Feedback-control induced pattern formation in cardiac myocytes: A mathematical modeling study

Journal of Theoretical Biology

Volumn 266, Issue 3, 2010, Pages 408-418

  Gaeta, Stephen A ^a   Krogh Madsen, Trine ^a   Christini, David J ^a  

^a WEILL CORNELL MEDICAL COLLEGE   (United States)

Author keywords

Alternans; Arrhythmia; Cardiac electrophysiology; Subcellular alternans

Indexed keywords

MORPHOGEN;

ALGORITHM; ANATOMY; CARDIOLOGY; CELL ORGANELLE; EXPERIMENTAL STUDY; FEEDBACK MECHANISM; MUSCLE; NUMERICAL MODEL; SYMMETRY; THEORETICAL STUDY;

ALGORITHM; ARTICLE; CALCIUM TRANSPORT; CARDIAC ALTERNANS; CONTROLLED STUDY; EXPERIMENTAL STUDY; FEEDBACK SYSTEM; HEART ARRHYTHMIA; HEART BEAT; HEART MUSCLE CELL; HEART MUSCLE FIBER MEMBRANE POTENTIAL; HEART PACING; MATHEMATICAL MODEL; MUSCLE FIBER CONTRACTION; PRIORITY JOURNAL; SUBCELLULAR ALTERNANS; THEORETICAL STUDY;

ACTION POTENTIALS; ALGORITHMS; ANIMALS; ARRHYTHMIAS, CARDIAC; CALCIUM; COMPUTER SIMULATION; FEEDBACK, PHYSIOLOGICAL; HUMANS; INTRACELLULAR SPACE; MODELS, CARDIOVASCULAR; MYOCYTES, CARDIAC; SARCOMERES; SODIUM-CALCIUM EXCHANGER;

EID: 77954857260     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2010.06.041     Document Type: Article

References (33)

1. Aistrup G.L., Kelly J.E., Kapur S., Kowalczyk M., Sysman-Wolpin I., Kadish A.H., Wasserstrom J.A. Pacing-induced heterogeneities in intracellular ca2+ signaling, cardiac alternans, and ventricular arrhythmias in intact rat heart. Circ. Res. 2006, 99(7):e65-e73.
2. Aistrup G.L., Shiferaw Y., Kapur S., Kadish A.H., Wasserstrom J.A. Mechanisms underlying the formation and dynamics of subcellular calcium alternans in the intact rat heart. Circ. Res. 2009, 104(5):639-649.
3. Bassani J.W., Yuan W., Bers D.M. Fractional sr ca release is regulated by trigger ca and sr ca content in cardiac myocytes. Am. J. Physiol. 1995, 268(5 Pt 1):C1313-C1319.
4. Cheng H., Lederer W.J. Calcium sparks. Physiol. Rev. 2008, 88(4):1491-1545.
5. Christini D.J., Riccio M.L., Culianu C.A., Fox J.J., Karma A., Gilmour R.F. Control of electrical alternans in canine cardiac purkinje fibers. Phys. Rev. Lett. 2006, 96(10):104101.
6. Cordeiro J.M., Malone J.E., Diego J.M.D., Scornik F.S., Aistrup G.L., Antzelevitch C., Wasserstrom J.A. Cellular and subcellular alternans in the canine left ventricle. Am. J. Physiol. Heart Circ. Physiol. 2007, 293(6):H3506-H3516.
7. Díaz M.E., Eisner D.A., O'Neill S.C. Depressed ryanodine receptor activity increases variability and duration of the systolic ca2+ transient in rat ventricular myocytes. Circ. Res. 2002, 91(7):585-593.
8. Díaz M.E., O'Neill S.C., Eisner D.A. Sarcoplasmic reticulum calcium content fluctuation is the key to cardiac alternans. Circ. Res. 2004, 94(5):650-656.
9. Euler D.E. Cardiac alternans: mechanisms and pathophysiological significance. Cardiovasc. Res. 1999, 42(3):583-590.
10. Franzini-Armstrong C., Peachey L.D. Striated muscle-contractile and control mechanisms. J. Cell Biol. 1981, 91(3 Pt 2):166s-186s.
11. Gaeta S.A., Bub G., Abbott G.W., Christini D.J. Dynamical mechanism for subcellular alternans in cardiac myocytes. Circ. Res. 2009, 105(4):335-342.
12. Gierer A., Meinhardt H. A theory of biological pattern formation. Kybernetik 1972, 12(1):30-39.
13. Hall G.M., Gauthier D.J. Experimental control of cardiac muscle alternans. Phys. Rev. Lett. 2002, 88(19):198102.
14. Hall, K., Christini, D.J., 2001. Restricted feedback control of one-dimensional maps. Phys. Rev. E 63 (4), 046204. doi:10.1103/PhysRevE.63.046204.
15. Jordan P.N., Christini D.J. Characterizing the contribution of voltage- and calcium-dependent coupling to action potential stability: implications for repolarization alternans. Am. J. Physiol. Heart Circ. Physiol. 2007, 293(4):H2109-H2118.
16. Kapur S., Wasserstrom J.A., Kelly J.E., Kadish A.H., Aistrup G.L. Acidosis and ischemia increase cellular ca2+ transient alternans and repolarization alternans susceptibility in the intact rat heart. Am. J. Physiol. Heart Circ. Physiol. 2009, 296(5):H1491-H1512.
17. Karma A., Gilmour R. Nonlinear dynamics of heart rhythm disorders. Phys. Today 2007, 60(3):51.
18. Kockskämper J., Blatter L.A. Subcellular ca2+ alternans represents a novel mechanism for the generation of arrhythmogenic ca2+ waves in cat atrial myocytes. J. Physiol. (Lond.) 2002, 545(Pt 1):65-79.
19. Li M., Otani N.F. Ion channel basis for alternans and memory in cardiac myocytes. Ann. Biomed. Eng. 2003, 31(10):1213-1230.
20. Mahajan A., Shiferaw Y., Sato D., Baher A., Olcese R., Xie L.-H., Yang M.-J., Chen P.-S., Restrepo J.G., Karma A., Garfinkel A., Qu Z., Weiss J.N. A rabbit ventricular action potential model replicating cardiac dynamics at rapid heart rates. Biophys. J. 2008, 94(2):392-410.
21. Meinhardt H., Gierer A. Pattern formation by local self-activation and lateral inhibition. Bioessays 2000, 22(8):753-760.
22. Murray J. Mathematical Biology 2003, Springer Verlag.
23. Narayan S. T-wave alternans and the susceptibility to ventricular arrhythmias. J. Am. College Cardiol. 2006, 47(2):269-281.
24. Pastore J.M., Girouard S.D., Laurita K.R., Akar F.G., Rosenbaum D.S. Mechanism linking t-wave alternans to the genesis of cardiac fibrillation. Circulation 1999, 99(10):1385-1394.
25. Qu, Z., Shiferaw, Y., Weiss, J., 2007. Nonlinear dynamics of cardiac excitation-contraction coupling: an iterated map study. Phys. Rev. E 75, 011927-01-011927-13.
26. Qu Z., Weiss J.N. The chicken or the egg? Voltage and calcium dynamics in the heart. Am. J. Physiol. Heart Circ. Physiol. 2007, 293(4):H2054-H2055. doi:10.1152/ajpheart.00830.2007.
27. Rubenstein D.S., Lipsius S.L. Premature beats elicit a phase reversal of mechanoelectrical alternans in cat ventricular myocytes. A possible mechanism for reentrant arrhythmias. Circulation 1995, 91(1):201-214.
28. Shiferaw Y., Karma A. Turing instability mediated by voltage and calcium diffusion in paced cardiac cells. Proc. Natl. Acad. Sci. USA 2006, 103(15):5670-5675.
29. Shiferaw Y., Sato D., Karma A. Coupled dynamics of voltage and calcium in paced cardiac cells. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2005, 71(2 Part 1):021903.
30. Shiferaw Y., Watanabe M.A., Garfinkel A., Weiss J.N., Karma A. Model of intracellular calcium cycling in ventricular myocytes. Biophys. J. 2003, 85(6):3666-3686.
31. Turing A.M. The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci. 1952, 237(641):37-72.
32. Weiss J.N., Karma A., Shiferaw Y., Chen P.-S., Garfinkel A., Qu Z. From pulsus to pulseless: the saga of cardiac alternans. Circ. Res. 2006, 98(10):1244-1253.
33. Xie, L., Weiss, J.N., 2009. Arrhythmogenic consequences of intracellular calcium waves. Am. J. Physiol. Heart Circ. Physiol. 297 (3), H997-H1002. doi:10.1152/ajpheart.00390.2009.