Matching Items (11)
Filtering by
- Creators: School of Mathematical and Statistical Sciences
- 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
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
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.
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
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
Description
Background.
Type 2 Diabetes Mellitus (T2DM) is a leading cause of health disparities, among Hispanic populations, which are disproportionately afflicted by T2DM. The growing research strongly argues that diabetes treatment interventions should be culturally sensitive to address the needs of their target populations. Nonetheless, there is little consensus regarding the necessary components of a culturally sensitive intervention. This review will examine the intervention contents and activities, and the strategies that have been implemented into culturally sensitive diabetes treatment interventions. This review will also to observe how interventions handle complex issues such as the heterogeneity of Hispanic populations and communities. The overarching research questions examined in this study were, “What are the core components of the culturally tailored diabetes interventions currently implemented with Hispanic populations in the US, and why are they needed?” and 2) “How are studies evaluating the impact of their interventions, and how can the proposed study designs be improved?”
Method.
A systematic review across 3 databases was used to identify culturally sensitive diabetes treatment interventions (CSDTI) developed for Hispanic populations. Accordingly, we searched for studies designed to treat Hispanic individuals already diagnosed with having T2DM. All identified studies provided information on the core components of these culturally sensitive interventions, while only studies that included a control or comparison group were used to assess how the studies evaluated outcomes.
Results.
First, we examined intervention effects as examined from two study designs. We examined a total of [17] interventions in this section. Our review of one study design (Design #1 Studies) includes 12 studies that developed a culturally sensitive intervention and evaluated it using a one-group pretest posttest design, or did not evaluate their intervention at all. A second study design (Design #2 Studies) includes 5 studies. These consisted of a two-group randomized controlled field study that conducted pre-post analyses of the culturally adapted intervention comparing it against a control or comparison group. The heterogeneity of all studies made a conventional meta-analysis impossible.
Second, another review section focused on examining and describing various culturally sensitive core components, we examined a total of 17 studies to describe the types of culturally sensitive components that were incorporated into the diabetes treatment intervention. This analysis resulted in a list of 11 general types of culturally sensitive components as included within these 17 interventions. Of the articles that used control or comparison groups, the manner in which interventions evaluated different outcome measures and their conclusions regarding success were examined.
Discussion.
The culturally sensitive aspects identified from these articles were used to address diverse issues that included: (a) communication barriers, (b) the inclusion of cultural relevant content, for relevance to Hispanic/Latinx patients’ lives, (c) selecting appropriate channels and settings for interventions, and (d) addressing specific cultural values, traditions, and beliefs that can either help or hinder healthy behaviors. It should be noted that the Hispanic populations are extremely heterogeneous, and so interventions that would be sensitive culturally to some sectors of a Hispanic community may not be sensitive to other Hispanic sectors of that same community. The issue of heterogeneity of Hispanic communities was addressed well by the authors of some articles and ignored by others.
Conclusions.
It was ultimately impossible draw quantitative conclusions regarding the efficacy or effectiveness of these two types of diabetes treatment interventions (CSDTIs) as delivered to their targeted sample of Hispanic participants. An emerging conclusion is that factors including ethics, cost, and lack of community acceptance, may constitute factors contributing to the higher proportion of one-group pre-test post-test designs and lower proportion of rigorous scientific designs. In the latter case, some communities oppose the use of randomized controlled studies within their community, and thus that objection may explain the low numbers of these randomized controlled studies. The use of viable and rigorous alternatives to RCTs have been proposed to address this community concern. In this review, the author sought to conduct comparative studies between culturally adapted interventions and their associated unaltered or minimally altered evidence-based interventions, although there exists various difficulties that are associated with the conduct of these analyses.
Core components of CSDTIs for Hispanic adults were identified, and their purposes were explained. Additionally, suggestions for improvement to studies were made, to aid in improving our knowledge of CSDTIs through future studies.
Type 2 Diabetes Mellitus (T2DM) is a leading cause of health disparities, among Hispanic populations, which are disproportionately afflicted by T2DM. The growing research strongly argues that diabetes treatment interventions should be culturally sensitive to address the needs of their target populations. Nonetheless, there is little consensus regarding the necessary components of a culturally sensitive intervention. This review will examine the intervention contents and activities, and the strategies that have been implemented into culturally sensitive diabetes treatment interventions. This review will also to observe how interventions handle complex issues such as the heterogeneity of Hispanic populations and communities. The overarching research questions examined in this study were, “What are the core components of the culturally tailored diabetes interventions currently implemented with Hispanic populations in the US, and why are they needed?” and 2) “How are studies evaluating the impact of their interventions, and how can the proposed study designs be improved?”
Method.
A systematic review across 3 databases was used to identify culturally sensitive diabetes treatment interventions (CSDTI) developed for Hispanic populations. Accordingly, we searched for studies designed to treat Hispanic individuals already diagnosed with having T2DM. All identified studies provided information on the core components of these culturally sensitive interventions, while only studies that included a control or comparison group were used to assess how the studies evaluated outcomes.
Results.
First, we examined intervention effects as examined from two study designs. We examined a total of [17] interventions in this section. Our review of one study design (Design #1 Studies) includes 12 studies that developed a culturally sensitive intervention and evaluated it using a one-group pretest posttest design, or did not evaluate their intervention at all. A second study design (Design #2 Studies) includes 5 studies. These consisted of a two-group randomized controlled field study that conducted pre-post analyses of the culturally adapted intervention comparing it against a control or comparison group. The heterogeneity of all studies made a conventional meta-analysis impossible.
Second, another review section focused on examining and describing various culturally sensitive core components, we examined a total of 17 studies to describe the types of culturally sensitive components that were incorporated into the diabetes treatment intervention. This analysis resulted in a list of 11 general types of culturally sensitive components as included within these 17 interventions. Of the articles that used control or comparison groups, the manner in which interventions evaluated different outcome measures and their conclusions regarding success were examined.
Discussion.
The culturally sensitive aspects identified from these articles were used to address diverse issues that included: (a) communication barriers, (b) the inclusion of cultural relevant content, for relevance to Hispanic/Latinx patients’ lives, (c) selecting appropriate channels and settings for interventions, and (d) addressing specific cultural values, traditions, and beliefs that can either help or hinder healthy behaviors. It should be noted that the Hispanic populations are extremely heterogeneous, and so interventions that would be sensitive culturally to some sectors of a Hispanic community may not be sensitive to other Hispanic sectors of that same community. The issue of heterogeneity of Hispanic communities was addressed well by the authors of some articles and ignored by others.
Conclusions.
It was ultimately impossible draw quantitative conclusions regarding the efficacy or effectiveness of these two types of diabetes treatment interventions (CSDTIs) as delivered to their targeted sample of Hispanic participants. An emerging conclusion is that factors including ethics, cost, and lack of community acceptance, may constitute factors contributing to the higher proportion of one-group pre-test post-test designs and lower proportion of rigorous scientific designs. In the latter case, some communities oppose the use of randomized controlled studies within their community, and thus that objection may explain the low numbers of these randomized controlled studies. The use of viable and rigorous alternatives to RCTs have been proposed to address this community concern. In this review, the author sought to conduct comparative studies between culturally adapted interventions and their associated unaltered or minimally altered evidence-based interventions, although there exists various difficulties that are associated with the conduct of these analyses.
Core components of CSDTIs for Hispanic adults were identified, and their purposes were explained. Additionally, suggestions for improvement to studies were made, to aid in improving our knowledge of CSDTIs through future studies.
ContributorsDilli, Christopher Joe (Author) / Castro, Felipe Gonzalez (Thesis director) / Shaibi, Gabriel (Committee member) / School of Molecular Sciences (Contributor) / School of International Letters and Cultures (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05