Diffeomorphic Registration Research Articles

Nonparametric Aggregation of Geodesic Trends for Longitudinal Data Analysis.

We propose a technique for analyzing longitudinal imaging data that models individual changes with diffeomorphic geodesic regression and aggregates these geodesics into a nonparametric group average trend. Our model is specifically tailored to the unbalanced and sparse characteristics of longitudinal imaging studies. That is, each individual has few data points measured over a short period of time, while the study population as a whole spans a wide age range. We use geodesic regression to estimate individual trends, which is an appropriate model for capturing shape changes over a short time window, as is typically found within an individual. Geodesics are also adept at handling the low sample sizes found within individuals, and can model the change between as few as two timepoints. However, geodesics are limited for modeling longer-term trends, where constant velocity may not be appropriate. Therefore, we develop a novel nonparametric regression to aggregate individual trends into an average group trend. We demonstrate the power of our method to capture non-geodesic group trends on hippocampal volume (real-valued data) and diffeomorphic registration of full 3D MRI from the longitudinal OASIS data.

Cytoarchitectonically-driven MRI atlas of nonhuman primate hippocampus: Preservation of subfield volumes in aging.

Identification of primate hippocampal subfields in vivo using structural MRI imaging relies on variable anatomical guidelines, signal intensity differences, and heuristics to differentiate between regions (Yushkevich et al., 2015a). Thus, a clear anatomically-driven basis for subfield demarcation is lacking. Recent work, however, has begun to develop methods to use ex vivo histology or ex vivo MRI (Adler et al., 2014; Iglesias et al., 2015) that have the potential to inform subfield demarcations of in vivo images. For optimal results, however, ex vivo and in vivo images should ideally be matched within the same healthy brains, with the goal to develop a neuroanatomically-driven basis for in vivo structural MRI images. Here, we address this issue in young and aging rhesus macaques (young n = 5 and old n = 5) using ex vivo Nissl-stained sections in which we identified the dentate gyrus, CA3, CA2, CA1, subiculum, presubiculum, and parasubiculum guided by morphological cell properties (30 μm thick sections spaced at 240 μm intervals and imaged at 161 nm/pixel). The histologically identified boundaries were merged with in vivo structural MRIs (0.625 × 0.625 × 1 mm) from the same subjects via iterative rigid and diffeomorphic registration resulting in probabilistic atlases of young and old rhesus macaques. Our results indicate stability in hippocampal subfield volumes over an age range of 13 to 32 years, consistent with previous results showing preserved whole hippocampal volume in aged macaques (Shamy et al., 2006). Together, our methods provide a novel approach for identifying hippocampal subfields in non-human primates and a potential 'ground truth' for more accurate identification of hippocampal subfield boundaries on in vivo MRIs. This could, in turn, have applications in humans where accurately identifying hippocampal subfields in vivo is a critical research goal.

Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

This paper proposes a method for primal-dual convex optimization in variational large deformation diffeomorphic metric mapping problems formulated with robust regularizers and robust image similarity metrics. The method is based on Chambolle and Pock primal-dual algorithm for solving general convex optimization problems. Diagonal preconditioning is used to ensure the convergence of the algorithm to the global minimum. We consider three robust regularizers liable to provide acceptable results in diffeomorphic registration: Huber, V-Huber and total generalized variation. The Huber norm is used in the image similarity term. The primal-dual equations are derived for the stationary and the non-stationary parameterizations of diffeomorphisms. The resulting algorithms have been implemented for running in the GPU using Cuda. For the most memory consuming methods, we have developed a multi-GPU implementation. The GPU implementations allowed us to perform an exhaustive evaluation study in NIREP and LPBA40 databases. The experiments showed that, for all the considered regularizers, the proposed method converges to diffeomorphic solutions while better preserving discontinuities at the boundaries of the objects compared to baseline diffeomorphic registration methods. In most cases, the evaluation showed a competitive performance for the robust regularizers, close to the performance of the baseline diffeomorphic registration methods.

3D MRI image super‐resolution for brain combining rigid and large diffeomorphic registration

Most of the recent leading multiple magnetic resonance imaging (MRI) super-resolution techniques for brain are limited to rigid motion. In this study, the authors aim to develop a super-resolution technique with diffeomorphism mainly for longitudinal brain MRI data. For the images from different time slots, unpredicted deformation may occur. In previous studies, sole rigid registration or traditional non-rigid registration has been frequently used to achieve multi-plane super-resolution. However, non-rigid motion of two brains from different time slots is difficult to model, since brain contains a wealth of complex structure such as the cerebral cortex. In order to address such problem, rigid and large diffeomorphic registration has been embedded into their super-resolution framework. In addition, many previous researchers use L 2 norm to achieve super-resolution framework. In this work, L 1 norm minimisation and regularisation based on a bilateral prior are adopted. These operations ensure its robustness to the assumed model of data and noise. Their approach is evaluated using Alzheimer datasets from seven different resolutions. Results show that their reconstructions have advantages over rigid and conventional non-rigid registration-based super-resolution, in terms of the root-mean-square error and structure similarity. Furthermore, their reconstruction results improve the precision of brain automatic segmentation.

3D non-rigid image registration with inverse consistency constraint on elastodynamics wave equation

In this work, a new inverse consistent non-rigid image registration method is presented. The inter-subject deformations are modeled as elastic waves which tend to propagate over the image domain while recovering the nonlinear discrepancies between the two images. An inverse consistency constraint is introduced into the inertial force that is part of the elastodynamics wave equation which governs the underlying non-rigid deformations. The proposed registration method was analyzed over 3D MR brain scans both quantitatively and qualitatively. Normalized cross-correlation (NCC) was utilized to check the registration accuracy, and it revealed that the performance of proposed registration method with and without inverse consistency constraint is comparable in terms of NCC which increased by $$13\%$$ from its initial value. Moreover, Dice coefficient for segmented structures was computed and compared against state-of-the-art symmetric image normalization method, free form deformation and diffeomorphic demons registration methods. The extent to which the proposed registration scheme enforced inverse consistency was analyzed through inverse consistency error. The results showed that the inverse consistency error reduced by $$99\%$$ with the proposed inverse consistent registration method as compared to the inverse inconsistent counterpart.

Voxel-based morphometry-diffeomorphic anatomical registration through exponentiated lie algebra algorithm evaluation of brain structural of recent-onset pediatric post-traumatic stress disorder patients

Objective To compare brain structure differences between recent-onset pediatric posttraumatic stress disorder (PTSD) patients and trauma-exposed controls without PTSD (TEC) using voxel-based morphometry (VBM)-diffeomorphic anatomical registration through exponentiated lie algebra (DARTEL) algorithm, and evaluate the relationship between volume of altered brain areas and symptom severity. Methods High-resolution 3-dimensional T1WI images were obtained from 28 first-episode treatment-naive pediatric PTSD patients group and 26 age and gender-matched TEC group within 7-15 months after a major earthquake. With the General Linear Model (GLM), gray matter volume (GMV) was compared between the two groups using VBM-DARTEL algorithm of SPM8 software running in MatLab 2012b. The statistical map cluster level had a threshold of P 113). In regions with significant group differences, the relationships between volumes of altered structures and clinician-administered PTSD scale (CAPS) and PTSD checklist (PCL) scores in patients were evaluated with age as covariates. Results Compared to TEC, pediatric PTSD patients showed GMV reduction in the left inferior frontal gyrus (IFG), precuneus, supplementary motor area (SMA), and bilateral cerebellum (voxel size=230, 118, 134, 298, 325, P<0.005). Correlation analyses showed that GMV of the left precuneus and SMA were positively correlated with CAPS scores in PTSD patients group, respectively (r=0.402, P=0.037; r=0.41, P=0.034). In addition, gray matter volume of the left SMA was positively correlated with PCL scores in PTSD group (r=0.383, P=0.049). Conclusions The characteristics of brain in recent-onset pediatric PTSD patients are mainly atrophy in some gray matter regions compared with TEC. Gray matter reduction in cerebellum may be the unique structural feature in pediatric PTSD. Key words: Stress disorders, post-traumatic; Magnetic resonance imaging; Brain

Prediction and classification of Alzheimer disease based on quantification of MRI deformation.

Detecting early morphological changes in the brain and making early diagnosis are important for Alzheimer’s disease (AD). High resolution magnetic resonance imaging can be used to help diagnosis and prediction of the disease. In this paper, we proposed a machine learning method to discriminate patients with AD or mild cognitive impairment (MCI) from healthy elderly and to predict the AD conversion in MCI patients by computing and analyzing the regional morphological differences of brain between groups. Distance between each pair of subjects was quantified from a symmetric diffeomorphic registration, followed by an embedding algorithm and a learning approach for classification. The proposed method obtained accuracy of 96.5% in differentiating mild AD from healthy elderly with the whole-brain gray matter or temporal lobe as region of interest (ROI), 91.74% in differentiating progressive MCI from healthy elderly and 88.99% in classifying progressive MCI versus stable MCI with amygdala or hippocampus as ROI. This deformation-based method has made full use of the pair-wise macroscopic shape difference between groups and consequently increased the power for discrimination.

Mid-space-independent deformable image registration

Aligning images in a mid-space is a common approach to ensuring that deformable image registration is symmetric – that it does not depend on the arbitrary ordering of the input images. The results are, however, generally dependent on the mathematical definition of the mid-space. In particular, the set of possible solutions is typically restricted by the constraints that are enforced on the transformations to prevent the mid-space from drifting too far from the native image spaces. The use of an implicit atlas has been proposed as an approach to mid-space image registration. In this work, we show that when the atlas is aligned to each image in the native image space, the data term of implicit-atlas-based deformable registration is inherently independent of the mid-space. In addition, we show that the regularization term can be reformulated independently of the mid-space as well. We derive a new symmetric cost function that only depends on the transformation morphing the images to each other, rather than to the atlas. This eliminates the need for anti-drift constraints, thereby expanding the space of allowable deformations. We provide an implementation scheme for the proposed framework, and validate it through diffeomorphic registration experiments on brain magnetic resonance images.

Automated Bone Segmentation and Surface Evaluation of a Small Animal Model of Post-Traumatic Osteoarthritis.

MicroCT imaging allows for noninvasive microstructural evaluation of mineralized bone tissue, and is essential in studies of small animal models of bone and joint diseases. Automatic segmentation and evaluation of articular surfaces is challenging. Here, we present a novel method to create knee joint surface models, for the evaluation of PTOA-related joint changes in the rat using an atlas-based diffeomorphic registration to automatically isolate bone from surrounding tissues. As validation, two independent raters manually segment datasets and the resulting segmentations were compared to our novel automatic segmentation process. Data were evaluated using label map volumes, overlap metrics, Euclidean distance mapping, and a time trial. Intraclass correlation coefficients were calculated to compare methods, and were greater than 0.90. Total overlap, union overlap, and mean overlap were calculated to compare the automatic and manual methods and ranged from 0.85 to 0.99. A Euclidean distance comparison was also performed and showed no measurable difference between manual and automatic segmentations. Furthermore, our new method was 18 times faster than manual segmentation. Overall, this study describes a reliable, accurate, and automatic segmentation method for mineralized knee structures from microCT images, and will allow for efficient assessment of bony changes in small animal models of PTOA.

Langevin Equations for Landmark Image Registration with Uncertainty

Registration of images parameterized by landmarks provides a useful method of describing shape variations by computing the minimum-energy time-dependent deformation field that flows from one landmark set to the other. This is sometimes known as the geodesic interpolating spline and can be solved via a Hamiltonian boundary-value problem to give a diffeomorphic registration between images. However, small changes in the positions of the landmarks can produce large changes in the resulting diffeomorphism. We formulate a Langevin equation for looking at small random perturbations of this registration. The Langevin equation and three computationally convenient approximations are introduced and used as prior distributions. A Bayesian framework is then used to compute a posterior distribution for the registration, and also to formulate an average of multiple sets of landmarks.

Locally affine diffeomorphic surface registration for planning of metopic craniosynostosis surgery.

The outcome of cranial vault reconstruction for the surgical treatment of craniosynostosis heavily depends on the surgeon's expertise because of the lack of an objective target shape. We introduce a surface-based diffeomorphic registration framework to create the optimal post-surgical cranial shape during craniosynostosis treatment. Our framework estimates and labels where each bone piece needs to be cut using a reference template. Then, it calculates how much each bone piece needs to be translated and in which direction, using the closest normal shape from a multi-atlas as a reference. With our locally affine approach, the method also allows for bone bending, modeling independently the transformation of each bone piece while ensuring the consistency of the global transformation. We evaluated the optimal plan for 15 patients with metopic craniosynostosis. Our results showed that the automated surgical planning creates cranial shapes with a reduction in cranial malformations of 51.43% and curvature discrepancies of 35.09%, which are the two indices proposed in the literature to quantify cranial deformities objectively. In addition, the cranial shapes created were within healthy ranges.

Image Stitching for Achilles Tendon Ultrasonography Using Particle Swarm Optimization of Boundary Vector Field Based Similarity and Log-Domain Diffeomorphic Registration

Image Stitching for Achilles Tendon Ultrasonography Using Particle Swarm Optimization of Boundary Vector Field Based Similarity and Log-Domain Diffeomorphic Registration

In vivo delineation of subdivisions of the human amygdaloid complex in a high-resolution group template.

The nuclei of the human amygdala remain difficult to distinguish in individual subject structural magnetic resonance images. However, interpretation of the amygdala's role in whole brain networks requires accurate localization of functional activity to a particular nucleus or subgroup of nuclei. To address this, high spatial resolution, three-dimensional templates, using joint high accuracy diffeomorphic registration of T1- and T2-weighted structural images from 168 typical adults between 22 and 35 years old released by the Human Connectome Project were constructed. Several internuclear boundaries are clearly visible in these templates, which would otherwise be impossible to delineate in individual subject data. A probabilistic atlas of major nuclei and nuclear groups was constructed in this template space and mapped back to individual spaces by inversion of the individual diffeomorphisms. Group level analyses revealed a slight (∼2%) bias toward larger total amygdala and nuclear volumes in the right hemisphere. No substantial sex or age differences were found in amygdala volumes normalized to total intracranial volume, or subdivision volumes normalized to amygdala volume. The current delineation provides a finer parcellation of the amygdala with more accurate external boundary definition than current histology-based atlases when used in conjunction with high accuracy registration methods, such as diffeomorphic warping. These templates and delineation are intended to be an open and evolving resource for future functional and structural imaging studies of the human amygdala. Hum Brain Mapp 37:3979-3998, 2016. © 2016 Wiley Periodicals, Inc.

Longitudinal Analysis of Image Time Series with Diffeomorphic Deformations: A Computational Framework Based on Stationary Velocity Fields.

We propose and detail a deformation-based morphometry computational framework, called Longitudinal Log-Demons Framework (LLDF), to estimate the longitudinal brain deformations from image data series, transport them in a common space and perform statistical group-wise analyses. It is based on freely available software and tools, and consists of three main steps: (i) Pre-processing, (ii) Position correction, and (iii) Non-linear deformation analysis. It is based on the LCC log-Demons non-linear symmetric diffeomorphic registration algorithm with an additional modulation of the similarity term using a confidence mask to increase the robustness with respect to brain boundary intensity artifacts. The pipeline is exemplified on the longitudinal Open Access Series of Imaging Studies (OASIS) database and all the parameters values are given so that the study can be reproduced. We investigate the group-wise differences between the patients with Alzheimer's disease and the healthy control group, and show that the proposed pipeline increases the sensitivity with no decrease in the specificity of the statistical study done on the longitudinal deformations.

Vessel-based registration of an optical shape sensing catheter for MR navigation.

Magnetic resonance navigation (MRN), achieved with an upgraded MRI scanner, aims to guide therapeutic nanoparticles from their release in the hepatic vascular network to embolize highly vascularized liver tumors. Visualizing the catheter in real-time within the arterial network is important for selective embolization within the MR gantry. To achieve this, a new MR-compatible catheter tracking technology based on optical shape sensing is used. This paper proposes a vessel-based registration pipeline to co-align this novel catheter tracking technology to the patient's diagnostic MR angiography (MRA) with 3D roadmapping. The method first extracts the 3D hepatic arteries from a diagnostic MRA based on concurrent deformable models, creating a detailed representation of the patient's internal anatomy. Once the optical shape sensing fibers, inserted in a double-lumen catheter, is guided into the hepatic arteries, the 3D centerline of the catheter is inferred and updated in real-time using strain measurements derived from fiber Bragg gratings sensors. Using both centerlines, a diffeomorphic registration based on a spectral representation of the high-level geometrical primitives is applied. Results show promise in registration accuracy in five phantom models created from stereolithography of patient-specific vascular anatomies, with maximum target registration errors below 2mm. Furthermore, registration accuracy with the shape sensing tracking technology remains insensitive to the magnetic field of the MR magnet. This study demonstrates that an accurate registration procedure of a shape sensing catheter with diagnostic imaging is feasible.

DR-TAMAS: Diffeomorphic Registration for Tensor Accurate Alignment of Anatomical Structures

In this work, we propose DR-TAMAS (Diffeomorphic Registration for Tensor Accurate alignMent of Anatomical Structures), a novel framework for intersubject registration of Diffusion Tensor Imaging (DTI) data sets. This framework is optimized for brain data and its main goal is to achieve an accurate alignment of all brain structures, including white matter (WM), gray matter (GM), and spaces containing cerebrospinal fluid (CSF). Currently most DTI-based spatial normalization algorithms emphasize alignment of anisotropic structures. While some diffusion-derived metrics, such as diffusion anisotropy and tensor eigenvector orientation, are highly informative for proper alignment of WM, other tensor metrics such as the trace or mean diffusivity (MD) are fundamental for a proper alignment of GM and CSF boundaries. Moreover, it is desirable to include information from structural MRI data, e.g., T1-weighted or T2-weighted images, which are usually available together with the diffusion data. The fundamental property of DR-TAMAS is to achieve global anatomical accuracy by incorporating in its cost function the most informative metrics locally. Another important feature of DR-TAMAS is a symmetric time-varying velocity-based transformation model, which enables it to account for potentially large anatomical variability in healthy subjects and patients. The performance of DR-TAMAS is evaluated with several data sets and compared with other widely-used diffeomorphic image registration techniques employing both full tensor information and/or DTI-derived scalar maps. Our results show that the proposed method has excellent overall performance in the entire brain, while being equivalent to the best existing methods in WM.

Diffeomorphic Surface Registration with Atrophy Constraints.

Diffeomorphic registration using optimal control on the diffeomorphism group and on shape spaces has become widely used since the development of the large deformation diffeomorphic metric mapping (LDDMM) algorithm. More recently, a series of algorithms involving sub-Riemannian constraints have been introduced in which the velocity fields that control the shapes in the LDDMM framework are constrained in accordance with a specific deformation model. Here, we extend this setting by considering, for the first time, inequality constraints in order to estimate surface deformations that only allow for atrophy, introducing for this purpose an algorithm that uses the augmented Lagrangian method. We prove the existence of solutions of the associated optimal control problem and the consistency of our approximation scheme. These developments are illustrated by numerical experiments on simulated and real data.

Kernel Bundle Diffeomorphic Image Registration Using Stationary Velocity Fields and Wendland Basis Functions.

In this paper, we propose a multi-scale, multi-kernel shape, compactly supported kernel bundle framework for stationary velocity field-based image registration (Wendland kernel bundle stationary velocity field, wKB-SVF). We exploit the possibility of directly choosing kernels to construct a reproducing kernel Hilbert space (RKHS) instead of imposing it from a differential operator. The proposed framework allows us to minimize computational cost without sacrificing the theoretical foundations of SVF-based diffeomorphic registration. In order to recover deformations occurring at different scales, we use compactly supported Wendland kernels at multiple scales and orders to parameterize the velocity fields, and the framework allows simultaneous optimization over all scales. The performance of wKB-SVF is extensively compared to the 14 non-rigid registration algorithms presented in a recent comparison paper. On both MGH10 and CUMC12 datasets, the accuracy of wKB-SVF is improved when compared to other registration algorithms. In a disease-specific application for intra-subject registration, atrophy scores estimated using the proposed registration scheme separates the diagnostic groups of Alzheimer's and normal controls better than the state-of-the-art segmentation technique. Experimental results show that wKB-SVF is a robust, flexible registration framework that allows theoretically well-founded and computationally efficient multi-scale representation of deformations and is equally well-suited for both inter- and intra-subject image registration.

Accelerating Neuroimage Registration through Parallel Computation of Similarity Metric.

Neuroimage registration is crucial for brain morphometric analysis and treatment efficacy evaluation. However, existing advanced registration algorithms such as FLIRT and ANTs are not efficient enough for clinical use. In this paper, a GPU implementation of FLIRT with the correlation ratio (CR) as the similarity metric and a GPU accelerated correlation coefficient (CC) calculation for the symmetric diffeomorphic registration of ANTs have been developed. The comparison with their corresponding original tools shows that our accelerated algorithms can greatly outperform the original algorithm in terms of computational efficiency. This paper demonstrates the great potential of applying these registration tools in clinical applications.

Evaluation on diffusion tensor image registration algorithms

With the application in many neuroimaging studies, diffusion tensor image (DTI) registration has generated considerable interest and been studied widely. Although a number of DTI registration methods have been developed, their performances have not yet been compared systematically. This work addresses this gap by comparing a large number of existing DTI registration methods and gives the comprehensive evaluation results. In this paper, the open-access IXI DTI dataset were used. In order to compare the accuracy of tensor matching, 11 open-source registration methods were evaluated with 7 quantitative and open-access evaluation criteria that measure the similarity among tensors (namely tensor-based techniques) or scalar images derived from diffusion tensors (namely scalar-based techniques). The evaluation results indicate that the diffeomorphic deformable tensor registration method (referred to as DTI-TK) is the best method, followed by the symmetric image normalization method (referred to as SyN).