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Overview of fMRI Analysis Andy James fMRI Methods Journal Club Tuesday, February 8, 2005 Experiment Steps • • • • • • • Hypothesis formation In practice, data Subject selection analysis will dictate Paradigm design all other steps, Data collection including what hypotheses can Data preprocessing feasibly be answered! Data Analysis Publication Classifying statistical approaches By response / dependent variable • qualitative (accuracy, keypress) • quantitative (RT, BOLD) By model dependence • Model dependent (t-test, GLM, Fourier) • Model independent (ICA, correlational) Model-dependent: t-test Question: By how many standard deviations do response samples for two tasks differ? x-y t= s xy (Huettel, 2004) Statistical Parametric Map (SPM) Each voxel represents a statistical value or probability (i.e. a t-score). Map is color coded for ease of reading. (Peterson et al., 1990) Model-dependent: General Linear Model (GLM) • • Made popular by SPM (Friston, 1995) GLM is a linear regression in which a) Model is constructed from stimulus paradigm b) Data is fitted to model c) Goodness of Fit is evaluated • With fMRI, typically univariate (just one dependent variable: BOLD activity) Assumption: Relationships are LINEAR and ADDITIVE Understanding GLM Equations y(t) = b * x(t) + c + e(t) y(t) : Dependent / Response Variable x(t) : Independent / Predictor Variable e(t): error b: beta weight relating x(t) to y(t). c: constant (baseline activity) Understanding GLM Equations Time y(t) = b * x(t) + c + e(t) 300 312 298 305 = b* 452 465 445 0 0 0 0 1 1 1 + 300 + 300 + 300 + 300 + 300 + 300 + 300 + 0 + 12 + (-2) + 5 + 2 + 15 + (-5) Understanding GLM Equations y(t) = b * x(t) + c + e(t) What value of b best fits these equations? (Least Sum of Squares) 300 312 298 305 452 465 445 = = = = = = = 0 0 0 0 b b b + 300 + 300 + 300 + 300 + 300 + 300 + 300 + 0 + 12 + (-2) + 5 + 2 + 15 + (-5) Note: Still univariate Graphical Model representation Graphical model for two independent variables: x1(t) = visual stimulation x2(t) = auditory stimulation Test yourself: Univariate or multivariate? Time y(t) = b1*x1(t) + b2*x2(t) + c + e(t) x1(t) x2(t) y(t) = b1*x1(t) + b2*x2(t) + b3*[x1(t)*x2(t)] + c + e(t) Interaction effects: “is the whole greater than the sum of the parts?” ex: thalamic response to simultaneous visual and auditory stimuli Time Modeling Interaction Effects x1(t) x2(t) x1(t)*x2(t) Modeling the Whole Brain • BrainVoyager software calculates a separate GLM for each voxel • Is SPM software’s GLM multivariate? • EPI: 128 x 128 x 36 voxels = ~80,000 voxels • With a = .05; expect 4,000 false positives! How can we control for this false positive rate? Controlling for False Positives • Bonferonni correction: a / # comparisons .05 / 80,000 a = .0000006! Too conservative! • Spatial smoothing: Clump voxels into groups (ex: cubes of 27 voxels) to reduce # comparisons (80,0003,000) • Clustering Only include significantly active voxels that are adjacent to N significantly active voxels Multicollinearity • b value assess how well predictor individually predicts response. • What if two IVs are correlated? (i.e. leg length) • Can GLM handle multicollinearity? GLM: The Model is Everything! • Trash in, trash out – bad model = meaningless findings • A “good” GLM is one that can… …model interaction effects …test viability of additional predictors (“F-drop”) …assess correlations among independent variables • Can BrainVoyager and SPM do this? Multiple Subjects Statistics • Requires standardization of brains (MNI) • Fixed-effects analyses – Only examines within-session variance • Mixed or Random-effects analyses – – – – Incorporate within- and across-session variance Allows broader generalization to population More conservative Requires large N. (“large” > 10) Non-GLM approaches • Structural equation modeling – Make assumptions of directionality of influences (i.e. frontal SMA Motor strip) – Test strength of directional influences – BUT bound by model! • Fourier analysis – Model brain response by stimulus frequency Fourier analysis (Huettel, 2004) Next session: Temporally Invariant Techniques • • • • Factor Analysis Independent Component Analysis (ICA) Temporal Clustering Analysis (TCA) Connectivity Analysis (“correlational”) – within-condition interregional covariate analysis (WICA) – all other correlational approaches are subset References • Huettel SA, Song AW & McCarthy G. (2004). Functional Magnetic Resonance Imaging. Sinauer Associates Inc; Sunderland, Massachusetts USA. • Peterson SE, Fox PT, Snyder AZ & Raichle ME. (1990). Activation of the extrastriate and frontal cortical areas by visual words and word-like stimuli. Science, 249(4972), 1041-1044. • SPM software: http://www.fil.ion.ucl.ac.uk/spm/