 500, and 600 mJ)

Büchel et al. (2002). Büchel et al. (2002). The Journal of Neuroscience, 22The Journal of Neuroscience, 22: 970-6: 970-6

– Assumptions:Assumptions:


Büchel et al. (2002). Büchel et al. (2002). The Journal of Neuroscience, 22The Journal of Neuroscience, 22: 970-6: 970-6

Stimulus presenceStimulus presence

Pain intensityPain intensity

Stimulus intensityStimulus intensity

OverviewOverview







A1A1 A2A2

B2B2B1B1

Task (1/2)Task (1/2)ViewingViewing Naming Naming

Stim

uli (

A/B

)S

timul

i (A

/B)

Obj

ects

C

olou

rsO

bjec

ts

Col

ours

Colours Objects Colours ObjectsColours Objects Colours Objects

interaction effectinteraction effect (Stimuli x Task)(Stimuli x Task)

ViewingViewing NamingNaming

Factorial designs: Main effects and Factorial designs: Main effects and InteractionsInteractions

• Main effect of task:Main effect of task: (A1 + B1) – (A2 + (A1 + B1) – (A2 + B2)B2)

• Main effect of stimuli: Main effect of stimuli: (A1 + A2) – (B1 + (A1 + A2) – (B1 + B2)B2)

• Interaction of task and stimuli: Interaction of task and stimuli: Can show a failure of pure insertionCan show a failure of pure insertion

(A1 – B1) – (A2 – (A1 – B1) – (A2 – B2)B2)

Interactions and pure insertionInteractions and pure insertion

Object-naming-specific activationsObject-naming-specific activations

Interaction effects in the Interaction effects in the left inferotemporal regionleft inferotemporal region Context: Context: no naming namingno naming naming

adju

sted

rCB

Fad

just

ed rC

BF

ComponentsComponentsVisual processingVisual processing VVObject recognition Object recognition RRPhonological retrievalPhonological retrieval PPInteractionInteraction RxPRxP

ConjunctionConjunction(name object - colour) & (view object - colour)(name object - colour) & (view object - colour)= (R += (R + RxP RxP) & R = R) & R = R

InteractionInteraction(name object - colour) - (view object - colour)(name object - colour) - (view object - colour)= (R + = (R + RxPRxP) - R = ) - R = RxPRxP

Interactions and pure insertionInteractions and pure insertion

Interactions: Interactions:

cross-over cross-over

and and

simplesimple

We can selectively We can selectively inspect our data for one inspect our data for one or the other by masking or the other by masking during inferenceduring inference

OverviewOverview







A (Linear) A (Linear) Time-by-ConditionTime-by-Condition

InteractionInteraction(“Generation strategy”?) (“Generation strategy”?)

Contrast: [5 3 1 -1 -3 -5]Contrast: [5 3 1 -1 -3 -5] [-1 1][-1 1]

Linear Parametric InteractionLinear Parametric Interaction

Factorial Design with 2 factors:Factorial Design with 2 factors:

1.1. Gen/Rep (Categorical, 2 levels)Gen/Rep (Categorical, 2 levels)2.2. Time (Parametric, 6 levels)Time (Parametric, 6 levels)

Time effects modelled with both linear Time effects modelled with both linear and quadratic components…and quadratic components…

G-R TimeLin

G x TLin

TimeQuad

G x TQuad

F-contrast tests for nonlinearF-contrast tests for nonlinearGeneration-by-Time interactionGeneration-by-Time interaction

(including both linear and (including both linear and Quadratic components)Quadratic components)

Nonlinear Parametric InteractionNonlinear Parametric Interaction

OverviewOverview







ContextContext

sourcesource

targettarget

XX

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)

Psycho-physiological Interaction (PPI)Psycho-physiological Interaction (PPI)

stimulistimuli

Modulation of Modulation of stimulus-specific stimulus-specific

responsesresponses

sourcesource

targettarget

SetSet

Context-sensitiveContext-sensitiveconnectivityconnectivity

sourcesource

targettarget

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)


SPM{Z}SPM{Z}

Attentional modulation ofAttentional modulation ofV1 - V5 contributionV1 - V5 contribution

AttentionAttention

V1V1

V5V5

attention

no attention

V1 activityV1 activity

V5

activ

ity

timetime

V1

activ

ity


SPM{Z}SPM{Z}

attention

no attention

V1 activityV1 activity

V5

activ

ity

timetime

V1

activ

ity

V1 Att V1 x Att

0 0 1


adju

sted

rCB

Fad

just

ed rC

BF

medial parietal activitymedial parietal activity

FacesFaces

ObjectsObjects

Stimuli:Stimuli:Faces or objectsFaces or objects

PPCPPC

ITIT

SPM{Z}SPM{Z}


• PPIs tested by a GLM with form:PPIs tested by a GLM with form:

yy = ( = (V1V1AA).b).b11 + + V1V1.b.b22 + + AA.b.b33 + + ee c = [1 0 0]c = [1 0 0]

• However, the interaction term of interest, However, the interaction term of interest, V1V1AA, is the product of V1 activity and , is the product of V1 activity and Attention block AFTER convolution with HRFAttention block AFTER convolution with HRF

• We are really interested in interaction at neural level, but:We are really interested in interaction at neural level, but:

(HRF (HRF V1) V1) (HRF (HRF A) A) HRF HRF (V1 (V1 A A) )

(unless A low frequency, e.g., blocked; mainly problem for event-related PPIs)(unless A low frequency, e.g., blocked; mainly problem for event-related PPIs)

• SPM5 can effect a SPM5 can effect a deconvolutiondeconvolution of physiological regressors (V1), before of physiological regressors (V1), before calculating interaction term and reconvolving with the HRF – the “PPI button”calculating interaction term and reconvolving with the HRF – the “PPI button”


OverviewOverview







• ““Bonus”: Mixed designsBonus”: 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: Sensitivity, or “efficiency”, e: e(e(c,Xc,X) = ) = { { ccT T ((XXTTXX))-1 -1 cc } }-1-1

• XXTTX represents covariance of regressors in design matrix; high X represents covariance of regressors in design matrix; high covariance increases elements of (Xcovariance increases elements of (XTTX)X)-1-1

High correlation between regressors leads to High correlation between regressors leads to low sensitivity to each regressor alonelow sensitivity to each regressor alone

Mixed DesignsMixed Designs

Efficiency = 565Efficiency = 565(Item Effect) (Item Effect)

Design Matrix Design Matrix (X)(X)

Blocks = 40s, Blocks = 40s, Fixed SOAFixed SOA = 4s = 4s

OK…OK…

Item effect onlyItem effect only



Correlation = .97Correlation = .97

Blocks = 40s, Blocks = 40s, Fixed SOAFixed SOA = 4s = 4s

Not good…Not good…

Item and state effectsItem and state effects



Correlation = .78Correlation = .78

Blocks = 40s, Blocks = 40s, Randomised SOARandomised SOAminmin= 2s= 2s

Better!Better!

Item and state effectsItem and state effects

• Visual stimulus = dots periodically changing in colour or motionVisual stimulus = dots periodically changing in colour or motion

• Epochs of attention to: 1) motion, or 2) colourEpochs of attention to: 1) motion, or 2) colour

• Events are target stimuli differing in motion or colourEvents are target stimuli differing in motion or colour

• Randomised, long SOAs between events (targets) to decorrelate Randomised, long SOAs between events (targets) to decorrelate epoch and event-related covariatesepoch and event-related covariates

• Attention modulates BOTH: Attention modulates BOTH: – 1) baseline activity (state-effect, additive) 1) baseline activity (state-effect, additive) – 2) evoked response (item-effect, multiplicative) 2) evoked response (item-effect, multiplicative)

Mixed design example: Chawla et al. Mixed design example: Chawla et al. (1999)(1999)

V5 Motion change under attention to

motion (red) or color (blue)

V4 Color change under attention to

motion (red) or color (blue)

Mixed Designs (Chawla et al 1999)

StateEffect

(Baseline)

ItemEffect

(Evoked)

Mixed design example: Chawla et al. Mixed design example: Chawla et al. (1999)(1999)

Experimental Design

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