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- All Subjects: Anisotropy
- Creators: Desch, Steven J
Description
There are many lines of evidence for anisotropy at all scales in the explosions of core collapse supernovae, e.g. visual inspection of the images of resolved supernova remnants, polarization measurements, velocity profiles, "natal kicks" of neutron stars, or spectroscopic observations of different regions of remnants. Theoretical stability considerations and detailed numerical simulations have shown that Rayleigh-Taylor (RT) instabilities arise in the star after the explosion, which leads to the early fragmentation of parts of the ejecta. The clumps thus created are of interest to a variety of topics, one of them being the formation environment of the solar system. There is a high probability that the solar system formed in the vicinity of a massive star that, shortly after its formation, exploded as a core collapse supernova. As argued in this thesis as well as other works, a core collapse supernova generally is a good candidate for chemically enriching the forming solar system with material. As forming proto--planetary systems in general have a high probability of being contaminated with supernova material, a method was developed for detecting tracer elements indicative supernova contamination in proto--planetary systems.The degree of the anisotropy of the supernova explosion can have dramatic effects on the mode of delivery of that material to the solar system, or proto--planetary systems in general. Thus it is of particular interest to be able to predict the structure of the supernova ejecta. Numerical simulations of the explosions of core collapse supernovae were done in 3 dimensions in order to study the formation of structure. It is found that RT instabilities result in clumps in the He- and C+O rich regions in the exploding star that are overdense by 1-2 orders of magnitude. These clumps are potential candidates for enriching the solar system with material. In the course of the further evolution of the supernova remnant, these RT clumps are likely to evolve into ejecta knots of the type observed in the Cassiopeia A supernova remnant.
ContributorsEllinger, Carola I (Author) / Young, Patrick A (Thesis advisor) / Desch, Steven J (Committee member) / Timmes, Francis (Committee member) / Scannapieco, Evan (Committee member) / Lunardini, Cecilia (Committee member) / Arizona State University (Publisher)
Created2011
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