Experimental Design Course: Methods and models for fMRI data analysis in neuroeconomics Christian Ruff Laboratory for Social and Neural Systems Research IEW, University of Zurich ICN & FIL, University College London With thanks to: Rik Henson Daniel Glaser Course: Methods and models for fMRI data analysis in neuroeconomics Christian Ruff Laboratory for Social and Neural Systems Research IEW, University of Zurich ICN & FIL, University College London With thanks to: Rik Henson Daniel Glaser

RealignmentSmoothing Normalisation General linear model Statistical parametric map (SPM) Image time-series Parameter estimates Design matrix Template Kernel Gaussian field theory p <0.05 Statisticalinference

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

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

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

Differential event-related fMRI Parahippocampal responses to words BOLD EPI fMRI at 2T, TR 3.2sec. Words presented every 16 secs; (i) studied words or (ii) new words SPM{F} testing for evoked responses Evoked responses “Baseline” here corresponds to session mean (and thus processing during “rest”) “Baseline” here corresponds to session mean (and thus processing during “rest”) Null events or long SOAs essential for estimation Null events or long SOAs essential for estimation “Cognitive” interpretation hardly possible, but useful to define regions generally involved in task “Cognitive” interpretation hardly possible, but useful to define regions generally involved in task “Baseline” here corresponds to session mean (and thus processing during “rest”) “Baseline” here corresponds to session mean (and thus processing during “rest”) Null events or long SOAs essential for estimation Null events or long SOAs essential for estimation “Cognitive” interpretation hardly possible, but useful to define regions generally involved in task “Cognitive” interpretation hardly possible, but useful to define regions generally involved in task

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

Experimental design Word generationG Word repetitionR R G R G R G R G R G R G Experimental design Word generationG Word repetitionR R G R G R G R G R G R G G - R = Intrinsic word generation …under assumption of pure insertion G - R = Intrinsic word generation …under assumption of pure insertion A categorical analysis

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

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 commonalitiesOne 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”A test for such activation common to several independent contrasts is called “Conjunction” Conjunctions can be conducted across a whole variety of different contexts:Conjunctions can be conducted across a whole variety of different contexts: tasks tasks stimuli stimuli 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! 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 commonalitiesOne 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”A test for such activation common to several independent contrasts is called “Conjunction” Conjunctions can be conducted across a whole variety of different contexts:Conjunctions can be conducted across a whole variety of different contexts: tasks tasks stimuli stimuli 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, independent of task (naming vs viewing)? Example: Which neural structures support object recognition, independent of task (naming vs viewing)? A1A1A2A2 B2B2B1B1 Task (1/2) Naming Viewing Stimuli (A/B) Colours Objects Visual Processing V Object Recognition R Phonological Retrieval P (Object - Colour viewing) & (Object - Colour naming)  [ ] & [ ]  [ R,V - V ] & [ P,R,V - P,V ] = R & R = R (assuming no interaction RxP; see later) Visual Processing V Object Recognition R Phonological Retrieval P (Object - Colour viewing) & (Object - Colour naming)  [ ] & [ ]  [ R,V - V ] & [ P,R,V - P,V ] = R & R = R (assuming no interaction RxP; see later) ConjunctionsConjunctions Price et al, 1997 Common object recognition response (R ) Common object recognition response (R )

ConjunctionsConjunctions

SPM8 offers two general ways to test the significance of conjunctions: SPM8 offers two general ways to test the significance of conjunctions: Test of global null hypothesis: Significant set of consistent effectsTest 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 effectsTest 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)Choice of test depends on hypothesis and congruence of contrasts; the global null test is more sensitive (i.e., when direction of effects hypothesised) SPM8 offers two general ways to test the significance of conjunctions: SPM8 offers two general ways to test the significance of conjunctions: Test of global null hypothesis: Significant set of consistent effectsTest 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 effectsTest 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)Choice of test depends on hypothesis and congruence of contrasts; the global null test is more sensitive (i.e., when direction of effects hypothesised) Two flavours of inference about conjunctions A1-A2 B1-B2 p(A1=A2)<p + + p(B1=B2)<p + + Friston et al.Neuroimage, 25: Friston et al. (2005). Neuroimage, 25: Nichols et al. (2005). Neuroimage, 25: Friston et al.Neuroimage, 25: Friston et al. (2005). Neuroimage, 25: Nichols et al. (2005). Neuroimage, 25:

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

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

Linear effect of time Linear effect of time A linear parametric contrast

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

Inverted ‘U’ response to increasing word presentation rate in the DLPFC Inverted ‘U’ response to increasing word presentation rate in the DLPFC SPM{F}SPM{F} Polynomial expansion: f(x) ~ f(x) ~ b 1 x + b 2 x …up to (N-1)th order for N levels Polynomial expansion: f(x) ~ f(x) ~ b 1 x + b 2 x …up to (N-1)th order for N levels Linear Quadratic E.g, F-contrast [0 1 0] on Quadratic Parameter => E.g, F-contrast [0 1 0] on Quadratic Parameter => Nonlinear parametric design matrix (SPM8 GUI offers polynomial expansion as option during creation of parametric modulation regressors)

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

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) 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) Büchel et al. (2002). The Journal of Neuroscience, 22: – : – Assumptions:

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

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

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

A1A1A2A2 B2B2B1B1 Task (1/2) Naming Viewing Naming Viewing Stimuli (A/B) Colours Objects Colours Objects Colours Objects Colours Objects Colours Objects interaction effect (Task x Stimuli) (Task x Stimuli) interaction effect (Task x Stimuli) (Task x Stimuli) ViewingViewingNamingNaming Factorial designs: Main effects and Interactions Main effect of task:(A1 + B1) – (A2 + B2)Main effect of task:(A1 + B1) – (A2 + B2) Main effect of stimuli: (A1 + A2) – (B1 + B2)Main effect of stimuli: (A1 + A2) – (B1 + B2) Interaction of task and stimuli: Can show a failure of pure insertionInteraction of task and stimuli: Can show a failure of pure insertion (A1 – B1) – (A2 – B2) Main effect of task:(A1 + B1) – (A2 + B2)Main effect of task:(A1 + B1) – (A2 + B2) Main effect of stimuli: (A1 + A2) – (B1 + B2)Main effect of stimuli: (A1 + A2) – (B1 + B2) Interaction of task and stimuli: Can show a failure of pure insertionInteraction of task and stimuli: Can show a failure of pure insertion (A1 – B1) – (A2 – B2)

Interactions and pure insertion Object-naming-specific activations Context: no naming naming adjusted rCBF Components Visual processingV Object recognition R Phonological retrievalP InteractionRxP Interaction (name object - colour) - (view object - colour)  [ ] - [ ] = [ P,R,V + RxP - P,V ] - [ R,V - V ] = RxP Components Visual processingV Object recognition R Phonological retrievalP InteractionRxP Interaction (name object - colour) - (view object - colour)  [ ] - [ ] = [ P,R,V + RxP - P,V ] - [ R,V - V ] = RxP

Interactions and pure insertion Interactions:cross-overandsimple We can selectively inspect our data for one or the other by masking during inference Interactions:cross-overandsimple A1 A2 B1 B2

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

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

Factorial Design with 2 factors: 1. Gen/Rep (Categorical, 2 levels) 2. Time (Parametric, 6 levels) Time effects modelled with both linear and quadratic components… Factorial Design with 2 factors: 1. Gen/Rep (Categorical, 2 levels) 2. Time (Parametric, 6 levels) Time effects modelled with both linear and quadratic components… G-R Time Lin Time Lin G x T Lin G x T Lin Time Quad Time Quad G x T Quad G x T Quad F-contrast tests for nonlinear Generation-by-Time interaction (including both linear and Quadratic components) F-contrast tests for nonlinear Generation-by-Time interaction (including both linear and Quadratic components) Nonlinear Parametric Interaction

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

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) 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)

stimulistimuli Modulation of stimulus-specific responses sourcesource targettarget SetSet Context-sensitiveconnectivityContext-sensitiveconnectivity 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) 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)

SPM{Z} Attentional modulation of V1 - V5 contribution Attentional modulation of V1 - V5 contribution AttentionAttention V1V1 V5V5 attention no attention V1 activity V5 activity time V1 activity Psycho-physiological Interaction (PPI)

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

adjusted rCBF medial parietal activity FacesFaces ObjectsObjects Stimuli: Faces or objects Stimuli: PPCPPC ITIT SPM{Z}SPM{Z} Psycho-physiological Interaction (PPI)

PPIs tested by a GLM with form:PPIs tested by a GLM with form: y = (V1  A).b 1 + V1.b 2 + A.b 3 + ec = [1 0 0] However, the interaction term of interest, V1  A, is the product of V1 activity and Attention block AFTER convolution with HRFHowever, 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: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”SPM5 can effect a deconvolution of physiological regressors (V1), before calculating interaction term and reconvolving with the HRF – the “PPI button” PPIs tested by a GLM with form:PPIs tested by a GLM with form: y = (V1  A).b 1 + V1.b 2 + A.b 3 + ec = [1 0 0] However, the interaction term of interest, V1  A, is the product of V1 activity and Attention block AFTER convolution with HRFHowever, 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: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”SPM5 can effect a deconvolution of physiological regressors (V1), before calculating interaction term and reconvolving with the HRF – the “PPI button” Psycho-physiological Interaction (PPI)

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

Simultaneously measuring effects that are:Simultaneously measuring effects that are: –transient (“item- or event-related”) –sustained (“state- or epoch-related”) What is the best design to estimate both…?What is the best design to estimate both…? Simultaneously measuring effects that are:Simultaneously measuring effects that are: –transient (“item- or event-related”) –sustained (“state- or epoch-related”) What is the best design to estimate both…?What is the best design to estimate both…? Mixed Designs

Sensitivity, or “efficiency”, e:Sensitivity, or “efficiency”, e: e(c,X) = { c T (X T X) -1 c } -1 e(c,X) = { c T (X T X) -1 c } -1 X T X represents covariance of regressors in design matrixX T X represents covariance of regressors in design matrix High covariance increases elements of (X T X) -1High covariance increases elements of (X T X) -1 => So, when correlation between regressors is high, sensitivity to each regressor alone is low Sensitivity, or “efficiency”, e:Sensitivity, or “efficiency”, e: e(c,X) = { c T (X T X) -1 c } -1 e(c,X) = { c T (X T X) -1 c } -1 X T X represents covariance of regressors in design matrixX T X represents covariance of regressors in design matrix High covariance increases elements of (X T X) -1High covariance increases elements of (X T X) -1 => So, when correlation between regressors is high, sensitivity to each regressor alone is low A bit more formally…”Efficiency”

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

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

Efficiency = 54 (Item Effect) Design Matrix (X) Correlation =.78 Blocks = 40s, Randomised SOA min = 2s Better! Item 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 epoch and event-related covariatesRandomised, long SOAs between events (targets) to decorrelate epoch and event-related covariates Attention modulates BOTH:Attention modulates BOTH: –1) baseline activity (state-effect, additive) –2) evoked response (item-effect, multiplicative) 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 epoch and event-related covariatesRandomised, long SOAs between events (targets) to decorrelate epoch and event-related covariates Attention modulates BOTH:Attention modulates BOTH: –1) baseline activity (state-effect, additive) –2) evoked response (item-effect, multiplicative) Mixed design example: Chawla et al. (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) State Effect (Baseline) Item Effect (Evoked) Mixed design example: Chawla et al. (1999)