Optimal control of the cell dynamics in the granulosa of ovulatory follicles

The aim of this paper is to seek for the optimal cellular changes in the granulosa of ovarian follicles, leading to ovulation in minimal time. The granulosa cell population consists of proliferating, differentiated and apoptotic cells. Cell numbers are ruled by a system of differential equations, in which the control variables are the cell cycle exit and apoptosis rates. The conditions for ovulation are represented by three different constraints on the granulosa final state. We prove that the optimal strategy consists in applying permanently the minimal apoptosis rate and in switching the cell cycle exit rate from its minimal bound to its maximal one. We finally apply the optimal strategy on data providing the changes in the total cell number of ewe follicles during their terminal development.