%0 Journal Article
%T Numerical simulation of the selection process of the ovarian follicles
%A Aymard Benjamin
%A Cl¨¦ment Fr¨¦d¨¦rique
%A Coquel Fr¨¦d¨¦ric
%A Postel Marie
%J ESAIM : Proceedings
%D 2013
%I EDP Sciences
%R 10.1051/proc/201238006
%X This paper presents the design and implementation of a numerical method to simulate a multiscale model describing the selection process in ovarian follicles. The PDE model consists in a quasi-linear hyperbolic system of large size, namely Nf ¡Á Nf, ruling the time evolution of the cell density functions of Nf follicles (in practice Nf is of the order of a few to twenty). These equations are weakly coupled through the sum of the first order moments of the density functions. The time-dependent equations make use of two structuring variables, age and maturity, which play the roles of space variables. The problem is naturally set over a compact domain of R2. The formulation of the time-dependent controlled transport coefficients accounts for available biological knowledge on follicular cell kinetics. We introduce a dedicated numerical scheme that is amenable to parallelization, by taking advantage of the weak coupling. Numerical illustrations assess th e relevance of the proposed method both in term of accuracy and HPC achievements. Ce document pr¨¦sente la conception et l¡¯impl¨¦mentation d¡¯une m¨¦thode num¨¦rique servant ¨¤ simuler un mod¨¨le multi¨¦chelle d¨¦crivant le processus de s¨¦lection des follicules ovariens. Le mod¨¨le EDP consiste en un syst¨¨me hyperbolique quasi lin¨¦aire de grande taille, typiquement Nf ¡Á Nf, gouvernant l¡¯¨¦volution des fonctions de densit¨¦ cellulaire pour Nf follicules (en pratique Nf est de l¡¯ordre de quelques-uns ¨¤ une vingtaine). Ces ¨¦quations d¡¯¨¦volution utilisent deux variables structurantes, l¡¯age et la maturit¨¦, qui jouent le r le de variables d¡¯espace. Le probl¨¨me est naturellement pos¨¦ sur un domaine compact de R2. La formulation du transport ¨¤ coefficients variables au cours du temps en fonction du contr le est issue des connaissances disponibles sur la cin¨¦tique cellulaire au sein des follicules ovariens. Nous pr¨¦sentons un sch¨¦ma num¨¦rique d¨¦di¨¦ au probl¨¨me parall¨¦lisable en tirant parti du faible couplage. Des simulations num¨¦riques permettent d¡¯¨¦valuer la pertinence de la m¨¦thode propos¨¦e tant en terme de pr¨¦cision que de calcul haute performance.
%U dx.doi.org/10.1051/proc/201238006