Mathematical modeling of cancer is of significant interest due to its potential to aid in our understanding of the disease, including investigation into which factors are most important in the progression of cancer. With this knowledge and model different paths of treatment can be examined; (e.g. simulation of different treatment techniques followed by the more costly venture of testing on animal models). Significant work has been done in the field of cancer modeling with models ranging from the more broad systems, avascular tumor models, to smaller systems, models of angiogenic pathways. A preliminary model of a vascularized tumor has been developed; the model is based on fundamental principles of mechanics and will serve as the framework for a more detailed model in the future. The current model is a system of nonlinear partial differential equations (PDEs) separated into two basic sub-models, avascular and angiogenesis. The avascular sub-model is primarily based of Fickian diffusion of nutrients into the tumor. While the angiogenesis sub-model is based on the diffusion and chemotaxis of active sprout tips into the tumor. These two portions of the models allow the effects of microvessels on nutrient concentration within the tumor, as well as the effect of the tumor in driving angiogenesis, to be examined. The results of the model have been compared to experimental measurements of tumor growth over time in animal models, and have been found to be in good agreement with a correlation coefficient of (r2=0.98). / Master of Science

CD4+ T cells are a group of lymphocytes that play critical roles in the immune system. By releasing cytokines, CD4+ T cells regulate other immune cells for maximizing the efficiency of the system. Naive CD4+ T cells are activated and become mature upon engagement with antigens, and the mature CD4+ T cells have several subsets, which play diverse regulatory functions. For the past two decades, our understanding of CD4+ T cells has been advanced through the studies on the differentiation process and the lineage specification of various subsets of these cells. Although in most experimental studies of CD4+ T cells, researchers focused on how transcription factors and signaling molecules influence the differentiation of a particular subset of these cells, many evidence have shown that the differentiation of CD4+ T cells can be heterogeneous in terms of the phenotypes of the cells involved. This dissertation describes a framework that uses mathematical models of the dynamics of the signaling pathways to explain heterogeneous differentiation. We show that the mutual inhibitions among the master regulators govern the formation of multi-stability behavior, which in turn gives rise to heterogeneous differentiation. The framework can be applied to systems with two or more master regulators, and models based on the framework can make specific predictions about heterogeneous differentiations. In addition, this dissertation describes an experimental study on CD4+ T cell differentiation. Being part of the adaptive immune system, the differentiation of CD4+ T cells was previously known to be induced by the signals from the innate immune cells. However, the expression of Toll-like receptor in CD4+ T cells suggests that microbial products can also influence the differentiation directly. Using an in vitro cell differentiation approach, we show that the differentiation and proliferation of CD4+ T cells can be influenced by lipopolysaccharide under the condition that would favor the differentiation of induced regulatory T cells. These theoretical and experimental studies give novel insights on how CD4+ T cells differentiate in response to pathogenic challenges, and help to gain deeper understanding of regulatory mechanisms of the complex immune system. / Ph. D.

This study creates and analyzes a model of the Hypothalamus-Pituitary-Adrenal axis to better understand cortisol rhythmicity perpetuated by circadian inputs, system dynamics and feedback inherent within the system. Differential equations are created to model human physiology with cortisol and precursor hormone outputs fit to physiologic data. The model is created with an input of circadian cues from the hypothalamus which are designed to create a more realistic stimulation of the cortisol cascade over predecessors. The study also incorporates additional signaling pathways unique to this model. The project explores the properties of the model under mathematical analysis; then, the simulation of known medical pathologies is used to analyze the model's predictive ability. It is found that incorporating the additional signaling pathway of Arginine Vasopressin increases the model's predictive capability in certain pathological conditions over predecessor models. Additionally, the origination of ultradian rhythm is explored through simulation and two possible explanations are found. First, pulsatile release of Adrenocorticotropic Hormone combined with negative feedback into the system from glucocorticoid receptors elicits the observed ultradian oscillations in humans. Additionally, simulations of increased hypothalamic monitoring and control of cortisol concentrations create a natural oscillation within the desired period. Results from numerical perturbation simulations and dynamic sensitivity analysis are employed to offer justification for known pathological conditions developing from circadian dysregulation. / Master of Science / This study aims to better understand the body's natural cortisol rhythm by creating a mathematical model of the Hypothalamus-Pituitary-Adrenal axis. The model uses differential equations to simulate human physiology and includes circadian cues from the suprachiasmatic nucleus to create a more accurate representation of how cortisol is released in the body. The study also incorporates additional signaling pathways and interactions unique to this model. By analyzing the model and simulating known medical conditions, it was found found that incorporating these additional signaling pathways improved the model's predictive ability in certain situations. Then, numerical simulations were used to investigate how circadian dysregulation can lead to pathological conditions.The study also explored the origin of ultradian rhythm, or short-term fluctuations in cortisol levels, and found two possible explanations. One explanation is the pulsatile release of Adrenocorticotropic Hormone combined with negative feedback from glucocorticoid receptors. Another explanation is increased hypothalamic control of cortisol concentrations. Overall, this study provides insights into the complex dynamics of the Hypothalamus-Pituitary-Adrenal axis and the origination of pathology in the system.

A hard chromium electroplating process is normally used for preventing mechanical and electrical parts such as roller, piston and mold from the harmful environments and giving the good physical properties on the surface such as increased wear resistance, increased hardness, low frictional coefficient as well as good aesthetic look on the surface of workpieces. The problem that often found in this process is the deflected workpieces after plating process due to the low plating performance during a plating period. These deflected workpieces are needed to replating it again. However, the replating method causes a large amount of resource consumptions and increases the production time. To handle this problem, the plating solution temperature is needed to maintain the plating solution temperature at a set point about 50 °C in order to improve the plating performance during the plating period and decrease the occurrence of the deflected workpieces. In this work, the mathematical models are developed to explain the dynamic behavior of the plating solution temperature during the plating time and validated with the real data from a plant. The conventional (PID) controller is applied to this process for the purpose of keeping the plating solution temperature at the set point throughout the plating time. The result demonstrates that the developed mathematical models can be used to explain the dynamic behavior of the plating solution temperature because it gives the good simulation of the plating solution temperature with a slightly different from the real data. Furthermore, the PID controller shows the high control performance for maintaining the plating solution temperature at the set point throughout the plating period with small overshoot at the beginning of every batch.

The last five years have shown us the profound impact that SARS-CoV-2 pandemic has had on human kind and made us aware of the dangers that emerging pathogens can present. The goal of this dissertation is to use mathematical models in connection with data to uncover mechanistic interactions governing viral infections. To acquire a holistic understanding of the impact of viral infections, it is necessary to develop mathematical techniques and models that bridge knowledge on multiple biological scales. This dissertation explores the relationship between within-host virus dynamics, the environment and the between-host viral transmission. We will validate the models against data from SARS-CoV-2 infections, and data from infections with an emerging pathogen, the Usutu virus. Our models of SARS-CoV-2 infection looked at the relationship between infectious virus and viral RNA in the body and in the environment. Using golden hamster data and within-host mathematical models, we determined that infectious virus shedding early in infection correlates with transmission events, shedding of infectious virus diminishes late in the infection, and high viral RNA levels late in the infection are a poor indicator of transmission. We further showed that viral infectiousness increases in a density dependent manner with viral RNA and that their relative ratio is time-dependent. Such information is useful for designing interventions. Our models of Usutu virus infection looked at differences between different virus strains during bird infections. Within-host models applied to data showed heterogeneity in viral strain dynamics, and correlated high basic reproductive number with short infected cell lifespan (indicative of immune responses) and correlated low basic reproductive number with low viral peaks and longer lasting viremia (due to lower infection rates and high infected cell lifespan). We expanded the models to investigate multiscale dynamics connecting within-host scale, bird-to-vector transmission scale, and vector-borne epidemiological scale. One important direction of this dissertation is the investigation of uncertainty in parameter estimation and overall model identifiability. We conducted identifiability studies (using several theoretical tools) in the multiscale models of Usutu virus infection and in several within-host influenza models. Model identifiability is critical to the reproducibility of modeling results in any biological systems. In this dissertation, we will show how insights from such analyses inform both modeling practices and experimental design. / Doctor of Philosophy / The last five years have shown us the profound impact that SARS-CoV-2 pandemic has had on human kind and made us aware of the dangers that emerging pathogens can present. Within-host mathematical models are tools that can be used to study the dynamics of virus infections. These models help us gain an understanding of biological quantities of interest, relationships between biological processes in a quantitative and qualitative ways, and disease outcome. However, to acquire a holistic understanding of the impact of viral infections, it is necessary to develop mathematical tools and models that bridge knowledge on multiple biological scales. This dissertation explores the relationship between virus infection characteristics over time in a single host and larger biological scales including virus' release into the environment and spread of virus between hosts. Biological and public health insights about SARS-CoV-2 and Usutu virus were gained through these modeling efforts.

Orientador: Laercio Luis Vendite / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Ciencia da Computação / Made available in DSpace on 2018-08-09T23:40:27Z (GMT). No. of bitstreams: 1 Alonso_AnaCamilaRodrigues_M.pdf: 1099108 bytes, checksum: f7bd5d3bc8e683d7332a70d7a75c8405 (MD5) Previous issue date: 2007 / Resumo: O câncer de ovário é a neoplasia mais letal do aparelho genital feminino. É necessário fazer um estabelecimento precoce de seu diagnóstico e uma correta abordagem terapêutica para interferir na sua história natural. Com a intenção de melhorar a metodologia para distinguir benignidade de malignidade dos tumores de ovário foram estudadas associações de métodos. Jacobs et al. foram os primeiros autores a idealizar um índice de risco de malignidade (IRM) para tumores de ovário, incorporando estado menopausal, achados ultra-sonográficos e o nível sérico do CA 125. Neste trabalho, um modelo matemático é elaborado para auxiliar no diagnóstico diferencial de benignidade e malignidade dos tumores ovarianos clinicamente restritos aos ovários. A ferramenta utilizada para desenvolver o modelo é a teoria dos conjuntos, por sua capacidade em lidar com incertezas. Inicialmente, as variáveis de entrada - Estado Menopausal, Achados ultrasonográficos e Nível de CA 125 - e a variável de saída do sistema - Tipo de Tumor ¿ foram consideradas como variáveis lingüísticas e seus valores como conjuntos fuzzy. O modelo construído é mais abrangente que o índice de risco de malignidade proposto por Torres et al., pois no modelo temos que o estado menopausal e os achados ultra-sonográficos são considerados como variáveis contínuas. A saída dos sistema, também contínua, propicia uma transição gradual entre tumor benigno e maligno, o que é mais coerente com a realidade / Abstract: The ovarian cancer is the most lethal neoplasy of the femine genital system. It is necessary to do a precocious establishment of its diagnosis and a correct therapeutical approach to intervene in the natural history. With the intention to improve the methodology to distinguish benignancy from malignancy of the ovarian tumors methods¿s associations had been studied. Jacobs et al. were the first authors to idealize the risk of malignance index for ovarian tumors, incorporating menopausal status, ultrasound findings and the serum level CA 125. In this work, a mathematical model is elaborated to auxiliary in the diferential diagnosis of the benignancy clinically restricted to the ovaries. The tool used to developed the model is the fuzzy sets theory for capacity in dealing with uncertainties. Inicially, input variables - menopausal status, ultrasound findings and CA 125 level ¿ and the system output variables - tumor¿s type - they had been considered with linguistics variables and its values with fuzzy sets. The constructed model is more comprehensive than risk of malignancy index propose to Torres et al., therefore the menopausal status and the ultrasound findings are considered as a continuous variable. The system output, also continuous, give a gradual transition between benign and malignant tumor, what is more coherent with the reality / Mestrado / Biomatematica / Mestre em Matemática Aplicada

Thesis (M.Statistics) North-West University, Mafikeng Campus, 2010

Bootstrap and Markov chain Monte Carlo methods have received much attention in recent years. We study computer intensive methods that can be used in complex situations where it is not possible to express the likelihood estimates or the posterior analytically. The work is inspired by a set of car crash data from real traffic. We formulate and develop a model for car crash data that aims to estimate and compare the relative collision safety among different car models. This model works sufficiently well, although complications arise due to a growing vector of incidental parameters. The bootstrap is shown to be a useful tool for studying uncertainties of the estimates of the structural parameters. This model is further extended to include driver characteristics. In a Poisson model with similar, but simpler structure, estimates of the structural parameter in the presence of incidental parameters are studied. The profile likelihood, bootstrap and the delta method are compared for deterministic and random incidental parameters. The same asymptotic properties, up to first order, are seen for deterministic as well as random incidental parameters. The search for suitable methods that work in complex model structures leads us to consider Markov chain Monte Carlo (MCMC) methods. In the area of MCMC, we consider particularly the question of how and when to claim convergence of the MCMC run in situations where it is only possible to analyse the output values of the run and also how to compare different MCMC modellings. In Metropolis-Hastings algorithm, different proposal functions lead to different realisations. We develop a new convergence diagnostic, based on the Kullback-Leibler distance, which is shown to be particularly useful when comparing different runs. Comparisons with established methods turn out favourably for the KL. In both models, a Bayesian analysis is made where the posterior distribution is obtained by MCMC methods. The credible intervals are compared to the corresponding confidence intervals from the bootstrap analysis and are shown to give the same qualitative conclusions.

The purpose of this study is to develop mathematical models to explore the mixing and its related phenomena in converter bath. Specifically, first, a mathematical model of a physical model converter, which was scaled down to 1/6th of a 30 t vessel, was developed in this study. A number of parameters were studied and their effects on the mixing time were recorded in a top blown converter. Second, a mathematical model for a combined top-bottom blown was built to investigate the optimization process. Then, a side tuyere was introduced in the combined top-bottom blown converter and its effects on the mixing and wall shear stress were studied. Moreover, based on the above results, the kinetic energy transfer phenomena in a real converter were investigated by applying the mathematical models. A simplified model, in which the calculation region was reduced to save calculation compared to simulations of the whole region of the converter, was used in the mathematical simulation. In addition, this method was also used in the simulation of real converters. This approach makes it possible to simulate the Laval nozzle flow jet and the cavity separately when using different turbulence models. In the top blown converter model, a comparison between the physical model and the mathematical model showed a good relative difference of 2.5% and 6.1% for the cavity depth and radius, respectively. In addition, the predicted mixing time showed a good relative difference of 2.8% in comparison to the experimental data. In an optimization of a combined top-bottom blown converter, a new bottom tuyere scheme with an asymmetrical configuration was found to be one of the best cases with respect to a decreased mixing time in the bath. An industrial investigation showed that the application effects of the new tuyere scheme yield a better stirring condition in the bath compared to the original case. Furthermore, the results indicated that the mixing time for a combined top-bottom-side blown converter was decreased profoundly compared to a conventional combined top-bottom blown converter. It was found that the side wall shear stress is increased by introducing side blowing, especially in the region near the side blowing plume. For a 100 t converter in real, the fundamental aspects of kinetic energy transfer from a top and bottom gas to the bath were explored. The analyses revealed that the energy transfer is less efficient when the top lance height is lowered or the flowrate is increased in the top blowing operations. However, an inverse trend was found. Namely, that the kinetic energy transfer is increased when the bottom flowrate is increased in the current bottom blowing operations. In addition, the slag on top of the bath is found to dissipate 6.6%, 9.4% and 11.2% for the slag masses 5, 9 and 15 t compared to the case without slag on top of the surface of the bath, respectively. / <p>QC 20151015</p>

A steady-state mathematical model for the stripping section of an industrial EPDM rubber production process was developed for a three-tank process, and two four-tank processes. The experiments that were conducted to determine model parameters such as equivalent radius for EPDM particles, as well as solubility and diffusivity parameters for hexane and ENB in EPDM polymer are described. A single-particle multiple-tank model was developed first, and a process model that accounts for the residence-time distribution of crumb particles was developed second. Plant data as well as input data from an existing steady-state model was used to determine estimates for the tuning parameters used in the multiple-particle, multiple-tank model. Using plant data to assess the model’s predictive accuracy, the resulting three-tank and four-tank process B models provide accurate model predictions with a typical error of 0.35 parts per hundred resin (phr) and 0.12 phr. The four-tank process A model provides less-accurate model predictions for residual crumb concentrations in the second tank and has an overall typical error of 1.05 phr. Additional plant data from the three- and four-tank processes would increase the estimability of the parameter values for parameter ranking and estimations steps and thus, yield increased model predictive accuracy. / Thesis (Master, Chemical Engineering) -- Queen's University, 2012-10-23 21:06:05.509