Matching Items (91)
Description
In this research we consider stochastic models of Glioblastoma Multiforme brain tumors. We first look at a model by K. Swanson et al., which describes the dynamics as random diffusion plus deterministic logistic growth. We introduce a stochastic component in the logistic growth in the form of a random growth rate defined by a Poisson process. We show that this stochastic logistic growth model leads to a more accurate evaluation of the tumor growth compared its deterministic counterpart. We also discuss future plans to incorporate individual patient geometry, extend the model to three dimensions and to incorporate effects of different treatments into our model, in collaboration with a local hospital.
ContributorsManning, Michael Clare (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Letters and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2013-12
Description
Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm3 to 62 mm3, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.
ContributorsRutter, Erica (Author) / Stepien, Tracy (Author) / Anderies, Barrett (Author) / Plasencia, Jonathan (Author) / Woolf, Eric C. (Author) / Scheck, Adrienne C. (Author) / Turner, Gregory H. (Author) / Liu, Qingwei (Author) / Frakes, David (Author) / Kodibagkar, Vikram (Author) / Kuang, Yang (Author) / Preul, Mark C. (Author) / Kostelich, Eric (Author) / College of Liberal Arts and Sciences (Contributor)
Created2017-05-31
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
Description
Some cyanobacteria, referred to as boring or euendolithic, are capable of excavating tunnels into calcareous substrates, both mineral and biogenic. The erosive activity of these cyanobacteria results in the destruction of coastal limestones and dead corals, the reworking of carbonate sands, and the cementation of microbialites. They thus link the biological and mineral parts of the global carbon cycle directly. They are also relevant for marine aquaculture as pests of mollusk populations. In spite of their importance, the mechanism by which these cyanobacteria bore remains unknown. In fact, boring by phototrophs is geochemically paradoxical, in that they should promote precipitation of carbonates, not dissolution. To approach this paradox experimentally, I developed an empirical model based on a newly isolated euendolith, which I characterized physiologically, ultrastructurally and phylogenetically (Mastigocoleus testarum BC008); it bores on pure calcite in the laboratory under controlled conditions. Mechanistic hypotheses suggesting the aid of accompanying heterotrophic bacteria, or the spatial/temporal separation of photosynthesis and boring could be readily rejected. Real-time Ca2+ mapping by laser scanning confocal microscopy of boring BC008 cells showed that boring resulted in undersaturation at the boring front and supersaturation in and around boreholes. This is consistent with a process of uptake of Ca2+ from the boring front, trans-cellular mobilization, and extrusion at the distal end of the filaments (borehole entrance). Ca2+ disequilibrium could be inhibited by ceasing illumination, preventing ATP generation, and, more specifically, by blocking P-type Ca2+ ATPase transporters. This demonstrates that BC008 bores by promoting calcite dissolution locally at the boring front through Ca2+ uptake, an unprecedented capacity among living organisms. Parallel studies using mixed microbial assemblages of euendoliths boring into Caribbean, Mediterranean, North and South Pacific marine carbonates, demonstrate that the mechanism operating in BC008 is widespread, but perhaps not universal.
ContributorsRamírez-Reinat, Edgardo L (Author) / Garcia-Pichel, Ferran (Thesis advisor) / Chandler, Douglas (Committee member) / Farmer, Jack (Committee member) / Neuer, Susanne (Committee member) / Arizona State University (Publisher)
Created2010
Description
The experiments conducted in this report supported previous evidence (Bethany et al., 2019) that a newly identified predatory bacterium causes a higher rate of mortality in the biological soil crust cyanobacterium M. vaginatus when in hot soils than in cold soils. I predicted that the extracellular propagules of this predatory bacterium were inactivated at seasonally low temperatures, rendering them non-viable when introduced to M. vaginatus at room temperature. However, I found that the predatory bacterium became only transiently inactive at low temperatures, recovering its pathogenicity when later exposed to warmer temperatures. By contrast, inactivation of infectivity was complete by exposure in both liquid and dry conditions for five days at 40 °C. I also expected that its infectivity towards M. vaginatus was temperature dependent. Indeed, infection was hampered and did not cause high mortality when predator and prey were incubated at or below 10 °C, which could have been due to slowed metabolisms of M. vaginatus or to an inability of the predatory bacterium to attack in cold conditions. Above 10 °C, when M. vaginatus grew faster, time to full death of predator/prey incubations correlated with the rate of growth of healthy cultures.
The experiments in this study observed a correlation between the growth rate of uninfected cultures and the decay rate of infected cultures, meaning that temperatures that cultures that displayed a higher growth rate for uninfected M. vaginatus would die faster when infected with the predatory bacterium. Infected cultures that were incubated at temperatures 4 and 10 °C did not display death and this could have been due to lower activity of M. vaginatus at lower temperatures or the inability for the predatory bacterium to attack at lower temperatures.
The experiments in this study observed a correlation between the growth rate of uninfected cultures and the decay rate of infected cultures, meaning that temperatures that cultures that displayed a higher growth rate for uninfected M. vaginatus would die faster when infected with the predatory bacterium. Infected cultures that were incubated at temperatures 4 and 10 °C did not display death and this could have been due to lower activity of M. vaginatus at lower temperatures or the inability for the predatory bacterium to attack at lower temperatures.
ContributorsAhamed, Anisa Nour (Author) / Garcia-Pichel, Ferran (Thesis director) / Giraldo Silva, Ana Maria (Committee member) / Bethany Rakes, Julie (Committee member) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
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
Prostate cancer is the second most common kind of cancer in men. Fortunately, it has a 99% survival rate. To achieve such a survival rate, a variety of aggressive therapies are used to treat prostate cancers that are caught early. Androgen deprivation therapy (ADT) is a therapy that is given in cycles to patients. This study attempted to analyze what factors in a group of 79 patients caused them to stick with or discontinue the treatment. This was done using naïve Bayes classification, a machine-learning algorithm. The usage of this algorithm identified high testosterone as an indicator of a patient persevering with the treatment, but failed to produce statistically significant high rates of prediction.
ContributorsMillea, Timothy Michael (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
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
The oceanic biological carbon pump is a key component of the global carbon cycle in which dissolved carbon dioxide is taken up by phytoplankton during photosynthesis, a fraction of which then sinks to depth and contributes to oceanic carbon storage. The small-celled phytoplankton (<5 µm) that dominate the phytoplankton community in oligotrophic oceans have traditionally been viewed as contributing little to export production due to their small size. However, recent studies have shown that the picocyanobacterium Synechococcus produces transparent exopolymer particles (TEP), the sticky matrix of marine aggregates, and forms abundant microaggregates (5-60 µm), which is enhanced under nutrient limited growth conditions. Whether other small phytoplankton species exude TEP and form microaggregates, and if these are enhanced under growth-limiting conditions remains to be investigated. This study aims to analyze how nutrient limitation affects TEP production and microaggregate formation of species that are found to be associated with sinking particles in the Sargasso Sea. The pico-cyanobacterium Prochlorococcus marinus (0.8 µm), the nano-diatom Minutocellus polymorphus (2 µm), and the pico-prasinophyte Ostreococcus lucimarinus (0.6 µm) were grown in axenic batch culture experiments under nutrient replete and limited conditions. It was hypothesized that phytoplankton subject to nutrient limitation will aggregate more than those under replete conditions due to an increased exudation of TEP and that Minutocellus would produce the most TEP and microaggregates while Prochlorococcus would produce the least TEP and microaggregates of the three phytoplankton groups. As hypothesized, nutrient limitation increased TEP concentration in all three species, however they were only significant in nitrogen-limited treatments of Prochlorococcus as well as nitrogen- and phosphorus-limited treatments of Minutocellus. Formation of microaggregates was significantly enhanced in Minutocellus and Ostreococcus cultures in distinct microaggregate size ranges. Minutocellus produced the most TEP per cell and aggregated at higher volume concentrations compared to Prochlorococcus and Ostreococcus. Surprisingly, Ostreococcus produced more TEP than Prochlorococcus and Minutocellus per unit cell volume. These findings show for the first time how nutrient limited conditions enhance TEP production and microaggregation of Prochlorococcus, Minutocellus, and Ostreococcus, providing a mechanism for their incorporation into larger, sinking particles and contribution to export production in oligotrophic oceans.
ContributorsShurtleff, Catrina (Author) / Neuer, Susanne (Thesis advisor) / Lomas, Michael W. (Committee member) / Garcia-Pichel, Ferran (Committee member) / Arizona State University (Publisher)
Created2022
Description
Under current climate conditions northern peatlands mostly act as C sinks; however, changes in climate and environmental conditions, can change the soil carbon decomposition cascade, thus altering the sink status. Here I studied one of the most abundant northern peatland types, poor fen, situated along a climate gradient from tundra (Daring Lake, Canada) to boreal forest (Lutose, Canada) to temperate broadleaf and mixed forest (Bog Lake, MN and Chicago Bog, NY) biomes to assess patterns of microbial abundance across the climate gradient. Principal component regression analysis of the microbial community and environmental variables determined that mean annual temperature (MAT) (r2=0.85), mean annual precipitation (MAP) (r2=0.88), and soil temperature (r2=0.77), were the top significant drivers of microbial community composition (p < 0.001). Niche breadth analysis revealed the relative abundance of Intrasporangiaceae, Methanobacteriaceae and Candidatus Methanoflorentaceae fam. nov. to increase when MAT and MAP decrease. The same analysis showed Spirochaetaceae, Methanosaetaceae and Methanoregulaceae to increase in relative abundance when MAP, soil temperature and MAT increased, respectively. These findings indicated that climate variables were the strongest predictors of microbial community composition and that certain taxa, especially methanogenic families demonstrate distinct patterns across the climate gradient. To evaluate microbial production of methanogenic substrates, I carried out High Resolution-DNA-Stable Isotope Probing (HR-DNA-SIP) to evaluate the active portion of the community’s intermediary ecosystem metabolic processes. HR-DNA-SIP revealed several challenges in efficiency of labelling and statistical identification of responders, however families like Veillonellaceae, Magnetospirillaceae, Acidobacteriaceae 1, were found ubiquitously active in glucose amended incubations. Differences in metabolic byproducts from glucose amendments show distinct patterns in acetate and propionate accumulation across sites. Families like Spirochaetaceae and Sphingomonadaceae were only found to be active in select sites of propionate amended incubations. By-product analysis from propionate incubations indicate that the northernmost sites were acetate-accumulating communities.
These results indicate that microbial communities found in poor fen northern peatlands are strongly influenced by climate variables predicted to change under current climate scenarios. I have identified patterns of relative abundance and activity of select microbial taxa, indicating the potential for climate variables to influence the metabolic pathway in which carbon moves through peatland systems.
ContributorsSarno, Analissa Flores (Author) / Cadillo-Quiroz, Hinsby (Thesis advisor) / Garcia-Pichel, Ferran (Committee member) / Krajmalnik-Brown, Rosa (Committee member) / Childers, Daniel (Committee member) / Arizona State University (Publisher)
Created2022