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Numerical Basics of Bioimpedance Measurements

  • Alexander Danilov
  • Sergey Rudnev
  • Yuri Vassilevski
Chapter

Abstract

Fundamental issues in various areas of bioimpedance application, such as impedance cardiography, electrical impedance tomography, and bioimpedance analysis of body composition and spectroscopy, require mathematical models. Highly inhomogeneous and anisotropic structure of the human body makes the numerical simulation of bioimpedance measurements the inevitable tool. In this chapter, we present essential elements and the workflow of the finite element method (FEM)-based computational technology in bioimpedance modeling: 3D image segmentation, adaptive mesh generation, finite element discretization, as well as construction and visualization of current density, potential, and sensitivity fields. The cornerstone of the technology is an anatomically correct 3D model of the human body from the Visible Human Project (VHP). The technology provides an online numerical simulator of bioimpedance measurements using a conventional 4-electrode and 10-electrode placement schemes.

Notes

Acknowledgements

The authors thank V.Yu. Salamatova, V.K. Kramarenko, and A.S. Yurova for segmentation of the VHP data and performing numerical experiments, G.V. Kopytov for the development of user’s interface for the online numerical simulator, and D.V. Nikolaev and A.V. Smirnov for problem formulation, valuable discussion, and financial support of the initial part of this study. Our work was supported by the Russian Foundation for Basic Research (RFBR grants 17-01-00886 and 17-51-53160).

References

  1. Ackerman, M. J. (2003). The National Library of Medicine’s Visible Human Project. Accessed November 10, 2017. https://www.nlm.nih.gov/research/visible/
  2. Adler, A., Lionheart, W. R. B., & Polydorides, N. (2015). EIDORS: electrical impedance tomography and diffuse optical tomography reconstruction software. Accessed November 10, 2017. http://eidors3d.sourceforge.net/
  3. Bayford, R. H., Gibson, A., Tizzard, A., Tidswell, T., & Holder, D. S. (2001). Solving the forward problem in electrical impedance tomography for the human head using IDEAS (integrated design engineering analysis software), a finite element modelling tool. Physiological Measurement, 22(1), 55–64.Google Scholar
  4. Beckmann, L., van Riesen, D., & Leonhardt, S. (2007). Optimal electrode placement and frequency range selection for the detection of lung water using bioimpedance spectroscopy. In 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (pp. 2685–2688).Google Scholar
  5. Belalcazar, A., & Patterson, R. P. (2004). Improved lung edema monitoring with coronary vein pacing leads: a simulation study. Physiological Measurement, 25(2), 475–487.Google Scholar
  6. Bera, T. K. (2014). Bioelectrical impedance methods for noninvasive health monitoring: a review. Journal of Medical Engineering, 2014, 381251.Google Scholar
  7. Brantlov, S., Andersen, T. B., Jødal, L., Rittig, S., & Lange, A. (2016). Bioimpedance spectroscopy in healthy children. Journal of Clinical Engineering, 41(1), 33–39.Google Scholar
  8. Canali, C., Heiskanen, A., Muhammad, H. B., Hoym, P., Pettersen, F. J., Hemmingsen, M., Wolff, A., Dufva, M., Martinsen, O. G., & Emnéus, J. (2015). Bioimpedance monitoring of 3D cell culturing—Complementary electrode configurations for enhanced spatial sensitivity. Biosensors and Bioelectronics, 63, 72–79.Google Scholar
  9. Caon, M. (2004). Voxel-based computational models of real human anatomy: a review. Radiation and Environmental Biophysics, 42(4), 229–235.Google Scholar
  10. Cybulski, G. (2011). Ambulatory impedance cardiography. Berlin-Heidelberg: Springer.Google Scholar
  11. Danilov, A. A., Kopytov, G. V., & Vassilevski, Y. V. (2017). Online simulator for bioimpedance measurements. Accessed November 10, 2017. http://dodo.inm.ras.ru/bia/
  12. Danilov, A. A., Kramarenko, V. K., Nikolaev, D. V., & Yurova, A. S. (2013). Personalized model adaptation for bioimpedance measurements optimization. Russian Journal of Numerical Analysis and Mathematical Modelling, 28(5), 459–470.Google Scholar
  13. Danilov, A. A., Nikolaev, D. V., Rudnev, S. G., Salamatova, V. Y., & Vassilevski, Y. V. (2012). Modelling of bioimpedance measurements: unstructured mesh application to real human anatomy. Russian Journal of Numerical Analysis and Mathematical Modelling, 27(5), 431–440.Google Scholar
  14. de Sitter, A., Verdaasdonk, R. M., & Faes, T. J. C. (2016). Do mathematical model studies settle the controversy on the origin of cardiac synchronous trans-thoracic electrical impedance variations? A systematic review. Physiological Measurement, 37(9), R88–R108.Google Scholar
  15. Dowrick, T., Blochet, C., & Holder, D. (2016). In vivo bioimpedance measurement of healthy and ischaemic rat brain: implications for stroke imaging using electrical impedance tomography. Physiological Measurement, 36(6), 1273–1282.Google Scholar
  16. Gabriel, S., Lau, R. W., & Gabriel, C. (1996a). The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Physics in Medicine and Biology, 41(11), 2251–2269.Google Scholar
  17. Gabriel, S., Lau, R. W., & Gabriel, C. (1996b). The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Physics in Medicine and Biology, 41(11), 2271–2293.Google Scholar
  18. Geselowitz, D. B. (1971). An application of electrocardiographic lead theory to impedance plethysmography. IEEE Transactions on Biomedical Engineering BME, 18(1), 38–41.Google Scholar
  19. Gosselin, M. C., Neufeld, E., Moder, H., Huber, E., Farcito, S., Gerber, L., Jedensjö, M., Hilber, I., Gennaro, F. D., Lloyd, B., Cherubini, E., Szczerba, D., Kainz, W., & Kuster, N. (2014). Development of a new generation of high-resolution anatomical models for medical device evaluation: the Virtual Population 3.0. Physics in Medicine and Biology, 59(18), 5287–5304.Google Scholar
  20. Grimnes, S., & Martinsen, O. (2014). Bioimpedance and bioelectricity basics (3rd ed.) London: Academic.Google Scholar
  21. Höhne, K. H., Pflesser, B., Pommert, A., Riemer, M., Schubert, R., Schiemann, T., Tiede, U., & Schumacher, U. (2000). A realistic model of the inner organs from the visible human data. In Medical Image Computing and Computer-Assisted Intervention – MICCAI 2000 (pp. 776–785). Berlin: Springer Nature.Google Scholar
  22. Holder, D. S. (2005). Electrical impedance tomography. Bristol: IOP.Google Scholar
  23. Jaffrin, M. Y., & Morel, H. (2008). Body fluid volumes measurements by impedance: a review of bioimpedance spectroscopy (BIS) and bioimpedance analysis (BIA) methods. Medical Engineering & Physics, 30, 1257–1269.Google Scholar
  24. Jindal, G. D., Sawant, M. S., Jain, R. K., Sinha, V., Bhat, S. N., & Deshpande, A. K. (2016). Seventy-five years of use of impedance plethysmography in physiological data acquisition and medical diagnostics. MGM Journal of Medical Sciences, 3, 84–90.Google Scholar
  25. Kaporin, I. E. (1998). High quality preconditioning of a general symmetric positive definite matrix based on its u t u + u t r + r t u-decomposition. Numerical Linear Algebra with Applications, 5(6), 483–509.Google Scholar
  26. Kauppinen, P. K., Hyttinen, J. A., & Malmivuo, J. A. (1998). Sensitivity distributions of impedance cardiography using band and spot electrodes analyzed by a three-dimensional computer model. Annals of Biomedical Engineering, 26(4), 694–702.Google Scholar
  27. Lipnikov, K. N., & Vassilevski, Y. V. (2007). Advanced numerical instruments 3D. Accessed November 10, 2017. https://sourceforge.net/projects/ani3d/
  28. Ness, T. V., Chintaluri, C., Potworowski, J., Leski, S., Glabska, H., Wojcik, D. L., & Einevoll, G. T. (2015). Modelling and analysis of electrical potentials recorded in microelectrode arrays (MEA). Neuroinformatics, 13(4), 403–426.CrossRefGoogle Scholar
  29. Orschulik, J., Petkau, R., Wartzek, T., Hochhausen, N., Czaplik, M., Leonhardt, S., & Teichmann, D. (2016). Improved electrode positions for local impedance measurements in the lung—a simulation study. Physiological Measurement, 37(12), 2111–2129.CrossRefGoogle Scholar
  30. Patterson, R. P. (2010). Impedance cardiography: what is the source of the signal? Journal of Physics: Conference Series, 224, 012118.Google Scholar
  31. Pettersen, F. J., & Høgetveit, J. O. (2011), From 3D tissue data to impedance using Simpleware ScanFE+IP and COMSOL Multiphysics—a tutorial. Journal of Electrical Bioimpedance, 2, 13–32.CrossRefGoogle Scholar
  32. Rineau, L., & Yvinec, M. (2007). A generic software design for Delaunay refinement meshing. Computational Geometry, 38(1–2), 100–110.MathSciNetCrossRefzbMATHGoogle Scholar
  33. Saltarelli, A. J., Roseth, C. J., & Saltarelli, W. A. (2014). Human cadavers vs multimedia simulation: a study of student learning in anatomy. Anatomical Sciences Education, 7(5), 331–339.CrossRefGoogle Scholar
  34. Serra, J. (1984). Image analysis and mathematical morphology. London: Academic.Google Scholar
  35. Ulbrich, M., Marleaux, B., Mühlsteff, J., Schoth, F., Koos, R., Teichmann, D., & Leonhardt, S. (2013). High and temporal resolution 4D FEM simulation of the thoracic bioimpedance using MRI scans. Journal of Physics: Conference Series, 434, 012074.Google Scholar
  36. Vassilevski, Y. V. (2010). Mathematical technologies for electroimpedance diagnostics and monitoring of cardiovascular and respiratory diseases, Report. Accessed November 10, 2017 (in Russian). http://dodo.inm.ras.ru/research/_media/fcp/14.740.11.0844-report-1.pdf Google Scholar
  37. Vassilevski, Y. V., Danilov, A. A., Nikolaev, D. V., Rudnev, S. G., Salamatova, V. Y., & Smirnov, A. V. (2012). Finite-element analysis of bioimpedance measurements. Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki, 52(4), 733–745 (in Russian).zbMATHGoogle Scholar
  38. Xu, X. G. (2014). An exponential growth of computational phantom research in radiation protection, imaging, and radiotherapy: a review of the fifty-year history. Physics in Medicine and Biology, 59(18), R233–R302.CrossRefGoogle Scholar
  39. Yushkevich, P. A., Piven, J., Hazlett, H. C., Smith, R. G., Ho, S., Gee, J. C., & Gerig, G. (2006). User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. NeuroImage, 31(3), 1116–1128.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Alexander Danilov
    • 1
    • 2
    • 3
  • Sergey Rudnev
    • 1
    • 4
    • 5
  • Yuri Vassilevski
    • 1
    • 2
    • 3
  1. 1.Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyMoscowRussia
  3. 3.Sechenov UniversityMoscowRussia
  4. 4.Lomonosov Moscow State UniversityMoscowRussia
  5. 5.Federal Research Institute for Health Organization and InformaticsMoscowRussia

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