Smoothed particle hydrodynamics for root growth mechanics

Abstract

A major challenge of plant developmental biology is to understand how cells grow during the formation of an organ. To date, it has proved dicult 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 SPH framework. The framework identies 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.

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

“…However, choosing precise governing equations and coupling forces can be very challenging due to the innate complexity of biological systems, such as the integration of multiple processes in dynamic geometries. In this section, the relevant governing equations for biosynthesis describing density changes in root tissue growth are presented to understand how cells grow during organogenesis [117]. The coupled forces of liquid-phase SPH and solid-phase DEM in simple monodisperse suspensions of neutral buoyancy spheres characterizing the effects of flow and mixing on changes in digesta composition are also presented here [118].…”

“…Limitations of testing the biophysical hypothesis of selforganization create difficulties in formulating plausible models of plant tissue growth. Building on the SPH method, Mimault et al [117] linked experimental data to computational modeling to describe the growth of plant tissues at the cellular level by identifying cells as numerical particles. Cell mass increases during tissue growth due to the influx of water and wall thickening through the accumulation of pectin and polysaccharides during the growth process.…”

Particle-based model shows complex rearrangement of tissue mechanical properties are needed for roots to grow in hard soil

“…Particles describe the interior of the cell, and cell walls can be reconstructed from the kernel function. Flexible numerical schemes allowed computation of thousands of cells using a modern workstation [ 37 ], and the method could compute whole root meristems in three dimensions ( Fig 6 , S3 and S4 Videos ). Simulations could be performed using images of the root anatomy with limited image processing because only basic shape descriptions for the cells are needed as an input [ 7 ].…”

Cell-based model shows complex rearrangement of tissue mechanical properties are needed for roots to grow in hard soil

“…Particles describe the interior of the cell, and cell walls can be reconstructed from the kernel function (Figure 2). Flexible numerical schemes allowed computation of thousands of cells using a modern workstation (Mimault, et al, 2019). The SPH method proved amenable to high dimensional and multi-physics problems, tests performed on two-dimensional domains could be easily ported to three dimensional problems without the need for a new interpolation scheme (Supplementary Video 3 and 4).…”