Multiscale Modeling of Follicular Ovulation as a Mass and Maturity Dynamical System
Résumé
During each ovarian cycle, numerous follicles are in competition for their survival, only a few of them ovulate and participate to the reproduction as fertilizable oocyte. Therefore, the development of ovarian follicles is crucial for the survival of mammals species and a better understanding of this selection process is required to improve the treatment of infertility or to improve the reproduction potential in domestic species. In this work, we introduce the system of nonlinear PDEs which modelize the growth and maturation of ovarian follicles. Then we study the dynamic of this system of nonlinear PDEs using analysis and dynamical systems tools. 1. Introduction. Reproduction ability and efficiency are major assets in the natural selection of species. It is studied to improve the reproduction potential of cattle or to treat the infertility in the human researches (see [28, 23, 22]). Even if the infertility seems to be due for 40 percent to the male and 40 percent to the female (10 percent both and 10 percent without any reason), treatments and studies of infertility are mostly focused on female infertility [22, 23, 36, 24, 14]. During each menstrual cycle, eggs are developed. They are the culmination of a growth and maturation process of ovarian follicles which are, in some sense, the basic unit of female reproductive biology. Ovarian follicle is composed of roughly spherical aggregations of cells (granulosa) found in the ovary and contain a single oocyte. In the ovarian cycle (growth, i.e., cell division and maturation process), numerous follicles are in competition for their survival (see [3, 4, 5, 6, 14, 13, 21, 24, 28, 22]). Only a few number of them ovulate and participate to the reproduction as fertilizable oocyte(s), the others degenerate (atresia) (see [5, 14, 12]). Therefore, the development of ovarian follicles is crucial for the survival of mammals species and this cell-scale competition process leads to a specie-scale competition process through the reproduction [14, 13]. Thus, a better understanding of this selection process is required to improve the treatment of infertility or to improve the reproduction potential in domestic species. The follicular development result from a complex process involving the Follicle Stimulating Hormone (FSH) which controls the proliferation rate, the apoptosis rate and the differentiation rate of follicles. The follicles secrete hormones such as estradiol exerting a negative feedback on FSH release. At the end of this process, the survival follicles are those who are the less sensitive to the fall of plasmatic level of FSH in other words the most mature follicles, the others undergo atresia. In this work, we are interested in two models of the ovarian follicles development. In the first one, H. M. Lacker [21] considers that follicles are defined by their maturity which follow a dynamical system of coupled Ordinary Differential Equations. The assumptions, done by the authors, are mostly imputable to mathematical considerations. In the second one [14], proposed by the INRIA team Sisyphe, follicles are defined by the density of their cells, structured by their age a and maturity γ,
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