Report

Spatial preprocessing of fMRI data Klaas Enno Stephan Laboratory for Social and Neural Systrems Research Institute for Empirical Research in Economics University of Zurich With many thanks for helpful slides to: Functional Imaging Laboratory (FIL) Wellcome Trust Centre for Neuroimaging University College London Ged Ridgway John Ashburner Meike Grol Methods & models for fMRI data analysis in neuroeconomics 17 April 2010 Overview of SPM Image time-series Realignment Kernel Design matrix Smoothing General linear model Statistical parametric map (SPM) Statistical inference Normalisation Gaussian field theory p <0.05 Template Parameter estimates 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) EPI (T2*) dropout • Sampling speed: – 1 slice: 50-100 ms • Requires spatial pre-processing and statistical analysis. T1 Terminology of fMRI subjects sessions runs single run volume slices TR = repetition time time required to scan one volume voxel Terminology of fMRI Scan Volume: Field of View (FOV), e.g. 192 mm Axial slices Slice thickness e.g., 3 mm Matrix Size e.g., 64 x 64 In-plane resolution 192 mm / 64 = 3 mm 3 mm 3 mm 3 mm Voxel Size (volumetric pixel) Standard space The Talairach Atlas The MNI/ICBM AVG152 Template Why does fMRI require spatial preprocessing? • Head motion artefacts during scanning → Realignment • Problems of EPI acquisition: distortion and signal dropouts → “Unwarping” • Brains are quite different across subjects → Normalisation (“Warping”) → Smoothing 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! 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 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: x1 m 11 y m 1 21 z 1 m 31 1 0 m 12 m 13 m 22 m 23 m 32 m 33 0 0 m 14 x 0 m 24 y 0 m 34 z 0 1 1 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 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 1 0 0 0 0 0 1 0 0 1 0 0 Xtrans 1 Ytrans 0 Ztrans 0 1 0 Translations 0 0 cosΦ sinΦ sinΦ cosΦ 0 0 Pitch about x axis cosΘ 0 0 0 sinΘ 1 0 0 0 sinΘ 1 0 0 cosΘ 0 0 Roll about y axis cosΩ 0 sinΩ 0 0 1 0 0 sinΩ 0 cosΩ 0 0 0 1 0 0 0 1 Yaw about z axis 0 Realignment • Goal: minimise squared differences between source and reference image • Other methods available (e.g. mutual information) 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? 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 Joint and marginal histograms intensity frequency frequency intensity 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 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. Why does fMRI require spatial preprocessing? • Head motion artefacts during scanning → Realignment • Problems of EPI acquisition: distortion and signal dropouts → “Unwarping” • Brains are quite different across subjects → Normalisation (“Warping”) → Smoothing 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. 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 Movement by distortion interaction Movement by distortion interactions after head rotation original deformations deformations after realignment mismatch in deformations Andersson et al. 2001, NeuroImage Different strategies for correcting movement artefacts • liberal control: realignment only • moderate control: realignment + “unwarping” • strict control: realignment + inclusion of realignment parameters in statistical model Why does fMRI require spatial preprocessing? • Head motion artefacts during scanning → Realignment • Problems of EPI acquisition: distortion and signal dropouts → “Unwarping” • Brains are quite different across subjects → Normalisation (“Warping”) → Smoothing Individual brains differ in size, shape and folding 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 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 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 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). 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: log p ( | y ) log p ( y | ) log p ( ) log p ( y ) “Difference” between template and source image Squared distance between parameters and their expected values (regularisation) Spatial normalisation: overfitting Without regularisation, Template the non-linear image spatial normalisation can introduce unnecessary Non-linear warps. registration using regularisation. (2 = 302.7) Affine registration. (2 = 472.1) Non-linear registration without regularisation. (2 = 287.3) Segmentation GM and WM segmentations overlaid on original images Structural image, GM and WM segments, and brainmask (sum of GM and WM) 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 Unified segmentation with tissue class priors • Goal: for each voxel, compute probability that it belongs to a particular tissue type, given its intensity p (tissue | intensity) p (intensity | tissue) ∙ p (tissue) • 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 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”) Normalising structural image to T1 template Estimate normalization parameters (T1 -> T1 template) T1 image Apply the normalization parameters to the T1 image EPI time series And apply the normalization parameters to the (coregistered) functional images Normalising EPI images to EPI template Calculate mean of EPI time series Estimate normalization parameters (EPI -> EPI template) EPI time series Apply the normalization parameters to all EPI images T1 image Apply the normalization parameters to the (coregistered) T1 image 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 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 Summary: spatial preprocessing steps • Head motion artefacts during scanning → Realignment • Problems of EPI acquisition: distortion and signal dropouts → “Unwarping” • Brains are quite different across subjects → Normalisation (“Warping”) → Smoothing Thank you! Supplementary slides World space & voxel space x W 2 xV 9 2 y W 2 y V -1 2 8 z W 2 zV -7 4 (44, 66, 36) (4, 4, -2) Voxel index (45, 66, 35) World coords (2, 4, -4) mm (45, 65, 35) (2, 2, -4) Changing coordinate systems x W 2 xV 92 y W 2 y V - 128 z W 2z V - 74 By moving to 4D, one can include translations within a single matrix multiplication xW yW z W 2 0 0 xW yW z W 1 2 0 0 0 0 0 x V 0 y V 2 z V 0 0 2 0 0 2 0 0 0 2 92 128 74 92 x V 128 y V 74 z V 1 1 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 Representing rotations x 1 cos( θ ) y 1 sin( θ) sin( θ) x 0 cos( θ ) y 0 x 1 cos( θ ) y 1 sin( θ ) z 0 1 sin( θ ) cos( θ ) 0 0 x 0 0 y 0 1 z 0