(Headers MNI Space SMOOTH ANALYSIS Reorientation and registration demo Now to SPM for a more conventional slide-based talk, please see the video (with accompanying slides available) at www.fil.ion.ucl.ac.uk/spm/course/video/ B-spline Interpolation
A continuous function is represented by a linear combination of basis 2D B-spline basis functions of degrees 0, 1, 2 and 3 functions B-splines are piecewise polynomials Nearest neighbour and trilinear interpolation are the same as B-spline interpolation with degrees of 0 and 1. Coregistration (NMI) Intermodal coreg. Cant simply use
intensity difference Quantify how well one image predicts the other = how much shared info Info from joint probability distrib. Estimated from joint histogram fMRI time-series movie Motion in fMRI Is important! Increases residual variance and reduces sensitivity Data may get completely lost with sudden movements
Movements may be correlated with the task Try to minimise movement (dont scan for too long!) Motion correction using realignment Each volume rigidly registered to reference Least squares objective function Realigned images must be resliced for analysis Not necessary if they will be normalised anyway Residual Errors from aligned fMRI 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 Gaps between slices can cause aliasing artefacts Re-sampling can introduce interpolation errors Though higher degree spline interpolation mitigates Functions of the estimated motion parameters can be modelled as confounds in subsequent analyses fMRI movement by distortion interaction * Subject disrupts B0 field, rendering it inhomogeneous * distortions occur along the phaseencoding direction * Subject moves during EPI time series * Distortions vary with subject position
* shape varies (non-rigidly) Correcting for distortion changes using Unwarp Estimate reference from mean of all scans. Estimate new distortion fields for each image: estimate rate of change of field with respect to the current estimate of movement Unwarp time series. parameters in pitch and roll.
Estimate movement parameters. + B0 B0 Andersson et al, 2001 Spatial Normalisation Spatial Normalisation - Reasons 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 Standard spaces The Talairach Atlas The MNI/ICBM AVG152 Template The MNI template follows the convention of T&T, but doesnt match the particular brain
Normalisation via unified segmentation 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
Summary of the unified model SPM12 implements a generative model Principled Bayesian probabilistic formulation Gaussian mixture model segmentation with deformable tissue probability maps (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 Tissue intensity distributions (T1-w MRI) Mixture of Gaussians (MOG) 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 Non-Gaussian Intensity Distributions Multiple Gaussians per tissue class allow non-Gaussian intensity distributions to be modelled. E.g. accounting for partial volume effects Modelling inhomogeneity A multiplicative bias field can be modelled as a linear combination of basis functions. Corrupted image
Bias Field Corrected image Tissue Probability Maps Tissue probability maps (TPMs) are used as the prior, instead of the proportion of voxels in each class Deforming the Tissue Probability Maps * Tissue probability images are warped to match the subject *
The inverse transform warps to the TPMs Optimisation Find the best parameters according to an objective function (minimised or maximised) Objective functions can often be related to a probabilistic model (Bayes -> MAP -> ML -> LSQ) Global optimum Objective function (most probable)
Local optimum Value of parameter Local optimum Optimisation of multiple parameters Optimum Contours of a two-dimensional objective function landscape Segmentation results 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) Spatial normalisation results Affine registration Non-linear registration Spatial normalisation Overfitting Without regularisation, the non-linear spatial
without using regularisation regularisation (error = 287.3) (error = 302.7) Spatial normalisation regularisation 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 Spatial normalisation Limitations 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 Smoothing Why would we deliberately blur the data? Improves spatial overlap by blurring over minor anatomical differences and registration errors Averaging neighbouring voxels suppresses noise 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 How is it implemented? Convolution with a 3D Gaussian kernel, of specified full-width at half-maximum (FWHM) in mm Preprocessing overview Input Output fMRI time-series Anatomical MRI
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