Longitudinal Brain MRI Analysis with Uncertain Registration IBME Ivor J.A. Simpson 1, 2 , Mark W. Woolrich 2,3 , Adrian R. Groves 2 , Julia A. Schnabel 1 Institute of Biomedical Engineering University of Oxford 1 Institute of Biomedical Engineering, University of Oxford 2 FMRIB Centre, University of Oxford 3 OHBA Centre, University of Oxford
Longitudinal Analysis of Alzheimer's Disease Alzheimer's Disease is a progressive neurodegenerative condition. Longitudinal anatomical changes provide information on the rate of progression. Quantitative analysis of these changes can be evaluated using non-rigid registration (Freeborough and Fox, 98). To perform statistical analysis of these features across a population, these data need to be examined in a common anatomical space. Achieved by spatial normalisation. 1.1 0.95 Follow-up Baseline Jacobian I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 2
Spatial Normalisation Current approaches to spatial normalisation only consider the single most likely mapping (under some constraints). This is assumed to produce a perfect mapping. However, this ignores all the other “probable” mappings. I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 3
Compensating for an Imperfect Mapping Imperfect registration is commonly compensated for by smoothing the data using a Gaussian kernel. Assumes all data suffers from the same level of mis-registration, which is constant across the image. • Likely to over-/under-smooth some data. This affects the ability to localise consistent features, regardless of the choice of statistical inference. We propose a method for image smoothing based on a measure of uncertainty derived from the registration. I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 4
Probabilistic Image Registration Algorithm We use a probabilistic registration model, where we assume a generative model for the image: Y = T ( X , w ) + E . • Y and X are the target and source images. • Transformation T ( X , w ) uses B-spline FFD model due to the compact parameterisation of w . • E is i.i.d. Gaussian noise . We infer on the model parameters using variational Bayes (Jordan et al. 1999): • Provides a mechanism for inferring the level of warp regularisation (Simpson et al., Neuroimage (In press)). • Allows tractable inference of approximate posterior distributions, rather than just point estimates. • Uses the mean-field approximation between parameter groups. I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 5
Uncertainty in Registration Previous work mainly focused on visualisation of registration uncertainty (Hub 2009, Kybic 2010, Risholm 2010). In our approach, the approximate posterior distributions provide a measure of the uncertainty of the inferred parameters. P( w | Y ) ≈ q( w ) = MVN( μ , Υ ). The covariance matrix Υ contains information on the uncertainty of the estimated mapping parameters μ . Calculate variance/cross directional co-variance for each FFD control point: Interpolate to the voxel level using the B-spline basis set. Voxelwise uncertainty distribution. Average over the set of probable mappings by smoothing. I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 6
Example Spatial Normalisation = Normalised Subject Subject Atlas I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 7
Compensating for Uncertain Registration Estimate local 3D anisotropic Gaussian kernel to smooth each voxel. I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 8
Compensating for Uncertain Registration Estimate local 3D anisotropic Gaussian kernel to smooth each voxel. I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 9
Experiments – Registration Pipeline Atlas Baseline Follow-up 1.1 0.95 Spatially normalised Jacobian Jacobian I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 10
Experiments Data was used from the Alzhiemers Disease Neuroimaging Initiative (ADNI) study (Mueller et al. 2005). Subjects with a minimal scan interval of 1 year were split into: 162 subjects used for training (81 AD, 81 NC). 149 subjects used for testing (68 AD, 81 NC). Each subject’s Jacobian map was normalised to a single year. Spatially normalised Jacobian maps were either: Not smoothed Smoothed with a Gaussian kernel (σ = 2mm) Smoothed based on the registration uncertainty. I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 11
Voxelwise statistical significance of spatially normalised Jacobian maps Voxelwise statistical significance of spatially normalised Jacobians assessed by t-test between the populations. – Log scale shows the level of statistical significance (p-value). 1x10 -25 1x10 -25 1x10 -25 1x10 -10 1x10 -10 1x10 -10 Un-smoothed data Adaptively smoothed 2mm Gaussian data smoothed data I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 12
Difference in voxelwise statistical significance under different smoothing Voxelwise statistical significance depends on data smoothing. Blue log scale shows the factor of increase in statistical significance of adaptive smoothing over the other two methods. 20000 x 1x10 -25 20x 1x10 -10 2x 2x Increase in factor of Adaptively smoothed Increase in factor of statistical significance from level of statistical statistical significance from un-smoothed data significance 2mm Gaussian smoothed data I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 13
Results – Discrimination between classes Classify between AD and NC. Mask spatially normalised Jacobian maps based on t-test on training set. Decompose data using unsupervised dimensionality reduction (PCA). Classify subject using the principal components which make up 99% of the full sample variance using an SVM with a RBF kernel. Each method had a robust set of optimal parameters evaluated using leave-one out cross-validation on the training set. Correct rate Sensitivity Specificity RBF σ Soft Margin Smoothing method No smoothing 0.852 0.838 0.864 33 100 Gaussian Smoothing 0.866 0.838 0.889 51 100 (σ= 2mm) Adaptive Smoothing 0.873 0.838 0.9012 55 100 I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 14
Results – Discrimination between classes Classify between AD and NC Select 2000 most significant voxels from the spatially normalised Jacobian maps (assessed by t-test on the training set) to use as features. Classify subjects using an SVM with a RBF kernel. Each method had a robust set of optimal parameters evaluated using leave-one out cross-validation on the training set. Correct rate Sensitivity Specificity RBF σ Soft Margin Smoothing method 10 4 No smoothing 0.846 0.721 0.95 110 10 4 Gaussian Smoothing 0.846 0.721 0.95 150 (σ= 2mm) 10 3 Adaptive Smoothing 0.873 0.75 0.975 40 I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 15
Results - Average Uncertainty Average registration derived uncertainty from NC subjects Average AD uncertainty is 5% higher I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 16
Conclusions We have presented a probabilistic registration tool which can provide measurements of the uncertainty of an estimated mapping. We have shown how this uncertainty can then be used to estimate a local smoothing kernel. We have demonstrated that this principled approach to image smoothing improves our ability to classify subjects with AD using longitudinal image features. I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 17
Acknowledgments IJAS would like to acknowledge funding from the EPSRC through the Life Sciences Interface Doctoral Training Centre, Oxford, UK. Thanks to Guarantors of Brain for their generous travel funding. Thanks to ADNI for providing access to their dataset. I. Simpson: Longitudinal IBME Brain MRI Analysis with Uncertain Registration Institute of Biomedical Engineering University of Oxford Page 18
Recommend
More recommend
