INCOMPRESSIBLE LIMIT OF A CONTINUUM MODEL OF TISSUE GROWTH WITH SEGREGATION FOR TWO CELL POPULATIONS
vendredi 10 janvier 2020, 11h00 - 12h00
In developmental biology, the mechanisms by which an organ knows when it has reached its adult size and shape and stops growing are still poorly understand. Among a lot of explanations, the role of mechanical feedback has emerged. In some tissue, mechanical forces such as stretching and compression may arise during the development due to segregation of different type of cell. We propose a model for two interacting populations of cells which avoid mixing. The dynamics is driven by pressure and cohesion forces on the one hand and proliferation on the other hand. To prevent the mixing of the populations the model incorporates a repulsion force that enforces segregation. We study the influence of the model parameters thanks to one-dimensional simulations using a finite-volume method. In addition, following earlier works on the single population case, we show that the model approximates a free boundary Hele Shaw type model that we characterise using both analytical and numerical arguments. Finally, on two dimensional simulation we observe the the mechanical stress arising in the in biological tissue.