[en] The pore-size distribution (PSD) has an important influence on the complex gas transport phenomena (02 and CO(2)) that occur in apple tissue during storage under controlled atmosphere conditions. It defines the apple tissue microstructure that is correlated to many other apple properties. In this article multifractal analysis (MFA) has been used to study the multiscale structure of the PSD using generalized dimensions in three varieties of apples (Jonagold, Greenstar, and Kanzi) based on X-ray imaging technology (8.5 mu m resolution). Tomographic images of apple samples were taken at two positions within the parenchyma tissue: close to the peel and near to the core. The images showed suitable scaling properties. The generalized dimensions were determined with an R(2) greater than 0.98 in the range of moment orders between -1 and +10. The variation of D(q) with respect to q and the shape of the multifractal generalized spectrum revealed that the PSD structure of apple tissue has properties close to multifractal self-similarity measures. Comparisons among cultivars showed that, in spite of the complexity and variability of the pore space of these apple samples, the extracted generalized dimensions from PSD were significantly different (p < 0.05). The generalized dimensions D(0), D(1), D(2), and the quantity D(0)-D(2) could be used to discriminate tissue samples from different positions or cultivars. Also, high correlations were found between these parameters and the porosity (R(2) >= 0.935). These results demonstrate that MFA is an appropriate tool for characterizing the internal pore-size distribution of apple tissue and thus may be used as a quantitative measure to understand how tissue microstructure affects important physical properties of apple. (C) 2010 Elsevier Ltd. All rights reserved.
Multifractal properties of pore-size distribution in apple tissue using X-ray imaging
Publication date :
2010
Journal title :
Journal of Food Engineering
ISSN :
0260-8774
Publisher :
Elsevier Sci Ltd, Oxford, United Kingdom
Volume :
99
Issue :
2
Pages :
206-215
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
K.U. Leuven [OT 04/31] Fund for Scientific Research Flanders (F.W.O. - Vlaanderen) [G.0200.02]
Commentary :
The authors wish to thank to K.U. Leuven (Project OT 04/31) and the Fund for Scientific Research Flanders (F.W.O. - Vlaanderen, Project G.0200.02) for financial support for this investigation.
Alamilla-Beltrán L., Chanona-Pérez J.J., Jiménez-Aparicio A.R., and Gutierrez-López G.F. Description of morphological changes of particles along spray drying. Journal of Food Engineering 67 (2005) 179-184
Baoping, J., 1999. Nondestructive technology for fruits grading. In: Proceedings of 99 International Conference on Agricultural Engineering, Beijing, China, December, pp. IV127-IV133.
Baumann H., and Henze J. Intercellular space volume of fruit. Acta Horticulturae 138 (1983) 107-111
Bear J. Dynamics of Fluids in Porous Media (1972), Dover Publishing Co., New York
Celia M., Reeves P., and Ferrand L. Recent advances in pore scale models for multiphase flow in porous media. Reviews of Geophysics Supplement 33 (1995) 1049-1057
Cheng Q., Banks N.H., Nicholson S.E., Kingsley A.M., and Mackay B.R. Effects of temperature on gas exchange of 'Braeburn' apples. New Zealand Journal of Crop and Horticultural Science 26 (1998) 299-306
Chhabra A., and Jensen R.V. Direct determination of the f (α) singularity spectrum. Physical Review Letters 62 12 (1989) 1327-1330
Cox L.B., and Wang J.S.Y. Fractal surfaces: measurements and applications in earth sciences. Fractals 1 (1993) 87-117
Dathe A., Tarquis A.M., and Perrier E. Multifractal analysis of pore- and solid-phases in binary two-dimensional images of natural porous structures. Geoderma 134 (2006) 318-326
De Smedt V., Pauwels E., De Baerdemaeker J., and Nicolaï B.M. Microscopic observation of mealiness in apples: a quantitative approach. Postharvest Biology and Technology 14 (1998) 151-158
Dražeta L., Lang A., Alistair J.H., Richard K.V., and Paula E.J. Air volume measurement of 'Braeburn' apple fruit. Journal of Experimental Botany 55 (2004) 1061-1069
Eghball B., Schepers J.S., Negahban M., and Schlemmer M.R. Spatial and temporal variability of soil nitrate and corn yield: multifractal analysis. Agronomy Journal 95 (2003) 339-346
Esau K. Anatomy of Seed Plants. second ed. (1977), John Wiley and Sons, New York
Evertsz C.J.G., and Mandelbrot B.B. Multifractal measures. In: Peitgen H., Jürgens H., and Saupe D. (Eds). Chaos and Fractals (1992), Springer, Berlin 922-953
Feder J. Fractals (1988), Plenum Press, New York
FracLab, 2003. Notes on the generalized dimension spectrum and multifractality. FracLac for ImageJ. URL: .
Franck C., Lammertyn J., Ho Q.T., Verboven P., Verlinden B.E., and Nicolai B.M. Browning disorders in pear fruit. Postharvest Biology and Technology 43 (2007) 1-13
Gonzales-Barron U., and Butler F. Fractal texture analysis of bread crumb digital images. European Food Research And Technology 226 (2008) 721-729
Grassberger P., and Procaccia I. Characterization of strange attractors. Physical Review Letters 50 (1983) 346-349
Hagiwara T., Wang H.L., Suzuki T., and Takai R. Fractal analysis of ice crystals in frozen food. Journal Of Agricultural And Food Chemistry 50 (2002) 3085-3089
Halsey T.C., Jensen M.H., Kadanoff L.P., Procaccia I., and Shraiman B.I. Fractal measures and their singularities: the characterization of strange sets. Physical Review A 33 2 (1986) 1141-1151
Harker F.R., and Ferguson I.B. Calcium ion transport across discs of the cortical flesh of apple fruit in relation to fruit development. Physiol Plant 74 (1988) 695-700
Harker F.R., and Hallet I.C. Physiological changes associated with development of mealiness of apple fruit during cool storage. HortScience 27 (1992) 1291-1294
Harker F.R., Watkins C.B., Brookfield P.L., Miller M.J., Reid S., Jackson P.J., Bieleski R.L., and Bartley T. Maturity and regional influences on watercore development and its postharvest disappearance in 'Fuji' apples. Journal of the American Soil Science Society 124 (1999) 166-172
Hentchel H.G.E., and Procaccia I. The infinite number of generalized dimensions of fractals and strange attractors. Physica D 8 (1983) 435-444
Ho Q.T., Verlinden B.E., Verboven P., and Nicolaï B.M. Gas diffusion properties at different positions in the pear. Postharvest Biology and Technology 41 (2006) 113-120
Ho Q.T., Verboven P., Verlinden B.E., Lammertyn J., Vandewalle S., and Nicolaï B.M. A continuum model for gas exchange in pear fruit. PLOS Computational Biology 4 3 (2008) e1000023
Ho Q.T., Verboven P., Mebatsion H.K., Verlinden B.E., Vandewalle S., and Nicolaï B.M. Microscale mechanisms of gas exchange in fruit tissue. New Phytologist (2009) 10.1111/j.1469-8137.2008.02732.x
Ho, Q.T., Verboven, P., Verlinden, B.E., Schenk, A., Rolletschek, H., Vercammen, J., Nicolaï, B.M., 2010. Genotype effects on internal gas gradients in apple fruit. Journal of Experimental Botany, submitted for publication.
Kerdpiboon S., Devahastin S., and Kerr W.L. Comparative fractal characterization of physical changes of different food products during drying. Journal Of Food Engineering 83 (2007) 570-580
Ketipearachchi K.W., and Tatsumi J. Local fractal dimensions and multifractal analysis of the root system of legumes. Plant Production Science 3 (2000) 289-295
Khan A.A., and Vincent J.F.V. Anisotropy of apple parenchyma. Journal of the Science of Food and Agriculture 52 (1990) 455-466
Khan A.A., and Vincent J.F.V. Compressive stiffness and fracture properties of apple and potato parenchyma. Journal of Texture Studies 24 (1993) 423-435
Khan A.A., and Vincent J.F.V. Anisotropy in the fracture properties of apple flesh as investigated by crack-opening tests. Journal of Materials Science 28 (1993) 45-51
Korvin G. Fractals Models in the Earth Sciences (1992), Elsevier, Amsterdam
Kravchenko A.N., Boast C.W., and Bullock D.G. Multifractal analysis of soil variability. Agronomy Journal 91 (1999) 1033-1041
Kuroki S., Oshita S., Sotome I., Kawagoe Y., and Seo Y. Visualization of 3-D network of gas-filled intercellular spaces in cucumber fruit after harvest. Postharvest Biology and Technology 33 (2004) 255-262
Lévi Véhel J. Fractal approaches in signal processing. In: Evertsz C.J.G., Peitgen H.O., and Voss R.F. (Eds). Fractal Geometry and Analysis. The Mandelbrot Festschrift, Curacao 1995 (1996), World Scientific Singapore
Machs J., Mas F., and Sagues F. Two representations in multifractal analysis. Journal of Physics A: Mathematics and General 28 (1995) 5607-5622
Mandelbrot B.B. The Fractal Geometry of Nature (1989), Freeman, San Francisco
Mardia K.V., and Hainsworth T.J. A spatial thresholding method for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 6 (1988) 919-927
Mebatsion H.K., Verboven P., Verlinden B.E., Ho Q.T., Nguyen T.A., and Nicolaï B. Microscale modeling of fruit tissue using Voronoi tessellations. Computers and Electronics in Agriculture 52 (2006) 36-48
Mebatsion H.K., Verboven P., Ho Q.T., Mendoza F., Verlinden B.E., Nguyen T.A., and Nicolaï B. Modeling fruit microstructure using novel ellipse tessellations algorithm. Computer Modeling in Engineering and Science 14 (2006) 1-14
Mendoza, F., Verboven, P., Ho, Q.T., Mebatsion, H.K., Nguyen, T.A., Webers, M., Nicolaï, B.M., 2006. 3-D Microscale geometry of apple tissue using X-ray computed microtomography. In: Proceedings of IUFoST 13th World Congress of Food Sciences and Technology, FOOD IS LIFE, Nantes, France.
Mendoza F., Verboven P., Mebatsion H.K., Kerckhofs G., Wevers M., and Nicolaï B.M. Three-dimensional pore space quantification of apple tissue using X-ray computed microtomography. Planta 226 (2007) 559-570
Oh W., and Lindquist W. Image thresholding by indicator kriging. IEEE Transactions on Pattern Analysis and Machine Intelligence 21 (1999) 590-602
Pascual M., Ascioti F.A., and Caswell H. Intermittency in the plankton: a multifractal analysis of zooplankton biomass variability. Journal of Plankton Research 17 (1995) 1209-1232
Plotnick R.E., Gardner R.H., Hargrove W.W., Prestegaard K., and Perlmutter M. Lacunarity analysis: a general technique for the analysis of spatial patterns. Physical Review E 53 5 (1996) 5461-5468
Posadas A., Giménez D., Quiroz R., and Protz R. Multifractal characterization of soil pore systems. Journal of the American Soil Science Society 65 (2003) 1361-1369
Quevedo R., López-G C., Aguilera J.M., and Cadoche L. Description of food surfaces and microstructural changes using fractal image texture analysis. Journal of Food Engineering 53 (2002) 361-371
Quevedo R., Mendoza F., Aguilera J.M., Chanona J., and Gutiérrez-López G. Determination of senescent spotting in banana (Musa cavendish) using fractal texture Fourier image. Journal of Food Engineering 53 (2008) 361-371
Quevedo R., Jaramillo M., Diaz O., Pedreschi F., and Aguilera J.M. Quantification of enzymatic browning in apple slices applying the fractal texture Fourier image. Journal of Food Engineering 95 (2009) 285-290
Rahman M.S. Physical meaning and interpretation of fractal dimensions of fine particles measured by different methods. Journal of Food Engineering 32 (1997) 447-456
Rajapakse N.C., Banks N.H., Hewett E.W., and Cleland D.J. Development of oxygen concentration gradients in flesh tissues of bulky plant organs. Journal of the American Society for Horticultural Science 115 (1990) 793-797
Raven J.A. Into the voids: the distribution, function, development and maintenance of gas spaces in plants. Annals Botany 78 (1996) 137-142
Rényi A. On a new axiomatic theory of probability. Acta Mathematica Hungarica VI 3-4 (1995) 285-335
Scheuring I., and Riedi R.H. Application of multifractals to the analysis of vegetation pattern. Journal of Vegetation Science 5 (1994) 489-496
Shannon C.E., and Weaver W. The Mathematical Theory of Communication (1949), University of Illinois Press, Chicago
Tang D.M., and Marangoni A.G. Fractal dimensions of simulated and real fat crystal networks in 3D space. Journal Of The American Oil Chemists Society 85 (2008) 495-499
Tu K., De Baerdemaeker J., Deltour R., and de Barsy T. Monitoring post-harvest quality of Granny Smith apple under simulated shelf-life conditions: destructive, non-destructive and analytical measurements. International Journal of Food Science and Technology 31 (1996) 267-276
Verboven P., Kerckhofs G., Mebatsion H.K., Ho Q.T., Temst K., Wevers M., Cloetens P., and Nicolaï B.M. 3-D gas exchange pathways in pome fruit characterized by synchrotron X-ray computed tomography. Plant Physiology 147 (2008) 518-527
Vincent J.F.V. Relationships between density and stiffness of apple flesh. Journal of the Science of Food and Agriculture 31 (1989) 267-276
Vicsek T. Fractal Growth Phenomena. second ed. (1992), Word Scientific Publishing Co., Singapore
Voss R.F. Fractals in nature: From characterization to simulation. In: Peitgen H., and Saupe D. (Eds). The sciences of Fractal Images (1988), Springer, New York 21-69
Volz R.K., Harker F.R., Hallet I.C., and Lang A. Development of texture in apple fruit - a biophysical perspective. Acta Horticulturae 636 (2004) 473-479
Westwood M.N., Batjer L.P., and Billingsley H.D. Cell size, cell number and fruit density of apples as related to fruit size, position in the cluster and thinning method. Proceedings of the American Society for Horticultural Science 91 (1967) 51-62
Xiaoyan G., Peiling Y., Shumei R., and Yunkai L. Multifractal analysis of soil structure under long-term wastewater irrigation based on digital image technology. New Zealand Journal of Agricultural Research 50 (2007) 789-796
Yamaki S., and Ino M. Alteration of cellular compartmentation and membrane permeability to sugars in immature and mature apple fruit. Journal of the American Society for Horticultural Science 117 (1992) 951-954
Yearsley C.W., Banks N.H., and Ganesh S. Temperature effects on the internal lower oxygen limits of apple fruit. Postharvest Biology and Technology 11 (1997) 73-83
Yearsley C.W., Banks N.H., and Ganesh S. Effects of carbon dioxide on the internal lower oxygen limits of apple fruit. Postharvest Biology and Technology 12 (1997) 1-13
