M. Abera, S. Fanta, P. Verboven, P. Van Liedekerke , B. Nicolaï , J. Carmeliet
Fruit tissues are very heterogeneous at the microscale and the cellular architec¬ture 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.
Abera, M., Fanta, S., Verboven, P., Van Liedekerke , P., Nicolaï , B. and Carmeliet, J. (2011). VIRTUAL FRUIT TISSUE GENERATION USING CELL GROWTH MODELING. Acta Hortic. 919, 107-114
DOI: 10.17660/ActaHortic.2011.919.13
cellular architecture, biomechanics, turgor pressure, Voronoi tessellation, thin-walled structure, Hooke's law, expansive growth

Acta Horticulturae