Matching Items (13)
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- All Subjects: Cancer
- Creators: School of Mathematical and Statistical Sciences
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
The detection and characterization of transients in signals is important in many wide-ranging applications from computer vision to audio processing. Edge detection on images is typically realized using small, local, discrete convolution kernels, but this is not possible when samples are measured directly in the frequency domain. The concentration factor edge detection method was therefore developed to realize an edge detector directly from spectral data. This thesis explores the possibilities of detecting edges from the phase of the spectral data, that is, without the magnitude of the sampled spectral data. Prior work has demonstrated that the spectral phase contains particularly important information about underlying features in a signal. Furthermore, the concentration factor method yields some insight into the detection of edges in spectral phase data. An iterative design approach was taken to realize an edge detector using only the spectral phase data, also allowing for the design of an edge detector when phase data are intermittent or corrupted. Problem formulations showing the power of the design approach are given throughout. A post-processing scheme relying on the difference of multiple edge approximations yields a strong edge detector which is shown to be resilient under noisy, intermittent phase data. Lastly, a thresholding technique is applied to give an explicit enhanced edge detector ready to be used. Examples throughout are demonstrate both on signals and images.
ContributorsReynolds, Alexander Bryce (Author) / Gelb, Anne (Thesis director) / Cochran, Douglas (Committee member) / Viswanathan, Adityavikram (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Despite the 40-year war on cancer, very limited progress has been made in developing a cure for the disease. This failure has prompted the reevaluation of the causes and development of cancer. One resulting model, coined the atavistic model of cancer, posits that cancer is a default phenotype of the cells of multicellular organisms which arises when the cell is subjected to an unusual amount of stress. Since this default phenotype is similar across cell types and even organisms, it seems it must be an evolutionarily ancestral phenotype. We take a phylostratigraphical approach, but systematically add species divergence time data to estimate gene ages numerically and use these ages to investigate the ages of genes involved in cancer. We find that ancient disease-recessive cancer genes are significantly enriched for DNA repair and SOS activity, which seems to imply that a core component of cancer development is not the regulation of growth, but the regulation of mutation. Verification of this finding could drastically improve cancer treatment and prevention.
ContributorsOrr, Adam James (Author) / Davies, Paul (Thesis director) / Bussey, Kimberly (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor) / School of Life Sciences (Contributor)
Created2015-05
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
In many systems, it is difficult or impossible to measure the phase of a signal. Direct recovery from magnitude is an ill-posed problem. Nevertheless, with a sufficiently large set of magnitude measurements, it is often possible to reconstruct the original signal using algorithms that implicitly impose regularization conditions on this ill-posed problem. Two such algorithms were examined: alternating projections, utilizing iterative Fourier transforms with manipulations performed in each domain on every iteration, and phase lifting, converting the problem to that of trace minimization, allowing for the use of convex optimization algorithms to perform the signal recovery. These recovery algorithms were compared on a basis of robustness as a function of signal-to-noise ratio. A second problem examined was that of unimodular polyphase radar waveform design. Under a finite signal energy constraint, the maximal energy return of a scene operator is obtained by transmitting the eigenvector of the scene Gramian associated with the largest eigenvalue. It is shown that if instead the problem is considered under a power constraint, a unimodular signal can be constructed starting from such an eigenvector that will have a greater return.
ContributorsJones, Scott Robert (Author) / Cochran, Douglas (Thesis director) / Diaz, Rodolfo (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Passive radar can be used to reduce the demand for radio frequency spectrum bandwidth. This paper will explain how a MATLAB simulation tool was developed to analyze the feasibility of using passive radar with digitally modulated communication signals. The first stage of the simulation creates a binary phase-shift keying (BPSK) signal, quadrature phase-shift keying (QPSK) signal, or digital terrestrial television (DTTV) signal. A scenario is then created using user defined parameters that simulates reception of the original signal on two different channels, a reference channel and a surveillance channel. The signal on the surveillance channel is delayed and Doppler shifted according to a point target scattering profile. An ambiguity function detector is implemented to identify the time delays and Doppler shifts associated with reflections off of the targets created. The results of an example are included in this report to demonstrate the simulation capabilities.
ContributorsScarborough, Gillian Donnelly (Author) / Cochran, Douglas (Thesis director) / Berisha, Visar (Committee member) / Wang, Chao (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
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
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 rates vary between people, between cultures, and between tissue types, driven by clinically relevant distinctions in the risk factors that lead to different cancer types. Despite the importance of cancer location in human health, little is known about tissue-specific cancers in non-human animals. We can gain significant insight into how evolutionary history has shaped mechanisms of cancer suppression by examining how life history traits impact cancer susceptibility across species. Here, we perform multi-level analysis to test how species-level life history strategies are associated with differences in neoplasia prevalence, and apply this to mammary neoplasia within mammals. We propose that the same patterns of cancer prevalence that have been reported across species will be maintained at the tissue-specific level. We used a combination of factor analysis and phylogenetic regression on 13 life history traits across 90 mammalian species to determine the correlation between a life history trait and how it relates to mammary neoplasia prevalence. The factor analysis presented ways to calculate quantifiable underlying factors that contribute to covariance of entangled life history variables. A greater risk of mammary neoplasia was found to be correlated most significantly with shorter gestation length. With this analysis, a framework is provided for how different life history modalities can influence cancer vulnerability. Additionally, statistical methods developed for this project present a framework for future comparative oncology studies and have the potential for many diverse applications.
ContributorsFox, Morgan Shane (Author) / Maley, Carlo C. (Thesis director) / Boddy, Amy (Committee member) / Compton, Zachary (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Molecular Sciences (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The use of conventional weather radar in vulcanology leads to two problems: the radars often use wavelengths which are too long to detect the fine ash particles, and they cannot be field–adjusted to fit the wide variety of eruptions. Thus, to better study these geologic processes, a new radar must be developed that is easily reconfigurable to allow for flexibility and can operate at sufficiently short wavelengths.
This thesis investigates how to design a radar using a field–programmable gate array board to generate the radar signal, and process the returned signal to determine the distance and concentration of objects (in this case, ash). The purpose of using such a board lies in its reconfigurability—a design can (relatively easily) be adjusted, recompiled, and reuploaded to the hardware with none of the cost or time overhead required of a standard weather radar.
The design operates on the principle of frequency–modulated continuous–waves, in which the output signal frequency changes as a function of time. The difference in transmit and echo frequencies determines the distance of an object, while the magnitude of a particular difference frequency corresponds to concentration. Thus, by viewing a spectrum of frequency differences, one is able to see both the concentration and distances of ash from the radar.
The transmit signal data was created in MATLAB®, while the radar was designed with MATLAB® Simulink® using hardware IP blocks and implemented on the ROACH2 signal processing hardware, which utilizes a Xilinx® Virtex®–6 chip. The output is read from a computer linked to the hardware through Ethernet, using a Python™ script. Testing revealed minor flaws due to the usage of lower–grade components in the prototype. However, the functionality of the proposed radar design was proven, making this approach to radar a promising path for modern vulcanology.
This thesis investigates how to design a radar using a field–programmable gate array board to generate the radar signal, and process the returned signal to determine the distance and concentration of objects (in this case, ash). The purpose of using such a board lies in its reconfigurability—a design can (relatively easily) be adjusted, recompiled, and reuploaded to the hardware with none of the cost or time overhead required of a standard weather radar.
The design operates on the principle of frequency–modulated continuous–waves, in which the output signal frequency changes as a function of time. The difference in transmit and echo frequencies determines the distance of an object, while the magnitude of a particular difference frequency corresponds to concentration. Thus, by viewing a spectrum of frequency differences, one is able to see both the concentration and distances of ash from the radar.
The transmit signal data was created in MATLAB®, while the radar was designed with MATLAB® Simulink® using hardware IP blocks and implemented on the ROACH2 signal processing hardware, which utilizes a Xilinx® Virtex®–6 chip. The output is read from a computer linked to the hardware through Ethernet, using a Python™ script. Testing revealed minor flaws due to the usage of lower–grade components in the prototype. However, the functionality of the proposed radar design was proven, making this approach to radar a promising path for modern vulcanology.
ContributorsXi, Andrew Jinchi (Co-author) / Lee, Matthew Byeongmok (Co-author) / Groppi, Christopher (Thesis director) / Mauskopf, Philip (Committee member) / Cochran, Douglas (Committee member) / Baumann, Alicia (Committee member) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05