The Electrical Conductivity of Living Tissue: A Parameter in the Bioelectrical Inverse Problem

  • Maria J. Peters
  • Jeroen G. Stinstra
  • Ibolya Leveles
Part of the Bioelectric Engineering book series (BEEG)


Electrically active cells within the human body generate currents in the tissues surrounding these cells. These currents are called volume currents. The volume currents in turn give rise to potential differences between electrodes attached to the body. When these electrodes are attached to the torso, electrical potential differences generated by the heart are recorded. The recording of these electrical potential differences as a function of time is called an electrocardiogram (ECG). ECG measurements can be used to compute the generators within the heart. This is called the solution of the ECG inverse problem. This solution may be of interest for diagnostic purposes. For instance, it can be used to localize an extra conducting pathway between atria and ventricles. This pathway can then subsequently be removed by radio-frequent ablation through a catheter. When the active cells are situated within the brain and the electrodes are attached to the scalp, the recording of the potential difference measured between two electrodes as a function of time is called an electroencephalogram (EEG). The EEG inverse problem can, for example, be used to localize an epileptic focus as part of the presurgical evaluation. The frequencies involved in electrocardiograms and electroencephalograms are in the range of 1-1000Hz. Therefore, the Maxwell equations can be used in a quasi-static approximation, implicating that capacitive and inductive effects and wave phenomena are ignored as argued by (1967).


Interstitial Fluid Electrical Impedance Tomography Effective Conductivity Volume Conductor Cementation Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Archie, G.E., 1942, The electrical resistivity log as an aid in determining some reservoir characteristics, Trans. Am. Institut. Min. Metal. Eng., 146: 55–62.Google Scholar
  2. Aseyev, 1998, Electrolytes. Interparticle interactions. Theory, calculation methods and experimental data, Begell House inc., New York.Google Scholar
  3. Baumann, S.B., Wozny, D.R., Kelly, S.K., and Meno, F.M., 1997, The electrical conductivity of human cerebrospinal fluid at body temperature, IEEE T. Bio-Med. Eng., 44: 220–223.CrossRefGoogle Scholar
  4. Baynham, C.T., Knisley, S.B., 1999, Effective resistance of rabbit ventricles, Ann. of Biomed. Eng., 27: 96–102.CrossRefGoogle Scholar
  5. Boned, C., and Peyrelasse, J., 1983, Etude de la permittivite complexe d’ellipsoïdes disperses dans un milieu continu. Analyses theorique et numerique, Colloid Polym. Sci., 261:600–612.CrossRefGoogle Scholar
  6. Boyle, M. H., 1985, The electrical properties of heterogeneous mixtures containing an oriented spheroidal dispersed phase, Colloid Polym. Sci., 263:51–57.CrossRefGoogle Scholar
  7. Brace, R.A., 1998, Fluid distribution in the fetus and neonate, in: Fetal and neonatal Physiology. (R. A. Polin, and W.W. Fox, eds.), Saunders Comp., Philadelphia, pp. 1703–1713.Google Scholar
  8. Burger, H. C., and Dongen, R. van, 1961, Specific electric resistance of body tissues, Phys. Med. Biol., 5: 431–437.CrossRefGoogle Scholar
  9. Burger, H. C., and Milaan, J. B. van, 1943, Measurement of the specific resistance of the human body to direct current, Act. Med. Scand., 114:585–607.Google Scholar
  10. Burik, M. J. van, 1999, Physical aspects of EEG, PhD thesis, University of Twente, the NetherlandsGoogle Scholar
  11. Chapman, R.A., and Frye, C.H., 1978, An analysis of the cable properties of frog ventricular myocardium, J. Physiol., 283:263–283.Google Scholar
  12. Clerc, L., 1976, Directional differences of impulse spread in trabecular muscle from mammalian heart, Ibid 255:335–346.Google Scholar
  13. Cohen, D., and Cuffin, B.N., 1983, Demonstration of useful differences between magnetoencephalogram and electroencephalogram, Electroen. clin. Neuro., 56:38–51.CrossRefGoogle Scholar
  14. Cole, K. S., Li, C., and Bak, A. F., 1969, Electrical analogues for tissues, Exp. Neurol., 24:459–473.CrossRefGoogle Scholar
  15. Costarino, A.T., and Brans, Y. W., 1998, Fetal and neonatal body fluid composition with reference to growth and development, in Fetal and neonatal Physiology, (R. A. Polin, and W. W. Fox, eds.), Saunders Comp., Philadelphia, pp. 1713–1721.Google Scholar
  16. De Luca, F., Cametti, C., Zimatore, G., Maraviglia, B., and Pachi, A., 1996, Use of low-frequency electrical impedance measurements to determine phospholipid content in amniotic fluid, Phys. Med. Biol., 41:1863–1869.CrossRefGoogle Scholar
  17. Epstein, B. R., and Foster, K. R., 1983, Anisotropy in the dielectric properties of skeletal muscle, Med. Biol. Eng. Comput., 21:51–55.CrossRefGoogle Scholar
  18. Eyüboĝlu, B. M., Pilkington, T. C., and Wolf, P. D., 1994, Estimation of tissue resistivities from multiple-electrode measurements, Phys. Med. Biol. 39:1–17.CrossRefGoogle Scholar
  19. Foster, K. R., and Schwan, H. P., 1989, Dielectric properties of issues and biological materials: a critical review, Crit. Rev. Biomed. Eng., 17:25–104.Google Scholar
  20. Foster, K. R., and Schwan, H. P., 1986, Dielectric permittivity and electrical conductivity of biological materials, in: Handbook of Biological Effects of Electromagnetic Fields, (C. Polk, and E. Postow, eds.), CRC Press, Inc., Boca Raton, pp. 27.Google Scholar
  21. Fricke, H., 1953, The Maxwell-Wagner dispersion in a suspension of ellipsoids, J. Phys. Chem., 57:934–937.CrossRefGoogle Scholar
  22. Gabriel, S., Lau, R. W., and Gabriel, C., 1996a, The dielectric properties of tissue: II. Measurements in the frequency range 10Hz to 20GHz, Phys Med Biol., 41:2251–2269.CrossRefGoogle Scholar
  23. Gabriel, S., Lau, R. W., and Gabriel, C., 1996b, The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues, Phys. Med. Biol., 41:2271–2293.CrossRefGoogle Scholar
  24. Geddes, L. A., and Baker, L. E., 1967, The specific resistance of biological material—A compendium of data for the biomedical engineer and physiologist, Med. Biol. Eng., 5:271–293.CrossRefGoogle Scholar
  25. Geddes, L. A., and Sadler, C., 1973, The specific resistance of blood at body temperature, Med. Biol. Eng., 11:336–339.CrossRefGoogle Scholar
  26. Gersing, E., 1998, Monitoring temperature induced changes in tissue during hyperthermia by impedance methods, Proc. of the X.ICEBI, Universitat Politecnica de Cataluya.Google Scholar
  27. Gielen, F., 1983, Electrical conductivity and histological structure of skeletal muscle. PhD Thesis, University of Twente, the Netherlands.Google Scholar
  28. Gielen, F. L. H., Wallinga-de Jonge, W., and Boon, K. L., 1984, Electrical conductivity of skeletal tissue: experimental results from different muscles in vivo, Med. Biol. Eng. Comput., 22:569–577.CrossRefGoogle Scholar
  29. Gonçalves, S., Munck, J. C. de, Heethaar, R. M., Lopes da Silva F. H., and Dijk, B. W. van, 2000, The application of electrical impedance tomography to reduce systematic errors in the EEG inverse problem—a simulation study, Physiol. Meas., 21:379–393.CrossRefGoogle Scholar
  30. Grandqvist, C. G., and Hunderi, O., 1978, Conductivity of inhomogeneous materials: effective medium theory with dipole-dipole interaction, Phys. Rev. B, 18:1554–1561.CrossRefGoogle Scholar
  31. Hanai, T., 1960, Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions, Kolloid-Z., 171: 23–31.CrossRefGoogle Scholar
  32. Harreveld, A. van, and Ochs, S., 1956, Cerebral impedance charges after circulatory arrest, Am. J. Physiol., 187:203–207.Google Scholar
  33. Hart, F. X., Berner N. J., and McMillen, R. L., 1999, Modelling the anistropic electrical properties of skeletal muscle, Phys. Med Biol., 44:413–421.CrossRefGoogle Scholar
  34. Hashin, Z., and Shtrikman S., 1962, A variational approach to the theory of the effective magnetic permeability of multiphase materials, J. Appl. Phys., 33:3125–3131.MATHCrossRefGoogle Scholar
  35. Havstad, J. W., 1967, Electrical impedance of cerebral cortex: an experimental and theoretical investigation, PhD Thesis, Stanford University.Google Scholar
  36. Hoekema, R., Huiskamp, G. J. M., Wieneke, G. H., Leijten, F. S. S., van Veelen, C. W. M., van Rijen, P. C., and van Huffelen, A. C., 2001, Measurement of the conductivity of the skull, tempoarily removed during epilepsy surgery, Biomed Tech., 46:103–105.CrossRefGoogle Scholar
  37. Homma, S., Musha, T., Nakajima, Y., Okamoto, Y., Blom, S., Flink, R., Hagbach, K. E., and Moström, U., 1994, Location of electric current sources in the human brain estimated by the dipole tracing method of the scalp-skull-brain (SSB) head model, Electroen. Clin. Neuro., 91:374–382.CrossRefGoogle Scholar
  38. Kobayashi, N., and Yonemura, K., 1967, The extracellular space in red and white muscles of the rat, Jap. J. Physiol., 17:698–707.Google Scholar
  39. Kotnik, T., Bobanović, F., and Miklavĉiĉ, D., 1997, Sensitivity of transmembrane voltage induced by applied electric fields-a theoretical analysis, Bioelectroch. Bioener., 43:285–291.CrossRefGoogle Scholar
  40. Law, S. K., 1993, Thickness and resistivity variations over the upper surface of the human skull, Brain Topogr., 6:99–109.CrossRefGoogle Scholar
  41. Ludt, H., and Hermann, H. D., 1973, In vitro measurement of tissue impedance over a wide frequency range, Biophys. J., 10:337–345.Google Scholar
  42. Maxwell, J. C., 1891, A treatise on electricity and magnetism, volume 1, Arts. 311–314, Dover Publ. New York.Google Scholar
  43. Mc Rae, D. A., and Esrick, M. A., 1993, Changes in electrical impedance of skeletal muscle measured during hyperthermia, Int. J. Hyperthermia, 9:247–261.CrossRefGoogle Scholar
  44. Nicholson, C., and Rice, M. E., 1986, The migration of substances in the neural microenvironment, Ann. New York Academy of Sciences, 481:55–71.CrossRefGoogle Scholar
  45. Nicholson, P. W., 1965, Specific impedance of cerebral white matter, Exp. Neurol., 13:386–401.CrossRefGoogle Scholar
  46. Oostendorp, T. F., Delbeke, J., and Stegeman, D. F., 2000, The conductivity of the human skull; Results of in vivo and in vitro measurements, IEEE T. Bio-Med. Eng., 47:1487–1492.CrossRefGoogle Scholar
  47. Peters, M. J., Hendriks, M., and Stinstra, J. G., 2001, The passive DC conductivity of human tissue described by cells in solution, Bioelectroch., 53:155–160.CrossRefGoogle Scholar
  48. Pehtig, R., and Kell, D. B., 1987, The passive electrical properties of biological systems: their significance in physiology, biophysics and biotechnology, Phys. Med. Biol., 32:933–970.CrossRefGoogle Scholar
  49. Pfützner H., 1984, Dielectric analysis of blood by means of a raster-electrode technique, Med. Biol. Eng. Comput., 22:142–146.CrossRefGoogle Scholar
  50. Plonsey, R., and Barr, R.C., 1986, Effect of microscopic and macroscopic discontinuities on the response of cardiac tissue to defibrilating (stimulating) current, Med. Biol. Eng. Comput., 24:130–136.CrossRefGoogle Scholar
  51. Plonsey, R., and Heppner, D.B., 1967, Considerations of quasi-stationarity in electrophysiological systems, Bulletin of mathematical Biophysics, 29:657–664.CrossRefGoogle Scholar
  52. Raicu, V., Saibara, T., and Irimajiri, A., 1998a, Dielectric properties of rat liver in vivo: a non-invasive approach using an open-ended coaxial probe at audio/radio frequencies, Bioelectroch. Bioener., 47: 325–332.CrossRefGoogle Scholar
  53. Raicu, V., Saibara, T., Enzan H., and Irimajiri, A., 1998b, Dielectric properties of rat liver in vivo: analysis by modeling hepatocytes in the tissue architecture, Bioelectroch. Bioener., 47:333–342.CrossRefGoogle Scholar
  54. Robillard, P. N., and Poussart Y., 1977, Specific-impedance measurements of brain tissues, Med. Biol. Eng. Comput., 15:438–445.CrossRefGoogle Scholar
  55. Rosell, J., Colominas, J., Riu, P., Pallas-Areny, R., and Webster, J. G., 1988, Skin impedance from 1 Hz to 1 MHz, IEEE T. Bio-Med. Eng., 35:649–651.CrossRefGoogle Scholar
  56. Rush, S., 1967, A principle for solving a class of anisotropic current flow problems and applications to electrocardiography, IEEE T. Bio-Med. Eng., BME-14:18–22.CrossRefGoogle Scholar
  57. Rush, S., Abildskov, J.A., and Mc Fee, R., 1963, Resistivity of body tissues at low frequencies, Circ. Res., XII:40–50.Google Scholar
  58. Rush, S., Mehtar, M., and Baldwin, A. F., 1984, Normalisation of body impedance data: a theoretical study, Med. Biol. Eng. Comput., 22:285–286.CrossRefGoogle Scholar
  59. Schwan, H. P., 1985, Dielectric properties of cells and tissues, in: Interactions between Electromagnetic Fields and Cells, (A Chiabrera, C. Nicolini, and H. P. Schwan, eds.) NATO ASI series, vol. 97, Plenum Press, New York, pp. 75–103.Google Scholar
  60. Schwan, H. P., and Foster, K. R., 1980, RF-Field interactions with biological systems: Electrical properties and biophysical mechanisms, Proc. of the IEEE, 68:104–113.CrossRefGoogle Scholar
  61. Schwan, H. P., and Takashima, S., 1993, Electrical conduction and dielectric behaviour in biological systems, Encyclopedia of Applied Physics, 5:177–199.Google Scholar
  62. Sekine, K., 2000, Application of boundary element method to calculation of the complex permittivity of suspensions of cells in shape of D∞h symmetry, Electroch. 52:1–7.Google Scholar
  63. Semrov, D., Karba, R., and Valencic, V., 1997, DC Electrical stimulation for chronic wound healing enhancement. Part 2. Parameter determination by numerical modelling, Bioelectroch. Bioener., 43:271–277.CrossRefGoogle Scholar
  64. Sillars, R. W., 1937, The properties of a dielectric containing semi-conducting particles of various shapes, J. Ins. Electrical Eng., 80:378–394.Google Scholar
  65. Stanley, P. C., Pilkington, T. C., and Morrow, M. N., 1986, The effects of thoracic inhomogeneities on the relationship between epicardial and torso potentials, IEEE T. Bio-Med. Eng., BME-33:273–284.CrossRefGoogle Scholar
  66. Stanley, P. C., Pilkington, T. C., Morrow, M. N., and Ideker, R. E., 1991, An assessment of variable thickness and fiber orientation of the skeletal muscle layer on electrocardiographic calculations, IEEE T. Bio-Med. Eng., 38:1069–1076.CrossRefGoogle Scholar
  67. Stinstra, J. G., 2001, Reliability of fetal magnetocardiography, PhD thesis, University of Twente, the Netherlands.Google Scholar
  68. Stuchly, M. A., and Stuchly, S. S., 1980, Dielectric properties of biological substances-Tabulated, J. Microwave Power, 15:19–26.Google Scholar
  69. Takashima, S., 1989, Electrical properties of biopolymers and membranes, IOP Publishing Ltd, Bristol.Google Scholar
  70. Trautman, E. D., and Newbower, R. S., 1983, A practical analysis of the electrical conductivity of blood, IEEE T. Bio-Med. Eng., BME-30:141–153.CrossRefGoogle Scholar
  71. Ülgen, Y., and Sezdi, M., 1998, Electrical parameters of human blood, Proceedings 20th Ann. Int. Conference, IEEE/EMBS, Hongkong, 2983–2986.Google Scholar
  72. Veelen, C. van, Debets, R., Huffelen, A. van, Emde Boas, W. van, Binnie, C., Storm van Leeuwen, W., Velis, D. N., and Dieren, A. van, 1990, Combined use of subdural and intracerebral electrodes in preoperative evaluation of epilepsy, Neurosurgery, 26:93–101.CrossRefGoogle Scholar
  73. Yamamoto, T., and Yamamoto, Y., 1976, Electrical properties of epidermal stratum corneum, Med. Biol. Eng., 3:151–158.CrossRefGoogle Scholar
  74. Zheng, E., Shao, S., and Webster, J. G., 1984, Impedance of skeletal muscle from 1 Hz to 1 MHz, IEEET. Bio-Med. Eng., BME-31:477–481.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers, New York 2004

Authors and Affiliations

  • Maria J. Peters
    • 1
  • Jeroen G. Stinstra
    • 1
  • Ibolya Leveles
    • 1
    • 2
  1. 1.Faculty of Applied Physics, Low Temperature DivisionUniversity of TwenteEnschedeThe Netherlands
  2. 2.Faculty of Applied PhysicsUniversity of TwenteEnschedeThe Netherlands

Personalised recommendations