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- All Subjects: Cancer
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
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
Mr. Green has stage 4 prostate cancer which has spread to the bones and liver and has become resistant to radiation and standard chemotherapy treatment. After 3 rounds of chemotherapy, his primary oncologist recommends that he participate in a clinical trial. He went to Dr. Red at the Saguaro Clinic after reading on the internet about a new Phase 1 clinical trial that the clinic is hosting, which is designed to target a specific receptor called AB-111 that may be present in malignant prostate, cervical, ovarian, and breast cells. After signing consent and completing the blood screens in the morning at the clinic, Mr. Green is told his liver enzymes are too high and the ranges specified in the protocol prohibit him from enrolling. Mr. Green is noticeably affected and distressed at this news, and Dr. Red recommends end-of-life care. Behind the scenes, this event is noted on official medical documents and trial study rosters as a "screen fail." This narrative, while fictional, is realistic because similar events occur in cancer clinical trial sites on a regular basis. I look at the inner "world" and mental journey of possible clinical trial candidates as they seek out information about clinical trials and gain understanding of their function \u2014 specifically in the context of Phase 1 cancer clinical trials. To whom is the language of the term "screen failure" useful? How does excluding individuals from clinical trials protect their health and does the integrity of the trial data supersede the person's curative goals? What is the message that cancer patients (potential research subjects) receive regarding clinical trials from sources outside their oncologists?
ContributorsMcKane, Alexandra (Author) / Maienschein, Jane (Thesis director) / Ellison, Karin (Committee member) / Foy, Joseph (Committee member) / Barrett, The Honors College (Contributor)
Created2013-12
Description
The interaction between England and Scotland is complicated and continually changing. Scottish writer Sir Walter Scott examines this long-standing relationship through his various writings. Scott conveys a presence that is both acutely aware of the damages enacted upon Scotland by various English political efforts, and sensitive to the delicate relationship that the two regions had begun to form during his lifetime. Through a critical analysis of Scott's novel, Rob Roy, one can see the various strategies Scott used to balance the need to address prior controversies within the relationship, and the petition to move beyond the prior conflict and develop a mutual understanding of each culture. Through this, Scott is able to regenerate a sense of Scottish nationalism for his people, and encourage improved relations within the British Isles.
ContributorsChotena, Chelsea (Author) / Facinelli, Diane (Thesis director) / Foy, Joseph (Committee member) / White, Julianne (Committee member) / Barrett, The Honors College (Contributor)
Created2013-05
Description
Glioblastoma Multiforme (GBM) is an aggressive and deadly form of brain cancer with a median survival time of about a year with treatment. Due to the aggressive nature of these tumors and the tendency of gliomas to follow white matter tracks in the brain, each tumor mass has a unique growth pattern. Consequently it is difficult for neurosurgeons to anticipate where the tumor will spread in the brain, making treatment planning difficult. Archival patient data including MRI scans depicting the progress of tumors have been helpful in developing a model to predict Glioblastoma proliferation, but limited scans per patient make the tumor growth rate difficult to determine. Furthermore, patient treatment between scan points can significantly compound the challenge of accurately predicting the tumor growth. A partnership with Barrow Neurological Institute has allowed murine studies to be conducted in order to closely observe tumor growth and potentially improve the current model to more closely resemble intermittent stages of GBM growth without treatment effects.
ContributorsSnyder, Lena Haley (Author) / Kostelich, Eric (Thesis director) / Frakes, David (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05
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
My mother died after a long battle with breast cancer in 2008. I was only nine when she was first diagnosed, and so much of my life has been shaped by her struggle for survival. She will always be the most amazing women I have ever known, and she taught me more about life, kindness, hope, and overcoming the odds than anyone else. I want to share my experience with you as a friend \u2014 not as a doctor, or a counselor, but as a friend. I want to tell you some of my stories with the emotions behind them. I will share how I learned t cope with whatever situation came our way and how I found unexpected ways to help my mom. I want you to find solace through our shared emotions even if they are at different times in our journeys. This is why in the following chapters, my stories are not chronological but categorized through the major emotions that drove my stories. I hope this book can help those who find themselves in similar situations to the one I found myself in when my mom picked me up from fourth grade with a bandana on her head instead of her normal, beautiful brown hair. This thesis is a creative exploration of emotions and finding hope in times of great loss.
ContributorsTornabene, Kathleen Elizabeth (Author) / Foy, Joseph (Thesis director) / Facinelli, Diane (Committee member) / Hyde, Suzanne (Committee member) / Barrett, The Honors College (Contributor)
Created2012-05
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
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
This paper examines the physics behind cancer treatment and more specifically radiation therapy. A phenomenon known as Compton scattering has played a substantial role in the treatment of breast cancer and improvement of lives of women around the world. Through Compton scattering, radiation therapy has been tremendously improved and has allowed for the most accurate and effective treatment in breast cancer patients today.
ContributorsRombaoa, Matthew Bryce (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Barrett, The Honors College (Contributor) / School of Molecular Sciences (Contributor) / Department of Psychology (Contributor)
Created2023-05