Metadel Abera

Virtual Fruit Tissue Generation Based on Cell Growth Modelling

A cell-growth-based algorithm is presented based on the biomechanics of plant cells in tissues to help explain the typical differences in cellular architecture found between different pome fruit species, cultivars and tissues. The cell was considered as a closed thin-walled structure, maintained in tension by turgor pressure. The cell walls of adjacent cells were modelled as parallel and linearly elastic elements, which obeyed Hooke’s law. A Voronoi tessellation was used to generate the initial topology of the cells. Cell expansion then resulted from turgor pressure acting on the yielding cell wall material. To find the sequence positions of each vertex of the cell walls, and thus, the shape of the cells with time, a system of differential equations for the positions and velocities of each vertex were established and solved using a Runge–Kutta fourth and fifth order (ODE45) method. The model was used to generate realistic 2D fruit tissue structures composed of cells of random shapes and sizes, cell walls and intercellular spaces. Comparison was made with fruit tissue micrographs. The virtual tissues can be used for numerical simulation of heat and mass transfer phenomena or mechanical deformation during controlled atmosphere storage of fresh pome fruit.

Automatic analysis of the 3-D microstructure of fruit parenchyma tissue using X-ray micro-CT explains differences in aeration

Background3D high-resolution X-ray imaging methods have emerged over the last years for visualising the anatomy of tissue samples without substantial sample preparation. Quantitative analysis of cells and intercellular spaces in these images has, however, been difficult and was largely based on manual image processing. We present here an automated procedure for processing high-resolution X-ray images of parenchyma tissues of apple (Malus × domestica Borkh.) and pear (Pyrus communis L.) as a rapid objective method for characterizing 3D plant tissue anatomy at the level of single cells and intercellular spaces.ResultsWe isolated neighboring cells in 3D images of apple and pear cortex tissues, and constructed a virtual sieve to discard incorrectly segmented cell particles or unseparated clumps of cells. Void networks were stripped down until their essential connectivity features remained. Statistical analysis of structural parameters showed significant differences between genotypes in the void and cell networks that relate to differences in aeration properties of the tissues.ConclusionsA new model for effective oxygen diffusivity of parenchyma tissue is proposed that not only accounts for the tortuosity of interconnected voids, but also for significant diffusion across cells where the void network is not connected. This will significantly aid interpretation and analysis of future tissue aeration studies. The automated image analysis methodology will also support pheno- and genotyping studies where the 3D tissue anatomy plays a role.

3D Virtual Pome Fruit Tissue Generation Based on Cell Growth Modeling

A 3D virtual fruit tissue generator is presented that can distinctly define the microstructural components of a fruit tissue and that can be used to model important physical processes such as gas transport during controlled atmosphere storage. The model is based on the biomechanics of plant cells in tissues. The main merit of this algorithm is that it can account for typical differences in intercellular air space networks and in cell size and shape found between different fruit species and tissues. 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, linear elastic elements which obey Hookes law. A 3D Voronoi tessellation is used to generate the initial topology of the cells. Intercellular air spaces of schizogenous origin are generated by separating the Voronoi cells along the edges where three Voronoi cells are in contact; while intercellular air spaces of lysigenous origin are generated by deleting (killing) some of the Voronoi cells randomly. Cell expansion then results from turgor pressure acting on the yielding cell wall material. To find the sequence of positions of each vertex and thus the shape of the tissue with time, a system of differential equations for the positions and velocities of each vertex is established and solved using a Matlab ordinary differential equation solver. Statistical comparison with synchrotron tomography images of fruit tissue is excellent. The virtual tissues can be used to study tissue mechanics and exchange processes of important metabolites.

A multiphase pore scale network model of gas exchange in apple fruit

A multiphase pore scale network model was developed to describe mass transfer in apple fruit. The 3D microscale geometry of the tissue was reconstructed from synchrotron radiation tomography images. Individual cells and pores were identified using a watershed segmentation procedure on a Euclidean distance map of the tissue microstructure. Further morphological characteristics of each individual pore, including its volume, connections to the neighbors and the connected area between the pore and its neighbors, were determined. The tissue was represented by a network of nodes (simplified individual pores and cells) that were interconnected by tubes. The transport of the respiratory gases O2 and CO2 between two nodes was modelled using diffusion laws and irreversible thermodynamics, while respiration was taken into account in the individual cellular nodes. A numerical procedure was applied to simulate the gas transport within the discrete network and to compute the local diffusivities of the links in the network. The predicted overall gas diffusivities compared well to experimental data and results computed from a microscale continuum model, thereby validating the pore scale network model. This approach is a computationally attractive alternative to a continuum multiphase approach for modelling gas transport in fruit.

Multiscale Modeling of Food Processes

Food unit operations involve complex transport phenomena. As experimental characterization of transport processes is not usually straightforward, mathematical models are often used to improve our understanding of them, and, more importantly, to design and optimize food processes. Contrary to typical engineering materials such as steel or brick, food tissues are intrinsically multiscale assemblies with different characteristics at each spatial scale. As a consequence, multiscale modeling is required. This article gives a systematic introduction to multiscale modeling in food processes, including imaging techniques for food microstructure, model formulation, and numerical solution techniques. Several applications in food process engineering will be presented. The article concludes with a discussion on future prospects for the use of multiscale modeling.

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.