Oscillations of conduction, action potential duration, and refractoriness. A mechanism for spontaneous termination of reentrant tachycardias.

Frame, Lawrence H.; Simson, Michael B.

doi:10.1161/01.cir.78.5.1277

Cited by 172 publications

(88 citation statements)

References 34 publications

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“…For both cases, we find here that l is independent of L, in contrast to the oscillations produced by a pulse circulating in a ring where it is known that l Ӎ 2L͑͞2i 1 1͒ for weak dispersion [5] (with i integer and L ring perimeter). As will be discussed elsewhere, our theory applied to the ring shows that the bifurcation to alternans is finite dimensional with i 0 being the most unstable mode, in agreement with the fact that it is this mode that is generically selected in experiments [4] and ionic model simulations [5][6][7]. In addition, it shows that the gradient term ͑2w≠ x a͒ can lead to quasiperiodicity even in the absence of dispersion ͑c 0 0͒.…”

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confidence: 81%

Instability and Spatiotemporal Dynamics of Alternans in Paced Cardiac Tissue

2002

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We derive an equation that governs the spatiotemporal dynamics of small amplitude alternans in paced cardiac tissue. We show that a pattern-forming linear instability leads to the spontaneous formation of stationary or traveling waves whose nodes divide the tissue into regions with opposite phase of oscillation of action potential duration. This instability is important because it creates dynamically a heterogeneous electrical substrate for the formation of conduction blocks and the induction of fibrillation if the tissue size exceeds a fraction of the pattern wavelength. We derive an analytical expression for this wavelength as a function of three basic length scales related to dispersion and intercellular electrical coupling. DOI: 10.1103/PhysRevLett.88.208101 PACS numbers: 87.19.Hh, 05.45. -a, 05.45.Gg, 89.75. -k It is well established that the duration of cardiac excitation can oscillate from beat to beat at sufficiently short pacing interval [1]. Pioneering studies by Nolasco and Dahlen [2] and Guevara et al. [3] have demonstrated that the generic sequence LSLS . . . of long and short action potential duration (APD), known as alternans, is a direct consequence of the restitution relationshipbetween the APD generated by the nth 1 1 stimulus, APD n11 , and the diastolic time interval DI n during which the tissue recovers its resting properties after the end of the previous ͑nth͒ action potential. If we denote the interval between the nth and nth 1 1 stimulus by T n , we must have DI n T n 2 APD n . Then, for a fixed period: T n t for all n, Eq. (1) yields the map APD n f͑t 2 APD n21 ͒, whose slope f 0 typically increases with decreasing period. If the slope of the restitution curve exceeds unity, the map undergoes a period doubling bifurcation to alternans.Over the last decade, the study of alternans [4 -11], and their control [12], has become a main focus of research because of the potentially crucial link of this dynamical instability with cardiac fibrillation [13]. However, there is presently no simple analytical understanding of how the bifurcation to alternans is manifested spatiotemporally in paced cardiac tissue. Analytical progress to date is limited to the one-dimensional circulation of electrical impulse in a ring of tissue [5 -7].In this Letter, we derive an equation that governs the spatiotemporal dynamics of alternans close to the onset of instability. This enables us to obtain a quantitative analytical understanding of the formation of recently observed complex patterns of APD oscillations that can promote fibrillation [8 -11]. A crucial feature of these patterns is that the APD oscillates with opposite phases in two (or more) spatially extended regions of tissue, i.e., with a sequence LSLS . . . in one region and SLSL . . . in the other. These "discordant alternans" have been observed experimentally in both two-dimensional [8] and linear strands [9] of cardiac tissue, as well as in ionic model simulations [9][10][11]. Moreover, they have been shown to lead to the formation of conduction bl...

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confidence: 81%

Instability and Spatiotemporal Dynamics of Alternans in Paced Cardiac Tissue

2002

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“…They correspond to the onset of meander of the primary spiral wave, which is mathematically a transition to quasiperiodicity, and has been shown to cause quasiperiodic modulations of period and amplitude in heart tissue (29,50,51). Theoretical studies of cardiac wave propagation in one-dimensional rings of tissue (52) have attributed the onset of quasiperiodicity to APD restitution and the restitution of (dV/dt) max , and similar quasiperiodic modulations have been observed in rings of cardiac tissue (53).…”

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confidence: 75%

Quasiperiodicity and chaos in cardiac fibrillation.

et al. 1997

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In cardiac fibrillation, disorganized waves of electrical activity meander through the heart, and coherent contractile function is lost. We studied fibrillation in three stationary forms: in human chronic atrial fibrillation, in a stabilized form of canine ventricular fibrillation, and in fibrillationlike activity in thin sheets of canine and human ventricular tissue in vitro. We also created a computer model of fibrillation. In all four studies, evidence indicated that fibrillation arose through a quasiperiodic stage of period and amplitude modulation, thus exemplifying the "quasiperiodic transition to chaos" first suggested by Ruelle and Takens. This suggests that fibrillation is a form of spatio-temporal chaos, a finding that implies new therapeutic approaches. ( J. Clin. Invest. 1997. 99:305-314.)

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“…Steeply sloped restitution curves, ie, a large change in APD for a relatively small change in diastolic interval, have been shown to be associated with complex unstable dynamics. [5][6][7][8][9] Computer modeling and experiments have shown that increasing the steepness of APD restitution results in progressive instability and spiral wave breakup, 9,10 whereas reducing the slope by drugs suppresses ventricular fibrillation attributable to suppressing spiral breakup. 11,12 We have previously shown in a porcine model that adrenaline increases the slope of the ventricular APD restitution curve.…”

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Effect of Adrenergic Stimulation on Action Potential Duration Restitution in Humans

et al. 2003

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Background-Enhanced sympathetic activity facilitates complex ventricular arrhythmias and fibrillation. The restitution properties of action potential duration (APD) are important determinants of electrical stability in the myocardium. Steepening of the slope of APD restitution has been shown to promote wave break and ventricular fibrillation. The effect of adrenergic stimulation on APD restitution in humans is unknown. Methods and Results-Monophasic action potentials were recorded from the right ventricular septum in 18 patients.Standard APD restitution curves were constructed at 3 basic drive cycle lengths (CLs) of 600, 500, and 400 ms under resting conditions and during infusion of isoprenaline (15 patients) or adrenaline (3 patients). The maximum slope of the restitution curves was measured by piecewise linear regression segments of sequential 40-ms ranges of diastolic intervals in steps of 10 ms. Under control conditions, the maximum slope was steeper at longer basic CLs; eg, mean values for the maximum slope were 1.053Ϯ0.092 at CL 600 ms and 0.711Ϯ0.049 at CL 400 ms (ϮSEM). Isoprenaline increased the steepness of the maximum slope of APD restitution, eg, from a maximum slope of 0.923Ϯ0.058 to a maximum slope of 1.202Ϯ0.121 at CL 500 ms. The effect of isoprenaline was greater at the shorter basic CLs. A similar overall effect was observed with adrenaline. Conclusions-The

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Oscillations of conduction, action potential duration, and refractoriness. A mechanism for spontaneous termination of reentrant tachycardias.

Cited by 172 publications

References 34 publications

Instability and Spatiotemporal Dynamics of Alternans in Paced Cardiac Tissue

Instability and Spatiotemporal Dynamics of Alternans in Paced Cardiac Tissue

Quasiperiodicity and chaos in cardiac fibrillation.

Effect of Adrenergic Stimulation on Action Potential Duration Restitution in Humans

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