Multiscale Modeling of Follicular Ovulation as a Reachability Problem

During each ovarian cycle, only a definite number of follicles ovulate, whilethe others undergo a degeneration process called atresia. We have designed amulti-scale mathematical model where ovulation and atresia result from ahormonal controlled selection process. A 2D-conservation law describes the ageand maturity structuration of the follicular cell population. In this paper, wefocus on the operating mode of the control, through the study of thecharacteristics of the conservation law. We describe in particular the set ofmicroscopic initial conditions leading to the macroscopic phenomenon of eitherovulation or atresia, in the framework of backwards reachable sets theory