Medical imaging is an important tool for diagnosis and treatment planning today. However as the demand for efficiency increases at the same time as the data volumes grow immensely, the need for computer assisted analysis, such as image segmentation, to help and guide the practitioner increases. Medical image segmentation could be used for various different tasks, the localization and delineation of pathologies such as cancer tumors is just one example. Numerous problems with noise and image artifacts in the generated images make the segmentation a difficult task, and the developer is forced to choose between speed and performance. In clinical practise, however, this is impossible as both speed and performance are crucial. One solution to this problem might be to involve the user more in the segmentation, using interactivite algorithms where the user might influence the segmentation for an improved result. This thesis has concentrated on finding a fast and interactive segmentation method for liver tumor segmentation. Various different methods were explored, and a few were chosen for implementation and further development. Two methods appeared to be the most promising, Bayesian Region Growing (BRG) and Level Set. An interactive Level Set algorithm emerged as the best alternative for the interactivity of the algorithm, and could be used in combination with both BRG and Level Set. A new data term based on a probability model instead of image edges was also explored for the Level Set-method, and proved to be more promising than the original one. The probability based Level Set and the BRG method both provided good quality results, but the fastest of the two was the BRG-method, which could segment a tumor present in 25 CT image slices in less than 10 seconds when implemented in Matlab and mex-C++ code on an ACPI x64-based PC with two 2.4 GHz Intel(R) Core(TM) 2CPU and 8 GB RAM memory. The interactive Level Set could be succesfully used as an interactive addition to the automatic method, but its usefulness was somewhat reduced by its slow processing time ( 1.5 s/slice) and the relative complexity of the needed user interactions.

Cette thèse porte sur l'optimisation de forme via la méthode des "level sets" pour deux comportements mécaniques induisant des déplacements non différentiables par rapport à la forme: le contact et la plasticité. Pour y remédier, nous utilisons des problèmes approchés issus de méthode de pénalisation et de régularisation.Dans la première partie, nous présentons quelques notions fondamentales d'optimisation de forme (chapitre 1). Puis nous exposons les résultats qui seront utiles à l'analyse des deux problèmes mécaniques considérés et nous illustrons ces résultats.La deuxième partie introduit les modèles statiques de contact (chapitre 3) et le modèle statique de plasticité (chapitre 4) que nous utilisons dans le manuscrit. Pour chacun, nous donnons les bases de la modélisation mécanique, une analyse mathématique des inéquations variationnelles associées et nous expliquons quels solveurs nous avons implémentés.La dernière partie se focalise sur l'optimisation de forme. Dans chacun des chapitres nous donnons les versions pénalisées et régularisées des modèles, prouvons, pour certains, leur convergence vers les modèles exactes, calculons leurs gradients de forme et proposons des exemples 2D et, en contact, 3D. Ainsi, dans le chapitre 5, traitons-nous du contact et considérons deux sortes de problèmes: le premier dans lequel la zone de contact est fixe, le second dans lequel la zone de contact est optimisable. Pour ce dernier, nous introduisons deux méthodes pour résoudre du contact sans discrétiser la zone de contact. Dans le chapitre 6, nous abordons le modèle de Hencky que nous approximons grâce à une pénalisation de Perzyna ainsi que grâce à un modèle de notre crue. / The main purpose of this thesis is to perform shape optimisation, in the framework of the level set method, for two mechanical behaviours inducing displacement which are not shape differentiable: contact and plasticity. To overcome this obstacle, we use approximate problems found by penalisation and regularisation.In the first part, we present some classical notions in optimal design (chapter 1). Then we give the mathematical results needed for the analysis of the two mechanical problems in consideration and illustrate these results.The second part is meant to introduce the five static contact models (chapter 3) and the static plasticity model (chapter 4) we use in the manuscript. For each chapter we provide the basis of the mechanical modeling, a mathematical analysis of the related variational inequations and, finally, explain how we implement the associated solvers.Eventually the last part, consisting of two chapters is devoted to shape optimisation. In each of them, we state the regularised versions of the models, prove, for some of them, the convergence to the exact ones, compute shape gradients and perform some numerical experiments in 2D and, for contact, in 3D. Thus, in chapter 5, we focus on contact and consider two types of optimal design problems: one with a fixed contact zone and another one with a mobile contact zone. For this last type, we introduce two ways to solve frictionless contact without meshing the contact zone. One of them is new and the other one has never been employed in this framework. In chapter 6, we deal with the Hencky model which we approximate thanks to a Perzyna penalised problem as well as a home-made one.

This work deals with a fast level-set approach for segmentation of anatomical structures in volumetric medical images. The fast level-set method evolves a closed 3D surface in time propagating the surface form an initial position. The major contribution of this work is the implementation of the level-set method and construction of an interactive tool for segmentation of 3D medical data using this method. The tool is able to interactively change parameters of the evolution during the segmentation process itself. Due to the nature of level-set method, the evolution process can be stopped at any time, or backtracked and restarted from any previous step with a different configuration.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18585号 / 工博第3946号 / 新制||工||1606(附属図書館) / 31485 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 教授 田畑 修, 教授 松原 厚 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This work is rooted in a need for dermatologists to explore skin characteristicsin depth. The inuence of skin disease such as acne in dermal tissues is stilla complex task to assess. Among the possibilities, high frequency ultrasoundimaging is a paradigm shift to probe and characterizes upper and deep dermis.For this purpose, a cohort of 58 high-frequency 3D images has been acquiredby the French laboratory Pierre Fabre in order to study acne vulgaris disease.This common skin disorder is a societal challenge and burden aecting late adolescentsacross the world. The medical protocol developed by Pierre Fabre wasto screen a lesion every day during 9 days for dierent patients with ultrasoundimaging. The provided data features skin epidermis and dermis structure witha fantastic resolution. The strategy we led to study these data can be explainedin three steps. First, epidermis surface is detected among artifacts and noisethanks to a robust level-set algorithm. Secondly, acne spots are located on theresulting height map and associated to each other among the data by computingand thresholding a local variance. And eventually potential inammatorydermal cavities related to each lesion are geometrically and statistically characterizedin order to assess the evolution of the disease. The results presentan automatic algorithm which permits dermatologists to screen acne vulgarislesions and to characterize them in a complete data set. It can hence be a powerfultoolbox to assess the eciency of a treatment. / Detta arbete är grundat i en dermatologs behov att undersöka hudens egenskaperpå djupet. Påverkan av hudsjukdomar så som acne på dermala vävanderär fortfarande svårt att bedöma. Bland möjligheterna är högfrekvent ultraljudsavbildningett paradigmskifte för undersökning och karakterisering av övre ochdjupa dermis. I detta syfte har en kohort av 58 högfrekventa 3D bilder förvärvatsav det Franska laboratoriet Pierre Fabre för att studera sjukdomen acne vulgaris.Denna vanliga hudsjukdom är en utmaning för samhället och en bördasom påverkar de i slutet av tonåren över hela världen. Protokollet utvecklatav Pierre Fabre innebar att undersöka en lesion varje dag över 9 dagar förolika patienter med ultraljudavbildning. Den insamlade datan visar hudens epidermisoch dermis struktur med en fantastiskt hög upplösning. Strategin vianvände för att studera denna data kan förklaras i tre steg. För det första,hittas epidermis yta bland artifakter och brus tack vare en robust level-set algoritm.För det andra, acne äckar hittas på höjdkartan och associeras tillvarandra bland mätdatan genom en tröskeljämförelse över lokala variationer.Även potentiellt inammatoriska dermala hålrum relaterade till varje lesion blirgeometriskt ochj statistiskt kännetecknade för att bedöma sjukdomens förlopp.Resultaten framför en automatisk algoritm som gör det möjligt för dermatologeratt undersöka acne vulgaris lesioner och utmärka de i ett dataset. Detta kandärmed vara en kraftfull verktygslåda för att undersöka inverkan av en behandlingtill denna sjukdom.

This dissertation develops a computational method for simulating laser-induced cavitation and investigates the mechanism behind the formation of non-spherical bubbles induced by long-pulsed lasers. The proposed computational method accounts for the laser emission and absorption, phase transition, and the dynamics and thermodynamics of a two-phase fluid flow. In this new method, the model combines the Navier-Stokes (NS) equations for a compressible inviscid two-phase fluid flow, a new laser radiation equation, and a novel local thermodynamic model of phase transition. The Navier-Stokes equations are solved using the FInite Volume method with Exact two-phase Riemann solvers (FIVER). Following this method, numerical fluxes across phase boundaries are computed by constructing and solving one-dimensional bi-material Riemann problems. The new laser radiation equation is derived by customizing the radiative transfer equation (RTE) using the special properties of laser, including monochromaticity, directionality, high intensity, and a measurable focusing or diverging angle. An embedded boundary finite volume method is developed to solve the laser radiation equation on the same mesh created for the NS equations. The fluid mesh usually does not resolve the boundary and propagation directions of the laser beam, leading to the challenges of imposing the boundary conditions on the laser domain. To overcome this challenge, ghost nodes outside the laser domain are populated by mirroring and interpolation techniques. The existence and uniqueness of the solution are proved for the two-dimensional case, leveraging the special geometry of the laser domain. The method is up to second-order accuracy, which is also proved, and verified using numerical tests. A method of latent heat reservoir is developed to predict the onset of vaporization, which accounts for the accumulation and release of latent heat. In this work, the localized level set method is employed to track the bubble surface. Furthermore, the continuation of phase transition is possible in laser-induced cavitation problems, especially for long-pulsed lasers. A method of local correction and reinitialization is developed to account for continuous phase transitions. Several numerical tests are presented to verify the convergence of these methods. This multiphase laser-fluid coupled computational model is employed to simulate the formation and expansion of bubbles with different shapes induced by different long-pulsed lasers. The simulation results show that the computational method can capture the key phenomena in the laser-induced cavitation problems, including non-spherical bubble expansion, shock waves, and the ``Moses effect''. Additionally, the observed complex non-spherical shapes of vapor bubbles generated by long-pulsed laser reflect some characteristics (e.g., direction, width) of the laser beam. The dissertation also investigates the relation between bubble shapes and laser parameters and explores the transition between two commonly observed shapes -- namely, a rounded pear-like shape and an elongated conical shape -- using the proposed computational model. Two laboratory experiments are simulated, in which Holmium:YAG and Thulium fiber lasers are used respectively to generate bubbles of different shapes. In both cases, the predicted bubble nucleation and morphology agree reasonably well with the experimental observation. The full-field results of laser radiance, temperature, velocity, and pressure are analyzed to explain bubble dynamics and energy transmission. It is found that due to the lasting energy input, the vapor bubble's dynamics is driven not only by advection, but also by the continued vaporization at its surface. Vaporization lasts less than 1 microsecond in the case of the pear-shaped bubble, compared to over 50 microseconds for the elongated bubble. It is thus hypothesized that the bubble's morphology is determined by a competition between the speed of bubble growth due to advection and continuous vaporization. When the speed of advection is higher than that of vaporization, the bubble tends to grow spherically. Otherwise, it elongates along the laser beam direction. To test this hypothesis, the two speeds are defined analytically using a model problem and then estimated for the experiments using simulation results. The results support the hypothesis and also suggest that when the laser's power is fixed, a higher laser absorption coefficient and a narrower beam facilitate bubble elongation. / Doctor of Philosophy / Laser-induced cavitation is a process where laser beams create bubbles in a liquid. This phenomenon is widely applied in research and microfluidic applications for precise control of bubble dynamics. It also naturally occurs in various laser-based processes involving liquid environments. Understanding laser-induced cavitation is important for enhancing the effectiveness and safety of related technologies. However, experimental studies encounter limitations, highlighting the development of numerical methods to advance the understanding of laser-induced cavitation. The laser-induced cavitation can be roughly described as localized boiling through thermal radiation. The detailed physics involves the absorption of laser light by a liquid, the formation of vapor bubbles due to localized heating, and the dynamics of both the bubbles and the surrounding liquid. The first part of the dissertation introduces a new computational method for modeling these phenomena. The dynamics of the two-phase flow are modeled by the Navier-Stokes equations, which are solved using the FInite Volume method with Exact two-phase Riemann solvers (FIVER). The absorption of the laser light is modeled by a new laser radiation equation, which is derived from laser energy conservation and special properties of the laser. An embedded boundary finite volume method is developed to solve this equation on the same mesh created for the NS equations. Additionally, a method of latent heat reservoir is developed to predict the onset of vaporization. In this work, the level set method is employed to track the bubble surface, and a method of local correction and reinitialization is developed to account for possible continuous phase transitions. After developing this new method, several test cases are simulated. The simulation results show that the method can capture the key phenomena in the laser-induced cavitation problems, including the absorption of laser light, non-spherical bubble expansion, and shock waves. When the laser pulse is comparable to or longer than the acoustic time scale (long-pulsed laser), vapor bubbles generated often have complex non-spherical shapes. The bubble shapes reflect some characteristics (e.g., direction, width) of the laser beam. The second part of the dissertation investigates the relation between bubble shapes and laser parameters. Two laboratory experiments are simulated, in which two different lasers are used to generate bubbles of different shapes, namely, a rounded pear-like shape and an elongated conical shape. In both cases, the simulated bubbles exhibit shapes and sizes that reasonably match the experimental results. The simulation results of temperature, pressure, and velocity fields are analyzed to explain bubble dynamics and energy transmission. The analysis shows that the expansion of bubbles induced by long-pulsed lasers is determined not only by advection but also by the continued vaporization at its surface. Vaporization lasts less than $1$ microsecond in the case of the pear-shaped bubble, compared to over $50$ microseconds for the elongated bubble. It is thus hypothesized that the bubble expansion is determined by a competition between the speed of bubble growth due to advection and continuous vaporization. When the speed of advection is higher than that of vaporization, the bubble tends to grow spherically. Otherwise, it elongates along the laser beam direction. To test this hypothesis, the two speeds are defined analytically using a model problem and then estimated for the experiments using simulation results. The results support the hypothesis and also suggest that when the laser's power is fixed, a higher laser absorption coefficient and a narrower beam facilitate bubble elongation.

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京都大学 / 新制・課程博士 / 博士(理学) / 甲第23677号 / 理博第4767号 / 新制||理||1683(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 SVADLENKA Karel, 教授 泉 正己, 教授 坂上 貴之 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

A coupled solution approach is presented for numerically simulating a near-field underwater explosion (UNDEX). An UNDEX consists of a complicated sequence of events over a wide range of time scales. Due to the complex physics, separate simulations for near/far-field and early/late-time are common in practice. This work focuses on near-field early-time UNDEX simulations. Using the assumption of compressible, inviscid and adiabatic flow, the fluid flow is governed by a set of Euler fluid equations. In practical simulations, we often encounter computational difficulties that include large displacements, shocks, multi-fluid flows with cavitation, spurious waves reflecting from boundaries and fluid-structure coupling. Existing methods and codes are not able to simultaneously consider all of these characteristics. A robust numerical method that is capable of treating large displacements, capturing shocks, handling two-fluid flows with cavitation, imposing non-reflecting boundary conditions (NRBC) and allowing the movement of fluid grids is required. This method is developed by combining numerical techniques that include a high-order accurate numerical method with a shock capturing scheme, a multi-fluid method to handle explosive gas-water flows and cavitating flows, and an Arbitrary Lagrangian Eulerian (ALE) deformable fluid mesh. These combined approaches are unique for numerically simulating various near-field UNDEX phenomena within a robust single framework. A review of the literature indicates that a fully coupled methodology with all of these characteristics for near-field UNDEX phenomena has not yet been developed. A set of governing equations in the ALE description is discretized by a Runge Kutta Discontinuous Galerkin (RKDG) method. For multi-fluid flows, a Direct Ghost Fluid (DGF) Method coupled with the Level Set (LS) interface method is incorporated in the RKDG framework. The combination of RKDG and DGF methods (RKDG-DGF) is the main contribution of this work which improves the quality and stability of near-field UNDEX flow simulations. Unlike other methods, this method is simpler to apply for various UNDEX applications and easier to extend to multi-dimensions. / Ph. D.