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Mathematical Models of Androgen Resistance in Prostate Cancer Patients under Intermittent Androgen Suppression Therapy

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…

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
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Statistical Properties of Coherent Structures in Two Dimensional Turbulence

Description
Coherent vortices are ubiquitous structures in natural flows that affect mixing and transport of substances and momentum/energy. Being able to detect these coherent structures is important for pollutant mitigation, ecological conservation and many other aspects. In recent years, mathematical criteria and algorithms have been developed to extract these coherent structures…

Coherent vortices are ubiquitous structures in natural flows that affect mixing and transport of substances and momentum/energy. Being able to detect these coherent structures is important for pollutant mitigation, ecological conservation and many other aspects. In recent years, mathematical criteria and algorithms have been developed to extract these coherent structures in turbulent flows. In this study, we will apply these tools to extract important coherent structures and analyze their statistical properties as well as their implications on kinematics and dynamics of the flow. Such information will aide representation of small-scale nonlinear processes that large-scale models of natural processes may not be able to resolve.
ContributorsCass, Brentlee Jerry (Author) / Tang, Wenbo (Thesis director) / Kostelich, Eric (Committee member) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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Initial experiment of Adaptive Therapy to control Breast Cancer

Description

Adaptive therapy utilizes competitive interactions between resistant and sensitive cells by keeping some sensitive cells to control tumor burden with the aim of increasing overall survival and time to progression. The use of adaptive therapy to treat breast cancer, ovarian cancer, and pancreatic cancer in preclinical models has shown significant…

Adaptive therapy utilizes competitive interactions between resistant and sensitive cells by keeping some sensitive cells to control tumor burden with the aim of increasing overall survival and time to progression. The use of adaptive therapy to treat breast cancer, ovarian cancer, and pancreatic cancer in preclinical models has shown significant results in controlling tumor growth. The purpose of this thesis is to draft a protocol to study adaptive therapy in a preclinical model of breast cancer on MCF7, estrogen receptor-positive, cells that have evolved resistance to fulvestrant and palbociclib (MCF7 R). In this study, we used two protocols: drug dose adjustment and intermittent therapy. The MCF7 R cell lines were injected into the mammary fat pads of 11-month-old NOD/SCID gamma (NSG) mice (18 mice) which were then treated with gemcitabine.<br/>The results of this experiment did not provide complete information because of the short-term treatments. In addition, we saw an increase in the tumor size of a few of the treated mice, which could be due to the metabolism of the drug at that age, or because of the difference in injection times. Therefore, these adaptive therapy protocols on hormone-refractory breast cancer cell lines will be repeated on young, 6-week old mice by injecting the cell lines at the same time for all mice, which helps the results to be more consistent and accurate.
ContributorsConti, Aviona (Author) / Maley, Carlo (Thesis director) / Blattman, Joseph (Committee member) / Seyedi, Sareh (Committee member) / School of Life Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Drug Modeling Dynamics in the Treatment of Prostate Cancer

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…

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.
ContributorsReckell, Trevor (Author) / Kostelich, Eric (Thesis advisor) / Kuang, Yang (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2020