Smooth representation of thin shells and volume structures for isogeometric analysis

The purpose of this study is to develop self-contained methods for obtaining smooth meshes which are compatible with isogeometric analysis (IGA). The study contains three main parts. We start by developing a better understanding of shapes and splines through the study of an image-related problem. Then we proceed towards obtaining smooth volumetric meshes of the given voxel-based images. Finally, we treat the smoothness issue on the multi-patch domains with C1 coupling. Following are the highlights of each part. First, we present a B-spline convolution method for boundary representation of voxel-based images. We adopt the filtering technique to compute the B-spline coefficients and gradients of the images effectively. We then implement the B-spline convolution for developing a non-rigid images registration method. The proposed method is in some sense of “isoparametric”, for which all the computation is done within the B-splines framework. Particularly, updating the images by using B-spline composition promote smooth transformation map between the images. We show the possible medical applications of our method by applying it for registration of brain images. Secondly, we develop a self-contained volumetric parametrization method based on the B-splines boundary representation. We aim to convert a given voxel-based data to a matching C1 representation with hierarchical cubic splines. The concept of the osculating circle is employed to enhance the geometric approximation, where it is done by a single template and linear transformations (scaling, translations, and rotations) without the need for solving an optimization problem. Moreover, we use the Laplacian smoothing and refinement techniques to avoid irregular meshes and to improve mesh quality. We show with several examples that the method is capable of handling complex 2D and 3D configurations. In particular, we parametrize the 3D Stanford bunny which contains irregular shapes and voids. Finally, we propose the B´ezier ordinates approach and splines approach for C1 coupling. In the first approach, the new basis functions are defined in terms of the B´ezier Bernstein polynomials. For the second approach, the new basis is defined as a linear combination of C0 basis functions. The methods are not limited to planar or bilinear mappings. They allow the modeling of solutions to fourth order partial differential equations (PDEs) on complex geometric domains, provided that the given patches are G1 continuous. Both methods have their advantages. In particular, the B´ezier approach offer more degree of freedoms, while the spline approach is more computationally efficient. In addition, we proposed partial degree elevation to overcome the C1-locking issue caused by the over constraining of the solution space. We demonstrate the potential of the resulting C1 basis functions for application in IGA which involve fourth order PDEs such as those appearing in Kirchhoff-Love shell models, Cahn-Hilliard phase field application, and biharmonic problems

Assessing primate skull shape variation in relation to habitat: a 3D geometric morphometric approach

The advancement of digital imaging and open-source geometric morphometric (GM) software is positively impacting the way we understand morphological adaptation as an evolutionary response. Shape-space data and multivariate statistics quantify shape variation patterning and, therefore, consolidate hominoid systematic procedures. This thesis identifies ecomorphological patterns of variation within extant primates. Through a comparative, multivariate and geometric morphometric approach, this research provides a better understanding of the effects of the environment on craniomandibular form in early hominins. In this study, 107 cranial and 108 mandible specimens of 9 modern primate species were 3D imaged, and geometric morphometrics statistics were used to quantify and assess the patterns of variation between intra- and interspecific datasets concerning habitat type. Results were visualised through Principal Component scatter plots and Thin-plate Spline deformation warps, which identified critical morphological high-to-low-energy bending areas. This application addressed the questions: • to what extent does ecology influence craniomandibular morphology? • what are the main environmental pressures that encourage morphological variance in hominins? The main methodological aims sought to a) create accurate 3D digital renderings of primate skull specimens and b) define a reproducible geometric morphometric technique, which could be used as a valid and precise statistical procedure for future studies regarding hominin ecomorphology. This was achieved by pilot testing laser scanning hardware, digitising cranial and mandibular specimen, testing 3D scanning accuracy, and the best practice for capturing accurate 3D imagery, e.g. environment, lighting and meshing multiple scans. The pilot phase of this thesis also tested statistical programming toolkits capable of carrying out the finalised geometric morphometric methodology. This was achieved through trials of landmarking and statistical procedures on various data processing software, e.g. Checkpoint, TINA, and MeshLabs. Ultimately, the R Project software and accompanying IDE, R Studio, was used to collect, process and analyse the specimen shape data. This thesis contributes to the study of hominin ecomorphological patterning through a comparative approach investigating primate skull adaptation. The main findings showed habitat type as having statistical significance on the cranium's morphology but quantifiably more so in the mandible, which reported 63.71% of the overall variance observed in the first two Principal Components. This was an increase of 10.44% compared to the interspecific cranial dataset and was supported by Two-block Partial Least Squares and Procrustes ANOVA analysis. The geometric morphometric results showed significant environmental influence on the morphology of the primate cranium, most notably concerned with locomotive functions and visualises a distinction between primates who are more arboreally inclined versus those whose primary form of locomotion is terrestrial. The study also found that dietary specialisations are particularly distinguished by patterns of variation between highly folivorous versus more frugivorous species in both inter-and intraspecific groups

NURBS-Enhanced Finite Element Method (NEFEM)

The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.Peer ReviewedPostprint (published version

NURBS-Enhanced Finite Element Method (NEFEM)

The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques

Heterogeneous volumetric data mapping and its medical applications

With the advance of data acquisition techniques, massive solid geometries are being collected routinely in scientific tasks, these complex and unstructured data need to be effectively correlated for various processing and analysis. Volumetric mapping solves bijective low-distortion correspondence between/among 3D geometric data, and can serve as an important preprocessing step in many tasks in compute-aided design and analysis, industrial manufacturing, medical image analysis, to name a few. This dissertation studied two important volumetric mapping problems: the mapping of heterogeneous volumes (with nonuniform inner structures/layers) and the mapping of sequential dynamic volumes. To effectively handle heterogeneous volumes, first, we studied the feature-aligned harmonic volumetric mapping. Compared to previous harmonic mapping, it supports the point, curve, and iso-surface alignment, which are important low-dimensional structures in heterogeneous volumetric data. Second, we proposed a biharmonic model for volumetric mapping. Unlike the conventional harmonic volumetric mapping that only supports positional continuity on the boundary, this new model allows us to have higher order continuity $C^1$ along the boundary surface. This suggests a potential model to solve the volumetric mapping of complex and big geometries through divide-and-conquer. We also studied the medical applications of our volumetric mapping in lung tumor respiratory motion modeling. We were building an effective digital platform for lung tumor radiotherapy based on effective volumetric CT/MRI image matching and analysis. We developed and integrated in this platform a set of geometric/image processing techniques including advanced image segmentation, finite element meshing, volumetric registration and interpolation. The lung organ/tumor and surrounding tissues are treated as a heterogeneous region and a dynamic 4D registration framework is developed for lung tumor motion modeling and tracking. Compared to the previous 3D pairwise registration, our new 4D parameterization model leads to a significantly improved registration accuracy. The constructed deforming model can hence approximate the deformation of the tissues and tumor

Coronary Artery Segmentation and Motion Modelling

Conventional coronary artery bypass surgery requires invasive sternotomy and the use of a cardiopulmonary bypass, which leads to long recovery period and has high infectious potential. Totally endoscopic coronary artery bypass (TECAB) surgery based on image guided robotic surgical approaches have been developed to allow the clinicians to conduct the bypass surgery off-pump with only three pin holes incisions in the chest cavity, through which two robotic arms and one stereo endoscopic camera are inserted. However, the restricted field of view of the stereo endoscopic images leads to possible vessel misidentification and coronary artery mis-localization. This results in 20-30% conversion rates from TECAB surgery to the conventional approach. We have constructed patient-specific 3D + time coronary artery and left ventricle motion models from preoperative 4D Computed Tomography Angiography (CTA) scans. Through temporally and spatially aligning this model with the intraoperative endoscopic views of the patient's beating heart, this work assists the surgeon to identify and locate the correct coronaries during the TECAB precedures. Thus this work has the prospect of reducing the conversion rate from TECAB to conventional coronary bypass procedures. This thesis mainly focus on designing segmentation and motion tracking methods of the coronary arteries in order to build pre-operative patient-specific motion models. Various vessel centreline extraction and lumen segmentation algorithms are presented, including intensity based approaches, geometric model matching method and morphology-based method. A probabilistic atlas of the coronary arteries is formed from a group of subjects to facilitate the vascular segmentation and registration procedures. Non-rigid registration framework based on a free-form deformation model and multi-level multi-channel large deformation diffeomorphic metric mapping are proposed to track the coronary motion. The methods are applied to 4D CTA images acquired from various groups of patients and quantitatively evaluated

Generating anatomical substructures for physically-based facial animation.

Physically-based facial animation techniques are capable of producing realistic facial deformations, but have failed to find meaningful use outside the academic community because they are notoriously difficult to create, reuse, and art-direct, in comparison to other methods of facial animation. This thesis addresses these shortcomings and presents a series of methods for automatically generating a skull, the superficial musculoaponeurotic system (SMAS – a layer of fascia investing and interlinking the mimic muscle system), and mimic muscles for any given 3D face model. This is done toward (the goal of) a production-viable framework or rig-builder for physically-based facial animation. This workflow consists of three major steps. First, a generic skull is fitted to a given head model using thin-plate splines computed from the correspondence between landmarks placed on both models. Second, the SMAS is constructed as a variational implicit or radial basis function surface in the interface between the head model and the generic skull fitted to it. Lastly, muscle fibres are generated as boundary-value straightest geodesics, connecting muscle attachment regions defined on the surface of the SMAS. Each step of this workflow is developed with speed, realism and reusability in mind