Mathematical Modeling of the GnRH Pulse and Surge Generator

We propose a mathematical model allowing for the alternating pulse and surge pattern of gonadotropin releasing hormone (GnRH) secretion. The model is based on the coupling between two systems running on different time scales. The faster system corresponds to the average activity of GnRH neurons, while the slower one corresponds to the average activity of regulatory neurons. The analysis of the slow/fast dynamics exhibited within and between both systems allows for explaining the sequence of different secretion patterns (slow oscillations, fast oscillations, and periodical surge) of GnRH secretion as a hysteresis loop. Specifications on the model parameter values are derived from physiological knowledge in terms of amplitude, frequency, and plateau length of oscillations. The behavior of the model is finally illustrated by numerical simulations reproducing natural ovarian cycles and either direct or indirect actions of ovarian steroids on GnRH secretion.