Experimental determination of Philodendron melinonii and Arabidopsis thaliana tissue microstructure and geometric modeling via finite-edge centroidal Voronoi tessellation

Plant petioles and stems are hierarchical cellular structures, displaying structural features defined at multiple length scales. One or more of the intermediate hierarchical levels consists of tissues, in which the cellular distribution is quasirandom. The current work focuses on the realistic modeling of plant tissue microstructures. The finite-edge centroidal Voronoi tessellation (FECVT) is here introduced to overcome the drawbacks of the semi-infinite edges of a typical Voronoi model. FECVT can generate a realistic model of a tissue microstructure, which might have finite edges at its border, be defined by a boundary contour of any shape, and include complex heterogeneity and cellular gradients. The centroid-based Voronoi tessellation is applied to model the microstructure of the Philodendron melinonii petiole and the Arabidopsis thaliana stem, which both display intense cellular gradients. FECVT coupled with a digital image processing algorithm is implemented to capture the nonperiodic microstructures of plant tissues. The results obtained via this method satisfactorily obey the geometric, statistical, and topological laws of naturally evolved cellular solids. The predicted models are also validated by experimental data.