Experimental design of fMRI studies

Methods & models for fMRI data analysis in neuroeconomicsNovember 2010

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

Realignment Smoothing

Normalisation

General linear model

Statistical parametric map (SPM)Image time-series

Parameter estimates

Design matrix

Template

Kernel

Gaussian field theory

p <0.05

Statisticalinference

• 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

- P implicit in control condition?

„Queen!“ „Aunt Jenny?“

• „Related“ stimuli

- Several components differ!

• „Distant“ stimuli

Name Person! Name Gender!

- Interaction of task and stimuli (i.e. do task differences depend on stimuli chosen)?

• Same stimuli, different task

Cognitive subtraction: Baseline problems

Experimental design

Word generation GWord repetition R

R G R G R G R G R G R G

G - R = Intrinsic word generation

…under 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, independent of task (naming vs viewing)?

A1 A2

B2B1

Task (1/2)

Viewing Naming

Stim

uli (

A/B

)

Obj

ects

C

olou

rs

Visual Processing V Object Recognition RPhonological Retrieval P

Object viewing (B1) V,RColour viewing (A1) VObject naming (B2) P,V,RColour naming (A2) P,V

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

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

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

Price et al. 1997

Common object recognition response (R)

A1 B1 A2 B2

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?”

Null hypothesis: No contrast is significant: k = 0

does not correspond to a logical AND !

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

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

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

corresponds to a logical AND

A1-A2

B

1-B

2 p(A1-A2) <

+p(B1-B2) <

+

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

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

Two types of conjunctions

SPM offers both types of conjunctions

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

specificity

sensitivity

Global null:k = 0

(or k<1)

Conjunction null:k < n

F-test vs. conjunction based on global null

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

grey area:bivariate t-distriutionunder global null hypothesis

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

Friston et al. 2005, Neuroimage, 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 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 presence

Pain intensity

Stimulus 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– Bayesian learners

• use these predictions to define regressors

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

Model-based fMRI analysis

Gläscher & O‘Doherty 2010, WIREs Cogn. Sci.

Model-based fMRI analysis

Gläscher & O‘Doherty 2010, WIREs Cogn. Sci.

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

Learning of dynamic audio-visual associations

CS Response

Time (ms)

0 200 400 600 800 2000 ± 650

or

Target StimulusConditioning Stimulus

or

TS

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

p(f

ace)

trial

CS1

CS2

den Ouden et al. 2010, J. Neurosci .

Bayesian learning model

observed events

probabilistic association

volatility

k

vt-1 vt

rt rt+1

ut ut+1

)exp(,~,|1 ttttt vrDirvrrp

)exp(,~,|1 kvNkvvp ttt

1kp

1: 1 1 1 1 1 1 1: 1 1 1

1: 1

1:

1: 1

prediction: , , , , , ,

, ,update: , ,

, ,

t t t t t t t t t t t t t

t t t t t

t t t

t t t t t t t

p r v K u p r r v p v v K p r v K u dr dv

p r v K u p u rp r v K u

p r v K u p u r dr dv dK

Behrens et al. 2007, Nat. Neurosci.

400 440 480 520 560 600

trial

CS1volatilitytarget

400 440 480 520 560 6000

0.2

0.4

0.6

0.8

1

p(F

|CS

)

trial

CS1CS2

100 200 300 400 500

10

20

30

40

50

60

70

80100 200 300 400 500

5

10

15

20

25

30

35

40

45

50

po

ster

ior

pd

f

Probability Volatility

po

ster

ior

pd

f

Putamen Premotor cortex

Stimulus-independent prediction error

p < 0.05 (SVC)

p < 0.05 (cluster-level whole- brain corrected)

p(F) p(H)-2

-1.5

-1

-0.5

0

BO

LD

re

sp.

(a.u

.)

p(F) p(H)-2

-1.5

-1

-0.5

0

BO

LD

re

sp.

(a.u

.)

den Ouden et al. 2010, J. Neurosci.

• 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

A1 A2

B2B1

Task (1/2)Viewing Naming

Stim

uli (

A/B

)

Obj

ects

Col

ours

Colours Objects Colours Objects

interaction effect (Stimuli x Task)

Viewing Naming

• 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)

Example: evidence for inequality-aversion

Tricomi et al. 2010, Nature

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

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

V1

V1 x Att.

=

V5

V5

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.

V1 V5 V1

V5

attention

V1

attention

e

βVTT

βV

TT y

BA

BA

3

2

1

1 )(

1

)(

Thank you

Parametric modulation of regressors

→ inverted ‘U’ response toincreasing word presentation

rate in the DLPFCSPM{F}

Polynomial expansion:f(x) ~ b1 x + b2 x2 + b3 x3 ...

Lin

ear

Qu

adr

atic

F-contrast [0 1 0] on quadratic parameter

SPM offers polynomial expansion as option for parametric modulation of

regressors

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