Free-boundary conformal parameterization of point clouds

With the advancement in 3D scanning technology, there has been a surge of interest in the use of point clouds in science and engineering. To facilitate the computations and analyses of point clouds, prior works have considered parameterizing them onto some simple planar domains with a fixed boundary shape such as a unit circle or a rectangle. However, the geometry of the fixed shape may lead to some undesirable distortion in the parameterization. It is therefore more natural to consider free-boundary conformal parameterizations of point clouds, which minimize the local geometric distortion of the mapping without constraining the overall shape. In this work, we develop a free-boundary conformal parameterization method for disk-type point clouds, which involves a novel approximation scheme of the point cloud Laplacian with accumulated cotangent weights together with a special treatment at the boundary points. With the aid of the free-boundary conformal parameterization, high-quality point cloud meshing can be easily achieved. Furthermore, we show that using the idea of conformal welding in complex analysis, the point cloud conformal parameterization can be computed in a divide-and-conquer manner. Experimental results are presented to demonstrate the effectiveness of the proposed method

Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory

Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering. However, most of the existing conformal parameterization algorithms only focus on simply-connected surfaces and cannot be directly applied to surfaces with holes. In this work, we propose two novel algorithms for computing the conformal parameterization of multiply-connected surfaces. We first develop an efficient method for conformally parameterizing an open surface with one hole to an annulus on the plane. Based on this method, we then develop an efficient method for conformally parameterizing an open surface with $k$ holes onto a unit disk with $k$ circular holes. The conformality and bijectivity of the mappings are ensured by quasi-conformal theory. Numerical experiments and applications are presented to demonstrate the effectiveness of the proposed methods

Motion at low Reynolds number

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (p. 181-192).The work described in this thesis centers on inertialess motion at low Reynolds numbers at the crossroad between biofluids and microfluids. Here we address questions regarding locomotion of micro-swimmers, transport of nutrient around micro-organisms as well as mixing and heat exchange inside micro-droplets of water. A general framework for the investigation of optimal locomotion strategies for slender swimmers has been developed and applied to different systems. Here we exclusively study the hydrodynamical aspects of locomotion without further consideration for the swimmers internal dynamics. The first system studied is the "three-link" swimmer, first introduced and discussed by Nobel prize laureate E.M. Purcell in his famous lecture "Life at low Reynolds number" [121]. For this simple swimmer, we find and later discuss optimal stroke kinematics and swimmer geometries. We then further investigate flagellated swimmers and verify the convergence of the optimization procedure in the case of a single flagellum, for which the optimal stroke kinematics are known analytically. Optimal stroke kinematics and geometries for unifiagellates are also computed and found to be relevant in the context of biological microorganisms.(cont.) We then turn our attention to stroke kinematics of biflagellates and demonstrate that all the different strokes, which are experimentally observed to be performed by biflagellated organisms such as green algae chlamydomonas, are found to be local hydrodynamical optima. These observations strongly suggest the central role of hydrodynamics in the internal dynamical organization of the stroke patterns. Finally, we present experimental results on convective transport and mixing inside small droplets of water sitting on superhydrophobic substrates. We demonstrate by a scaling analysis, that the regular convection pattern is due to a thermocapillary driven Marangoni flow at the surface of the droplet. We develop an analytical solution for the temperature and flow field inside the droplet, which is found to be in agreement with our experimentally recorded data.by Daniel See-Wai Tam.Ph.D

Fish armor

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from PDF version of thesis.Includes bibliographical references (p. 261-282).Biological materials have developed hierarchical and heterogeneous material nanostructures and microstructures to provide protection against various environmental threats that, in turn, provide bioinspired clues to man-made, protective material designs. In particular, designs of dermal fish armor are a tradeoff between protection and mobility. A comprehensive knowledge base of the materials and mechanical design principles of fish armor has broad applicability to the development of synthetic engineered protective/flexible materials. In this thesis, two fish armor model systems have been investigated by means of structure-property-function relationships, ultimately answering how the armor systems have been designed in response to their environmental threats. The first model system, Polypterus senegalus are descendants of ancient fish and their body is covered by a natural armor consisting of small bony scales. The quadlayered armor scales are composed of ganoine, dentin, isopedine and bone, to protect against predatory biting attacks. First of all, multilayer design principles of P. senegalus scales were understood with respect to penetration resistance by the multiscale experimental and computational study. The quad-layered scales exhibit mechanical gradient within and between material layers and have geometrically corrugated junctions with an undetectable gradation; all of which lead to effective penetration resistance including load-dependent effective material properties, circumferential surface cracking, plastic dissipation in the underlying dentin layer, stress redistribution around the interfaces with suppression of interfacial failure. Secondly, since the outmost ganoine is structurally anisotropic, the roles of anisotropy of ganoine in the entire system have been investigated by combining orientation-dependant indentation and mechanical modeling. The elastic-plastic anisotropy of the ganoine layer enhances the load-dependent penetration resistance of the multilayered armor compared with the isotropic ganoine layer mainly by (i) enhancing the transmission of stress and dissipation to the underlying dentin layer, (ii) lowering the ganoine/dentin interfacial stresses and hence reducing any propensity toward delamination, and (iii) providing discrete structural pathways for cracks to propagate normal to the surface for easy arrest by the underlying dentin layer. Inspired by P. senegalus scales, threat-protection interaction and structurefunction relationships among various layered armor systems have been investigated using parametric studies with finite element (FE) models. Geometry, microstructure and mechanical properties of a threat system significantly influence its ability to effectively penetrate into the armor system or to be defeated by the armor. Simultaneously, three structure parameters of multilayered armor designs are mainly considered: (i) the thickness of the outmost layer; (ii) the quad-layered vs. bilayer structure; and (iii) the sequence of the outer two layers. The role of the armor microstructure in defeating threats as well as providing avenues of energy dissipation to withstand biting attacks is identified. Microstructural length scale and material property matching between the threat and armor is clearly observed. Bilayered and quadlayred models are mechanically comparable, but the quad-layer model achieves a weight reduction. Studies of predatorprey threat-protection interactions may lead to insights into tunability in mechanical functionality of each system in conjunction with adaptive phenotypic plasticity of the tooth and scale microstructure and geometry, "adaptive stalemates," and the so-called evolutionary "arms race." The second model system, Gasterosteus aculeatus, is well-known for light-weight and morphologically varied armor structure among different G. aculeatus populations. Marine and freshwater G. aculeatus armor structures have been assessed quantitatively by micro-computed tomography ([mu]CT) technique. The convolution of plate geometry in conjunction with plate-to-plate overlap allows a relatively constant armor thickness to be maintained throughout the assembly, promoting spatially homogeneous protection and thereby avoiding weakness at the armor unit interconnections. Plate-to-plate junctures act to register and join the plates while permitting compliance in sliding and rotation in selected directions. SEM and [mu]CT revealed a porous, sandwich-like cross-section of lateral plates beneficial for bending stiffness and strength at minimum weight. Moreover, the structural parameters of the pelvic assemblies were also quantified via pCT, which include the spatial dependence of the suture amplitude and frequency, the suture plate inclination angle, and the suture gap. Significant differences in these structural parameters were observed between the different G. aculeatus populations. Composite analytical and finite element computational models were developed and used in conjunction with the pCT data to simulate the mechanical behavior of the pelvic assembly, to predict the effective suture stiffness and to understand the conformational change of the pelvic assembly from the "rest" to "offensive" states. This study elucidates the structural and functional differences between different divergent populations of G. aculeatus and serves as a model for other systems of interest in evolutionary biology.by Juha Song.Ph.D

La viscosité : un architecte pour le système respiratoire ?

The mammals respiratory system characteristics have been selected because they bring benefits other characteristics do not. At first approximation, such benefices can be estimated through the minimization of energetic costs relatively to one or several of these characteristics. The cost is the consequence of a complex interaction between many phenomena, amongst which physiology, organ development, its inner physics and chemistry, and its surrounding environment. My work aims at building idealized cost functions which, I hypothesized, represent approximations of the real cost optimized by evolution. To build and study these cost functions, I use mathematical modeling processes often based on dedicated mathematical and numerical tools. The costs we propose try to retain only the core phenomena involved in the organ functioning. Then I compare the model predictions with physiology and discuss its validity. I applied this approach to different organs of the respiratory system where the role of viscous dissipation of fluids on the selection of their characteristics may have been the strongest.The cost function we built for the tracheobronchial tree is based on the trade-off between lung’s hydrodynamic resistance and the size of the lung’s exchange surface. We showed that a tree structure associated to such a cost is stable for a dynamic process such as evolution only if the air flows in the bottom of the tree are regulated. We proposed an original and parsimonious model for tracheobronchial tree development based on a physical instability. The predictions of this model are in agreement with most of the experiments in the literature. We were able to relate the geometrical parameters of the adult lungs with parameters of our development model. We showed that biological noise during lung’s development may have influenced the selection of the geometry of the tracheobronchial tree by shifting its multi-scaled geometry to branches slightly wider than the theoretical optimal and by implying asymmetric branching. The role of biological noise on tracheobronchial tree selection is an archetypal example of a more general framework we developed about the role of biological noise on evolution. Cliff-edge theory states that biological noise can be viewed as an evolutionary mechanism. We proposed and validated a general population dynamics model that includes cliff-edge effects and explains its mechanisms.Our models and results for the tracheobronchial tree were also used in the frame of two medical applications. The first, based on patients data, aimed at testing whether variations at patient level of the multi-scale geometry may be correlated with chronic obstructive pulmonary disease (COPD). The second medical application aimed at understanding the underlying biophysics involved in chest physiotherapy and at arising a scientific background to a discipline that is, as of today, mostly empirical.Another important organ involved in the respiratory system that uses a fluid to transport oxygen is blood network, and more specifically arterial network, where most of the system pressure drop occurs. Arterial system couples a multi-scaled tree structure with a non-Newtonian rheofluidifying fluid (blood), submitted to phase separation effects in small vessels (F ̊ahræus effect). We proposed that both the multi- scale property of arterial network geometry and the red blood cells fraction in blood (hematocrit) may have been selected through a trade-off inspired from Murray’s original optimization principle. The cost we propose is based on fluid dissipation, metabolic energetic cost of blood and a given total oxygen flow in the tree. We showed that the dissipation is mostly driven by branches mean shear rates which checks a scaling law related to that of the tree. The multi-scaled geometry of arterial network and blood hematocrit are close to the minimal configuration for the cost we propose, thus indicating it may have played a role on the selection of blood arterial network properties.In capillaries, the red blood cells fraction in blood is smaller than in the large circulation because of a phase separation effects on plasma and red blood cells. Thus, we modeled by numerical means the flow and deformation of a periodic train of red blood cells in a capillary using a dedicated numerical method - the camera method. Using the same cost function than for the arterial network, we predicted that the typical concentration of red blood cells in the capillaries also optimized the same cost in capillaries. With our numerical model, we also studied the oxygen transfer through the alveolo-capillary membrane and its capture by the red blood cells in the pulmonary capillaries.My work brought out scenarios that explain how viscous dissipation of biological fluids may have played a role on the selection of some mammals respiratory system characteristics, and most particularly of its geometries. These scenarios are however based on simplification hypotheses which must be accounted for when confronted with the real objects. Nevertheless, the predictions made by the different models studied are consistent with physiology, which indicates that the models probably capture main behaviors. My research also highlights that the inherent fluctuations arising from organ’s development may affect the adult organ function and consequently the organ selection. Finally, some of the models and concepts developed in my work expanded into medical applications

Streamlining the Design and Use of Array Coils for In Vivo Magnetic Resonance Imaging of Small Animals

Small-animal models such as rodents and non-human primates play an important pre-clinical role in the study of human disease, with particular application to cancer, cardiovascular, and neuroscience models. To study these animal models, magnetic resonance imaging (MRI) is advantageous as a non-invasive technique due to its versatile contrast mechanisms, large and flexible field of view, and straightforward comparison/translation to human applications. However, signal-to-noise ratio (SNR) limits the practicality of achieving the high-resolution necessary to image the smaller features of animals in an amount of time suitable for in vivo animal MRI. In human MRI, it is standard to achieve an increase in SNR through the use of array coils; however, the design, construction, and use of array coils for animal imaging remains challenging due to copper-loss related issues from small array elements and design complexities of incorporating multiple elements and associated array hardware in a limited space. In this work, a streamlined strategy for animal coil array design, construction, and use is presented and the use for multiple animal models is demonstrated. New matching network circuits, materials, assembly techniques, body-restraining systems and integrated mechanical designs are demonstrated for streamlining high-resolution MRI of both anesthetized and awake animals. The increased SNR achieved with the arrays is shown to enable high-resolution in vivo imaging of mice and common marmosets with a reduced time for experimental setup

Sub-pixel Registration In Computational Imaging And Applications To Enhancement Of Maxillofacial Ct Data

In computational imaging, data acquired by sampling the same scene or object at different times or from different orientations result in images in different coordinate systems. Registration is a crucial step in order to be able to compare, integrate and fuse the data obtained from different measurements. Tomography is the method of imaging a single plane or slice of an object. A Computed Tomography (CT) scan, also known as a CAT scan (Computed Axial Tomography scan), is a Helical Tomography, which traditionally produces a 2D image of the structures in a thin section of the body. It uses X-ray, which is ionizing radiation. Although the actual dose is typically low, repeated scans should be limited. In dentistry, implant dentistry in specific, there is a need for 3D visualization of internal anatomy. The internal visualization is mainly based on CT scanning technologies. The most important technological advancement which dramatically enhanced the clinician\u27s ability to diagnose, treat, and plan dental implants has been the CT scan. Advanced 3D modeling and visualization techniques permit highly refined and accurate assessment of the CT scan data. However, in addition to imperfections of the instrument and the imaging process, it is not uncommon to encounter other unwanted artifacts in the form of bright regions, flares and erroneous pixels due to dental bridges, metal braces, etc. Currently, removing and cleaning up the data from acquisition backscattering imperfections and unwanted artifacts is performed manually, which is as good as the experience level of the technician. On the other hand the process is error prone, since the editing process needs to be performed image by image. We address some of these issues by proposing novel registration methods and using stonecast models of patient\u27s dental imprint as reference ground truth data. Stone-cast models were originally used by dentists to make complete or partial dentures. The CT scan of such stone-cast models can be used to automatically guide the cleaning of patients\u27 CT scans from defects or unwanted artifacts, and also as an automatic segmentation system for the outliers of the CT scan data without use of stone-cast models. Segmented data is subsequently used to clean the data from artifacts using a new proposed 3D inpainting approach