ASU Electronic Theses and Dissertations
This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.
In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.
Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.
Displaying 1 - 10 of 15
Filtering by
- All Subjects: Biology
- Creators: Kuang, Yang
- Creators: LaBaer, Joshua
Description
There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.
ContributorsPeace, Angela (Author) / Kuang, Yang (Thesis advisor) / Elser, James J (Committee member) / Baer, Steven (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
The phycologist, M. R. Droop, studied vitamin B12 limitation in the flagellate Monochrysis lutheri and concluded that its specific growth rate depended on the concentration of the vitamin within the cell; i.e. the cell quota of the vitamin B12. The Droop model provides a mathematical expression to link growth rate to the intracellular concentration of a limiting nutrient. Although the Droop model has been an important modeling tool in ecology, it has only recently been applied to study cancer biology. Cancer cells live in an ecological setting, interacting and competing with normal and other cancerous cells for nutrients and space, and evolving and adapting to their environment. Here, the Droop equation is used to model three cancers.
First, prostate cancer is modeled, where androgen is considered the limiting nutrient since most tumors depend on androgen for proliferation and survival. The model's accuracy for predicting the biomarker for patients on intermittent androgen deprivation therapy is tested by comparing the simulation results to clinical data as well as to an existing simpler model. The results suggest that a simpler model may be more beneficial for a predictive use, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting.
Next, two chronic myeloid leukemia models are compared that consider Imatinib treatment, a drug that inhibits the constitutively active tyrosine kinase BCR-ABL. Both models describe the competition of leukemic and normal cells, however the first model also describes intracellular dynamics by considering BCR-ABL as the limiting nutrient. Using clinical data, the differences in estimated parameters between the models and the capacity for each model to predict drug resistance are analyzed.
Last, a simple model is presented that considers ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. In this environment, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. Mathematical analysis of the model is presented and model simulation results are compared to pre-clinical data. This simple model is able to fit both on- and off-treatment data using the same biologically relevant parameters.
First, prostate cancer is modeled, where androgen is considered the limiting nutrient since most tumors depend on androgen for proliferation and survival. The model's accuracy for predicting the biomarker for patients on intermittent androgen deprivation therapy is tested by comparing the simulation results to clinical data as well as to an existing simpler model. The results suggest that a simpler model may be more beneficial for a predictive use, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting.
Next, two chronic myeloid leukemia models are compared that consider Imatinib treatment, a drug that inhibits the constitutively active tyrosine kinase BCR-ABL. Both models describe the competition of leukemic and normal cells, however the first model also describes intracellular dynamics by considering BCR-ABL as the limiting nutrient. Using clinical data, the differences in estimated parameters between the models and the capacity for each model to predict drug resistance are analyzed.
Last, a simple model is presented that considers ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. In this environment, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. Mathematical analysis of the model is presented and model simulation results are compared to pre-clinical data. This simple model is able to fit both on- and off-treatment data using the same biologically relevant parameters.
ContributorsEverett, Rebecca Anne (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Milner, Fabio (Committee member) / Crook, Sharon (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Arizona State University (Publisher)
Created2015
Description
Type 1 diabetes (T1D) is a chronic autoimmune disease characterized by progressive autoimmune destruction of insulin-producing pancreatic β-cells. Genetic, immunological and environmental factors contribute to T1D development. The focus of this dissertation is to track the humoral immune response in T1D by profiling autoantibodies (AAbs) and anti-viral antibodies using an innovative protein array platform called Nucleic Acid Programmable Protein Array (NAPPA).
AAbs provide value in identifying individuals at risk, stratifying patients with different clinical courses, improving our understanding of autoimmune destructions, identifying antigens for cellular immune response and providing candidates for prevention trials in T1D. A two-stage serological AAb screening against 6,000 human proteins was performed. A dual specificity tyrosine-phosphorylation-regulated kinase 2 (DYRK2) was validated with 36% sensitivity at 98% specificity by an orthogonal immunoassay. This is the first systematic screening for novel AAbs against large number of human proteins by protein arrays in T1D. A more comprehensive search for novel AAbs was performed using a knowledge-based approach by ELISA and a screening-based approach against 10,000 human proteins by NAPPA. Six AAbs were identified and validated with sensitivities ranged from 16% to 27% at 95% specificity. These two studies enriched the T1D “autoantigenome” and provided insights into T1D pathophysiology in an unprecedented breadth and width.
The rapid rise of T1D incidence suggests the potential involvement of environmental factors including viral infections. Sero-reactivity to 646 viral antigens was assessed in new-onset T1D patients. Antibody positive rate of EBV was significantly higher in cases than controls that suggested a potential role of EBV in T1D development. A high density-NAPPA platform was demonstrated with high reproducibility and sensitivity in profiling anti-viral antibodies.
This dissertation shows the power of a protein-array based immunoproteomics approach to characterize humoral immunoprofile against human and viral proteomes. The identification of novel T1D-specific AAbs and T1D-associated viruses will help to connect the nodes in T1D etiology and provide better understanding of T1D pathophysiology.
AAbs provide value in identifying individuals at risk, stratifying patients with different clinical courses, improving our understanding of autoimmune destructions, identifying antigens for cellular immune response and providing candidates for prevention trials in T1D. A two-stage serological AAb screening against 6,000 human proteins was performed. A dual specificity tyrosine-phosphorylation-regulated kinase 2 (DYRK2) was validated with 36% sensitivity at 98% specificity by an orthogonal immunoassay. This is the first systematic screening for novel AAbs against large number of human proteins by protein arrays in T1D. A more comprehensive search for novel AAbs was performed using a knowledge-based approach by ELISA and a screening-based approach against 10,000 human proteins by NAPPA. Six AAbs were identified and validated with sensitivities ranged from 16% to 27% at 95% specificity. These two studies enriched the T1D “autoantigenome” and provided insights into T1D pathophysiology in an unprecedented breadth and width.
The rapid rise of T1D incidence suggests the potential involvement of environmental factors including viral infections. Sero-reactivity to 646 viral antigens was assessed in new-onset T1D patients. Antibody positive rate of EBV was significantly higher in cases than controls that suggested a potential role of EBV in T1D development. A high density-NAPPA platform was demonstrated with high reproducibility and sensitivity in profiling anti-viral antibodies.
This dissertation shows the power of a protein-array based immunoproteomics approach to characterize humoral immunoprofile against human and viral proteomes. The identification of novel T1D-specific AAbs and T1D-associated viruses will help to connect the nodes in T1D etiology and provide better understanding of T1D pathophysiology.
ContributorsBian, Xiaofang (Author) / LaBaer, Joshua (Thesis advisor) / Mandarino, Lawrence (Committee member) / Chang, Yung (Committee member) / Arizona State University (Publisher)
Created2015
Description
In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth is directly dependent on intracellular nutrient concentration is useful for understanding the dynamics in many ecological systems. The cell quota in particular lends itself to ecological stoichiometry, which is a powerful framework for mathematical ecology. Three models are developed based on the cell quota principal in order to demonstrate its applications beyond chemostat culture.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
ContributorsPacker, Aaron (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
Predicting resistant prostate cancer is critical for lowering medical costs and improving the quality of life of advanced prostate cancer patients. I formulate, compare, and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). I accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). I demonstrate that the inverse problem of parameter estimation might be too complicated and simply relying on data fitting can give incorrect conclusions, since there is a large error in parameter values estimated and parameters might be unidentifiable. I provide confidence intervals to give estimate forecasts using data assimilation via an ensemble Kalman Filter. Using the ensemble Kalman Filter, I perform dual estimation of parameters and state variables to test the prediction accuracy of the models. Finally, I present a novel model with time delay and a delay-dependent parameter. I provide a geometric stability result to study the behavior of this model and show that the inclusion of time delay may improve the accuracy of predictions. Also, I demonstrate with clinical data that the inclusion of the delay-dependent parameter facilitates the identification and estimation of parameters.
ContributorsBaez, Javier (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric (Committee member) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2017
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
Emerging pathogens present several challenges to medical diagnostics. Primarily, the exponential spread of a novel pathogen through naïve populations require a rapid and overwhelming diagnostic response at the site of outbreak. While point-of-care (PoC) platforms have been developed for detection of antigens, serologic responses, and pathogenic genomes, only nucleic acid diagnostics currently have the potential to be developed and manufactured within weeks of an outbreak owing to the speed of next-generation sequencing and custom DNA synthesis. Among nucleic acid diagnostics, isothermal amplification strategies are uniquely suited for PoC implementation due to their simple instrumentation and lack of thermocycling requirement. Unfortunately, isothermal strategies are currently prone to spurious nonspecific amplification, hindering their specificity and necessitating extensive empirical design pipelines that are both time and resource intensive. In this work, isothermal amplification strategies are extensively compared for their feasibility of implementation in outbreak response scenarios. One such technology, Loop-mediated Amplification (LAMP), is identified as having high-potential for rapid development and PoC deployment. Various approaches to abrogating nonspecific amplification are described including a novel in silico design tool based on coarse-grained simulation of interactions between thermophilic DNA polymerase and DNA strands in isothermal reaction conditions. Nonspecific amplification is shown to be due to stabilization of primer secondary structures by high concentrations of Bst DNA polymerase and a mechanism of micro-complement-mediated cross-priming is demonstrated as causal via nanopore sequencing of nonspecific reaction products. The resulting computational model predicts primer set background in 64% of 67 test assays and its usefulness is illustrated further by determining problematic primers in a West Nile Virus-specific LAMP primer set and optimizing primer 3’ nucleotides to eliminate micro-complements within the reaction, resulting in inhibition of background accumulation. Finally, the emergence of Orthopox monkeypox (MPXV) as a recurring threat is discussed and SimCycle is utilized to develop a novel technique for clade-specific discrimination of MPXV based on bridging viral genomic rearrangements (Bridging LAMP). Bridging LAMP is implemented in a 4-plex microfluidic format and demonstrates 100% sensitivity in detection of 100 copies of viral lysates and 45 crude MPXV-positive patient samples collected during the 2022 Clade IIb outbreak.
ContributorsKnappenberger, Mark Daniel (Author) / Anderson, Karen S (Thesis advisor) / LaBaer, Joshua (Committee member) / Roberson, Robert (Committee member) / Lindsay, Stuart (Committee member) / Arizona State University (Publisher)
Created2023
Description
According to the World Health Organization, cancer is one of the leading causes of death around the world. Although early diagnostics using biomarkers and improved treatments with targeted therapy have reduced the rate of cancer related mortalities, there remain many unknowns regarding the contributions of the tumor microenvironment to cancer progression and therapeutic resistance. The tumor microenvironment plays a significant role by manipulating the progression of cancer cells through biochemical and biophysical signals from the surrounding stromal cells along with the extracellular matrix. As such, there is a critical need to understand how the tumor microenvironment influences the molecular mechanisms underlying cancer metastasis to facilitate the discovery of better therapies. This thesis described the development of microfluidic technologies to study the interplay of cancer cells with their surrounding microenvironment. The microfluidic model was used to assess how exposure to chemoattractant, epidermal growth factor (EGF), impacted 3D breast cancer cell invasion and enhanced cell motility speed was noted in the presence of EGF validating physiological cell behavior. Additionally, breast cancer and patient-derived cancer-associated fibroblast (CAF) cells were co-cultured to study cell-cell crosstalk and how it affected cancer invasion. GPNMB was identified as a novel gene of interest and it was shown that CAFs enhanced breast cancer invasion by up-regulating the expression of GPNMB on breast cancer cells resulting in increased migration speed. Lastly, this thesis described the design, biological validation, and use of this microfluidic platform as a new in vitro 3D organotypic model to study mechanisms of glioma stem cell (GSC) invasion in the context of a vascular niche. It was confirmed that CXCL12-CXCR4 signaling is involved in promoting GSC invasion in a 3D vascular microenvironment, while also demonstrating the effectiveness of the microfluidic as a drug screening assay. Taken together, the broader impacts of the microfluidic model developed in this dissertation include, a possible alternative platform to animal testing that is focused on mimicking human physiology, a potential ex vivo platform using patient-derived cells for studying the interplay of cancer cells with its surrounding microenvironment, and development of future therapeutic strategies tailored toward disrupting key molecular pathways involved in regulatory mechanisms of cancer invasion.
ContributorsTruong, Danh, Ph.D (Author) / Nikkhah, Mehdi (Thesis advisor) / LaBaer, Joshua (Committee member) / Smith, Barbara (Committee member) / Mouneimne, Ghassan (Committee member) / Vernon, Brent (Committee member) / Arizona State University (Publisher)
Created2018
Description
Efforts to treat prostate cancer have seen an uptick, as the world’s most commoncancer in men continues to have increasing global incidence. Clinically, metastatic
prostate cancer is most commonly treated with hormonal therapy. The idea behind
hormonal therapy is to reduce androgen production, which prostate cancer cells
require for growth. Recently, the exploration of the synergistic effects of the drugs
used in hormonal therapy has begun. The aim was to build off of these recent
advancements and further refine the synergistic drug model. The advancements I
implement come by addressing biological shortcomings and improving the model’s
internal mechanistic structure. The drug families being modeled, anti-androgens,
and gonadotropin-releasing hormone analogs, interact with androgen production in a
way that is not completely understood in the scientific community. Thus the models
representing the drugs show progress through their ability to capture their effect
on serum androgen. Prostate-specific antigen is the primary biomarker for prostate
cancer and is generally how population models on the subject are validated. Fitting
the model to clinical data and comparing it to other clinical models through the
ability to fit and forecast prostate-specific antigen and serum androgen is how this
improved model achieves validation. The improved model results further suggest that
the drugs’ dynamics should be considered in adaptive therapy for prostate cancer.
prostate cancer is most commonly treated with hormonal therapy. The idea behind
hormonal therapy is to reduce androgen production, which prostate cancer cells
require for growth. Recently, the exploration of the synergistic effects of the drugs
used in hormonal therapy has begun. The aim was to build off of these recent
advancements and further refine the synergistic drug model. The advancements I
implement come by addressing biological shortcomings and improving the model’s
internal mechanistic structure. The drug families being modeled, anti-androgens,
and gonadotropin-releasing hormone analogs, interact with androgen production in a
way that is not completely understood in the scientific community. Thus the models
representing the drugs show progress through their ability to capture their effect
on serum androgen. Prostate-specific antigen is the primary biomarker for prostate
cancer and is generally how population models on the subject are validated. Fitting
the model to clinical data and comparing it to other clinical models through the
ability to fit and forecast prostate-specific antigen and serum androgen is how this
improved model achieves validation. The improved model results further suggest that
the drugs’ dynamics should be considered in adaptive therapy for prostate cancer.
ContributorsReckell, Trevor (Author) / Kostelich, Eric (Thesis advisor) / Kuang, Yang (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2020
Description
Cancer is a disease involving abnormal growth of cells. Its growth dynamics is perplexing. Mathematical modeling is a way to shed light on this progress and its medical treatments. This dissertation is to study cancer invasion in time and space using a mathematical approach. Chapter 1 presents a detailed review of literature on cancer modeling.
Chapter 2 focuses sorely on time where the escape of a generic cancer out of immune control is described by stochastic delayed differential equations (SDDEs). Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and stochasticity in the tumor proliferation rate are studied by including delay and noise in the model. Stability, persistence and extinction of the tumor are analyzed. The result shows that both time delay and noise can induce the transition from low tumor burden equilibrium to high tumor equilibrium. The aforementioned work has been published (Han et al., 2019b).
In Chapter 3, Glioblastoma multiforme (GBM) is studied using a partial differential equation (PDE) model. GBM is an aggressive brain cancer with a grim prognosis. A mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. A novel method is developed to approximate key characteristics of the wave profile, which can be compared with MRI data. Several test cases of MRI data of GBM patients are used to yield personalized parameterizations of the model. The aforementioned work has been published (Han et al., 2019a).
Chapter 4 presents an innovative way of forecasting spatial cancer invasion. Most mathematical models, including the ones described in previous chapters, are formulated based on strong assumptions, which are hard, if not impossible, to verify due to complexity of biological processes and lack of quality data. Instead, a nonparametric forecasting method using Gaussian processes is proposed. By exploiting the local nature of the spatio-temporal process, sparse (in terms of time) data is sufficient for forecasting. Desirable properties of Gaussian processes facilitate selection of the size of the local neighborhood and computationally efficient propagation of uncertainty. The method is tested on synthetic data and demonstrates promising results.
Chapter 2 focuses sorely on time where the escape of a generic cancer out of immune control is described by stochastic delayed differential equations (SDDEs). Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and stochasticity in the tumor proliferation rate are studied by including delay and noise in the model. Stability, persistence and extinction of the tumor are analyzed. The result shows that both time delay and noise can induce the transition from low tumor burden equilibrium to high tumor equilibrium. The aforementioned work has been published (Han et al., 2019b).
In Chapter 3, Glioblastoma multiforme (GBM) is studied using a partial differential equation (PDE) model. GBM is an aggressive brain cancer with a grim prognosis. A mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. A novel method is developed to approximate key characteristics of the wave profile, which can be compared with MRI data. Several test cases of MRI data of GBM patients are used to yield personalized parameterizations of the model. The aforementioned work has been published (Han et al., 2019a).
Chapter 4 presents an innovative way of forecasting spatial cancer invasion. Most mathematical models, including the ones described in previous chapters, are formulated based on strong assumptions, which are hard, if not impossible, to verify due to complexity of biological processes and lack of quality data. Instead, a nonparametric forecasting method using Gaussian processes is proposed. By exploiting the local nature of the spatio-temporal process, sparse (in terms of time) data is sufficient for forecasting. Desirable properties of Gaussian processes facilitate selection of the size of the local neighborhood and computationally efficient propagation of uncertainty. The method is tested on synthetic data and demonstrates promising results.
ContributorsHan, Lifeng (Author) / Kuang, Yang (Thesis advisor) / Fricks, John (Thesis advisor) / Kostelich, Eric (Committee member) / Baer, Steve (Committee member) / Gumel, Abba (Committee member) / Arizona State University (Publisher)
Created2020