Statistical shape analysis: From landmarks to diffeomorphisms

DiffeoRaptor: diffeomorphic inter-modal image registration using RaPTOR

PURPOSE

Diffeomorphic image registration is essential in many medical imaging applications. Several registration algorithms of such type have been proposed, but primarily for intra-contrast alignment. Currently, efficient inter-modal/contrast diffeomorphic registration, which is vital in numerous applications, remains a challenging task.

METHODS

We proposed a novel inter-modal/contrast registration algorithm that leverages Robust PaTch-based cOrrelation Ratio metric to allow inter-modal/contrast image alignment and bandlimited geodesic shooting demonstrated in Fourier-Approximated Lie Algebras (FLASH) algorithm for fast diffeomorphic registration.

RESULTS

The proposed algorithm, named DiffeoRaptor, was validated with three public databases for the tasks of brain and abdominal image registration while comparing the results against three state-of-the-art techniques, including FLASH, NiftyReg, and Symmetric image Normalization (SyN).

CONCLUSIONS

Our results demonstrated that DiffeoRaptor offered comparable or better registration performance in terms of registration accuracy. Moreover, DiffeoRaptor produces smoother deformations than SyN in inter-modal and contrast registration. The code for DiffeoRaptor is publicly available at https://github.com/nimamasoumi/DiffeoRaptor .

Characterization of surface motion patterns in highly deformable soft tissue organs from dynamic MRI: An application to assess 4D bladder motion

BACKGROUND AND OBJECTIVES

Dynamic Magnetic Resonance Imaging (MRI) may capture temporal anatomical changes in soft tissue organs with high-contrast but the obtained sequences usually suffer from limited volume coverage which makes the high-resolution reconstruction of organ shape trajectories a major challenge in temporal studies. Because of the variability of abdominal organ shapes across time and subjects, the objective of the present study is to go towards 3D dense velocity measurements to fully cover the entire surface and to extract meaningful features characterizing the observed organ deformations and enabling clinical action or decision.

METHODS

We present a pipeline for characterization of bladder surface dynamics during deep respiratory movements. For a compact shape representation, the reconstructed temporal volumes were first used to establish subject-specific dynamical 4D mesh sequences using the large deformation diffeomorphic metric mapping (LDDMM) framework. Then, we performed a statistical characterization of organ dynamics from mechanical parameters such as mesh elongations and distortions. Since we refer to organs as non-flat surfaces, we have also used the mean curvature change as metric to quantify surface evolution. However, the numerical computation of curvature is strongly dependant on the surface parameterization (i.e. the mesh resolution). To cope with this dependency, we employed a non-parametric method for surface deformation analysis. Independent of parameterization and minimizing the length of the geodesic curves, it stretches smoothly the surface curves towards a sphere by minimizing a Dirichlet energy. An Eulerian PDE approach is used to derive a shape descriptor from the curve-shortening flow. Intercorrelations between individuals' motion patterns are computed using the Laplace-Beltrami Operator (LBO) eigenfunctions for spherical mapping.

RESULTS

Application to extracting characterization correlation curves for locally-controlled simulated shape trajectories demonstrates the stability of the proposed shape descriptor. Its usability was shown on MRI acquired for seven healthy participants for which the bladder was highly deformed by maximum of inspiration. As expected, the study showed that deformations occured essentially on the top lateral regions.

CONCLUSION

Promising results were obtained, showing the organ in its 3D complexity during deformation due to strain conditions. Smooth genus-0 manifold reconstruction from sparse dynamic MRI data is employed to perform a statistical shape analysis for the determination of bladder deformation.

Tetrahedral spectral feature-Based bayesian manifold learning for grey matter morphometry: Findings from the Alzheimer's disease neuroimaging initiative

Structural and anatomical analyses of magnetic resonance imaging (MRI) data often require a reconstruction of the three-dimensional anatomy to a statistical shape model. Our prior work demonstrated the usefulness of tetrahedral spectral features for grey matter morphometry. However, most of the current methods provide a large number of descriptive shape features, but lack an unsupervised scheme to automatically extract a concise set of features with clear biological interpretations and that also carries strong statistical power. Here we introduce a new tetrahedral spectral feature-based Bayesian manifold learning framework for effective statistical analysis of grey matter morphology. We start by solving the technical issue of generating tetrahedral meshes which preserve the details of the grey matter geometry. We then derive explicit weak-form tetrahedral discretizations of the Hamiltonian operator (HO) and the Laplace-Beltrami operator (LBO). Next, the Schrödinger's equation is solved for constructing the scale-invariant wave kernel signature (SIWKS) as the shape descriptor. By solving the heat equation and utilizing the SIWKS, we design a morphometric Gaussian process (M-GP) regression framework and an active learning strategy to select landmarks as concrete shape descriptors. We evaluate the proposed system on publicly available data from the Alzheimers Disease Neuroimaging Initiative (ADNI), using subjects structural MRI covering the range from cognitively unimpaired (CU) to full blown Alzheimer's disease (AD). Our analyses suggest that the SIWKS and M-GP compare favorably with seven other baseline algorithms to obtain grey matter morphometry-based diagnoses. Our work may inspire more tetrahedral spectral feature-based Bayesian learning research in medical image analysis.

Nonlinear interaction between APOE ε4 allele load and age in the hippocampal surface of cognitively intact individuals

The ε4 allele of the gene Apolipoprotein E is the major genetic risk factor for Alzheimer's Disease. APOE ε4 has been associated with changes in brain structure in cognitively impaired and unimpaired subjects, including atrophy of the hippocampus, which is one of the brain structures that is early affected by AD. In this work we analyzed the impact of APOE ε4 gene dose and its association with age, on hippocampal shape assessed with multivariate surface analysis, in a ε4‐enriched cohort of n = 479 cognitively healthy individuals. Furthermore, we sought to replicate our findings on an independent dataset of n = 969 individuals covering the entire AD spectrum. We segmented the hippocampus of the subjects with a multi‐atlas‐based approach, obtaining high‐dimensional meshes that can be analyzed in a multivariate way. We analyzed the effects of different factors including APOE, sex, and age (in both cohorts) as well as clinical diagnosis on the local 3D hippocampal surface changes. We found specific regions on the hippocampal surface where the effect is modulated by significant APOE ε4 linear and quadratic interactions with age. We compared between APOE and diagnosis effects from both cohorts, finding similarities between APOE ε4 and AD effects on specific regions, and suggesting that age may modulate the effect of APOE ε4 and AD in a similar way.