Abstract
A cell-growth-based algorithm is presented based on the biomechanics of plant cells in tissues to help explain the typical differences in cellular architecture found between different pome fruit species, cultivars and tissues. The cell was considered as a closed thin-walled structure, maintained in tension by turgor pressure. The cell walls of adjacent cells were modelled as parallel and linearly elastic elements, which obeyed Hooke’s law. A Voronoi tessellation was used to generate the initial topology of the cells. Cell expansion then resulted from turgor pressure acting on the yielding cell wall material. To find the sequence positions of each vertex of the cell walls, and thus, the shape of the cells with time, a system of differential equations for the positions and velocities of each vertex were established and solved using a Runge–Kutta fourth and fifth order (ODE45) method. The model was used to generate realistic 2D fruit tissue structures composed of cells of random shapes and sizes, cell walls and intercellular spaces. Comparison was made with fruit tissue micrographs. The virtual tissues can be used for numerical simulation of heat and mass transfer phenomena or mechanical deformation during controlled atmosphere storage of fresh pome fruit.
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References
Baskin, T. I. (2005). An anisotropic expansion of the plant cell wall. Annual Review of Cell and Developmental Biology, 21, 203–222.
Dupuy, L., Mackenzie, J., & Haseloff, J. (2010). Coordination of plant cell division and expansion in a simple morphogenetic system. Proceedings of the National Academy of Sciences of the United States of America, 107(6), 2711–2716.
Dupuy, L., Mackenzie, J., Rudge, T., & Haseloff, J. (2008). A system for modeling cell–cell interactions during plant morphogenesis. Annals of Botany, 101(8), 1255–1265.
Fisher, J. B., & Honda, H. (1977). Computer simulations of branching pattern and geometry in Terminalia (Combretacea), a tropical tree. Botanical Gazette, 138(4), 377–384.
Fisher, J. B., & Honda, H. (1979). Branch geometry and effective leaf area: A study of Terminalia-branching pattern parts I & II. American Journal of Botany, 66, 633–655.
Franck, C., Lammertyn, J., Ho, Q., Verboven, P., Verlinden, B., & Nicolaï, B. (2007). Browning disorders in pear fruit. Postharvest Biology and Technology, 43(1), 1–13.
Ho, Q., Verboven, P., Mebatsion, H., Verlinden, B., Vandewalle, S., & Nicolaï, B. (2009). Microscale mechanisms of gas exchange in fruit tissue. The New Phytologist, 182(1), 163–174.
Ho, Q., Verboven, P., Verlinden, B., Herremans, E., Wevers, M., Carmeliet, J., & Nicolaï, B. (2011). A 3-D multiscale model for gas exchange in fruit. Plant Physiology, 155(3), 1158–1168.
Ho, Q. T., Verboven, P., Verlinden, B. E., Lammertyn, J., Vandewalle, S., & Nicolaï, B. M. (2008). A continuum model for metabolic gas exchange in pear fruit. PLoS Computational Biology, 4(3), e1000023.
Ho, Q., Verboven, P., Verlinden, B., Schenk, A., Delele, M., Rolletschek, H., Vercammen, J., & Nicolaï, B. (2010). Genotype effects on internal gas gradients in apple fruit. Journal of Experimental Botany, 61(10), 2745–2755.
Ho, Q., Verlinden, B., Verboven, P., Vandewalle, S., & Nicolaï, B. (2006). A permeation-diffusion-reaction model of gas transport in cellular tissue of plant materials. Journal of Experimental Botany, 57(15), 4215–4224.
Justel, A., Pena, D., & Zamar, R. (1997). A multivariant Kolmogorov–Smirnov test of goodness of fit. Statistics and Probability Letters, 35, 251–259.
Lammertyn, J., Scheerlinck, N., Jancsók, P., Verlinden, B., & Nicolaï, B. (2003a). A respiration-diffusion model for 'Conference' pears I: model development and validation. Postharvest Biology and Technology, 30(1), 29–42.
Lammertyn, J., Scheerlinck, N., Jancsók, P., Verlinden, B. E., & Nicolaï, B. M. (2003b). A respiration-diffusion model for 'conference' pears. II. simulations and relation to core breakdown. Postharvest Biology and Technology, 30(1), 43–55.
Lindenmayer, A. (1968). Mathematical model for cellular interaction in development, parts I & II. Journal of Theoretical Biology, 18, 280–315.
Lindenmayer, A. (1984). Models of plant tissue development with cell division orientation regulated by preprophase bands of microtubules. Differentiation, 26, 1–10.
Lindenmayer, A. (1987). Models for multicellular development: Characterization, inference and complexity of L-Systems. In A. Kelmonovà & J. Kelmen (Eds.), Trends, techniques and problems in theoretical computer science (Lecture notes in computer science 281, pp. 138–168). Berlin: Springer.
Lindenmayer, A., & Prusinkiewicz, P. (1989). Developmental models of multicellular organisms: A computer graphics perspective. In C. Langton (Ed.), Artificial life: Proceedings of an interdisciplinary workshop on the synthesis and simulations of living systems held on September, 1987, in Los Alamos, New Mexico (pp. 221–249). Redwood City: Addison-Wisley.
Mebatsion, H. K., Verboven, P., Ho, Q. T., Mendoza, F., Verlinden, B. E., Nguyen, T. A., & Nicolaï, B. M. (2006b). Modelling fruit microstructure using novel ellipse essellation algorithm. CMES: Computer Modeling in Engineering & Sciences, 14(1), 1–14.
Mebatsion, H., Verboven, P., Jancsók, P., Ho, Q., Verlinden, B., & Nicolaï, B. (2008). Modelling 3D fruit tissue microstructure using a novel ellipsoid tessellation algorithm. CMES: Computer Modeling in Engineering & Sciences, 29(3), 137–149.
Mebatsion, H., Verboven, P., Melesse, A. E., Billen, J., Ho, Q., & Nicola, B. (2009). A novel method for 3-D microstructure modelling of pome fruit tissue using synchrotron radiation tomography image. Journal of Food Engineering, 93(2), 141–148.
Mebatsion, H. K., Verboven, P., Verlinden, B. E., Ho, Q. T., Nguyen, T. A., & Nicolaï, B. M. (2006a). Microscale modelling of fruit tissue using Voronoi tessellations. Computers and Electronics in Agriculture, 52, 36–48.
Nakamura, A., Lindenmayer, A., & Aizawa, A. (1986). Some systems for map generation. In G. Rozenberg & A. Salomaa (Eds.), The Book of L (pp. 323–332). Springer-Verlag, Berlin.
Nguyen, T. A., Dresselaers, T., Verboven, P., D'hallewin, G., Culeddu, N., Van Hecke, P., & Nicolaï, B. M. (2006). Finite element modelling and MRI validation of 3d transient water profiles in pears during postharvest storage. Journal of the Science of Food and Agriculture, 86(5), 745–756.
Rudge, T., & Haseloff, J. (2005). A computational model of cellular morphogenesis in plants. Lecture Notes in Computer Science: Advances in Artificial Life, 3630, 78–87.
Studman, J. (1999). Fruit and vegetables, handling systems and packaging. In F. W. Bakker-Arkema (Ed.), The International Commission of Agricultural Engineering, Hand Book of Agricultural Engineering, Agro Processing Engineering (pp. 291–339). Niles Road: The Society for Engineering in Agriculture, Food, and Biological Systems.
Tao, S. T., Khanizadeh, S., & Zhang, S. L. (2009). Anatomy, ultrastructure and lignin distribution of stone cells in two Pyrus species. Plant Science, 176, 413–419.
Verboven, P., Kerckhofs, G., Mebatsion, H. K., Ho, Q. T., Temst, K., Wevers, M., Cloetens, P., & Nicolaï, B. M. (2008). 3-D gas exchange pathways in pome fruit characterised by synchrotron X-ray computed tomography. Plant Physiology, 47, 518–527.
Wu, N., & Pitts, M. J. (1999). Development and validation of a finite element model of an apple fruit cell. Postharvest Biology and Technology, 16, 1–8.
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Financial support by the Flanders Fund for Scientific Research (project FWO G.0603.08), K.U. Leuven (project OT 08/023) and the EC (project InsideFood FP7-226783) is gratefully acknowledged.
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Abera, M.K., Fanta, S.W., Verboven, P. et al. Virtual Fruit Tissue Generation Based on Cell Growth Modelling. Food Bioprocess Technol 6, 859–869 (2013). https://doi.org/10.1007/s11947-011-0775-4
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DOI: https://doi.org/10.1007/s11947-011-0775-4