Models of an Autonomous Rhythmic Hormone Delivery System
Wednesday, June 25, 2003 - 1:00pm - 2:00pm
Certain disorders in sexual development and reproductive function are traced to disorders in the rhythmic, pulsatile secretion of gonadotropin releasing hormone (GnRH) from the hypothalamus. These disorders may require long-term hormone replacement therapy, and rhythmic delivery of GnRH is essential. Since GnRH is exceptionally potent, implantable hormone delivery systems may be considered. We are developing such a system, in which autonomous modulation of permeability of a hydrogel membrane to GnRH is driven by endogenous glucose, via a chemomechanical limit cycle established by feedback between the membrane and an enzyme. Several mathematical models of this system have been developed, with different levels of complexity. We will present results of a lumped, ODE-based model, for which the bifurcation structure has been worked out, and will also progress towards a more detailed, distributed (PDE-based) model.