This project involves biomedical research at levels from experiment design to the biophysical interpretation of mathematical models. When data cannot be obtained from the literature, an experimental protocol must be initiated. The design of such a protocol involves identifying quantities of interest, promising measurement techniques, and plans of action which should yield results which can be evaluated for reliability and significance using applicable statistical techniques. Once good data have been obtained, the process of mathematical modeling proceeds. This may involve differential equations which describe changes in the system over space or time, such as the Navier-Stokes equations, and fits to experimental data. Complicated systems are often simplified by techniques such as dimensional analysis or WKB methods. The resulting simplified equations may be amenable to analytical techniques which yield information on properties of the solutions, such as existence and uniqueness. Numerical techniques such as finite differences are usually employed to solve the systems. The development is designed with an eye toward interpretation of the results, for it is at this point that the descriptive and predictive powers of the model are revealed.
