Spatial preprocessing of fMRI data

1. Spatial preprocessing of fMRI data 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 Methods & models for fMRI data analysis in neuroeconomics17 April 2010

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

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*) dropout T1

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

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

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

7. 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

8. 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!

9. 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: Registration: optimising six parameters that describe a rigid body transformation between the source and a reference image Transformation:re-sampling according to the determined transformation

10. Linear (affine) transformations • Rigid-body transformations are a subset • Parallel lines remain parallel • Operations can be represented by: • x1 = m11x0 + m12y0 + m13z0 + m14 • y1 = m21x0 + m22y0 + m23z0 + m24 • z1 = m31x0 + m32y0 + m33z0 + m34 • Or as matrices:

11. 2D affine transforms • Translations by tx and ty • x1 = 1 x0 + 0 y0 + tx • y1 = 0 x0 + 1 y0 + ty • Rotation around the origin by  radians • x1 = cos() x0 + sin() y0 + 0 • y1 = -sin() x0 + cos() y0 + 0 • Zooms by sx and sy: • x1 = sx x0 + 0 y0 + 0 • y1 = 0 x0 + sy y0 + 0 Shear x1 = 1 x0 + h y0 + 0 y1 = 0 x0 + 1 y0 + 0

12. 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 Translations Pitch about x axis Roll about y axis Yaw about z axis

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

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

15. Coregistration • also affine registration (like realignment) • used to register a structural image to a (mean) functional one • allows more accurate anatomical localisation of activations • must be done before spatial normalisation(if warping parameters are estimated from the T1 image) • examples in SPM8 Manual, Chapters 28, 29 Practical demonstration: realignment & coregistration

16. Joint and marginal histograms intensity frequency frequency intensity

17. Interpolation • Nearest neighbour • Take the value of the closest voxel • linear (2D: bilinear; 3D: trilinear) • Just a weighted average of the neighbouring voxels • f5 = f1 x2 + f2 x1 • f6 = f3 x2 + f4 x1 • f7 = f5 y2 + f6 y1

18. B-spline interpolation A continuous function is represented by a linear combination of basis functions 2D B-spline basis functions of degrees 0, 1, 2 and 3 B-splines are piecewise polynomials 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 mismatch in deformations deformations after realignment Andersson et al. 2001, NeuroImage

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: • Not always 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. Squared distance between parameters and their expected values (regularisation) “Difference” between template and source image 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 Deformation parameters MAP:

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

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). p (tissue|intensity) p (intensity|tissue) ∙ p (tissue) Ashburner & Friston 2005, NeuroImage

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. Estimate normalization parameters (T1 -> T1 template) T1 image Apply the normalization parameters to the T1 image And apply the normalization parameters to the (coregistered) functional images EPI time series Normalising structural image to T1 template

38. Calculate mean of EPI time series Estimate normalization parameters (EPI -> EPI template) Apply the normalization parameters to all EPI images Apply the normalization parameters to the (coregistered) T1 image T1 image Normalising EPI images to EPI template EPI time series

39. 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

40. Smoothing 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. Before convolution Convolved with a circle Convolved with a Gaussian

41. 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

42. Thank you!

43. Supplementary slides

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

45. Changing coordinate systems By moving to 4D, one can includetranslations 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

46. Representing rotations