Tuskegee University

Title: Mathematical Modeling and Computation for the Growth of Tumors

Directors: Tommy Johnson, Carolyn Sippial, Hesmat Aglan, and Herman Windham

Dates of Program: June 8 - August 2, 2008

Summary: This is a continuation of last year's project. We applied two numerical schemes, implicit and explicit finite difference methods and obtained results quite different than those presented in existing literature. We will look more into this and also implement different schemes such as the Crank-Nicholson method or the finite element method which might better explain the model.

Students will study a mathematical model recently developed by several mathematicians (Byrne, Chaplain and Friedman, etc) for the growth of a tumor consisting of live cells. According to the researchers mentioned above the model is in the form of a free-boundary problem whereby the tumor grows (or shrinks) due to cell proliferation or death according to the level of a diffusing nutrient concentration. Using techniques from numerical analysis mentioned above, students will analyze the solutions and graph these solutions at different stages. Several questions will be considered, such as when the tumor growth will reach its maximum rate and if there is any kind of parameter control to keep the growth at its lowest level. Stability and convergence of the numerical schemes will also be studied as time permits.

Student Researchers Supported by MAA: