Matching Items (100)
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
Microplastics, plastics smaller than 5 mm, are an emerging concern worldwide due to their potential adverse effects on the environment and human health. Microplastics have the potential to biomagnify through the food chain, and are prone to adsorbing organic pollutants and heavy metals. Therefore, there is an urgent need to assess the extent of microplastic contamination in different environments. The occurrence of microplastics in the atmosphere of Tempe, AZ was investigated and results show concentrations as high as 1.1 microplastics/m3. The most abundant identified polymer was polyvinyl chloride. However, chemical characterization is fraught with challenges, with a majority of microplastics remaining chemically unidentified. Laboratory experiments simulating weathering of microplastics revealed that Raman spectra of microplastics change over time due to weathering processes. This work also studied the spatial variation of microplastics in soil in Phoenix and the surrounding areas of the Sonoran Desert, and microplastic abundances ranged from 122 to 1299 microplastics/kg with no clear trends between different locations, and substantial total deposition of microplastics occurring in the same location with resuspension and redistribution of deposited microplastics likely contributing to unclear spatial trends. Temporal variation of soil microplastics from 2005 to 2015 show a systematic increase in the abundance of microplastics. Polyethylene was prominent in all soil samples.
Further, recreational surface waters were investigated as a potential source of microplastics in aquatic environments. The temporal variation of microplastics in the Salt River, AZ over the course of one day depicted an increase of 8 times in microplastic concentration at peak activity time of 16:00 hr compared to 8:00 hr. Concurrently, microplastic concentrations in surface water samples from apartment community swimming pools in Tempe, AZ depicted substantial variability with concentrations as high as 254,574 MPs/m3. Polyester and Polyamide fibers were prevalent in surface water samples, indicating a release from synthetic fabrics. Finally, a method for distinguishing tire wear microplastics from soot in ambient aerosol samples was developed using Programmed Thermal Analysis, that allows for the quantification of Elemental Carbon. The method was successfully applied on urban aerosol samples with results depicting substantial fractions of tire wear in urban atmospheric environments.
ContributorsChandrakanthan, Kanchana (Author) / Herckes, Pierre (Thesis advisor) / Fraser, Matthew (Committee member) / Shock, Everett (Committee member) / Arizona State University (Publisher)
Created2024
Description
The most advanced social insects, the eusocial insects, form often large societies in which there is reproductive division of labor, queens and workers, have overlapping generations, and cooperative brood care where daughter workers remain in the nest with their queen mother and care for their siblings. The eusocial insects are composed of representative species of bees and wasps, and all species of ants and termites. Much is known about their organizational structure, but remains to be discovered.
The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
ContributorsRodríguez Messan, Marisabel (Author) / Kang, Yun (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Kuang, Yang (Committee member) / Page Jr., Robert E (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2018
Description
Atmospheric particulate matter (PM) has a pronounced effect on our climate, and exposure to PM causes negative health outcomes and elevated mortality rates in urban populations. Reactions that occur in fog can form new secondary organic aerosol material from gas-phase species or primary organic aerosols. It is important to understand these reactions, as well as how organic material is scavenged and deposited, so that climate and health effects can be fully assessed. Stable carbon isotopes have been used widely in studying gas- and particle-phase atmospheric chemistry. However, the processing of organic matter by fog has not yet been studied, even though stable isotopes can be used to track all aspects of atmospheric processing, from particle formation, particle scavenging, reactions that form secondary organic aerosol material, and particle deposition. Here, carbon isotope analysis is used for the first time to assess the processing of carbonaceous particles by fog.
This work first compares carbon isotope measurements (δ13C) of particulate matter and fog from locations across the globe to assess how different primary aerosol sources are reflected in the atmosphere. Three field campaigns are then discussed that highlight different aspects of PM formation, composition, and processing. In Tempe, AZ, seasonal and size-dependent differences in the δ13C of total carbon and n-alkanes in PM were studied. δ13C was influenced by seasonal trends, including inversion, transport, population density, and photochemical activity. Variations in δ13C among particle size fractions were caused by sources that generate particles in different size modes.
An analysis of PM from urban and suburban sites in northeastern France shows how both fog and rain can cause measurable changes in the δ13C of PM. The δ13C of PM was consistent over time when no weather events occurred, but particles were isotopically depleted by up to 1.1‰ in the presence of fog due to preferential scavenging of larger isotopically enriched particles. Finally, the δ13C of the dissolved organic carbon in fog collected on the coast of Southern California is discussed. Here, temporal depletion of the δ13C of fog by up to 1.2‰ demonstrates its use in observing the scavenging and deposition of organic PM.
This work first compares carbon isotope measurements (δ13C) of particulate matter and fog from locations across the globe to assess how different primary aerosol sources are reflected in the atmosphere. Three field campaigns are then discussed that highlight different aspects of PM formation, composition, and processing. In Tempe, AZ, seasonal and size-dependent differences in the δ13C of total carbon and n-alkanes in PM were studied. δ13C was influenced by seasonal trends, including inversion, transport, population density, and photochemical activity. Variations in δ13C among particle size fractions were caused by sources that generate particles in different size modes.
An analysis of PM from urban and suburban sites in northeastern France shows how both fog and rain can cause measurable changes in the δ13C of PM. The δ13C of PM was consistent over time when no weather events occurred, but particles were isotopically depleted by up to 1.1‰ in the presence of fog due to preferential scavenging of larger isotopically enriched particles. Finally, the δ13C of the dissolved organic carbon in fog collected on the coast of Southern California is discussed. Here, temporal depletion of the δ13C of fog by up to 1.2‰ demonstrates its use in observing the scavenging and deposition of organic PM.
ContributorsNapolitano, Denise (Author) / Herckes, Pierre (Thesis advisor) / Fraser, Matthew (Committee member) / Shock, Everett (Committee member) / Arizona State University (Publisher)
Created2018
Description
The role of climate change, as measured in terms of changes in the climatology of geophysical variables (such as temperature and rainfall), on the global distribution and burden of vector-borne diseases (VBDs) remains a subject of considerable debate. This dissertation attempts to contribute to this debate via the use of mathematical (compartmental) modeling and statistical data analysis. In particular, the objective is to find suitable values and/or ranges of the climate variables considered (typically temperature and rainfall) for maximum vector abundance and consequently, maximum transmission intensity of the disease(s) they cause.
Motivated by the fact that understanding the dynamics of disease vector is crucial to understanding the transmission and control of the VBDs they cause, a novel weather-driven deterministic model for the population biology of the mosquito is formulated and rigorously analyzed. Numerical simulations, using relevant weather and entomological data for Anopheles mosquito (the vector for malaria), show that maximum mosquito abundance occurs when temperature and rainfall values lie in the range [20-25]C and [105-115] mm, respectively.
The Anopheles mosquito ecology model is extended to incorporate human dynamics. The resulting weather-driven malaria transmission model, which includes many of the key aspects of malaria (such as disease transmission by asymptomatically-infectious humans, and enhanced malaria immunity due to repeated exposure), was rigorously analyzed. The model which also incorporates the effect of diurnal temperature range (DTR) on malaria transmission dynamics shows that increasing DTR shifts the peak temperature value for malaria transmission from 29C (when DTR is 0C) to about 25C (when DTR is 15C).
Finally, the malaria model is adapted and used to study the transmission dynamics of chikungunya, dengue and Zika, three diseases co-circulating in the Americas caused by the same vector (Aedes aegypti). The resulting model, which is fitted using data from Mexico, is used to assess a few hypotheses (such as those associated with the possible impact the newly-released dengue vaccine will have on Zika) and the impact of variability in climate variables on the dynamics of the three diseases. Suitable temperature and rainfall ranges for the maximum transmission intensity of the three diseases are obtained.
Motivated by the fact that understanding the dynamics of disease vector is crucial to understanding the transmission and control of the VBDs they cause, a novel weather-driven deterministic model for the population biology of the mosquito is formulated and rigorously analyzed. Numerical simulations, using relevant weather and entomological data for Anopheles mosquito (the vector for malaria), show that maximum mosquito abundance occurs when temperature and rainfall values lie in the range [20-25]C and [105-115] mm, respectively.
The Anopheles mosquito ecology model is extended to incorporate human dynamics. The resulting weather-driven malaria transmission model, which includes many of the key aspects of malaria (such as disease transmission by asymptomatically-infectious humans, and enhanced malaria immunity due to repeated exposure), was rigorously analyzed. The model which also incorporates the effect of diurnal temperature range (DTR) on malaria transmission dynamics shows that increasing DTR shifts the peak temperature value for malaria transmission from 29C (when DTR is 0C) to about 25C (when DTR is 15C).
Finally, the malaria model is adapted and used to study the transmission dynamics of chikungunya, dengue and Zika, three diseases co-circulating in the Americas caused by the same vector (Aedes aegypti). The resulting model, which is fitted using data from Mexico, is used to assess a few hypotheses (such as those associated with the possible impact the newly-released dengue vaccine will have on Zika) and the impact of variability in climate variables on the dynamics of the three diseases. Suitable temperature and rainfall ranges for the maximum transmission intensity of the three diseases are obtained.
ContributorsOkuneye, Kamaldeen O (Author) / Gumel, Abba B (Thesis advisor) / Kuang, Yang (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2018
Description
Rabies is an infectious viral disease. It is usually fatal if a victim reaches the rabid stage, which starts after the appearance of disease symptoms. The disease virus attacks the central nervous system, and then it migrates from peripheral nerves to the spinal cord and brain. At the time when the rabies virus reaches the brain, the incubation period is over and the symptoms of clinical disease appear on the victim. From the brain, the virus travels via nerves to the salivary glands and saliva.
A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration
over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds.
Further, a numerical algorithm is described for the simulation
of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by
the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit
continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest
is in how the partition of rabid foxes into
territorial and diffusing rabid foxes influences
the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis
to latent periods of fixed length and to exponentially
distributed latent periods.
The results of the numerical calculations
are compared for latent periods
of fixed and exponentially distributed length
and for various proportions of territorial
and wandering rabid foxes.
The speeds of spread observed in the
simulations are compared
to spreading speeds obtained by numerically solving the analytic formulas
and to observed speeds of epizootic frontlines
in the European rabies outbreak 1940 to 1980.
A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration
over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds.
Further, a numerical algorithm is described for the simulation
of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by
the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit
continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest
is in how the partition of rabid foxes into
territorial and diffusing rabid foxes influences
the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis
to latent periods of fixed length and to exponentially
distributed latent periods.
The results of the numerical calculations
are compared for latent periods
of fixed and exponentially distributed length
and for various proportions of territorial
and wandering rabid foxes.
The speeds of spread observed in the
simulations are compared
to spreading speeds obtained by numerically solving the analytic formulas
and to observed speeds of epizootic frontlines
in the European rabies outbreak 1940 to 1980.
ContributorsAlanazi, Khalaf Matar (Author) / Thieme, Horst R. (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Baer, Steven (Committee member) / Gardner, Carl (Committee member) / Kuang, Yang (Committee member) / Smith, Hal (Committee member) / Arizona State University (Publisher)
Created2018
Description
Ideas from coding theory are employed to theoretically demonstrate the engineering of mutation-tolerant genes, genes that can sustain up to some arbitrarily chosen number of mutations and still express the originally intended protein. Attention is restricted to tolerating substitution mutations. Future advances in genomic engineering will make possible the ability to synthesize entire genomes from scratch. This presents an opportunity to embed desirable capabilities like mutation-tolerance, which will be useful in preventing cell deaths in organisms intended for research or industrial applications in highly mutagenic environments. In the extreme case, mutation-tolerant genes (mutols) can make organisms resistant to retroviral infections.
An algebraic representation of the nucleotide bases is developed. This algebraic representation makes it possible to convert nucleotide sequences into algebraic sequences, apply mathematical ideas and convert results back into nucleotide terms. Using the algebra developed, a mapping is found from the naturally-occurring codons to an alternative set of codons which makes genes constructed from them mutation-tolerant, provided no more than one substitution mutation occurs per codon. The ideas discussed naturally extend to finding codons that can tolerate t arbitrarily chosen number of mutations per codon. Finally, random substitution events are simulated in both a wild-type green fluorescent protein (GFP) gene and its mutol variant and the amino acid sequence expressed from each post-mutation is compared with the amino acid sequence pre-mutation.
This work assumes the existence of synthetic protein-assembling entities that function like tRNAs but can read k nucleotides at a time, with k greater than or equal to 5. The realization of this assumption is presented as a challenge to the research community.
An algebraic representation of the nucleotide bases is developed. This algebraic representation makes it possible to convert nucleotide sequences into algebraic sequences, apply mathematical ideas and convert results back into nucleotide terms. Using the algebra developed, a mapping is found from the naturally-occurring codons to an alternative set of codons which makes genes constructed from them mutation-tolerant, provided no more than one substitution mutation occurs per codon. The ideas discussed naturally extend to finding codons that can tolerate t arbitrarily chosen number of mutations per codon. Finally, random substitution events are simulated in both a wild-type green fluorescent protein (GFP) gene and its mutol variant and the amino acid sequence expressed from each post-mutation is compared with the amino acid sequence pre-mutation.
This work assumes the existence of synthetic protein-assembling entities that function like tRNAs but can read k nucleotides at a time, with k greater than or equal to 5. The realization of this assumption is presented as a challenge to the research community.
ContributorsAmpofo, Prince Kwame (Author) / Tian, Xiaojun (Thesis advisor) / Kiani, Samira (Committee member) / Kuang, Yang (Committee member) / Arizona State University (Publisher)
Created2019
Description
Chemical and physical interactions of flowing ice and rock have inexorably shaped planetary surfaces. Weathering in glacial environments is a significant link in biogeochemical cycles – carbon and strontium – on Earth, and may have once played an important role in altering Mars’ surface. Despite growing recognition of the importance of low-temperature chemical weathering, these processes are still not well understood. Debris-coated glaciers are also present on Mars, emphasizing the need to study ice-related processes in the evolution of planetary surfaces. During Earth’s history, subglacial environments are thought to have sheltered communities of microorganisms from extreme climate variations. On Amazonian Mars, glaciers such as lobate debris aprons (LDA) could have hosted chemolithotrophic communities, making Mars’ present glaciers candidates for life preservation. This study characterizes glacial processes on both Earth and Mars.
Chemical weathering at Robertson Glacier, a small alpine glacier in the Canadian Rocky Mountains, is examined with a multidisciplinary approach. The relative proportions of differing dissolution reactions at various stages in the glacial system are empirically determined using aqueous geochemistry. Synthesis of laboratory and orbital thermal infrared spectroscopy allows identification of dissolution rinds on hand samples and characterization of carbonate dissolution signals at orbital scales, while chemical and morphological evidence for thin, discontinuous weathering rinds at microscales are evident from electron microscopy. Subglacial dissolution rates are found to outpace those of the proglacial till plain; biologically-mediated pyrite oxidation drives the bulk of this acidic weathering.
Second, the area-elevation relationship, or hypsometry, of LDA in the midlatitudes of Mars is characterized. These glaciers are believed to have formed ~500 Ma during a climate excursion. Hypsometric measurements of these debris-covered glaciers enable insight into past flow regimes and drive predictions about past climate scenarios. The LDA in this study fall into three major groups, strongly dependent on basal elevation, implying regional and climatic controls on ice formation and flow.
I show that biologically-mediated mineral reactions drive high subglacial dissolution rates, such that variations within the valley can be detected with remote sensing techniques. In future work, these insights can be applied to examining Mars’ glacial regions for signs of chemical alteration and biosignatures.
Chemical weathering at Robertson Glacier, a small alpine glacier in the Canadian Rocky Mountains, is examined with a multidisciplinary approach. The relative proportions of differing dissolution reactions at various stages in the glacial system are empirically determined using aqueous geochemistry. Synthesis of laboratory and orbital thermal infrared spectroscopy allows identification of dissolution rinds on hand samples and characterization of carbonate dissolution signals at orbital scales, while chemical and morphological evidence for thin, discontinuous weathering rinds at microscales are evident from electron microscopy. Subglacial dissolution rates are found to outpace those of the proglacial till plain; biologically-mediated pyrite oxidation drives the bulk of this acidic weathering.
Second, the area-elevation relationship, or hypsometry, of LDA in the midlatitudes of Mars is characterized. These glaciers are believed to have formed ~500 Ma during a climate excursion. Hypsometric measurements of these debris-covered glaciers enable insight into past flow regimes and drive predictions about past climate scenarios. The LDA in this study fall into three major groups, strongly dependent on basal elevation, implying regional and climatic controls on ice formation and flow.
I show that biologically-mediated mineral reactions drive high subglacial dissolution rates, such that variations within the valley can be detected with remote sensing techniques. In future work, these insights can be applied to examining Mars’ glacial regions for signs of chemical alteration and biosignatures.
ContributorsRutledge, Alicia Marie (Author) / Christensen, Philip R. (Thesis advisor) / Shock, Everett (Committee member) / Clarke, Amanda (Committee member) / Sharp, Thomas (Committee member) / Whipple, Kelin (Committee member) / Arizona State University (Publisher)
Created2015
Description
Natural variations in 238U/235U of marine carbonates might provide a useful way of constraining redox conditions of ancient environments. In order to evaluate the reliability of this proxy, we conducted aragonite and calcite coprecipitation experiments at pH ~7.5 and ~ 8.5 to study possible U isotope fractionation during incorporation into these minerals.
Small but significant U isotope fractionation was observed in aragonite experiments at pH ~ 8.5, with heavier U in the solid phase. 238U/235U of dissolved U in these experiments can be fit by Rayleigh fractionation curves with fractionation factors of 1.00007+0.00002/-0.00003, 1.00005 ± 0.00001, and 1.00003 ± 0.00001. In contrast, no resolvable U isotope fractionation was observed in an aragonite experiment at pH ~7.5 or in calcite experiments at either pH. Equilibrium isotope fractionation among different aqueous U species is the most likely explanation for these findings. Certain charged U species are preferentially incorporated into calcium carbonate relative to the uncharged U species Ca2UO2(CO3)3(aq), which we hypothesize has a lighter equilibrium U isotope composition than most of the charged species. According to this hypothesis, the magnitude of U isotope fractionation should scale with the fraction of dissolved U that is present as Ca2UO2(CO3)3 (aq). This expectation is confirmed by equilibrium speciation modeling of our experiments. Theoretical calculation of the U isotope fractionation factors between different U species could further test this hypothesis and our proposed fractionation mechanism.
These findings suggest that U isotope variations in ancient carbonates could be controlled by changes in the aqueous speciation of seawater U, particularly changes in seawater pH, PCO2, [Ca], or [Mg] concentrations. In general, these effects are likely to be small (<0.13 ‰), but are nevertheless potentially significant because of the small natural range of variation of 238U/235U.
Small but significant U isotope fractionation was observed in aragonite experiments at pH ~ 8.5, with heavier U in the solid phase. 238U/235U of dissolved U in these experiments can be fit by Rayleigh fractionation curves with fractionation factors of 1.00007+0.00002/-0.00003, 1.00005 ± 0.00001, and 1.00003 ± 0.00001. In contrast, no resolvable U isotope fractionation was observed in an aragonite experiment at pH ~7.5 or in calcite experiments at either pH. Equilibrium isotope fractionation among different aqueous U species is the most likely explanation for these findings. Certain charged U species are preferentially incorporated into calcium carbonate relative to the uncharged U species Ca2UO2(CO3)3(aq), which we hypothesize has a lighter equilibrium U isotope composition than most of the charged species. According to this hypothesis, the magnitude of U isotope fractionation should scale with the fraction of dissolved U that is present as Ca2UO2(CO3)3 (aq). This expectation is confirmed by equilibrium speciation modeling of our experiments. Theoretical calculation of the U isotope fractionation factors between different U species could further test this hypothesis and our proposed fractionation mechanism.
These findings suggest that U isotope variations in ancient carbonates could be controlled by changes in the aqueous speciation of seawater U, particularly changes in seawater pH, PCO2, [Ca], or [Mg] concentrations. In general, these effects are likely to be small (<0.13 ‰), but are nevertheless potentially significant because of the small natural range of variation of 238U/235U.
ContributorsChen, Xinming (Author) / Anbar, Ariel (Thesis advisor) / Herckes, Pierre (Committee member) / Shock, Everett (Committee member) / Arizona State University (Publisher)
Created2015
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