Matching Items (53)

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Microglia Motility in the Context of a PDGF Induced Glioblastoma

Description

Tumor associated microglia-and-macrophages (TAMS) may constitute up to 30% of the composition of glioblastoma. Through mechanisms not well understood, TAMS are thought to aid the progression and invasiveness of glioblastoma.

Tumor associated microglia-and-macrophages (TAMS) may constitute up to 30% of the composition of glioblastoma. Through mechanisms not well understood, TAMS are thought to aid the progression and invasiveness of glioblastoma. In an effort to investigate properties of TAMS in the context of glioblastoma, I utilized data from a PDGF-driven rat model of glioma that highly resembles human glioblastoma. Data was collected from time-lapse microscopy of slice cultures that differentially labels glioma cells and also microglia cells within and outside the tumor microenvironment. Here I show that microglia localize in the tumor and move with greater speed and migration than microglia outside the tumor environment. Following previous studies that show microglia can be characterized by certain movement distributions based on environmental influences, in this study, the majority of microglia movement was characterized by a power law distribution with a characteristic power law exponent lower than outside the tumor region. This indicates that microglia travel at greater distances within the tumor region than outside of it.

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Date Created
  • 2013-12

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Visualizing Lagrangian Coherent Structures from Realistic Flow Data

Description

The goal of this project was to examine the separatricies that define regions of distinct flow behaviors in realistic time-dependent dynamical systems. In particular, we adapted previously available methods for

The goal of this project was to examine the separatricies that define regions of distinct flow behaviors in realistic time-dependent dynamical systems. In particular, we adapted previously available methods for computing the Finite-Time Lyapunov Exponent (FTLE) to a set of measured wind velocity data in order to visualize the separatricies as ridges of the FTLE field in a section of the atmosphere. This visualization required a number of alterations to the original methods, including interpolation techniques and two different adaptive refinement schemes for producing more detailed results. Overall, there were two computations performed with the wind velocity data: once along a single spherical surface, on which the separatricies could be visualized as material lines, and then along a three-dimensional section of the atmosphere, for which the separatricies were material surfaces. The resulting figures provide an image of the Antarctic polar vortex from the wind velocity data, which is consistent with other data gathered on the same date.

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Date Created
  • 2014-05

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Estimating GL-261 cell growth: A murine model for Glioblastoma Multiforme

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

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.

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  • 2014-05

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Wada basins of attraction in diffeomorphic maps

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

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.

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Created

Date Created
  • 2013-05

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Lagrangian Skeletons in Hurricane Katrina

Description

This thesis shows analyses of mixing and transport patterns associated with Hurricane Katrina as it hit the United States in August of 2005. Specifically, by applying atmospheric velocity information from

This thesis shows analyses of mixing and transport patterns associated with Hurricane Katrina as it hit the United States in August of 2005. Specifically, by applying atmospheric velocity information from the Weather Research and Forecasting System, finite-time Lyapunov exponents have been computed and the Lagrangian Coherent Structures have been identified. The chaotic dynamics of material transport induced by the hurricane are results from these structures within the flow. Boundaries of the coherent structures are highlighted by the FTLE field. Individual particle transport within the hurricane is affected by the location of these boundaries. In addition to idealized fluid particles, we also studied inertial particles which have finite size and inertia. Basing on established Maxey-Riley equations of the dynamics of particles of finite size, we obtain a reduced equation governing the position process. Using methods derived from computer graphics, we identify maximizers of the FTLE field. Following and applying these ideas, we analyze the dynamics of inertial particle transport within Hurricane Katrina, through comparison of trajectories of dierent sized particles and by pinpointing the location of the Lagrangian Coherent Structures.

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Date Created
  • 2012-12

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Modeling Brain Tumors: Simulating individual Patient Cases of Glioblastoma Multiforme

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

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.

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Date Created
  • 2012-12

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Predicting Glioblastoma Growth Using a Poisson Process

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

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.

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Created

Date Created
  • 2013-12

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Lagrangian Transport of Inertial Particles in Hurricane Katrina

Description

Using weather data from the Weather Research and Forecasting model (WRF), we analyze the transport of inertial particles in Hurricane Katrina in order to identify coherent patterns of motion. For

Using weather data from the Weather Research and Forecasting model (WRF), we analyze the transport of inertial particles in Hurricane Katrina in order to identify coherent patterns of motion. For our analysis, we choose a Lagrangian approach instead of an Eulerian approach because the Lagrangian approach is objective and frame-independent, and gives results which are better defined. In particular, we locate Lagrangian Coherent Structures (LCS), which are smooth sets of fluid particles which are locally most hyperbolic (either attracting or repelling). We implement a variational method for locating LCS and compare the results to previous computation of LCS using Finite-Time Lyapunov Exponents (FTLE) to identify regions of high stretching in the fluid flow.

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Date Created
  • 2013-05

Application of Individual Based Models in Modeding Brain Tumor

Description

Cancer modeling has brought a lot of attention in recent years. It had been proven to be a difficult task to model the behavior of cancer cells, since little about

Cancer modeling has brought a lot of attention in recent years. It had been proven to be a difficult task to model the behavior of cancer cells, since little about the "rules" a cell follows has been known. Existing models for cancer cells can be generalized into two categories: macroscopic models which studies the tumor structure as a whole, and microscopic models which focus on the behavior of individual cells. Both modeling strategies strive the same goal of creating a model that can be validated with experimental data, and is reliable for predicting tumor growth. In order to achieve this goal, models must be developed based on certain rules that tumor structures follow. This paper will introduce how such rules can be implemented in a mathematical model, with the example of individual based modeling.

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Date Created
  • 2016-12

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A Numerical and Analytical Study of Wave Reflection and Transmission across the Tropopause

Description

A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a shar

A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial wave reflection. A validation for the numerical method through comparisons with the corresponding analytical solutions will be provided. Then, the method is applied to more realistic profiles of the stability to study the impact of these profiles on wave propagation through the tropopause.

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Date Created
  • 2017-05