Experimental Design

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

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

Overview • 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

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

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

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

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}

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

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!

Conjunctions Task (1/2) NamingViewing A1 A2 Colours Objects Stimuli (A/B) B1 B2 Common object recognition response (R) Price et al, 1997 Example: Which neural structures support object recognition, independent of task (naming vs viewing)? Visual Processing V Object Recognition R Phonological Retrieval P (Object - Colour viewing) & (Object - Colour naming)  [1 -1 0 0] & [0 0 1 -1] [ R,V - V ] & [ P,R,V - P,V ] = R & R = R (assuming no interaction RxP; see later)

Conjunctions

Two flavours of inference about conjunctions + + p(B1=B2)<p p(A1=A2)<p B1-B2 A1-A2 • SPM8 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) Friston et al.(2005). Neuroimage, 25:661-7. Nichols et al. (2005). Neuroimage, 25:653-60.

Parametric Designs: General Approach • 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 : • Linear • Nonlinear: Quadratic/cubic/etc. • „Data-driven“ (e.g., neurometric functions) • Model-based

A linear parametric contrast Linear effect of time

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

Nonlinear parametric design matrix Quadratic Linear SPM{F} E.g, F-contrast [0 1 0] on Quadratic Parameter => Inverted ‘U’ response to increasing word presentation rate in the DLPFC Polynomial expansion: f(x) ~ b1 x + b2 x2 + ... …up to (N-1)th order for N levels (SPM8 GUI offers polynomial expansion as option during creation of parametric modulation regressors)

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

Parametric Designs: Neurometric functions • Assumptions: 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: 970-6

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

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

Factorial designs: Main effects and Interactions Task (1/2) Naming Viewing A1 A2 Colours Objects Stimuli (A/B) B1 B2 • 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 (Task x Stimuli) Colours Objects Colours Objects Viewing Naming

Interactions and pure insertion Components Visual processing V Object recognition R Phonological retrieval P Interaction RxP Interaction (name object - colour) - (view object - colour)  [1 -1 0 0] - [0 0 1 -1] = [ P,R,V + RxP- P,V ] - [ R,V - V ] = RxP Object-naming-specific activations adjusted rCBF Context: no naming naming

Interactions and pure insertion Interactions: cross-over and simple We can selectively inspect our data for one or the other by masking during inference A1 A2B1 B2 A1 A2B1 B2

Linear Parametric Interaction A (Linear) Time-by-Condition Interaction (“Generation strategy”?) Contrast: [5 3 1 -1 -3 -5][-1 1] = [-5 5 -3 3 -1 1 1 -1 3 -3 5 -5]

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

Psycho-physiological Interaction (PPI) Context X source target 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) stimuli Set Context-sensitive connectivity Modulation of stimulus-specific responses source source target target 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} Attention V1 V5 V1 activity time attention V5 activity no attention Attentional modulation of V1 - V5 contribution V1 activity

Psycho-physiological Interaction (PPI) SPM{Z} V1 Att V1 x Att 0 0 1 V1 activity time attention V5 activity no attention V1 activity

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

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”

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

A bit more formally…”Efficiency” • 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 => So, when correlation between regressors is high, sensitivity to each regressor alone is low

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

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

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

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)

Mixed design example: Chawla et al. (1999) V5 Motion change under attention to motion (red) or color (blue) State Effect (Baseline) Item Effect (Evoked) V4 Color change under attention to motion (red) or color (blue) Mixed Designs (Chawla et al 1999)

Experimental Design