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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
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
Development of the cerebral cortex requires the complex integration of extracellular stimuli to affect changes in gene expression. Trophic stimulation activates specialized intracellular signaling cascades to instruct processes necessary for the elaborate cellular diversity, architecture, and function of the cortex. The canonical RAS/RAF/MEK/ERK (ERK/MAPK) cascade is a ubiquitously expressed kinase pathway that regulates crucial aspects of neurodevelopment. Mutations in the ERK/MAPK pathway or its regulators give rise to neurodevelopmental syndromes termed the “RASopathies.” RASopathy individuals present with neurological symptoms that include intellectual disability, ADHD, and seizures. The precise cellular mechanisms that drive neurological impairments in RASopathy individuals remain unclear. In this thesis, I aimed to 1) address how RASopathy mutations affect neurodevelopment, 2) elucidate fundamental requirements of ERK/MAPK in GABAergic circuits, and 3) determine how aberrant ERK/MAPK signaling disrupts GABAergic development.
Here, I show that a Noonan Syndrome-linked gain-of-function mutation Raf1L613V, drives modest changes in astrocyte and oligodendrocyte progenitor cell (OPC) density in the mouse cortex and hippocampus. Raf1L613V mutant mice exhibited enhanced performance in hippocampal-dependent spatial reference and working memory and amygdala-dependent fear learning tasks. However, we observed normal perineuronal net (PNN) accumulation around mutant parvalbumin-expressing (PV) interneurons. Though PV-interneurons were minimally affected by the Raf1L613V mutation, other RASopathy mutations converge on aberrant GABAergic development as a mediator of neurological dysfunction.
I therefore hypothesized interneuron expression of the constitutively active Mek1S217/221E (caMek1) mutation would be sufficient to perturb GABAergic circuit development. Interestingly, the caMek1 mutation selectively disrupted crucial PV-interneuron developmental processes. During embryogenesis, I detected expression of cleaved-caspase 3 (CC3) in the medial ganglionic eminence (MGE). Interestingly, adult mutant cortices displayed a selective 50% reduction in PV-expressing interneurons, but not other interneuron subtypes. PV-interneuron loss was associated with seizure-like activity in mutants and coincided with reduced perisomatic synapses. Mature mutant PV-interneurons exhibited somal hypertrophy and a substantial increase in PNN accumulation. Aberrant GABAergic development culminated in reduced behavioral response inhibition, a process linked to ADHD-like behaviors. Collectively, these data provide insight into the mechanistic underpinnings of RASopathy neuropathology and suggest that modulation of GABAergic circuits may be an effective therapeutic option for RASopathy individuals.
Here, I show that a Noonan Syndrome-linked gain-of-function mutation Raf1L613V, drives modest changes in astrocyte and oligodendrocyte progenitor cell (OPC) density in the mouse cortex and hippocampus. Raf1L613V mutant mice exhibited enhanced performance in hippocampal-dependent spatial reference and working memory and amygdala-dependent fear learning tasks. However, we observed normal perineuronal net (PNN) accumulation around mutant parvalbumin-expressing (PV) interneurons. Though PV-interneurons were minimally affected by the Raf1L613V mutation, other RASopathy mutations converge on aberrant GABAergic development as a mediator of neurological dysfunction.
I therefore hypothesized interneuron expression of the constitutively active Mek1S217/221E (caMek1) mutation would be sufficient to perturb GABAergic circuit development. Interestingly, the caMek1 mutation selectively disrupted crucial PV-interneuron developmental processes. During embryogenesis, I detected expression of cleaved-caspase 3 (CC3) in the medial ganglionic eminence (MGE). Interestingly, adult mutant cortices displayed a selective 50% reduction in PV-expressing interneurons, but not other interneuron subtypes. PV-interneuron loss was associated with seizure-like activity in mutants and coincided with reduced perisomatic synapses. Mature mutant PV-interneurons exhibited somal hypertrophy and a substantial increase in PNN accumulation. Aberrant GABAergic development culminated in reduced behavioral response inhibition, a process linked to ADHD-like behaviors. Collectively, these data provide insight into the mechanistic underpinnings of RASopathy neuropathology and suggest that modulation of GABAergic circuits may be an effective therapeutic option for RASopathy individuals.
ContributorsHolter, Michael (Author) / Newbern, Jason (Thesis advisor) / Anderson, Trent (Committee member) / Mehta, Shwetal (Committee member) / Neisewander, Janet (Committee member) / Arizona State University (Publisher)
Created2019