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- Creators: School of Mathematical and Statistical Sciences
- Creators: Department of Psychology
- Status: Published
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
Background: Noninvasive MRI methods that can accurately detect subtle brain changes are highly desirable when studying disease-modifying interventions. Texture analysis is a novel imaging technique which utilizes the extraction of a large number of image features with high specificity and predictive power. In this investigation, we use texture analysis to assess and classify age-related changes in the right and left hippocampal regions, the areas known to show some of the earliest change in Alzheimer's disease (AD). Apolipoprotein E (APOE)'s e4 allele confers an increased risk for AD, so studying differences in APOE e4 carriers may help to ascertain subtle brain changes before there has been an obvious change in behavior. We examined texture analysis measures that predict age-related changes, which reflect atrophy in a group of cognitively normal individuals. We hypothesized that the APOE e4 carriers would exhibit significant age-related differences in texture features compared to non-carriers, so that the predictive texture features hold promise for early assessment of AD. Methods: 120 normal adults between the ages of 32 and 90 were recruited for this neuroimaging study from a larger parent study at Mayo Clinic Arizona studying longitudinal cognitive functioning (Caselli et al., 2009). As part of the parent study, the participants were genotyped for APOE genetic polymorphisms and received comprehensive cognitive testing every two years, on average. Neuroimaging was done at Barrow Neurological Institute and a 3D T1-weighted magnetic resonance image was obtained during scanning that allowed for subsequent texture analysis processing. Voxel-based features of the appearance, structure, and arrangement of these regions of interest were extracted utilizing the Mayo Clinic Python Texture Analysis Pipeline (pyTAP). Algorithms applied in feature extraction included Grey-Level Co-Occurrence Matrix (GLCM), Gabor Filter Banks (GFB), Local Binary Patterns (LBP), Discrete Orthogonal Stockwell Transform (DOST), and Laplacian-of-Gaussian Histograms (LoGH). Principal component (PC) analysis was used to reduce the dimensionality of the algorithmically selected features to 13 PCs. A stepwise forward regression model was used to determine the effect of APOE status (APOE e4 carriers vs. noncarriers), and the texture feature principal components on age (as a continuous variable). After identification of 5 significant predictors of age in the model, the individual feature coefficients of those principal components were examined to determine which features contributed most significantly to the prediction of an aging brain. Results: 70 texture features were extracted for the two regions of interest in each participant's scan. The texture features were coded as 70 initial components andwere rotated to generate 13 principal components (PC) that contributed 75% of the variance in the dataset by scree plot analysis. The forward stepwise regression model used in this exploratory study significantly predicted age, accounting for approximately 40% of the variance in the data. The regression model revealed 5 significant regressors (2 right PC's, APOE status, and 2 left PC by APOE interactions). Finally, the specific texture features that contributed to each significant PCs were identified. Conclusion: Analysis of image texture features resulted in a statistical model that was able to detect subtle changes in brain integrity associated with age in a group of participants who are cognitively normal, but have an increased risk of developing AD based on the presence of the APOE e4 phenotype. This is an important finding, given that detecting subtle changes in regions vulnerable to the effects of AD in patients could allow certain texture features to serve as noninvasive, sensitive biomarkers predictive of AD. Even with only a small number of patients, the ability for us to determine sensitive imaging biomarkers could facilitate great improvement in speed of detection and effectiveness of AD interventions..
ContributorsSilva, Annelise Michelle (Author) / Baxter, Leslie (Thesis director) / McBeath, Michael (Committee member) / Presson, Clark (Committee member) / School of Life Sciences (Contributor) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The reconstruction of piecewise smooth functions from non-uniform Fourier data arises in sensing applications such as magnetic resonance imaging (MRI). This thesis presents a new polynomial based resampling method (PRM) for 1-dimensional problems which uses edge information to recover the Fourier transform at its integer coefficients, thereby enabling the use of the inverse fast Fourier transform algorithm. By minimizing the error of the PRM approximation at the sampled Fourier modes, the PRM can also be used to improve on initial edge location estimates. Numerical examples show that using the PRM to improve on initial edge location estimates and then taking of the PRM approximation of the integer frequency Fourier coefficients is a viable way to reconstruct the underlying function in one dimension. In particular, the PRM is shown to converge more quickly and to be more robust than current resampling techniques used in MRI, and is particularly amenable to highly irregular sampling patterns.
ContributorsGutierrez, Alexander Jay (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Viswanathan, Adityavikram (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
Description
The objective of the research presented here was to validate the use of kinetic models for the analysis of the dynamic behavior of a contrast agent in tumor tissue and evaluate the utility of such models in determining kinetic properties - in particular perfusion and molecular binding uptake associated with tissue hypoxia - of the imaged tissue, from concentration data acquired with dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) procedure. Data from two separate DCE-MRI experiments, performed in the past, using a standard contrast agent and a hypoxia-binding agent respectively, were analyzed. The results of the analysis demonstrated that the models used may provide novel characterization of the tumor tissue properties. Future research will work to further characterize the physical significance of the estimated parameters, particularly to provide quantitative oxygenation data for the imaged tissue.
ContributorsMartin, Jonathan Michael (Author) / Kodibagkar, Vikram (Thesis director) / Rege, Kaushal (Committee member) / Barrett, The Honors College (Contributor) / Chemical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-12
Description
In applications such as Magnetic Resonance Imaging (MRI), data are acquired as Fourier samples. Since the underlying images are only piecewise smooth, standard recon- struction techniques will yield the Gibbs phenomenon, which can lead to misdiagnosis. Although filtering will reduce the oscillations at jump locations, it can often have the adverse effect of blurring at these critical junctures, which can also lead to misdiagno- sis. Incorporating prior information into reconstruction methods can help reconstruct a sharper solution. For example, compressed sensing (CS) algorithms exploit the expected sparsity of some features of the image. In this thesis, we develop a method to exploit the sparsity in the edges of the underlying image. We design a convex optimization problem that exploits this sparsity to provide an approximation of the underlying image. Our method successfully reduces the Gibbs phenomenon with only minimal "blurring" at the discontinuities. In addition, we see a high rate of convergence in smooth regions.
ContributorsWasserman, Gabriel Kanter (Author) / Gelb, Anne (Thesis director) / Cochran, Doug (Committee member) / Archibald, Rick (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Smart contrast agents allow for noninvasive study of specific events or tissue conditions inside of a patient's body using Magnetic Resonance Imaging (MRI). This research aims to develop and characterize novel smart contrast agents for MRI that respond to temperature changes in tissue microenvironments. Transmission Electron Microscopy, Nuclear Magnetic Resonance, and cell culture growth assays were used to characterize the physical, magnetic, and cytotoxic properties of candidate nanoprobes. The nanoprobes displayed thermosensitve MR properties with decreasing relaxivity with temperature. Future work will be focused on generating and characterizing photo-active analogues of the nanoprobes that could be used for both treatment of tissues and assessment of therapy.
ContributorsHussain, Khateeb Hyder (Author) / Kodibagkar, Vikram (Thesis director) / Stabenfeldt, Sarah (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering 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
Abstract The BIO 189 Life Sciences Career Paths course is a seminar course that is intended to acclimate incoming freshmen into the School of Life Sciences (SOLS). While there are instructors who organize and present in the class, upper division undergraduate students are primarily responsible for facilitating lectures and discussions and mentoring the freshmen. Prior research has demonstrated that the mentor-mentee relationship is a very important predictor of success and retention within all university first-year programs. While past studies focused on the student mentor-mentee relationships, there is limited research that measures student satisfaction within freshmen seminar courses, especially in areas of science, technology, engineering, and mathematics (STEM). The purpose of this project is to survey students about their perception of the BIO 189 course. The effort of the project is on pre-health students, as they initiate their undergraduate careers and attempt to achieve acceptance into professional school four years later. Analysis of Likert scale surveys distributed to 561 freshmen revealed that students with an emphasis on "medicine" in their majors preferred a BIO 189 course geared to pre-health interests whereas students seeking an emphasis on research (ecology and cell biology/genetics) sought a BIO 189 course focused on internship and employment opportunities. Assessment of the mentor-mentee relationship revealed that students (n = 561) preferred one-on-one meetings with mentors outside of class (44%) compared to those who preferred interaction in class (30%). A sizable 61.68% of students (n = 548) were most concerned with attaining favorable GPAs, highlighting strong emphasis on academic performance. Overall, 61% of respondents (n = 561) expressed satisfaction with SOLS resources and involvement opportunities, which was hypothesized. These results give substantial insight into the efficacy of a first-year success seminar-mentoring program for college freshmen in STEM.
ContributorsMaalouf, Nicholas Elie (Author) / Haydel, Shelley (Thesis director) / Harrell, Carita (Committee member) / Capco, David (Committee member) / Department of Psychology (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
The recovery of edge information in the physical domain from non-uniform Fourier data is of importance in a variety of applications, particularly in the practice of magnetic resonance imaging (MRI). Edge detection can be important as a goal in and of itself in the identification of tissue boundaries such as those defining the locations of tumors. It can also be an invaluable tool in the amelioration of the negative effects of the Gibbs phenomenon on reconstructions of functions with discontinuities or images in multi-dimensions with internal edges. In this thesis we develop a novel method for recovering edges from non-uniform Fourier data by adapting the "convolutional gridding" method of function reconstruction. We analyze the behavior of the method in one dimension and then extend it to two dimensions on several examples.
ContributorsMartinez, Adam (Author) / Gelb, Anne (Thesis director) / Cochran, Douglas (Committee member) / Platte, Rodrigo (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
Description
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.
ContributorsNumani, Asfia (Co-author) / Mishra, Shambhavi (Co-author) / Sweazea, Karen (Thesis director) / Plasencia, Jon (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05