Paul Van Liedekerke

Mechanisms of soft cellular tissue bruising. A particle based simulation approach

This paper is concerned with modeling the mechanical behavior of cellular tissue in response to dynamic stimuli. The objective is to investigate the formation of bruises and other damage in tissue under excessive loading. We propose a particle based model to numerically study cells and aggregates of cells described on to subcellular detail. The model focuses on a parenchyma cell type in which two important features are present: the cells interior liquid-like phase inducing hydrodynamic phenomena; and the cell wall, a viscoelastic-plastic solid membrane that encloses the protoplast. The cell fluid is modeled by a Smoothed Particle Hydrodynamics (SPH) technique, while for the cell wall and cell adhesion a nonlinear discrete element model is proposed. Failure in the system is addressed to either cell wall rupture or to debonding of the middle lamella. We show that the model is able to reproduce experimental data of quasistatic compression, and investigate the role of the protoplasm viscosity and the cellular structure on the dynamics of the aggregate system. This indicates that a high viscosity causes better guidance of mechanical stresses through the tissue and can result in a higher penetration of damage, whereas low values will cause more local bruising effects.

A cell based modelling framework for skeletal tissue engineering applications

In this study, a cell based lattice free modelling framework is proposed to study cell aggregate behaviour in bone tissue engineering applications. The model encompasses cell-to-cell and cell-environment interactions such as adhesion, repulsion and drag forces. Oxygen, nutrients, waste products, growth factors and inhibitors are explicitly represented in the model influencing cellular behaviour. Furthermore, a model for cell metabolism is incorporated representing the basic enzymic reactions of glycolysis and the Krebs cycle. Various types of cell death such as necrosis, apoptosis and anoikis are implemented. Finally, an explicit model of the cell cycle controls the proliferation process, taking into account the presence or absence of various metabolites, sufficient space and mechanical stress. Several examples are presented demonstrating the potential of the modelling framework. The behaviour of a synchronised cell aggregate under ideal circumstances is simulated, clearly showing the different stages of the cell cycle and the resulting growth of the aggregate. Also the difference in aggregate development under ideal (normoxic) and hypoxic conditions is simulated, showing hypoxia induced necrosis mainly in the centre of the aggregate grown under hypoxic conditions. The next step in this research will be the application of this modelling framework to specific experimental set-ups for bone tissue engineering applications.

Virtual Fruit Tissue Generation Using Cell Growth Modelling

Fruit tissues are very heterogeneous at the microscale and the cellular architecture determines to a large extent the behaviour and development of the fruit and their behaviour during postharvest storage. The cellular architecture is established during the growth of the fruit after fertilization. Understanding the development and the changes of the microstructure of fruits would be an important step to help explain and optimize fruit production and postharvest storage. Pome fruit tissue generators exist today but are based on digitized 2-D or 3-D images of the cellular architecture, which require experimental input in terms of microscopic images. Furthermore, the algorithms today do not provide insight in the reasons why a certain tissue structure develops. To close this knowledge gap, a cell growth-based algorithm is being developed using the biomechanics of plant cells in tissues to help explain the typical differences in cellular architecture found between different fruit species and cultivars. The cell is considered as a closed thin walled structure, maintained in tension by turgor pressure. The cell walls of adjacent cells are modeled as parallel and linearly elastic elements which obey Hooke’s law. A Voronoi tessellation is used to generate the initial topology of the cells. Cell expansion is then resulted from turgor pressure acting on the yielding cell wall material. To find the sequence positions of each vertex and thus the shape of the layer with time, a system of differential equations for the positions and velocities of each vertex are established and solved using a forward Euler method. The model is implemented in Matlab (The Mathworks, Natick, MA) and is used to generate realistic fruit tissue structures composed of cells of random shapes and sizes, cell walls and intercellular spaces. Comparison is made with fruit tissue micrographs at different development stages. The virtual tissues can be applied to study tissue mechanics and exchange processes of important metabolites.