  In silico, cell based approaches for modeling biological morphogenesis are
used to test and validate our understanding of the biological and mechanical
process that are at work during the growth and the organization of multi-cell
tissues. As compared to in vivo experiments, computer based frameworks
dedicated to tissue modeling allow us to easily test different hypotheses, and
to quantify the impact of various biophysically relevant parameters.
  Here, we propose a formalism based on a detailed, yet simple, description of
cells that accounts for intra-, inter- and extra-cellular mechanisms. More
precisely, the cell growth and division is described through the space and time
evolution of the membrane vertices. These vertices follow a Newtonian dynamics,
meaning that their evolution is controlled by different types of forces: a
membrane force (spring and bending), an adherence force (inter cellular
spring), external and internal pressure forces. In addition to the cells
dynamics, our formalism further relies on a lattice Boltzmann method, using the
Palabos library, to simulate the diffusion of chemical signals. The latter aims
at driving the growth and migration of a tissue by simply changing the state of
the cells.
  All of this leads to an accurate description of the growth and division of
cells, with realistic cell shapes and where membranes can have different
properties. While this work is of methodological nature, we also propose to
validate our framework through simple, yet biologically relevant benchmark
tests at both single-cell and full tissue scales. This includes free and
chemically controlled cell tissue growth in an unbounded domain. The ability of
our framework to simulate cell migration, cell compression and morphogenesis
under external constraints is also investigated in a qualitative manner.
