I consider myself both an Applied Mathematician and a Mathematical Biologist. Particularly, I am interested in the application of ordinary and partial differential equations; especially to modeling the genesis, progression and treatment of cancer. In keeping with the belief that mathematical modeling should be a quantitive representation of some experimental paradigm, I actively seek collaborations with experimentalists in both academia and in industry. Although I have very broad scientific interests, I have focused my research program around the following questions in cancer biology.
1. "How do tumors form capsules?" This problem involves the mechanics of interacting tissues and to assist in answering this question I am developing multi-phase models of tumor tissue, extracellular matrix, and interstitial fluid involvement in the encapsulation process.
2. "How does the cascade of events culminating in programmed cell death influence the genesis, progression, and eventual drug resistance of tumors?" In order suggest new hypotheses and aid in the understanding of these events, I am developing mathematical models of the receptor-ligand binding system associated with the initial death signal as well as the intracellular events which ultimately lead to the death of a cell.
3. "How do traditional and drug targeting chemotherapeutic strategies compare in terms of tumor reduction and host toxicity?" Improving traditional chemotherapy is of crucial importance in cancer research. I develop mathematical models of novel therapeutic strategies which can test, compare, and contrast performance of the particular approaches even under conditions which are experimentally inaccessible.
