In this paper we present an overview of agentbased models that are used to simulate mechanical and physiological phenomena in cells and tissues, and we discuss underlying concepts, limitations, and future perspectives of these models. As the interest in cell and tissue mechanics increase, agent-based models are becoming more common the modeling community. We overview the physical aspects, complexity, shortcomings, and capabilities of the major agent-based model categories: lattice-based models (cellular automata, lattice gas cellular automata, cellular Potts models), off-lattice models (center-based models, deformable cell models, vertex models), and hybrid discrete-continuum models. In this way, we hope to assist future researchers in choosing a model for the phenomenon they want to model and understand. The article also contains some novel results.

Adhesion governs to a large extent the mechanical interaction between a cell and its microenvironment. As initial cell spreading is purely adhesion driven, understanding this phenomenon leads to profound insight in both cell adhesion and cell-substrate interaction. It has been found that across a wide variety of cell types, initial spreading behavior universally follows the same power laws. The simplest cell type providing this scaling of the radius of the spreading area with time are modified red blood cells (RBCs), whose elastic responses are well characterized. Using a mechanistic description of the contact interaction between a cell and its substrate in combination with a deformable RBC model, we are now able to investigate in detail the mechanisms behind this universal power law. The presented model suggests that the initial slope of the spreading curve with time results from a purely geometrical effect facilitated mainly by dissipation upon contact. Later on, the spreading rate decreases due to increasing tension and dissipation in the cell's cortex as the cell spreads more and more. To reproduce this observed initial spreading, no irreversible deformations are required. Since the model created in this effort is extensible to more complex cell types and can cope with arbitrarily shaped, smooth mechanical microenvironments of the cells, it can be useful for a wide range of investigations where forces at the cell boundary play a decisive role.

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.

Since many years food engineers have attempted to describe physical phenomena such as heat and mass 31 transfer that occur in food during unit operations by means of mathematical models. Foods are hierarchi-32 cally structured and have features that extend from the molecular scale to the food plant scale. In order to 33 reduce computational complexity, food features at the fine scale are usually not modeled explicitly but 34 incorporated through averaging procedures into models that operate at the coarse scale. As a conse-35 quence, detailed insight into the processes at the microscale is lost, and the coarse scale model parame-36 ters are apparent rather than physical parameters. As it is impractical to measure these parameters for 37 the large number of foods that exist, the use of advanced mathematical models in the food industry is 38 still limited. A new modeling paradigm -multiscale modeling -has appeared that may alleviate these 39 problems. Multiscale models are essentially a hierarchy of sub-models which describe the material 40 behavior at different spatial scales in such a way that the sub-models are interconnected. In this article 41 we will introduce the underlying physical and computational concepts. We will give an overview of 42 applications of multiscale modeling in food engineering, and discuss future prospects. 43

This paper is concerned with addressing how biological cells react to mechanical impulse. We propose a particle based model to numerically study the mechanical response of these cells with subcellular detail. The model focuses on a plant cell in which two important features are present: (1) the cell's interior liquidlike phase inducing hydrodynamic phenomena, and (2) the cell wall, a viscoelastic solid membrane that encloses the protoplast. In this particle modeling framework, the cell fluid is modeled by a standard smoothed particle hydrodynamics (SPH) technique. For the viscoelastic solid phase (cell wall), a discrete element method (DEM) is proposed. The cell wall hydraulic conductivity (permeability) is built in through a constitutive relation in the SPH formulation. Simulations show that the SPH-DEM model is in reasonable agreement with compression experiments on an in vitro cell and with analytical models for the basic dynamical modes of a spherical liquid filled shell. We have performed simulations to explore more complex situations such as relaxation and impact, thereby considering two cell types: a stiff plant type and a soft animal-like type. Their particular behavior (force transmission) as a function of protoplasm and cell wall viscosity is discussed. We also show that the mechanics during and after cell failure can be modeled adequately. This methodology has large flexibility and opens possibilities to quantify problems dealing with the response of biological cells to mechanical impulses, e.g., impact, and the prediction of damage on a (sub)cellular scale.