Experimental Design

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## Experimental Design

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**Experimental Design**Christian Ruff 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: • Neuronal structures underlying 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 the 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**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**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)**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.**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**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.**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**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**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**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…**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**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 = (V1A).b1 + V1.b2 + A.b3 + e c = [1 0 0] • However, the interaction term of interest, V1A, 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**• 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