Skip to main content

News about Scitation

In December 2016 Scitation will launch with a new design, enhanced navigation and a much improved user experience.

To ensure a smooth transition, from today, we are temporarily stopping new account registration and single article purchases. If you already have an account you can continue to use the site as normal.

For help or more information please visit our FAQs.

banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
/content/aip/journal/chaos/20/4/10.1063/1.3518362
1.
1.Aistrup, G. L. , Kelly, J. E. , Kapur, S. , Kowalczyk, M. , Sysman-Wolpin, I. , Kadish, A. H. , and Wasserstrom, J. A. , “Pacing-induced heterogeneities in intracellular signaling, cardiac alternans, and ventricular arrhythmias in intact rat heart,” Circ. Res. 99, E65E73 (2006).
http://dx.doi.org/10.1161/01.RES.0000244087.36230.bf
2.
2.Beeler, G. W. and Reuter, H. , “Reconstruction of the action potential of ventricular myocardial fibers,” J. Physiol. (London) 268, 177210 (1977).
3.
3.Bers, D. M. , “Cardiac excitation-contraction coupling,” Nature (London) 415, 198205 (2002).
http://dx.doi.org/10.1038/415198a
4.
4.Blatter, L. , Kockskämper, J. , Sheehan, K. , Zima, A. , Hüser, J. , and Lipsius, S. , “Local calcium gradients during excitation-contraction coupling and alternans in atrial myocytes,” J. Physiol. (London) 546, 1931 (2003).
http://dx.doi.org/10.1113/jphysiol.2002.025239
5.
5.Cannell, M. B. , Cheng, H. , and Lederer, W. J. , “The control of calcium release in heart muscle,” Science 268, 10451049 (1995).
http://dx.doi.org/10.1126/science.7754384
6.
6.Cheng, H. , Lederer, W. J. , and Cannell, M. B. , “Calcium sparks: Elementary events underlying excitation-contraction coupling in heart muscle,” Science 262, 740744 (1993).
http://dx.doi.org/10.1126/science.8235594
7.
7.Chudin, E. , Goldhaber, J. , Garfinkel, A. , Weiss, J. , and Kogan, B. , “Intracellular dynamics and the stability of ventricular tachycardia,” Biophys. J. 77, 29302941 (1999).
http://dx.doi.org/10.1016/S0006-3495(99)77126-2
8.
8.Clayton, R. , Bernus, O. , Cherry, E. , Dierckx, H. , Fenton, F. , Mirabella, L. , Panfilov, A. , Sachse, F. , Seemann, G. , and Zhang, H. , “Models of cardiac tissue electrophysiology: Progress, challenges and open questions,” Prog. Biophys. Mol. Biol. (in press).
9.
9.Coombes, S. , “The effect of ion pumps on the speed of travelling waves in the fire-diffuse-fire model of release,” Bull. Math. Biol. 63, 120 (2001).
http://dx.doi.org/10.1006/bulm.2000.0193
10.
10.Coombes, S. and Timofeeva, Y. , “Sparks and waves in a stochastic fire-diffuse-fire model of calcium release,” Phys. Rev. E 68, 021915 (2003).
http://dx.doi.org/10.1103/PhysRevE.68.021915
11.
11.Cordeiro, J. M. , Malone, J. E. , Diego, J. M. D. , Scornik, F. S. , Aistrup, G. L. , Antzelevitch, C. , and Wasserstrom, J. A. , “Cellular and subcellular alternans in the canine left ventricle,” Am. J. Physiol. Heart Circ. Physiol. 293, H3506H3516 (2007).
http://dx.doi.org/10.1152/ajpheart.00757.2007
12.
12.Dai, S. and Schaeffer, D. G. , “Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans,” Chaos 20, 023131 (2010).
http://dx.doi.org/10.1063/1.3456058
13.
13.Echebarria, B. and Karma, A. , “Instability and spatiotemporal dynamics of alternans in paced cardiac tissue,” Phys. Rev. Lett. 88, 208101 (2002).
http://dx.doi.org/10.1103/PhysRevLett.88.208101
14.
14.Fenton, F. H. and Cherry, E. M. , “Models of cardiac cell,” Scholarpedia 3, 1868 (2008).
http://dx.doi.org/10.4249/scholarpedia.1868
15.
15.Gaeta, S. A. , Bub, G. , Abbott, G. W. , and Christini, D. J. , “Dynamical mechanism for subcellular alternans in cardiac myocytes,” Circ. Res. 105, 335342 (2009).
http://dx.doi.org/10.1161/CIRCRESAHA.109.197590
16.
16.Higgins, E. R. , Goel, P. , Puglisi, J. L. , Bers, D. M. , Cannell, M. , and Sneyd, J. , “Modelling calcium microdomains using homogenisation,” J. Theor. Biol. 247, 623644 (2007).
http://dx.doi.org/10.1016/j.jtbi.2007.03.019
17.
17.Huertas, M. A. , Smith, G. D. , and Györke, S. , “ alternans in a cardiac myocyte model that uses moment equations to represent heterogeneous junctional SR ,” Biophys. J. 99, 377387 (2010).
http://dx.doi.org/10.1016/j.bpj.2010.04.032
18.
18.Jordan, P. N. and 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. 293, H2109H2118 (2007).
http://dx.doi.org/10.1152/ajpheart.00609.2007
19.
19.Kockskämper, J. and Blatter, L. , “Subcellular alternans represents a novel mechanism for the generation of arrhythmogenic waves in cat atrial myocytes,” J. Physiol. (London) 545, 6579 (2002).
http://dx.doi.org/10.1113/jphysiol.2002.025502
20.
20.Laurita, K. R. and Rosenbaum, D. S. , “Cellular mechanisms of arrhythmogenic cardiac alternans,” Prog. Biophys. Mol. Biol. 97, 332347 (2008).
http://dx.doi.org/10.1016/j.pbiomolbio.2008.02.014
21.
21.Leonhardt, H. , Zaks, M. , Falcke, M. , and Schimansky-Geier, L. , “Stochastic hierarchical systems: Excitable dynamics,” J. Biol. Phys. 34, 521538 (2008).
http://dx.doi.org/10.1007/s10867-008-9112-1
22.
22.Luo, C. and Rudy, Y. , “A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes,” Circ. Res. 74, 10711096 (1994).
23.
23.Luo, C. H. and Rudy, Y. , “A model of the ventricular cardiac action potential, depolarization, repolarization and their interaction,” Circ. Res. 68, 15011526 (1991).
24.
24.Matthes, J. and Herzig, S. , “Less is more, or enough is enough? -dependent inactivation revisited,” J. Physiol. (London) 588, 1516 (2010).
http://dx.doi.org/10.1113/jphysiol.2009.184846
25.
25.McKean, H. P. , “Nagumo’s equation,” Adv. Math. 4, 209223 (1970).
http://dx.doi.org/10.1016/0001-8708(70)90023-X
26.
26.Myles, R. C. , Burton, F. L. , Cobbe, S. M. , and Smith, G. L. , “The link between repolarisation alternans and ventricular arrhythmia: Does the cellular phenomenon extend to the clinical problem?,” J. Mol. Cell. Cardiol. 45, 110 (2008).
http://dx.doi.org/10.1016/j.yjmcc.2008.03.024
27.
27.Noble, D. , “A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pacemaker potentials,” J. Physiol. (London) 160, 317352 (1962).
28.
28.Noble, D. , “Modeling the heart,” Physiology 19, 191197 (2004).
http://dx.doi.org/10.1152/physiol.00004.2004
29.
29.Pecora, L. M. and Carroll, T. L. , “Master stability functions for synchronized coupled systems,” Phys. Rev. Lett. 80, 2109 (1998).
http://dx.doi.org/10.1103/PhysRevLett.80.2109
30.
30.Qu, Z. and Weiss, J. N. , “The chicken or the egg? Voltage and calcium dynamics in the heart,” Am. J. Physiol. Heart Circ. Physiol. 293, H2054H2055 (2007).
http://dx.doi.org/10.1152/ajpheart.00830.2007
31.
31.Restrepo, J. G. and Karma, A. , “Spatiotemporal intracellular calcium dynamics during cardiac alternans,” Chaos 19, 037115 (2009).
http://dx.doi.org/10.1063/1.3207835
32.
32.Shiferaw, Y. and Karma, A. , “Turing instability mediated by voltage and calcium diffusion in paced cardiac cells,” Proc. Natl. Acad. Sci. U.S.A. 103, 56705675 (2006).
http://dx.doi.org/10.1073/pnas.0511061103
33.
33.Shiferaw, Y. , Sato, D. , and Karma, A. , “Coupled dynamics of voltage and calcium in paced cardiac cells,” Phys. Rev. E 71, 021903 (2005).
http://dx.doi.org/10.1103/PhysRevE.71.021903
34.
34.Shiferaw, Y. , Watanabe, M. A. , Garfinkel, A. , Weiss, J. N. , and Karma, A. , “Model of intracellular calcium cycling in ventricular myocytes,” Biophys. J. 85, 36663686 (2003).
http://dx.doi.org/10.1016/S0006-3495(03)74784-5
35.
35.Sipido, K. R. , “Understanding cardiac alternans: The answer lies in the store,” Circ. Res. 94, 570572 (2004).
http://dx.doi.org/10.1161/01.RES.0000124606.14903.6F
36.
36.Thul, R. and Falcke, M. , “Waiting time distributions for clusters of complex molecules,” Europhys. Lett. 79, 38003 (2007).
http://dx.doi.org/10.1209/0295-5075/79/38003
37.
37.Trafford, A. , Diaz, M. , and Eisner, D. , “Coordinated control of cell loading and triggered release from the sarcoplasmic reticulum underlies the rapid inotropic response to increased L-type current,” Circ. Res. 88, 195201 (2001).
38.
38.Xie, L. -H. , Sato, D. , Garfinkel, A. , Qu, Z. , and Weiss, J. N. , “Intracellular Ca alternans: Coordinated regulation by sarcoplasmic reticulum release, uptake, and leak,” Biophys. J. 95, 31003110 (2008).
http://dx.doi.org/10.1529/biophysj.108.130955
39.
39.Zhao, X. , “Indeterminacy of spatiotemporal cardiac alternans,” Phys. Rev. E 78, 011902 (2008).
http://dx.doi.org/10.1103/PhysRevE.78.011902
http://aip.metastore.ingenta.com/content/aip/journal/chaos/20/4/10.1063/1.3518362
Loading
/content/aip/journal/chaos/20/4/10.1063/1.3518362
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/chaos/20/4/10.1063/1.3518362
2010-12-30
2016-12-05

Abstract

Cardiac alternans is a beat-to-beat alternation in action potential duration (APD) and intracellular calcium cycling seen in cardiac myocytes under rapid pacing that is believed to be a precursor to fibrillation. The cellular mechanisms of these rhythms and the coupling between cellular and voltage dynamics have been extensively studied leading to the development of a class of physiologically detailed models. These have been shown numerically to reproduce many of the features of myocyte response to pacing, including alternans, and have been analyzed mathematically using various approximation techniques that allow for the formulation of a low dimensional map to describe the evolution of APDs. The seminal work by Shiferaw and Karma is of particular interest in this regard [Shiferaw, Y. and Karma, A., “Turing instability mediated by voltage and calcium diffusion in paced cardiac cells,” Proc. Natl. Acad. Sci. U.S.A.103, 5670–5675 (2006)]. Here, we establish that the key dynamical behaviors of the Shiferaw–Karma model are arranged around a set of switches. These are shown to be the main elements for organizing the nonlinear behavior of the model. Exploiting this observation, we show that a piecewise linear caricature of the Shiferaw–Karma model, with a set of appropriate switching manifolds, can be constructed that preserves the physiological interpretation of the original model while being amenable to a systematic mathematical analysis. In illustration of this point, we formulate the dynamics of cycling (in response to pacing) and compute the properties of periodic orbits in terms of a stroboscopic map that can be constructed without approximation. Using this, we show that alternans emerge via a period-doubling instability and track this bifurcation in terms of physiologically important parameters. We also show that when coupled to a spatially extended model for transport, the model supports spatially varying patterns of alternans. We analyze the onset of this instability with a generalization of the master stability approach to accommodate the nonsmooth nature of our system.

Loading

Full text loading...

/deliver/fulltext/aip/journal/chaos/20/4/1.3518362.html;jsessionid=EbrPqka6dFFcUbrHGzdZQUhX.x-aip-live-02?itemId=/content/aip/journal/chaos/20/4/10.1063/1.3518362&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/chaos
true
true

Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
/content/realmedia?fmt=ahah&adPositionList=
&advertTargetUrl=//oascentral.aip.org/RealMedia/ads/&sitePageValue=chaos.aip.org/20/4/10.1063/1.3518362&pageURL=http://scitation.aip.org/content/aip/journal/chaos/20/4/10.1063/1.3518362'
Right1,Right2,Right3,