Modeling 3D Fruit Tissue Microstructure Using a Novel Ellipsoid Tessellation Algorithm

Transport processes of gas and moisture are among the most important physiological processes in plant tissue. Microscale transport models based on Navier-Stokes equations provide insight into such processes at the microscopic scale. Due to microscopic complexity, numerical solutions based on the finite element or finite volume methods are mandatory. Therefore, a 3D geometric model of the tissue is essential. In this article, a novel algorithm for geometric reconstruction of 2D slices of synchrotron tomographic images is presented. The boundaries of 2D cells on individual slices were digitized to establish a set of boundary coordinates and the slice index of individual cells. Then, ellipsoids that fit these sets of points were determined using the Least Squared Fitted Ellipsoids (LSFEs) algorithm. This algorithm is a modified version of Minimum Volume Circumscribing Ellipsoid (MVCE) algorithm that produces minimum volume ellipsoids that encloses all sets of points. Using LSFEs, the size of the MVCEs were optimized to fit the set of points in a least square sense. The 3D model tissue geometry was then generated from these sets of ellipsoids, which were truncated when neighbouring volumes overlapped. As a result, a virtual 3D microstructure consisting of truncated ellipsoids fills up the entire volume with the same number of cells as that of the tomographic images. Keyword: Multi-scale modelling, gas transport, water transport, virtual tissue, microtomog1 BIOSYST-MeBioS, Katholieke Universiteit Leuven, W. De Croylaan 42, B-3001 Leuven, Belgium 2 Corresponding author. Phone: +32 16320590; E-mail: Hibru.Mebatsion@biw.kuleuven.be; Fax: +32 16322955 3 Flanders Center of Postharvest Technology, W. De Croylaan 42, B-3001 Leuven, Belgium raphy

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