Experimental design of fMRI studies

Methods & models for fMRI data analysis12 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 Christian Ruff

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

• Categorical designsSubtraction - Pure insertion, evoked / differential

responses

Conjunction - Testing multiple hypotheses

• Parametric designsLinear - Adaptation, cognitive dimensions

Nonlinear - Polynomial expansions, neurometric functions

• Factorial designsCategorical - Interactions and pure insertion

Parametric - Linear and nonlinear interactions

- Psychophysiological Interactions

Overview

• 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:

Cognitive subtraction

-- 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 task Interaction of process and task ??

• Same stimuli, different taskSame stimuli, different task

Cognitive subtraction: Baseline problems

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

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

Evoked responses

Differential responses

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

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 pure insertionunder assumption of pure insertion

A categorical analysis

• Categorical designsSubtraction - Pure insertion, evoked / differential

responses

Conjunction - Testing multiple hypotheses

• Parametric designsLinear - Adaptation, cognitive dimensions

Nonlinear - Polynomial expansions, neurometric functions

• Factorial designsCategorical - Interactions and pure insertion

Parametric - Linear and nonlinear interactions

- Psychophysiological Interactions

Overview

• 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.

• Note: the contrasts entering a conjunction must be orthogonal !

Conjunctions

Conjunctions

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 V,RV,RColour viewingColour viewing VVObject namingObject naming P,V,RP,V,RColour 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]

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

Price et al. 1997

Common object Common object recognition response (Rrecognition response (R))

Conjunctions

• Test of Test of global null hypothesisglobal 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?”

Null hypothesis:Null hypothesis: No contrast is significant: No contrast is significant: k = 0k = 0

does not correspond to a logical AND !does not correspond to a logical AND !

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

““Which voxels show, for each specified Which voxels show, for each specified contrast, significant effects?” contrast, significant effects?”

Null hypothesis:Null hypothesis: Not all contrasts are significant: Not all contrasts are significant: k < nk < n

corresponds to a logical ANDcorresponds to a logical AND

A1-A2

B

1-B

2 p(A1-A2) <

+p(B1-B2) <

+

Friston et al.Friston et al. (2005). Neuroimage, Neuroimage, 25:661-667.25:661-667.

Nichols et al. (2005). Nichols et al. (2005). Neuroimage, Neuroimage, 25:653-660.25:653-660.

Two types of conjunctions

SPM offers both conjunctions

Friston et al.Friston et al. 2005, Neuroimage, Neuroimage, 25:661-667.25:661-667.

specificity

specificity

Global null:k = 0

Conjunction null:k < n

F-test vs. conjunction based on global null

Friston et al.Friston et al. 2005, Neuroimage, Neuroimage, 25:661-667.25:661-667.

Using the conjunction null is easy to interpret, but can be very conservative

Friston et al.Friston et al. 2005, Neuroimage, Neuroimage, 25:661-667.25:661-667.

• Categorical designsSubtraction - Pure insertion, evoked / differential

responses

Conjunction - Testing multiple hypotheses

• Parametric designsLinear - Adaptation, cognitive dimensions

Nonlinear - Polynomial expansions, neurometric functions

• Factorial designsCategorical - Interactions and pure insertion

Parametric - Linear and nonlinear interactions

- Psychophysiological Interactions

Overview

Parametric designs

• Parametric designs approach the baseline problem by:

– Varying the stimulus-parameter of interest on a continuum, in multiple (n>2) steps...

– ... and relating measured BOLD signal to this parameter

• Possible tests for such relations are manifold:• Linear

• Nonlinear: Quadratic/cubic/etc. (polynomial expansion)

• Model-based (e.g. predictions from learning models)

Parametric modulation of regressors

→ → 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 + b3 x3 ...

Lin

ear

Qu

adr

atic

F-contrast [0 1 0] on F-contrast [0 1 0] on quadratic parameterquadratic parameter

SPM5 offers polynomial expansion SPM5 offers polynomial expansion as option for parametric modulation as option for parametric modulation

of regressorsof regressors

Büchel et al. 1996, NeuroImage 4:60-66

Parametric modulation of regressors by time

Büchel et al. 1998, NeuroImage 8:140-148

“User-specified” parametric modulation of regressors

Polynomial expansion&orthogonalisation

Büchel et al. 1998, NeuroImage 8:140-148

Investigating neurometric functions (= relation between a stimulus property and the neuronal

response)

Stimulusawareness

Stimulusintensity

PainintensityPain threshold: 410 mJ

P1 P2 P3 P4

P0-P4: Variation of intensity of a laser stimulus applied to the right hand (0, 300, 400, 500, and 600 mJ)

Büchel et al. 2002, J. Neurosci. 22:970-976

Neurometric functions

Stimulus presenceStimulus presence

Pain intensityPain intensity

Stimulus intensityStimulus intensity

Büchel et al. 2002, J. Neurosci. 22:970-976

Model-based regressors

• general idea:generate predictions from a computational model, e.g. of learning or decision-making

• Commonly used models:– Rescorla-Wagner learning model– temporal difference (TD) learning model

• use these predictions to define regressors

• include these regressors in a GLM and test for significant correlations with voxel-wise BOLD responses

TD model of reinforcement learning

• appetitive conditing with pleasant taste reward• activity in ventral striatum and OFC correlated with TD prediction error at

the time of the CS

O‘Doherty et al. 2003, Neuron

)()1()()(

)1(

tVtVtRtV

tV

• Categorical designsSubtraction - Pure insertion, evoked / differential

responses

Conjunction - Testing multiple hypotheses

• Parametric designsLinear - Adaptation, cognitive dimensions

Nonlinear - Polynomial expansions, neurometric functions

• Factorial designsCategorical - Interactions and pure insertion

Parametric - Linear and nonlinear interactions

- Psychophysiological Interactions

Overview

Main effects and interactions

A1A1 A2A2

B2B2B1B1

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

Stim

uli (

A/B

)S

timul

i (A

/B)

Obj

ects

Col

ours

Obj

ects

Col

ours

Colours Objects Colours ObjectsColours Objects Colours Objects

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

ViewingViewing NamingNaming

• 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 – B2)(A1 – B1) – (A2 – B2)

Parametric interactions

p < 0.05, correctedrandom effects, n=16

during learning, predictive tones

- increasingly activate V1 & PUT in the absence of predicted visual stimuli,

- increasingly deactivate V1 & PUT in the presence of predicted vis. stimuli

Significant four-way interaction in V1 and putamen:

V1PUT

-60

-40

-20

0

20

40

60

80

100

120

Be

ta

CS+ (TO

)

CS+ (CS

)

CS- (TO

)

CS- (CS

)

A+ A-

V+ V- V+ V-

V+ V- V+ V-

A+ A-

Primary visual cortex

0 100 200 300 400 500 600 700 8000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Trial

As

so

cia

tio

n

CS+ A+

CS+ A-

CS- A+

CS- A-

Rescorla-Wagner learningcurves (=0.075):

den Ouden et al. 2009, Cereb. Cortex

Psycho-physiological interactions (PPI)

We can replace one main effect in the GLM by the time series of an area that shows this main effect.

E.g. let's replace the main effect of stimulus type by the time series of area V1:

Task factorTask A Task B

Sti

m 1

Sti

m 2

Sti

mu

lus

fact

or

TA/S1 TB/S1

TA/S2 TB/S2

e

βVTT

βV

TT y

BA

BA

3

2

1

1 )(

1

)(

e

βVTT

βV

TT y

BA

BA

3

2

1

1 )(

1

)(

e

βSSTT

βSS

TT y

BA

BA

321

221

1

)( )(

)(

)(

e

βSSTT

βSS

TT y

BA

BA

321

221

1

)( )(

)(

)(

GLM of a 2x2 factorial design:

main effectof task

main effectof stim. type

interaction

main effectof taskV1 time series main effectof stim. typepsycho-physiologicalinteraction

PPI example: attentional modulation of V1→V5

attention

no attention

V1 activity

V5 a

ctiv

ity

SPM{Z}

time

V5 a

ctiv

ity

Friston et al. 1997, NeuroImage 6:218-229Büchel & Friston 1997, Cereb. Cortex 7:768-778

V1V1

V1 x Att.V1 x Att.

=

V5V5

V5V5

Attention

PPI: interpretation

Two possible interpretations of the PPI

term:

V1

Modulation of V1V5 by attention

Modulation of the impact of attention on V5 by V1.

V1V1 V5V5 V1

V5V5

attentionattention

V1V1

attentionattention

e

βVTT

βV

TT y

BA

BA

3

2

1

1 )(

1

)(

e

βVTT

βV

TT y

BA

BA

3

2

1

1 )(

1

)(

Thank you