Particle-based model shows complex rearrangement of tissue mechanical properties are needed for roots to grow in hard soil
Fig 3
Impact of anisotropy of mechanical properties on the morphology of a growing tissue.
(A) Three cases were used to test the ability of the model to describe tissue morphogenesis. The isotropic case (A, left) was modeled using a radial Young modulus ER equal to the axial Young modulus EA. The anisotropic case (A, right) was modeled using ER equal to the maximal radial Young modulus EH. The balanced case (A, center) was modeled using a ER increasing smoothly from EA at the tip to EH at the base, using parameters shown in Table 1. Arrows describe the resulting strain rates in the growing tissue with the axial strain εA shown in red and radial strain εR shown in green. Simulations were initiated with particles distributed on a 2D cartesian lattice. (B) Comparison of SPH predictions with analytical solutions for the isotropic, anisotropic, and balanced cases for axial strain (B, left) and radial strain (B, right). Dashed curves represent analytical solutions and solid curve numerical results. The isotropic, balanced, and anisotropic cases are represented in blue, green, and orange, respectively. Analytical solutions are computed from Eq 8.