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A description of numerical and analytical work pertaining to models that describe the growth and progression of glioblastoma multiforme (GBM), an aggressive form of primary brain cancer. Two reaction-diffusion models are used: the Fisher-Kolmogorov-Petrovsky-Piskunov equation and a 2-population model that divides the tumor into actively proliferating and quiescent (or necrotic) cells. The numerical portion of this work (chapter 2) focuses on simulating GBM expansion in patients undergoing treatment for recurrence of tumor following initial surgery. The models are simulated on 3-dimensional brain geometries derived from magnetic resonance imaging (MRI) scans provided by the Barrow Neurological Institute. The study consists of 17 clinical time intervals across 10 patients that have been followed in detail, each of whom shows significant progression of tumor over a period of 1 to 3 months on sequential follow up scans. A Taguchi sampling design is implemented to estimate the variability of the predicted tumors to using 144 different choices of model parameters. In 9 cases, model parameters can be identified such that the simulated tumor contains at least 40 percent of the volume of the observed tumor. In the analytical portion of the paper (chapters 3 and 4), a positively invariant region for our 2-population model is identified. Then, a rigorous derivation of the critical patch size associated with the model is performed. The critical patch (KISS) size is the minimum habitat size needed for a population to survive in a region. Habitats larger than the critical patch size allow a population to persist, while smaller habitats lead to extinction. The critical patch size of the 2-population model is consistent with that of the Fisher-Kolmogorov-Petrovsky-Piskunov equation, one of the first reaction-diffusion models proposed for GBM. The critical patch size may indicate that GBM tumors have a minimum size depending on the location in the brain. A theoretical relationship between the size of a GBM tumor at steady-state and its maximum cell density is also derived, which has potential applications for patient-specific parameter estimation based on magnetic resonance imaging data.
ContributorsHarris, Duane C. (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J. (Thesis advisor) / Preul, Mark C. (Committee member) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2023
Description
Cancer is a major health problem in the world today and is expected to become an even larger one in the future. Although cancer therapy has improved for many cancers in the last several decades, there is much room for further improvement. Mathematical modeling has the advantage of being able to test many theoretical therapies without having to perform clinical trials and experiments. Mathematical oncology will continue to be an important tool in the future regarding cancer therapies and management.
This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.
As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.
Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.
This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.
As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.
Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.
ContributorsRutter, Erica Marie (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J (Thesis advisor) / Frakes, David (Committee member) / Gardner, Carl (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Arizona State University (Publisher)
Created2016
Description
Obesity impairs skeletal muscle maintenance and regeneration, a condition that can progressively lead to muscle loss, but the mechanisms behind it are unknown. Muscle is primarily composed of multinucleated cells called myotubes which are derived by the fusion of mononucleated myocytes. A key mediator in this process is the cellular fusion protein syncytin-1. This led to the hypothesis that syncytin-1 could be decreased in the muscle of obese/insulin resistant individuals. In contrast, it was found that obese/insulin resistant subjects had higher syncytin-1 expression in the muscle compared to that of the lean subjects. Across the subjects, syncytin-1 correlated significantly with body mass index, percent body fat, blood glucose and HbA1c levels, insulin sensitivity and muscle protein fractional synthesis rate. The concentrations of specific plasma fatty acids, such as the saturated fatty acid (palmitate) and monounsaturated fatty acid (oleate) are known to be altered in obese/insulin resistant humans, and also to influence the protein synthesis in muscle. Therefore, it was evaluated that the effects of palmitate and oleate on syncytin-1 expression, as well as 4E-BP1 phosphorylation, a key mechanism regulating muscle protein synthesis in insulin stimulated C2C12 myotubes. The results showed that treatment with 20 nM insulin, 300 µM oleate, 300 µM oleate +20 nM insulin and 300 µM palmitate + 300 µM oleate elevated 4E-BP1 phosphorylation. At the same time, 20 nM insulin, 300 µM palmitate, 300 µM oleate + 20 nM insulin and 300 µM palmitate + 300 µM oleate elevated syncytin-1 expression. Insulin stimulated muscle syncytin-1 expression and 4E-BP1 phosphorylation, and this effect was comparable to that observed in the presence of oleate alone. However, the presence of palmitate + oleate diminished the stimulatory effect of insulin on muscle syncytin-1 expression and 4E-BP1 phosphorylation. These findings indicate oleate but not palmitate increased total 4E-BP1 phosphorylation regardless of insulin and the presence of palmitate in insulin mediated C2C12 cells. The presence of palmitate inhibited the upregulation of total 4EB-P1 phosphorylation. Palmitate but not oleate increased syncytin-1 expression in insulin mediated C2C12 myotubes. It is possible that chronic hyperinsulinemia in obesity and/or elevated levels of fatty acids such as palmitate in plasma could have contributed to syncytin-1 overexpression and decreased muscle protein fractional synthesis rate in obese/insulin resistant human muscle.
ContributorsRavichandran, Jayachandran (Author) / Katsanos, Christos (Thesis advisor) / Coletta, Dawn (Committee member) / Dickinson, Jared (Committee member) / Arizona State University (Publisher)
Created2017