1. Spatial preprocessing of fMRI data Methods & models for fMRI data analysis 25 February 2009 Klaas Enno Stephan Laboratory for Social and Neural Systrems Research Institute for Empirical Research in Economics University of Zurich Functional Imaging Laboratory (FIL) Wellcome Trust Centre for Neuroimaging University College London With many thanks for helpful slides to: John Ashburner Meike Grol Ged Ridgway

2. Overview of SPM RealignmentSmoothing Normalisation General linear model Statistical parametric map (SPM) Image time-series Parameter estimates Design matrix Template Kernel Gaussian field theory p <0.05 Statisticalinference

3. Functional MRI (fMRI) Uses echo planar imaging (EPI) for fast acquisition of T2*-weighted images. Spatial resolution: –3 mm(standard 1.5 T scanner) –< 200 μm(high-field systems) Sampling speed: –1 slice: 50-100 ms Requires spatial pre-processing and statistical analysis. EPI (T2 * ) T1 dropout

4. subjects sessions runs single run volume slices Terminology of fMRI TR = repetition time time required to scan one volume voxel

5. Terminology of fMRI Slice thickness e.g., 3 mm Scan Volume: Field of View (FOV), e.g. 192 mm Axial slices 3 mm Voxel Size (volumetric pixel) Matrix Size e.g., 64 x 64 In-plane resolution 192 mm / 64 = 3 mm

6. Standard space The Talairach AtlasThe MNI/ICBM AVG152 Template

7. World coords (2, 4, -4) mm (4, 4, -2) (2, 2, -4) Voxel index (45, 66, 35) (44, 66, 36) (45, 65, 35) World space & voxel space

8. By moving to 4D, one can include translations within a single matrix multiplication These 4-by-4 “homogeneous matrices” are the currency of voxel-world mappings, affine coreg. and realignment. In SPM5 & SPM8, they are stored in the.hdr files. In SPM2, they are stored in.mat files. To find inverse mappings, or results of concatenating multiple transformations, we simply follow the rules of matrix algebra Changing coordinate systems

9. Why does fMRI require spatial preprocessing? Head motion artefacts during scanning Problems of EPI acquisition: distortion and signal dropouts Brains are quite different across subjects → Realignment → “Unwarping” → Normalisation (“Warping”) → Smoothing

10. Realignment or “motion correction” Even small head movements can be a major problem: –increase in residual variance –data may get completely lost if sudden movements occur during a single volume –movements may be correlated with the task performed Therefore: –always constrain the volunteer’s head –instruct him/her explicitly to remain as calm as possible –do not scan for too long – everyone will move after while ! minimising movements is one of the most important factors for ensuring good data quality!

11. Realignment = rigid-body registration Assumes that all movements are those of a rigid body, i.e. the shape of the brain does not change Two steps: ptimising six parameters that describe a rigid body transformation between the source and a reference image Registration: optimising six parameters that describe a rigid body transformation between the source and a reference image re-sampling according to the determined transformation Transformation: re-sampling according to the determined transformation

12. Linear (affine) transformations Rigid-body transformations are a subset Parallel lines remain parallel Operations can be represented by: x 1 = m 11 x 0 + m 12 y 0 + m 13 z 0 + m 14 y 1 = m 21 x 0 + m 22 y 0 + m 23 z 0 + m 24 z 1 = m 31 x 0 + m 32 y 0 + m 33 z 0 + m 34 Or as matrices:

13. 2D affine transforms Translations by t x and t y x 1 = 1 x 0 + 0 y 0 + t x y 1 = 0 x 0 + 1 y 0 + t y Rotation around the origin by  radians x 1 = cos(  ) x 0 + sin(  ) y 0 + 0 y 1 = -sin(  ) x 0 + cos(  ) y 0 + 0 Zooms by s x and s y : x 1 = s x x 0 + 0 y 0 + 0 y 1 = 0 x 0 + s y y 0 + 0 Shear x 1 = 1 x 0 + h y 0 + 0 y 1 = 0 x 0 + 1 y 0 + 0

14. 3D rigid-body transformations A 3D rigid body transform is defined by: –3 translations - in X, Y & Z directions –3 rotations - about X, Y & Z axes Non-commutative: the order of the operations matters TranslationsPitch about x axis Roll about y axis Yaw about z axis

15. Realignment Goal: minimise squared differences between source and reference image Other methods available (e.g. mutual information)

16. A special case... If a subject remained perfectly still during a fMRI study, would realignment still be a good idea to perform? When is this issue of practical relevance?

17. Nearest neighbour –Take the value of the closest voxel linear (2D: bilinear; 3D: trilinear) –Just a weighted average of the neighbouring voxels –f 5 = f 1 x 2 + f 2 x 1 –f 6 = f 3 x 2 + f 4 x 1 –f 7 = f 5 y 2 + f 6 y 1 Simple interpolation

18. B-spline interpolation B-splines are piecewise polynomials A continuous function is represented by a linear combination of basis functions 2D B-spline basis functions of degrees 0, 1, 2 and 3 Nearest neighbour and trilinear interpolation are the same as B-spline interpolation with degrees 0 and 1.

19. Why does fMRI require spatial preprocessing? Head motion artefacts during scanning Problems of EPI acquisition: distortion and signal dropouts Brains are quite different across subjects → Realignment → “Unwarping” → Normalisation (“Warping”) → Smoothing

20. Residual errors after realignment Resampling can introduce interpolation errors Slices are not acquired simultaneously –rapid movements not accounted for by rigid body model Image artefacts may not move according to a rigid body model –image distortion –image dropout –Nyquist ghost Functions of the estimated motion parameters can be included as confound regressors in subsequent statistical analyses.

21. Movement by distortion interactions Subject disrupts B0 field, rendering it inhomogeneous → distortions in phase-encode direction Subject moves during EPI time series → distortions vary with subject orientation → shape of imaged brain varies Andersson et al. 2001, NeuroImage

22. Movement by distortion interaction

23. Movement by distortion interactions after head rotation original deformations deformations after realignment mismatch in deformations

24. Different strategies for correcting movement artefacts liberal control: realignment only moderate control: realignment + “unwarping” strict control: realignment + inclusion of realignment parameters in statistical model

25. Why does fMRI require spatial preprocessing? Head motion artefacts during scanning Problems of EPI acquisition: distortion and signal dropouts Brains are quite different across subjects → Realignment → “Unwarping” → Normalisation (“Warping”) → Smoothing

26. Individual brains differ in size, shape and folding

27. Spatial normalisation: why necessary? Inter-subject averaging –Increase sensitivity with more subjects Fixed-effects analysis –Extrapolate findings to the population as a whole Random / mixed-effects analysis Make results from different studies comparable by bringing them into a standard coordinate system –e.g. MNI space

28. Spatial normalisation: objective Warp the images such that functionally corresponding regions from different subjects are as close together as possible Problems: –No exact match between structure and function –Different brains are organised differently –Computational problems (local minima, not enough information in the images, computationally expensive) Compromise by correcting gross differences followed by smoothing of normalised images

29. Spatial normalisation: affine step The first part is a 12 parameter affine transform –3 translations –3 rotations –3 zooms –3 shears Fits overall shape and size

30. Spatial normalisation: non-linear step Deformations consist of a linear combination of smooth basis functions. These basis functions result from a 3D discrete cosine transform (DCT).

31. Spatial normalisation: Bayesian regularisation Deformations consist of a linear combination of smooth basis functions  set of frequencies from a 3D discrete cosine transform. Find maximum a posteriori (MAP) estimates: simultaneously minimise –squared difference between template and source image –squared difference between parameters and their priors MAP: Deformation parameters “Difference” between template and source image Squared distance between parameters and their expected values (regularisation)

32. Template image Affine registration. (  2 = 472.1) Non-linear registration without regularisation. (  2 = 287.3) Non-linear registration using regularisation. (  2 = 302.7) Without regularisation, the non-linear spatial normalisation can introduce unnecessary warps. Spatial normalisation: overfitting

33. Segmentation GM and WM segmentations overlaid on original images Structural image, GM and WM segments, and brain- mask (sum of GM and WM)

34. Segmentation & normalisation Circular relationship between segmentation & normalisation: –Knowing which tissue type a voxel belongs to helps normalisation. –Knowing where a voxel is (in standard space) helps segmentation. Build a joint generative model: –model how voxel intensities result from mixture of tissue type distributions –model how tissue types of one brain have to be spatially deformed to match those of another brain Using a priori knowledge about the parameters: adopt Bayesian approach and maximise the posterior probability Ashburner & Friston 2005, NeuroImage

35. Unified segmentation with tissue class priors Goal: for each voxel, compute probability that it belongs to a particular tissue type, given its intensity Likelihood model: Intensities are modelled by a mixture of Gaussian distributions representing different tissue classes (e.g. GM, WM, CSF). Priors are obtained from tissue probability maps (segmented images of 151 subjects). Goal: for each voxel, compute probability that it belongs to a particular tissue type, given its intensity Likelihood model: Intensities are modelled by a mixture of Gaussian distributions representing different tissue classes (e.g. GM, WM, CSF). Priors are obtained from tissue probability maps (segmented images of 151 subjects). Ashburner & Friston 2005, NeuroImage p (tissue | intensity)  p (intensity | tissue) ∙ p (tissue)

36. Normalisation options in practice Conventional normalisation: –either warp functional scans to EPI template directly –or coregister structural scan to functional scans and then warp structural scan to T1 template; then apply these parameters to functional scans (“Normalise: Write”) Unified segmentation: –coregister structural scan to functional scans –unified segmentation provides normalisation parameters –apply these parameters to functional scans (“Normalise: Write”)

37. Smoothing Why smooth? –increase signal to noise –inter-subject averaging –increase validity of Gaussian Random Field theory In SPM, smoothing is a convolution with a Gaussian kernel. Kernel defined in terms of FWHM (full width at half maximum). Gaussian convolution is separable Gaussian smoothing kernel

38. Smoothing Before convolutionConvolved with a circleConvolved with a Gaussian Smoothing is done by convolving with a 3D Gaussian which is defined by its full width at half maximum (FWHM). Each voxel after smoothing effectively becomes the result of applying a weighted region of interest.

39. Summary: spatial preprocessing steps Head motion artefacts during scanning Problems of EPI acquisition: distortion and signal dropouts Brains are quite different across subjects → Realignment → “Unwarping” → Normalisation (“Warping”) → Smoothing

40. Thank you!

42. Representing rotations