No abstract

During each ovarian cycle, only a definite number of follicles ovulate, while the others undergo a degeneration process called atresia. We have designed a multi-scale mathematical model where ovulation and atresia result from a hormonal controlled selection process. A 2D-conservation law describes the age and maturity structuration of the follicular cell population. In this paper, we focus on the operating mode of the control, through the study of the characteristics associated with the conservation law. We describe in particular the set of microscopic initial conditions leading to the macroscopic phenomenon of either ovulation or atresia, in the framework of backwards reachable sets theory.

The biological meaning of follicular development is to free fertilizable oocytes at the time of ovulation. The selection of ovulatory follicles in mammal ovaries is an FSH-dependent selection process. In this paper, we design a multi-scale model of follicular development, where selection arises from the feedback between the ovaries and the pituitary gland and appeals to control theory concepts. Each ovarian follicle is characterized by a 2D density function giving an age and maturity-structured description of its cell population. The control intervenes in the velocity and loss terms of the conservation law ruling the changes in the density. The numerical outputs of the model, integrated with the finite volume method, are consistent with physiological knowledge.

No abstract

The biological meaning of follicular development is to free fertilizable oocytes at the time of ovulation. The selection of ovulatory follicles in mammal ovaries is an FSHdependent selection process. In this paper, we design a multiscale model of follicular development, where selection arises from the feedback between the ovaries and the pituitary gland and appeals to control theory concepts. Each ovarian follicle is characterized by a 2D density function giving an age and maturity-structured description of its cell population. The control intervenes in the velocity and loss terms of the conservation law ruling the changes in the density. The numerical outputs of the model, integrated with the finite volume method, are consistent with physiological knowledge.