My long-term interest is mathematical modeling of solute and water transport across epithelia, specifically the renal epithelia. For a number of years attention was restricted to proximal tubule physiology, but the current focus is on a mathematical model of the mammalian distal nephron. The model represents Na, K, and acid/base transport under normal and pathological conditions, and predicts their renal excretion, given distal delivery.
An important aspect of this work is simulation of distal nephron dysfunction. In experimental models, specific segmental transport defects have been identified. The model can be used to assess the extent to which known defects can account for observed solute excretion patterns. Conversely, simulations of clinical tests of distal nephron function can be used to evaluate their accuracy in defining a specific transport defect.
A second aspect of this project is investigation into the theory of cell volume regulation during fluctuations of net transport. Critical to epithelial cell viability is homeostasis of cell volume and composition during changes in transcellular transport. Mathematical models of epithelia may be extended with the inclusion of functional dependence of membrane transport coefficients on cell variables (e.g. volume, solute concentrations, or electrical potential). This effort entails a systematic examination of homeostasis in epithelial models, and provides a framework for identification of candidate control parameters.