A cell growth algorithm for virtual leaf tissue generation is presented based on the biomechanics of plant cells in tissues. The algorithm can account for typical differences in epidermal layers, palisade mesophyll layer and spongy mesophyll layer which have characteristic differences in the shape of cells, arrangement of cells and void fractions present in each layer. The cell is considered as a closed thin walled structure, maintained in tension by turgor pressure. The cell walls are modelled as linear elastic elements which obey Hooke's law. A Voronoi tessellation was used to generate the initial topology of the cells in the spongy mesophyll layer. Then two layers of brick structured cells are added to the top of it to represent the palisade mesophyll and upper epidermis and a single layer is added at bottom of the Voronoi tessellation to represent the lower epidermal layer. Intercellular air spaces are generated by separating the Voronoi cells along the edges starting from where three Voronoi cells are in contact (schizogenous origin) and/or by deleting some of the Voronoi cells (lysigenous origin). 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 the ordinary differential equation solver in MatLab. Statistical comparison of the cellular characteristics with 2D cross-sectional slices of real leaf tissue of tomato is excellent. The virtual tissues can be used to systematically study effects of leaf structure on water and gas exchange.
- Hooke's law
- Intercellular air space formation
- Newton's law
- Palisade mesophyll
- Spongy mesophyll