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Law R, Levin M. Bioelectric memory: modeling resting potential bistability in amphibian embryos and mammalian cells. Theor Biol Med Model 2015; 12:22. [PMID: 26472354 PMCID: PMC4608135 DOI: 10.1186/s12976-015-0019-9] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2015] [Accepted: 09/27/2015] [Indexed: 12/20/2022] Open
Abstract
Background Bioelectric gradients among all cells, not just within excitable nerve and muscle, play instructive roles in developmental and regenerative pattern formation. Plasma membrane resting potential gradients regulate cell behaviors by regulating downstream transcriptional and epigenetic events. Unlike neurons, which fire rapidly and typically return to the same polarized state, developmental bioelectric signaling involves many cell types stably maintaining various levels of resting potential during morphogenetic events. It is important to begin to quantitatively model the stability of bioelectric states in cells, to understand computation and pattern maintenance during regeneration and remodeling. Method To facilitate the analysis of endogenous bioelectric signaling and the exploitation of voltage-based cellular controls in synthetic bioengineering applications, we sought to understand the conditions under which somatic cells can stably maintain distinct resting potential values (a type of state memory). Using the Channelpedia ion channel database, we generated an array of amphibian oocyte and mammalian membrane models for voltage evolution. These models were analyzed and searched, by simulation, for a simple dynamical property, multistability, which forms a type of voltage memory. Results We find that typical mammalian models and amphibian oocyte models exhibit bistability when expressing different ion channel subsets, with either persistent sodium or inward-rectifying potassium, respectively, playing a facilitative role in bistable memory formation. We illustrate this difference using fast sodium channel dynamics for which a comprehensive theory exists, where the same model exhibits bistability under mammalian conditions but not amphibian conditions. In amphibians, potassium channels from the Kv1.x and Kv2.x families tend to disrupt this bistable memory formation. We also identify some common principles under which physiological memory emerges, which suggest specific strategies for implementing memories in bioengineering contexts. Conclusion Our results reveal conditions under which cells can stably maintain one of several resting voltage potential values. These models suggest testable predictions for experiments in developmental bioelectricity, and illustrate how cells can be used as versatile physiological memory elements in synthetic biology, and unconventional computation contexts. Electronic supplementary material The online version of this article (doi:10.1186/s12976-015-0019-9) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Robert Law
- Department of Neuroscience, Brown University, Box G, Providence, RI, 02912, USA.
| | - Michael Levin
- Department of Biology and Tufts Center for Regenerative and Developmental Biology, Tufts University, 200 Boston Avenue, Medford, MA, 02155, USA.
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Abstract
In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.
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Affiliation(s)
- Zhilin Qu
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Correspondence to: Zhilin Qu, PhD, Department of Medicine, Division of Cardiology, David Geffen School of Medicine at UCLA, A2-237 CHS, 650 Charles E. Young Drive South, Los Angeles, CA 90095, Tel: 310-794-6050, Fax: 310-206-9133,
| | - Gang Hu
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Alan Garfinkel
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Department of Integrative Biology and Physiology, University of California, Los Angeles, California 90095, USA
| | - James N. Weiss
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
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Huang X, Liu X, Zheng L, Mi Y, Qian Y. Effects of pacing magnitudes and forms on bistability width in a modeled ventricular tissue. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:012711. [PMID: 23944495 DOI: 10.1103/physreve.88.012711] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2013] [Revised: 06/16/2013] [Indexed: 06/02/2023]
Abstract
Bistability in periodically paced cardiac tissue is relevant to cardiac arrhythmias and its control. In the present paper, one-dimensional tissue of the phase I Luo-Rudy model is numerically investigated. The effects of various parameters of pacing signals on bistability width are studied. The following conclusions are obtained: (i) Pacing can be classified into two types: pulsatile and sinusoidal types. Pulsatile pacing reduces bistability width as its magnitude is increased. Sinusoidal pacing increases the width as its amplitude is increased. (ii) In a pacing period the hyperpolarizing part plays a more important role than the depolarizing part. Variations of the hyperpolarizing ratio in a period evidently change the width of bistability and its variation tendency. (iii) A dynamical mechanism is proposed to qualitatively explain the phenomena, which reveals the reason for the different effects of pulsatile and sinusoidal pacing on bistability. The methods for changing bistability width by external pacing may help control arrhythmias in cardiology.
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Affiliation(s)
- Xiaodong Huang
- Department of Physics, South China University of Technology, Guangzhou 510640, China.
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Huang X, Qian Y, Zhang X, Hu G. Hysteresis and bistability in periodically paced cardiac tissue. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:051903. [PMID: 20866257 DOI: 10.1103/physreve.81.051903] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2009] [Revised: 03/08/2010] [Indexed: 05/29/2023]
Abstract
Hysteresis in periodically paced cardiac tissue is an important issue due to its relevance to cardiac arrhythmias. In the present paper, the mechanism of hysteresis formation and the related properties are interpreted by numerically investigating the phase I Luo-Rudy model. A formula calculating the width of hysteresis is proposed and well confirmed by numerical simulations. We also find that hysteresis in cardiac tissue shows several characteristics due to couplings among cardiac cells which are absent in a single cell. The influences of the physiological parameters are studied in detail. The model dependence of hysteresis is elucidated by considering a number of well-known models of excitable media. Moreover, the influence of bistability on controlling arrhythmias is revealed.
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Affiliation(s)
- Xiaodong Huang
- Department of Physics, Beijing Normal University, Beijing 100875, China
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Gottwald GA. Bifurcation analysis of a normal form for excitable media: are stable dynamical alternans on a ring possible? CHAOS (WOODBURY, N.Y.) 2008; 18:013129. [PMID: 18377080 DOI: 10.1063/1.2890430] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We present a bifurcation analysis of a normal form for traveling waves in one-dimensional excitable media. The normal form that has been recently proposed on phenomenological grounds is given in the form of a differential delay equation. The normal form exhibits a symmetry-preserving Hopf bifurcation that may coalesce with a saddle node in a Bogdanov-Takens point, and a symmetry-breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf bifurcation for the propagation of a single pulse in a ring by means of a center manifold reduction, and for a wave train by means of a multiscale analysis leading to a real Ginzburg-Landau equation as the corresponding amplitude equation. Both the center manifold reduction and the multiscale analysis show that the Hopf bifurcation is always subcritical independent of the parameters. This may have links to cardiac alternans, which have so far been believed to be stable oscillations emanating from a supercritical bifurcation. We discuss the implications for cardiac alternans and revisit the instability in some excitable media where the oscillations had been believed to be stable. In particular, we show that our condition for the onset of the Hopf bifurcation coincides with the well known restitution condition for cardiac alternans.
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Affiliation(s)
- Georg A Gottwald
- School of Mathematics and Statistics and Centre for Mathematical Biology, University of Sydney, Sydney, NSW 2006, Australia.
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Chen W, Potse M, Vinet A. Dynamics of sustained reentry in a loop model with discrete gap junction resistances. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021928. [PMID: 17930086 DOI: 10.1103/physreve.76.021928] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2007] [Revised: 07/25/2007] [Indexed: 05/25/2023]
Abstract
The dynamics of reentry is studied in a one-dimensional loop of model cardiac cells with discrete intercellular gap junction resistance (R). Each cell is represented by a continuous cable with ionic current given by a modified Beeler-Reuter formulation. For R below a limiting value, propagation is found to change from period-1 to quasiperiodic (QP) at a critical loop length (L(crit)) that decreases with R. Quasiperiodic reentry exists from L(crit) to a minimum length (L(min)), which also shortens with R. The decrease of L(crit) (R) is not a simple scaling, but the bifurcation can still be predicted from the slope of the restitution curve giving the duration of the action potential as a function of the diastolic interval. However, the shape of the restitution curve changes with R. An increase of R does not seem to increase the number of possible QP solutions since, as in the continuous cable, only two QP modes of propagation were found despite an extensive search through alternative initial conditions.
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Affiliation(s)
- Wei Chen
- Department of Physiology, Institute of Biomedical Engineering, Université de Montréal, Montréal, Canada H4J-1C5.
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Comtois P, Vinet A. Alternans amplification following a two-stimulus protocol in a one-dimensional cardiac ionic model of reentry: from annihilation to double-wave quasiperiodic reentry. CHAOS (WOODBURY, N.Y.) 2007; 17:023125. [PMID: 17614679 DOI: 10.1063/1.2740673] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Electrical pacing is a common procedure in both experimental and clinical settings to study and/or annihilate anatomical reentry. A previous study [Comtois and Vinet, Chaos 12, 903 (2002)] has described new ways to terminate reentry in a one-dimensional loop model by a protocol consisting of only two stimulations. Annihilation of the reentrant activity was much more likely with these new scenarios than through a unidirectional block. This paper investigates the sensitivity of these scenarios of annihilation to the length of the pathway. It shows that double-pulse stimulation can stop the reentry if the circuit is shorter than a limiting length. Beyond this upper limit, stimulation rather yields sustained double-wave reentry. The same dynamical mechanism, labeled alternans amplification, is found to be responsible for these two types of post-stimulus dynamics.
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Affiliation(s)
- P Comtois
- Research Centre, Montreal Heart Institute and Department of Pharmacology, McGill University, Montreal, Quebec, H3G 1Y6, Canada
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Comtois P, Vinet A. Multistability of reentrant rhythms in an ionic model of a two-dimensional annulus of cardiac tissue. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:051927. [PMID: 16383665 DOI: 10.1103/physreve.72.051927] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2004] [Revised: 12/08/2004] [Indexed: 05/05/2023]
Abstract
The dynamics of reentry in a model of a two-dimensional annulus of homogeneous cardiac tissue, with a Beeler-Reuter type formulation of the membrane ionic currents, is examined. The bifurcation structure of the sustained propagated solutions is described as a function of Rin and Rout, the inner and outer radii of the annulus. The transition from periodic to quasiperiodic reentry occurs at a critical Rin, which first diminishes and then saturates as Rout is increased. The reduction of the critical Rin is a consequence of the increase of the wave-front curvature. There is a range of Rin below the critical radius in which two distinct quasiperiodic solutions coexist. Each of these solutions disappears at its own specific value of Rin, and their annihilation is preceded by a new type of bifurcation leading to a regime of propagation with transient successive detachments of the wave front from the inner border of the annulus.
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Affiliation(s)
- Philippe Comtois
- Research Centre, Montreal Heart Institute and Department of Pharmacology, McGill University, Montreal, Quebec H3G 1Y6, Canada.
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Chen X, Fenton FH, Gray RA. Head-tail interactions in numerical simulations of reentry in a ring of cardiac tissue. Heart Rhythm 2005; 2:1038-46. [PMID: 16184649 DOI: 10.1016/j.hrthm.2005.08.015] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
BACKGROUND The relationships between action potential duration (APD) and conduction velocity (CV) to the previous diastolic interval (DI) are known as the APD and CV restitution relationships. There is considerable debate regarding the importance of these relationships in the development and stability of reentry. OBJECTIVES The purpose of this study was to increase the understanding of the ionic basis for restitution during reentry. METHODS APD and CV were studied numerically during one-dimensional reentry as ring length (L) was shortened. A three-state variable model (u, v, w) was used to analyze the effect of gating variables of the fast (v) and slow (w) currents on the spatial and temporal dynamics of transmembrane potential (u). Three parameter sets were used corresponding to three APD and CV restitution curves. RESULTS Sustained spatial oscillations of APD and CV larger than the ring length were observed in two of the parameter sets (cytochalasin-D model [CYTO] and model 3 [M3]) before block occurred at L = 6 cm. The last model (diacetyl monoxime [DAM]) resulted in uniform APD and CV for all L until block occurred at L = 3 cm. Multivalued APD and CV restitution relationships due to "dephasing" of w and v with DI were observed in M3 and CYTO simulations. Overall, these dynamics could be explained by the wavelength-to-ring length ratio and the sensitivity of APD on the value of the gating variables w and v. CONCLUSION Propagation stability is mostly controlled by APD sensitivity to w, but the APD restitution slope does not always reflect this sensitivity. The interaction of the dynamic history (i.e., memory) of the fast and slow currents and electrotonic effects resulted in multivalued restitution curves.
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Affiliation(s)
- Xiaozhong Chen
- Department of Biomedical Engineering, University of Alabama at Birmingham, Birmingham, Alabama 35294, USA
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Chen X, Fenton FH, Gray RA. Head-tail interactions in numerical simulations of reentry in a ring of cardiac tissue. Heart Rhythm 2005; 2:851-9. [PMID: 16051124 DOI: 10.1016/j.hrthm.2005.05.012] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/04/2004] [Accepted: 05/10/2005] [Indexed: 10/25/2022]
Abstract
BACKGROUND The relationships between action potential duration (APD) and conduction velocity (CV) to the previous diastolic interval (DI) are known as the APD and CV restitution relationships. There is considerable debate regarding the importance of these relationships in the development and stability of reentry. OBJECTIVES The purpose of this study was to increase the understanding of the ionic basis for restitution during reentry. METHODS APD and CV were studied numerically during one-dimensional reentry as ring length (L) was shortened. A three-state variable model (u, v, w) was used to analyze the effect of gating variables of the fast (v) and slow (w) currents on the spatial and temporal dynamics of transmembrane potential (u). Three parameter sets were used corresponding to three APD and CV restitution curves. RESULTS Sustained spatial oscillations of APD and CV larger than the ring length were observed in two of the parameter sets (cytochalasin-D model [CYTO] and model 3 [M3]) before block occurred at L = 6 cm. The last model (diacetyl monoxime [DAM]) resulted in uniform APD and CV for all L until block occurred at L = 3 cm. Multivalued APD and CV restitution relationships due to "dephasing" of w and v with DI were observed in M3 and CYTO simulations. Overall, these dynamics could be explained by the wavelength-to-ring length ratio and the sensitivity of APD on the value of the gating variables w and v. CONCLUSION Propagation stability is mostly controlled by APD sensitivity to w, but the APD restitution slope does not always reflect this sensitivity. The interaction of the dynamic history (i.e., memory) of the fast and slow currents and electrotonic effects resulted in multivalued restitution curves.
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Affiliation(s)
- Xiaozhong Chen
- Department of Biomedical Engineering, University of Alabama at Birmingham, Birmingham, Alabama 35294-0019, USA
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Banville I, Chattipakorn N, Gray RA. Restitution Dynamics During Pacing and Arrhythmias in Isolated Pig Hearts. J Cardiovasc Electrophysiol 2004; 15:455-63. [PMID: 15089996 DOI: 10.1046/j.1540-8167.2004.03330.x] [Citation(s) in RCA: 72] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
INTRODUCTION The dependence of action potential duration (APD) on the preceding diastolic interval (DI), i.e., restitution, has been purported to predict the development of alternans and reentrant arrhythmias. However, restitution depends on the history of activation (i.e., memory), and its relevance to arrhythmia induction and maintenance is unknown. METHODS AND RESULTS Using a dual-camera video imaging system, we recorded action potentials from thousands of sites on the surface of the isolated pig heart. A steady-state pacing (SSP) protocol was performed to generate the SSP APD restitution curve. During SSP, the minimum DI and APD were 57 +/- 6 ms and 107 +/- 6 ms, respectively. The restitution slope was >1 for DIs <85 +/- 5 ms; however, alternans were not observed. Abrupt decreases in cycle length (CL) resulted in a rapid (<5 beats) decrease in APD followed by a slower decrease to "steady state." DI, APD pairs for the initial beats following these rate changes were significantly above the SSP restitution curve. DI, APD pairs measured during sustained ventricular fibrillation clustered significantly below the SSP restitution curve, at significantly shorter APDs (57 +/- 4 ms) and DIs (49 +/- 6 ms) than could be achieved during SSP. In addition, abrupt increases in CL following SSP resulted in APDs significantly shorter than those predicted from the SSP restitution curve. CONCLUSION Our results indicate that the responses of APD and DI to sudden rate changes and during arrhythmias are not predicted by the SSP restitution relationship. Acute dynamics act to damp out the proarrhythmic oscillations predicted from the SSP restitution curve.
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Affiliation(s)
- Isabelle Banville
- Department of Biomedical Engineering, University of Alabama at Birmingham, 1670 University Boulevard, Birmingham, AL 35294, USA
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Comtois P, Vinet A. Stability and bifurcation in an integral-delay model of cardiac reentry including spatial coupling in repolarization. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:051903. [PMID: 14682816 DOI: 10.1103/physreve.68.051903] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2002] [Revised: 04/25/2003] [Indexed: 05/24/2023]
Abstract
We present the bifurcation analysis of a revised version of the integral-delay model [Courtemanche et al., Siam J. Appl. Math. 56, 119 (1996)] of reentry in a one-dimensional ring that includes a spatial coupling in the calculation of the action potential duration. This coupling is meant to reproduce the modulation of repolarization by the diffusive current flowing through the intercellular resistance. We show that coupling modifies the criterion for the stability of the period-1 solution, which is no longer uniquely related to the action potential restitution curve, but depends also on the degree of coupling between cells and on the dispersion relation of the velocity. Coupling also changes the scenario from an infinite-dimension Hopf bifurcation to a finite sequence of Hopf bifurcations that take place at different ring lengths.
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Affiliation(s)
- Philippe Comtois
- Institute of Biomedical Engineering, Université de Montréal and Research Centre, Hôpital du Sacré-Coeur, 5400 Gouin W., Montréal (Québec), Canada H4J 1C5
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Arce H, Lopez A, Guevara MR. Triggered alternans in an ionic model of ischemic cardiac ventricular muscle. CHAOS (WOODBURY, N.Y.) 2002; 12:807-818. [PMID: 12779609 DOI: 10.1063/1.1499275] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
It has been known for several decades that electrical alternans occurs during myocardial ischemia in both clinical and experimental work. There are a few reports showing that this alternans can be triggered into existence by a premature ventricular contraction. Detriggering of alternans by a premature ventricular contraction, as well as pause-induced triggering and detriggering, have also been reported. We conduct a search for triggered alternans in an ionic model of ischemic ventricular muscle in which alternans has been described recently: a one-dimensional cable of length 3 cm, containing a central ischemic zone 1 cm long, with 1 cm segments of normal (i.e., nonischemic) tissue at each end. We use a modified form of the Luo-Rudy [Circ. Res. 68, 1501-1526 (1991)] ionic model to represent the ventricular tissue, modeling the effect of ischemia by raising the external potassium ion concentration ([K(+)](o)) in the central ischemic zone. As [K(+)](o) is increased at a fixed pacing cycle length of 400 ms, there is first a transition from 1:1 rhythm to alternans or 2:2 rhythm, and then a transition from 2:2 rhythm to 2:1 block. There is a range of [K(+)](o) over which there is coexistence of 1:1 and 2:2 rhythms, so that dropping a stimulus from the periodic drive train during 1:1 rhythm can result in the conversion of 1:1 to 2:2 rhythm. Within the bistable range, the reverse transition from 2:2 to 1:1 rhythm can be produced by injection of a well-timed extrastimulus. Using a stimulation protocol involving delivery of pre- and post-mature stimuli, we derive a one-dimensional map that captures the salient features of the results of the cable simulations, i.e., the {1:1-->2:2-->2:1} transitions with {1:1<-->2:2} bistability. This map uses a new index of the global activity in the cable, the normalized voltage integral. Finally, we put forth a simple piecewise linear map that replicates the {1:1<-->2:2} bistability observed in the cable simulations and in the normalized voltage integral map. (c) 2002 American Institute of Physics.
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Affiliation(s)
- Humberto Arce
- Departamento de Fisica, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-542, 04510 Mexico, Distrito Federal, Mexico
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Comtois P, Vinet A. Resetting and annihilation of reentrant activity in a model of a one-dimensional loop of ventricular tissue. CHAOS (WOODBURY, N.Y.) 2002; 12:903-922. [PMID: 12779615 DOI: 10.1063/1.1501175] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Resetting and annihilation of reentrant activity by a single stimulus pulse (S1) or a pair (S1-S2) of coupled pulses are studied in a model of one-dimensional loop of cardiac tissue using a Beeler-Reuter-type ionic model. Different modes of reentry termination are described. The classical mode of termination by unidirectional block, in which a stimulus produces only a retrograde front that collides with the activation front of the reentry, can be obtained for both S1 and S1-S2 applied over a small vulnerable window. We demonstrate that another scenario of termination-that we term collision block-can also be induced by the S1-S2 protocol. This scenario is obtained over a much wider range of S1-S2 coupling intervals than the one leading to a unidirectional block. In the collision block, S1 produces a retrograde front, colliding with the activation front of the pre-existing reentry, and an antegrade front propagating in the same direction as the initial reentry. Then, S2 also produces an antegrade and a retrograde front. However, the propagation of these fronts in the spatial profile of repolarization left by S1 leads to a termination of the reentrant activity. More complex behaviors also occur in which the antegrade fronts produced by S1 and S2 both persist for several turns, displaying a growing alternation in action potential duration ("alternans amplification") that may lead to the termination of the reentrant activity. The hypothesis that both collision block and alternans amplification depend on the interaction between the action potential duration restitution curve and the recovery curve of conduction velocity is supported by the fact that the dynamical behaviors were reproduced using an integro-delay equation based on these two properties. We thus describe two new mechanisms (collision block and alternans amplification) whereby electrical stimulation can terminate reentrant activity. (c) 2002 American Institute of Physics.
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Affiliation(s)
- Philippe Comtois
- Institute of Biomedical Engineering, Universite de Montreal, Montreal, Quebec, Canada
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