Neuroimage Processing
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1 Neuroimage Processing Instructor: Moo K. Chung Lecture 2. General Linear Models (GLM) Multivariate General Linear Models (MGLM) September 11, 2009
2 Research Projects If you have your own imaging data, you can do your own project after consultation with me but you need to apply various techniques covered in class. If you don t have your own data, simply use the in-class data sets.
3 Least squares estimation (LSE) A method for determining unknown parameters of an overdetermined linear system by minimizing the sum of squared residuals.
4 Properties of LSE Invented by Gauss in LSE can be done without any statistical assumption. LSE is the maximum likelihood estimation with Gaussian noise. Always try LSE first before you try anything more complicated.
5 Example. Solve the following over determined system: a= 1 a= 2 Sum of squared residual = (a-1)^2 + (a-2)^2. The minimum is given by a=1.5, the sample mean.
6 Normal equations a= 1 a= a = 1 2 (1,1) 1 1 a = (1,1) 1 2 2a = 3
7 General Linear Model (GLM) The general linear model (GLM) is a very flexible and general statistical framework encompassing a wide variety of fixed effect models such as the multiple regressions, the analysis of variance (ANOVA), the multivariate analysis of variance (MANOVA), the analysis of covariance (ANCOVA) and the multivariate analysis of covariance (MANCOVA) The parameters of the model are mainly estimated by the least squares estimation and has been implemented in many statistical packages such as R or Splus and brain imaging packages such as SPM and fmri-stat.
8 Read section 2.9 of the textbook Model
9 Inference
10 Estimation
11 Summary Variables of interest Nuisance covariates Computing the sum of squared errors (residuals) requires the least squares estimation (LSE) of unknown parameters.
12 Application: GLM on cortical thickness
13 Cortical surfaces Skull Outer Cortical Surface Gray Matter Inner Cortical Surface White Matter
14 Deformable surface algorithm McDonalds et al. (2001) NeuroImage Multiscale triangle subdivision at each iteration increases the complexity of anatomical boundary
15 Cortical Surface Polygonal mesh Mesh resolution 3mm 82,190 triangles 40,962 vertices
16 Outer and inner cortical surfaces Read Chung et al., 2003 NeuroImage for more detail
17 GLM on thickness
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19 Why GLM? The effect of nuisance covariates such as age and gender Age distribution for autistic subjects: 16.1 (s.d. 4.5) Age distribution for control subjects: 17.1 (s.d. 2.8)
20 p-value map for t-test on cortical thickness difference Decrease: left superior temporal sulcus, left occipital-temporal gyrus, right orbital prefrontal Increase: left superior temporal gyrus, left middle temporal gyrus, left and right postcentral sulci
21 p-value map for F-test removing age effect Decrease: left superior temporal sulcus left occipital-temporal gyrus right orbital prefrontal
22 It is better to remove the age effect in anatomical data especially for developmental age range (10-20 years).
23 MATLAB demonstration of GLM /matlab/cmn.lecture02.mglm m
24 Keith Worsley ( ) Brain imaging research done for 21 years between The first major publication in 1992.
25 Keith Worsley s SurfStat Package SurfStat is a Matlab toolbox for the statistical analysis of univariate and multivariate surface and volumetric data using linear mixed effects models and random field theory. Brain substructure modeling:
26 Reference: Worsley, K.J., Taylor, J.E., Carbonell, F., Chung, M.K., Duerden, E., Bernhardt, B., Lyttelton, O., Boucher, M., Evans, A.C. (2009). SurfStat: A Matlab toolbox for the statistical analysis of univariate and multivariate surface and volumetric data using linear mixed effects models and random field theory. NeuroImage, OHBM Chung, M.K., Worsley, K.J., Nacewicz, B.M., Dalton, K.M., Davidson, R.J General multivariate linear modeling of surface shapes using SurfStat. 53:
27 Multivariate General Linear Model Multivariate version of general linear model. SPM, AFNI do not have it. Only SurfStat has it. Read section 5.3 of the textbook
28 Given vector data P, we set up covariance matrix displacement vector variable of interest nuisance covariates noise
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31 Lecture 3 topics Least squares estimation Fourier representation Iterative Residual Fitting Please read: shen.2003 styner.2006 chung.2010.ni
32 Li Shen Seminar Next week Thursday Mok-am Hall Bldg 500 2:00pm Friday 11:00am This room
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