[PPT] - IBME Ivor J.A. Simpson 1, 2 , Mark W. Woolrich 2,3 , Adrian R. Groves PowerPoint Presentation

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IBME

Institute of Biomedical Engineering University of Oxford

Longitudinal Brain MRI Analysis with Uncertain Registration

Ivor J.A. Simpson1, 2, Mark W. Woolrich2,3, Adrian R. Groves2, Julia A. Schnabel1

1 Institute of Biomedical Engineering, University of Oxford 2 FMRIB Centre, University of Oxford 3 OHBA Centre, University of Oxford

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 2

IBME

Institute of Biomedical Engineering University of Oxford

Longitudinal Analysis of Alzheimer's Disease

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Alzheimer's Disease is a progressive neurodegenerative condition.

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Longitudinal anatomical changes provide information on the rate of progression.

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Quantitative analysis of these changes can be evaluated using non-rigid registration (Freeborough and Fox, 98).

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To perform statistical analysis of these features across a population, these data need to

be examined in a common anatomical space.

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Achieved by spatial normalisation.

Baseline Follow-up Jacobian

1.1 0.95

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 3

IBME

Institute of Biomedical Engineering University of Oxford

Spatial Normalisation

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Current approaches to spatial normalisation only consider the single most likely mapping (under some constraints).

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This is assumed to produce a perfect mapping.

However, this ignores all the other “probable” mappings.

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 4

IBME

Institute of Biomedical Engineering University of Oxford

Compensating for an Imperfect Mapping

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Imperfect registration is commonly compensated for by smoothing the data using a Gaussian kernel.

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Assumes all data suffers from the same level of mis-registration, which is constant across the image.

Likely to over-/under-smooth some data.

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This affects the ability to localise consistent features, regardless of the choice of statistical inference.

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We propose a method for image smoothing based on a measure of uncertainty derived from the registration.

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 5

IBME

Institute of Biomedical Engineering University of Oxford

Probabilistic Image Registration Algorithm

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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.

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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.

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 6

IBME

Institute of Biomedical Engineering University of Oxford

Uncertainty in Registration

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Previous work mainly focused on visualisation of registration uncertainty (Hub 2009, Kybic 2010, Risholm 2010).

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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.

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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.

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 7

IBME

Institute of Biomedical Engineering University of Oxford

Example Spatial Normalisation

Atlas Subject Normalised Subject

=

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 8

IBME

Institute of Biomedical Engineering University of Oxford

Compensating for Uncertain Registration

Estimate local 3D anisotropic Gaussian kernel to smooth each voxel.

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 9

IBME

Institute of Biomedical Engineering University of Oxford

Compensating for Uncertain Registration

Estimate local 3D anisotropic Gaussian kernel to smooth each voxel.

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 10

IBME

Institute of Biomedical Engineering University of Oxford

Experiments – Registration Pipeline

Follow-up Baseline Atlas Jacobian Spatially normalised Jacobian

1.1 0.95

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 11

IBME

Institute of Biomedical Engineering University of Oxford

Experiments

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Data was used from the Alzhiemers Disease Neuroimaging Initiative (ADNI) study (Mueller et al. 2005).

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Subjects with a minimal scan interval of 1 year were split into:

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162 subjects used for training (81 AD, 81 NC).

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149 subjects used for testing (68 AD, 81 NC).

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Each subject’s Jacobian map was normalised to a single year.

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Spatially normalised Jacobian maps were either:

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Not smoothed

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Smoothed with a Gaussian kernel (σ = 2mm)

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Smoothed based on the registration uncertainty.

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 12

IBME

Institute of Biomedical Engineering University of Oxford

Voxelwise statistical significance of spatially normalised Jacobian maps

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Voxelwise statistical significance of spatially normalised Jacobians assessed by t-test between the populations.

– Log scale shows the level of statistical significance (p-value). Un-smoothed data 2mm Gaussian smoothed data

1x10-10 1x10-25 1x10-10 1x10-25 1x10-10 1x10-25

Adaptively smoothed data

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 13

IBME

Institute of Biomedical Engineering University of Oxford

Difference in voxelwise statistical significance under different smoothing

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Voxelwise statistical significance depends on data smoothing.

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Blue log scale shows the factor of increase in statistical significance of adaptive smoothing over the other two methods.

2x 20x 2x 20000 x

Increase in factor of statistical significance from un-smoothed data Increase in factor of statistical significance from 2mm Gaussian smoothed data

1x10-10 1x10-25

Adaptively smoothed level of statistical significance

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 14

IBME

Institute of Biomedical Engineering University of Oxford

Results – Discrimination between classes

 Classify between AD and NC.

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Mask spatially normalised Jacobian maps based on t-test on training set.

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Decompose data using unsupervised dimensionality reduction (PCA).

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Classify subject using the principal components which make up 99% of the full sample variance using an SVM with a RBF kernel.

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Each method had a robust set of optimal parameters evaluated using leave-one out cross-validation on the training set. Smoothing method Correct rate Sensitivity Specificity RBF σ Soft Margin No smoothing 0.852 0.838 0.864 33 100 Gaussian Smoothing (σ= 2mm) 0.866 0.838 0.889 51 100 Adaptive Smoothing 0.873 0.838 0.9012 55 100

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 15

IBME

Institute of Biomedical Engineering University of Oxford

Results – Discrimination between classes

 Classify between AD and NC

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Select 2000 most significant voxels from the spatially normalised Jacobian maps (assessed by t-test on the training set) to use as features.

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Classify subjects using an SVM with a RBF kernel.

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Each method had a robust set of optimal parameters evaluated using leave-one out cross-validation on the training set. Smoothing method Correct rate Sensitivity Specificity RBF σ Soft Margin No smoothing 0.846 0.721 0.95 110 104 Gaussian Smoothing (σ= 2mm) 0.846 0.721 0.95 150 104 Adaptive Smoothing 0.873 0.75 0.975 40 103

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 16

IBME

Institute of Biomedical Engineering University of Oxford

Results - Average Uncertainty

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Average registration derived uncertainty from NC subjects Average AD uncertainty is 5% higher

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 17

IBME

Institute of Biomedical Engineering University of Oxford

Conclusions

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We have presented a probabilistic registration tool which can provide measurements of the uncertainty of an estimated mapping.

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We have shown how this uncertainty can then be used to estimate a local smoothing kernel.

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We have demonstrated that this principled approach to image smoothing improves our ability to classify subjects with AD using longitudinal image features.

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 18

IBME

Institute of Biomedical Engineering University of Oxford

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.

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 19

IBME

Institute of Biomedical Engineering University of Oxford

References

Freeborough P.A., Fox N.C., Modeling brain deformations in Alzheimer's disease by fluid registration of serial 3D MR images, Journal Computer Assisted Tomography (1998) Jordan, M.I., Ghahramani, Z., Jaakkola, T.S., Saul, L.K., An introduction to variational methods for graphical models. Machine learning (1999) Simpson, I.J.A., Schnabel, J.A., Groves, A.R., Andersson, J.L.R., Woolrich, M.W., Probabilistic inference

f regularisation in non-rigid registration. Neuroimage (In press)

Kybic, J., Bootstrap resampling for image registration uncertainty estimation without ground truth, IEEE Transactions on Image Processing (2010) ฀ Hub, M., Kessler, M. L., & Karger, C. P., A stochastic approach to estimate the uncertainty involved in B- spline image registration. IEEE transactions on medical imaging (2009) Risholm, P., Pieper, S., Samset, E., & Wells, W. M., Summarizing and visualizing uncertainty in non-rigid registration, P. Risholm, MICCAI (2010) Mueller, S.G. and Weiner, M.W. and Thal, L.J. and Petersen, R.C. and Jack, C. and Jagust, W. and Trojanowski, J.Q. and Toga, A.W. and Beckett, L., The Alzheimer's disease neuroimaging initiative, Neuroimaging Clinics of North America (2005)

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 20

IBME

Institute of Biomedical Engineering University of Oxford

Questions?

Any additional questions or comments, please email me at ivor.simpson@eng.ox.ac.uk

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 21

IBME

Institute of Biomedical Engineering University of Oxford

Variability in uncertainty in example subject

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 22

IBME

Institute of Biomedical Engineering University of Oxford

Variability in Average Uncertainty Maps

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 23

IBME

Institute of Biomedical Engineering University of Oxford

Variability Across Subjects

2mm 0.4mm

Standard deviation of uncertainty from population average

NC AD

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I. Simpson: Longitudinal

Brain MRI Analysis with Uncertain Registration Page 24

IBME

Institute of Biomedical Engineering University of Oxford

Original Results

 Spatially normalised t-test masked Jacobian maps

decomposed using PCA.

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Classification of principal components which make up 99% of the full sample variance using an SVM with a RBF kernel

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Leave-two-out experiments. Smoothing method Correct rate Sensitivity Specificity RBF σ Soft Margin No smoothing 0.796 0.704 0.888 2 1 Gaussian Smoothing (σ= 2mm) 0.788 0.904 0.670 2 1 Adaptive Smoothing 0.840 0.968 0.710 2 1