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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

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
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2D fetal echocardiography (ECHO) can be used for monitoring heart development in utero. This study’s purpose is to empirically model normal fetal heart growth and function changes during development by ECHO and compare these to fetuses diagnosed with and without cardiomyopathy with diabetic mothers. There are existing mathematical models describing

2D fetal echocardiography (ECHO) can be used for monitoring heart development in utero. This study’s purpose is to empirically model normal fetal heart growth and function changes during development by ECHO and compare these to fetuses diagnosed with and without cardiomyopathy with diabetic mothers. There are existing mathematical models describing fetal heart development but they warrant revalidation and adjustment. 377 normal fetuses with healthy mothers, 98 normal fetuses with diabetic mothers, and 37 fetuses with cardiomyopathy and diabetic mothers had their cardiac structural dimensions, cardiothoracic ratio, valve flow velocities, and heart rates measured by fetal ECHO in a retrospective chart review. Cardiac features were fitted to linear functions, with respect to gestational age, femur length, head circumference, and biparietal diameter and z-scores were created to model normal fetal growth for all parameters. These z-scores were used to assess what metrics had no difference in means between the normal fetuses of both healthy and diabetic mothers but differed from those diagnosed with cardiomyopathy. It was found that functional metrics like mitral and tricuspid E wave and pulmonary velocity could be important predictors for cardiomyopathy when fitted by gestational age, femur length, head circumference, and biparietal diameter. Additionally, aortic and tricuspid annulus diameters when fitted to estimated gestational age showed potential to be predictors for fetal cardiomyopathy. While the metrics overlapped over their full range, combining them together may have the potential for predicting cardiomyopathy in utero. Future directions of this study will explore creating a classifier model that can predict cardiomyopathy using the metrics assessed in this study.

ContributorsMishra, Shambhavi (Co-author) / Numani, Asfia (Co-author) / Sweazea, Karen (Thesis director) / Plasencia, Jonathan (Committee member) / Economics Program in CLAS (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05