Browsing by Subject "Mathematical modeling"

Now showing 1 - 6 of 6
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    Computational Modeling For The Vertical Bridgman Growth Of Babrcl:Eu Crystal
    (2020-03) Zhang, Chang
    In recent years, many new scintillator crystals for X-ray or gamma-ray detection have been discovered. They have great potential to be used in security devices or medical imaging devices. However, there are a couple challenges need to be overcome before these scintillator crystals can be commercialized. Firstly, the internal physical processes during the growth of these crystals are hard to be observed, making it difficult to control and optimize the processes. Secondly, cracking is a main issue that hinders the growth of high quality, large size scintillator crystals. Slow cooling, a conventional way to reduce thermo-elastic stress, fails to completely prevent cracking in scintillator crystals. In this thesis, we, together with our experimental collaborators, will demonstrate that computational modeling and advanced experimental tools can help researchers overcome these challenges and manufacture high quality, large size scintillator crystals. BaBrCl:Eu crystal and vertical Bridgman method are chosen as the candidate material and candidate crystal growth method in this thesis. Tremsin and coworkers developed a neutron imaging system to observe the vertical Bridgman growth process of scintillator crystals. Their measurements provided a direct observation of segregation and interface shape within a vertical gradient freeze system (VGF) that is large enough to exhibit the complex interplay of heat transfer, fluid flow, segregation, and phase change characteristic of an industrially relevant melt-growth process. We have applied continuum models to simulate a VGF growth process of BaBrCl:Eu crystal conducted in the neutron imaging system. Our models provide a rigorous framework in which to understand the mechanisms that are responsible for the complicated evolution of interface shape and dopant distribution in the growth experiment. We explain how a transition in the solid/liquid interface shape from concave to convex is driven by changes in radial heat transfer caused by furnace design. We also provide a mechanistic explanation of how dynamic growth conditions and changes of the flow structure in the melt result in complicated segregation patterns in this system. Onken and coworkers used neutron diffraction to measure the crystal structure evolution of BaBrCl:Eu at different temperature levels. Their results showed that the chemical stress induced by the lattice mismatch between Eu dopant and BaBrCl is responsible for the cracking of BaBrCl:Eu crystal during cooling process. We developed finite element models to analyze the chemical stress in BaBrCl:Eu crystal under different growth conditions based on the study of Onken and coworkers. To our knowledge, these are the first computations for chemical stress in bulk crystal growth process. Our results showed that the melt/crystal interface shape and the associated melt flows have a strong influence on the radial segregation outcome of Eu, which determines the chemical stress profile in the crystal. Counterintuitively, growing this crystal at slow growth rates can lead to high stress levels and tensile stress states near the cylindrical surface that promote cracking. However, a slightly faster growth rate can produce Eu radial concentration gradients that provide a protective, compressive force layer that would suppress cracking. Our results show that the chemical stress could be tailored by designing appropriate interface shapes and melt flows.
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    Modeling cancer evolution and inferring its parameters
    (2022-06) Gunnarsson, Einar
    Cancer is a group of diseases characterized by uncontrolled cell proliferation. The initiation of cancer usually involves a series of mutations in genes responsible for regulating the cell cycle. As the cancer-initiating cell expands into a tumor, the tumor cells continue to accumulate mutations, which induces substantial genetic heterogeneity within the tumor. In recent years, it has been increasingly recognized that epigenetic mechanisms, which are chemical changes to DNA or the chromatin structure which houses DNA, play an equally important role in tumor evolution. Due to their reversible and rapid nature, epigenetic mechanisms can enable cancer cells to switch dynamically between two or more phenotypic states, which commonly show differential responses to drug treatments. This dissertation consists of four projects which each involves using a mathematical model to study the evolutionary dynamics of cancer. The projects range from addressing the process of cancer initiation to the evolution of drug resistance, and they take both genetic and non-genetic perspectives. In Chapter 2, we study the dynamics of cancer initiation in multilayered tissue under a two-step mutational model of cancer. In Chapter 3, we study the accumulation of neutral mutations during tumor progression, which are mutations that do not affect the division rate of tumor cells. In Chapter 4, we study the role of phenotypic switching in the evolution of stable drug resistance. Finally, in Chapter 5, we develop a statistical framework for inferring the rates of cell division, cell death and phenotypic switching in cancer.
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    Modeling, Robust Control, and Experimental Validation of a Supercavitating Vehicle
    (2015-06) Escobar Sanabria, David
    This dissertation considers the mathematical modeling, control under uncertainty, and experimental validation of an underwater supercavitating vehicle. By traveling inside a gas cavity, a supercavitating vehicle reduces hydrodynamic drag, increases speed, and minimizes power consumption. The attainable speed and power efficiency make these vehicles attractive for undersea exploration, high-speed transportation, and defense. However, the benefits of traveling inside a cavity come with difficulties in controlling the vehicle dynamics. The main challenge is the nonlinear force that arises when the back-end of the vehicle pierces the cavity. This force, referred to as planing, leads to oscillatory motion and instability. Control technologies that are robust to planing and suited for practical implementation need to be developed. To enable these technologies, a low-order vehicle model that accounts for inaccuracy in the characterization of planing is required. Additionally, an experimental method to evaluate possible pitfalls in the models and controllers is necessary before undersea testing. The major contribution of this dissertation is a unified framework for mathematical modeling, robust control synthesis, and experimental validation of a supercavitating vehicle. First, we introduce affordable experimental methods for mathematical modeling and controller testing under planing and realistic flow conditions. Then, using experimental observations and physical principles, we create a low-order nonlinear model of the longitudinal vehicle motion. This model quantifies the planing uncertainty and is suitable for robust controller synthesis. Next, based on the vehicle model, we develop automated tools for synthesizing controllers that deliver a certificate of performance in the face of nonlinear and uncertain planing forces. We demonstrate theoretically and experimentally that the proposed controllers ensure higher performance when the uncertain planing dynamics are considered. Finally, we discuss future directions in supercavitating vehicle control.
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    Modulation of BMP signaling during Dorsal-Ventral patterning in Drosophila melanogaster
    (2014-02) Brakken-Thal, Christina
    Bone Morphogenic Protein (BMP) signaling is a conserved pathway used for development and homeostasis. In the model system Drosophila melanogaster patterning of the dorsal surface is controlled by Decapentapolegic (DPP), a BMP protein that robustly stimulates the BMP signaling pathway in a narrow domain of cells on the dorsal surface of the embryo. The levels of Dpp are estimated to be between 10-100 molecules / nucleus, which would predict a significant level of noise in Dpp signaling. However this is not observed, so there must be mechanisms that dampen noise in signaling pathways. I used molecular biology, genetics, and mathematical modeling to identify possible mechanisms for feedback control of BMP signaling and to elucidate mechanisms to dampen stochastic fluctuations in signaling molecules. I have identified a new novel allele of nejire with a stop codon in the 12th exon. This mutation truncates part of the glutamine rich domain at the end of the protein. This new allele has a highly variable phenotype with all embryos showing varying degrees of loss of Dpp signaling in the pre-cephalic furrow embryos, and half showing recovery just before and during gastrulation. I also studied the phenotype of Crossveinless-2 (Cv-2) during dorsal surface patterning. I found that cv-2 is a Dpp response gene that is a negative inhibitor of Dpp signaling during dorsal surface patterning. Cv-2 null embryos have a 20% wider area of Dpp signaling on the dorsal surface, and this change leads to a larger amnioserosa later in development. Interestingly loss of Cv-2 leads to a slight increase in noise in the width of pMad, the intracellular signaling of Dpp receptor activation. I followed up on this finding with a 3D stochastic model of Dpp for a single nuclear compartment which suggests that competition for BMP from the receptor could increase noise in signaling. In addition, the stochastic model suggests that endocytosis of Dpp bound receptors and nuclear accumulation of transcription factors may be mechanisms to decrease noise and increase robustness of Dpp signaling.
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    Noninvasive imaging of three-dimensional ventricular electrical activity
    (2012-08) Han, Chengzong
    Noninvasive imaging of cardiac electrical activity is of great importance and can facilitate basic cardiovascular research and clinical diagnosis and management of various malignant cardiac arrhythmias. This dissertation research is aimed to investigate a novel physical-model-based 3-dimensional cardiac electrical imaging (3DCEI) approach. The 3DCEI approach is developed by mathematically combining high-density body surface electrocardiograms (ECGs) with the anatomical information. Computer simulation study and animal experiments were conducted to rigorously evaluate the performance of 3DCEI. The simulation results demonstrate that 3DCEI can localize the origin of activation and image the activation sequence throughout the three-dimensional ventricular myocardium. The performance of 3DCEI was also experimentally and rigorously evaluated through well-controlled animal validation studies in both the small animal model (rabbit) and large animal model (canine), with the aid of simultaneous intramural recordings from intra-cardiac mapping using plunge-needle electrodes inserted in the ventricular myocardium. The clinical relevance of 3DCEI was further demonstrated by investigating 3DCEI in cardiac arrhythmias from animal models with experimentally-induced cardiovascular diseases. The consistent agreement between the non-invasively imaged activation sequences and its directly measured counterparts in both the rabbit heart and canine heart implies that 3DCEI is feasible in reconstructing the spatial patterns of ventricular activation sequences, localizing the arrhythmogenic foci, and imaging dynamically changing arrhythmia on a beat-to-beat basis. The promising results presented in this dissertation study suggest that this cardiac electrical imaging approach may provide an important alternative for non-invasively imaging cardiac electrical activity throughout ventricular myocardium and may potentially become an important tool to facilitate clinical diagnosis and treatments of malignant ventricular arrhythmias.
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    Quantitative analysis of gene regulatory networks: from single cells to cell communities
    (2013-06) Biliouris, Konstantinos
    Although the great advances in experimental biology have fueled our ability to explore the behavior of natural and synthetic biological systems, key challenges still exist. A major shortcoming is that, unlike other research areas, biological systems are significantly non-linear with unknown molecular components. In addition, the inherent stochasticity of biological systems forces identical cells to behave dissimilarly even when exposed to the same environmental conditions. These challenges limit in-depth understanding of biological systems using solely experimental techniques. The current research is focused on the joint frontier of mathematical modeling and experimental work in biology. Guided by experimental observations, quantitative modeling analysis of two natural and two synthetic biological systems was carried out. These systems are all gene regulatory networks and range from the single cell level to the population level. The objective of this research is three-fold: 1) The development of detailed mathematical models that capture the relevant biomolecular interactions of the systems of interest. Experimental data are used to inform and validate these models. 2) The use of the models as a means for understanding the complexity underlying biological systems. This allows for explaining the behavior of biological systems by quantifying the molecular interactions involved. 3) The simulation of the behavior of biological systems and the associated molecular parts. This helps to quickly and inexpensively predict the behavior of these systems under various conditions and motivates new sets of experiments.