Geodesic shape regression with multiple geometries and sparse parameters

MRI-based axis-referenced morphometric model corresponding to lamellar organization for assessing hippocampal atrophy in dementia

Research on the local hippocampal atrophy for early detection of dementia has gained considerable attention. However, accurately quantifying subtle atrophy remains challenging in existing morphological methods due to the lack of consistent biological correspondence with the complex curving regions like the hippocampal head. Thereby, this article presents an innovative axis-referenced morphometric model (ARMM) that follows the anatomical lamellar organization of the hippocampus, which capture its precise and consistent longitudinal curving trajectory. Specifically, we establish an "axis-referenced coordinate system" based on a 7 T ex vivo hippocampal atlas following its entire curving longitudinal axis and orthogonal distributed lamellae. We then align individual hippocampi by deforming this template coordinate system to target spaces using boundary-guided diffeomorphic transformation, while ensuring that the lamellar vectors adhere to the constraint of medial-axis geometry. Finally, we measure local thickness and curvatures based on the coordinate system and boundary surface reconstructed from vector tips. The morphometric accuracy is evaluated by comparing reconstructed surfaces with those directly extracted from 7 T and 3 T MRI hippocampi. The results demonstrate that ARMM achieves the best performance, particularly in the curving head, surpassing the state-of-the-art morphological models. Additionally, morphological measurements from ARMM exhibit higher discriminatory power in distinguishing early Alzheimer's disease from mild cognitive impairment compared to volume-based measurements. Overall, the ARMM offers a precise morphometric assessment of hippocampal morphology on MR images, and sheds light on discovering potential image markers for neurodegeneration associated with hippocampal impairment.

Geodesic shape regression based deep learning segmentation for assessing longitudinal hippocampal atrophy in dementia progression

Longitudinal hippocampal atrophy is commonly used as progressive marker assisting clinical diagnose of dementia. However, precise quantification of the atrophy is limited by longitudinal segmentation errors resulting from MRI artifacts across multiple independent scans. To accurately segment the hippocampal morphology from longitudinal 3T T1-weighted MR images, we propose a diffeomorphic geodesic guided deep learning method called the GeoLongSeg to mitigate the longitudinal variabilities that unrelated to diseases by enhancing intra-individual morphological consistency. Specifically, we integrate geodesic shape regression, an evolutional model that estimates smooth deformation process of anatomical shapes, into a two-stage segmentation network. We adopt a 3D U-Net in the first-stage network with an enhanced attention mechanism for independent segmentation. Then, a hippocampal shape evolutional trajectory is estimated by geodesic shape regression and fed into the second network to refine the independent segmentation. We verify that GeoLongSeg outperforms other four state-of-the-art segmentation pipelines in longitudinal morphological consistency evaluated by test-retest reliability, variance ratio and atrophy trajectories. When assessing hippocampal atrophy in longitudinal data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), results based on GeoLongSeg exhibit spatial and temporal local atrophy in bilateral hippocampi of dementia patients. These features derived from GeoLongSeg segmentation exhibit the greatest discriminatory capability compared to the outcomes of other methods in distinguishing between patients and normal controls. Overall, GeoLongSeg provides an accurate and efficient segmentation network for extracting hippocampal morphology from longitudinal MR images, which assist precise atrophy measurement of the hippocampus in early stage of dementia.

Data-driven cranial suture growth model enables predicting phenotypes of craniosynostosis

We present the first data-driven pediatric model that explains cranial sutural growth in the pediatric population. We segmented the cranial bones in the neurocranium from the cross-sectional CT images of 2068 normative subjects (age 0-10 years), and we used a 2D manifold-based cranial representation to establish local anatomical correspondences between subjects guided by the location of the cranial sutures. We designed a diffeomorphic spatiotemporal model of cranial bone development as a function of local sutural growth rates, and we inferred its parameters statistically from our cross-sectional dataset. We used the constructed model to predict growth for 51 independent normative patients who had longitudinal images. Moreover, we used our model to simulate the phenotypes of single suture craniosynostosis, which we compared to the observations from 212 patients. We also evaluated the accuracy predicting personalized cranial growth for 10 patients with craniosynostosis who had pre-surgical longitudinal images. Unlike existing statistical and simulation methods, our model was inferred from real image observations, explains cranial bone expansion and displacement as a consequence of sutural growth and it can simulate craniosynostosis. This pediatric cranial suture growth model constitutes a necessary tool to study abnormal development in the presence of cranial suture pathology.

Morphological Variation in the Pelvic Floor Muscle Complex of Nulliparous, Pregnant, and Parous Women

Specific levator ani muscle imaging measures change with pregnancy and vaginal parity, though entire pelvic floor muscle complex (PFMC) shape variation related to pregnancy-induced and postpartum remodeling has never been quantified. We used statistical shape modeling to compute the 3D variation in PFMC morphology of reproductive-aged nulliparous, late pregnant, and parous women. Pelvic magnetic resonance images were collected retrospectively and PFMCs were segmented. Modes of variation and principal component scores, generated via statistical shape modeling, defined significant morphological variation. Nulliparous (have never given birth), late pregnant (3rd trimester), and parous (have given birth and not currently pregnant) PFMCs were compared via MANCOVA. The overall PFMC shape, mode 2, and mode 3 significantly differed across patient groups (p < 0.001, = 0.002, = 0.001, respectively). This statistical shape analysis described greater perineal and external anal sphincter descent, increased iliococcygeus concavity, and a proportionally wider mid-posterior levator hiatus in late pregnant compared to nulliparous and parous women. The late pregnant group was the most divergent, highlighting differences that likely reduce the mechanical burden of vaginal childbirth. This robust quantification of PFMC shape provides insight to pregnancy and postpartum remodeling and allows for generation of representative non-patient-specific PFMCs that can be used in biomechanical simulations.

CLAIRE-Parallelized Diffeomorphic Image Registration for Large-Scale Biomedical Imaging Applications

We study the performance of CLAIRE—a diffeomorphic multi-node, multi-GPU image-registration algorithm and software—in large-scale biomedical imaging applications with billions of voxels. At such resolutions, most existing software packages for diffeomorphic image registration are prohibitively expensive. As a result, practitioners first significantly downsample the original images and then register them using existing tools. Our main contribution is an extensive analysis of the impact of downsampling on registration performance. We study this impact by comparing full-resolution registrations obtained with CLAIRE to lower resolution registrations for synthetic and real-world imaging datasets. Our results suggest that registration at full resolution can yield a superior registration quality—but not always. For example, downsampling a synthetic image from 10243 to 2563 decreases the Dice coefficient from 92% to 79%. However, the differences are less pronounced for noisy or low contrast high resolution images. CLAIRE allows us not only to register images of clinically relevant size in a few seconds but also to register images at unprecedented resolution in reasonable time. The highest resolution considered are CLARITY images of size 2816×3016×1162. To the best of our knowledge, this is the first study on image registration quality at such resolutions.

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.

Predictive Statistical Model of Early Cranial Development

OBJECTIVE

We present a data-driven method to build a spatiotemporal statistical shape model predictive of normal cranial growth from birth to the age of 2 years.

METHODS

The model was constructed using a normative cross-sectional computed tomography image dataset of 278 subjects. First, we propose a new standard representation of the calvaria using spherical maps to establish anatomical correspondences between subjects at the cranial sutures - the main areas of cranial bone expansion. Then, we model the cranial bone shape as a bilinear function of two factors: inter-subject anatomical variability and temporal growth. We estimate these factors using principal component analysis on the spatial and temporal dimensions, using a novel coarse-to-fine temporal multi-resolution approach to mitigate the lack of longitudinal images of the same patient.

RESULTS

Our model achieved an accuracy of 1.54 ± 1.05 mm predicting development on an independent longitudinal dataset. We also used the model to calculate the cranial volume, cephalic index and cranial bone surface changes during the first two years of age, which were in agreement with clinical observations.

SIGNIFICANCE

To our knowledge, this is the first data-driven and personalized predictive model of cranial bone shape development during infancy and it can serve as a baseline to study abnormal growth patterns in the population.

Geodesic density regression for correcting 4DCT pulmonary respiratory motion artifacts

Pulmonary respiratory motion artifacts are common in four-dimensional computed tomography (4DCT) of lungs and are caused by missing, duplicated, and misaligned image data. This paper presents a geodesic density regression (GDR) algorithm to correct motion artifacts in 4DCT by correcting artifacts in one breathing phase with artifact-free data from corresponding regions of other breathing phases. The GDR algorithm estimates an artifact-free lung template image and a smooth, dense, 4D (space plus time) vector field that deforms the template image to each breathing phase to produce an artifact-free 4DCT scan. Correspondences are estimated by accounting for the local tissue density change associated with air entering and leaving the lungs, and using binary artifact masks to exclude regions with artifacts from image regression. The artifact-free lung template image is generated by mapping the artifact-free regions of each phase volume to a common reference coordinate system using the estimated correspondences and then averaging. This procedure generates a fixed view of the lung with an improved signal-to-noise ratio. The GDR algorithm was evaluated and compared to a state-of-the-art geodesic intensity regression (GIR) algorithm using simulated CT time-series and 4DCT scans with clinically observed motion artifacts. The simulation shows that the GDR algorithm has achieved significantly more accurate Jacobian images and sharper template images, and is less sensitive to data dropout than the GIR algorithm. We also demonstrate that the GDR algorithm is more effective than the GIR algorithm for removing clinically observed motion artifacts in treatment planning 4DCT scans. Our code is freely available at https://github.com/Wei-Shao-Reg/GDR.

Fast GPU 3D diffeomorphic image registration

3D image registration is one of the most fundamental and computationally expensive operations in medical image analysis. Here, we present a mixed-precision, Gauss-Newton-Krylov solver for diffeomorphic registration of two images. Our work extends the publicly available CLAIRE library to GPU architectures. Despite the importance of image registration, only a few implementations of large deformation diffeomorphic registration packages support GPUs. Our contributions are new algorithms to significantly reduce the run time of the two main computational kernels in CLAIRE: calculation of derivatives and scattered-data interpolation. We deploy (i) highly-optimized, mixed-precision GPU-kernels for the evaluation of scattered-data interpolation, (ii) replace Fast-Fourier-Transform (FFT)-based first-order derivatives with optimized 8th-order finite differences, and (iii) compare with state-of-the-art CPU and GPU implementations. As a highlight, we demonstrate that we can register 2563 clinical images in less than 6 seconds on a single NVIDIA Tesla V100. This amounts to over 20× speed-up over the current version of CLAIRE and over 30× speed-up over existing GPU implementations.

Multi-Node Multi-GPU Diffeomorphic Image Registration for Large-Scale Imaging Problems

We present a Gauss-Newton-Krylov solver for large deformation diffeomorphic image registration. We extend the publicly available CLAIRE library to multi-node multi-graphics processing unit (GPUs) systems and introduce novel algorithmic modifications that significantly improve performance. Our contributions comprise (i) a new preconditioner for the reduced-space Gauss-Newton Hessian system, (ii) a highly-optimized multi-node multi-GPU implementation exploiting device direct communication for the main computational kernels (interpolation, high-order finite difference operators and Fast-Fourier-Transform), and (iii) a comparison with state-of-the-art CPU and GPU implementations. We solve a 256³-resolution image registration problem in five seconds on a single NVIDIA Tesla V100, with a performance speedup of 70% compared to the state-of-the-art. In our largest run, we register 2048³ resolution images (25 B unknowns; approximately 152× larger than the largest problem solved in state-of-the-art GPU implementations) on 64 nodes with 256 GPUs on TACC's Longhorn system.

Pelvic floor shape variations during pregnancy and after vaginal delivery

BACKGROUND AND OBJECTIVE

Strong evidence suggests that pelvic soft tissues soften during pregnancy to facilitate vaginal delivery while protecting against maternal birth injury. We hypothesized that these adaptations likely result in changes to the shape of the pelvic floor. Thus, this study aimed to compare midsagittal pelvic floor shapes from MRIs of nulliparous, gravid, and vaginally parous women using statistical shape modeling.

METHODS

A retrospective study of 22 nulliparous, 29 gravid (vaginally nulliparous), and 18 vaginally parous women who underwent pelvic MRI was performed. The pelvic floor was segmented from pubic symphysis to coccyx as a 2D polyline in the midsagittal plane. Once corresponding landmarks were computed and the variances between them determined by principal component analysis, the principal component scores were calculated for modes that explained variance greater than noise. These became the dependent variables in a MANOVA with univariate ANOVAs, linear regressions, and Benjamini-Hochberg corrections post hoc. Two initial statistical shape analyses were conducted to analyze differences based on gestational age (1^st/2^nd vs 3^rd trimester) and vaginal parity (VP1 vs VP2-4). There were significant differences based on gestational age, but not vaginal parity. Thus, the final statistical shape analysis evaluated pelvic floor shapes of nulliparous, 3rd trimester gravid, and all vaginally parous subjects.

RESULTS

In the final analysis, six modes described variance-a measure of shape variability-greater than noise. Groups differed significantly for modes 1, 2, and 4 (p < 0.001, p = 0.021, and p = 0.015, respectively) and only differed between the nulliparous and gravid groups (p < 0.001, p = 0.018, and p = 0.012, respectively). Anatomically, these modes described levator plate relaxation and level III support protrusion in gravid compared to nulliparous subjects while the parous group straddled the other two.

CONCLUSIONS

The shape of the pelvic floor changes significantly during pregnancy and some of those changes are present after vaginal delivery. The fact that the nulliparous and gravid groups differ while the parous is similar to both suggests that some parous women regain their nulliparous shape after pregnancy and delivery while others do not. This indicates that remodeling during pregnancy and/or injury during vaginal delivery can have lasting effects on the pelvic floor.

CLAIRE: A DISTRIBUTED-MEMORY SOLVER FOR CONSTRAINED LARGE DEFORMATION DIFFEOMORPHIC IMAGE REGISTRATION

With this work we release CLAIRE, a distributed-memory implementation of an effective solver for constrained large deformation diifeomorphic image registration problems in three dimensions. We consider an optimal control formulation. We invert for a stationary velocity field that parameterizes the deformation map. Our solver is based on a globalized, preconditioned, inexact reduced space Gauss‒Newton‒Krylov scheme. We exploit state-of-the-art techniques in scientific computing to develop an eifective solver that scales to thousands of distributed memory nodes on high-end clusters. We present the formulation, discuss algorithmic features, describe the software package, and introduce an improved preconditioner for the reduced space Hessian to speed up the convergence of our solver. We test registration performance on synthetic and real data. We Demonstrate registration accuracy on several neuroimaging datasets. We compare the performance of our scheme against diiferent flavors of the Demons algorithm for diifeomorphic image registration. We study convergence of our preconditioner and our overall algorithm. We report scalability results on state-of-the-art supercomputing platforms. We Demonstrate that we can solve registration problems for clinically relevant data sizes in two to four minutes on a standard compute node with 20 cores, attaining excellent data fidelity. With the present work we achieve a speedup of (on average) 5× with a peak performance of up to 17× compared to our former work.

Level set distribution model of nested structures using logarithmic transformation

In this study, we propose a method for constructing a multishape statistical shape model (SSM) for nested structures such that each is a subset or superset of another. The proposed method has potential application to any pair of shapes with an inclusive relationship. These types of shapes are often found in anatomy, such as the brain surface and ventricles. The main contribution of this paper is to introduce a new shape representation called log-transformed level set function (LT-LSF), which has a vector space structure that preserves the correct inclusive relationship of the nested shape. In addition, our method is applicable to an arbitrary number of nested shapes. We demonstrate the effectiveness of the proposed shape representation by modeling the anatomy of human embryos, including the brain, ventricles, and choroid plexus volumes. The performance of the SSM was evaluated in terms of generalization and specificity ability. Additionally, we measured leakage criteria to assess the ability to preserve inclusive relationships. A quantitative comparison of our SSM with conventional multishape SSMs demonstrates the superiority of the proposed method.

Model selection for spatiotemporal modeling of early childhood sub-cortical development

Spatiotemporal shape models capture the dynamics of shape change over time and are an essential tool for monitoring and measuring anatomical growth or degeneration. In this paper we evaluate non-parametric shape regression on the challenging problem of modeling early childhood sub-cortical development starting from birth. Due to the flexibility of the model, it can be challenging to choose parameters which lead to a good model fit yet does not over fit. We systematically test a variety of parameter settings to evaluate model fit as well as the sensitivity of the method to specific parameters, and we explore the impact of missing data on model estimation.

ESTIMATING SHAPE CORRESPONDENCE FOR POPULATIONS OF OBJECTS WITH COMPLEX TOPOLOGY

Statistical shape analysis captures the geometric properties of a given set of shapes, obtained from medical images, by means of statistical methods. Orthognathic surgery is a type of craniofacial surgery that is aimed at correcting severe skeletal deformities in the mandible and maxilla. Methods assuming spherical topology cannot represent the class of anatomical structures exhibiting complex geometries and topologies, including the mandible. In this paper we propose methodology based on non-rigid deformations of 3D geometries to be applied to objects with thin, complex structures. We are able to accurately and quantitatively characterize bone healing at the osteotomy site as well as condylar remodeling for three orthognathic surgery cases, demonstrating the effectiveness of the proposed methodology.

4D CONTINUOUS MEDIAL REPRESENTATION BY GEODESIC SHAPE REGRESSION

Longitudinal shape analysis has shown great potential to model anatomical processes from baseline to follow-up observations. Shape regression estimates a continuous trajectory of time-discrete anatomical shapes to quantify temporal changes. The need for shape alignment and point-to-point correspondences represent limitations of current shape analysis methodologies, and present significant challenges in shape evaluation. We propose a method that estimates a continuous trajectory of continuous medial representations (CM-Rep) from a set of time-discrete observed shapes. To avoid the traditional step of aligning individual objects, shape changes are modeled via diffeomorphic ambient space deformations. Using a medial shape representation, we separately capture object pose changes and intrinsic geometry changes. Tests and validation with synthetic and real anatomical shapes demonstrate that the new method captures extrinsic shape changes as well as intrinsic shape changes encoded with CM-Reps, a highly relevant property for studying growth and disease processes.