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.
Understanding cardiac alternans: A piecewise linear modeling framework
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, E65–E73 (2006).
2.Beeler, G. W. and Reuter, H. , “Reconstruction of the action potential of ventricular myocardial fibers,” J. Physiol. (London) 268, 177–210 (1977).
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, 19–31 (2003).
6.Cheng, H. , Lederer, W. J. , and Cannell, M. B. , “Calcium sparks: Elementary events underlying excitation-contraction coupling in heart muscle,” Science 262, 740–744 (1993).
7.Chudin, E. , Goldhaber, J. , Garfinkel, A. , Weiss, J. , and Kogan, B. , “Intracellular dynamics and the stability of ventricular tachycardia,” Biophys. J. 77, 2930–2941 (1999).
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).
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, H3506–H3516 (2007).
12.Dai, S. and Schaeffer, D. G. , “Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans,” Chaos 20, 023131 (2010).
15.Gaeta, S. A. , Bub, G. , Abbott, G. W. , and Christini, D. J. , “Dynamical mechanism for subcellular alternans in cardiac myocytes,” Circ. Res. 105, 335–342 (2009).
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, 623–644 (2007).
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, 377–387 (2010).
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, H2109–H2118 (2007).
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, 65–79 (2002).
21.Leonhardt, H. , Zaks, M. , Falcke, M. , and Schimansky-Geier, L. , “Stochastic hierarchical systems: Excitable dynamics,” J. Biol. Phys. 34, 521–538 (2008).
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, 1071–1096 (1994).
23.Luo, C. H. and Rudy, Y. , “A model of the ventricular cardiac action potential, depolarization, repolarization and their interaction,” Circ. Res. 68, 1501–1526 (1991).
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, 1–10 (2008).
27.Noble, D. , “A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pacemaker potentials,” J. Physiol. (London) 160, 317–352 (1962).
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, 5670–5675 (2006).
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, 3666–3686 (2003).
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, 195–201 (2001).
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, 3100–3110 (2008).
Article metrics loading...
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.
Full text loading...
Most read this month