Modeling Fruit Microstructure Using an Ellipse Tessellation Algorithm

Modeling plant microstructure is of great interest to food engineers to simulate the behavior of the physical properties (e.g., concerning mass transfer, mechanics) of plant tissues at the cellular level. The generation of geometrical models of microscopic structures is considered a prime requirement to develop microscale models to study and describe these properties. For this end, this paper presents a novel ellipse tessellation algorithm to generate a 2D geometrical model of apple tissue. Ellipses are used to quantify the orientation and aspect ratio of cells on a microscopic image. The cell areas and centroids of each cell are also determined by means of a numerical procedure. These characteristic quantities are then described by means of probability density functions. The model tissue geometry is generated from the ellipses which are truncated when neighboring areas overlap. As a result, a virtual microstructure consisting of truncated ellipses fills up the entire space with the same number of cells as that of microscopic images and with similar area, orientation and aspect ratio distribution. The spatial variability of the geometric characteristics (cell area size, cell shape, cell orientation and tissue porosity) of the virtual cellular structure was also evaluated and compared to that of the microscopic images. Statistical analysis showed that the virtual geometry generated with this approach yields spatially equivalent geometries to that of real fruit microstructures. Compared to the more common algorithm of Voronoi diagrams, ellipse tesselation is superior for generating the microstructure of tissue. The extension of the algorithm to 3D is straightforward. These representative tissues will be exported into a finite element environment via interfacing codes to perform in silico experiments for estimating gas and moisture diffusivities and investigating their relation with fruit microstructure.