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- All Subjects: Glioblastoma Multiforme
- Creators: Kostelich, Eric
- Creators: Johnson, Kory Alfred
- Member of: Theses and Dissertations
Description
I investigate two models interacting agent systems: the first is motivated by the flocking and swarming behaviors in biological systems, while the second models opinion formation in social networks. In each setting, I define natural notions of convergence (to a ``flock" and to a ``consensus'', respectively), and study the convergence properties of each in the limit as $t \rightarrow \infty$. Specifically, I provide sufficient conditions for the convergence of both of the models, and conduct numerical experiments to study the resulting solutions.
ContributorsTheisen, Ryan (Author) / Motsch, Sebastien (Thesis advisor) / Lanchier, Nicholas (Committee member) / Kostelich, Eric (Committee member) / Arizona State University (Publisher)
Created2018
Description
In this research we consider stochastic models of Glioblastoma Multiforme brain tumors. We first look at a model by K. Swanson et al., which describes the dynamics as random diffusion plus deterministic logistic growth. We introduce a stochastic component in the logistic growth in the form of a random growth rate defined by a Poisson process. We show that this stochastic logistic growth model leads to a more accurate evaluation of the tumor growth compared its deterministic counterpart. We also discuss future plans to incorporate individual patient geometry, extend the model to three dimensions and to incorporate effects of different treatments into our model, in collaboration with a local hospital.
ContributorsManning, Michael Clare (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Letters and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2013-12
Description
Much research has been devoted to identifying trends in either convergence upon a neoliberal model or divergence among welfare states in connection to globalization, but most research has focused on advanced industrialized countries. This has limited our understanding of the current state of convergence or divergence, especially among welfare states in developing regions. To address this research gap and contribute to the broader convergence vs. divergence debate, this research explores welfare state variation found within Latin America, in terms of the health policy domain, through the use of cross-national data from 18 countries collected between the period of 1995 to 2010 and the application of a series of descriptive and regression analysis techniques. Analyses revealed divergence within Latin America in the form of three distinct welfare states, and that among these welfare states income inequality, trust in traditional public institutions, and democratization, are significantly related to welfare state type and health performance.
ContributorsJohnson, Kory Alfred (Author) / Martin, Nathan (Thesis director) / Gonzales, Vanna (Committee member) / Barrett, The Honors College (Contributor) / School of Social Transformation (Contributor) / School of Politics and Global Studies (Contributor)
Created2014-05
Description
Glioblastoma multiforme (GBMs) is the most prevalent brain tumor type and causes approximately 40% of all non-metastic primary tumors in adult patients [1]. GBMs are malignant, grade-4 brain tumors, the most aggressive classication as established by the World Health Organization and are marked by their low survival rate; the median survival time is only twelve months from initial diagnosis: Patients who live more than three years are considered long-term survivors [2]. GBMs are highly invasive and their diffusive growth pattern makes it impossible to remove the tumors by surgery alone [3]. The purpose of this paper is to use individual patient data to parameterize a model of GBMs that allows for data on tumor growth and development to be captured on a clinically relevant time scale. Such an endeavor is the rst step to a clinically applicable predictions of GBMs. Previous research has yielded models that adequately represent the development of GBMs, but they have not attempted to follow specic patient cases through the entire tumor process. Using the model utilized by Kostelich et al. [4], I will attempt to redress this deciency. In doing so, I will improve upon a family of models that can be used to approximate the time of development and/or structure evolution in GBMs. The eventual goal is to incorporate Magnetic Resonance Imaging (MRI) data into a parameterized model of GBMs in such a way that it can be used clinically to predict tumor growth and behavior. Furthermore, I hope to come to a denitive conclusion as to the accuracy of the Koteslich et al. model throughout the development of GBMs tumors.
ContributorsManning, Miles (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Preul, Mark (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Glioblastoma Multiforme is a prevalent and aggressive brain tumor. It has an average 5-year survival rate of 6% and average survival time of 14 months. Using patient-specific MRI data from the Barrow Neurological Institute, this thesis investigates the impact of parameter manipulation on reaction-diffusion models for predicting and simulating glioblastoma growth. The study aims to explore key factors influencing tumor morphology and to contribute to enhancing prediction techniques for treatment.
ContributorsShayegan, Tara (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Barrett, The Honors College (Contributor) / School of Human Evolution & Social Change (Contributor)
Created2024-05