The topology of defibrillation

Journal of Theoretical Biology

Volumn 230, Issue 4 SPEC. ISS., 2004, Pages 459-473

  Keener, James P ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

Defibrillation; Phase singularity; Reentry; Scroll wave; Spiral wave

Indexed keywords

BIOLOGY;

CALCULATION; DEFIBRILLATION; ELECTRODE; HEART; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PRIORITY JOURNAL; REVIEW; STIMULUS;

EID: 4444334417     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jtbi.2003.11.033     Document Type: Article

References (46)

1. Caulfield J.B., Borg T.K. The collagen network of the heart. Lab. Invest. 40:1979;364-372
2. Choi B.-R., Nho W., Liu T., Salama G. Life span of ventricular fibrillation frequencies. Circ. Res. 91:2002;339
3. Cytrynbaum, E., 2001. Using low dimensional models to understand cardiac arrhythmias. Ph.D. Thesis. University of Utah, Salt Lake City, UT.
4. Eason J., Trayanova N. Phase singularities and termination of spiral wave reentry. J. Cardiovasc. Electrophys. 13:2002;672-679
5. Efimov I.R., Aguel F., Cheng Y., Wollenzier B., Trayanova N. Virtual electrode polarization in the far field. implications for external defibrillation Am. J. Physiol. 279:2000;H1055-H1070
6. Efimov I.R., Gray R.A., Roth B.J. Virtual electrodes and deexcitation. New insights into fibrillation induction and defibrillation J. Cardiovasc. Electrophysiol. 11:2000;339-353
7. Fast V.G., Rohr S., Gillis A.M., Kleber A.G. Activation of cardiac tissue by extracellular electrical shocks. Circ. Res. 82:1998;375-385
8. Fishler M.G. Synctial heterogeneity as a mechanism underlying cardiac far-field stimulation during defibrillation-level shocks. J. Cardiovasc. Electrophysiol. 9(4):1998;384-394
9. Fishler M.G., Vepa K. Spatiotemporal effects of syncytial heterogeneities on cardiac far-field excitations during monophasic and biphasic shocks. J. Cardiovasc. Electrophysiol. 9(12):1998;1310-1324
10. Gedeon G., Glass L. Continuity of resetting curves for FitzHugh-Nagumo equations on a circle. Fields Inst. Commun. 21:1998;225-236
11. Gillis A.M., Fast V.G., Rohr S., Kleber A.G. Spatial changes in transmembrane potential during extracellular electric shocks in cultured monlayers of neonatal rat ventricular myocytes. Circ. Res. 79:1996;676-690
12. Glass L., Josephson M.E. Resetting and annihilation of reentrant abnormally rapid heartbeat. Phys. Rev. Lett. 75:1995;2059-2062
13. Gold M.R., Higgins S., Gilliam F.R., Koppelman H., Hessen J., Payne S.A., Strickberger D., Breiter S., Hahn S. Efficacy and temporal stability of reduced safety margins for ventricular defibrillation:primary results from the Low Energy Safety Study (LESS). Circulation. 105:2002;2043-2048
14. Gray R.A., Jalife J., Panfilov A., Baxter W.T., Cabo C., Davidenko J.M., Pertsov A.M. Mechanisms of cardiac fibrillation. Science. 270:1995;1222-1223
15. Hooks D.A., Tomlinson K.A., Marsden S.G., LeGrice I.J., Smaill B.H., Pullan A.J., Hunter P.J. Cardiac microstructure. implications for electrical propagation and defibrillation in the heart Circ. Res. 91:2002;331-338
16. Ideker, R.E., Tang, A.S.L., Frazier, D.W., Shibata, N., Chen, P.-S., Wharton, J.M., 1991. In: Glass, L., Hunter, P., McCulloch, A. (Eds.), Theory of Heart. Basic Mechanisms of Ventricular Defibrillation. Springer, New York, pp. 533-560 (Chapter 20).
17. Iyer A.N., Gray R.A. An experimentalist's approach to accurate location of phase singularities during reentry. Ann. Biomed. Eng. 29:2001;47-59
18. Jalife, J., Berenfeld, O., 2004. Molecular mechanisms and global dynamics of fibrillation : an integrative approach to the underlying basis of vortex-like reentry. J. Theor. Biol. x-ref: doi:10.1016/j.jtbi.2003.11.033.
19. Keener J.P. Direct activation and defibrillation of cardiac tissue. J. Theor. Biol. 178:1996;313-324
20. Keener J.P. The effect of gap junctional distribution on defibrillation. Chaos. 8:1998;175-187
21. Keener J.P. Principles of Applied Mathematics: Transformation and Approximation. 2nd Edition:1999;Perseus, Cambridge, MA
22. Keener J.P., Cytrynbaum E. The effect of spatial scale of resistive inhomogeneity on defibrillation of cardiac tissue. J. Theor. Biol. 223:2003;232-248
23. Keener J.P., Lewis T.J. The biphasic mystery: Why a biphasic shock is more effective than a monophasic shock for defibrillation. J. Theor. Biol. 200:1999;1-17
24. Keener J.P., Panfilov A.V. A biophysical model for defibrillation of cardiac tissue. Biophys. J. 71:1996;1335-1345
25. Keener J.P., Sneyd J. Mathematical Physiology. 1998;Springer, New York
26. Knisely S.B., Hill B.C., Ideker R.E. Virtual electrode effects in myocardial fibers. Biophys. J. 66:1994;719-728
27. Krassowska W., Pilkington T.C., Ideker R.E. Periodic conductivity as a mechanism for cardiac stimulation and defibrillation. IEEE Trans. Biomed. Eng. 34:1987;555-559
28. Krassowska W., Pilkington T.C., Ideker R.E. Potential distribution in three-dimensional periodic myocardium - Part I. solution with two-scale asymptotic analysis IEEE Trans. Biomed. Eng. 37:1990;252-266
29. Krinsky V.I., Pumir A. Models of defibrillation of cardiac tissue. Chaos. 8:1998;188-203
30. Panfilov A.V. Spiral breakup as a model of ventricular fibrillation. Chaos. 8:1998;57-64
31. Panfilov A.V. Three-dimensional organization of electrical turbulence in the heart. Phys. Rev. Lett. 59:1999;R6251-R6254
32. Pertsov A.M., Krinskii V.I., Kokoz Y.M., Kuz'minykh S.B. Analysis of the electrophysioogical characteristics of the membrane of the trabecula of the frog auricle from ionic currents on potential clamping. Biophys. 22:1977;102-108
33. Pertsov A.M., Shapovalova L.M., Shcheglova Y.A. Analysis of the electrophysiological characteristics of the membrane of the trabecula of the frog auricle from records of ionic currents on potential clamping - II. accomodation, repeat responses, anode-breaking excitation. Biophys. 22:1977;302-307
34. Robinson T.F., Gould-Cohen L., Factor S.M. Skeletal framework of mammalian heart muscle. Lab. Invest. 49:1983;482-498
35. Roth B.J. A mathematical model of make and break electrical stimulation of cardiac tissue by a unipolar anode or cathode. IEEE Trans. Biomed. Eng. 42:1995;1174-1183
36. Roth B.J. An S1 gradient of refractoriness is not essential for reentry induction by an S2 stimulus. IEEE Trans. Biomed. Eng. 47:2000;820-821
37. White J.B., Walcott G.P., Pollard A.E., Ideker R.E. Myocardial discontinuities. a substrate for producing virtual electrodes that directly excite the myocardium by shocks Circulation. 97:1998;1738-1745
38. Wiener N., Rosenblueth A. The mathematical formulation of the problem of conduction of inpulses in a network of connected excitable elements, specifically in cardiac muscle. Arch. Inst. Cardiol. Mex. 16:1946;205-265
39. Wikswo J.P. Jr., Lin S.F., Abbas R.A. The complexities of cardiac cables. virtual electrode effects Biophys. J. 66:1994;551b-553b
40. Wikswo J.P. Jr., Lin S.F., Abbas R.A. Virtual electrodes in cardiac tissue. A common mechanism for anodal and cathodal stimulation Biophys. J. 69:1995;2195-2210
41. Winfree A.T. Scroll-shaped waves of chemical activity in three dimension. Science. 181:1973;937-939
42. Winfree A.T. Sudden cardiac death, a problem in topology. Sci. Am. 248:1983;114-161
43. Winfree A.T. When Time Breaks Down. 1987;Princeton University Press, Princeton, NJ
44. Winfree A.T. Electrical instability in cardiac muscle. phase singularities and rotors J. Theor. Biol. 138:1989;353-405
45. Winfree A.T. Various ways to make phase singularities by electric shock. J. Cardiovasc. Electrophys. 11:2000;286-289
46. Zhou X., Knisely S.B., Smith W.M., Rollins D., Pollard A.E., Ideker R.E. Spatial changes in the transmembrane potential during extracellular electric stimulation. Circ. Res. 83:1998;1003-1014