Mechanical Modeling of Three-dimensional Plant Tissue Indented by a Probe

Morphogenesis in a developing organism depends on the mechanics of the structural elements of the organism. In plants, typical experiments involve indenting tissues with a probe and measuring the force needed to reach a given depth. However, the heterogeneous structure and complex geometry of living tissues makes it a challenge to determine how such measurements are related to mechanical properties of the tissue, such as elastic moduli or internal pressure. Indeed, this task requires to perform a large number of direct mechanical simulations with a mesh representing the tissue. Here we propose a framework to achieve this task, using the Simulation Open Framework Architecture (SOFA) platform. We start from a realistic tissue structure corresponding to an early flower bud. We use a mesh where cells are polyhedral-shaped and are made of a liquid under pressure and where the faces separating two cells are thin elastic plates undergoing bending and stretching, and we model the interaction of this mesh with a spherical rigid probe. We obtain force versus depth curves that can be compared to experimental data. Thus our framework enables a comprehensive exploration of how mechanical parameters and probe position influence experimental outcomes, yielding a first step toward understanding the mechanical basis of morphogenesis.