Diffeomorphic image registration of diffusion MRI using spherical harmonics

Manifold-based respiratory phase estimation enables motion and distortion correction of free-breathing cardiac diffusion tensor MRI

PURPOSE

For in vivo cardiac DTI, breathing motion and B₀ field inhomogeneities produce misalignment and geometric distortion in diffusion-weighted (DW) images acquired with conventional single-shot EPI. We propose using a dimensionality reduction method to retrospectively estimate the respiratory phase of DW images and facilitate both distortion correction (DisCo) and motion compensation.

METHODS

Free-breathing electrocardiogram-triggered whole left-ventricular cardiac DTI using a second-order motion-compensated spin echo EPI sequence and alternating directionality of phase encoding blips was performed on 11 healthy volunteers. The respiratory phase of each DW image was estimated after projecting the DW images into a 2D space with Laplacian eigenmaps. DisCo and motion compensation were applied to the respiratory sorted DW images. The results were compared against conventional breath-held T₂ half-Fourier single shot turbo spin echo. Cardiac DTI parameters including fractional anisotropy, mean diffusivity, and helix angle transmurality were compared with and without DisCo.

RESULTS

The left-ventricular geometries after DisCo and motion compensation resulted in significantly improved alignment of DW images with T₂ reference. DisCo reduced the distance between the left-ventricular contours by 13.2% ± 19.2%, P < .05 (2.0 ± 0.4 for DisCo and 2.4 ± 0.5 mm for uncorrected). DisCo DTI parameter maps yielded no significant differences (mean diffusivity: 1.55 ± 0.13 × 10^-3 mm² /s and 1.53 ± 0.13 × 10^-3 mm² /s, P = .09; fractional anisotropy: 0.375 ± 0.041 and 0.379 ± 0.045, P = .11; helix angle transmurality: 1.00% ± 0.10°/% and 0.99% ± 0.12°/%, P = .44), although the orientation of individual tensors differed.

CONCLUSION

Retrospective respiratory phase estimation with LE-based DisCo and motion compensation in free-breathing cardiac DTI resulting in significantly reduced geometric distortion and improved alignment within and across slices.

Symplectomorphic registration with phase space regularization by entropy spectrum pathways

PURPOSE

The ability to register image data to a common coordinate system is a critical feature of virtually all imaging studies. However, in spite of the abundance of literature on the subject and the existence of several variants of registration algorithms, their practical utility remains problematic, as commonly acknowledged even by developers of these methods.

METHODS

A new registration method is presented that utilizes a Hamiltonian formalism and constructs registration as a sequence of symplectomorphic maps in conjunction with a novel phase space regularization. For validation of the framework a panel of deformations expressed in analytical form is developed that includes deformations based on known physical processes in MRI and reproduces various distortions and artifacts typically present in images collected using these different MRI modalities.

RESULTS

The method is demonstrated on the three different magnetic resonance imaging (MRI) modalities by mapping between high resolution anatomical (HRA) volumes, medium resolution diffusion weighted MRI (DW-MRI) and HRA volumes, and low resolution functional MRI (fMRI) and HRA volumes.

CONCLUSIONS

The method has shown an excellent performance and the panel of deformations was instrumental to quantify its repeatability and reproducibility in comparison to several available alternative approaches.

Sparse registration of diffusion weighted images

BACKGROUND AND OBJECTIVE

Registration is a critical step in group analysis of diffusion weighted images (DWI). Image registration is also necessary for construction of white matter atlases that can be used to identify white matter changes. A challenge in the registration of DWI is that the orientation of the fiber bundles should be considered in the process, making their registration more challenging than that of the scalar images. Most of the current registration methods use a model of diffusion profile, limiting the method to the used model.

METHODS

We propose a model-independent method for DWI registration. The proposed method uses a multi-level free-form deformation (FFD), a sparse similarity measure, and a dictionary. We also propose a synthesis K-SVD algorithm for sparse interpolation of images during the registration process. We utilize two dictionaries: analysis dictionary is learned based on diffusion signals while synthesis dictionary is generated based on image patches. The proposed multi-level approach registers anatomical structures at different scales. T-test is used to determine the significance of the differences between different methods.

RESULTS

We have shown the efficiency of the proposed approach using real data. The method results in smaller generalized fractional anisotropy (GFA) root mean square (RMS) error (0.05 improvements, p = 0.0237) and angular error (0.37 ° improvement, p = 0.0330) compared to the large deformation diffeomorphic metric mapping (LDDMM) method and advanced normalization tools (ANTs).

CONCLUSION

Sparse registration of diffusion signals enables registration of diffusion weighted images without using a diffusion model.

Shape analysis of the human brain: a brief survey

The survey outlines and compares popular computational techniques for quantitative description of shapes of major structural parts of the human brain, including medial axis and skeletal analysis, geodesic distances, Procrustes analysis, deformable models, spherical harmonics, and deformation morphometry, as well as other less widely used techniques. Their advantages, drawbacks, and emerging trends, as well as results of applications, in particular, for computer-aided diagnostics, are discussed.

A highly accurate symmetric optical flow based high-dimensional nonlinear spatial normalization of brain images

Spatial normalization plays a key role in voxel-based analyses of brain images. We propose a highly accurate algorithm for high-dimensional spatial normalization of brain images based on the technique of symmetric optical flow. We first construct a three dimension optical model with the consistency assumption of intensity and consistency of the gradient of intensity under a constraint of discontinuity-preserving spatio-temporal smoothness. Then, an efficient inverse consistency optical flow is proposed with aims of higher registration accuracy, where the flow is naturally symmetric. By employing a hierarchical strategy ranging from coarse to fine scales of resolution and a method of Euler-Lagrange numerical analysis, our algorithm is capable of registering brain images data. Experiments using both simulated and real datasets demonstrated that the accuracy of our algorithm is not only better than that of those traditional optical flow algorithms, but also comparable to other registration methods used extensively in the medical imaging community. Moreover, our registration algorithm is fully automated, requiring a very limited number of parameters and no manual intervention.

Diffeomorphic metric mapping and probabilistic atlas generation of hybrid diffusion imaging based on BFOR signal basis

We first propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI). We denote this algorithm as LDDMM-HYDI. We then propose a Bayesian probabilistic model for estimating the white matter atlas from HYDIs. We adopt the work given in Hosseinbor et al. (2013) and represent the q-space diffusion signal with the Bessel Fourier orientation reconstruction (BFOR) signal basis. The BFOR framework provides the representation of mDWI in the q-space and the analytic form of the emsemble average propagator (EAP) reconstruction, as well as reduces memory requirement. In addition, since the BFOR signal basis is orthonormal, the L(2) norm that quantifies the differences in the q-space signals of any two mDWI datasets can be easily computed as the sum of the squared differences in the BFOR expansion coefficients. In this work, we show that the reorientation of the q-space signal due to spatial transformation can be easily defined on the BFOR signal basis. We incorporate the BFOR signal basis into the LDDMM framework and derive the gradient descent algorithm for LDDMM-HYDI with explicit orientation optimization. Additionally, we extend the previous Bayesian atlas estimation framework for scalar-valued images to HYDIs and derive the expectation-maximization algorithm for solving the HYDI atlas estimation problem. Using real HYDI datasets, we show that the Bayesian model generates the white matter atlas with anatomical details. Moreover, we show that it is important to consider the variation of mDWI reorientation due to a small change in diffeomorphic transformation in the LDDMM-HYDI optimization and to incorporate the full information of HYDI for aligning mDWI. Finally, we show that the LDDMM-HYDI outperforms the LDDMM algorithm with diffusion tensors generated from each shell of HYDI.

Large deformation diffeomorphic registration of diffusion-weighted imaging data

Registration plays an important role in group analysis of diffusion-weighted imaging (DWI) data. It can be used to build a reference anatomy for investigating structural variation or tracking changes in white matter. Unlike traditional scalar image registration where spatial alignment is the only focus, registration of DWI data requires both spatial alignment of structures and reorientation of local signal profiles. As such, DWI registration is much more complex and challenging than scalar image registration. Although a variety of algorithms has been proposed to tackle the problem, most of them are restricted by the diffusion model used for registration, making it difficult to fit to the registered data a different model. In this paper we describe a method that allows any diffusion model to be fitted after registration for subsequent multifaceted analysis. This is achieved by directly aligning DWI data using a large deformation diffeomorphic registration framework. Our algorithm seeks the optimal coordinate mapping by simultaneously considering structural alignment, local signal profile reorientation, and deformation regularization. Our algorithm also incorporates a multi-kernel strategy to concurrently register anatomical structures at different scales. We demonstrate the efficacy of our approach using in vivo data and report detailed qualitative and quantitative results in comparison with several different registration strategies.

Estimation of the CSA-ODF using Bayesian compressed sensing of multi-shell HARDI

PURPOSE

Diffusion MRI provides important information about the brain white matter structures and has opened new avenues for neuroscience and translational research. However, acquisition time needed for advanced applications can still be a challenge in clinical settings. There is consequently a need to accelerate diffusion MRI acquisitions.

METHODS

A multi-task Bayesian compressive sensing (MT-BCS) framework is proposed to directly estimate the constant solid angle orientation distribution function (CSA-ODF) from under-sampled (i.e., accelerated image acquisition) multi-shell high angular resolution diffusion imaging (HARDI) datasets, and accurately recover HARDI data at higher resolution in q-space. The proposed MT-BCS approach exploits the spatial redundancy of the data by modeling the statistical relationships within groups (clusters) of diffusion signal. This framework also provides uncertainty estimates of the computed CSA-ODF and diffusion signal, directly computed from the compressive measurements. Experiments validating the proposed framework are performed using realistic multi-shell synthetic images and in vivo multi-shell high angular resolution HARDI datasets.

RESULTS

Results indicate a practical reduction in the number of required diffusion volumes (q-space samples) by at least a factor of four to estimate the CSA-ODF from multi-shell data.

CONCLUSION

This work presents, for the first time, a multi-task Bayesian compressive sensing approach to simultaneously estimate the full posterior of the CSA-ODF and diffusion-weighted volumes from multi-shell HARDI acquisitions. It demonstrates improvement of the quality of acquired datasets by means of CS de-noising, and accurate estimation of the CSA-ODF, as well as enables a reduction in the acquisition time by a factor of two to four, especially when "staggered" q-space sampling schemes are used. The proposed MT-BCS framework can naturally be combined with parallel MR imaging to further accelerate HARDI acquisitions.

Diffeomorphic metric mapping of hybrid diffusion imaging based on BFOR signal basis

In this paper, we propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI), denoted as LDDMM-HYDI. We adopt the work given in Hosseinbor et al. (2012) and represent the q-space diffusion signal with the Bessel Fourier orientation reconstruction (BFOR) signal basis. The BFOR framework provides the representation of mDWI in the q-space and thus reduces memory requirement. In addition, since the BFOR signal basis is orthonormal, the L2 norm that quantifies the differences in q-space signals of any two mDWI datasets can be easily computed as the sum of the squared differences in the BFOR expansion coefficients. In this work, we show that the reorientation of the q-space signal due to spatial transformation can be easily defined on the BFOR signal basis. We incorporate the BFOR signal basis into the LDDMM framework and derive the gradient descent algorithm for LDDMM-HYDI with explicit orientation optimization. Using real HYDI datasets, we show that it is important to consider the variation of mDWI reorientation due to a small change in diffeomorphic transformation in the LDDMM-HYDI optimization.

Diffeomorphic metric mapping of high angular resolution diffusion imaging based on Riemannian structure of orientation distribution functions

In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. To this end, we first review the Riemannian manifold of ODFs. We then define the reorientation of an ODF when an affine transformation is applied and subsequently, define the diffeomorphic group action to be applied on the ODF based on this reorientation. We incorporate the Riemannian metric of ODFs for quantifying the similarity of two HARDI images into a variational problem defined under the large deformation diffeomorphic metric mapping framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.

Medical image registration: a review

This paper presents a review of automated image registration methodologies that have been used in the medical field. The aim of this paper is to be an introduction to the field, provide knowledge on the work that has been developed and to be a suitable reference for those who are looking for registration methods for a specific application. The registration methodologies under review are classified into intensity or feature based. The main steps of these methodologies, the common geometric transformations, the similarity measures and accuracy assessment techniques are introduced and described.

Reorientation of fiber orientation distributions using apodized point spread functions

Using high angular resolution diffusion-weighted images, spherical deconvolution enables multiple white matter fiber populations to be resolved within a single voxel by computing the fiber orientation distribution (FOD). Higher order information provided by FODs could improve several methods for investigating population differences in white matter, including image registration, voxel-based analysis, atlas-based segmentation and labeling, and group average fiber tractography. All of these methods require spatial normalization of FODs. In this article, a novel method to reorient the FOD is presented, which is an important step required for FOD spatial normalization. The proposed method was assessed using both qualitative and quantitative experiments, with numerical simulations and in vivo human data. Results demonstrate that the proposed method improves FOD reorientation accuracy, removes undesired artefacts, and decreases computation time compared to a previous approach. The utility of the proposed method is illustrated by nonlinear FOD spatial normalization of 10 human subjects. Accurate reorientation and normalization of FODs is a critical step toward investigating white matter tissue in the context of multiple fiber orientations.

White matter atlas generation using HARDI based automated parcellation

Most diffusion imaging studies have used subject registration to an atlas space for enhanced quantification of anatomy. However, standard diffusion tensor atlases lack information in regions of fiber crossing and are based on adult anatomy. The degree of error associated with applying these atlases to studies of children for example has not yet been estimated but may lead to suboptimal results. This paper describes a novel technique for generating population-specific high angular resolution diffusion imaging (HARDI)-based atlases consisting of labeled regions of homogenous white matter. Our approach uses a fiber orientation distribution (FOD) diffusion model and a data driven clustering algorithm. White matter regional labeling is achieved by our automated data driven clustering algorithm that has the potential to delineate white matter regions based on fiber complexity and orientation. The advantage of such an atlas is that it is study specific and more comprehensive in describing regions of white matter homogeneity as compared to standard anatomical atlases. We have applied this state of the art technique to a dataset consisting of adolescent and preadolescent children, creating one of the first examples of a HARDI-based atlas, thereby establishing the feasibility of the atlas creation framework. The white matter regions generated by our automated clustering algorithm have lower FOD variance than when compared to the regions created from a standard anatomical atlas.