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Unformatted text preview: This Time • Experimental Design • Initial GLM Intro GLM • General Linear Model • Single subject fMRI modeling Single Subject fMRI Data • Data at one voxel – Rest vs. passive word listening • Is there an effect? A Linear Model Intensity Time = 1 2 + + error x 1 x 2 • “Linear” in parameters 1 & 2 Linear model, in image form… = + + 1 2 Y 1 1 x 2 2 x … in image matrix form… = + 2 1 Y X … in matrix form. X Y = + Y Y X N 1 N N 1 1 p p N: Number of scans, p: Number of regressors Linear Model Predictors • Signal Predictors – Block designs – Eventrelated responses • Nuisance Predictors – Drift – Regression parameters X Y Signal Predictors • Linear TimeInvariant system • LTI specified solely by – Stimulus function of experiment – Hemodynamic Response Function (HRF) • Response to instantaneous impulse Blocks Events X Y Convolution Examples Hemodynamic Response Function Predicted Response Block Design Experimental Stimulus Function X Y EventRelated LTI Pet Peeve • LTI/convolution approach implies antisymmetry – Shape of rise must match inverted shape of fall Bump here must match... ...bump here X Y HRF Models • Canonical HRF – Most sensitive if it is correct – If wrong, leads to bias and/or poor fit • E.g. True response may be faster/slower • E.g. True response may have smaller/ bigger undershoot SPM’s HRF X Y HRF Models • Smooth Basis HRFs – More flexible – Less interpretable • No one parameter explains the response – Less sensitive relative to canonical (only if canonical is correct) Gamma Basis Fourier Basis X Y HRF Models • Deconvolution – Most flexible • Allows any shape • Even bizarre, nonsensical ones – Least sensitive relative to canonical (again, if canonical is correct) Deconvolution Basis X Y Drift Models • Drift – Slowly varying – Nuisance variability – Even seen in cadavers! • A. Smith et al, NI, 1999, 9:526533 • Models – Linear, quadratic – Discrete Cosine Transform Discrete Cosine Transform Basis X Y Some Terminology Some Terminology Some Terminology • SPM (“Statistical Parametric Mapping”) is a massively univariate approach  meaning that a statistic (e.g., Tvalue) is calculated for every voxel  using the “General Linear Model” • Experimental manipulations are specified in a model (“design matrix”) which is fit to each voxel to estimate the size of the experimental effects (“parameter estimates”) in that voxel… • … on which one or more hypotheses (“contrasts”) are tested to make statistical inferences (“pvalues”), correcting for multiple comparisons across voxels (using “Random Field Theory”) • The parametric statistics assume continuousvalued data and...
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 Spring '10
 Cudeback
 Regression Analysis, Standard Deviation, general linear model, HRF

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