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Description
Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or computed tomography (CT). Treatment is informed by medical images and includes chemotherapy, radiation therapy, and surgical removal if the tumor is surgically accessible. Treatment seldom results in a significant increase in longevity, partly due to the lack of precise information regarding tumor size and location. This lack of information arises from the physical limitations of MR and CT imaging coupled with the diffusive nature of glioblastoma tumors. GBM tumor cells can migrate far beyond the visible boundaries of the tumor and will result in a recurring tumor if not killed or removed. Since medical images are the only readily available information about the tumor, we aim to improve mathematical models of tumor growth to better estimate the missing information. Particularly, we investigate the effect of random variation in tumor cell behavior (anisotropy) using stochastic parameterizations of an established proliferation-diffusion model of tumor growth. To evaluate the performance of our mathematical model, we use MR images from an animal model consisting of Murine GL261 tumors implanted in immunocompetent mice, which provides consistency in tumor initiation and location, immune response, genetic variation, and treatment. Compared to non-stochastic simulations, stochastic simulations showed improved volume accuracy when proliferation variability was high, but diffusion variability was found to only marginally affect tumor volume estimates. Neither proliferation nor diffusion variability significantly affected the spatial distribution accuracy of the simulations. While certain cases of stochastic parameterizations improved volume accuracy, they failed to significantly improve simulation accuracy overall. Both the non-stochastic and stochastic simulations failed to achieve over 75% spatial distribution accuracy, suggesting that the underlying structure of the model fails to capture one or more biological processes that affect tumor growth. Two biological features that are candidates for further investigation are angiogenesis and anisotropy resulting from differences between white and gray matter. Time-dependent proliferation and diffusion terms could be introduced to model angiogenesis, and diffusion weighed imaging (DTI) could be used to differentiate between white and gray matter, which might allow for improved estimates brain anisotropy.
ContributorsAnderies, Barrett James (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Stepien, Tracy (Committee member) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study is to look at classrooms and educators across six high achieving countries to identify and compare teaching strategies being used. In Finland, Hong Kong, Japan, New Zealand, Singapore, and Switzerland, twenty educators were interviewed and fourteen educators were observed teaching. Themes were first identified by comparing individual teacher responses within each country. These themes were then grouped together across countries and eight emerging patterns were identified. These strategies include students active involvement in the classroom, students given written feedback on assessments, students involvement in thoughtful discussion about mathematical concepts, students solving and explaining mathematics problems at the board, students exploring mathematical concepts either before or after being taught the material, students engagement in practical applications, students making connections between concepts, and students having confidence in their ability to understand mathematics. The strategies identified across these six high achieving countries can inform educators in their efforts of increasing student understanding of mathematical concepts and lead to an improvement in mathematics performance.
ContributorsAnglin, Julia Mae (Author) / Middleton, James (Thesis director) / Vicich, James (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-12
Description
In this paper, I analyze representations of nature in popular film, using the feminist / deconstructionist concept of a dualism to structure my critique. Using Val Plumwood’s analysis of the logical structure of dualism and the 5 ‘features of a dualism’ that she identifies, I critique 5 popular movies – Star Wars, Lord of the Rings, Brave, Grizzly Man, and Planet Earth – by locating within each of them one of the 5 features and explaining how the movie functions to reinforce the Nature/Culture dualism . By showing how the Nature/Culture dualism shapes and is shaped by popular cinema, I show how “Nature” is a social construct, created as part of this very dualism, and reified through popular culture. I conclude with the introduction of a number of ‘subversive’ pieces of visual art that undermine and actively deconstruct the Nature/Culture dualism and show to the viewer a more honest presentation of the non-human world.
ContributorsBarton, Christopher Joseph (Author) / Broglio, Ron (Thesis director) / Minteer, Ben (Committee member) / Barrett, The Honors College (Contributor) / School of Sustainability (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Geographical Sciences and Urban Planning (Contributor)
Created2015-05
Description
Despite the 40-year war on cancer, very limited progress has been made in developing a cure for the disease. This failure has prompted the reevaluation of the causes and development of cancer. One resulting model, coined the atavistic model of cancer, posits that cancer is a default phenotype of the cells of multicellular organisms which arises when the cell is subjected to an unusual amount of stress. Since this default phenotype is similar across cell types and even organisms, it seems it must be an evolutionarily ancestral phenotype. We take a phylostratigraphical approach, but systematically add species divergence time data to estimate gene ages numerically and use these ages to investigate the ages of genes involved in cancer. We find that ancient disease-recessive cancer genes are significantly enriched for DNA repair and SOS activity, which seems to imply that a core component of cancer development is not the regulation of growth, but the regulation of mutation. Verification of this finding could drastically improve cancer treatment and prevention.
ContributorsOrr, Adam James (Author) / Davies, Paul (Thesis director) / Bussey, Kimberly (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
Magnetic resonance imaging (MRI) data of metastatic brain cancer patients at the Barrow Neurological Institute sparked interest in the radiology department due to the possibility that tumor size distributions might mimic a power law or an exponential distribution. In order to consider the question regarding the growth trends of metastatic brain tumors, this thesis analyzes the volume measurements of the tumor sizes from the BNI data and attempts to explain such size distributions through mathematical models. More specifically, a basic stochastic cellular automaton model is used and has three-dimensional results that show similar size distributions of those of the BNI data. Results of the models are investigated using the likelihood ratio test suggesting that, when the tumor volumes are measured based on assuming tumor sphericity, the tumor size distributions significantly mimic the power law over an exponential distribution.
ContributorsFreed, Rebecca (Co-author) / Snopko, Morgan (Co-author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / WPC Graduate Programs (Contributor) / School of Accountancy (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
From 2007 to 2017, the state of California experienced two major droughts that required significant governmental action to decrease urban water demand. The purpose of this project is to isolate and explore the effects of these policy changes on water use during and after these droughts, and to see how these policies interact with hydroclimatic variability. As explanatory variables in multiple linear regression (MLR) models, water use policies were found to be significant at both the zip code and city levels. Policies that specifically target behavioral changes were significant mathematical drivers of water use in city-level models. Policy data was aggregated into a timeline and coded based on categories including user type, whether the policy was voluntary or mandatory, the targeted water use type, and whether the change in question concerns active or passive conservation. The analyzed policies include but are not limited to state drought declarations, regulatory municipal ordinances, and incentive programs for household appliances. Spatial averages of available hydroclimatic data have been computed and validated using inverse distance weighting methods. The data was aggregated at the zip code level to be comparable to the available water use data for use in MLR models. Factors already known to affect water use, such as temperature, precipitation, income, and water stress, were brought into the MLR models as explanatory variables. After controlling for these factors, the timeline policies were brought into the model as coded variables to test their effect on water demand during the years 2000-2017. Clearly identifying which policy traits are effective will inform future policymaking in cities aiming to conserve water. The findings suggest that drought-related policies impact per capita urban water use. The results of the city level MLR models indicate that implementation of mandatory policies that target water use behaviors effectively reduce water use. Temperature, income, unemployment, and the WaSSI were also observed to be mathematical drivers of water use. Interaction effects between policies and the WaSSI were statistically significant at both model scales.
ContributorsHjelmstad, Annika Margaret (Author) / Garcia, Margaret (Thesis director) / Larson, Kelli (Committee member) / Civil, Environmental and Sustainable Eng Program (Contributor, Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
As society's energy crisis continues to become more imminent many industries and niches are seeking a new, sustainable and renewable source of electricity production. Similar to solar, wind and tidal energy, kinetic energy has the potential to generate electricity as an extremely renewable source of energy generation. While stationary bicycles can generate small amounts of electricity, the idea behind this project was to expand energy generation into the more common weight lifting side of exercising. The method for solving this problem was to find the average amount of power generated per user on a Smith machine and determine how much power was available from an accompanying energy generator. The generator consists of three phases: a copper coil and magnet generator, a full wave bridge rectifying circuit and a rheostat. These three phases working together formed a fully functioning controllable generator. The resulting issue with the kinetic energy generator was that the system was too inefficient to serve as a viable system for electricity generation. The electrical production of the generator only saved about 2 cents per year based on current Arizona electricity rates. In the end it was determined that the project was not a sustainable energy generation system and did not warrant further experimentation.
ContributorsO'Halloran, Ryan James (Author) / Middleton, James (Thesis director) / Hinrichs, Richard (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / The Design School (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Glioblastoma Multiforme (GBM) is an aggressive and deadly form of brain cancer with a median survival time of about a year with treatment. Due to the aggressive nature of these tumors and the tendency of gliomas to follow white matter tracks in the brain, each tumor mass has a unique growth pattern. Consequently it is difficult for neurosurgeons to anticipate where the tumor will spread in the brain, making treatment planning difficult. Archival patient data including MRI scans depicting the progress of tumors have been helpful in developing a model to predict Glioblastoma proliferation, but limited scans per patient make the tumor growth rate difficult to determine. Furthermore, patient treatment between scan points can significantly compound the challenge of accurately predicting the tumor growth. A partnership with Barrow Neurological Institute has allowed murine studies to be conducted in order to closely observe tumor growth and potentially improve the current model to more closely resemble intermittent stages of GBM growth without treatment effects.
ContributorsSnyder, Lena Haley (Author) / Kostelich, Eric (Thesis director) / Frakes, David (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05
Description
Plastics continue to benefit society in innumerable ways, even though recent public focus on plastics has centered mostly on human health and environmental concerns, including their endocrine-disrupting properties and the long-term pollution they represent. The benefits of plastics are particularly apparent in medicine and public health. Plastics are versatile, cost-effective, require less energy to produce than alternative materials like metal or glass, and can be manufactured to have many different properties. Due to these characteristics, polymers are used in diverse health applications like disposable syringes and intravenous bags, sterile packaging for medical instruments as well as in joint replacements, tissue engineering, etc. However, not all current uses of plastics are prudent and sustainable, as illustrated by the widespread, unwanted human exposure to endocrine-disrupting bisphenol A (BPA) and di-(2-ethylhexyl) phthalate (DEHP), problems arising from the large quantities of plastic being disposed of, and depletion of non-renewable petroleum resources as a result of the ever-increasing mass production of plastic consumer articles. Using the health-care sector as example, this review concentrates on the benefits and downsides of plastics and identifies opportunities to change the composition and disposal practices of these invaluable polymers for a more sustainable future consumption. It highlights ongoing efforts to phase out DEHP and BPA in the health-care and food industry and discusses biodegradable options for plastic packaging, opportunities for reducing plastic medical waste, and recycling in medical facilities in the quest to reap a maximum of benefits from polymers without compromising human health or the environment in the process.
ContributorsNorth, Emily Jean (Co-author) / Halden, Rolf (Co-author, Thesis director) / Mikhail, Chester (Committee member) / Hurlbut, Ben (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Chemical Engineering Program (Contributor)
Created2013-05
Description
Over time, tumor treatment resistance inadvertently develops when androgen de-privation therapy (ADT) is applied to metastasized prostate cancer (PCa). To combat tumor resistance, while reducing the harsh side effects of hormone therapy, the clinician may opt to cyclically alternates the patient’s treatment on and off. This method,known as intermittent ADT, is an alternative to continuous ADT that improves the patient’s quality of life while testosterone levels recover between cycles. In this paper,we explore the response of intermittent ADT to metastasized prostate cancer by employing a previously clinical data validated mathematical model to new clinical data from patients undergoing Abiraterone therapy. This cell quota model, a system of ordinary differential equations constructed using Droop’s nutrient limiting theory, assumes the tumor comprises of castration-sensitive (CS) and castration-resistant (CR)cancer sub-populations. The two sub-populations rely on varying levels of intracellular androgen for growth, death and transformation. Due to the complexity of the model,we carry out sensitivity analyses to study the effect of certain parameters on their outputs, and to increase the identifiability of each patient’s unique parameter set. The model’s forecasting results show consistent accuracy for patients with sufficient data,which means the model could give useful information in practice, especially to decide whether an additional round of treatment would be effective.
ContributorsBennett, Justin Klark (Author) / Kuang, Yang (Thesis director) / Kostelich, Eric (Committee member) / Phan, Tin (Committee member) / School of Mathematical and Statistical Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05