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京都大学 / 新制・課程博士 / 博士(理学) / 甲第25095号 / 理博第5002号 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 小野 薫, 教授 大木谷 耕司, 准教授 入江 慶 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Glioblastoma (GBM) is the most aggressive and malignant glioma. It accounts for 48.6% of all primary, malignant gliomas with a median survival of 15 months. Infiltration into the surrounding parenchyma is a hallmark of GBM. Radiotherapy is used to address the invasion; however, recent studies have implicated that radiation contributes to increased invasiveness of glioma. Although the effect of radiation on cells has been studied extensively, its effect on the transport of fluid is not well characterized. Transport in the brain which has significant roles in physiology, GBM pathophysiology, and GBM treatment. Thus, understanding the effect of radiation on transport within the lesion and surrounding interstitium will be beneficial in characterizing the effects of radiotherapy in GBM patients. This dissertation seeks to explore the relationship between radiation, transport, and movement of glioma cells and includes the following: 1) Characterizing in vitro motility metrics of glioma stem cell lines in and relating them to in vivo invasion. 2) Studying the effect of radiation on motility, flow-mediated invasion, extracellular matrix components, and transport within the lesion and interstitium. 3) Assessing transport in clinical images and relating transport parameters to progression of GBM. 4) Developing a novel pipeline for applying vector field topology to the study of interstitial fluid flow in glioma. Surprisingly, we found that motility metrics in vitro have a negative correlation trend with in vivo invasion. Next, we found that radiation causes a transient increase in advective flow, and a more sustained decrease in diffusivity in a murine glioma model. Tenascin C was found to correlate significantly with invasion and diffusivity, indicating that it might be a link between radiation, transport, and invasion. Furthermore, interstitial fluid flow was calculated and assessed in clinical images. This showed that interstitial fluid flow velocity magnitude in the tumor correlates with overall survival in GBM patients. Lastly, vector field topology was introduced as a novel method of studying transport that provides more detailed information to identify potential drivers of transport within a flow field. Altogether, this work presents novel insight into the effects of radiation on invasion and transport in GBM. Hopefully, this work can provide a foundation to build upon in efforts of improving treatment planning and clinical outcomes for GBM patients. / Doctor of Philosophy / Glioblastoma (GBM) is the most aggressive glioma. It accounts for 48.6% of all primary, malignant gliomas with a median survival of 15 months. The movement of cancer cells into the surrounding tissue is a defining factor of GBM. Radiotherapy is used after surgery to treat the remaining cancer cells in tissue surrounding the tumor; however, recent studies have implicated that radiation contributes to increased movement of glioma into surrounding tissue. Although the effect of radiation on cells has been studied extensively, its effect on transport of fluid is not well characterized. Interstitial fluid flow in the brain has significant roles in healthy bodily functions, GBM disease state, and GBM treatment. Thus, understanding the effect of radiation on transport within the tumor and surrounding tissue is beneficial in better characterizing the effects of radiotherapy. This dissertation seeks to explore the relationship between radiation, transport, and movement of glioma cells and includes the following: 1) Characterizing in vitro motility metrics of glioma cells in and relating them to in vivo movement into healthy tissue. 2) Studying the effect of radiation on motility, flow-mediated infiltration into healthy tissue, tissue matrix components, and fluid flow within the tumor and surrounding tissue. 3) Assessing transport in clinical images and relating transport parameters to progression of GBM. 4) Developing a novel pipeline for applying vector field topology to the study of interstitial fluid flow in glioma. Surprisingly, we found that motility metrics in vitro have a negative correlation trend with in vivo invasion. Next, we found that radiation causes a transient increase in flow velocity magnitude, and a more sustained decrease in diffusivity in a murine glioma model. Tenascin C, a component of the tissue matrix, was found to correlate significantly with invasion and diffusivity. This indicates that Tenascin C might be a link between radiation, transport, and invasion. Furthermore, interstitial fluid flow was calculated and assessed in clinical images which showed that interstitial fluid flow velocity magnitude in the tumor correlates with survival. Lastly, vector field topology was introduced as a novel method of studying fluid flow in glioma that provides more detailed information regarding the flow field. Altogether, this work presents novel insight into the effects of radiation on fluid flow and cellular movement in GBM. Hopefully, this work can provide a foundation to build upon in efforts of improving treatment planning and clinical outcomes for GBM patients.

Quantum trajectories are investigated within the complex quantum Hamilton-Jacobi formalism. A unified description is presented for complex quantum trajectories for one-dimensional time-dependent and time-independent problems. Complex quantum trajectories are examined for the free Gaussian wave packet, the coherent state in the harmonic potential, and the the barrier scattering problems. We analyze the variations of the complex-valued kinetic energy, the classical potential, and the quantum potential along the complex quantum trajectories. For one-dimensional time-independent scattering problems, we demonstrate general properties and similar structures of the complex quantum trajectories and the quantum potentials. In addition, it is shown that a quantum vortex forms around a node in the wave function in complex space, and the quantized circulation integral originates from the discontinuity in the real part of the complex action. Although the quantum momentum field displays hyperbolic flow around a node, the corresponding Polya vector field displays circular flow. Moreover, local topologies of the quantum momentum function and the Polya vector field are thoroughly analyzed near a stagnation point or a pole (including circular, hyperbolic, and attractive or repulsive structures). The local structure of the quantum momentum function and the Polya vector field around a stagnation point are related to the first derivative of the quantum momentum function. However, the magnitude of the asymptotic structures for these two fields near a pole depends only on the order of the node in the wave function. Finally, quantum interference is investigated and it leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. Moreover, the wrapping time for a specific trajectory is determined by the divergence and vorticity of the quantum momentum field. The lifetime for interference features is determined by the rotational dynamics of the nodal line in the complex plane. Therefore, these results demonstrate that the complex quantum trajectory method provides a novel perspective for analysis and interpretation of quantum phenomena. / text

Lorentz TEM observations of magnetic nanoparticles contain information on the magnetic and electrostatic potentials of the sample. These potentials can be extracted from the electron wave phase shift by separating electrostatic and magnetic phase shifts, followed by 3D tomographic reconstructions. In past, Vector Field Electron Tomography (VFET) was utilized to perform the reconstruction. However, VFET is based on a conventional tomography method called filtered back-projection (FBP). Consequently, the VFET approach tends to produce inconsistencies that are prominent along the edges of the sample. We propose a model-based iterative reconstruction (MBIR) approach to improve the reconstruction of magnetic vector potential, A(r). In the case of scalar tomography, the MBIR method is known to yield better reconstructions than the conventional FBP approach, due to the fact that MBIR can incorporate prior knowledge about the system to be reconstructed. For the same reason, we seek to use the MBIR approach to optimize vector field tomographic reconstructions via incorporation of prior knowledge. We combine a forward model for image formation in TEM experiments with a prior model to formulate the tomographic problem as a maximum a posteriori probability estimation problem (MAP). The MAP cost function is minimized iteratively to deduce the vector potential. A detailed study of reconstructions from simulated as well as experimental data sets is provided to establish the superiority of the MBIR approach over the VFET approach.

Two well-known types of water waves are shallow water waves and the solitary waves. The former waves are those waves which have larger wavelength than the local water depth and the latter waves are used for the ones which retain their shape and speed after colliding with each other. The most well known of the latter waves are Korteweg de Vries (KdV) equations, which are widely used in many branches of physics and engineering. These equations are nonlinear long waves and mathematically represented by partial differential equations (PDEs). For solving the KdV and KdV-type equations, several numerical methods were developed in the recent years which preserve their geometric structure, i.e. the Hamiltonian form, symplecticity and the integrals. All these methods are classified as symplectic and multisymplectic integrators. They produce stable solutions in long term integration, but they do not preserve the Hamiltonian and the symplectic structure at the same time. This thesis concerns the application of energy preserving average vector field integrator(AVF) to nonlinear Hamiltonian partial differential equations (PDEs) in canonical and non-canonical forms. Among the PDEs, Korteweg de Vries (KdV) equation, modified KdV equation, the Ito&rsquo / s system and the KdV-KdV systems are discetrized in space by preserving the skew-symmetry of the Hamiltonian structure. The resulting ordinary differential equations (ODEs) are solved with the AVF method. Numerical examples confirm that the energy is preserved in long term integration and the other integrals are well preserved too. Soliton and traveling wave solutions for the KdV type equations are accurate as those solved by other methods. The preservation of the dispersive properties of the AVF method is also shown for each PDE.

The goal of this thesis is the development of a fast and robust algorithm that is able to detect patterns in flow fields independent from their orientation and adequately visualize the results for a human user. This thesis is an interdisciplinary work in the field of vector field visualization and the field of pattern recognition. A vector field can be best imagined as an area or a volume containing a lot of arrows. The direction of the arrow describes the direction of a flow or force at the point where it starts and the length its velocity or strength. This builds a bridge to vector field visualization, because drawing these arrows is one of the fundamental techniques to illustrate a vector field. The main challenge of vector field visualization is to decide which of them should be drawn. If you do not draw enough arrows, you may miss the feature you are interested in. If you draw too many arrows, your image will be black all over. We assume that the user is interested in a certain feature of the vector field: a certain pattern. To prevent clutter and occlusion of the interesting parts, we first look for this pattern and then apply a visualization that emphasizes its occurrences. In general, the user wants to find all instances of the interesting pattern, no matter if they are smaller or bigger, weaker or stronger or oriented in some other direction than his reference input pattern. But looking for all these transformed versions would take far too long. That is why, we look for an algorithm that detects the occurrences of the pattern independent from these transformations. In the second part of this thesis, we work with moment invariants. Moments are the projections of a function to a function space basis. In order to compare the functions, it is sufficient to compare their moments. Normalization is the act of transforming a function into a predefined standard position. Moment invariants are characteristic numbers like fingerprints that are constructed from moments and do not change under certain transformations. They can be produced by normalization, because if all the functions are in one standard position, their prior position has no influence on their normalized moments. With this technique, we were able to solve the pattern detection task for 2D and 3D flow fields by mathematically proving the invariance of the moments with respect to translation, rotation, and scaling. In practical applications, this invariance is disturbed by the discretization. We applied our method to several analytic and real world data sets and showed that it works on discrete fields in a robust way.

Deformable image registration (DIR) is a type of registration that calculates a deformable vector field (DVF) between two image data sets and permits contour and dose propagation. However the calculation of a DVF is considered an ill-posed problem, as there is no exact solution to a deformation problem, therefore all DVFs calculated contain errors. As a result it is important to evaluate and assess the accuracy and limitations of any DIR algorithm intended for clinical use. The influence of image quality on the DIR algorithms performance was also evaluated. The hybrid DIR algorithm in RayStation 4.0.1.4 was assessed using a number of evaluation methods and data. The evaluation methods were point of interest (POI) propagation, contour propagation and dose measurements. The data types used were phantom and patient data. A number of metrics were used for quantitative analysis and visual inspection was used for qualitative analysis. The quantitative and qualitative results indicated that all DVFs calculated by the DIR algorithm contained errors which translated into errors in the propagated contours and propagated dose. The results showed that the errors were largest for small contour volumes (<20cm3) and for large anatomical volume changes between the image sets, which pushes the algorithms ability to deform, a significant decrease in accuracy was observed for anatomical volume changes of greater than 10%. When the propagated contours in the head and neck were used for planning the errors in the DVF were found to cause under dosing to the target tumour by up to 32% and over dosing to the organs at risk (OAR) by up to 12% which is clinically significant. The results also indicated that the image quality does not have a significant effect on the DIR algorithms calculations. Dose measurements indicated errors in the DVF calculations that could potentially be clinically significant. The results indicate that contour propagation and dose propagation must be used with caution if clinical use is intended. For clinical use contour propagation requires evaluation of every propagated contour by an expert user and dose propagation requires thorough evaluation of the DVF.

Orientador: Paulo Ricardo da Silva / Banca: Weber Flavio Pereira / Banca: Marcelo Messias / Resumo: Consideramos dois casos principais de bifurcação de órbitas periódicas não hiperbólicas que dão origem a ciclos limite. Nosso estudo é feito para sistemas lineares por partes com três zonas em sua fórmula mais geral, que inclui situações sem simetria. Obtemos estimativas tanto para a amplitude como para o período do ciclo limite e apresentamos uma aplicação de interesse em engenharia: sistemas de controle. / Abstract: We consider two main cases of bifurcation of non hyperbolic periodic orbits that give rise to limit cycles. Our study is done concerning piecewise linear systems with three zones in the more general formula that includes situations without symmetry. We obtain estimates for both the amplitude and the period of limit cycles and we present a applications of interest in engineering: control systems. / Mestre

We prove that a torus transverse to an Axiom A vector field that does not exhibit sinks, sources or null homotopic periodic orbits on a closed irreducible 3-manifold is incompressible. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Provaremos que um toro transversal a um campo de vetores Axioma A que não exibe poço, fonte e órbita periódica homotópica a um ponto sobre uma variedade tridimensional, fechada, irredutível é incompressível.