A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.

[1]  Pratik Mukherjee,et al.  Visualizing white matter pathways in the living human brain: diffusion tensor imaging and beyond. , 2007, Neuroimaging clinics of North America.

[2]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[3]  L. Chambers.  Practical methods of optimization (2nd edn) , by R. Fletcher. Pp. 436. £34.95. 2000. ISBN 0 471 49463 1 (Wiley). , 2001, The Mathematical Gazette.

[4]  Hsiao-Wen Chung,et al.  Effects of interpolation methods in spatial normalization of diffusion tensor imaging data on group comparison of fractional anisotropy. , 2009, Magnetic resonance imaging.

[5]  Michael Brady,et al.  Improved Optimization for the Robust and Accurate Linear Registration and Motion Correction of Brain Images , 2002, NeuroImage.

[6]  P. Basser,et al.  Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. , 1996, Journal of magnetic resonance. Series B.

[7]  G. Sapiro,et al.  Comprehensive in vivo Mapping of the Human Basal Ganglia and Thalamic Connectome in Individuals Using 7T MRI , 2012, PloS one.

[8]  Paul A. Yushkevich,et al.  Deformable registration of diffusion tensor MR images with explicit orientation optimization , 2006, Medical Image Anal..

[9]  Carlo Pierpaoli,et al.  Probabilistic Identification and Estimation of Noise (piesno): a Self-consistent Approach and Its Applications in Mri , 2009 .

[10]  Nicholas Ayache,et al.  Fast and Simple Calculus on Tensors in the Log-Euclidean Framework , 2005, MICCAI.

[11]  M. Horsfield,et al.  Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging , 1999, Magnetic resonance in medicine.

[12]  Christian Beaulieu,et al.  Assessment of Averaging Spatially Correlated Noise for 3-D Radial Imaging , 2011, IEEE Transactions on Medical Imaging.

[13]  S. Bouix,et al.  Building an Average Population HARDI Atlas , 2010 .

[14]  Baba C. Vemuri,et al.  Non-rigid Registration of High Angular Resolution Diffusion Images Represented by Gaussian Mixture Fields , 2009, MICCAI.

[15]  S. Skare,et al.  Noise considerations in the determination of diffusion tensor anisotropy. , 2000, Magnetic resonance imaging.

[16]  P. Basser,et al.  Toward a quantitative assessment of diffusion anisotropy , 1996, Magnetic resonance in medicine.

[17]  Peter A. Calabresi,et al.  Tract probability maps in stereotaxic spaces: Analyses of white matter anatomy and tract-specific quantification , 2008, NeuroImage.

[18]  Olivier Clatz,et al.  DT-REFinD: Diffusion Tensor Registration With Exact Finite-Strain Differential , 2009, IEEE Transactions on Medical Imaging.

[19]  D. Koshland.  Frontiers in neuroscience. , 1988, Science.

[20]  Stuart Crozier,et al.  Symmetric diffeomorphic registration of fibre orientation distributions , 2011, NeuroImage.

[21]  M. Jenkinson.  Non-linear registration aka Spatial normalisation , 2007 .

[22]  Martin Styner,et al.  DTI registration in atlas based fiber analysis of infantile Krabbe disease , 2011, NeuroImage.

[23]  N. Higham.  Computing the polar decomposition with applications , 1986 .

[24]  Baba C. Vemuri,et al.  Registration of High Angular Resolution Diffusion MRI Images Using 4 th Order Tensors , 2007, MICCAI.

[25]  P. Basser,et al.  MR diffusion tensor spectroscopy and imaging. , 1994, Biophysical journal.

[26]  Timothy Edward John Behrens,et al.  Characterization and propagation of uncertainty in diffusion‐weighted MR imaging , 2003, Magnetic resonance in medicine.

[27]  Arno Klein,et al.  Evaluation of 14 nonlinear deformation algorithms applied to human brain MRI registration , 2009, NeuroImage.

[28]  James C. Gee,et al.  Spatial transformations of diffusion tensor magnetic resonance images , 2001, IEEE Transactions on Medical Imaging.

[29]  J. Gilmore,et al.  Non-Parametric Deformable Registration of High Angular Resolution Diffusion Data Using Diffusion Profile Statistics , 2009 .

[30]  Luke Bloy,et al.  Demons registration of high angular resolution diffusion images , 2010, 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[31]  A. Filler.  MAGNETIC RESONANCE NEUROGRAPHY AND DIFFUSION TENSOR IMAGING: ORIGINS, HISTORY, AND CLINICAL IMPACT OF THE FIRST 50 000 CASES WITH AN ASSESSMENT OF EFFICACY AND UTILITY IN A PROSPECTIVE 5000‐PATIENT STUDY GROUP , 2009, Neurosurgery.

[32]  Anqi Qiu,et al.  Diffeomorphic Metric Mapping of High Angular Resolution Diffusion Imaging Based on Riemannian Structure of Orientation Distribution Functions , 2011, IEEE Transactions on Medical Imaging.

[33]  Derek K. Jones,et al.  Diffusion‐tensor MRI: theory, experimental design and data analysis – a technical review , 2002 .

[34]  Yihong Yang,et al.  Diffeomorphic Image Registration of Diffusion MRI Using Spherical Harmonics , 2011, IEEE Transactions on Medical Imaging.

[35]  Essa Yacoub,et al.  Magnetic Resonance Field Strength Effects on Diffusion Measures and Brain Connectivity Networks , 2013, Brain Connect..

[36]  J. E. Tanner,et al.  Spin diffusion measurements : spin echoes in the presence of a time-dependent field gradient , 1965 .

[37]  Essa Yacoub,et al.  Generalized Constant Solid Angle ODF and Optimal Acquisition Protocol for Fiber Orientation Mapping , 2012 .

[38]  Fabrice Heitz,et al.  Retrospective evaluation of a topology preserving non-rigid registration method , 2006, Medical Image Anal..

[39]  F. Maes,et al.  Spatial Transformations of High Angular Resolution Diffusion Imaging Data in Q-space , 2010 .

[40]  Raghu Machiraju,et al.  Automatic Deformable Diffusion Tensor Registration for Fiber Population Analysis , 2008, MICCAI.

[41]  Rachid Deriche,et al.  Apparent diffusion profile estimation from high angular resolution diffusion images , 2006, SPIE Medical Imaging.

[42]  A. Filler.  MAGNETIC RESONANCE NEUROGRAPHY AND DIFFUSION TENSOR IMAGING : ORIGINS , HISTORY , AND CLINICAL IMPACT OF THE FIRST 50 000 CASES WITH AN ASSESSMENT OF EFFICACY AND UTILITY IN A PROSPECTIVE 5000-PATIENT STUDY GROUP , 2022 .

[43]  Sébastien Ourselin,et al.  Block Matching: A General Framework to Improve Robustness of Rigid Registration of Medical Images , 2000, MICCAI.

[44]  James V. Miller,et al.  A Method for Registering Diffusion Weighted Magnetic Resonance Images , 2006, MICCAI.