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Fractional-Order Models of Vegetable Tissues

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Fractional-Order Devices

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSNONLINCIRC))

Abstract

In this chapter, we probe a bit further into the study of electrical impedance spectroscopy and what it can tell us about how nature does things. Vegetable matter can be thought of as nature’s fractional-order (FO) devices. They exhibit FO dynamics over a very wide frequency range. We investigate living tissue from the perspective of the electrochemist and electrical engineer. Such exploration can help make additional connections between distinct scientific areas.

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References

  1. Y. Ando, Y. Maeda, K. Mizutani, N. Wakatsuki, S. Hagiwara, H. Nabetani, Effect of air-dehydration pretreatment before freezing on the electrical impedance characteristics and texture of carrots. J. Food Eng. 169, 114–121 (2016)

    Article  Google Scholar 

  2. Y. Ando, K. Mizutani, N. Wakatsuki, Electrical impedance analysis of potato tissues during drying. J. Food Eng. 121, 24–31 (2014)

    Article  Google Scholar 

  3. E. Borges, A. Matos, J. Cardoso, C. Correia, T. Vasconcelos, N. Gomes, Early detection and monitoring of plant diseases by bioelectric impedance spectroscopy, in 2012 IEEE 2nd Portuguese Meeting in Bioengineering (ENBENG) (IEEE, 2012), pp. 1–4

    Google Scholar 

  4. C.J.F. Böttcher, O.C. van Belle, P. Bordewijk, A. Rip, Theory of Electric Polarization, vol. 2 (Elsevier Science Ltd, 1978)

    Google Scholar 

  5. Y. Cao, T. Repo, R. Silvennoinen, T. Lehto, P. Pelkonen, Analysis of the willow root system by electrical impedance spectroscopy. J. Exp. Bot. 62(1), 351–358 (2011)

    Article  Google Scholar 

  6. A. Chowdhury, T. Bera, D. Ghoshal, B. Chakraborty, Studying the electrical impedance variations in banana ripening using electrical impedance spectroscopy (EIS), in Third International Conference on Computer, Communication, Control and Information Technology (C3IT) (IEEE, 2015), pp. 1–4

    Google Scholar 

  7. K.S. Cole, R.H. Cole, Dispersion and absorption in dielectrics I. Alternating current characteristics. J. Chem. Phys. 9(4), 341–351 (1941)

    Article  Google Scholar 

  8. D. Davidson, R. Cole, Dielectric relaxation in glycerol, propylene glycol, and \(n\)-propanol. J. Chem. Phys. 19(12), 1484–1490 (1951)

    Article  Google Scholar 

  9. P. Debye, Interferenz von Röntgenstrahlen und Wärmebewegung. Ann. Phys. 348(1), 49–92 (1913)

    Article  Google Scholar 

  10. P.J.W. Debye, Polar Molecules (Chemical Catalog Company, Incorporated, 1929)

    Google Scholar 

  11. P. Dejmek, O. Miyawaki, Relationship between the electrical and rheological properties of potato tuber tissue after various forms of processing. Biosci. Biotechnol. Biochem. 66(6), 1218–1223 (2002)

    Article  Google Scholar 

  12. D. El Khaled, N. Castellano, J. Gazquez, R.G. Salvador, F. Manzano-Agugliaro, Cleaner quality control system using bioimpedance methods: a review for fruits and vegetables. J. Clean. Prod. (2015)

    Google Scholar 

  13. T. Ellis, W. Murray, L. Kavalieris, Electrical capacitance of bean (Vicia faba) root systems was related to tissue density—a test for the Dalton model. Plant Soil 366(1–2), 575–584 (2013)

    Article  Google Scholar 

  14. S. Emmert, M. Wolf, R. Gulich, S. Krohns, S. Kastner, P. Lunkenheimer, A. Loidl, Electrode polarization effects in broadband dielectric spectroscopy. Eur. Phys. J. B 83(2), 157–165 (2011)

    Article  Google Scholar 

  15. Y. Feldman, A. Puzenko, Y. Ryabov, Non-Debye dielectric relaxation in complex materials. Chem. Phys. 284(1), 139–168 (2002)

    Article  Google Scholar 

  16. T.J. Freeborn, A survey of fractional-order circuit models for biology and biomedicine. IEEE J. Emerg. Sel. Top. Circuits Syst. 3(3), 416–424 (2013)

    Article  Google Scholar 

  17. T.J. Freeborn, B. Maundy, A.S. Elwakil, Cole impedance extractions from the step-response of a current excited fruit sample. Comput. Electron. Agric. 98, 100–108 (2013)

    Article  Google Scholar 

  18. H. Fröhlich, Theory of Dielectrics: Dielectric Constant and Dielectric Loss (Clarendon Press, 1958)

    Google Scholar 

  19. R. Garra, A. Giusti, F. Mainardi, G. Pagnini, Fractional relaxation with time-varying coefficient. Fract. Calc. Appl.Anal. 17(2), 424–439 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  20. R. Garrappa, F. Mainardi, G. Maione, Models of dielectric relaxation based on completely monotone functions. Fract. Calc. Appl. Anal. 19(5), 1105–1160 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  21. C. Greenham, Bruise and pressure injury in apple fruits. J. Exp. Bot. 17(2), 404–409 (1966)

    Article  Google Scholar 

  22. C. Greenham, K. Helms, W. Müller, Influence of virus inflections on impedance parameters. J. Exp. Bot. 29(4), 867–877 (1978)

    Article  Google Scholar 

  23. S. Havriliak, S. Negami, A complex plane analysis of \(\alpha \)-dispersions in some polymer systems. J. Polym. Sci. Part C: Polym. Symp. 14,99–117 (1966) (Wiley Online Library)

    Google Scholar 

  24. R. Hilfer, Analytical representations for relaxation functions of glasses. J. Non-Crystal. Solids 305(1), 122–126 (2002)

    Article  Google Scholar 

  25. I.S. Jesus, J.T. Tenreiro Machado, J.B. Cunha, Fractional electrical impedances in botanical elements. J. Vib. Control 14(9–10), 1389–1402 (2008)

    Article  MATH  Google Scholar 

  26. X. Kou, L. Chai, L. Jiang, S. Zhao, S. Yan, Modeling of the permittivity of holly leaves in frozen environments. IEEE Trans. Geosci. Remote Sens. 53(11), 6048–6057 (2015)

    Article  Google Scholar 

  27. W. Kuang, S. Nelson, Dielectric relaxation characteristics of fresh fruits and vegetables from 3 to 20 GHz. J. Microwave Power Electromagn. Energy 32(2), 115–123 (1997)

    Article  Google Scholar 

  28. A. Laogun, N. Ajayi, Radio-frequency dielectric properties of some tropical african leaf vegetables. Technical report, International Centre for Theoretical Physics, Trieste (Italy) (1985)

    Google Scholar 

  29. S. Laufer, A. Ivorra, V.E. Reuter, B. Rubinsky, S.B. Solomon, Electrical impedance characterization of normal and cancerous human hepatic tissue. Physiol. Meas. 31(7), 995 (2010)

    Article  Google Scholar 

  30. A.M. Lopes, J.A. Tenreiro Machado, Dynamic analysis of earthquake phenomena by means of pseudo phase plane. Nonlinear Dyn. 74(4), 1191–1202 (2013)

    Article  Google Scholar 

  31. A.M. Lopes, J.A. Tenreiro Machado, Fractional order models of leaves. J. Vib. Control 20(7), 998–1008 (2014)

    Article  MathSciNet  Google Scholar 

  32. A.M. Lopes, J.A. Tenreiro Machado, Modeling vegetable fractals by means of fractional-order equations. J. Vib. Control 22(8), 2100–2108 (2016)

    Article  Google Scholar 

  33. A.M. Lopes, J.A. Tenreiro Machado, E. Ramalho, On the fractional-order modeling of wine. Eur. Food Res. Technol. 1–9 (2016)

    Google Scholar 

  34. S. Mancuso, Seasonal dynamics of electrical impedance parameters in shoots and leaves related to rooting ability of olive (Olea europea) cuttings. Tree Physiol. 19(2), 95–101 (1999)

    Article  Google Scholar 

  35. B. Maundy, A. Elwakil, Extracting single dispersion Cole-Cole impedance model parameters using an integrator setup. Analog Integr. Circuits Signal Process. 71(1), 107–110 (2012)

    Article  Google Scholar 

  36. B. Maundy, A. Elwakil, A. Allagui, Extracting the parameters of the single-dispersion Cole bioimpedance model using a magnitude-only method. Comput. Electron. Agric. 119, 153–157 (2015)

    Article  Google Scholar 

  37. Y. Mizukami, K. Yamada, Y. Sawai, Y. Yamaguchi, Measurement of fresh tea leaf growth using electrical impedance spectroscopy. Agric. J. 2(1), 134–139 (2007)

    Google Scholar 

  38. F. Murtagh, A survey of recent advances in hierarchical clustering algorithms. Comput. J. 26(4), 354–359 (1983)

    Article  MATH  Google Scholar 

  39. S.O. Nelson, S. Trabelsi, Factors influencing the dielectric properties of agricultural and food products. J. Microwave Power Electromagn. Energy 46(2), 93–107 (2012)

    Article  Google Scholar 

  40. R. Nigmatullin, S. Nelson, Recognition of the “fractional” kinetics in complex systems: dielectric properties of fresh fruits and vegetables from 0.01 to 1.8 GHz. Signal Process. 86(10), 2744–2759 (2006)

    Article  MATH  Google Scholar 

  41. R. Nigmatullin, Y.E. Ryabov, Cole-Davidson dielectric relaxation as a self-similar relaxation process. Phys. Solid State 39(1), 87–90 (1997)

    Article  Google Scholar 

  42. V. Novikov, K. Wojciechowski, O. Komkova, T. Thiel, Anomalous relaxation in dielectrics. Equations with fractional derivatives. Mater. Sci. Wroclaw 23(4), 977 (2005)

    Google Scholar 

  43. S. Ohnishi, O. Miyawaki, Osmotic dehydrofreezing for protection of rheological properties of agricultural products from freezing-injury. Food Sci. Technol. Res. 11(1), 52–58 (2005)

    Article  Google Scholar 

  44. E.C. de Oliveira, F. Mainardi, J. Vaz Jr., Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics. Eur. Phys. J. Spec. Top. 193(1), 161–171 (2011)

    Article  Google Scholar 

  45. E.C. de Oliveira, F. Mainardi, J. Vaz Jr., Fractional models of anomalous relaxation based on the Kilbas and Saigo function. Meccanica 49(9), 2049–2060 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  46. H. Ozier-Lafontaine, T. Bajazet, Analysis of root growth by impedance spectroscopy (EIS). Plant Soil 277(1–2), 299–313 (2005)

    Article  Google Scholar 

  47. U. Pliquett, Bioimpedance: a review for food processing. Food Eng. Rev. 2(2), 74–94 (2010)

    Article  Google Scholar 

  48. T. Repo, S. Pulli, Application of impedance spectroscopy for selecting frost hardy varieties of english ryegrass. Ann. Bot. 78(5), 605–609 (1996)

    Article  Google Scholar 

  49. E.C. Rosa, E.C. de Oliveira, Relaxation equations: fractional models (2015), arXiv:1510.01681

  50. Sibatov, R.T., Uchaikin, D.V.: Fractional relaxation and wave equations for dielectrics characterized by the Havriliak-Negami response function (2010), arXiv:1008.3972

  51. A. Stanislavsky, K. Weron, J. Trzmiel, Subordination model of anomalous diffusion leading to the two-power-law relaxation responses. EPL (Europhys. Lett.) 91(4), 40,003 (2010)

    Google Scholar 

  52. M. Tiitta, L. Tomppo, H. Järnström, M. Löija, T. Laakso, A. Harju, M. Venäläinen, H. Iitti, L. Paajanen, P. Saranpää et al., Spectral and chemical analyses of mould development on Scots pine heartwood. Eur. J. Wood Wood Prod. 67(2), 151–158 (2009)

    Article  Google Scholar 

  53. K. Toyoda, R.N. Tsenkova, M. Nakamura, Characterization of osmotic dehydration and swelling of apple tissues by bioelectrical impedance spectroscopy. Drying Technol. 19(8), 1683–1695 (2001)

    Article  Google Scholar 

  54. J. Urban, R. Bequet, R. Mainiero, Assessing the applicability of the earth impedance method for in situ studies of tree root systems. J. Exp. Bot. 62(6), 1857–1869 (2011)

    Google Scholar 

  55. A. Väinölä, T. Repo, Impedance spectroscopy in frost hardiness evaluation of rhododendron leaves. Ann. Bot. 86(4), 799–805 (2000)

    Article  Google Scholar 

  56. Z. Vosika, M. Lazarević, J. Simic-Krstić, D. Koruga, Modeling of bioimpedance for human skin based on fractional distributed-order modified Cole model. FME Trans. 42(1), 74–81 (2014)

    Article  Google Scholar 

  57. T. Watanabe, T. Orikasa, H. Shono, S. Koide, Y. Ando, T. Shiina, A. Tagawa, The influence of inhibit avoid water defect responses by heat pretreatment on hot air drying rate of spinach. J. Food Eng. 168, 113–118 (2016)

    Article  Google Scholar 

  58. L. Wu, Y. Ogawa, A. Tagawa, Electrical impedance spectroscopy analysis of eggplant pulp and effects of drying and freezing-thawing treatments on its impedance characteristics. J. Food Eng. 87(2), 274–280 (2008)

    Article  Google Scholar 

  59. L. Wu, T. Orikasa, K. Tokuyasu, T. Shiina, A. Tagawa, Applicability of vacuum-dehydrofreezing technique for the long-term preservation of fresh-cut eggplant: effects of process conditions on the quality attributes of the samples. J. Food Eng. 91(4), 560–565 (2009)

    Article  Google Scholar 

  60. L. XiaoHong, H. TingLin, W. GuoDong, Z. Gang et al., Effect of salt stress on electrical impedance spectroscopy parameters of wheat (Triticum aestivum l.) leaves. J. Zhejiang Univ. (Agric. Life Sci.) 35(5), 564–568 (2009)

    Google Scholar 

  61. M. Zhang, T. Repo, J. Willison, S. Sutinen, Electrical impedance analysis in plant tissues: on the biological meaning of Cole-Cole \(\alpha \) in Scots pine needles. Eur. Biophys. J. 24(2), 99–106 (1995)

    Article  Google Scholar 

  62. M. Zhang, J. Willison, Electrical impedance analysis in plant tissues: the effect of freeze-thaw injury on the electrical properties of potato tuber and carrot root tissues. Can. J. Plant Sci. 72(2), 545–553 (1992)

    Article  Google Scholar 

  63. M. Zhang, J. Willison, Electrical impedance analysis in plant tissues. J. Exp. Bot. 44(8), 1369–1375 (1993)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India

    Karabi Biswas

  2. Department of Physics and Materials Science, University of Memphis, Memphis, TN, USA

    Gary Bohannan

  3. Department of Electrical, Electronics and Computer Engineering, University of Catania, Catania, Italy

    Riccardo Caponetto

  4. UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal

    António Mendes Lopes

  5. Department of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Porto, Portugal

    José António Tenreiro Machado

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  1. Karabi Biswas
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  2. Gary Bohannan
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  3. Riccardo Caponetto
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  4. António Mendes Lopes
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  5. José António Tenreiro Machado
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Correspondence to Riccardo Caponetto .

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Biswas, K., Bohannan, G., Caponetto, R., Mendes Lopes, A., Tenreiro Machado, J.A. (2017). Fractional-Order Models of Vegetable Tissues. In: Fractional-Order Devices. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-54460-1_4

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  • DOI: https://doi.org/10.1007/978-3-319-54460-1_4

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  • Online ISBN: 978-3-319-54460-1

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