## Colloquium: “Mathematical Modeling and Simulation for Biological Applications”

Marshall University Math Colloquium

April 11, 2014

Dr. Lingxing Yao

*Case Western Reserve University*

**Abstract**

In this talk, I will go over some of my research projects in mathematical modeling and simulation for biological applications. I will focus on the analysis of a Hydrogel/Enzyme drug delivery oscillator, which involved mathematical modeling and dynamical analysis of models. It is well known that hydrogels are soft materials similar to natural tissue, and can be found in applications such as food additives, contact lens, cosmetic surgery, wound healing, and drug delivery devices. Since hydrogels are made of cross linked polymer networks that are capable of absorbing large amounts of water, they can be present in swollen or collapsed state. Under carefully designed physical and chemical conditions, we could observe volume phase transitions in polyelectrolyte hydrogels between those states, sometimes repeatedly. In this presentation, I will address the modeling of gel swelling, by combining the theory of the elastic, electrostatic and mixing energy in a model membrane made of polyelectrolyte hydrogel. Based on these energy principles, it is possible to propose the mathematical model system which is capable of explaining the oscillatory volume phase transition seen in a real membrane oscillator built in engineering laboratory for the purpose of hormone drug delivery. Some detailed analysis and results of the model system will be presented.