Model-based control of cardiac alternans on a ring

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 80, Issue 2, 2009, Pages

  Garzón, Alejandro ^a   Grigoriev, Roman O ^a   Fenton, Flavio H ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b Department of Molecular Biology and Genetics   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTO-SYNCHRONIZATION; CARDIAC ALTERNANS; CONDUCTION BLOCK; CONTROL CURRENT; CONTROL ELECTRODE; CONTROL METHODS; ELECTRICAL ACTIVITIES; ELECTRICAL STATE; EXTERNAL CURRENTS; INHERENT COMPLEXITY; LINEAR QUADRATIC REGULATOR; MODEL-BASED CONTROL; SPIRAL WAVES; UNSTABLE MODES; VENTRICULAR FIBRILLATION; VENTRICULAR TACHYCARDIA;

WAVES;

DELAY CONTROL SYSTEMS;

EID: 70349097979     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.021932     Document Type: Article

References (55)

1. W. Rosamond, Circulation 117, e25 (2008). 10.1161/CIRCULATIONAHA.107. 187998
2. K. Nanthakumar, J. Jalife, S. Masse, E. Downar, M. Pop, J. Asta, H. Ross, V. Rao, S. Mironov, E. Sevaptsidis, Am. J. Physiol. Heart Circ. Physiol. 293, H875 (2007). 10.1152/ajpheart.01415.2006
3. F. Qu, C. M. Ripplinger, V. P. Nikolski, C. Grimm, and I. R. Efimov, J. Biomed. Opt. 12, 044019 (2007). 10.1117/1.2753748
4. E. M. Cherry and F. H. Fenton, New J. Phys. 10, 125016 (2008). 10.1088/1367-2630/10/12/125016
5. A. Karma, Chaos 4, 461 (1994). 10.1063/1.166024
6. M. Courtemanche and A. T. Winfree, Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 431 (1991). 10.1142/S0218127491000336
7. F. H. Samie and J. Jalife, Cardiovasc. Res. 50, 242 (2001). 10.1016/S0008-6363(00)00289-3
8. A. V. Panfilov, Phys. Rev. Lett. 88, 118101 (2002). 10.1103/PhysRevLett. 88.118101
9. F. H. Fenton, E. M. Cherry, H. M. Hastings, and S. J. Evans, Chaos 12, 852 (2002). 10.1063/1.1504242
10. J. Jalife, Annu. Rev. Physiol. 62, 25 (2000). 10.1146/annurev.physiol.62. 1.25
11. J. M. Rogers and R. E. Ideker, Circ. Res. 86, 369 (2000).
12. T. J. Wu, S. F. Lin, J. N. Weiss, C. T. Ting, and P.-S. Chen, Circulation 106, 1859 (2002). 10.1161/01.CIR.0000031334.49170.FB
13. S. Nattel, J. Cardiovasc. Pharmacol. Ther. 8, S5 (2003). 10.1177/107424840300800102
14. R. E. Ideker and J. M. Rogers, Circulation 114, 530 (2006). 10.1161/CIRCULATIONAHA.106.644765
15. J. B. Nolasco and R. W. Dahlen, J. Appl. Physiol. 25, 191 (1968).
16. M. R. Guevara, G. Ward, A. Shrier, and L. Glass, in Computers in Cardiology 1984 (IEEE Computer Society, Long Beach, CA, 1984), p. 167.
17. J. M. Pastore, S. D. Girouard, K. R. Laurita, F. G. Akar, and D. S. Rosenbaum, Circulation 99, 1385 (1999).
18. Z.-L. Qu, A. Garfinkel, P.-S. Chen, and J. N. Weiss, Circulation 102, 1664 (2000).
19. T. Watanabe, F. Fenton, S. Evans, H. Hastings, and A. Karma, J. Cardiovasc. Electrophysiol. 12, 196 (2001). 10.1046/j.1540-8167.2001.00196.x
20. J. J. Fox, M. L. Riccio, F. Hua, E. Bodenschatz, and R. F. Gilmour, Jr., Circ. Res. 90, 289 (2002). 10.1161/hh0302.104723
21. B. R. Choi, W.-C. Jang, and G. Salama, Heart Rhythm 4, 1057 (2007). 10.1016/j.hrthm.2007.03.037
22. R. C. Myles, F. L. Burton, S. M. Cobbe, and G. L. Smith, J. Mol. Cell. Cardiol. 45, 1 (2008). 10.1016/j.yjmcc.2008.03.024
23. D. S. Rosenbaum, L. E. Jackson, J. M. Smith, H. Garam, J. N. Ruskin, and R. J. Cohen, N. Engl. J. Med. 330, 235 (1994). 10.1056/NEJM199401273300402
24. M. L. Walker and D. S. Rosenbaum, Cardiovasc. Res. 57, 599 (2003). 10.1016/S0008-6363(02)00737-X
25. W. J. Rappel, F. Fenton, and A. Karma, Phys. Rev. Lett. 83, 456 (1999). 10.1103/PhysRevLett.83.456
26. B. Echebarria and A. Karma, Chaos 12, 923 (2002). 10.1063/1.1501544
27. D. J. Christini, M. L. Riccio, C. A. Culianu, J. J. Fox, A. Karma, and R. F. Gilmour, Jr., Phys. Rev. Lett. 96, 104101 (2006). 10.1103/PhysRevLett.96. 104101
28. M. Li and N. F. Otani, Ann. Biomed. Eng. 32, 784 (2004). 10.1023/B:ABME.0000030254.33176.f8
29. D. Allexandre and N. F. Otani, Phys. Rev. E 70, 061903 (2004). 10.1103/PhysRevE.70.061903
30. S. Dubljevic, Int. J. Robust Nonlinear Control 19, 135 (2009). 10.1002/rnc.1298
31. S. Dubljevic, S.-F. Lin, and P. D. Christofides, Comput. Chem. Eng. 32, 2086 (2008). 10.1016/j.compchemeng.2007.10.019
32. B. Echebarria and A. Karma, Phys. Rev. Lett. 88, 208101 (2002). 10.1103/PhysRevLett.88.208101
33. M. L. Koller, M. L. Riccio, and R. F. Gilmour, Jr., Am. J. Physiol. Heart Circ. Physiol. 275, H1635 (1998).
34. G. Dominguez and H. A. Fozzard, Am. J. Physiol. 237, C119 (1979).
35. P. Dorato, C. Abdallah, and V. Cerone, Linear-Quadratic Control: An Introduction (Prentice Hall, Englewood Cliffs, NJ, 1995).
36. B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods (Prentice Hall, Englewood Cliffs, NJ, 1990).
37. F. Fenton and A. Karma, Chaos 8, 20 (1998). 10.1063/1.166311
38. A. Bueno-Orovio, E. M. Cherry, and F. H. Fenton, J. Theor. Biol. 253, 544 (2008). 10.1016/j.jtbi.2008.03.029
39. F. Fenton and A. Karma, Chaos 8, 879 (1998). 10.1063/1.166374
40. M. Courtemanche, L. Glass, and J. P. Keener, Phys. Rev. Lett. 70, 2182 (1993). 10.1103/PhysRevLett.70.2182
41. P. Comtois and A. Vinet, Chaos 17, 023125 (2007). 10.1063/1.2740673
42. Y. Lan and P. Cvitanović, Phys. Rev. E 69, 016217 (2004). 10.1103/PhysRevE.69.016217
43. E. G. Tolkacheva, D. G. Schaeffer, D. J. Gauthier, and C. C. Mitchell, Chaos 12, 1034 (2002). 10.1063/1.1515170
44. V. Jacquemet, Math. Biosci. 208, 241 (2007). 10.1016/j.mbs.2006.10.007
45. R. B. Lehoucq, D. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM Publications, Philadelphia, 1998).
46. N. F. Otani and R. F. Gilmour, Jr., J. Theor. Biol. 187, 409 (1997). 10.1006/jtbi.1997.0447
47. S. M. Narayan and J. M. Smith, J. Am. Coll. Cardiol. 35, 1485 (2000). 10.1016/S0735-1097(00)00580-5
48. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, N.Y., 1985).
49. T. Kailath, Linear Systems (Prentice Hall, Englewood Cliffs, N.J., 1980).
50. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, New York, 1998).
51. G. Hagen and I. Mezić, Proceedings of the 2000 American Control Conference, Vol. 6 (American Automatic Control Council, New York, 2000), pp. 3783-3787.
52. A. Al-Khadra, V. Nikolski, and I. R. Efimov, Circ. Res. 87, 797 (2000).
53. V. P. Nikolski and I. R. Efimov, Europace 7, S146 (2005). 10.1016/j.eupc.2005.04.011
54. H. Tachibana, I. Kubota, M. Yamaki, T. Watanabe, and H. Tomoike, Am. J. Physiol. Heart Circ. Physiol. 275, H116 (1998).
55. R. Grigoriev, Physica D 140, 171 (2000). 10.1016/S0167-2789(00)00014-2