Matching Items (7)
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- All Subjects: MATLAB
- All Subjects: Glioblastoma Multiforme
- Creators: Kostelich, Eric
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
In this research we consider stochastic models of Glioblastoma Multiforme brain tumors. We first look at a model by K. Swanson et al., which describes the dynamics as random diffusion plus deterministic logistic growth. We introduce a stochastic component in the logistic growth in the form of a random growth rate defined by a Poisson process. We show that this stochastic logistic growth model leads to a more accurate evaluation of the tumor growth compared its deterministic counterpart. We also discuss future plans to incorporate individual patient geometry, extend the model to three dimensions and to incorporate effects of different treatments into our model, in collaboration with a local hospital.
ContributorsManning, Michael Clare (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Letters and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2013-12
Description
Glioblastoma multiforme (GBMs) is the most prevalent brain tumor type and causes approximately 40% of all non-metastic primary tumors in adult patients [1]. GBMs are malignant, grade-4 brain tumors, the most aggressive classication as established by the World Health Organization and are marked by their low survival rate; the median survival time is only twelve months from initial diagnosis: Patients who live more than three years are considered long-term survivors [2]. GBMs are highly invasive and their diffusive growth pattern makes it impossible to remove the tumors by surgery alone [3]. The purpose of this paper is to use individual patient data to parameterize a model of GBMs that allows for data on tumor growth and development to be captured on a clinically relevant time scale. Such an endeavor is the rst step to a clinically applicable predictions of GBMs. Previous research has yielded models that adequately represent the development of GBMs, but they have not attempted to follow specic patient cases through the entire tumor process. Using the model utilized by Kostelich et al. [4], I will attempt to redress this deciency. In doing so, I will improve upon a family of models that can be used to approximate the time of development and/or structure evolution in GBMs. The eventual goal is to incorporate Magnetic Resonance Imaging (MRI) data into a parameterized model of GBMs in such a way that it can be used clinically to predict tumor growth and behavior. Furthermore, I hope to come to a denitive conclusion as to the accuracy of the Koteslich et al. model throughout the development of GBMs tumors.
ContributorsManning, Miles (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Preul, Mark (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
Description
Glioblastoma Multiforme is a prevalent and aggressive brain tumor. It has an average 5-year survival rate of 6% and average survival time of 14 months. Using patient-specific MRI data from the Barrow Neurological Institute, this thesis investigates the impact of parameter manipulation on reaction-diffusion models for predicting and simulating glioblastoma growth. The study aims to explore key factors influencing tumor morphology and to contribute to enhancing prediction techniques for treatment.
ContributorsShayegan, Tara (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Barrett, The Honors College (Contributor) / School of Human Evolution & Social Change (Contributor)
Created2024-05
Description
This Creative Project was carried out in coordination with the capstone project, Around the Corner Imaging with Terahertz Waves. This capstone project deals with a system designed to implement Around the Corner, or Non Line-of-Sight (NLoS) Imaging. This document discusses the creation of a GUI using MATLAB to control the Terahertz Imaging system. The GUI was developed in response to a need for synchronization, ease of operation, easy parameter modification, and data management. Along the way, many design decisions were made ranging from choosing a software platform to determining how variables should be passed. These decisions and considerations are discussed in this document. The resulting GUI has measured up to the design criteria and will be able to be used by anyone wishing to use the Terahertz Imaging System for further research in the field of Around the Corner or NLoS Imaging.
ContributorsWood, Jacob Cannon (Author) / Trichopoulos, Georgios (Thesis director) / Aberle, James (Committee member) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
The purpose of this project is to analyze the MIT OpenCourseWare coffee can radar design and modify it to be better suited for drone based synthetic aperture radar (SAR) applications while maintaining the low-cost aspect of the original design. The MIT coffee can radar can function as a ranged radar, a Doppler radar, or as SAR. Through simulations and research, the suggestions for how to modify the radar resulted in swapping the coffee can monopole antennas for patch antenna arrays or helical ordinary end-fire antennas, adding an Arduino for automatic recording of output pulses, and switching from a breadboard construction to a PCB to shrink form factor and keep costs and construction time low.
ContributorsRivera, Danielle (Author) / Trichopoulos, Georgios (Thesis director) / Aberle, James (Committee member) / Department of Information Systems (Contributor) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-12