2020– Thesis
My thesis entails using mathematical modeling to understand how genetic expressions affect branching patterns in embryonic lungs. Specifically, I am investigating how the geometry of embryonic lungs affect the location of Fibroblast Growth Factor 10 (FGF10) expression and epithelial lung branching. We use a system of reaction-diffusion equations to model FGF10 expression at the lung surface and the resulting diffusion into the surrounding lung tissue. I am currently developing a computational model of the embryonic lungs by applying the surface finite element method to obtain numerical approximations of the reaction-diffusion equations via the C++ based program library deal.ii. The novelty of this research is the development of a new technique that involves the application of the surface finite element method to study the expression of key molecules in lung development. Results from this study would offer new insights into the mechanism of embryonic lung development, and the techniques used in this study could be extended to examine other branching organs such as the kidney and mammary glands.
2020 — Analytic Tools for the Finite Element Method on Parabolic Equations
This final project examines error analysis techniques for the Schnakenberg Equations on the surface of a sphere.
2020 –SDSU Student Colloquium
This poster was presented at the San Diego State University student colloquium series. It summarises my thesis progress as of February 2020.
2019 — AMS Fall Western Sectional
This presentation was given at University of California, Riverside. It summaries my thesis progress as of November 2019.
2019 — Contact Lens Drug Delivery
I was among a team of 7 graduate students and 1 advisor to formulate a model for drug diffusion from a contact lens into the cornea of the eye, as part of the GSMMC workshop held at the University of Delaware. At the end of the workshop, I presented our model to the workshop attendies (video below)
2019 – Pattern Formation in Lung Development
In this final research project, I gave an analytical solution to the Schnakenberg equation and found the parameter thresholds for Turing patterns in the context of genetic patterning on the surface of the lung.
2018 – Modeling Gene Expression in Lung Development
This final research paper examined a simplified PDE model of genetic expression on epithelial buds in fetal murine lungs.
2018 – Mapping Stable Manifolds
This group project investigated methods for visualizing stable manifolds in Discrete Dynamical systems with chaos.
2018 – Lotka-Volterra Modeling
This project uses data from Lynx and Hare populations from 1900-1930 to model species competition.
2018 – SIR Influenza Modeling
This project investigated a theoretical outbreak of influenza and the effectiveness of various treatment methods.