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Virtual Electrode Theory of Pacing

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Cardiac Bioelectric Therapy

One of the most important contributions of biomedical engineering to medicine is the devel¬opment of pacemakers, external defibrillators, and implantable cardioverters/defibrillators.1 Engineers have been quite successful in designing these devices empirically, without a funda¬mental understanding of the underlying biophysical mechanisms. Over the past 15 years, two areas of research — optical mapping of electrical activity in the heart2 and mathematical modeling of the heart using the bidomain model3 — have provided insight into the basic mechanisms by which cardiac electric fields are produced and how externally applied electric fields interact with cardiac tissue. The goal of this chapter is to describe this research and to summarize what has been learned from it. We survey the contributions of many researchers, but the emphasis is on our own work, which, of course, we know best. We focus on basic mechanisms; clinical applications are better described by other authors.4 The fundamental knowledge gained from basic research in cardiac shock response is enabling the development of detailed mathematical models5,6 that can guide the further optimization of implantable cardiac stimulators.

The electrical properties of the heart have been reviewed elsewhere. In 1993 Henriquez3 summarized the bidomain model in a seminal paper that serves as an excellent foundation for the discussions in our chapter. Neu and Krassowska7 examined the limitations of the bidomain as a continuum model. Roth8 described mechanisms of electrical stimulation of excitable tissue, including cardiac tissue. In the past 10 years much work has been published in this field, particularly on comparing numerical simulations to experimental data. The agreement between theory and experiment is an important topic9 and is the focus of this review.

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References

  1. Jeffrey K.Machines in Our Hearts: The Cardiac Pacemaker, the Implantable Defibrillator, and American Health Care. Baltimore, MD: Johns Hopkins University Press; 2001

    Google Scholar 

  2. Rosenbaum DS, Jalife J. Optical Mapping of Cardiac Excitation and Arrhythmias. Armonk, NY: Futura; 2001

    Google Scholar 

  3. Henriquez CS. Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit Rev Biomed Eng1993;21:1–77

    PubMed  CAS  Google Scholar 

  4. Zipes DP, Jalife J. Cardiac Electrophysiology: From Cell to Bedside, Ed. 4. Philadelphia, PA: Saunders; 2004

    Google Scholar 

  5. Burton RAB, Plank G, Schneider JE, Grau V, Ahammer H, Keeling SL, Lee J, Smith NP, Gavaghan D, Trayanova N, Kohl P. Three-dimensional models of individual cardiac histoanatomy: tools and challenges. Ann N Y Acad Sci2006;1080:301–319

    Article  PubMed  Google Scholar 

  6. Efimov IR, Aguel F, Cheng Y, Wollenzier B, Trayanova N. Virtual electrode polarization in the far field: implications for external defibrillation. Am J Physiol Heart2000;279:H1055–H1070

    CAS  Google Scholar 

  7. Neu JC, Krassowska W. Homogenization of syncytial tissues. Crit Rev Biomed Eng1993;21:137–199

    PubMed  CAS  Google Scholar 

  8. Roth BJ. Mechanisms for electrical stimulation of excitable tissue. Crit Rev Biomed Eng1994;22:253–305

    PubMed  CAS  Google Scholar 

  9. Roth BJ. Artifacts, assumptions, and ambiguity: pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation. Chaos2002;12:973–981

    Article  PubMed  Google Scholar 

  10. Schmitt OH. Biological information processing using the concept of interpenetrating domains. In: Leibovic KN, ed. Information Processing in the Nervous System. New York: Springer; 1969:325–331

    Google Scholar 

  11. Muler AL, Markin VS. Electrical properties of anisotropic nerve-muscle syncytia — I. Distribution of the electrotonic potential. Biofizika1977;22:307–312

    PubMed  CAS  Google Scholar 

  12. Miller WT III, Geselowitz DB. Simulation studies of the electrocardiogram I. The normal heart. Circ Res1978;43:301–315

    PubMed  CAS  Google Scholar 

  13. Tung L. A bi-domain model for describing ischemic myocardial D-C potentials. Ph.D. dissertation, Cambridge, MA: MIT; 1978

    Google Scholar 

  14. Geselowitz DB, Miller WT III. A bidomain model for anisotropic cardiac muscle. Ann Biomed Eng1983;11:191–206

    Article  PubMed  CAS  Google Scholar 

  15. Plonsey R, Barr RC. Current flow patterns in two-dimensional anisotropic bisyncytia with normal and extreme conductivities. Biophys J1984;45:557–571

    PubMed  CAS  Google Scholar 

  16. Barr RC, Plonsey R. Propagation of excitation in idealized anisotropic two-dimensional tissue. Biophys J1984;45:1191–1202

    PubMed  CAS  Google Scholar 

  17. Roth BJ, Wikswo JP Jr. A bidomain model for the extracellular potential and magnetic field of cardiac tissue. IEEE Trans Biomed Eng1986;33:467–469

    Article  PubMed  CAS  Google Scholar 

  18. Plonsey R, Barr RC. Interstitial potentials and their change with depth into cardiac tissue. Biophys J1987;51:547–555

    PubMed  CAS  Google Scholar 

  19. Sepulveda NG, Wikswo JP Jr. Electric and magnetic fields from two-dimensional anisotropic bisyncytia. Biophys J1987;51:557–568

    PubMed  CAS  Google Scholar 

  20. Henriquez CS, Trayanova NA, Plonsey R. Potential and current distributions in a cylindrical bundle of cardiac tissue. Biophys J1988;53:907–918

    PubMed  CAS  Google Scholar 

  21. Sepulveda NG, Roth BJ, Wikswo JP Jr. Current injection into a two-dimensional anisotropic bidomain. Biophys J1989;55:987–999

    PubMed  CAS  Google Scholar 

  22. Dillon SM. Optical recordings in the rabbit heart show that defibrillation strength shocks prolong the duration of depolarization and the refractory period. Circ Res1991;69:842–856

    PubMed  CAS  Google Scholar 

  23. Knisley SB, Hill BC. Optical recordings of the effect of electrical stimulation on action potential repolarization and the induction of reentry in two-dimensional perfused rabbit epicardium. Circulation1993;88(Pt I):2402–2414

    Google Scholar 

  24. Sepulveda NG, Wikswo JP Jr. Electrical behavior of a cardiac bisyncytium during current injection. Bull APS1987;32:2131

    Google Scholar 

  25. Sepulveda NG, Roth BJ, Wikswo JP Jr. Finite element bidomain calculations. In: Harris GF, Walker C, eds. Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Piscataway, NJ: IEEE; 1988:950– 951

    Chapter  Google Scholar 

  26. Wikswo JP Jr, Roth BJ, Sepulveda NG. Current distributions in bisyncytial tissue. Phys Med Biol1988;33(Suppl 1):165

    Article  Google Scholar 

  27. Wikswo JP Jr, Kopelman HA, Roden DM. Cardiac excitability and space constants measured in vivo using the virtual cathode effect. Circulation1985;72:III-3

    Google Scholar 

  28. Kopelman HA, Bajaj AK, Wikswo JP Jr, Hondeghem LM, Woosley RL, Roden DM. Frequency-and direction-dependent effects of single and combinations of antiarrhyth-mic drugs on conduction velocity in vivo. J Am Coll Cardiol1986;7:82a

    Article  Google Scholar 

  29. Bajaj AK, Kopelman HA, Wikswo JP Jr, Cassidy F, Woosley RL, Roden DM. Frequency-and orientation-dependent effects of mexiletine and quinidine on conduction in the intact dog heart. Circulation1987;75:1065–1073

    PubMed  CAS  Google Scholar 

  30. Altemeier WA, Turgeon J, Wisialowski TA, Wikswo JP Jr, Roden DM. Contrasting effects of class I and class III antiarrhythmics on virtual cathode dimension. Circulation1988;78(Suppl II): II–414

    Google Scholar 

  31. Wikswo JP Jr, Barach JP, Altemeier WA, Roden DM. Measurement and modeling of virtual cathode effects in cardiac muscle. Phys Med Biol1988;33(Suppl 1):232

    Article  Google Scholar 

  32. Wisialowski TA, Wikswo JP Jr, Roden DM. Lidocaine (LID) contracts the virtual cathode in a frequency-dependent fashion. Circulation1990;82:SIII–99

    Google Scholar 

  33. Wikswo JP Jr, Wisialowski TA, Altemeier WA, Balser JR, Kopelman HA, Roden DM. Virtual cathode effects during stimulation of cardiac muscle: two-dimensional in vivo measurements. Circ Res1991;68:513–530

    PubMed  Google Scholar 

  34. Wiederholt WC. Threshold and conduction velocity in isolated mixed mammalian nerves. Neurology1970;20:347–352

    PubMed  CAS  Google Scholar 

  35. Cummins KL, Dorfman LJ, Perkel DH. Nerve-fiber conduction-velocity distributions. 2. Estimation based on 2 compound action potentials. Electroencephalogr Clin Neuro-physiol1979;46:647–658

    Article  CAS  Google Scholar 

  36. Rattay F. Analysis of models for external stimulation of axons. IEEE Trans Biomed Eng1986;33:974–977

    Article  PubMed  CAS  Google Scholar 

  37. Rattay F. Analysis of models for extracellular fiber stimulation. IEEE Trans Biomed Eng1989;36:676–682

    Article  PubMed  CAS  Google Scholar 

  38. Rattay F. Modeling the excitation of fibers under surface electrodes. IEEE Trans Biomed Eng1988;35:199–202

    Article  PubMed  CAS  Google Scholar 

  39. Sobie EA, Susil RC, Tung L. A generalized activating function for predicting virtual electrodes in cardiac tissue. Biophys J1997;73:1410–1423

    PubMed  CAS  Google Scholar 

  40. Terman FE, Helliwell RA, Pettit JM, Watkins DA, Rambo WR. Electronic and Radio Engineering, 4th edn. New York: McGraw Hill; 1955

    Google Scholar 

  41. Furman S, Hurzeler P, Parker B. Clinical thresholds of endocardial cardiac stimulation: a long-term study. J Surg Res1975;19:149–155

    Article  PubMed  CAS  Google Scholar 

  42. Goto M, Brooks CM. Membrane excitability of the frog ventricle examined by long pulses. Am J Physiol1969;217:1236–1245

    PubMed  CAS  Google Scholar 

  43. Hoshi T, Matsuda K. Excitability cycle of cardiac muscle examined by intracellular stimulation. Jpn J Physiol1962;12:433–446

    PubMed  CAS  Google Scholar 

  44. Hoffman BF, Cranefield PF. Excitability. Electrophysiology of the Heart. New York: McGraw-Hill; 1960:211–256

    Google Scholar 

  45. Roth BJ. How the anisotropy of intracellular and extracellular conductivities influences stimulation of cardiac muscle. J Math Biol1992;30:633–646

    Article  PubMed  CAS  Google Scholar 

  46. Roth BJ. Approximate analytical solutions to the bidomain equations with unequal anisotropy ratios. Phys Rev E1997;55:1819–1826

    Article  CAS  Google Scholar 

  47. Knisley SB. Transmembrane voltage changes during unipolar stimulation of rabbit ventricle. Circ Res1995;77:1229–1239

    PubMed  CAS  Google Scholar 

  48. Neunlist M, Tung L. Spatial distribution of cardiac transmembrane potentials around an extracellular electrode: dependence on fiber orientation. Biophys J1995;68:2310– 2322

    PubMed  CAS  Google Scholar 

  49. Wikswo JP Jr, Lin S-F, Abbas RA. Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation. Biophys J1995;69:2195–2210

    PubMed  CAS  Google Scholar 

  50. Dekker E. Direct current make and break thresholds for pacemaker electrodes on the canine ventricle. Circ Res1970;27:811–823

    PubMed  CAS  Google Scholar 

  51. Lindemans FW, Heetharr RM, Denier Van der Gon JJ, Zimmerman ANE. Site of initial excitation and current threshold as a function of electrode radius in heart muscle. Cardiovasc Res1975;9:95–104

    Article  PubMed  CAS  Google Scholar 

  52. Ehara T. Rectifier properties of canine papillary muscle. Jpn J Physiol.1971;21:49–69

    PubMed  CAS  Google Scholar 

  53. Roth BJ. A mathematical model of make and break electrical stimulation of cardiac tissue by a unipolar anode or cathode. IEEE Trans Biomed Eng1995;42:1174–1184

    Article  PubMed  CAS  Google Scholar 

  54. Roth BJ. Nonsustained reentry following successive stimulation of cardiac tissue through a unipolar electrode. J Cardiovasc Electrophysiol1997;8:768–778

    Article  PubMed  CAS  Google Scholar 

  55. Sidorov VY, Woods MC, Wikswo JP. Effects of elevated extracellular potassium on the stimulation mechanism of diastolic cardiac tissue. Biophys J.2003;84:3470–3479

    PubMed  CAS  Google Scholar 

  56. Sidorov VY, Woods MC, Baudenbacher P, Baudenbacher F. Examination of stimulation mechanism and strength–interval curve in cardiac tissue. Am J Physiol Heart2005;289:H2602–H2615

    Article  CAS  Google Scholar 

  57. Sidorov VY, Woods MC, Wikswo JP Jr. Elevated potassium concentration converts excitation mechanism from make to break. In: EMBS-BMES 2002, Proceedings of the Second Joint EMBS-BMES Conference, Oct. 23–26, Houston, TX. Piscataway, NJ: IEEE, 2002:1377–1378

    Google Scholar 

  58. Roth BJ, Patel SG. Effects of elevated extracellular potassium ion concentration on anodal excitation of cardiac tissue. J Cardiovasc Electrophysiol2003;14:1351–1355

    Article  PubMed  Google Scholar 

  59. Nikolski VP, Sambelashvili AT, Efimov IR. Mechanisms of make and break excitation revisited: paradoxical break excitation during diastolic stimulation. Am J Physiol Heart2002;282:H565–H575

    CAS  Google Scholar 

  60. Nikolski V, Sambelashvili A, Efimov IR. Anode-break excitation during end-diastolic stimulation is explained by half-cell double layer discharge. IEEE Trans Biomed Eng2002;49:1217–1220

    Article  PubMed  Google Scholar 

  61. Ranjan R, Chiamvimonvat N, Thakor NV, Tomaselli GF, Marban E. Mechanism of anode break stimulation in the heart. Biophys J1998;74:1850–1863

    PubMed  CAS  Google Scholar 

  62. Ranjan R, Tomaselli GF, Marban E. A novel mechanism of anode-break stimulation predicted by bidomain modeling. Circ Res1999;84:153–156

    PubMed  CAS  Google Scholar 

  63. Roth BJ, Chen J. Mechanism of anode break excitation in the heart: the relative influence of membrane and electrotonic factors. J Biol Syst1999;7:541–552

    Article  Google Scholar 

  64. van Dam RTh, Durrer D, Strackee J, van der Twell LH. The excitability cycle of the dog's left ventricle determined by anodal, cathodal and bipolar stimulation. Circ Res1956;4:196–204

    Google Scholar 

  65. Cranefield PF, Hoffman BF, Siebens AA. Anodal excitation of cardiac muscle. Am J Physiol1957;190:383–390

    PubMed  CAS  Google Scholar 

  66. Roth BJ. Strength—interval curves for cardiac tissue predicted using the bidomain model. J Cardiovasc Electrophysiol1996;7:722–737

    Article  PubMed  CAS  Google Scholar 

  67. Rodriguez B, Tice BM, Eason JC, Aguel F, Trayanova N. Cardiac vulnerability to electric shocks during phase 1A of acute global ischemia. Heart Rhythm2004;1:695– 703

    Article  PubMed  Google Scholar 

  68. Bray M-A, Roth BJ, The effect of electroporation on the strength—interval curve during unipolar stimulation of cardiac tissue. 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Oct. 30–Nov. 2. Chicago: IEEE; 1997:15–18

    Google Scholar 

  69. Mehra R, McMullen M, Furman S. Time-dependence of unipolar cathodal and anodal strength—interval curves. PAC E1980;3:526–530

    CAS  Google Scholar 

  70. Bennett JA, Roth BJ. Time dependence of anodal and cathodal refractory periods in cardiac tissue. PAC E1999;22:1031–1038

    CAS  Google Scholar 

  71. El-Sherif N, Mehra R, Gough WB, Zeiler RH. Reentrant ventricular arrhythmias in the late myocardial infarction period. Circulation1983;68:644–656

    PubMed  CAS  Google Scholar 

  72. Davidenko JM, Pertsov AM, Salomonsz R, Baxter W, Jalife J. Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature1992;355:349–351

    Article  PubMed  CAS  Google Scholar 

  73. Pertsov AM, Davidenko JM, Salomonsz R, Baxter W, Jalife J. Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle. Circ Res1993;72:631–650

    PubMed  CAS  Google Scholar 

  74. Gray RA, Jalife J, Panfilov AV, Baxter WT, Cabo C, Davidenko JM, Pertsov AM. Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart. Circulation1995;91:2454–2469

    PubMed  CAS  Google Scholar 

  75. Gray RA, Jalife J, Panfilov AV, Baxter WT, Cabo C, Davidenko JM, Pertsov AM. Mechanisms of cardiac fibrillation. Science1995;270:1222–1225

    Article  PubMed  CAS  Google Scholar 

  76. Frazier DW, Wolf PD, Wharton JM, Tang ASL, Smith WM, Ideker RE. Stimulus-induced critical point: mechanism for electrical initiation of reentry in normal canine myocardium. J Clin Invest1989;83:1039–1052

    Article  PubMed  CAS  Google Scholar 

  77. Winfree AT. When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias. Princeton, NJ: Princeton University Press; 1987

    Google Scholar 

  78. Shibata N, Chen P-S, Dixon EG, Wolf PD, Danieley ND, Smith WM, Ideker RE. Influence of shock strength and timing on induction of ventricular arrhythmias in dogs. Am J Physiol Heart1988;255:H891–H901

    CAS  Google Scholar 

  79. Matta RJ, Verrier RL, Lown B. Repetitive extrasystole as an index of vulnerability to ventricular fibrillation. Am J Physiol1976;230:1469–1473

    PubMed  CAS  Google Scholar 

  80. Winfree AT. Ventricular reentry in three dimensions. In: Zipes DP, Jalife J, eds. Cardiac Electrophysiology: From Cell to Bedside. Philadelphia: W.B. Saunders; 1990:224– 234

    Google Scholar 

  81. Saypol JM, Roth BJ. A mechanism for anisotropic reentry in electrically active tissue. J Cardiovasc Electrophysiol1992;3:558–566

    Google Scholar 

  82. Lin S-F, Roth BJ, Wikswo JP Jr. Quatrefoil reentry in myocardium: an optical imaging study of the induction mechanism. J Cardiovasc Electrophysiol1999;10:574–586

    Article  PubMed  CAS  Google Scholar 

  83. Sidorov VY, Aliev RR, Woods MC, Baudenbacher F, Baudenbacher P, Wikswo JP. Spatiotemporal dynamics of damped propagation in excitable cardiac tissue. Phys Rev Lett2003;91:208104

    Article  PubMed  CAS  Google Scholar 

  84. Gotoh M, Uchida T, Mandel WJ, Fishbein MC, Chen P-S, Karagueuzian HS. Cellular graded responses and ventricular vulnerability to reentry by a premature stimulus in isolated canine ventricle. Circulation1997;95:2141–2154

    PubMed  CAS  Google Scholar 

  85. Trayanova NA, Gray RA, Bourn DW, Eason JC. Virtual electrode-induced positive and negative graded responses: new insights into fibrillation induction and defibrillation. J Cardiovasc Electrophysiol2003;14:756–763

    PubMed  Google Scholar 

  86. Bray M-A, Lin S-F, Aliev RR, Roth BJ, Wikswo JP Jr. Experimental and theoretical analysis of phase singularity dynamics in cardiac tissue. J Cardiovasc Electrophysiol2001;12:716–722

    Article  PubMed  CAS  Google Scholar 

  87. Bray M-A, Wikswo JP Jr. Considerations in phase plane analysis for non-stationary reentrant cardiac behavior. Phys Rev E2002;65:051902

    Article  CAS  Google Scholar 

  88. Bray M-A, Wikswo JP. Interaction dynamics of a pair of vortex filament rings. Phys Rev Lett2003;90:238303

    Article  PubMed  CAS  Google Scholar 

  89. Gray RA, Iyer A, Bray M-A, Wikswo JP. Voltage-calcium state-space dynamics during initiation of reentry. Heart Rhythm2006;3:247–248

    Article  PubMed  Google Scholar 

  90. Choi BR, Burton F, Salama G. Cytosolic Ca2+ triggers early after depolarizations and torsade de pointes in rabbit hearts with type 2 long QT syndrome. J Physiol2002;543(2):615–631

    Article  PubMed  CAS  Google Scholar 

  91. Verrier RL, Brooks WW, Lown B. Protective zone and determination of vulnerability to ventricular-fibrillation. Am J Physiol1978;234:H592–H596

    PubMed  CAS  Google Scholar 

  92. Bonometti C, Hwang C, Hough D, Lee JJ, Fishbein MC, Karagueuzian HS, Chen P-S. Interaction between strong electrical stimulation and reentrant wavefronts in canine ventricular fibrillation. Circ Res1995;77:407–416

    PubMed  CAS  Google Scholar 

  93. Hwang C, Fan W, Chen PS. Recurrent appearance of protective zones after an unsuccessful defibrillation shock. Am J Physiol Heart1996;40:H1491–H1497

    Google Scholar 

  94. Hildebrandt MC, Roth BJ. Simulation of protective zones during quatrefoil reentry in cardiac tissue. J Cardiovasc Electrophysiol2001;12:1062–1067

    Article  PubMed  CAS  Google Scholar 

  95. Roth BJ. Art Winfree and the bidomain model of cardiac tissue. J Theor Biol2004;230:445–449

    Article  PubMed  Google Scholar 

  96. Winfree AT. Various ways to make phase singularities by electric shock. J Cardiovasc Electrophysiol2000;11:286–289

    Article  PubMed  CAS  Google Scholar 

  97. Winfree AT. The Geometry of Biological Time. New York: Springer; 2001

    Google Scholar 

  98. Roth BJ. An S1 gradient of refractoriness is not essential for reentry induction by an S2 stimulus. IEEE Trans Biomed Eng2000;47:820–821

    Article  PubMed  CAS  Google Scholar 

  99. Cheng YN, Nikolski V, Efimov IR. Reversal of repolarization gradient does not reverse the chirality of shock-induced reentry in the rabbit heart. J Cardiovasc Electrophysiol2000;11:998–1007

    Article  PubMed  CAS  Google Scholar 

  100. Sidorov VY, Woods MC, Baudenbacher F. Cathodal stimulation in the recovery phase of a propagating planar wave in the rabbit heart reveals four stimulation mechanisms. J Physiol2007;583:237–250

    Article  PubMed  CAS  Google Scholar 

  101. Lindblom AE, Roth BJ, Trayanova NA. Role of virtual electrodes in arrhythmogenesis: pinwheel experiment revisited. J Cardiovasc Electrophysiol2000;11:274–285

    Article  PubMed  CAS  Google Scholar 

  102. Lindblom AE, Aguel F, Trayanova NA. Virtual electrode polarization leads to reentry in the far field. J Cardiovasc Electrophysiol2001;12:946–956

    Article  PubMed  CAS  Google Scholar 

  103. Roth BJ. The pinwheel experiment revisited. J Theor Biol1998;190:389–393

    Article  PubMed  CAS  Google Scholar 

  104. Sambelashvili A, Efimov IR. The pinwheel experiment re-revisited. J Theor Biol2002;214:147–153

    Article  PubMed  Google Scholar 

  105. Efimov IR, Cheng YN, Biermann M, VanWagoner DR, Mazgalev TN, Tchou PJ. Trans-membrane voltage changes produced by real and virtual electrodes during monophasic defibrillation shock delivered by an implantable electrode. J Cardiovasc Electrophysiol1997;8:1031–1045

    Article  PubMed  CAS  Google Scholar 

  106. Efimov IR, Cheng Y, Van Wagoner DR, Mazgalev TN, Tchou PJ. Virtual electrode-induced phase singularity: a basic mechanism of defibrillation failure. Circ Res1998;82:918–925

    PubMed  CAS  Google Scholar 

  107. Cheng Y, Mowrey KA, Van Wagoner DR, Tchou PJ, Efimov IR. Virtual electrode-induced reexcitation: a mechanism of defibrillation. Circ Res1999;85:1056–1066

    PubMed  CAS  Google Scholar 

  108. Efimov IR, Cheng Y, Yamanouchi Y, Tchou PJ. Direct evidence of the role of virtual electrode-induced phase singularity in success and failure of defibrillation. J Cardiovasc Electrophysiol2000;11:861–868

    Article  PubMed  CAS  Google Scholar 

  109. Efimov IR, Gray RA, Roth BJ. Virtual electrodes and deexcitation: new insights into fibrillation induction and defibrillation. J Cardiovasc Electrophysiol2000;11:339–353

    Article  PubMed  CAS  Google Scholar 

  110. Trayanova NA, Skouibine KB, Moore PB. Virtual electrode effects in defibrillation. Prog Biophys Mol Biol1998;69:387–403

    Article  PubMed  CAS  Google Scholar 

  111. Skouibine KB, Trayanova NA. Anode/cathode make and break phenomena in a model of defibrillation. IEEE Trans Biomed Eng 1999;46:769–777

    Article  PubMed  CAS  Google Scholar 

  112. Skouibine K, Trayanova N, Moore P. Success and failure of the defibrillation shock: insights from a simulation study. J Cardiovasc Electrophysiol 2000;11:785– 796

    Article  PubMed  CAS  Google Scholar 

  113. Trayanova N. Induction of reentry and defibrillation: the role of virtual electrodes. In: Virag N, Blanc O, Kappenberger L, eds. Computer Simulation and Experimental Assessment of Cardiac Electrophysiology. Armonk, NY: Futura; 2001:165–172

    Google Scholar 

  114. Cheng Y, Mowrey KA, Nikolski V, Tchou PJ, Efimov IR. Mechanisms of shock-induced arrhythmogenesis during acute global ischemia. Am J Physiol Heart 2002;282:H2141–H2151

    CAS  Google Scholar 

  115. Rodriguez B, Tice BM, Eason JC, Aguel F, Ferrero JM, Trayanova N. Effect of acute global ischemia on the upper limit of vulnerability: a simulation study. Am J Physiol Heart 2004;286:H2078–H2088

    Article  CAS  Google Scholar 

  116. Hillebrenner MG, Eason JC, Trayanova NA. Mechanistic inquiry into decrease in probability of defibrillation success with increase in complexity of preshock reentrant activity. Am J Physiol Heart 2004;286:H909–H917

    Article  CAS  Google Scholar 

  117. Anderson C, Trayanova N, Skouibine K. Termination of spiral waves with biphasic shocks: role of virtual electrode polarization. J Cardiovasc Electrophysiol 2000;11:1386–1396

    Article  PubMed  CAS  Google Scholar 

  118. Rodriguez B, Li L, Eason JC, Efimov IR, Trayanova NA. Differences between left and right ventricular chamber geometry affect cardiac vulnerability to electric shocks. Circ Res 2005;97:168–175

    Article  PubMed  CAS  Google Scholar 

  119. Entcheva E, Eason J, Efimov IR, Cheng Y, Malkin RA, Claydon F. Virtual electrode effects in transvenous defibrillation-modulation by structure and interface: evidence from bidomain simulations and optical mapping. J Cardiovasc Electrophysiol 1998;9:949–961

    Article  PubMed  CAS  Google Scholar 

  120. 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 Eng 1993;40:899–908

    Article  PubMed  CAS  Google Scholar 

  121. Entcheva E, Trayanova NA, Claydon FJ. Patterns of and mechanisms for shock-induced polarization in the heart: a bidomain analysis. IEEE Trans Biomed Eng 1999;46:260–270

    Article  PubMed  CAS  Google Scholar 

  122. Knisley SB, Trayanova NA, Aguel F. Roles of electric field and fiber structure in cardiac electric stimulation. Biophys J 1999;77:1404–1417

    PubMed  CAS  Google Scholar 

  123. Latimer DC, Roth BJ. Effect of a bath on the epicardial transmembrane potential during internal defibrillation shocks. IEEE Trans Biomed Eng 1999;46:612–614

    Article  PubMed  CAS  Google Scholar 

  124. Lin S-F, Wikswo JP Jr. New perspectives in electrophysiology from the cardiac bidomain. In: Rosenbaum DS, Jalife J, eds. Optical Mapping of Cardiac Excitation and Arrhythmias. Armonk, NY: Futura Publishing; 2001:335–359

    Google Scholar 

  125. Fishler MG, Vepa K. Spatiotemporal effects of syncytial heterogeneities on cardiac far-field excitations during monophasic and biphasic shocks. J Cardiovasc Electrophysiol 1998;9:1310–1324

    Article  PubMed  CAS  Google Scholar 

  126. Hooks DA, Tomlinson KA, Marsden SG, LeGrice IJ, Smaill BH, Pullan AJ, Hunter PJ. Cardiac microstructure: implications for electrical propagation and defibrillation in the heart. Circ Res 2002;91:331–338

    Article  PubMed  CAS  Google Scholar 

  127. Fast VG, Sharifov OF, Cheek ER, Newton JC, Ideker RE. Intramural virtual electrodes during defibrillation shocks in left ventricular wall assessed by optical mapping of membrane potential. Circulation 2002;106:1007–1014

    Article  PubMed  Google Scholar 

  128. Sharifov OF, Fast VG. Optical mapping of transmural activation induced by electrical shocks in isolated left ventricular wall wedge preparations. J Cardiovasc Electrophysiol 2003;14:1215–1222

    Article  PubMed  Google Scholar 

  129. Sharifov OF, Ideker RE, Fast VG. High-resolution optical mapping of intramural virtual electrodes in porcine left ventricular wall. Cardiovasc Res 2004;64:448–456

    Article  PubMed  CAS  Google Scholar 

  130. Sharifov OF, Fast VG. Role of intramural virtual electrodes in shock-induced activation of left ventricle: optical measurements from the intact epicardial surface. Heart Rhythm 2006;3:1063–1073

    Article  PubMed  Google Scholar 

  131. Pitruzello AM, Woods MC, Wikswo JP Jr, Lin S-F. Differences in cardiac activation times for endocardium and epicardium in response to external electric shock. In: Blanchard SM, ed. Proceedings of the First Joint BMES/EMBS Conference: Serving Humanity Advancing Technology, Atlanta: Piscataway, NJ: IEEE; 1999:286

    Google Scholar 

  132. Woods MC, Pitruzello AM, Wikswo JP. Analysis of the shock-response of rabbit cardiac tissue. Presented at BMES Annual Fall Meeting, Philadelphia, PA, 2004

    Google Scholar 

  133. Woods MC. Field stimulation of the diastolic rabbit heart: the role of shock strength and duration on epicardial activation and propagation. In: The Response of the Cardiac Bidomain to Electrical Stimulation. Ph.D. Dissertation, Biomedical Engineering, Vanderbilt University; 2005:109–138

    Google Scholar 

  134. Woods MC, Maleckar MM, Sidorov VY, Holcomb MR, Mashburn DN, Trayanova NA, Wikswo JP. Negative virtual electrode polarization in the rabbit left ventricle delays activation during diastolic field stimulation. Heart Rhythm 2006;3(Suppl 1):S181–S182

    Article  Google Scholar 

  135. Maleckar MM, Woods MC, Sidorov VY, Holcomb MR, Mashburn DN, Wikswo JP, Trayanova NA. Polarity reversal lowers activation time during diastolic field stimulation of the rabbit ventricles: insights into mechanisms. Am J Physiol Heart Circ Physiol 2008;295;doi:10.1152/ajpheart.00706.2008

    Google Scholar 

  136. Holcomb MR. Measurement and Analysis of Cardiac Tissue during Electrical Stimulation. Ph.D. Dissertation, Physics, Vanderbilt University; 2007

    Google Scholar 

  137. Zemlin CW, Mironov S, Pertsov AM. Near-threshold field stimulation: intramural versus surface activation. Cardiovasc Res 2006;69:98–106

    Article  PubMed  CAS  Google Scholar 

  138. Roth BJ. A mechanism for the “no-response” phenomenon during anodal stimulation of cardiac tissue. In: Jaeger RJ, Robert J, eds. Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Oct. 30–Nov. 2, Chicago, IL. Piscataway, NJ: IEEE, 1997:176–179

    Google Scholar 

  139. Janks DL, Roth BJ. The bidomain theory of pacing. In: Efimov I, Kroll M, Tchou P, eds. Cardiac Bioelectric Therapy: Mechanisms and Practical Implications; New York: Springer; 2008:63–83

    Google Scholar 

  140. Chen P-S, Shibata N, Dixon EG, Martin RO, Ideker RE. Comparison of the defibrillation threshold and the upper limit of ventricular vulnerability. Circulation 1986;73:1022–1028

    PubMed  CAS  Google Scholar 

  141. Banville I, Gray RA, Ideker RE, Smith WM. Shock-induced figure-of-eight reentry in the isolated rabbit heart. Circ Res 1999;85:742–752

    PubMed  CAS  Google Scholar 

  142. Rodriguez B, Trayanova N. Upper limit of vulnerability in a defibrillation model of the rabbit ventricles. J Electrocardiol 2003;36:51–56

    Article  PubMed  Google Scholar 

  143. Langrill Beaudoin D, Roth BJ. The effect of the fiber curvature gradient on break excitation in cardiac tissue. PAC E2006;29:496–501

    Google Scholar 

  144. Langrill DM, Roth BJ. The effect of plunge electrodes during electrical stimulation of cardiac tissue. IEEE Trans Biomed Eng 2001;48:1207–1211

    Article  PubMed  CAS  Google Scholar 

  145. Langrill Beaudoin D, Roth BJ. Effect of plunge electrodes in active cardiac tissue with curving fibers. Heart Rhythm 2004;1:476–481

    Article  Google Scholar 

  146. Woods MC, Sidorov VY, Holcomb MR, Langrill Beaudoin D, Roth BJ, Wikswo JP. Virtual electrode effects around an artificial heterogeneity during field stimulation of cardiac tissue. Heart Rhythm 2006;3:751–752

    Article  PubMed  Google Scholar 

  147. Chattipakorn N, Fotuhi PC, Chattipakorn SC, Ideker RE. Three-dimensional mapping of earliest activation after near-threshold ventricular defibrillation shocks. J Cardiovasc Electrophysiol 2003;14:65–69

    Article  PubMed  Google Scholar 

  148. Patel SG, Roth BJ. How epicardial electrodes influence the transmembrane potential during a strong shock. Ann Biomed Eng 2001;29:1028–1031

    Article  PubMed  CAS  Google Scholar 

  149. Knisley SB, Pollard AE. Use of translucent indium tin oxide to measure stimulatory effects of a passive conductor during field stimulation of rabbit hearts. Am J Physiol Heart 2005;289:H1137–H1146

    Article  CAS  Google Scholar 

  150. Trayanova N, Skouibine K, Aguel F. The role of cardiac tissue structure in defibrilla-tion. Chaos 1998;8:221–233

    Article  PubMed  Google Scholar 

  151. Trayanova NA, Skouibine KB. Modeling defibrillation: effects of fiber curvature. J Electrocardiol 1998;31(Suppl):23–29

    Article  PubMed  Google Scholar 

  152. Roth BJ, Langrill Beaudoin D. Approximate analytical solutions of the bidomain equations for electrical stimulation of cardiac tissue with curving fibers. Phys Rev E 2003;67: 051925

    Article  CAS  Google Scholar 

  153. Roth BJ. Electrical conductivity values used with the bidomain model of cardiac tissue. IEEE Trans Biomed Eng 1997;44:326–328

    CAS  Google Scholar 

  154. Tung L, Kleber AG. Virtual sources associated with linear and curved strands of cardiac cells. Am J Physiol Heart 2000;279:H1579–H1590

    Google Scholar 

  155. Plonsey R, Barr RC. Effect of microscopic and macroscopic discontinuities on the response of cardiac tissue to defibrillation (stimulating) currents. Med Biol Eng Comput 1986;24:130–136

    Article  PubMed  CAS  Google Scholar 

  156. Krassowska W, Pilkington TC, Ideker RE. Periodic conductivity as a mechanism for cardiac stimulation and defibrillation. IEEE Trans Biomed Eng 1987;34:555–560

    Article  PubMed  CAS  Google Scholar 

  157. Keener JP. Direct activation and defibrillation of cardiac tissue. J Theor Biol 1996;178:313–324

    Article  PubMed  CAS  Google Scholar 

  158. Krinsky VI, Pumir A. Models of defibrillation of cardiac tissue. Chaos 1998;8:188–203

    Article  PubMed  Google Scholar 

  159. 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 Res 1996;79:676–690

    PubMed  CAS  Google Scholar 

  160. Zhou XH, Knisley SB, Smith WM, Rollins D, Pollard AE, Ideker RE. Spatial changes in the transmembrane potential during extracellular electric stimulation. Circ Res 1998;83:1003–1014

    PubMed  CAS  Google Scholar 

  161. Krassowska Kumar MS. The role of spatial interactions in creating the dispersion of transmembrane potential by premature electric shocks. Ann Biomed Eng 1997;25:949–963

    PubMed  CAS  Google Scholar 

  162. Fishler MG. Syncytial heterogeneity as a mechanism underlying cardiac far-field stimulation during defibrillation-level shocks. J Cardiovasc Electrophysiol 1998;9:384–394

    Article  PubMed  CAS  Google Scholar 

  163. Langrill Beaudoin D, Roth BJ. How the spatial frequency of polarization influences the induction of reentry in cardiac tissue. J Cardiovasc Electrophysiol 2005;16:748–752

    Article  Google Scholar 

  164. Woods MC, Holcomb MR, Sidorov VY, Gray RA, Wikswo JP. Transient virtual anodes during strong field shock of rabbit hearts. Presented at BMES Annual Fall Meeting, Los Angeles, CA, 2007

    Google Scholar 

  165. Woods MC. The Response of the Cardiac Bidomain to Electrical Stimulation. Ph.D. Dissertation, Biomedical Engineering, Vanderbilt University; 2005

    Google Scholar 

  166. Trew M, Sands GB. Shock-induced transmembrane potential fields in a model of cardiac microstructure. J Cardiovasc Electrophysiol2005;16:1024

    Article  PubMed  Google Scholar 

  167. Plank G, Prassl AJ, Vigmond EJ, Burton RAB, Schneider J, Trayanova NA, Kohl P. Development of a microanatomically accurate rabbit ventricular wedge model. Heart Rhythm2006;3(Suppl 1):S111–S112

    Article  Google Scholar 

  168. Gray RA. What exactly are optically recorded “action potentials”? J Cardiovasc Electrophysiol1999;10:1463–1466

    Article  PubMed  CAS  Google Scholar 

  169. Efimov IR, Sidorov V, Cheng Y, Wollenzier B. Evidence of three-dimensional scroll waves with ribbon-shaped filament as a mechanism of ventricular tachycardia in the isolated rabbit heart. J Cardiovasc Electrophysiol1999;10:1452–1462

    Article  PubMed  CAS  Google Scholar 

  170. Bray MA, Wikswo JP. Examination of optical depth effects on fluorescence imaging of cardiac propagation. Biophys J2003;85:4134–4145

    PubMed  CAS  Google Scholar 

  171. Janks DL, Roth BJ. Averaging over depth during optical mapping of unipolar stimulation. IEEE Trans Biomed Eng2002;49:1051–1054

    Article  PubMed  Google Scholar 

  172. Neunlist M, Tung L. Dose-dependent reduction of cardiac transmembrane potential by high-intensity electrical shocks. Am J Physiol Heart1997;42:H2817–H2825

    Google Scholar 

  173. Kodama I, Sakuma I, Shibata N, Honjo H, Toyama J. Arrhythmogenic changes in action potential configuration in the ventricle induced by DC shocks. J Electrocardiol1999;32(Suppl 1):92–99

    Article  PubMed  Google Scholar 

  174. Al Khadra A, Nikolski V, Efimov IR. The role of electroporation in defibrillation. Circ Res2000;87:797–804

    PubMed  CAS  Google Scholar 

  175. Janks DL, Roth BJ. Simulations of optical mapping during electroporation. EMBC 2004, 26th Annual International Conference of the Engineering in Medicine and Biology Society, San Francisco, CA. Piscataway, NJ: IEEE; 2004:3581–3584

    Google Scholar 

  176. Hyatt CJ, Mironov SF, Wellner M, Berenfeld O, Popp AK, Weitz DA, Jalife J, Pertsov AM. Synthesis of voltage-sensitive fluorescence signals from three-dimensional myocardial activation patterns. Biophys J2003;85:2673–2683

    PubMed  CAS  Google Scholar 

  177. Bernus O, Wellner M, Mironov SF, Pertsov AM. Simulation of voltage-sensitive optical signals in three-dimensional slabs of cardiac tissue: application to transillumination and coaxial imaging methods. Phys Med Biol2005;50:215–229

    Article  PubMed  CAS  Google Scholar 

  178. Bishop MJ, Rodriguez B, Eason J, Whiteley JP, Trayanova N, Gavaghan DJ. Synthesis of voltage-sensitive optical signals: application to panoramic optical mapping. Biophys J2006;90:2938–2945

    Article  PubMed  CAS  Google Scholar 

  179. Mironov SF, Vetter FJ, Pertsov AM. Fluorescence imaging of cardiac propagation: spectral properties and filtering of optical action potentials. Am J Physiol Heart Circ Physiol2006;291:H327–H335

    Article  PubMed  CAS  Google Scholar 

  180. Krassowska W, Neu JC. Effective boundary conditions for syncytial tissues. IEEE Trans Biomed Eng1994;41:143–150

    Article  PubMed  CAS  Google Scholar 

  181. Roth BJ. A comparison of two boundary-conditions used with the bidomain model of cardiac tissue. Ann Biomed Eng1991;19:669–678

    Article  PubMed  CAS  Google Scholar 

  182. Latimer DC, Roth BJ. Electrical stimulation of cardiac tissue by a bipolar electrode in a conductive bath. IEEE Trans Biomed Eng1998;45:1449–1458

    Article  PubMed  CAS  Google Scholar 

  183. Knisley SB, Pollard AE, Fast VG. Effects of electrode-myocardial separation on cardiac stimulation in conductive solution. J Cardiovasc Electrophysiol2000;11:1132– 1143

    Article  PubMed  CAS  Google Scholar 

  184. Trayanova NA. Effects of the tissue-bath interface on the induced transmembrane potential: a modeling study in cardiac stimulation. Ann Biomed Eng1997;25:783–792

    Article  PubMed  CAS  Google Scholar 

  185. Roth BJ. Mechanism for polarisation of cardiac tissue at a sealed boundary. Med Biol Eng Comput1999;37:523–525

    Article  PubMed  CAS  Google Scholar 

  186. Roth BJ, Patel SG, Murdick RA. The effect of the cut surface during electrical stimulation of a cardiac wedge preparation. IEEE Trans Biomed Eng2006;53:1187– 1190

    Article  PubMed  Google Scholar 

  187. Corbin LV II, Scher AM. The canine heart as an electrocardiographic generator. Dependence on cardiac cell orientation. Circ Res1977;41:58–67

    PubMed  Google Scholar 

  188. Roberts DE, Hersh LT, Scher AM. Influence of cardiac fiber orientation on wavefront voltage, conduction velocity, and tissue resistivity in the dog. Circ Res1979;44:701–712

    PubMed  CAS  Google Scholar 

  189. Roberts DE, Scher AM. Effect of tissue anisotropy on extracellular potential fields in canine myocardium in situ. Circ Res1982;50:342–351

    PubMed  CAS  Google Scholar 

  190. Barry WH, Fairbank WM, Harrison DC, Lehrman KL, Malmivuo JAV, Wikswo JP Jr. Measurement of the human magnetic heart vector. Science1977;198:1159–1162

    Article  PubMed  CAS  Google Scholar 

  191. Wikswo JP Jr. A theoretical analysis of the relation between cardiac electric and magnetic fields. Biophys J1978;21:91a

    Google Scholar 

  192. Wikswo JP Jr, Barach JP. Possible sources of new information in the magnetocardio-gram. J Theor Biol1982;95:721–729

    Article  PubMed  Google Scholar 

  193. Wikswo JP Jr, Barach JP, Gundersen SC, McLean MJ, Freeman JA. First magnetic measurements of action currents in isolated cardiac Purkinje fibers. IL Nuovo Cimento1983;2D:368–378

    Article  Google Scholar 

  194. Roth BJ, Wikswo JP Jr. Electrically silent magnetic fields. Biophys J1986;50:739–745

    PubMed  CAS  Google Scholar 

  195. Barach JP. A simulation of cardiac action currents having curl. IEEE Trans Biomed Eng1993;40:49–58

    Article  PubMed  CAS  Google Scholar 

  196. Barach JP, Wikswo JP Jr. Magnetic fields from simulated cardiac action currents. IEEE Trans Biomed Eng1994;41:969–974

    Article  PubMed  CAS  Google Scholar 

  197. Staton DJ, Friedman RN, Wikswo JP Jr. High-resolution SQUID imaging of octupolar currents in anisotropic cardiac tissue. IEEE Trans Appl Supercond1993;3:1934–1936

    Article  Google Scholar 

  198. Baudenbacher F, Peters NT, Baudenbacher P, Wikswo JP. High resolution imaging of biomagnetic fields generated by action currents in cardiac tissue using a LTS-SQUID microscope. Physica C2002;368:24–31

    Article  CAS  Google Scholar 

  199. Staton DJ. Magnetic imaging of applied and propagating action current in cardiac tissue slices: determination of anisotropic electrical conductivities in a two dimensional bidomain. Ph.D. dissertation, Physics, Vanderbilt University; 1994

    Google Scholar 

  200. Fong LE, Holzer JR, McBride KK, Lima EA, Baudenbacher F, Radparvar M. High-resolution room-temperature sample scanning superconducting quantum interference device microscope configurable for geological and biomagnetic applications. Rev Sci Instrum2005;76:053703

    Article  CAS  Google Scholar 

  201. Fong LE, Holzer JR, McBride K, Lima EA, Baudenbacher F, Radparvar M. High-resolution imaging of cardiac biomagnetic fields using a low-transition-temperature superconducting quantum interference device microscope. Appl Phys Lett2004;84:3190–3192

    Article  CAS  Google Scholar 

  202. Holzer JR, Fong LE, Sidorov VY, Wikswo JP Jr, Baudenbacher F. High resolution magnetic images of planar wave fronts reveal bidomain properties of cardiac tissue. Biophys J2004;87:4326–4332

    Article  PubMed  CAS  Google Scholar 

  203. Baudenbacher F, Peters NT, Wikswo JP Jr. High resolution low-temperature superconductivity superconducting quantum interference device microscope for imaging magnetic fields of samples at room temperatures. Rev Sci Instrum2002;73:1247–1254

    Article  CAS  Google Scholar 

  204. Roth BJ, Woods MC. The magnetic field associated with a plane wave front propagating through cardiac tissue. IEEE Trans Biomed Eng1999;46:1288–1292

    Article  PubMed  CAS  Google Scholar 

  205. Barbosa CRH. Simulation of a plane wavefront propagating in cardiac tissue using a cellular automata model. Phys Med Biol2003;48:4151–4164

    Article  PubMed  Google Scholar 

  206. dos Santos RW, Koch H. Interpreting biomagnetic fields of planar wave fronts in cardiac muscle. Biophys J2005;88:3731–3733

    Article  PubMed  CAS  Google Scholar 

  207. Murdick RA, Roth BJ. A comparative model of two mechanisms from which a magnetic field arises in the heart. J Appl Phys2004;95:5116–5122

    Article  CAS  Google Scholar 

  208. Baudenbacher F, Fong LE, Holzer JR, Radparvar M. Monolithic low-transition-temperature superconducting magnetometers for high resolution imaging magnetic fields of room temperature samples. Appl Phys Lett2003;82:3487–3489

    Article  CAS  Google Scholar 

  209. Ideker RE, Chattipakorn N, Gray RA. Defibrillation mechanisms: the parable of the blind men and the elephant. J Cardiovasc Electrophysiol2000;11:1008–1013

    Article  PubMed  CAS  Google Scholar 

  210. Roth BJ, Guo W-Q, Wikswo JP Jr. The effects of spiral anisotropy on the electric potential and the magnetic field at the apex of the heart. Math Biosci1988;88:191–221

    Article  Google Scholar 

  211. Roth BJ. The electrical potential produced by a strand of cardiac muscle: a bidomain analysis. Ann Biomed Eng1988;16:609–637

    Article  PubMed  CAS  Google Scholar 

  212. Knisley SB, Maruyama T, Buchanan JW. Interstitial potential during propagation in bathed ventricular muscle. Biophys J1991;59:509–515

    PubMed  CAS  Google Scholar 

  213. Plonsey R, Henriquez CS, Trayanova NA. Extracellular (volume conductor) effect on adjoining cardiac muscle electrophysiology. Med Biol Eng Comput1988;26:126–129

    Article  PubMed  CAS  Google Scholar 

  214. Wu J, Johnson EA, Kootsey JM. A quasi-one-dimensional theory for anisotropic propagation of excitation in cardiac muscle. Biophys J1996;71:2427–2439

    PubMed  CAS  Google Scholar 

  215. Wu J, Wikswo JP Jr. Effects of bath resistance on action potentials in the squid giant axon: myocardial implications. Biophys J1997;73:2347–2358

    Article  PubMed  CAS  Google Scholar 

  216. Roth BJ. Effect of a perfusing bath on the rate of rise of an action potential propagating through a slab of cardiac tissue. Ann Biomed Eng1996;24:639–646

    Article  PubMed  CAS  Google Scholar 

  217. Roth BJ. Influence of a perfusing bath on the foot of the cardiac action potential. Circ Res2000;86:E19–E22

    PubMed  CAS  Google Scholar 

  218. Roth BJ, Saypol JM. The formation of a re-entrant action potential wave front in tissue with unequal anisotropy ratios. Int J Bifurcat Chaos1991;1:927–928

    Article  Google Scholar 

  219. Roth BJ. Frequency locking of meandering spiral waves in cardiac tissue. Phys Rev E1998;57:R3735–R3738

    Article  CAS  Google Scholar 

  220. Roth BJ. Meandering of spiral waves in anisotropic cardiac tissue. Phys D: Nonlinear Phenomena2001;150:127–136

    Article  Google Scholar 

  221. Janks DL, Roth BJ. Quatrefoil reentry caused by burst pacing. J Cardiovasc Electro-physiol2006;17:1362–1368

    Article  Google Scholar 

  222. Spach MS, Miller WT III, Geselowitz DB, Barr RC, Kootsey JM, Johnson EA. The discontinuous nature of propagation in normal canine cardiac muscle. Circ Res1981;48:39–54

    PubMed  CAS  Google Scholar 

  223. Roth BJ, Lin S-F, Wikswo JP Jr. Unipolar stimulation of cardiac tissue. J Electrocar-diol1998;31(Suppl):6–12

    Article  Google Scholar 

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Authors and Affiliations

  1. Departments of Biomedical Engineering, Molecular Physiology and Biophysics, and Physics and Astronomy, The Vanderbilt Institute for Integrative Biosystems Research and Education, Vanderbilt University, Nashville, TN, USA

    John P. Wikswo

  2. Department of Physics, Oakland University, Rochester, MI, USA

    Bradley J. Roth

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  1. Department of Biomedical Engineering, Washington University, St. Louis, MO, USA

    Igor R. Efimov PhD

  2. Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, USA

    Mark W. Kroll PhD

  3. Cleveland Clinic Foundation, Cleveland, OH

    Patrick J. Tchou MD

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Wikswo, J.P., Roth, B.J. (2009). Virtual Electrode Theory of Pacing. In: Efimov, I.R., Kroll, M.W., Tchou, P.J. (eds) Cardiac Bioelectric Therapy. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-79403-7_12

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