Recent Student Projects

Projects with non-thesis students include

> Starting in Spring, 2011, I teamed up with Dr. Weihong Lin, Biological Sciences department, and two undergraduate researchers, Asmita Adhikari and Taylor Good, to work on the role of TRPM5 ion channels in mouse olfactory signal processing. This work was supported mainly by an NSF-funded UBM grant between the Mathematics and Biological Sciences departments. The experimental protocol involved calcium imaging to monitor intracellular calcium levels in response to chemical stimuli in isolated olfactory sensory neurons from wild type and TRPM5-knockout mice. While the experiments proceeded on pace, the mathematical modeling was hampered by a dearth of critical parameter values. So a change in project goals accompanied a second set of student researchers coming into the project at the end of the internships of Asmita and Taylor. Calcium imaging studies involving two types of stimuli were designed to activate major and minor signaling pathways within the isolated olfactory cells. A dynamical mathematical model has been developed to better understand the two pathways. Student researchers Andrew Coates and Jen Chang have put together a poster presentation summarizing the results so far, and this work can be viewed here.

> Spring, 2011 I worked with two students, Mobolaji Akinpelu and Jordan White . Mobolaji's project was to develop a program to determine the steady state distribution of potential in a small tree graph (modeling a dendritic tree) stimulated by a constant current source at one boundary vertex. One goal of his project is to determine if we can distinguish between two non-isotropic trees with identical boundary vertices from the voltage measurements at the boundary vertices. Jordan's project was to develop a working knowledge of a Python program called NetworkX. This application was developed at Los Alamos to explore network algorithms. Because of its flexibility, the project was to see what can be said about solution behavior of partial differential equations imposed on a graph versus its graph topology.

> For Fall, 2009 and Spring 2010 I worked with student Alexandria Volkening. Our project was to develop a mathematical model of vulnerable arterial plaques (thin-cap fibroatheromas, or TCFAs). TCFA ruptures are a major cause of heart attacks. Our model accounts for the thinning and weakening of the cap due to the degradation effects of the toxic plaque core and accumulation of contaminents within the "shoulders" of the cap. Competing growth rates of the cap and core determine whether the rupture happens early or later in the growth process.

> For Fall, 2008 and Spring, 2009 I worked with student Alison Ebaugh. Our project was to see if a comprehensive quantitative model for the induction and maintenance of chemical/structural modifications of synapses between certain types of nerve cells can help explain a variety of experimental observations concerning the long-term changes in synaptic strength due to specific types of stimuli.

> In Spring and summer sessions, 2008, I supervised training of a MARC student, Immanuel Williams, where we engaged in two projects from the area of pharmacodynamics. The first project involved examining conditions for temperature oscillations in a mathematical model for 8-OH-DPAT-induced hypothermia. The second project involved examining the dynamics of hepatitis C virus when pegylated interferon is administered. That is, what happens when the viral load is not in steady state when the drug is administered. He also made nice presentations at the annual Summer Undergraduate Research Fest (SURF) in August, 2008. He also did a presentation at the 2008 Annual Biomedical Research Conference for Minority Students (ABRCMS) conference.

> In Spring and summer sessions, 2007, I supervised training of another MARC student, Velvet Wright, where we investigated a population model involving two competing species, both prey to a third (predator) population. She analyzed necessary and sufficient conditions for the stability of such population systems, and what effect harvesting has on sustaining the populations. The two-competing-population system is unstabilty (one population with go to extinction), the the presence of the predator population can stabilize the three populations. Moderate harvesting of the predator population can destabilize the prey populations. She also gave presentations at 2007 SURF and the 2007 ABRCMS in Atlanta, where she won an outstanding presentation award.

> I was Principle Investigator on an NSF REU grant title "Summer Program in Computational Biology", which was run for 8 weeks in the summers of 2005, 2007, and 2008. Click on the program web site ( to get more information on the program and previous projects.

Regarding graduate student projects

> In the spring semester 2013 another Thai graduate student from Mahidol University, Wanwarat Anlamlert, visited to get started on a dissertation project with me. We worked on developing a model of the chemical dynamics in an arterial plaque. This is an initial effort in a longer term investigation to understand the growth and degradation of vulnerable plaques associated with cardiovascular disease.

> In 2012 Joshua Austin started a masters degree project about an inverse problem of finding a distributed parameter associated with a wave equation on an interval of the real line. This work involves modifying previous boundary control work with Dirichlet controls to one with Neumann controls. The goal is to implement the theory in an efficient algorithm.

> During academic year 2005-08 I have been working with UMBC graduate student Dan Wang on a partial differential equation constrained optimization approach to estimating a spatially distributed spine density parameter in a model of a dendrite with spines. Professor Florian Potra is co-advisor on this effort. She defended her thesis in May, 2008. Her dissertation title was "Partial Differential Equation Constrained Optimization and its Application to Parameter Estimation in Models of Nerve Dendrites".

> In the academic year 2006-7 I supervised research to a new Thai student, Kamonwan Kocharoen, concerning a two-compartment model with Hodgkin-Huxley type dynamics, but with modified sodium current terms. Geometric perturbation analysis is used to reduce the model and analyze behavior. The solution behavior under various scenarios resembles clinical observations. The model can explain differences between the action potential dynamics of a normal patient and those with myotonia or periodic paralysis. The work resulted in the paper "Dynamic Analysis of a Model of Skeletal Muscles with Myotonia or Periodic Paralysis",to appear, J. Nonlinear Studies. This work was part of her dissertation for a PhD at Mahidol University, Bangkok.

> In 2005 I worked with a Thai student, Sittipong Ruktamatakul, on a topic in neural field theory, resulting in the paper "Wave front solutions and their shape for continuous neuronal networks with lateral inhibition" (IMA J. Appl. Math. 71(2006),544-564). Our two-layer model has the first layer having inhibitory connections to the second layer, while the second layer has excitatory connections to the first layer. The dynamics of each layer constitutes partial differential integral equations. He shows the shape of the voltage wave depends very strongly on two parameters, the difference in time scales between layers, and a threshold parameter. This work was part of his dissertation for the PhD at Mahidol University, Bangkok.