Skip to main content
SpringerLink
Log in

The electrical potential produced by a strand of cardiac muscle: A bidomain analysis

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Analytic expressions are derived relating the transmembrane potential to the intracellular, interstitial and external potentials in a cylindrical strand of cardiac muscle lying in a saline bath. The bidomain model is used to account for the anisotropy and interstitial space in the tissue. The implications of this model for interpreting potential data from strands of cardiac muscle are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abramowitz, M.; Stegun, I.A. Handbook of mathematical functions with formulas, graphs, and mathematical tables. Washington, D.C.: National Bureau of Standards; 1970.

    Google Scholar 

  2. Barr, R.C.; Plonsey, R. Propagation of excitation in idealized anisotropic two-dimensional tissue. Biophys. J. 45:1191–1202; 1984.

    CAS  PubMed  Google Scholar 

  3. Buchanan, J.W., Jr.; Oshita, S.; Fujino, T.; Gettes, L.S. A method for measurement of intern resistance in papillary muscle. Am. J. Physiol. 251:H210-H217; 1986.

    PubMed  Google Scholar 

  4. Chapman, R.A.; Fry, C.H. An analysis of cable properties of frog ventricular myocardium. J. Physiol. 283:263–281; 1978.

    CAS  PubMed  Google Scholar 

  5. Clerc, L. Directional differenes of impulse spread in trabecular muscle from mammalian heart. J. Physiol. 255:335–346; 1976.

    CAS  PubMed  Google Scholar 

  6. Clark, J.W.; Plonsey, R. The extracellular field of the single active nerve fiber in a volume conductor. Biophys. J. 8:842–864;1968.

    CAS  PubMed  Google Scholar 

  7. Cole, K.S.; Curtis, H.J. Electric physiology. In: Glasser, O. ed. Medical Physics. Chicago: The Year Book Publ. Inc.; 1950.

    Google Scholar 

  8. Dodge, F.A.; Cranefield, P.F. Nonuniform conduction in cardiac Purkinje fibres. In: Carvalo, A.; Hoffman, B.F.; Lieberman, M., eds. Normal and abnormal conduction in the heart. New York: Futura Pub.; 1982.

    Google Scholar 

  9. Eisenberg, R.S.; Barcilon, V.; Mathias, R.T. Electrical properties of spherical syncytia. Biophys. J. 25:151–180; 1979.

    CAS  PubMed  Google Scholar 

  10. Freygang, W.H.; Trautwein, W. The structural implications of the linear electrical properties of cardiac Purkinje strands. J. Gen. Physiol. 55:524–547; 1970.

    Article  CAS  PubMed  Google Scholar 

  11. Ganapathy, N.; Clark, J.W., Jr.; Wilson, O.B.; Giles, W. Forward and inverse potential field solution for cardiac strands of cylindrical geometry. IEEE Trans. Biomed. Eng. 32:566–577; 1985.

    CAS  PubMed  Google Scholar 

  12. Geselowitz, D.B.; Barr, R.C.; Spach, M.S.; Miller, W.T., III. The impact of adjacent isotropic fluids on electrograms from anisotropic cardiac muscle: a modeling study. Circ. Res. 51:602–613; 1982.

    CAS  PubMed  Google Scholar 

  13. Greco, E.C.; Clark, J.W.; Harman, T.L. Solution of the forward and inverse problems associated with the potential field of a single active nerve fiber in a volume conductor. Math. Biosci. 33:235–256; 1977.

    Article  Google Scholar 

  14. Hellam, D.C.; Studt, J.W. A core-conductor model of the cardiac Purkinje fibre based on structural analysis. J. Physiol. 243:637–660; 1974.

    CAS  PubMed  Google Scholar 

  15. Henriquez, C.S.; Plonsey, R. Effect of resistive discontinuities on waveshape and velocity in a single cardiac fibre. Med. & Biol. Eng. & Comp. 25:428–438; 1987.

    CAS  Google Scholar 

  16. Jackson, J.D. Classical electrodynamics. New York: John Wiley & Sons; 1975.

    Google Scholar 

  17. Joyner, R.W.; Picone, J.; Veenstra, R.; Rawling, D. Propagation through electrically coupled cells. Effects of regional changes in membrane properties. Circ. Res. 53:526–534; 1983.

    CAS  PubMed  Google Scholar 

  18. Kleber, A.G.; Riegger, C.B.; Janse, M.J. Electrical uncoupling and increase of extracellular resistance after induction of ischemia in isolated, arterially perfused rabbit papillary muscle. Circ. Res. 61:271–279; 1987.

    CAS  PubMed  Google Scholar 

  19. Krassowska, W.; Pilkington, T.C.; Ideker, R.E. The closed form solution to the periodic coreconductor model using asymptotic analysis. IEEE Trans. Biomed. Eng. BME-34:519–531; 1987.

    CAS  Google Scholar 

  20. Levin, D.N.; Fozzard, H.A. A cleft model for cardiac Purkinje strands. Biophys. J. 33:383–408; 1981.

    CAS  PubMed  Google Scholar 

  21. Miller, W.T., III; Geselowitz, D.B. Simulation studies of the electrocardiogram, I. The normal heart. Circ. Res. 43:301–315; 1978.

    CAS  PubMed  Google Scholar 

  22. Pilkington, T.C.; Plonsey, R. Macroscopic cardiac sources. In: Pilkington, T.C.; Plonsey, R., eds. Engineering Contributions to Biophysical Electrocardiography. New York: IEEE Press; 1982.

    Google Scholar 

  23. Plonsey, R.; Barr, R.C. The four-electrode resistivity technique as applied to cardiac muscle. IEEE Trans. Biomed. Eng. BME-29:541–546; 1982.

    CAS  Google Scholar 

  24. Plonsey, R.; Barr, R.C. Current flow patterns in two-dimensional anisotropic bisyncytia with normal and extreme conductivities. Biophys. J. 45:557–571; 1984.

    CAS  PubMed  Google Scholar 

  25. Plonsey, R.; Barr, R.C. Effect of junctional resistance on source-strength in a linear cable. Ann. Biomed. Eng. 13:95–100; 1985.

    CAS  PubMed  Google Scholar 

  26. Plonsey, R.; Barr, R.C. Effect of microscopic and macroscopic discontinuities on the response of cardiac tissue to defibrillating (stimulating) currents. Med. & Bio. Eng. & Comput. 24:130–136; 1986.

    CAS  Google Scholar 

  27. Plonsey, R.; Barr, R.C. A critique of impedance measurements in cardiac tissue. Ann. Biomed. Eng. 14:307–322; 1986.

    Article  CAS  PubMed  Google Scholar 

  28. Plonsey, R.; Barr, R.C. Interstitial potentials and their change with depth into cardiac tissue. Biophys. J. 51:547–555; 1987.

    CAS  PubMed  Google Scholar 

  29. Plonsey, R.; Heppner, D. Considerations of quasi-stationarity in electrophysiological systems. Bull. Math. Biophys. 29:657–664; 1967.

    CAS  PubMed  Google Scholar 

  30. Roberts, D.E.; Hersh, L.T.; Scher, A.M. Influence of cardiac fiber orientation on wavefront voltage, conduction velocity, and tissue resistivity in the dog. Circ. Res. 44:701–712; 1979.

    CAS  PubMed  Google Scholar 

  31. Roberts, D.E.; Scher, A.M. Effects of tissue anisotropy on extracellular potential fields in canine myocardium in situ. Circ. Res. 50:342–351; 1982.

    CAS  PubMed  Google Scholar 

  32. Roth, B.J. Longitudinal resistance in strands of cardiac muscle. Ph. D. Dissertation, Vanderbilt University, Nashville, TN; 1987.

    Google Scholar 

  33. Roth, B.J.; Gielen, F.L.H.; Wikswo, J.P., Jr. Spatial and temporal frequency-dependent conductivities in volume conductor calculations of skeletal muscle. Math. Biosci. 88:159–189; 1988.

    Google Scholar 

  34. Roth, B.J.; Wikswo, J.P., Jr. A bidomain model for the extracellular potential and the magnetic field of cardiac tissue. IEEE Trans. Biomed. Eng. BME-32:467–469; 1986.

    Google Scholar 

  35. Schoenberg, M.; Fozzard, H.A. The influence of intracellular clefts on the electrical properties of sheep cardiac Purkinje fibers. Biophys. J. 25:217–234; 1979.

    CAS  PubMed  Google Scholar 

  36. Sepulveda, N.G.; Wikswo, J.P., Jr. Electric and magnetic fields from two-dimensional anisotropic bisyncytia. Biophys. J. 51:557–568; 1987.

    CAS  PubMed  Google Scholar 

  37. Spach, M.S.; Kootsey, J.M. Relating sodium current and conductance to the shape of transmembrane and extracellular potentials by simulation: Effects of propagation boundaries. IEEE Trans. Biomed. Eng. BME-32:743–755; 1985.

    CAS  Google Scholar 

  38. Spach, M.S.; Kootsey, J.M.; Sloan, J.D. Active modulation of electrical coupling between cardiac cells of the dog. Circ. Res. 51:347–362; 1982.

    CAS  PubMed  Google Scholar 

  39. Spach, M.S.; Miller, W.T., III; Geselowitz, D.B.; Barr, R.C.; Kootsey, J.M.; Johnson, E.A. The discontinuous nature of propagation in normal canine cardiac muscle. Evidence for recurrent discontinuities of intracellular resistance that affect membrane currents. Circ. Res. 48:39–54; 1981.

    CAS  PubMed  Google Scholar 

  40. Suenson, M. Interaction between ventricular cells during the early part of excitation in the ferret heart. Acta. Physiol. Scand. 125:81–90; 1985.

    CAS  PubMed  Google Scholar 

  41. Tung, L. A bi-domain model for describing ischemic myocardial d-c potentials. Ph. D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA; 1978.

    Google Scholar 

  42. Weidmann, S. Electrical constants of trabecular muscle from mammalian heart. J. Physiol. 210: 1041–1053; 1970.

    CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Living State Physics Group Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee

    Bradley J. Roth

Authors
  1. Bradley J. Roth
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roth, B.J. The electrical potential produced by a strand of cardiac muscle: A bidomain analysis. Ann Biomed Eng 16, 609–637 (1988). https://doi.org/10.1007/BF02368018

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02368018

Keywords

Search

Navigation