At Duke, as part of the PRUV Fellowship and for my thesis, under the guidance of Professor Anita Layton, I modeled fluid flow and filtration rate in the loop of Henle, a portion of a nephron, which forms the basic structural and functional unit of the kidney. A unique feature of the loop is a negative feedback system that tightly regulates ion concentration. Modeling the loop with a system of partial differential equations, we related pressure and flow with the Hagen-Poiseuille equation along with partial differential equations that took into account water flux, ion conservation, and Michaelis-Menten kinetics for active transport.

My contributions to the model permitted a compliant tube such that the change in radius varied proportionally to the difference in external and internal pressure. I also wrote routines in C to numerically solve the system of partial differential equations along with a front end in MATLAB that made for efficient simulations. Here, I gained an appreciation for how mathematical models illuminate biological phenomena in a way that would be infeasible through experimentation in a wet lab.

We found that ion concentration principally depended on transit time through the loop and that when pressure is perturbed, the loop acted as a low-pass filter for ion concentration.