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Statistical Parametric Mapping (SPM) Statistical Parametric Mapping (SPM) Finn Arupº Nielsen Neurobiology Research Unit, Copenhagen University Hospital Rigshospitalet; Informatics and Mathematical Modelling Technical University of Denmark March 3, 2005 Statistical Parametric Mapping (SPM) What is SPM? A method for processing and anal- Analysis software of first experiment in paper (top of list) SPM96 ysis of neuroimages. SPM99 SPM95 A method for voxel-based analysis AIR SPM of neuroimages using a \general lin- AFNI SPM97 ear model". SPM97d MRIcro In−house The summary images (i.e., result BRAINS Stimulate images) from an analysis: Statisti- SPM99d SPM99b cal parametric maps. SPM97d/SPM99 0 5 10 15 20 25 30 35 A Matlab program for processing Absolute frequency and analysis of functional neuroim- Figure 1: Histogram of used analysis software ages | and molecular neuroimages. as recorded in the Brede Database, see orig- inal at http://hendrix.imm.dtu.dk/services/jerne/- SPM is very dominating in func- brede/index bib stat.html tional neuroimaging Finn Arupº Nielsen 1 March 3, 2005 Statistical Parametric Mapping (SPM) SPM | the program Image registration, seg- mentation, smoothing, al- gebraic operations Analysis with general lin- ear model, random ¯eld theory, dynamic causal modeling Visualization Email list with 2000 » subscribers Figure 2: Image by Mark Schram Christensen. Finn Arupº Nielsen 2 March 3, 2005 Statistical Parametric Mapping (SPM) Data transformations Image data Kernel Design matrix Statistical parametric map 1 0.9 2 0.8 1 4 0.7 0.8 0.6 0.6 6 0.5 0.4 0.4 0.2 8 0.3 0 3 2 10 0.2 3 1 2 0 1 0.1 −1 0 −1 −2 12 −2 −3 −3 0 1 2 3 4 5 6 7 8 Realignment Smoothing General linear Model Spatial Gaussian random field Statistical False discovery rate Normalization Inference Maximum statistics permutation Template Finn Arupº Nielsen 3 March 3, 2005 Statistical Parametric Mapping (SPM) Image registration Image registration: Move and warp brain Motion realignment of consecutive scans (\realign"). Within subject Coregistration or intermodality reg- istration, e.g., to registation a PET and an MRI. Wihtin subject. Spatial normalization: Deform brain to a template. \MNI" Templates are distributed with SPM. Between Figure 3: Main window of SPM. Image registration are the three left upmost buttons. subjects. Finn Arupº Nielsen 4 March 3, 2005 Statistical Parametric Mapping (SPM) Realignment Several images in the same modality from the same subject Two-stage: 1) Estimate movement. SPM: \Determine parameters" 2) Resample images based on estimated movement In SPM resampling can be postponed and the estimated movement saved in a .mat ¯le with the \transformation matrix". Finn Arupº Nielsen 5 March 3, 2005 Statistical Parametric Mapping (SPM) Coregistration (a) PET template from SPM. (b) MRI T1 template from SPM. Figure 4: The areas with the highest values in two modalities of PET and MRI brain scans: For registration the problem is that they are di®erent! Finn Arupº Nielsen 6 March 3, 2005 Statistical Parametric Mapping (SPM) Realignment and coregistration (27, 40) = (−, −): 3.295837 60 60 8 10 9 50 7 50 8 6 7 40 40 5 6 30 30 5 4 PET values 4 3 20 20 3 2 2 10 10 1 1 0 10 20 30 40 50 60 10 20 30 40 50 60 T1 values (a) PET/PET. (b) MRI T1/PET templates from SPM. Figure 5: Grey level occurence matrix. Finn Arupº Nielsen 7 March 3, 2005 Statistical Parametric Mapping (SPM) Spatial normalization Figure 6: Warp of right subject to left subjects brain. Result in the middle. Image by Ulrik Kjems using MRIwarp. Finn Arupº Nielsen 8 March 3, 2005 Statistical Parametric Mapping (SPM) Spatial normalization | Batch programming Spatial normalization: Deform subject brain scans to a template. Determine warp parameters by matching a subjects anatomical MRI (\Source image") to a template (\Determine parameters") params = spm_normalise(Vtemplate, Vmri, matname, '', '', ... defaults.normalise.estimate); Apply (\Write normalised") the warp parameter to warp the functional image (\Images to write") spm_write_sn(Vpet, params, defaults.normalise.write, msk); By default SPM is normalizing to so-called \MNI-space" which is slightly di®erent from the original \Talairach atlas" (Talairach and Tournoux, 1988; Brett, 1999a). Finn Arupº Nielsen 9 March 3, 2005 Statistical Parametric Mapping (SPM) Spatial normalization batch programming defaults.normalise.estimate.smosrc = 8; defaults.normalise.estimate.smoref = 0; defaults.normalise.estimate.regtype = 'mni'; defaults.normalise.estimate.weight = ''; defaults.normalise.estimate.cutoff = 25; defaults.normalise.estimate.nits = 16; defaults.normalise.estimate.reg = 1; defaults.normalise.estimate.wtsrc = 0; defaults.normalise.write.preserve = 0; defaults.normalise.write.bb = [[-78 -112 -50];[78 76 85]]; defaults.normalise.write.vox = [2 2 2]; defaults.normalise.write.interp = 1; defaults.normalise.write.wrap = [0 0 0]; reg (regularization) and cutoff (cuto® of the discrete cosine basis func- tions) determine the smoothness of the warp. \[. ] if your normalized images appear distorted, then it may be an idea to increase the amount of regularization" (spm normalise ui.m) Finn Arupº Nielsen 10 March 3, 2005 Statistical Parametric Mapping (SPM) Spatial smoothing (a) Unsmoothed original. (b) Smoothed. FWHM=10mm. Figure 7: T1 single subject template from SPM99. Finn Arupº Nielsen 11 March 3, 2005 Statistical Parametric Mapping (SPM) Spatial smoothing Accounts for anatomical variability. 25 Might increase signal to noise ratio. Increase validity of SPM inference 20 Usually performed with with an 15 Gaussian kernel. Frequency 10 SPM command line 5 spm smooth(filenameIn, filenameOut, 16); 0 −5 0 5 10 15 20 25 FWHM spatial filter width [mm] Here 16 is the \full width half max- imum" in millimeters Figure 8: Histogram of smoothing width in the Brede database, see original at FWHM = p8 ln 2 σ 2:35σ: http://hendrix.imm.dtu.dk/services/jerne/- ¼ brede/index bib stat.html An \s" is pre¯xed on the ¯lename. Finn Arupº Nielsen 12 March 3, 2005 Statistical Parametric Mapping (SPM) Spatial masks Spatial mask: Exclude voxels from the statistical analysis, e.g., non-brain voxels and brain voxels not (likely) \signi¯cant". SPM terminology Threshold, \absolute", \relative" (\Grey matter threshold"). ² \Implicit mask": Omit voxels that are zero or NaN. ² \Explicit mask": A volume ¯le specifying the which voxels to include ² (ones and zeros). So-called \F-masking" appeared in early versions of SPM: SPM94/5/6. ² Finn Arupº Nielsen 13 March 3, 2005 Statistical Parametric Mapping (SPM) Spatial mask | Global mean What is the mean value of a brain 8000 Histogram Ordinary scan? 7000 SPM−type Ordinary/8 6000 A simple mean will be a®ected by 5000 the number of non-brain voxels. These are around zero. 4000 Frequency 3000 A more robust \global mean" 2000 can be calculated in two-stages: 1000 First the ordinary mean is com- puted, then the mean of values 0 0 50 100 150 200 250 300 350 400 450 Voxel values above mean/8. (Computed in spm global.m and spm global.c avail- Figure 9: Example of a histogram from a PET vol- ume (Noll et al., 1996). able at SPM.xGX.rg) The value is used for confounds and masking operations. Finn Arupº Nielsen 14 March 3, 2005 Statistical Parametric Mapping (SPM) Noll's PET motor SPM masking example SPM analysis: two-sample test, \no grand mean scaling", \omit global calculation". \Single-subject: conditions & co- variates", 0 covariates and nui- sances \no global normalization", \no grand mean scaling", mask (fullmean/8 mask). Without a mask many non-brain voxels appear with high statistics. Figure 10: PET motor, left hand ¯nger opposition task, 12 scans: Odd activation, even baseline (Noll et al., 1996). Red is without mask. Yellow with mask. Thresholded at t = 2:76 (P < 0:01). Finn Arupº Nielsen 15 March 3, 2005 Statistical Parametric Mapping (SPM) Analysis with the general linear model The general linear model has the form (Mardia et al., 1979, eq. 6.1.1) ² Y = XB + U; (1) where Y(scans voxels) is the image data, X(scans design variables) is the \design matrix"£ and B(design variables voxels£ ) contains para- meters to be estimated and tested. The residuals£ U are usually as- sumed Gaussian. Encapsulates many statistical models: t-test (paired, un-paired), F - ² test, ANOVA (one-way, two-way, main e®ect, factorial), MANOVA, ANCOVA, MANCOVA, simple regression, linear regression, multiple regression, multivariate regression, . Widely used in functional neuroimaging through the SPM program ² where it is performed in a mass-univerate setting | in parallel over the columns of Y (Friston et al., 1995). Finn Arupº Nielsen 16 March 3, 2005 Statistical Parametric Mapping (SPM) Process for analysis Specify design - Estimate - Test Specify design: Set up the design matrix Estimate: Find the parameters B and the residuals U Test: Specify a test (a \contrast") and test-statistic threshold and view the results. Finn Arupº Nielsen 17 March 3, 2005 Statistical Parametric Mapping (SPM) Basic models \Basic models" of SPM: one-sample t-test, two-sample t- test, paired t-test, one-way ANOVA, one-way ANOVA with constant, one-way ANOVA \within-subjects", simple regression (correlation), mul- tiple regression, multiple regression with constant, ANCOVA. The models only vary because of di®erence in speci¯cation of the de- sign matrix. Figure 11: SPM 2 main interface window with \Basic models" button high lighted. Finn Arupº Nielsen 18 March 3, 2005 Statistical Parametric Mapping (SPM) Regression model Regression model y = b1x1 + b2x2 + u; (2) where y contains the values of a speci¯c voxels across scans. = b + b 1 2 + x1 models, e.g., activation/rest or patients/controls. x2 is the intercept, | a con- x x y 1 2 stant value Figure 12: Regression model u the noise Finn Arupº Nielsen 19 March 3, 2005 Statistical Parametric Mapping (SPM) Categorical variables in design matrix Categorical variable can be coded in two di®erent ways: \Sigma-restricted", where two groups (e.g., male and female) are coded in one design variables T x = 1; 1; 1; 1; 1; 1; ; (3) (1) ¡ ¡ ¡ that leads to a design matrixh with full rank.
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