Large Deformation Diffeomorphic Mapping Research Articles

Large deformation diffeomorphic mapping of 3D shape variation reveals two distinct mandible and head capsule morphs in Atta vollenweideri leaf-cutter worker ants.

Ants are crucial ecosystem engineers, and their ecological success is facilitated by a division of labour among sterile "workers". In some ant lineages, workers have undergone further morphological differentiation, resulting in differences in body size, shape, or both. Distinguishing between changes in size and shape is not trivial. Traditional approaches based on allometry reduce complex 3D shapes into simple linear, areal, or volume metrics; modern approaches using geometric morphometrics typically rely on landmarks, introducing observer bias and a trade-off between effort and accuracy. Here, we use a landmark-free method based on large deformation diffeomorphic metric mapping (LDDMM) to assess the co-variation of size and 3D shape in the mandibles and head capsules of Atta vollenweideri leaf-cutter ants, a species exhibiting extreme worker size-variation. Body mass varied by more than two orders of magnitude, but a shape atlas created via LDDMM on μ-CT-derived 3D mesh files revealed only two distinct head capsule and mandibles shapes-one for the minims (body mass < 1 mg) and one for all other workers. We discuss the functional significance of the identified 3D shape variation, and its implications for the evolution of extreme polymorphism in Atta.

An Integrated Method for Large Deformable Registration of Brain Images.

Large deformable registration of brain images is essential for a variety of clinical imaging applications. State-of-the-art diffeomorphic registration methods, such as large deformation diffeomorphic mapping (LDDMM), have high computational complexity and often require pre-processing to account for large, global displacements or rotations. In this paper, we present an integrated method that fuses landmark-based thin-plate splines (TPS), patch-based B-spline and partial differential equation (PDE) based registrations synergistically to achieve improved accuracy and efficiency for large deformable registration of brain image. Landmark-based TPS and patch-based B-spline were used for global affine transformation followed by deformable registration using LDDMM. The anatomical discrepancies between the source and target images were significantly reduced after TPS and B-spline based registration. As a result, the PDE based deformable registration could be done efficiently and effectively. The performance of the proposed method has been evaluated using simulation and real human brain image data, which provided more accurate registration than spline or PDE-based methods. Moreover, the computational efficiency of our method was significantly better than PDE-based methods. The proposed method may be useful for handling large deformable registration of brain images in various brain imaging applications.

ESTIMATING DIFFEOMORPHIC MAPPINGS BETWEEN TEMPLATES AND NOISY DATA: VARIANCE BOUNDS ON THE ESTIMATED CANONICAL VOLUME FORM.

Anatomy is undergoing a renaissance driven by the availability of large digital data sets generated by light microscopy. A central computational task is to map individual data volumes to standardized templates. This is accomplished by regularized estimation of a diffeomorphic transformation between the coordinate systems of the individual data and the template, building the transformation incrementally by integrating a smooth flow field. The canonical volume form of this transformation is used to quantify local growth, atrophy, or cell density. While multiple implementations exist for this estimation, less attention has been paid to the variance of the estimated diffeomorphism for noisy data. Notably, there is an infinite dimensional unobservable space defined by those diffeomorphisms which leave the template invariant. These form the stabilizer subgroup of the diffeomorphic group acting on the template. The corresponding flat directions in the energy landscape are expected to lead to increased estimation variance. Here we show that a least-action principle used to generate geodesics in the space of diffeomor-phisms connecting the subject brain to the template removes the stabilizer. This provides reduced-variance estimates of the volume form. Using simulations we demonstrate that the asymmetric large deformation diffeomorphic mapping methods (LDDMM), which explicitly incorporate the asymmetry between idealized template images and noisy empirical images, provide lower variance estimators than their symmetrized counterparts (cf. ANTs). We derive Cramer-Rao bounds for the variances in the limit of small deformations. Analytical results are shown for the Jacobian in terms of perturbations of the vector fields and divergence of the vector field.

A Diffeomorphic Mapping Based Characterization of Temporal Sequences: Application to the Pelvic Organ Dynamics Assessment

In various imaging applications, shape variations are studied in order to define the transformations involved or to quantify a distance between each change performed. Regardless of the way the shapes may be extracted, with 2D imaging, shapes concern essentially curves or sets of points depending on the available data. Wether time is related to the shape variations or not, one can consider a set of shapes as the observation of the temporal evolution of an initial shape. In this context, we present a methodology aiming at quantifying the evolution of a set of contours without landmarks. Our characterization of temporal sequences is based on the large deformation diffeomorphic mapping paradigm and the shape representation based on currents, which allow both to propose a shape metric and a curve matching of the timed variations. Then, mechanics related features are extracted as they are physically meaningful and quite painless understandable. In this paper, the process is applied within the scope of a pelviperineology study. Available clinical diagnoses are combined with statistical analysis to show the soundness of the approach. Indeed, pelvic floor disorders are characterized by abnormal organ descents and deformations during abdominal strains. As they are soft-tissue organs, the pelvic organs have no fixed landmarks, in addition to wide shape differences. Routinely used, 2D sagittal mri sequences are segmented to provide the contour sets from which the characterization should highlight pelvic organ behaviors. We believe that a statistical analysis of these behaviors on several dynamic mri sequences could help to a better understanding of the pelvic floor pathophysiology. The methodology is applied on a dataset of 30 patients with different clinical diagnoses. Some promising results are presented, where the pathology detection capability of the deformation features is assessed, and the principal organ dynamics modes are computed, through an inter-patient analysis. Also, an organ parcellation is proposed thanks to the local deformation analysis, it identifies spatial references which are clinically relevant.

Patient-specific models of cardiac biomechanics

Patient-specific models of cardiac function have the potential to improve diagnosis and management of heart disease by integrating medical images with heterogeneous clinical measurements subject to constraints imposed by physical first principles and prior experimental knowledge. We describe new methods for creating three-dimensional patient-specific models of ventricular biomechanics in the failing heart. Three-dimensional bi-ventricular geometry is segmented from cardiac CT images at end-diastole from patients with heart failure. Human myofiber and sheet architecture is modeled using eigenvectors computed from diffusion tensor MR images from an isolated, fixed human organ-donor heart and transformed to the patient-specific geometric model using large deformation diffeomorphic mapping. Semi-automated methods were developed for optimizing the passive material properties while simultaneously computing the unloaded reference geometry of the ventricles for stress analysis. Material properties of active cardiac muscle contraction were optimized to match ventricular pressures measured by cardiac catheterization, and parameters of a lumped-parameter closed-loop model of the circulation were estimated with a circulatory adaptation algorithm making use of information derived from echocardiography. These components were then integrated to create a multi-scale model of the patient-specific heart. These methods were tested in five heart failure patients from the San Diego Veteran’s Affairs Medical Center who gave informed consent. The simulation results showed good agreement with measured echocardiographic and global functional parameters such as ejection fraction and peak cavity pressures.

Multi-Scale Modeling of Patient-Specific Ventricular Geometry, Fiber Structure, and Biomechanics

Patient-specific image data of the heart can now be obtained through advanced medical imaging. This data combined with clinical measurements can potentially be integrated into patient-specific computational models of regional cardiac function. We have developed a pipeline for patient-specific ventricular biomechanics simulations in the failing heart. Three-dimensional ventricular geometry was segmented from CT or MRI data at end-diastole from patients with congestive heart failure. Human myofiber and sheet architecture was estimated using eigenvectors computed from Diffusion Tensor MRI obtained in an isolated, fixed human organ donor heart and mapped to the patient-specific geometric model using large-deformation diffeomorphic mapping. Passive myocardial properties were optimized using semi-automated methods while simultaneously computing the unloaded reference geometry. Active cardiac-muscle contraction properties were optimized to match ventricular pressures measured by cardiac catheterization. Finally, echocardiographic data and an adaptation algorithm (CircAdapt) were used to estimate parameters of a lumped-parameter closed-loop model of the circulation. These methods were validated in three heart failure patients who gave informed consent at the San Diego VA Medical Center by comparing simulation results with echocardiographic measurements of regional wall motion and with predictions of empirical formulas derived from previous clinical studies.

Improved Segmentation of Hippocampus Using Landmark based Large Deformation Diffeomorphic Mapping

Improved Segmentation of Hippocampus Using Landmark based Large Deformation Diffeomorphic Mapping