Abstract
Cardiac muscle is considered to consist of an intracellular domain and an exracellular or interstitial domain. Current passes from one domain to the other through the cell membrane. Electric potentials in interstitial space are shown to be associated with current sources proportional to the spatial gradient of the cellular transmembrane action potential, φ m . Hence, given the distribution of φ m throughout the myocardium, one can calculate the surface electrocardiogram and extracorporeal magnetocardiogram. The problem is considerably complicated when anisotropy is considered. If interstitial space is approximately isotropic, however, the sources are still proportional to ∇φ m . It is shown that the effects of intracellular anisotropy on the surface electrocardiogram may be relatively small. The inverse problem is discussed briefly, with consideration of the relationship of the magnetocardiogram to the electrocardiogram. Finally, it is shown that if the heart can be considered to be bounded by a closed surface, then the value of φ m on this surface is uniquely related to the surface electrocardiogram to within a constant, provided there are no internal discontinuities. Such discontinuities, however, would be expected to occur in cases of ischemia and necrosis.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Arthur, R.M., D.B. Geselowitz, S.A. Briller, and R.F. Trost. Quadrupole components of the human surface electrocardiogram.Am. Heart J. 83:663–667, 1972.
Barr, L., and E. Jakobsson. The spread of current in electrical syncytia. InPhysiology of Smooth Muscle, edited by E. Bulbring and M.F. Shuba. New York: Raven Press, 1974, pp. 41–48.
Baule, G.M., and R. McFee. Theory of magnetic detection of the heart's electrical activity.J. Appl. Phys. 36:2066–2074, 1965.
Clerc, L. Directional differences of impulse spread in trabecular muscle from mammalian heart.J. Physiol. 255:335–346, 1976.
Geselowitz, D.B. On bioelectric potentials in an inhomogeneous volume conductor.Biophys. J. 7:1–11, 1967.
Geselowitz, D.B. On the magnetic field generated outside an inhomogeneous volume conductor by internal current sources.IEEE Trans. Magn. MAG-6:346–347, 1970.
Geselowitz, D.B. Representation of cardiac sources in anisotropic cardiac muscle.IEEE 1980 Frontiers of Engineering in Health Care. Proceedings of the 2nd American Conference EMBS, 1980, pp. 6–8.
Geselowitz, D.B., R.C. Barr, M.S. Spach, and W.T. Miller, III. The impact of adjacent isotropic fluids on electrograms from anisotropic cardiac muscle.Circ. Res. 51:602–613, 1982.
Geselowitz, D.B., and W.T. Miller, III. Active electric properties of cardiac muscle.Bioelectromagn. 3:127–132, 1982.
Holland, R.P., and M.F. Arnsdorf. Non-spatial determinants of electrograms in guinea pig ventricle.Am. J. Physiol. 240:C148-C160, 1981.
Lepeschkin, E. Physiological influences on transfer factors between heart currents and body-surface potentials. InThe Theoretical Basis of Electrocardiology, edited by C. V. Nelson and D.B. Geselowitz. London: Oxford University Press, 1976, pp. 135–161.
McFee, R. and F.D. Johnston. Electrocardiographic leads: I. Introduction.Circulation 8:554–568, 1953.
Miller, W. T., III and D.B. Geselowitz. Simulation studies of the electrocardiogram. I. The normal heart. II. Ischemia and infarction.Circ. Res. 43:301–323, 1978.
Plonsey, R., and Y. Rudy. Electrocardiogram sources in a 2-dimensional anisotropic activation model.Med. Biol. Eng. Comput. 18:87–94, 1980.
Roberts, D.E., L.T. Hersh, and A.M. Scher. Influence of cardiac fiber orientation on wavefront voltage, conduction velocity and tissue resistivity in the dog.Circ. Res. 44:701–712, 1979.
Rush, S. A principle for solving a class of anisotropic current flow problems and applications to electrocardiography.IEEE Trans. Biomed. Eng. BME-14:18–22, 1967.
Rush, S. On the independence of magnetic and electric body surface recordings.IEEE Trans. Biomed. Eng. BME-22:157–167, 1975.
Rush, S., J.A. Abildshov, and R. McFee. Resistivity of body tissue at low frequencies.Circ. Res. 12:40–50, 1963.
Schmitt, O.H. Averaging techniques employing several simultaneous physiological variables.Ann. N.Y. Acad. Sci. 115:952–975, 1964.
Schmitt, O.H. Biological information processing using the concept of interpenetrating domains. InInformation Processing in the Nervous System, edited by K.N. Leibovic, New York: Springer-Verlag, 1969, p. 329.
Spach, M.S. and R.C. Barr. Origin of epicardial ST-T wave potentials in the intact dog.Circ. Res. 39:475–487, 1976.
Spach, M.S., W.T. Miller, III, E. Miller-Jones, R.B. Warren, and R.C. Barr. Extracellular potentials related to intracellular action potentials during impulse conduction in anisotropic cardiac muscle.Circ. Res. 45:188–204, 1979.
Streeter, D.D., H.M. Spotnitz, D.P. Patel, J. Ross, and E.H. Sonnenblick. Fiber orientation in the canine left ventricle during diastole and systole.Circ. Res. 24:339–347, 1969.
Tasaki, I. and S. Hagiwara. Capacity of muscle fiber membrane.Am. J. Physiol. 188:423–429, 1957.
Weidmann, S. Electrical constants of trabecular muscle from mammalian heart.J. Physiol. 210:1041–1054, 1970.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Geselowitz, D.B., Miller, W.T. A bidomain model for anisotropic cardiac muscle. Ann Biomed Eng 11, 191–206 (1983). https://doi.org/10.1007/BF02363286
Issue Date:
DOI: https://doi.org/10.1007/BF02363286