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

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

Overview Parametric designs 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 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: Neuronal structures underlying face recognition?

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

Differential event-related fMRI 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 the task BOLD EPI fMRI at 2T, TR 3.2sec. Words presented every 16 secs; (i) studied words or (ii) new words

Differential event-related fMRI 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

Overview Parametric designs 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

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!

recognition response (R) Conjunctions Task (1/2) Viewing Naming Example: Which neural structures support object recognition, independent of task (naming vs viewing)? Stimuli (A/B) Objects Colours A1 A2 B2 B1 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) Common object recognition response (R) Price et al, 1997

Conjunctions

Two flavours of inference about conjunctions SPM5 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) A1-A2 B1-B2 p(A1=A2)<p + p(B1=B2)<p Friston et al. (2005). Neuroimage, 25:661-7. Nichols et al. (2005). Neuroimage, 25:653-60.

Overview Parametric designs 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

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}

Nonlinear parametric design matrix SPM{F} E.g, F-contrast [0 1 0] on Quadratic Parameter => Quadratic Linear 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 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) 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 Parametric designs 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

Factorial designs: Main effects and Interactions B2 B1 Task (1/2) Viewing Naming Stimuli (A/B) Objects Colours 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 (Stimuli x Task) 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 cross-over and simple We can selectively inspect our data for one or the other by masking during inference

Overview Parametric designs 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

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: Gen/Rep (Categorical, 2 levels) Time (Parametric, 6 levels) Time effects modelled with both linear and quadratic components… G-R Time Lin Time Quad G x T Lin G x T Quad

Overview Parametric designs 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

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 source target X

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 Context-sensitive connectivity source target stimuli Modulation of stimulus-specific responses source target

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

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

Overview Parametric designs 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