A particle-based model to simulate the micromechanics of single-plant parenchyma cells and aggregates

Abstract

This paper is concerned with addressing how plant tissue mechanics is related to the micromechanics of cells. To this end, we propose a mesh-free particle method to simulate the mechanics of both individual plant cells (parenchyma) and cell aggregates in response to external stresses. The model considers two important features in the plant cell: (1) the cell protoplasm, the interior liquid phase inducing hydrodynamic phenomena, and (2) the cell wall material, a viscoelastic solid material that contains the protoplasm. In this particle framework, the cell fluid is modeled by smoothed particle hydrodynamics (SPH), a mesh-free method typically used to address problems with gas and fluid dynamics. In the solid phase (cell wall) on the other hand, the particles are connected by pairwise interactions holding them together and preventing the fluid to penetrate the cell wall. The cell wall hydraulic conductivity (permeability) is built in as well through the SPH formulation. Although this model is also meant to be able to deal with dynamic and even violent situations (leading to cell wall rupture or cell-cell debonding), we have concentrated on quasi-static conditions. The results of single-cell compression simulations show that the conclusions found by analytical models and experiments can be reproduced at least qualitatively. Relaxation tests revealed that plant cells have short relaxation times (1 micros-10 micros) compared to mammalian cells. Simulations performed on cell aggregates indicated an influence of the cellular organization to the tissue response, as was also observed in experiments done on tissues with a similar structure.

A meshfree model for plant tissue deformations during drying

“…This wall particle-based cell-cell interaction model is computationally much more efficient than the fluid particle based method proposed by Van Liedekerke et al [15,16], since there are fewer neighbouring particle pairs.…”

“…Since cell fluid is mainly a water-based solution, sph is used to numerically model the cell fluid by treating it as a high viscous incompressible Newtonian fluid with low Reynolds number flow characteristics [15,16]. We use a similar cell fluid model to that of Karunasena et al [19,20], involving four types of force interactions: fluid pressure forces F p , fluid viscous forces F v , wall-fluid repulsion forces F rw and wall-fluid attraction forces F a (see Figure 3).…”

“…However, this fundamental tissue arrangement can be used as a step in developing larger tissue structures by aggregation. Following the tissue generation approach introduced by Van Liedekerke et al [16], a set of individual cells are initiated as squares and aggregated into a simplified tissue structure (see Figure 6(a)) by maintaining a fixed initial gap between them. The model accounts for the key physical property of the middle lamella (composed of pectin): its stiffness.…”

“…In this regard, the main factors involved are the particle resolution [19], influence domain particle number [10,23,19] and the initial relative locations of boundary and interior particles [23,19]. Here, the computational accuracy of the cylindrical cell model is defined in terms of the model consistency error which was defined by Van Liedekerke et al in their sph-dem cell model [16]. For moderate model resolutions, the optimum number of cell wall particles n w = 100 to minimize the model consistency error at a moderate computational cost [19].…”

“…sph is quite adaptive and new physics is easily incorporated [10]. With the use of sph and a discrete element method (dem), Van Liedekerke et al [15,16] recently developed a comprehensive numerical model to study the basic mechanical responses of plant cells. However, there is a clear research gap for a numerical model based on meshfree methods, specifically for deformations of plant cells during drying.…”