Geodesic
Modeling and analysis of adipocytes dynamic with a differentiation process
Jérôme Gilleron1 ; Thierry Goudon2 ; Frédéric Lagoutière3 ; Hugo Martin4 ; Benjamin Mauroy2 ; Pascal Millet5 ; Magali Ribot6 ; Cristina Vaghi7
1 Centre Méditerranéen de Médecine Moléculaire (C3M), UMR INSERM U1065/UNS,ARCHIMED, 151 route Saint Antoine de Ginestière, BP 2 3194, F-06204 Nice, France
2 Université Côte d’Azur, Inria, CNRS, LJAD
3 Université de Lyon, Université Claude Bernard Lyon 1, Institut Camille Jordan (CNRS UMR5208), 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
4 Laboratoire Jacques-Louis Lions, Sorbonne Université, CNRS, 4 place Jussieu, 75005 Paris
5 DMA-ENS, rue d’Ulm, Paris
6 Institut Denis Poisson, Université d’Orléans, CNRS, 45067 Orléans
7 Inria Bordeaux Sud-Ouest, team Monc
ESAIM. Proceedings, Tome 67 (2020), pp. 210-241.

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We propose in this article a model describing the dynamic of a system of adipocytes, structured by their sizes. This model takes into account the differentiation of a population of mesenchymal cells into preadipocytes and of preadipocytes into adipocytes; the differentiation rates depend on the mean adipocyte radius. The considered equations are therefore ordinary differential equations, coupled with an advection equation, the growth rate of which depends on food availability and on the total surface of adipocytes. Since this velocity is discontinuous, we need to introduce a convenient notion of solutions coming from Filippov theory. We are consequently able to determine the stationary solutions of the system, to prove the existence and uniqueness of solutions and to describe the asymptotic behavior of solutions in some simple cases. Finally, the parameters of the model are fitted thanks to some experimental data and numerical simulations are displayed; a spatial extension of the model is studied numerically.
DOI : 10.1051/proc/202067013

Jérôme Gilleron 1 ; Thierry Goudon 2 ; Frédéric Lagoutière 3 ; Hugo Martin 4 ; Benjamin Mauroy 2 ; Pascal Millet 5 ; Magali Ribot 6 ; Cristina Vaghi 7

1 Centre Méditerranéen de Médecine Moléculaire (C3M), UMR INSERM U1065/UNS,ARCHIMED, 151 route Saint Antoine de Ginestière, BP 2 3194, F-06204 Nice, France
2 Université Côte d’Azur, Inria, CNRS, LJAD
3 Université de Lyon, Université Claude Bernard Lyon 1, Institut Camille Jordan (CNRS UMR5208), 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
4 Laboratoire Jacques-Louis Lions, Sorbonne Université, CNRS, 4 place Jussieu, 75005 Paris
5 DMA-ENS, rue d’Ulm, Paris
6 Institut Denis Poisson, Université d’Orléans, CNRS, 45067 Orléans
7 Inria Bordeaux Sud-Ouest, team Monc 
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     author = {J\'er\^ome Gilleron and Thierry Goudon and Fr\'ed\'eric Lagouti\`ere and Hugo Martin and Benjamin Mauroy and Pascal Millet and Magali Ribot and Cristina Vaghi},
     title = {Modeling and analysis of adipocytes dynamic with a differentiation process},
     journal = {ESAIM. Proceedings},
     pages = {210--241},
     publisher = {mathdoc},
     volume = {67},
     year = {2020},
     doi = {10.1051/proc/202067013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202067013/}
}
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Jérôme Gilleron; Thierry Goudon; Frédéric Lagoutière; Hugo Martin; Benjamin Mauroy; Pascal Millet; Magali Ribot; Cristina Vaghi. Modeling and analysis of adipocytes dynamic with a differentiation process. ESAIM. Proceedings, Tome 67 (2020), pp. 210-241. doi : 10.1051/proc/202067013. http://geodesic.mathdoc.fr/articles/10.1051/proc/202067013/

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