The 7th Annual

NC State University

Undergraduate Summer Research Symposium

 

 

NC State REU in Modeling and Industrial Applied Mathematics abstracts


Abstracts are listed in alphabetical order by the last name of the corresponding author.

 

 

 


 

 

Student Author(s): 

Arnold, Rachel F.

Marous, Daniel R.

McLamb, April J.

Thompson, Karmethia C.

Woodruff, William R.

Home Institution:

Virginia Tech

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

Mansoor A. Haider/Mathematics

Janine M. Haugh/Mathematics

Title of Presentation:

Your Hips Don't Lie: Modeling Cartilage Regeneration

 

 

With an increasing life expectancy and a growing population participating in athletic activities, the need for an eective process for cartilage repair is paramount. Cartilage is a dense connective tissue comprised of specialized cells called chondrocytes. It is primarily found on the articular surfaces of the bones, e.g. the knees and hips. In particular, it serves as a protective covering on bone endings in joints, preventing a painful sensation from bone-on-bone contact. In a healthy environment, cartilage resides in a state of homeostasis, repairing any minor damages that it may incur. However, an unhealthy aging process or extensive injury can render the cartilage naturally irreparable. Consequently, researchers are seeking techniques to encourage cartilage regeneration. One such method involves injecting biocompatible scaolding materials seeded with chondrocytes into the defective areas. Because of its similarities to natural tissue, a hydrogel substance is a suitable selection for the material harboring these cells. With an ample nutrient supply, the chondrocytes are ideally able to restore the damaged cartilage to homeostasis. Researchers are in need of a mathematical model that describes this biological process. With a model at hand, they can better identify the characteristics of the hydrogel procedure that demand further investigation. In our work, we present a mathematical model that illustrates the regeneration of cartilage via a hydrogel substance. Our model is comprised of ordinary dierential equations that describe the rates at which the nutrient, hydrogel, and cartilage concentrations change throughout regeneration.

 

 


 

 

Student Author(s): 

Boudreaux, Brittany

Foster, Krista

Uttal, Cerena

Vogel, Thomas

Home Institution:

Youngstown State University

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

H.T. Banks/Center for Research in Scientific Computation

Amanda Criner/Mathematics

Title of Presentation:

Can Thermal Methods Detect Structural Damage?

 

 

Most modern aero and space structures are composed of composite materials containing significant porosity.  Although nondestructive analysis techniques have been developed to detect damage in homogeneous materials, little research has been done on heterogeneous materials.  This project uses the heat equation to simulate a thermal interrogation method for identifying damage in a porous compartment.  The model first uses different probability schemes to randomly generate pores and then flash heats the compartment along one of its boundaries.  Temperature data along the heated boundary is recorded and then analyzed to distinguish differences between the undamaged and damaged materials.  These results indicate that it is possible to detect damage of a certain size within a porous medium.

 


 

 

Student Author(s): 

Cousins, William B.

Deutsch, Steven R.

Stroka, Amy M.

Tessler, M. Henry

Washington, Janatta R.

Home Institution:

Keuka College

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

Pierre A. Gremaud/Mathematics

Title of Presentation:

Modeling of Traffic Congestion and Mass Evacuations

 

 

The destructive nature of hurricane seasons makes efficient mass evacuation plans a necessity. Mathematical modeling techniques were implemented in this project in order to accurately represent large scale evacuations for areas in the North Carolina coast. Traffic congestion was simulated through the use of a microscopic model, which predicts individual driver behavior using systems of Ordinary and Delay Differential Equations. In this model, the behavior of a car was determined entirely by the behavior of the car immediately preceding it. Another route taken utilized a macroscopic model derived from physical applications of scalar conservation laws. This model examines the densities of cars and velocity fields through the use of Partial Differential Equations. An additional tool used was SUMO (Simulation of Urban MObility), an open source traffic simulation software package developed by the Centre for Applied Informatics (ZAIK) and the Institute of Transport Research at the German Aerospace Centre. Simulations were created for the evacuations of Bird Island and the coast of North Carolina through the use of SUMO and the macroscopic model. These simulations were then compared and critically analyzed.

 

 


 

 

Student Author(s): 

Crompton, Kasey

Davis, Andrew

Ito, Satoru

Morton, Gregory

Olsen, Amanda

Home Institution:

LaGrange College

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

Mette S. Olufsen/Mathematics

Daniela Valdez-Jasso/Mathematics

Title of Presentation:

Viscoelasticity of the Arterial Wall

 

 

The design of stents and grafts require knowledge of the mechanical properties of the arterial wall, which can be hard to determine experimentally. Difficulties arise, since the mechanics differ in-vivo and in-vitro, and because the vessel wall displays viscoelastic behavior. This study utilizes a 2-parameter elastic model and a 4-parameter Kelvin viscoelastic model to predict elastic and viscoelastic properties of the arterial wall using in-vivo measurements of vessel area and blood pressure. Data were measured in the proximal ascending aorta in seven sheep at a number of different frequencies. Mechanical properties were predicted by estimating model parameters by solving the inverse problem, minimizing the least squares error between computed and measured values of vessel area. Results showed that we were able to estimate model parameters using only a portion of the data, and that parameter estimates did not differ significantly even without prior filtering of the data. While the vessel radius was not significantly impacted by changes in frequency, differences were observed in both elastic and viscoelastic parameters. Results of sensitivity analyses showed that all parameters were sensitive, and since all model parameters are independent, we conclude that it is possible to estimate all parameters. Moreover, results showed that the Kelvin viscoelastic model was able to capture the pressure-area hysteresis, which the elastic model could not predict. Finally, we showed that the hysteresis is significantly smaller in-vivo than in-vitro, a phenomenon, which may be a result of smooth muscle cell regulation and support of the tunica adventitia.

 

 

 


 

 

Student Author(s): 

Davis, Steven

Gadson, Sean E.

Tallis, William J.

Home Institution:

NCSU

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

Hien Tran/Mathematics

R. Lawrence Ives/Calabazas Creek Research, Inc.

Title of Presentation:

Computer Optimization of Electron Beam Devices

 

 

 

Electron beams can be used as power sources for high-frequency, high energy radio and microwave sources for a variety of applications including radar, communications, electronic countermeasures, and many defense and homeland security systems. Existing cylindrical beam designs cannot achieve the required beam power for some applications. Sheet beam guns can deliver much more power; however, at higher power levels the magnetic field containing the beam interacts with the electric field of the electrons to generate a force that curls the beam at the edges. Counteracting this curling requires adding components to alter the magnetic field at the edges of the beam. The shape of the beam is very sensitive to the location of these components, and the placement of components cannot be optimized independently. Consequently, the performance of the beam depends on too many parameters to be effectively optimized manually. Computer optimization can dramatically reduce the costs and time to develop new electron beam devices. Our research focused on an automated process for optimizing the focusing of electron beams, using a sheet beam gun as a real-world problem. Two optimization algorithms are being studied, including parallel implementations of both algorithms.
 

 


 

 

Student Author(s): 

Dodd, Val L.

Ritch, Ryan D.

Huff, Kelly J.

Home Institution:

Asbury College

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Industrial Applied Mathematics

Research Mentor(s)

Laura Ellwein/Industrial Applied Mathematics

Title of Presentation:

Analysis of Cardiovascular Models to Examine the Potential Effects of Particulate Matter

 

 

Recent studies have indicated an alarming connection between the inhalation of particulate matter (PM) and increases in morbidity and mortality. These tiny particles suspended in the air appear to be a substantial causitory factor of harmful respiratory and cardiovascular conditions. As cardiovascular events seem to compose the largest number of PM related deaths, we sought to discover the means through which PM affects the cardiovascular system. Because the exact composition of PM can vary widely depending upon its source, we focused on PM resulting from gasoline and diesel fumes. Previous studies indicate that some of the effects of PM on the cardiovascular system include elevated heart rate, arrhythmias, decreased compliance of the blood vessels, and increased blood viscosity. We examined several models of the cardiovascular system in order to establish a model that incorporates parameters that may be affected by PM. Investigation into PM is still in its early stages, so data on the exact changes effected by PM is limited. However, having discovered from previous studies how PM affects certain parameters and outptus in our model such as compliances and heart rate, we used a cadiovascular model to hypothesize how PM brings about harmful effects. By observing how the alterations of parameters change our model output, we may be able to determine more specifically how PM exerts its detrimental effects. Commonly seen effects of PM include changes in heart rate variation and the presence of abnormal beats. Because of this, we found a pulsatile model of the heart, incorporating fluctuations in blood volume and pressure associated with the beating of the heart, to be helpful in observing these specific effects of PM. Future collaboration with scientists would be useful in obtaining more exact data on how those parameters common to most cardiovascular models are affected by PM.       

 

 

 


 

 

Student Author(s): 

Durant, Ellen

Sawyer, Megan

Weissenstein, Eric

Home Institution:

NCSU

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

Sharon Lubkin/Mathematics

Title of Presentation:

Demonstration of Emergent Properties of Tissues by Stochastic Modeling

 

 

Cell movement provides the foundation for the development of cysts, tissues, organs, and, consequentially, entire organisms.  Morphogenesis in animals is mostly due to motion of individual cells and can be modeled using the relative strength of surface energies of touching cells. By adjusting these energies in a cluster of cells, we demonstrate different emergent properties of tissues.  We develop a modified cellular Potts algorithm in two- and three-dimensions that preserves area and cell sorting under differential adhesion.  Furthermore, we extend this model to include cell division and secretion of lumen, which, in combination with cell sorting, can model the creation of a cyst.

 


 

 

Student Author(s): 

Feldman, Jacob

Morgante, Anna

Pendeleton, Terrance

Reynolds, Doneshia

Home Institution:

Meredith College

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

James Selgrade/Mathematics

Title of Presentation:

Modeling Hormonal Regulation of the Menstrual Cycle

 


The aim of this project was to improve and to make additions to a mathematical model for regulation of the menstrual cycle of a normally cycling woman, which accurately predicts levels of the essential reproductive hormones.  Exposure to environmental estrogens, such as dioxin, polychlorinated biphenyls (PCBs), and oral contraceptives, in women today may have adverse effects on hormone levels and the metabolism of the body.  Elevated levels of estrogen are a possible contributing factor to breast cancer in women.  Two primary sources of reproductive hormone synthesis within the body: the pituitary gland located in the brain, and the ovaries.  Follicle stimulating hormone (FSH) and luteinizing hormone (LH) are synthesized by the pituitary gland, while the ovary is the primary producer of estradiol (E2), progesterone (P4), and inhibin (Ih).  We redeveloped an existing system of differential equations that models the rates of change of these five hormones.  Optimization techniques, as well as informed adjustments of the parameters, allowed us to increase the accuracy of the hormone models.  Our models were compared to published data and were found to portray the profile of each hormone accurately.  As a result of this project, these models can be used to predict the effects of changes in hormone levels on the reproductive endocrine system.

 

 


 

 

Student Author(s): 

Glover, Travious
Hallock, Lee
Shor, Joel
Wallace, John

Home Institution:

Virginia Tech

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

Ralph C. Smith/Mathematics

Title of Presentation:

Modeling Multifunctional Materials

 

 

Advanced aerospace, aeronautic, industrial, biomedical and nanotechnology applications increasingly rely on multifunctional materials to achieve design specifications.  These materials exhibit the capability of coupling electrical, magnetic, thermal and mechanical behavior, but do so at the cost of complex and nonlinear material dynamics.  This project focuses on the development of modeling, simulation and statistical techniques for these advanced materials.  We also consider methods to make the implementation of these models more efficient while maintaining enough accuracy so that the models remain applicable.

 

 


 

 

Student Author(s): 

McCall, Pearlie

Home Institution:

Spelman College

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

Sharon Lubkin/Mathematics

Title of Presentation:

Modeling Cellular Movement in Tissues

 


The movement of cells in tissues is an uncanny and intriguing phenomenon in the scientific world.  It is critical to understand the mechanisms of cellular movement because they illuminate the connection between development of humans and disease. In our research, we are creating mathematical models and using MatLab software to realistically mimic the movement of cells in tissues. 

 


 

 

Student Author(s): 

Moran, Patrick A.

Herwaldt, Bethany A.

Salter, Jeffrey

Home Institution:

College of Charleston

Program:

NC State REU in Modeling and Industrial Applied Mathematics 

College:

PAMS

Department(s):

Mathematics

Research Mentor(s)

Carl D. Meyer/Mathematics

Title of Presentation:

Feature Extraction From Textual Datasets

 

The Internet holds a wealth of new information, which is increasingly taking the form of user-generated content.  Many are interested in knowing the general opinions on a given topic without having to read thousands of reviews and articles.  Our goal is to find a technique that will allow us to identify the topics discussed in a group of documents, then determine the common opinion (positive or negative) of that topic. The first step of finding the topics is to find a list words which should be characteristic of the various topics. One way is through the nonnegative matrix factorization. Another technique we can use to obtain characteristic words is to compare the ratios of the frequencies of words in the document to the frequencies of those words in some large corpus of general English.  Once found, these words must be grouped into topics. We create a graph of the words, wherein the distance between two words is determined by WordNet similarity and word proximity. WordNet similarity is a measure of how semantically related two words are, independent of their context. Word proximity is based on the average number of words between the two words in the document collection. These terms can then be clustered with any traditional clustering algorithm. Topics are then scored for positivity or negativity with natural language programming. We attempt to detect associations between words characteristic of a given topic and words known to be positive or negative. We then use this information to try to score documents as having positive or negative opinions.

 


 

 

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Last modified June 2008 by Sharon E. Hunt