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- All Subjects: Cancer
- Creators: Kostelich, Eric
Lithium ion batteries are quintessential components of modern life. They are used to power smart devices — phones, tablets, laptops, and are rapidly becoming major elements in the automotive industry. Demand projections for lithium are skyrocketing with production struggling to keep up pace. This drive is due mostly to the rapid adoption of electric vehicles; sales of electric vehicles in 2020 are more than double what they were only a year prior. With such staggering growth it is important to understand how lithium is sourced and what that means for the environment. Will production even be capable of meeting the demand as more industries make use of this valuable element? How will the environmental impact of lithium affect growth? This thesis attempts to answer these questions as the world looks to a decade of rapid growth for lithium ion batteries.
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.
The purpose of this project is to analyze the current state of cancer nanomedicine and its challenges. Cancer is the second most deadly illness in the United States after heart disease. Nanomedicine, the use of materials between 1 and 100 nm to for the purpose of addressing healthcare-related problems, is particularly suited for treating it since nanoparticles have properties such as high surface area-to-volume ratios and favorable drug release profiles that make them more suitable for tasks such as consistent drug delivery to tumor tissue. The questions posed are: What are the current nanomedical treatments for cancer? What are the technical, social, and legal challenges related to nanomedical treatments and how can they be overcome? To answer the questions mentioned above, information from several scientific papers on nanomedical treatments for cancer as well as from social science journals was synthesized. Based on the findings, nanomedicine has a wide range of applications for cancer drug delivery, detection, and immunotherapy. The main technical challenge related to nanomedical treatments is navigating through biological barriers such as the mononuclear phagocyte system, the kidney, the blood-brain barrier, and the tumor microenvironment. Current approaches to meeting this challenge include altering the size, shape, and charge of nanoparticles for easier passage. The main social and legal challenge related to nanomedical treatments is the difficulty of regulating them due to factors such as the near impossibility of detecting nanowaste. Current approaches to meeting this challenge include the use of techniques such as scanning tunneling microscopy and atomic force microscopy to help distinguish nanowaste from the surroundings. More research will have to be done in these and other areas to enhance a major cancer-fighting tool.
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.