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Description
Rewired biological pathways and/or rewired microRNA (miRNA)-mRNA interactions might also influence the activity of biological pathways. Here, rewired biological pathways is defined as differential (rewiring) effect of genes on the topology of biological pathways between controls and cases. Similarly, rewired miRNA-mRNA interactions are defined as the differential (rewiring) effects of miRNAs on the topology of biological pathways between controls and cases. In the dissertation, it is discussed that how rewired biological pathways (Chapter 1) and/or rewired miRNA-mRNA interactions (Chapter 2) aberrantly influence the activity of biological pathways and their association with disease.
This dissertation proposes two PageRank-based analytical methods, Pathways of Topological Rank Analysis (PoTRA) and miR2Pathway, discussed in Chapter 1 and Chapter 2, respectively. PoTRA focuses on detecting pathways with an altered number of hub genes in corresponding pathways between two phenotypes. The basis for PoTRA is that the loss of connectivity is a common topological trait of cancer networks, as well as the prior knowledge that a normal biological network is a scale-free network whose degree distribution follows a power law where a small number of nodes are hubs and a large number of nodes are non-hubs. However, from normal to cancer, the process of the network losing connectivity might be the process of disrupting the scale-free structure of the network, namely, the number of hub genes might be altered in cancer compared to that in normal samples. Hence, it is hypothesized that if the number of hub genes is different in a pathway between normal and cancer, this pathway might be involved in cancer. MiR2Pathway focuses on quantifying the differential effects of miRNAs on the activity of a biological pathway when miRNA-mRNA connections are altered from normal to disease and rank disease risk of rewired miRNA-mediated biological pathways. This dissertation explores how rewired gene-gene interactions and rewired miRNA-mRNA interactions lead to aberrant activity of biological pathways, and rank pathways for their disease risk. The two methods proposed here can be used to complement existing genomics analysis methods to facilitate the study of biological mechanisms behind disease at the systems-level.
This dissertation proposes two PageRank-based analytical methods, Pathways of Topological Rank Analysis (PoTRA) and miR2Pathway, discussed in Chapter 1 and Chapter 2, respectively. PoTRA focuses on detecting pathways with an altered number of hub genes in corresponding pathways between two phenotypes. The basis for PoTRA is that the loss of connectivity is a common topological trait of cancer networks, as well as the prior knowledge that a normal biological network is a scale-free network whose degree distribution follows a power law where a small number of nodes are hubs and a large number of nodes are non-hubs. However, from normal to cancer, the process of the network losing connectivity might be the process of disrupting the scale-free structure of the network, namely, the number of hub genes might be altered in cancer compared to that in normal samples. Hence, it is hypothesized that if the number of hub genes is different in a pathway between normal and cancer, this pathway might be involved in cancer. MiR2Pathway focuses on quantifying the differential effects of miRNAs on the activity of a biological pathway when miRNA-mRNA connections are altered from normal to disease and rank disease risk of rewired miRNA-mediated biological pathways. This dissertation explores how rewired gene-gene interactions and rewired miRNA-mRNA interactions lead to aberrant activity of biological pathways, and rank pathways for their disease risk. The two methods proposed here can be used to complement existing genomics analysis methods to facilitate the study of biological mechanisms behind disease at the systems-level.
ContributorsLi, Chaoxing (Author) / Dinu, Valentin (Thesis advisor) / Kuang, Yang (Thesis advisor) / Liu, Li (Committee member) / Wang, Xiao (Committee member) / Arizona State University (Publisher)
Created2017
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
Description
Dengue is a mosquito-borne arboviral disease that causes significant public health burden in many trophical and sub-tropical parts of the world (where dengue is endemic). This dissertation is based on using mathematical modeling approaches, coupled with rigorous analysis and computation, to study the transmission dynamics and control of dengue disease. In Chapter 2, a new deterministic model was designed and used to assess the impact of local fluctuation of temperature and mosquito vertical (transvasorial) transmission on the population abundance of dengue mosquitoes and disease in a population. The model, which takes the form of a deterministic system of nonlinear differential equations, was parametrized using data from the Chiang Mai province of Thailand. The disease-free equilibrium of the model was shown to be globally-asymptotically stable when a certain epidemiological quantity is less than unity. Vertical transmission was shown to only have marginal impact on the disease dynamics, and its effect is temperature-dependent. Dengue burden in the province is maximized when the mean monthly temperature lie in the range [26-28] C. A new deterministic model was designed in Chapter 3 to assess the impact of the release of Wolbachia-infected mosquitoes on curtailing the mosquito population and dengue disease in a population. The model, which stratifies the mosquito population in terms of sex and Wolbachia-infection status, was rigorously analysed to characterize the bifurcation property of the model as well as the asymptotic stability of the various disease-free equilibria. Simulations, using Wolbachia-based mosquito control from Queensland, Australia, showed that the frequent release of mosquitoes infected with the bacterium can lead to the effective control of the local wild mosquito population, and that such effective control increases with increasing number of Wolbachia-infected mosquitoes released (up to 90% reduction in the wild mosquito population, from their baseline values, can be achieved). It was also shown that the well-known feature of cytoplasmic incompatibility has very little effect on the effectiveness of the Wolbachia-based mosquito control.
ContributorsTaghikhani, Rahim (Author) / Gumel, Abba (Thesis advisor) / Crook, Sharon (Committee member) / Espanol, Malena (Committee member) / Kuang, Yang (Committee member) / Scotch, Matthew (Committee member) / Arizona State University (Publisher)
Created2020
Description
This thesis introduces new techniques for clustering distributional data according to their geometric similarities. This work builds upon the optimal transportation (OT) problem that seeks global minimum cost for matching distributional data and leverages the connection between OT and power diagrams to solve different clustering problems. The OT formulation is based on the variational principle to differentiate hard cluster assignments, which was missing in the literature. This thesis shows multiple techniques to regularize and generalize OT to cope with various tasks including clustering, aligning, and interpolating distributional data. It also discusses the connections of the new formulation to other OT and clustering formulations to better understand their gaps and the means to close them. Finally, this thesis demonstrates the advantages of the proposed OT techniques in solving machine learning problems and their downstream applications in computer graphics, computer vision, and image processing.
ContributorsMi, Liang (Author) / Wang, Yalin (Thesis advisor) / Chen, Kewei (Committee member) / Karam, Lina (Committee member) / Li, Baoxin (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2020
Description
The analysis focuses on a two-population, three-dimensional model that attempts to accurately model the growth and diffusion of glioblastoma multiforme (GBM), a highly invasive brain cancer, throughout the brain. Analysis into the sensitivity of the model to
changes in the diffusion, growth, and death parameters was performed, in order to find a set of parameter values that accurately model observed tumor growth for a given patient. Additional changes were made to the diffusion parameters to account for the arrangement of nerve tracts in the brain, resulting in varying rates of diffusion. In general, small changes in the growth rates had a large impact on the outcome of the simulations, and for each patient there exists a set of parameters that allow the model to simulate a tumor that matches observed tumor growth in the patient over a period of two or three months. Furthermore, these results are more accurate with anisotropic diffusion, rather than isotropic diffusion. However, these parameters lead to inaccurate results for patients with tumors that undergo no observable growth over the given time interval. While it is possible to simulate long-term tumor growth, the simulation requires multiple comparisons to available MRI scans in order to find a set of parameters that provide an accurate prognosis.
changes in the diffusion, growth, and death parameters was performed, in order to find a set of parameter values that accurately model observed tumor growth for a given patient. Additional changes were made to the diffusion parameters to account for the arrangement of nerve tracts in the brain, resulting in varying rates of diffusion. In general, small changes in the growth rates had a large impact on the outcome of the simulations, and for each patient there exists a set of parameters that allow the model to simulate a tumor that matches observed tumor growth in the patient over a period of two or three months. Furthermore, these results are more accurate with anisotropic diffusion, rather than isotropic diffusion. However, these parameters lead to inaccurate results for patients with tumors that undergo no observable growth over the given time interval. While it is possible to simulate long-term tumor growth, the simulation requires multiple comparisons to available MRI scans in order to find a set of parameters that provide an accurate prognosis.
ContributorsTrent, Austin Lee (Author) / Kostelich, Eric (Thesis advisor) / Gumel, Abba (Committee member) / Kuang, Yang (Committee member) / Arizona State University (Publisher)
Created2020
Description
Mosquitoes are the greatest killers of mankind, and diseases caused by mosquitoes continue to induce major public health and socio-economic burden in many parts of the world (notably in the tropical sub-regions). This dissertation contributes in providing deeper qualitative insights into the transmission dynamics and control of some mosquito-borne diseases of major public health significance, such as malaria and dengue. The widespread use of chemical insecticides, in the form of long-lasting insecticidal nets (LLINs) and indoor residual spraying, has led to a dramatic decline in malaria burden in endemic areas for the period 2000-2015. This prompted a concerted global effort aiming for malaria eradication by 2040. Unfortunately, the gains recorded are threatened (or not sustainable) due to it Anopheles resistance to all the chemicals embedded in the existing insecticides. This dissertation addresses the all-important question of whether or not malaria eradication can indeed be achieved using insecticides-based control. A novel mathematical model, which incorporates the detailed Anopheles lifecycle and local temperature fluctuations, was designed to address this question. Rigorous analysis of the model, together with numerical simulations using relevant data from endemic areas, show that malaria elimination in meso- and holo-endemic areas is feasible using moderate coverage of moderately-effective and high coverage of highly-effective LLINs, respectively. Biological controls, such as the use of sterile insect technology, have also been advocated as vital for the malaria eradication effort. A new model was developed to determine whether the release of sterile male mosquitoes into the population of wild adult female Anopheles mosquito could lead to a significant reduction (or elimination) of the wild adult female mosquito population. It is shown that the frequent release of a large number of sterile male mosquitoes, over a one year period, could lead to the effective control of the targeted mosquito population. Finally, a new model was designed and used to study the transmission dynamics of dengue serotypes in a population where the Dengvaxia vaccine is used. It is shown that using of the vaccine in dengue-naive populations may induce increased risk of severe disease in these populations.
ContributorsIboi, Enahoro Amos (Author) / Gumel, Abba B. (Thesis advisor) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Kang, Yun (Committee member) / Paaijmans, Krijn (Committee member) / Arizona State University (Publisher)
Created2020
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
Immunotherapy has received great attention recently, as it has become a powerful tool in fighting certain types of cancer. Immunotherapeutic drugs strengthen the immune system's natural ability to identify and eradicate cancer cells. This work focuses on immune checkpoint inhibitor and oncolytic virus therapies. Immune checkpoint inhibitors act as blocking mechanisms against the binding partner proteins, enabling T-cell activation and stimulation of the immune response. Oncolytic virus therapy utilizes genetically engineered viruses that kill cancer cells upon lysing. To elucidate the interactions between a growing tumor and the employed drugs, mathematical modeling has proven instrumental. This dissertation introduces and analyzes three different ordinary differential equation models to investigate tumor immunotherapy dynamics.
The first model considers a monotherapy employing the immune checkpoint inhibitor anti-PD-1. The dynamics both with and without anti-PD-1 are studied, and mathematical analysis is performed in the case when no anti-PD-1 is administrated. Simulations are carried out to explore the effects of continuous treatment versus intermittent treatment. The outcome of the simulations does not demonstrate elimination of the tumor, suggesting the need for a combination type of treatment.
An extension of the aforementioned model is deployed to investigate the pairing of an immune checkpoint inhibitor anti-PD-L1 with an immunostimulant NHS-muIL12. Additionally, a generic drug-free model is developed to explore the dynamics of both exponential and logistic tumor growth functions. Experimental data are used for model fitting and parameter estimation in the monotherapy cases. The model is utilized to predict the outcome of combination therapy, and reveals a synergistic effect: Compared to the monotherapy case, only one-third of the dosage can successfully control the tumor in the combination case.
Finally, the treatment impact of oncolytic virus therapy in a previously developed and fit model is explored. To determine if one can trust the predictive abilities of the model, a practical identifiability analysis is performed. Particularly, the profile likelihood curves demonstrate practical unidentifiability, when all parameters are simultaneously fit. This observation poses concerns about the predictive abilities of the model. Further investigation showed that if half of the model parameters can be measured through biological experimentation, practical identifiability is achieved.
The first model considers a monotherapy employing the immune checkpoint inhibitor anti-PD-1. The dynamics both with and without anti-PD-1 are studied, and mathematical analysis is performed in the case when no anti-PD-1 is administrated. Simulations are carried out to explore the effects of continuous treatment versus intermittent treatment. The outcome of the simulations does not demonstrate elimination of the tumor, suggesting the need for a combination type of treatment.
An extension of the aforementioned model is deployed to investigate the pairing of an immune checkpoint inhibitor anti-PD-L1 with an immunostimulant NHS-muIL12. Additionally, a generic drug-free model is developed to explore the dynamics of both exponential and logistic tumor growth functions. Experimental data are used for model fitting and parameter estimation in the monotherapy cases. The model is utilized to predict the outcome of combination therapy, and reveals a synergistic effect: Compared to the monotherapy case, only one-third of the dosage can successfully control the tumor in the combination case.
Finally, the treatment impact of oncolytic virus therapy in a previously developed and fit model is explored. To determine if one can trust the predictive abilities of the model, a practical identifiability analysis is performed. Particularly, the profile likelihood curves demonstrate practical unidentifiability, when all parameters are simultaneously fit. This observation poses concerns about the predictive abilities of the model. Further investigation showed that if half of the model parameters can be measured through biological experimentation, practical identifiability is achieved.
ContributorsNikolopoulou, Elpiniki (Author) / Kuang, Yang (Thesis advisor) / Gardner, Carl (Committee member) / Gevertz, Jana (Committee member) / Kang, Yun (Committee member) / Kostellich, Eric (Committee member) / Arizona State University (Publisher)
Created2020
Description
Cancer is a worldwide burden in every aspect: physically, emotionally, and financially. A need for innovation in cancer research has led to a vast interdisciplinary effort to search for the next breakthrough. Mathematical modeling allows for a unique look into the underlying cellular dynamics and allows for testing treatment strategies without the need for clinical trials. This dissertation explores several iterations of a dendritic cell (DC) therapy model and correspondingly investigates what each iteration teaches about response to treatment.
In Chapter 2, motivated by the work of de Pillis et al. (2013), a mathematical model employing six ordinary differential (ODEs) and delay differential equations (DDEs) is formulated to understand the effectiveness of DC vaccines, accounting for cell trafficking with a blood and tumor compartment. A preliminary analysis is performed, with numerical simulations used to show the existence of oscillatory behavior. The model is then reduced to a system of four ODEs. Both models are validated using experimental data from melanoma-induced mice. Conditions under which the model admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability, are established. Mathematical analysis proves the existence of a backward bifurcation and establishes thresholds for R0 that ensure tumor elimination or existence. A sensitivity analysis determines which parameters most significantly impact the reproduction number R0. Identifiability analysis reveals parameters of interest for estimation. Results are framed in terms of treatment implications, including effective combination and monotherapy strategies.
In Chapter 3, a study of whether the observed complexity can be represented with a simplified model is conducted. The DC model of Chapter 2 is reduced to a non-dimensional system of two DDEs. Mathematical and numerical analysis explore the impact of immune response time on the stability and eradication of the tumor, including an analytical proof of conditions necessary for the existence of a Hopf bifurcation. In a limiting case, conditions for global stability of the tumor-free equilibrium are outlined.
Lastly, Chapter 4 discusses future directions to explore. There still remain open questions to investigate and much work to be done, particularly involving uncertainty analysis. An outline of these steps is provided for future undertakings.
In Chapter 2, motivated by the work of de Pillis et al. (2013), a mathematical model employing six ordinary differential (ODEs) and delay differential equations (DDEs) is formulated to understand the effectiveness of DC vaccines, accounting for cell trafficking with a blood and tumor compartment. A preliminary analysis is performed, with numerical simulations used to show the existence of oscillatory behavior. The model is then reduced to a system of four ODEs. Both models are validated using experimental data from melanoma-induced mice. Conditions under which the model admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability, are established. Mathematical analysis proves the existence of a backward bifurcation and establishes thresholds for R0 that ensure tumor elimination or existence. A sensitivity analysis determines which parameters most significantly impact the reproduction number R0. Identifiability analysis reveals parameters of interest for estimation. Results are framed in terms of treatment implications, including effective combination and monotherapy strategies.
In Chapter 3, a study of whether the observed complexity can be represented with a simplified model is conducted. The DC model of Chapter 2 is reduced to a non-dimensional system of two DDEs. Mathematical and numerical analysis explore the impact of immune response time on the stability and eradication of the tumor, including an analytical proof of conditions necessary for the existence of a Hopf bifurcation. In a limiting case, conditions for global stability of the tumor-free equilibrium are outlined.
Lastly, Chapter 4 discusses future directions to explore. There still remain open questions to investigate and much work to be done, particularly involving uncertainty analysis. An outline of these steps is provided for future undertakings.
ContributorsDickman, Lauren (Author) / Kuang, Yang (Thesis advisor) / Baer, Steven M. (Committee member) / Gardner, Carl (Committee member) / Gumel, Abba B. (Committee member) / Kostelich, Eric J. (Committee member) / Arizona State University (Publisher)
Created2020
Description
Gompertz’s empirical equation remains the most popular one in describing cancer cell population growth in a wide spectrum of bio-medical situations due to its good fit to data and simplicity. Many efforts were documented in the literature aimed at understanding the mechanisms that may support Gompertz’s elegant model equation. One of the most convincing efforts was carried out by Gyllenberg and Webb. They divide the cancer cell population into the proliferative cells and the quiescent cells. In their two dimensional model, the dead cells are assumed to be removed from the tumor instantly. In this paper, we modify their model by keeping track of the dead cells remaining in the tumor. We perform mathematical and computational studies on this three dimensional model and compare the model dynamics to that of the model of Gyllenberg and Webb. Our mathematical findings suggest that if an avascular tumor grows according to our three-compartment model, then as the death rate of quiescent cells decreases to zero, the percentage of proliferative cells also approaches to zero. Moreover, a slow dying quiescent population will increase the size of the tumor. On the other hand, while the tumor size does not depend on the dead cell removal rate, its early and intermediate growth stages are very sensitive to it.
ContributorsAlzahrani, E. O. (Author) / Asiri, Asim (Author) / El-Dessoky, M. M. (Author) / Kuang, Yang (Author) / College of Liberal Arts and Sciences (Contributor)
Created2014-08-01