Experimental Design Christian Ruff With thanks to Rik

Experimental Design Christian Ruff With thanks to: Rik Henson Daniel Glaser

Image time-series Kernel Design matrix Realignment Smoothing General linear model Statistical parametric map (SPM) Statistical inference Normalisation Gaussian field theory p <0. 05 Template Parameter estimates

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

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

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

Evoked responses Differential event-related f. MRI 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 BOLD EPI f. MRI at 2 T, TR 3. 2 sec. Words presented every 16 secs; (i) studied words or (ii) new words • “Cognitive” interpretation hardly possible, but useful to define regions generally involved in the task

Differential responses Differential event-related f. MRI SPM{F} testing for evoked responses SPM{F} testing for differences BOLD EPI f. MRI at 2 T, TR 3. 2 sec. Words presented every 16 secs; (i) studied words or (ii) new words Parahippocampal responses to words studied words new words Peri-stimulus time {secs}

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

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

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 Naming Colours V R P Viewing A 1 A 2 Objects Visual Processing Object Recognition Phonological Retrieval Task (1/2) Stimuli (A/B) Example: Which neural structures support object recognition, independent of task (naming vs viewing)? B 1 B 2 (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 Rx. P; see later) Price et al, 1997 Common object recognition response (R)

Conjunctions

Two flavours of inference about 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 B 1 -B 2 SPM 5 offers two general ways to test the significance of conjunctions: p(A 1=A 2)<p + + p(B 1=B 2)<p “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) A 1 -A 2 Friston et al. (2005). Neuroimage, 25: 661 -7. Nichols et al. (2005). Neuroimage, 25: 653 -60.

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

Parametric Designs: General Approach • 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)

A linear parametric contrast Linear effect of time

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

Inverted ‘U’ response to increasing word presentation rate in the DLPFC Polynomial expansion: f(x) ~ b 1 x + b 2 x 2 +. . . …up to (N-1)th order for N levels (SPM 8 GUI offers polynomial expansion as option during creation of parametric modulation regressors) SPM{F} Quadratic E. g, F-contrast [0 1 0] on Quadratic Parameter => Linear Nonlinear parametric design matrix

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

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 m. J) – Assumptions: 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.

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

Factorial designs: Main effects and Interactions Colours Objects Stimuli (A/B) Task (1/2) Viewing Naming A 1 A 2 B 1 B 2 • Main effect of task: (A 1 + B 1) – (A 2 + B 2) • Main effect of stimuli: (A 1 + A 2) – (B 1 + B 2) • Interaction of task and stimuli: Can show a failure of pure insertion (A 1 – B 1) – (A 2 – B 2) interaction effect (Stimuli x Task) Colours Objects Viewing Colours Objects Naming

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

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

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) 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 Quad Gx. T Lin Quad

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

Psycho-physiological Interaction (PPI) 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) Context X source target

Psycho-physiological Interaction (PPI) 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) Set stimuli Context-sensitive connectivity Modulation of stimulus-specific responses source target

Psycho-physiological Interaction (PPI) V 1 activity SPM{Z} Attention V 5 Attentional modulation of V 1 - V 5 contribution V 5 activity V 1 time attention no attention V 1 activity

Psycho-physiological Interaction (PPI) 0 0 1 V 1 activity SPM{Z} V 5 activity time attention no attention V 1 activity V 1 Att V 1 x Att

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

Psycho-physiological Interaction (PPI) • PPIs tested by a GLM with form: y = (V 1 A). b 1 + V 1. b 2 + A. b 3 + e c = [1 0 0] • However, the interaction term of interest, V 1 A, is the product of V 1 activity and Attention block AFTER convolution with HRF • We are really interested in interaction at neural level, but: (HRF V 1) (HRF A) HRF (V 1 A) (unless A low frequency, e. g. , blocked; mainly problem for event-related PPIs) • SPM 5 can effect a deconvolution of physiological regressors (V 1), before calculating interaction term and reconvolving with the HRF – the “PPI button”

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