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- All Subjects: Mathematical Modeling
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- Creators: School of Mathematical and Statistical Sciences
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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
Solid oxide fuel cells have become a promising candidate in the development of high-density clean energy sources for the rapidly increasing demands in energy and global sustainability. In order to understand more about solid oxide fuel cells, the important step is to understand how to model heterogeneous materials. Heterogeneous materials are abundant in nature and also created in various processes. The diverse properties exhibited by these materials result from their complex microstructures, which also make it hard to model the material. Microstructure modeling and reconstruction on a meso-scale level is needed in order to produce heterogeneous models without having to shave and image every slice of the physical material, which is a destructive and irreversible process. Yeong and Torquato [1] introduced a stochastic optimization technique that enables the generation of a model of the material with the use of correlation functions. Spatial correlation functions of each of the various phases within the heterogeneous structure are collected from a two-dimensional micrograph representing a slice of a solid oxide fuel cell through computational means. The assumption is that two-dimensional images contain key structural information representative of the associated full three-dimensional microstructure. The collected spatial correlation functions, a combination of one-point and two-point correlation functions are then outputted and are representative of the material. In the reconstruction process, the characteristic two-point correlation functions is then inputted through a series of computational modeling codes and software to generate a three-dimensional visual model that is statistically similar to that of the original two-dimensional micrograph. Furthermore, parameters of temperature cooling stages and number of pixel exchanges per temperature stage are utilized and altered accordingly to observe which parameters has a higher impact on the reconstruction results. Stochastic optimization techniques to produce three-dimensional visual models from two-dimensional micrographs are therefore a statistically reliable method to understanding heterogeneous materials.
ContributorsPhan, Richard Dylan (Author) / Jiao, Yang (Thesis director) / Ren, Yi (Committee member) / Chemical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The recovery of biofuels permits renewable alternatives to present day fossil fuels that cause devastating effects on the planet. Pervaporation is a separation process that shows promise for the separation of ethanol from biologically fermentation broths. The performance of thin film composite membranes of polydimethylsiloxane (PDMS) and zeolite imidazolate frameworks (ZIF-71) dip coated onto a porous substrate are analyzed. Pervaporation performance factors of flux, separation factor and selectivity are measured for varying ZIF-71 loadings of pure PDMS, 5 wt%, 12.5 wt% and 25 wt% at 60 oC with a 2 wt% ethanol/water feed. The increase in ZIF-71 loadings increased the performance of PDMS to produce higher flux, higher separation factor and high selectivity than pure polymeric films.
ContributorsLau, Ching Yan (Author) / Lind, Mary Laura (Thesis director) / Durgun, Pinar Cay (Committee member) / Lively, Ryan (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / Chemical Engineering Program (Contributor)
Created2014-05
Description
Currently, approximately 40% of the world’s electricity is generated from coal and coal power plants are one of the major sources of greenhouse gases accounting for a third of all CO2 emissions. The Integrated Gasification Combined Cycle (IGCC) has been shown to provide an increase in plant efficiency compared to traditional coal-based power generation processes resulting in a reduction of greenhouse gas emissions. The goal of this project was to analyze the performance of a new SNDC ceramic-carbonate dual-phase membrane for CO2 separation. The chemical formula for the SNDC-carbonate membrane was Sm0.075Nd0.075Ce0.85O1.925. This project also focused on the use of this membrane for pre-combustion CO2 capture coupled with a water gas shift (WGS) reaction for a 1000 MW power plant. The addition of this membrane to the traditional IGCC process provides a purer H2 stream for combustion in the gas turbine and results in lower operating costs and increased efficiencies for the plant. At 900 °C the CO2 flux and permeance of the SNDC-carbonate membrane were 0.65 mL/cm2•min and 1.0×10-7 mol/m2•s•Pa, respectively. Detailed in this report are the following: background regarding CO2 separation membranes and IGCC power plants, SNDC tubular membrane preparation and characterization, IGCC with membrane reactor plant design, process heat and mass balance, and plant cost estimations.
ContributorsDunteman, Nicholas Powell (Author) / Lin, Jerry (Thesis director) / Dong, Xueliang (Committee member) / Barrett, The Honors College (Contributor) / Chemical Engineering Program (Contributor) / School of Sustainability (Contributor)
Created2014-05
Description
The two central goals of this project were 1) to develop a testing method utilizing coatings on ultra-thin stainless steel to measure the thermal conductivity (k) of battery electrode materials and composites, and 2) to measure and compare the thermal conductivities of lithium iron phosphate (LiFePO4, "LFP") in industry-standard graphite/LFP mixtures as well as graphene/LFP mixtures and a synthesized graphene/LFP nanocomposite. Graphene synthesis was attempted before purchasing graphene materials, and further exploration of graphene synthesis is recommended due to limitations in purchased product quality. While it was determined after extensive experimentation that the graphene/LFP nanocomposite could not be successfully synthesized according to current literature information, a mixed composite of graphene/LFP was successfully tested and found to have k = 0.23 W/m*K. This result provides a starting point for further thermal testing method development and k optimization in Li-ion battery electrode nanocomposites.
ContributorsStehlik, Daniel Wesley (Author) / Chan, Candace K. (Thesis director) / Dai, Lenore (Committee member) / Barrett, The Honors College (Contributor) / Chemical Engineering Program (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
In microbial fuel cells (MFCs) the biocathode is developed as a potential alternative to chemical cathodic catalysts, which are deemed as expensive and unsustainable for applications. These cells utilize different types of microorganisms as catalysts to promote biodegradation of organic matter while simultaneously converting energy released in metabolic reactions into electrical energy. Most current research have focused more on the anodic microbes, including the current generating bacteria species, anodic microbial community composition, and the mechanisms of the extracellular electron transfer. Compared to the anode, research on the microbes of the biocathode of the MFCs are very limited and are heavily focused on the role of the bacteria in the system. Thus, further understand of the mechanism of the microbial community in the biocathode will create new engineering applications for sustainable energy. Previous research conducted by Strycharz-Glaven et al. presented an electrochemical analysis of a Marinobacter-dominated biocathode communitygrown on biocathodes in sediment/seawater-based MFCs. Chronoamperometry results indicated that current densities up to -0.04 A/m2 were produced for the biocathode. Cyclic voltammetry responses indicated a midpoint potential at 0.196 V ± 0.01 V. However, the reactor design for these experiments showed that no oxygen is supplied to the electrochemical system. By incorporating an air diffusion membrane to the cathode of the reactor, chronoamperometry results have produced current density in the system up to -0.15 A/m2. Cyclic voltammetry results have also displayed a midpoint potential of 0.25 V ± 0.01 V under scan rates of 0.2 mV/s. Thus, this electrochemical setup has increased the current output of the system.
ContributorsWang, Zixuan (Author) / Torres, Cesar (Thesis director) / Hart, Steven (Committee member) / Materials Science and Engineering Program (Contributor) / Chemical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Mortality of 1918 influenza virus was high, partly due to bacteria coinfections. We characterize pandemic mortality in Arizona, which had high prevalence of tuberculosis. We applied regressions to over 35,000 data points to estimate the basic reproduction number and excess mortality. Age-specific mortality curves show elevated mortality for all age groups, especially the young, and senior sparing effects. The low value for reproduction number indicates that transmissibility was moderately low.
ContributorsJenner, Melinda Eva (Author) / Chowell-Puente, Gerardo (Thesis director) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
While biodiesel production from photosynthesizing algae is a promising form of alternative energy, the process is water and nutrient intensive. I designed a mathematical model for a photobioreactor system that filters the reactor effluent and returns the permeate to the system so that unutilized nutrients are not wasted, addressing these problems. The model tracks soluble and biomass components that govern the rates of the processes within the photobioreactor (PBR). It considers light attenuation and inhibition, nutrient limitation, preference for ammonia consumption over nitrate, production of soluble microbial products (SMP) and extracellular polymeric substance (EPS), and competition with heterotrophic bacteria that predominately consume SMP. I model a continuous photobioreactor + microfiltration system under nine unique operation conditions - three dilution rates and three recycling rates. I also evaluate the health of a PBR under different dilution rates for two values of qpred. I evaluate the success of each run by calculating values such as biomass productivity and specific biomass yield. The model shows that for low dilution rates (D = <0.2 d-1) and high recycling rates (>66%), nutrient limitation can lead to a PBR crash. In balancing biomass productivity with water conservation, the most favorable runs were those in which the dilution rate and the recycling rate were highest. In a second part of my thesis, I developed a model that describes the interactions of phototrophs and their predators. The model also shows that dilution rates corresponding to realistic PBR operation can washout predators from the system, but the simulation outputs depend heavily on the accuracy of parameters that are not well defined.
ContributorsWik, Benjamin Philip (Author) / Marcus, Andrew (Thesis director) / Rittmann, Bruce (Committee member) / School of Sustainability (Contributor) / Chemical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.
ContributorsSecrest, Micah (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05