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A Novel Method for Estimating the Fractional Cole Impedance Model Using Single-Frequency DC-Biased Sinusoidal Excitation

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Abstract

The Cole model is a widely used fractional circuit model in electrical bioimpedance applications for evaluating the content and status of biological tissues and fluids. Existing methods for estimating the Cole impedance parameters are often based on multi-frequency data obtained from stepped-sine measurements fitted using a complex nonlinear least square (CNLS) algorithm. Newly emerged numerical methods from the magnitude of electrical bioimpedance data-only do not need CNLS fitting, but they still require multi-frequency stepped-sine data. This study proposes a novel approach to estimating the Cole impedance parameters that combines a numerical and time-domain fitting method based on a single-frequency DC-biased sinusoidal current excitation. First, the transient and steady-state voltage responses along with the current excitation are acquired in electrical bioimpedance measurement. From the sampled data, a numerical method is applied to provide the initial estimation of the Cole impedance parameters, which are then used in a time-domain iterative fitting algorithm. The accuracy of the algorithm proposed is tested with noisy electrical bioimpedance simulations. The maximum relative error of the estimated Cole impedance parameters is 1% considering 2% (34 dB) additive Gaussian noise. Experimental measurements performed on a 2R-1C circuit and some fruit samples show a mean difference less than 1% and 5%, respectively, compared to the Cole impedance parameters estimated from a commercial electrical bioimpedance analyzer performing stepped-sine measurements and CNLS fitting. This is the first method that allows estimating the Cole impedance parameters from single-frequency electrical bioimpedance data. The approach presented could find broad use in many applications, including single-frequency body impedance analysis.

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the first author on reasonable request.

References

  1. A. AboBakr, L.A. Said, A.H. Madian, A.S. Elwakil, A.G. Radwan, Experimental comparison of integer/fractional-order electrical models of plant. AEU-Int. J. Electron. Commun. 80, 1–9 (2017)

    Article  Google Scholar 

  2. A. Al-Ali, A.S. Elwakil, B. Maundy, T.J. Freeborn, Extraction of phase information from magnitude-only bio-impedance measurements using a modified kramers-kronig transform. Circ. Syst. Signal Process. 37(8), 3635–3650 (2018)

    Article  MathSciNet  Google Scholar 

  3. S. Alavi, C. Birkl, D. Howey, Time-domain fitting of battery electrochemical impedance models. J. Power Sources 288, 345–352 (2015)

    Article  Google Scholar 

  4. K.S. Cole, Permeability and impermeability of cell membranes for ions, in Cold Spring Harbor Symposia on Quantitative Biology, vol. 8, ed. by C.S. Harbor, N. Li (Cold Spring Harbor Laboratory Press, New York, 1940), pp. 110–122

    Google Scholar 

  5. A. De Lorenzo, A. Andreoli, J. Matthie, P. Withers, Predicting body cell mass with bioimpedance by using theoretical methods: a technological review. J. Appl. Physiol. 82(5), 1542–1558 (1997)

    Article  Google Scholar 

  6. A.S. Elwakil, B. Maundy, Extracting the Cole-Cole impedance model parameters without direct impedance measurement. Electron. Lett. 46(20), 1367–1368 (2010)

    Article  Google Scholar 

  7. 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 

  8. T.J. Freeborn, A.S. Elwakil, Rates and effects of local minima on fractional-order circuit model parameters extracted from supercapacitor discharging using least squares optimization. Circ. Syst. Signal Process. 38(5), 1907–1922 (2019)

    Article  Google Scholar 

  9. T.J. Freeborn, A.S. Elwakil, B. Maundy, Variability of Cole-model bioimpedance parameters using magnitude-only measurements of apples from a two-electrode configuration. Int. J. Food Prop. 20(sup1), S507–S519 (2017)

    Article  Google Scholar 

  10. T.J. Freeborn, B. Maundy, A.S. Elwakil, Numerical extraction of cole-cole impedance parameters from step response. Nonlinear Theory Its Appl. IEICE 2(4), 548–561 (2011)

    Article  Google Scholar 

  11. T.J. Freeborn, B. Maundy, A.S. Elwakil, Least squares estimation technique of Cole–Cole parameters from step response. Electron. Lett. 48(13), 752–754 (2012)

    Article  Google Scholar 

  12. 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 

  13. S. Gholami-Boroujeny, M. Bolic, Extraction of Cole parameters from the electrical bioimpedance spectrum using stochastic optimization algorithms. Med. Biol. Eng. Comput. 54(4), 643–651 (2016)

    Article  Google Scholar 

  14. S. Grimnes, O. Martinsen, Bioimpedance and Bioelectricity Basics, 3rd edn. (Academic Press, Oxford, 2014)

    Google Scholar 

  15. R.J. Halter, A. Hartov, K.D. Paulsen, A. Schned, J. Heaney, Genetic and least squares algorithms for estimating spectral EIS parameters of prostatic tissues. Physiol. Meas. 29(6), S111–S123 (2008)

    Article  Google Scholar 

  16. P. Ibba, A. Falco, B.D. Abera, G. Cantarella, L. Petti, P. Lugli, Bio-impedance and circuit parameters: An analysis for tracking fruit ripening. Postharvest Biol. Technol. 159, 110978 (2020)

    Article  Google Scholar 

  17. Z. Jiang, J. Yao, L. Wang, H. Wu, J. Huang, T. Zhao, M. Takei, Development of a portable electrochemical impedance spectroscopy system for bio-detection. IEEE Sens. J. 19(15), 5979–5987 (2019)

    Article  Google Scholar 

  18. S. Kapoulea, A. AbdelAty, A. Elwakil, C. Psychalinos, A. Radwan, Cole–Cole bio-impedance parameters extraction from a single time-domain measurement. in 2019 8th International Conference on Modern Circuits and Systems Technologies (MOCAST), pp. 1–4. IEEE (2019)

  19. S. Khubalkar, A. Chopade, A. Junghare, M. Aware, S. Das, Design and realization of stand-alone digital fractional order PID controller for Buck converter fed DC motor. Circ. Syst. Signal Process. 35(6), 2189–2211 (2016)

    Article  Google Scholar 

  20. S. Kun, B. Ristic, R. Peura, R. Dunn, Real-time extraction of tissue impedance model parameters for electrical impedance spectrometer. Med. Biol. Eng. Comput. 37(4), 428432 (1999)

    Article  Google Scholar 

  21. U.G. Kyle, I. Bosaeus, A.D. De Lorenzo, P. Deurenberg, M. Elia, J.M. Gómez, B.L. Heitmann, L. Kent-Smith, J.C. Melchior, M. Pirlich et al., Bioelectrical impedance analysis-part I: review of principles and methods. Clin. Nutr. 23(5), 1226–1243 (2004)

    Article  Google Scholar 

  22. E. Louarroudi, B. Sanchez, On the correct use of stepped-sine excitations for the measurement of time-varying bioimpedance. Physiol. Meas. 38(2), N73–N80 (2017)

    Article  Google Scholar 

  23. L. Lu, L. Hamzaoui, B. Brown, B. Rigaud, R. Smallwood, D. Barber, J. Morucci, Parametric modelling for electrical impedance spectroscopy system. Med Biol. Eng. Comput. 34(2), 122–126 (1996)

    Article  Google Scholar 

  24. B. Maundy, A.S. Elwakil, Extracting single dispersion Cole–Cole impedance model parameters using an integrator setup. Anal. Integr. Circ. Signal Process. 71(1), 107–110 (2012)

    Article  Google Scholar 

  25. B. Maundy, A.S. 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 

  26. M. Mohsen, L.A. Said, A.S. Elwakil, A.H. Madian, A.G. Radwan, Extracting optimized bio-impedance model parameters using different topologies of oscillators. IEEE Sens. J. 20(17), 9947–9954 (2020)

    Article  Google Scholar 

  27. A.G. Radwan, K.N. Salama, Fractional-order RC and RL circuits. Circ. Syst. Signal Process. 31(6), 1901–1915 (2012)

    Article  MathSciNet  Google Scholar 

  28. F. Slinde, L. Rossander-Hulthén, Bioelectrical impedance: effect of 3 identical meals on diurnal impedance variation and calculation of body composition. Am. J. Clin. Nutr. 74(4), 474–478 (2001)

    Article  Google Scholar 

  29. C. Vastarouchas, C. Psychalinos, A.S. Elwakil, A. Al-Ali, Novel two-measurements-only Cole–Cole bio-impedance parameters extraction technique. Measurement 131, 394–399 (2019)

    Article  Google Scholar 

  30. C. Vastarouchas, G. Tsirimokou, C. Psychalinos, Extraction of Cole–Cole model parameters through low-frequency measurements. AEU-Int. J. Electron. Commun. 84, 355–359 (2018)

    Article  Google Scholar 

  31. L.C. Ward, T. Essex, B.H. Cornish, Determination of Cole parameters in multiple frequency bioelectrical impedance analysis using only the measurement of impedances. Physiol. Meas. 27(9), 839 (2006)

    Article  Google Scholar 

  32. Y. Yang, W. Ni, Q. Sun, H. Wen, Z. Teng, Improved Cole parameter extraction based on the least absolute deviation method. Physiol. Meas. 34(10), 1239 (2013)

    Article  Google Scholar 

  33. S.Z. Yanovski, V.S. Hubbard, S.B. Heymsfield, H.C. Lukaski, Bioelectrical impedance analysis in body composition measurement: National institutes of health technology assessment conference statement. Am. J. Clin. Nutr. 64(3), 524S–532S (1996)

    Article  Google Scholar 

  34. D. Yousri, A.M. AbdelAty, L.A. Said, A. AboBakr, A.G. Radwan, Biological inspired optimization algorithms for Cole-impedance parameters identification. AEU-Int. J. Electron. Commun. 78, 79–89 (2017)

    Article  Google Scholar 

  35. F. Zhang, B. Sanchez, S.B. Rutkove, Y. Yang, H. Zhong, J. Li, Z. Teng, Numerical estimation of Fricke-Morse impedance model parameters using single-frequency sinusoidal excitation. Physiol. Meas. 40(9), 09NT01 (2019)

    Article  Google Scholar 

  36. F. Zhang, Z. Teng, S. Rutkove, Y. Yang, J. Li, A simplified time-domain fitting method based on fractional operational matrix for Cole parameter estimation. IEEE Trans. Instrum. Meas. 69(4), 1566–1575 (2019)

    Article  Google Scholar 

  37. F. Zhang, Z. Teng, H. Zhong, Y. Yang, J. Li, J. Sang, Wideband mirrored current source design based on differential difference amplifier for electrical bioimpedance spectroscopy. Biomed. Phys. Eng. Express 4(2), 025032 (2018)

    Article  Google Scholar 

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Acknowledgements

The work of F. Zhang was supported by China Scholarship Council through the Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, USA, under Grant 201706130103. The work of Z. Teng was supported by the National Key Research and Development Program of China under Grant 2016YFF0203402. The work of Y. Yang was supported in part by the National Natural Science Foundation of China under Grant 31671002, the Scientific Research Foundation of Shaanxi Province for Returned Chinese Scholars under Grant 2017004, and the Shaanxi Natural Science Foundation under Grant 2016JM6046. The work of J. Li was supported by the National Natural Science Foundation of China under Grant 51907062. The work of S. B. Rutkove was supported by NIH under Grant R01 NS091159. The work of B. Sanchez was supported by NIH under Grant R41 NS112029-01A1.

Author information

Authors and Affiliations

  1. College of Engineering and Design, Hunan Normal University, Changsha, 410081, China

    Fu Zhang, Yuxiang Yang & Jianmin Li

  2. Department of Electronic Science and Technology, Hunan University, Changsha, 410082, China

    Zhaosheng Teng & Haowen Zhong

  3. Department of Neurology, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, 02115, USA

    Haowen Zhong & Seward B. Rutkove

  4. Department of Electrical and Computer Engineering, University of Utah, Sorenson Molecular Biotechnology Building, Office 3721, 36 South Wasatch Drive, Salt Lake City, 84112, UT, USA

    Benjamin Sanchez

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  1. Fu Zhang
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Correspondence to Zhaosheng Teng or Benjamin Sanchez.

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Conflict of interest

Dr. Rutkove has equity in, and serves a consultant and scientific advisor to, Myolex, Inc., a company that designs impedance devices for clinical and research use; he is also a member of the company’s Board of Directors. The company also has an option to license patented impedance technology of which Dr. Rutkove is named as an inventor. Dr. Sanchez is Co-Founder and has equity in Haystack Dx, Inc. a company that commercializes needle impedance technology for clinical and research use. The company also has an option to license patented impedance technology of which Dr. Sanchez is named as an inventor. Dr. Sanchez serves as a Scientific Advisory Board Member for Ioniq Sciences, Inc., a company that commercializes impedance related technology for clinical use. He serves also as a consultant to Myolex, Inc., Impedimed, Inc., Texas Instruments, Inc., and Gideon Health, Inc., four companies that develop impedance related technology for consumer, research and clinical use.

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Zhang, F., Teng, Z., Yang, Y. et al. A Novel Method for Estimating the Fractional Cole Impedance Model Using Single-Frequency DC-Biased Sinusoidal Excitation. Circuits Syst Signal Process 40, 543–558 (2021). https://doi.org/10.1007/s00034-020-01512-9

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