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Yingying Wang 7/15/2014 Tuesday http://neurobrain.net/2014STBCH/index.html For MRI, which element within the body is most important? a) b) c) Oxygen Carbon Hydrogen An MRI system uses an Radio Frequency (RF) pulse to change the: a) b) c) Spin of atoms’ nuclei Shape of the nuclei Amount of metal in person’s cells 2 An MRI system creates an image when: All the hydrogen atoms in your body line up, creating an outline. b) Hydrogen atoms facing opposite directions cancel each other out, creating a reverse outline. c) The hydrogen atoms go back to their normal position, releasing energy. a) What component of an MRI system allows it to choose exactly where in the body to acquire an image? a) b) c) Gradient magnets Bore Contrast injector 3 What does an MRI system use to convert mathematical data into image? a) b) c) RF pulse converter Fourier transform Electron precession Higher BOLD signal intensities arise from increases in the concentration of oxygenated ________ since the blood magnetic susceptibility now more closely matches the tissue magnetic susceptibility. 4 Preprocessing Image time-series Realignment Kernel Smoothing Design matrix General linear model Statistical inference Normalization Template Statistical parametric map (SPM) Random field theory p <0.05 Parameter estimates 5 z y 3D Blood Oxygen-Level Dependent (BOLD) contrast images x Task Run/Session: Time Series of Images Task No Task … scan 1 time scan N 6 The Localized Time-series is the Fundamental Information Unit of fMRI Signal: Fluctuation through Blood oxygen level dependent (BOLD) contrast Noise: All other fluctuations Run/Session: Time Series of Images … scan 1 time scan N 7 8 1. Preprocessing Realignment Slice-Timing Correction Co-registration Unified Segmentation & Normalization Smoothing 9 10 11 Most functional MRI uses Echo-Planar Imaging (EPI) Each plane (slice) is typically acquired every 3mm normally axial… … requiring ~32 slices to cover cortex (40 to cover cerebellum too) (actually consists of slice-thickness, eg 2mm, and interslice gap, eg 1mm, sometimes expressed in terms of “distance factor”) (slices can be acquired contiguously, eg [1 2 3 4 5 6], or interleaved, eg [1 3 5 2 4 6]) Each plane (slice) takes about ~60ms to acquire… …entailing a typical TR for whole volume of 2-3s Volumes normally acquired continuously (though sometimes gap so that TR>TA) 2-3s between sampling the BOLD response in the first slice and the last slice (a problem for transient neural activity; less so for sustained neural activity) 12 Acquisition onset differs between slices STC: temporal alignment of all voxels in a volume Via sinc interpolation Sladky et al, NeuroImage 2011 13 14 15 16 Input Output fMRI time-series Anatomical MRI TPMs Segmentation Transformation (seg_sn.mat) Kernel REALIGN COREG SEGMENT m11 m21 m31 0 Motion corrected Mean functional NORM WRITE SMOOTH m12 m13 m14 m22 m23 m24 m32 m33 m34 0 0 1 (Headers changed) MNI Space GLM 17 18 fMRI time-series Aligns all volumes of all runs spatially Rigid-body transformation: three translations, three rotations REALIGN Objective function: mean squared error of corresponding voxel intensities Motion corrected Mean functional Voxel correspondence via Interpolation 19 Assume that brain of the same subject doesn’t change shape or size in the scanner. Head can move, but remains the same shape and size. Some exceptions: Image distortions. Brain slops about slightly because of gravity. Brain growth or atrophy over time. If the subject’s head moves, we need to correct the images. Do this by image registration. Two components: • Registration - i.e. Optimise the parameters that describe a spatial transformation between the source and reference images • Transformation - i.e. Re-sample according to the determined transformation parameters Translations by tx and ty Rotation around the origin by radians x1 = x0 + tx y1 = y0 + ty x1 = cos() x0 + sin() y0 y1 = -sin() x0 + cos() y0 Zooms by sx and sy x1 = sx x0 y1 = sy y0 *Shear *x1 = x0 + h y0 *y1 = y0 A 3D rigid body transform is defined by: 1 0 0 0 0 1 0 0 3 translations - in X, Y & Z directions 3 rotations - about X, Y & Z axes The order of the operations matters 0 Xtrans 1 0 0 0 cosΘ 0 sin Θ 0 cosΩ sin Ω 0 0 0 Ytrans 0 cosΦ sin Φ 0 0 1 0 0 sin Ω cosΩ 0 0 1 Zt rans 0 sin Φ cosΦ 0 sin Θ 0 cosΘ 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 Translations Pitch about x axis Roll about y axis Yaw about z axis roll yaw y translation z translation pitch x translation Most algorithms assume a rigid body (i.e., that brain doesn’t deform with movement) Align each volume of the brain to a target volume using six parameters: three translations and three rotations Target volume: the functional volume that is closest in time to the anatomical image 24 Intra-modal Mean squared difference (minimise) Normalised cross correlation (maximise) Inter-modal (or intra-modal) Mutual information (maximise) Normalised mutual information (maximise) Entropy correlation coefficient (maximise) Minimising mean-squared difference works for intra-modal registration (realignment) Simple relationship between intensities in one image, versus those in the other Assumes normally distributed differences Nearest neighbour Take the value of the closest voxel Tri-linear Just a weighted average of the neighbouring voxels f5 = f1 x2 + f2 x1 f6 = f3 x2 + f4 x1 f7 = f5 y2 + f6 y1 28 29 % signal change Z-Value: 3.9 Time (TRs) % signal change Crosshair location: Postcentral gyrus Z-Value: 3.8 Time (TRs) 30 Re-sampling can introduce interpolation errors Gaps between slices can cause aliasing artefacts Slices are not acquired simultaneously especially tri-linear interpolation 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 modelled as confounds in subsequent analyses 32 Anatomical MRI Aligns structural image to mean functional image Affine transformation: translations, rotations, scaling, shearing Objective function: mutual information, since contrast different COREG m11 m21 m31 0 Motion corrected Mean functional m12 m13 m14 m22 m23 m24 m32 m33 m34 0 0 1 (Headers changed) Typically only transformation matrix (“header”) changed (no reslicing) 33 • Inter-modal registration. • Match images from same subject but different modalities: –anatomical localisation of single subject activations –achieve more precise spatial normalisation of functional image using anatomical image. Useful, for example, to display functional results (EPI) onto high resolution structural image (T1)… …indeed, necessary if spatial normalisation is determined by T1 image Because different modality images have different properties (e.g., relative intensity of gray/white matter), cannot simply minimise difference between images Therefore, use Mutual Information as cost function, rather than squared differences… T2 T1 Transm EPI PD PET Used for between-modality registration Derived from joint histograms MI= ab P(a,b) log2 [P(a,b)/( P(a) P(b) )] Related to entropy: MI = -H(a,b) + H(a) + H(b) Where H(a) = -a P(a) log2P(a) and H(a,b) = -a P(a,b) log2P(a,b) Mean functional Anatomical MRI Joint and marginal Histogram Quantify how well one image predicts the other = how much shared info Joint probability distribution estimated from joint 37 38 39 Statistics or whatever fMRI time-series Anatomical MRI Template Smoothed Estimate Spatial Norm Motion Correct Smooth Coregister m11 m21 m31 0 Spatially normalised m12 m13 m14 m22 m23 m24 m32 m33 m34 0 0 1 Deformation Statistics or whatever fMRI time-series Template Smoothed Estimate Spatial Norm Motion Correct Smooth Spatially normalised Deformation Inter-subject averaging Increase sensitivity with more subjects Fixed-effects analysis Extrapolate findings to the population as a whole Mixed-effects analysis Make results from different studies comparable by aligning them to standard space e.g. The T&T convention, using the MNI template 42 43 Different people’s brains look different ‘Normalizing’ adjusts overall size and orientation Raw Images 44 Normalized Images The Talairach Atlas The MNI/ICBM AVG152 Template The MNI template follows the convention of T&T, but doesn’t match the particular brain Recommended reading: http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach 45 Anatomical MRI TPMs Segmentation Transformation (seg_sn.mat) SEGMENT m11 m21 m31 0 Motion corrected Mean functional NORM WRITE m12 m13 m14 m22 m23 m24 m32 m33 m34 0 0 1 (Headers changed) MNI Space 46 Goal: Probabilistically label voxels into their appropriate space How: Bayesian inference Use tissue probability maps (TPMs) are used as priors. Output: a spatial transformation (i.e. seg_sn.mat) that can be used for spatially normalising images. 47 MRI imperfections make normalisation harder Noise, artefacts, partial volume effect Intensity inhomogeneity or “bias” field Differences between sequences Normalising segmented tissue maps should be more robust and precise than using the original images ... … Tissue segmentation benefits from spatially-aligned prior tissue probability maps (from other segmentations) This circularity motivates simultaneous segmentation and normalisation in a unified model 48 SPM8 implements a generative model Principled Bayesian probabilistic formulation Gaussian mixture model segmentation with deformable tissue probability maps (TPMs, priors) The inverse of the transformation that aligns the TPMs can be used to normalise the original image Bias correction is included within the model 49 Classification is based on a Mixture of Gaussians model (MOG), which represents the intensity probability density by a number of Gaussian distributions. Frequency Image Intensity 50 51 Multiple Gaussians per tissue class allow non-Gaussian intensity distributions to be modelled. E.g. accounting for partial volume effects 52 A multiplicative bias field is modelled as a linear combination of basis functions. Corrupted image Bias Field Corrected image 53 Tissue probability maps (TPMs) are used as the prior, instead of the proportion of voxels in each class ICBM Tissue Probabilistic Atlases. These tissue probability maps were kindly provided by the International Consortium for Brain Mapping 54 Tissue probability maps images are warped to match the subject The inverse transform warps to the TPMs 55 Spatially normalised BrainWeb phantoms (T1, T2, PD) Tissue probability maps of GM and WM Cocosco, Kollokian, Kwan & Evans. “BrainWeb: Online Interface to a 3D MRI Simulated Brain Database”. NeuroImage 5(4):S425 (1997) 56 The “best” parameters according to the objective function may not be realistic In addition to similarity, regularisation terms or constraints are often needed to ensure a reasonable solution is found Also helps avoid poor local optima Can be considered as priors in a Bayesian framework, e.g. converting ML to MAP: log(posterior) = log(likelihood) + log(prior) + c 57 Seek to match functionally homologous regions, but... Challenging high-dimensional optimisation, many local optima Different cortices can have different folding patterns No exact match between structure and function [Interesting recent paper Amiez et al. (2013), PMID:23365257 ] Compromise Correct relatively large-scale variability (sizes of structures) Smooth over finer-scale residual differences 58 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 Kernel SMOOTH How is it implemented? Convolution with a 3D Gaussian kernel, of specified full-width at half-maximum (FWHM) in mm MNI Space GLM 59 • • Goal: Improve SNR, Matched-Filter Theorem How: Smooth with a 3D Gaussian Kernel o Each voxel after smoothing effectively becomes the result of applying a weighted region of interest (ROI). Before convolution Convolved with a Gaussian 60 Potentially increase signal to noise (matched filter theorem) Inter-subject averaging (allowing for residual differences after normalisation) Increase validity of statistics (more likely that errors distributed normally) • Kernel defined in terms of FWHM (full width at half maximum) of filter usually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussian • Ultimate smoothness is function of applied smoothing and intrinsic image smoothness (sometimes expressed as “resels” - RESolvable Elements) FWHM Gaussian smoothing kernel 61 Signal Change Z-Value 0mm smooth 9 8 7 6 5 4 3 2 1 0 -1 -2 8mm smooth 4mm smooth 20mm smooth Changes in Z-Values Across Four Random Voxels as a Function of Kernel Size (x=18, y=31, z=25) (x=20, y=20, z=25) (x=28, y=7, z=13) (x=18, y=42, z=23) Average Across Voxels 0 4 8 Kernel Size (mm) 12 20 Input Output fMRI time-series Anatomical MRI TPMs Segmentation Transformation (seg_sn.mat) Kernel REALIGN COREG SEGMENT m11 m21 m31 0 Motion corrected Mean functional NORM WRITE SMOOTH m12 m13 m14 m22 m23 m24 m32 m33 m34 0 0 1 (Headers changed) MNI Space GLM 63 Spikes are impulsive positive or negative going discontinuities in the time course, followed by a return to normal. Multiple sources: Electrical sparks (from gradient problems, metal in bore) Rapid motion (coughing) External interference They cannot be effectively removed by frequency domain filtering. ART (from Susan Gabrieli at MIT 64 ART is a GUI tool for remedying a number of problems in datasets. Among its tools is one for detecting and removing spikes from fMRI data. Examines the global mean signal and motion parameters to detect “anomalous” time points that need to be dealt with. 65 66 67 68 Internet resources: http://www.translationalneuromodeling.org/spmcourse-2014-presentation-slides/ 69