The Generalized Activating Function

  • Leslie Tung

Insight into the biophysical processes associated with electrical stimulation of the heart is important for the understanding of electrical pacing and defibrillation. When electrodes are physically placed on the myocardium, not only do they induce polarization changes in the cell membrane in regions in proximity to the electrodes, but they also induce polarization changes remote to the electrodes. How applied electrical currents are transduced into changes in cellular transmembrane potentials has been called the “missing link,”1 and many mechanisms have been proposed, including the so-called sawtooth pattern arising from discontinuities in fiber conductivity,2 “dog-bone” pattern arising from the anisotropic bido-main properties of cardiac tissue,3 surface polarization,4 fiber curvature,4 fiber rotation,5 and heterogeneities in intracellular volume fraction6 (also see reviews7–9 that describe the similarities among nerve, brain, and cardiac stimulation). More recently, studies of cardiac cell cultures grown in user-designed patterns10 have permitted detailed investigations of electric field-induced responses of linear strands,11 intercellular cleft spaces,12 fiber branches, expansions and bends,.13 and curved fibers.14

The concept of the activating function was proposed by Rattay15 for electrical excitation of unmyelinated nerve axons (based on earlier ground-breaking work by McNeal16 on myeli-nated axons), where a nerve fiber is stimulated by an externally applied electric field. The electric field generates a gradient of electrical potential in space, which is impressed upon the outer surface of the axon. Depending on the distribution of potential, an electromotive force can arise across the surface membrane that causes the flow of membrane current, which in turn perturbs the transmembrane potential. The details of this process are most easily understood for the case of a one-dimensional fiber lying in a three-dimensional volume conductor, as described in the next section. The definition of the activating function will then be generalized for cardiac tissue, followed by examination of the generalized activating function for a number of examples.


Cardiac Tissue Transmembrane Potential Virtual Cathode Virtual Source Extracellular Potential 
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. 1.
    Roth BJ, Krassowska W. The induction of reentry in cardiac tissue. The missing link:how electric fields alter transmembrane potential.Chaos1998;8(1):204–220PubMedCrossRefGoogle Scholar
  2. 2.
    Plonsey R, Barr RC. Effect of microscopic and macroscopic discontinuities on the response of cardiac tissue to defibrillating (stimulating) currents.Med Biol Eng Comput1986;24(2):130–136PubMedCrossRefGoogle Scholar
  3. 3.
    Sepulveda NG, Roth BJ, Wikswo JP Jr. Current injection into a two-dimensional anisotropic bidomain.Biophys J1989;55(5):987–999PubMedGoogle Scholar
  4. 4.
    Trayanova NA, Roth BJ, Malden LJ. The response of a spherical heart to a uniform electric field: a bidomain analysis of cardiac stimulation.IEEE Trans Biomed Eng1993;40(9):899–908PubMedCrossRefGoogle Scholar
  5. 5.
    Entcheva E, Trayanova NA, Claydon FJ. Patterns of and mechanisms for shock-induced polarization in the heart: a bidomain analysis.IEEE Trans Biomed Eng1999;46(3):260–270PubMedCrossRefGoogle Scholar
  6. 6.
    Fishler MG. Syncytial heterogeneity as a mechanism underlying cardiac far-field stimulation during defibrillation-level shocks.J Cardiovasc Electrophysiol1998;9(4):384–394PubMedCrossRefGoogle Scholar
  7. 7.
    Roth BJ. Mechanisms for electrical stimulation of excitable tissue.Crit Rev Biomed Eng1994;22(3–4):253–305PubMedGoogle Scholar
  8. 8.
    Newton JC, Knisley SB, Zhou X, Pollard AE, Ideker RE. Review of mechanisms by which electrical stimulation alters the transmembrane potential.J Cardiovasc Electro-physiol1999;10(2):234–243CrossRefGoogle Scholar
  9. 9.
    Basser PJ, Roth BJ. New currents in electrical stimulation of excitable tissues.Annu Rev Biomed Eng2000;2:377–397PubMedCrossRefGoogle Scholar
  10. 10.
    Rohr S, Fluckiger-Labrada R, Kucera JP. Photolithographically defined deposition of attachment factors as a versatile method for patterning the growth of different cell types in culture.Pflugers Arch2003;446(1):125–132PubMedGoogle Scholar
  11. 11.
    Gillis AM, Fast VG, Rohr S, Kleber AG. Spatial changes in transmembrane potential during extracellular electrical shocks in cultured monolayers of neonatal rat ventricular myocytes.Circ Res1996;79(4):676–690PubMedGoogle Scholar
  12. 12.
    Fast VG, Rohr S, Gillis AM, Kleber AG. Activation of cardiac tissue by extracellular electrical shocks: formation of ‘secondary sources’ at intracellular clefts in monolayers of cultured myocytes.Circ Res1998;82(3):375–385PubMedGoogle Scholar
  13. 13.
    Gillis AM, Fast VG, Rohr S, Kleber AG. Mechanism of ventricular defibrillation. The role of tissue geometry in the changes in transmembrane potential in patterned myocyte cultures.Circulation2000;101(20):2438–2445PubMedGoogle Scholar
  14. 14.
    Tung L, Kleber AG. Virtual sources associated with linear and curved strands of cardiac cells.Am J Physiol Heart Circ Physiol2000;279(4):H1579–H1590PubMedGoogle Scholar
  15. 15.
    Rattay F. Analysis of models for external stimulation of axons.IEEE Trans Biomed Eng1986;33(10):974–977PubMedCrossRefGoogle Scholar
  16. 16.
    McNeal DR. Analysis of a model for excitation of myelinated nerve.IEEE Trans Biomed Eng1976;23(4):329–337PubMedCrossRefGoogle Scholar
  17. 17.
    Barr RC, Plonsey R.Bioelectricity: A Quantitative Approach, 3rd edn. Berlin: Springer;2007Google Scholar
  18. 18.
    Rattay F. Ways to approximate current-distance relations for electrically stimulated fibers.J Theor Biol1987;125(3):339–349PubMedCrossRefGoogle Scholar
  19. 19.
    Hoshi T, Matsuda K. Excitability cycle of cardiac muscle examined by intracellular stimulation.Jpn J Physiol1962;12:433–446PubMedGoogle Scholar
  20. 20.
    Bonke FI. Passive electrical properties of atrial fibers of the rabbit heart.Pflugers Arch1973;339(1):1–15PubMedCrossRefGoogle Scholar
  21. 21.
    Henriquez CS. Simulating the electrical behavior of cardiac tissue using the bidomain model.Crit Rev Biomed Eng1993;21(1):1–77PubMedGoogle Scholar
  22. 22.
    Rattay F. The basic mechanism for the electrical stimulation of the nervous system.Neuroscience1999;89(2):335–346PubMedCrossRefGoogle Scholar
  23. 23.
    Plonsey R, Barr RC. Electric field stimulation of excitable tissue.IEEE Trans Biomed Eng1995;42(4):329–336PubMedCrossRefGoogle Scholar
  24. 24.
    Sobie EA, Susil RC, Tung L. A generalized activating function for predicting virtual electrodes in cardiac tissue.Biophys J1997;73(3):1410–1423PubMedGoogle Scholar
  25. 25.
    Roth BJ. How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle.J Math Biol1992;30(6):633–646PubMedCrossRefGoogle Scholar
  26. 26.
    Weidmann S. Electrical constants of trabecular muscle from mammalian heart.J Physiol1970;210(4):1041–1054PubMedGoogle Scholar
  27. 27.
    Susil RC, Sobie EA, Tung L. Separation between virtual sources modifies the response of cardiac tissue to field stimulation.J Cardiovasc Electrophysiol1999;10(5):715–727PubMedCrossRefGoogle Scholar
  28. 28.
    Krassowska W, Frazier DW, Pilkington TC, Ideker RE. Potential distribution in three-dimensional periodic myocardium — Part II: application to extracellular stimulation.IEEE Trans Biomed Eng1990;37(3):267–284PubMedCrossRefGoogle Scholar
  29. 29.
    Wikswo JP Jr, Lin SF, Abbas RA. Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation.Biophys J1995;69(6):2195–2210PubMedCrossRefGoogle Scholar
  30. 30.
    Warman EN, Grill WM, Durand D. Modeling the effects of electric fields on nerve fibers:determination of excitation thresholds.IEEE Trans Biomed Eng1992;39(12):1244–1254PubMedCrossRefGoogle Scholar
  31. 31.
    Neunlist M, Tung L. Spatial distribution of cardiac transmembrane potentials around an extracellular electrode: dependence on fiber orientation.Biophys J1995;68(6):2310–2322PubMedGoogle Scholar
  32. 32.
    Plonsey R. The nature of sources of bioelectric and biomagnetic fields.Biophys J1982;39(3):309–312PubMedGoogle Scholar
  33. 33.
    Frazier DW, Krassowska W, Chen PS, Wolf PD, Dixon EG, Smith WM, Ideker RE. Extracellular field required for excitation in three-dimensional anisotropic canine myocardium.Circ Res1988;63(1):147–164PubMedGoogle Scholar
  34. 34.
    Fast VG, Rohr S, Ideker RE. Nonlinear changes of transmembrane potential caused by defibrillation shocks in strands of cultured myocytes.Am J Physiol Heart Circ Physiol2000;278(3):H688–H697PubMedGoogle Scholar
  35. 35.
    Knisley SB, Trayanova N, Aguel F. Roles of electric field and fiber structure in cardiac electric stimulation.Biophys J1999;77(3):1404–1417PubMedGoogle Scholar
  36. 36.
    Trayanova N, Skouibine K, Aguel F. The role of cardiac tissue structure in defibrillation.Chaos1998;8(1):221–233PubMedCrossRefGoogle Scholar
  37. 37.
    Knisley SB. Evidence for roles of the activating function in electric stimulation.IEEE Tra n s B i o m ed E n g2000;47(8):1114–1119Google Scholar
  38. 38.
    Altman KW, Plonsey R. Analysis of excitable cell activation: relative effects of external electrical stimuli.Med Biol Eng Comput1990;28(6):574–580PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  • Leslie Tung
    • 1
  1. 1.Department of Biomedical Engineering, School of MedicineThe Johns Hopkins UniversityBaltimoreUSA

Personalised recommendations