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Experimental Design

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

  2. 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

  3. 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

  4. 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“

  5. 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 !

  6. 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

  7. 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}

  8. 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

  9. 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

  10. 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!

  11. 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)

  12. Conjunctions

  13. 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.

  14. 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

  15. 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

  16. A linear parametric contrast Linear effect of time

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

  18. 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)

  19. 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

  20. 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

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

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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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]

  29. 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…

  30. 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

  31. 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)

  32. 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)

  33. 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

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

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

  36. 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”

  37. 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