The General Linear Model SPM for fMRI Course Peter Zeidman Methods Group Wellcome Trust Centre for Neuroimaging Overview • Basics of the GLM • Improving the model • SPM files http://www.fil.ion.ucl.ac.uk/~pzeidman/teaching/GLM.ppt BASICS OF THE GLM Image time-series Realignment Spatial filter Design matrix Smoothing General Linear Model Statistical Parametric Map Statistical Inference Normalisation Anatomical reference Parameter estimates RFT p <0.05 A very simple fMRI experiment One session Passive word listening versus rest 7 cycles of rest and listening Blocks of 6 scans with 7 sec TR Question: Is there a change in the BOLD response between listening and rest? Modelling the measured data Why? How? data Make inferences about effects of interest 1. Decompose data into effects and error 2. Form statistic using estimates of effects and error linear model effects estimate error estimate statistic Time =1 BOLD signal + 2 x1 + x2 y x11 x2 2 e error Single voxel regression model e Mass-univariate analysis: voxel-wise GLM p 1 1 1 p y N = N X y X e e ~ N (0, I ) 2 + N e Model is specified by 1. Design matrix X 2. Assumptions about e N: number of scans p: number of regressors The design matrix embodies all available knowledge about experimentally controlled factors and potential confounds. Voxel-wise time series analysis Model specification Time Parameter estimation Hypothesis Statistic BOLD signal single voxel time series SPM IMPROVING THE MODEL What are the problems of this model? 1. BOLD responses have a delayed and dispersed form. 2. The BOLD signal includes substantial amounts of low-frequency noise (eg due to scanner drift). 3. Due to breathing, heartbeat & unmodeled neuronal activity, the errors are serially correlated. This violates the assumptions of the noise model in the GLM HRF Problem 1: Shape of BOLD response Solution: Convolution model Expected BOLD HRF Impulses = t f g (t ) f ( ) g (t )d 0 expected BOLD response = input function impulse response function (HRF) Convolution model of the BOLD response Convolve stimulus function with a canonical hemodynamic response function (HRF): t f g (t ) f ( ) g (t )d 0 HRF Problem 2: Low-frequency noise Solution: High pass filtering discrete cosine transform (DCT) set blue = black = green = account red = into data mean + low-frequency drift predicted response, taking into low-frequency drift predicted response, NOT taking account low-frequency drift High pass filtering discrete cosine transform (DCT) set Problem 3: Serial correlations et aet 1 t with t ~ N (0, 2 ) 1st order autoregressive process: AR(1) N Cov(e) autocovariance function N Multiple covariance components Ci V 2 i V jQ j ei ~ N (0, Ci ) enhanced noise model at voxel i V = 1 error covariance components Q and hyperparameters Q1 + 2 Q2 Estimation of hyperparameters with ReML (Restricted Maximum Likelihood). SPM FILES 1.Specify the model 1.Specify the model SPM files (after specifying the model) SPM.mat (after specifying the model) SPM.xY – Filenames of fMRI volumes SPM.Sess – Per-session experiment timing SPM.xX – Design matrix For documentation on these structures, type: help spm_spm SPM.xX (Design matrix) Design matrix imagesc(SPM.xX.X); SPM.xX (Design matrix) Confounds (HPF) imagesc(SPM.xX.K.X0); 2. Estimate the model SPM files (after estimation) SPM files (after estimation) beta_0001.nii – beta_0004.nii mask.nii SPM files (after estimation) ResMS.nii Residual variance estimate RPV.nii Estimated RESELS per voxel SPM files (after estimation) SPM files (after contrast estimation) Summary 1. We specify a general linear model of the data 2. The model is combined with the HRF, high-pass filtered and serial correlations corrected 3. The model is applied to every voxel, producing beta images. 4. Next we’ll compare betas to make inferences http://www.fil.ion.ucl.ac.uk/~pzeidman/teaching/GLM.ppt

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