Smoothed particle hydrodynamics for root growth mechanics

A major challenge of plant developmental biology is to understand how cells grow during the formation of an organ. To date, it has proved difficult to develop computational models of entire organs at cellular resolution and, as a result, the testing of hypotheses on the biophysics of self-organisation is currently limited. Here, we formulate a model for plant tissue growth in an Smoothed Particles Hydrodynamics (SPH) framework. The framework identifies the SPH particle with individual cells in a tissue, but the tissue growth is performed at the macroscopic level using SPH approximations. Plant tissue is represented as an anisotropic poro-elastic material where turgor pressure deforms the cell walls and biosynthesis and cell division control the density of the tissue. The performance of the model is evaluated through a series of tests and benchmarks. Results demonstrate good stability and convergence of simulations as well as readiness of the technique for more complex biological problems.