Use of topological charge to determine filament location and dynamics in a numerical model of scroll wave activity

IEEE Transactions on Biomedical Engineering

Volumn 49, Issue 10, 2002, Pages 1086-1093

  Bray, Mark Anthony ^b   Wikswo, John P ^a,c  

^a IEEE

^b VANDERBILT UNIVERSITY   (United States)

^c VANDERBILT UNIVERSITY   (United States)

Author keywords

Cardiac; Filament; Scroll waves; State space; Topological charge

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; TISSUE; TOPOLOGY;

CARDIAC ACTIVITY;

BIOMEDICAL ENGINEERING;

ANALYTIC METHOD; ARTICLE; CHEMICAL REACTION; DIFFUSION; DYNAMICS; HEART FIBRILLATION; HEART VENTRICLE FIBRILLATION; MODEL; TONOFILAMENT; WAVEFORM;

ACTION POTENTIALS; ALGORITHMS; BODY SURFACE POTENTIAL MAPPING; COMPUTER SIMULATION; ELECTROMAGNETIC FIELDS; HEART VENTRICLES; HUMANS; MEMBRANE POTENTIALS; MODELS, CARDIOVASCULAR; MYOCARDIAL CONTRACTION; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; TACHYCARDIA, ATRIOVENTRICULAR NODAL REENTRY; VENTRICULAR FIBRILLATION;

EID: 0036785235     PISSN: 00189294     EISSN: None     Source Type: Journal    
DOI: 10.1109/TBME.2002.803516     Document Type: Article

References (45)

1. A. T. Winfree, When Time Breaks Down: The Three-Dimensional Dynamics Of Electrochemical Waves and Cardiac Arrhythmias. Princeton, NJ: Princeton Univ. Press, 1987.
2. R. A. Gray and J. Jalife, "Spiral waves and the heart," Int. J. Bifurc. Chaos, vol. 6, no. 3, pp. 415-435, 1996.
3. S.-F Lin, B. J. Roth, and J. P. Wikswo Jr, "Quatrefoil reentry in myocardium: An optical imaging study of the induction mechanism," J. Cardiovasc. Electrophysiol., vol. 10, no. 4, pp. 574-586, 1999.
4. R. A. Gray, A. M. Pertsov, and J. Jalife, "Spatial and temporal organization during cardiac fibrillation," Nature, vol. 392, no. 6671, pp. 75-78, 1998.
5. I. Banville, R. A. Gray, and R. E. Ideker, "Shock-induced figure-eight reentry in the whole heart: An optical mapping study," Circ. Res., vol. 85, no. 8, pp. 742-752, 1999.
6. A. T. Winfree, S. Caudle, G. Chen, P. McGuire, and Z. Szilagyi, "Quantitative optical tomography of chemical waves and their organizing centers," Chaos, vol. 6, no. 4, pp. 617-626, 1996.
7. A. Pertsov, M. Vinson, and S. C. Muller, "Three-dimensional reconstruction of organizing centers in excitable chemical media," Physica D., vol. 63, no. 1-2, pp. 233-240, 1993.
8. R. A. Gray, J. Jalife, A. Panfilov, W. T. Baxter, C. Cabo, J. M. Davidenko, and A. M. Pertsov, "Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart," Circulation, vol. 91, no. 9, pp. 2454-2469, 1995.
9. I. R. Efimov, V. Sidorov, Y. Cheng, and B. Wollenzier, "Evidence of three-dimensional scroll waves with ribbon-shaped filament as a mechanism of ventricular tachycardia in the isolated rabbit heart," J. Cardiovasc. Electrophysiol., vol. 10, no. 11, pp. 1452-1462, 1999.
10. A. V. Zaitsev, O. Berenfeld, S. F. Mironov, J. Jalife, and A. M. Pertsov, "Distribution of excitation frequencies on the epicardial and endocardial surfaces of fibrillating ventricular wall of the sheep heart," Circ. Res., vol. 86, no. 4, pp. 408-417, 2000.
11. V. N. Biktashev, A. V. Holden, S. F. Mironov, A. M. Pertsov, and A. V. Zaitsev, "Three-dimensional aspects of re-entry in experimental and numerical models of ventricular fibrillation," Int. J. Bifurc. Chaos, vol. 9, no. 4, pp. 694-704, 1999.
12. P.-S Chen, P. D. Wolf, E. G. Dixon, N. D. Danieley, D. W. Frazier, W. M. Smith, and R. E. Ideker, "Mechanism of ventricular vulnerability to single premature stimuli in open-chest dogs," Circ. Res., vol. 62, no. 6, pp. 1191-1209, 2000.
13. W. T. Baxter, S. F. Mironov, A. V. Zaitsev, J. Jalife, and A. M. Pertsov, "Visualizing excitation waves inside cardiac muscle using transillumination," Biophys. J., vol. 80, no. 1, pp. 516-530, 2001.
14. M. Vinson, "Interactions of spiral waves in inhomogeneous excitable media," Physica D, vol. 116, no. 3, pp. 313-324, 1998.
15. O. Berenfeld and A. M. Pertsov, "Dynamics of intramural scroll waves in three-dimensional continuous myocardium with rotational anisotropy," J. Theor Biol., vol. 199, pp. 383-394, 1999.
16. A. M. Pertsov, M. Wellner, M. Vinson, and J. Jalife, "Topological constraint on scroll wave pinning," Phys. Rev. Lett., vol. 84, no. 12, pp. 2738-2741, 2000.
17. V. N. Biktashev, A. V. Holden, and H. Zhang, "Tension of organizing filaments of scroll waves," Phil. Trans. Roy. Soc. Lond. A. vol. 347, pp. 611-630, 1994.
18. F. Fenton and A. Karma, "Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation," Chaos, vol. 8, no. 1, pp. 20-47, 1998.
19. Z. Qu, J. Kil, F. Xie, A. Garfinkel, and J. N. Weiss, "Scroll wave dynamics in a three-dimensional cardiac tissue model: Roles of restitution, thickness, and fiber rotation," Biophys. J., vol. 78, no. 6, pp. 2761-2775, 2000.
20. J. Beaumont, N. Davidenko, J. M. Davidenko, and J. Jalife, "Spiral waves in two-dimensional models of ventricular muscle: Formation of a stationary core," Biophys. J., vol. 75, no. 1, pp. 1-14, 1998.
21. M.-A Bray, S.-F Lin, R. R. Aliev, B. J. Roth, and J. P. Wikswo Jr, "Experimental and theoretical analysis of phase singularity dynamics in cardiac tissue," J Cardiovasc. Electrophysiol., vol. 12, no. 6, pp. 716-722, 2001.
22. F. Takens, "Detecting strange attractors in turbulence," in Dynamical Systems and Turbulence, D. A. Rand and L.-S. Young, Eds. Berlin, Germany: Springer-Verlag, 1981, pp. 366-381.
23. A. M. Fraser and H. L. Swinney, "Independent coordinates for strange attractors from mutual information," Physical Rev. A, vol. 33, no. 2, pp. 1134-1140, 1986.
24. R. A. Gray and J. Jalife, "Video imaging of atrial defibrillation," in Cardiac Electrophysiology: From Cell to Bedside, 3rd ed, D. P. Zipes and J. Jalife, Eds. Philadelphia, PA: Saunders, 1999, pp. 432-439.
25. A. Goryachev and R. Kapral, "Spiral waves in chaotic systems," Phys. Rev. Lett., vol. 76, no. 10, pp. 1619-1622, 1996.
26. N. D. Mermin, "The topological theory of defects in ordered media," Rev. Mod. Phys., vol. 51, no. 3, pp. 591-648, 1979.
27. J. M. Hyman and M. Shashkov, "Natural discretizations for the divergence, gradient, and curl on logically rectangular grids," Comput. Math. Applicat., vol. 33, no. 4, pp. 81-104, 1997.
28. R. R. Aliev and A. V. Panfilov, "Modeling of heart excitation patterns caused by a local inhomogeneity," J. Theor. Biol., vol. 181, no. 1, pp. 33-40, 1996.
29. R. Fitzhugh, "Impulses and physiological states in theoretical models of nerve membrane," Biophys. J., vol. 1, no. 6, pp. 445-466, 1961.
30. M. Vinson and A. Pertsov, "Dynamics of scroll rings in a parameter gradient," Phys. Rev. E, vol. 59, no. 3, pp. 2764-2771, 1999.
31. A. V. Panfilov and A. M. Pertsov, "Vortex ring in a three-dimensional medium described by reaction-diffusion equations," Dokl. Biophys., vol. 274, no. 6, pp. 58-1, 1984.
32. D. W. Frazier, P. D. Wolf, J. M. Wharton, A. S. Tang, W. M. Smith, and R. E. Ideker, "Stimulus-induced critical point. Mechanism for electrical initiation of reentry in normal canine myocardium," J Clin. Investigat., vol. 83, no. 3, pp. 1039-1052, 1989.
33. A. T. Winfree, "Electrical turbulence in three-dimensional excitable media," Science, vol. 266, no. 5187, pp. 1003-1006, 1994.
34. S. M. Pogwizd and P. B. Corr, "Mechanisms underlying the development of ventricular fibrillation during early myocardial ischemia," Circ. Res., vol. 66, no. 3, pp. 672-695, 1990.
35. A. V. Panfilov, "Spiral breakup as a model of ventricular fibrillation," Chaos, vol. 8, no. 1, pp. 57-64, 1998.
36. R. R. Aliev and A. V. Panfilov, "A simple two-variable model of cardiac excitation," Chaos, Solitons, Fractals, vol. 7, no. 3, pp. 293-301, 1996.
37. R. A. Gray and J. Jalife, "Ventricular fibrillation and atrial fibrillation are two different beasts," Chaos, vol. 8, no. 1, pp. 65-78, 1998.
38. G. W. Beeler and H. Reuter, "Reconstruction of the action potential of ventricular myocardial fibers," J. Physiol. (Lond.), vol. 268, no. 1, pp. 177-210, 1977.
39. C. H. Luo and Y. Rudy, "A dynamic model of the cardiac ventricular action potential. I. simulations of ionic currents and concentration changes," Circ. Res., vol. 74, no. 6, pp. 1071-1096, 1994.
40. F. Fenton and A. Karma, "Fiber-rotation-induced vortex turbulence in thick myocardium," Phys. Rev. Lett., vol. 81, no. 2, pp. 481-484, 1998.
41. A. N. Iyer and R. A. Gray, "An experimentalist's approach to accurate localization of phase singularities during reentry," Ann. Biomed. Eng., vol. 29, no. 1, pp. 47-59, 2001.
42. R. C. Gonzales and R. E. Woods, Digital Image Processing. Reading, MA: Addison-Wesley, 1993.
43. A. S. Pikovsky, M. G. Rosenblum, G. V. Osipov, and J. Kurths, "Phase synchronization of chaotic oscillators by external driving," Physica D, vol. 104, no. 3-4, pp. 219-238, 1997.
44. T. Yalcinkaya and Y.-C Lai, "Phase characterization of chaos," Phys. Rev. Lett., vol. 79, no. 20, pp. 3885-3888, 1997.
45. R. A. Gray, J. P. Wikswo Jr, S.-F Lin, and F. Baudenbacher, "Phase mapping using both transmembrane potential and calcium," Pacing Clin. Electrophysiol., pt. II, vol. 23, no. 4, pp. 608-608, 2000.