Mathematical and numerical modelling of collective movement in epithelia

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Speciality : Mathématiques Appliquées

22/10/2024 - 14:00 Nathan Shourick (Université Grenoble Alpes) Auditorium du bâtiment IMAG, 150 place du Torrent, domaine universitaire, 38401, Saint Martin d'Hères

Cells and their environment constitute an active material at the origin of complex dynamics, for example during embryonic development or during the growth of a tumour. In an interdisciplinary approach combining mathematics and biophysics, this thesis focuses on the mathematical modelling of collective movement in epithelia, tissues made up of a monolayer of cells, which may be the site of collective movement to ensure a biological function: development and morphogenesis of embryos, expansion of a tumour, or recovery of an injured area in the case of tissue repair. We implement a thermodynamic formalism that takes into account the microstructure of the tissue to build a three-dimensional tissue model, then an original formalism for shallow approximations to reduce the latter to a two-dimensional system. We then propose a robust algorithm able to solve this system in both incompressible and compressible modes, on very general geometries. We demonstrate the power of our approach by determining continuous and semi-discrete energy estimates of our model and by carrying out numerical calculations on a strip with an obstacle, which is unprecedented in the literature for this type of models. Finally, we show the ability of our model to reproduce certain behaviours expected of epithelia on this geometry. The mathematical and numerical tools developed and the calculations carried out during this thesis thus provide an operational scientific framework for the dialogue between continuous modelling and experiments.

Directors:

  • Pierre Saramito
  • François Graner
  • Ibrahim Cheddadi

Raporteurs:

  • Olivier Saut
  • Matthias Merkel

Examinators:

  • Sébastien Boyaval
  • Valérie Laurent