Section: Application Domains

Physics of tissue organisation

Many new insights in the last years indicate that migration, growth and division of cells are largely impacted by cell and tissue mechanics  (Ingber, Proc. Natl. Acad. Sci (USA), 2005), (Trepat et. al., Nat. Phys. 2009), (Alessandri et. al., Proc. Natl. Acad. Sci. (USA) 2013). Centre-based growth models already account for many of the observed phenomena  (Drasdo and Hoehme, Phys. Biol. 2005), (Drasdo and Hoehme, New Journal of Physics 2012). They furthermore allow calculation of the stress tensor in the tissue. A critical shortcoming of centre-based models is that forces between cells are calculated based on pairwise interactions hence multi-cellular interactions leading to true cell compression cannot be taken into account.

In order to scope with this shortcoming we (1.) developed a strategy in which forces are calibrated with a high resolution agent based model (so called deformable cell model), so that stress in tissue can then be calculated also at high cell density [54]; (2.) integrated cell division in deformable cell models to permit direct simulations of phenomena with this model type; (3.) developed hybrid models permitting to simulate centre-based and deformable cell models in the same simulations to be able to reach sufficiently high cell numbers.

Deformable cell models  (Odenthal, Smeets, van Liedekerke, et. al., PloS Comput Biol. 2013) resolve cell surface at reasonable resolution, and allow to calculate cell deformation as function of stress emerging in the tissue, hence the stress tensor cannot only be resolved at the position of the cell centre, as in the case of centre-based models, but in this case at any point on the cell surface or inside the cell. The higher resolution causes much longer simulation times which is why currently simulation of large multi-cellular systems with deformable cell models on standard computers is not feasible.