Tumor Growth, Modeling HIV Infection
This project focuses on predicting the progression of HIV infection based on a compartmentalized mathematical model of HIV dynamics. Most of the available models in literature neglect one important factor of the disease, namely the viral reservoirs that are created after the infection has been established. For this reason, even though antiretroviral treatment has shown the capability to reduce viral concentration to a level below detection in the blood, the infection still persists. In order for mathematical models to accurately describe such a phenomenon, in addition to the blood system, we need to account for reservoirs of virus particles that exist throughout the body, with the prominent one being the lymphatic system.
Therefore, the goal is to develop a model that includes two interconnected compartments to represent the blood and lymphatic systems. By predicting the viral populations in both compartments, it will be possible to more accurately identify the efficiency of different treatment regimes and perform a sensitivity analysis. Ultimately, a more holistic understanding of the HIV infection is gained by observing how the interplay of two compartments allows the infection to persist under current treatments.
Modeling the Effect of Medication to Tumor Growth
Cancer is the leading cause of death worldwide with 7.9 million deaths in 2007. Progression of this disease depends on the intricate interplay between biological processes that span the molecular and macroscopic scales. Mathematical modeling provides an approach to systematically organize and analyze information regarding these complex interactions. This project focuses on the development of hybrid discrete-continuous models to simulate the effect of the spatial distribution of therapeutic agents on tumor progression. The project motivation stems from current complexities associated with how to attain high dosages to brain tumors through oral uptake.
The project will have two phases. The first will be a critical review of current articles in the open literature. The second phase will focus on developing accurate pharmacokinetics and pharmacodynamics models employing Matlab. A working knowledge of programming will be a partial objective of the second phase. Upon the successful completion of the model, the simulation results will be analyzed and compared to available experimental results in the literature. The ultimate focus of the project is the development of an accurate pharmacokinetics model that can be employed to improve the current treatment strategies.