OverviewOverview Motion correction Smoothing kernel Spatial normalisation Standard template fMRI time-series Statistical Parametric Map General Linear Model Design matrix Parameter Estimates

PHJ a) Direct Normalization i) Realign -> Slice Time* -> Normalization -> Smoothing b) Indirect Normalization i) Realign -> Slice Time* -> Coregistration - > Segmentation -> Normalization - >Smoothing * optional

fMRI time-series Motion correctedMean functional REALIGN Lars Kasper 3 Signal, Noise and Preprocessing Realignment  Aligns all volumes of all runs spatially  Rigid-body transformation: three translations, three rotations  Objective function: mean squared error of corresponding voxel intensities  Voxel correspondence via Interpolation

Realignment Output: Parameters Lars Kasper Signal, Noise and Preprocessing 4

The preprocessing sequence revisted Realignment –Motion correction: Adjust for movement between slices Coregistration –Overlay structural and functional images: Link functional scans to anatomical scan Normalisation –Warp images to fit to a standard template brain Smoothing –To increase signal-to-noise ratio Extras (optional) –Slice timing correction; unwarping

Co-registration Term co-registration applies to any method for aligning images –By this token, motion correction is also co- registration However, term is usually used to refer to alignment of images from different modalities. E.g.: –Low resolution T2* fMRI scan (EPI image) to high resolution, T1, structural image from the same individual

Co-registration: Principles behind this step of processing When several images of the same participants have been acquired, it is useful to have them all in register Image registration involves estimating a set of parameters describing a spatial transformation that ‘best ‘ matches the images together

fMRI to structural Matching the functional image to the structural image –Overlaying activation on individual anatomy –Better spatial image for normalisation Two significant differences between co-registering to structural scans and motion correction –When co-registering to structural, the images do not have the same signal intensity in the same areas; they cannot be subtracted –They may not be the same shape

Problem: Images are different Differences in signal intensity between the images Normalise to appropriate template (EPI to EPI; T1 to T1), then segment

Segmentation Use the gray/white estimates from the normalisation step as starting estimates of the probability of each voxel being grey or white matter Estimate the mean and variance of the gray/white matter signal intensities Reassign probabilities for voxels on basis of –Probability map from template –Signal intensity and distributions of intensity for gray/white matter Iterate until there is a good fit

Register segmented images Grey/white/CSF probability images for EPI (T2*) and T1 Combined least squares match (simultaneously) of gray/white/CSF images of EPI (T2*) + T1 segmented images

The preprocessing sequence revisted Realignment –Motion correction: Adjust for movement between slices Coregistration –Overlay structural and functional images: Link functional scans to anatomical scan Normalisation –Warp images to fit to a standard template brain Smoothing –To increase signal-to-noise ratio Extras (optional) –Slice timing correction; unwarping

Normalisation This enables: –Signal averaging across participants: Derive group statistics -> generalise findings to population Identify commonalities and differences between groups (e.g., patient vs. healthy) –Report results in standard co- ordinate system (e.g. Talairach and Tournoux stereotactic space) Goal: Register images from different participants into roughly the same co-ordinate system (where the co-ordinate system is defined by a template image) Goal: Register images from different participants into roughly the same co-ordinate system (where the co-ordinate system is defined by a template image)

Matthew Brett

Standard spaces The MNI template follows the convention of T&T, but doesn’t match the particular brain Recommended reading: ing/MniTalairachhttp://imaging.mrc-cbu.cam.ac.uk/imag ing/MniTalairach The Talairach AtlasThe MNI/ICBM AVG152 Template

SPM: Spatial Normalisation SPM adopts a two-stage procedure to determine a transformation that minimises the sum of squared differences between images: Step 1: Linear transformation (12-parameter affine) Step 2: Non-linear transformation (warping) High-dimensionality problem The affine and warping transformations are constrained within an empirical Bayesian framework (i.e., using prior knowledge of the variability of head shape and size): “maximum a posteriori” (MAP) estimates of the registration parameters

Step 1: Affine Transformation Determines the optimum 12-parameter affine transformation to match the size and position of the images 12 parameters = 3 translations and 3 rotations (rigid-body) + 3 shears and 3 zooms RotationShear TranslationZoom

Step 2: Non-linear Registration Assumes prior approximate registration with 12-parameter affine step Modelled by linear combinations of smooth discrete cosine basis functions (3D) Choice of basis functions depend on distribution of warps likely to be required For speed and simplicity, uses a “small” number of parameters (~1000)

Matthew Brett

2-D visualisation (horizontal and vertical deformations): Brain visualisation: visualisation: Ashburner; HBF Chap 3 Source Deformation field Warped image Template

SMOOTH GLM Kernel MNI Space Smoothing Signal, Noise and Preprocessing 22  Why blurring the data?  Improves spatial overlap by blurring over anatomical differences  Suppresses thermal noise (averaging)  Increases sensitivity to effects of similar scale to kernel (matched filter theorem)  Makes data more normally distributed (central limit theorem)  Reduces the effective number of multiple comparisons Lars Kasper  How is it implemented?  Convolution with a 3D Gaussian kernel, of specified full-width at half- maximum (FWHM) in mm

Smoothing Lars Kasper: A Toolbox 23