Numerical simulation of the selection process of the ovarian follicles

Benjamin Aymard; Frédérique Clément; Frédéric Coquel; Marie Postel

doi:10.1051/proc/201238006

Benjamin Aymard ^1,² ; Frédérique Clément ² ; Frédéric Coquel ³ ; Marie Postel ¹

¹UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
²Centre de Recherche INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105 - F-78153 Le Chesnay, France
³CMAP, Ecole Polytechnique, CNRS, route de Saclay, F-91128 Palaiseau Cédex-France

ESAIM. Proceedings, Tome 38 (2012), pp. 99-117

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Résumé

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 × 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.

DOI : 10.1051/proc/201238006

Affiliations des auteurs :

Benjamin Aymard ^{1
,

2} ; Frédérique Clément ² ; Frédéric Coquel ³ ; Marie Postel ¹

¹ UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
² Centre de Recherche INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105 - F-78153 Le Chesnay, France
³ CMAP, Ecole Polytechnique, CNRS, route de Saclay, F-91128 Palaiseau Cédex-France

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     author = {Benjamin Aymard and Fr\'ed\'erique Cl\'ement and Fr\'ed\'eric Coquel and Marie Postel},
     title = {Numerical simulation of the selection process of the ovarian follicles},
     journal = {ESAIM. Proceedings},
     pages = {99--117},
     year = {2012},
     volume = {38},
     doi = {10.1051/proc/201238006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201238006/}
}

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Benjamin Aymard; Frédérique Clément; Frédéric Coquel; Marie Postel. Numerical simulation of the selection process of the ovarian follicles. ESAIM. Proceedings, Tome 38 (2012), pp. 99-117. doi: 10.1051/proc/201238006

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