Alternans resonance and propagation block during supernormal conduction in cardiac tissue with decreased [K(+)](o)

Abstract

Cardiac restitution is an important factor in arrhythmogenesis. Steep positive action potential duration and conduction velocity (CV) restitution slopes promote alternans and reentrant arrhythmias. We examined the consequences of supernormal conduction (characterized by a negative CV restitution slope) on patterns of conduction and alternans in strands of Luo-Rudy model cells and in cultured cardiac cell strands. Interbeat intervals (IBIs) were analyzed as a function of distance during S1S2 protocols and during pacing at alternating cycle lengths. Supernormal conduction was induced by decreasing [K(+)](o). In control [K(+)](o) simulations, S1S2 intervals converged toward basic cycle length with a length constant determined by both CV and the CV restitution slope. During alternant pacing, the amplitude of IBI alternans converged with a shorter length constant, determined also by the action potential duration restitution slope. In contrast, during supernormal conduction, S1S2 intervals and the amplitude of alternans diverged. This amplification (resonance) led to phase-locked or more complex alternans patterns, and then to distal conduction block. The convergence/divergence of IBIs was verified in the cultured strands, in which naturally occurring tissue heterogeneities resulted in prominent discontinuities of the spatial IBI profiles. We conclude that supernormal conduction potentiates alternans and spatial analysis of IBIs represents a powerful method to locate tissue heterogeneities.

Figure 1

Theoretical considerations on the stability of conduction and on the deviation of the interbeat interval from BCL as a function of distance, for (A) normal conduction during an S1S2 protocol, (B) supernormal conduction during an S1S2 protocol, and (C) supernormal conduction during an alternant pacing protocol. See text for details.

Figure 2

S1S2 APD and CV restitution curves in the LR-I model fiber in (A) normal and (B) decreased [K⁺]_o, for different BCLs as indicated. The markers on the curves indicate the steady-state points, for which BCL = APD + DI. The tangents illustrate the slopes of the restitution curves at these operating points (α and γ, respectively, values indicated).

Figure 3

Time-course of final repolarization (top), I_Na availability (middle), and S1S2 CV restitution curves (bottom) in the minimal LR-I model, for (A) V_rest corresponding to [K⁺]_o = 5.4 mmol/L and (B) V_rest corresponding to [K⁺]_o = 2.0 mmol/L. Simulation results are shown for two repolarization time constants (30 and 10 ms). Solid lines correspond to the nominal I_Na formulation and dashed lines were obtained by disabling the j gate of I_Na, simulating accelerated recovery from inactivation. Time is measured from repolarization to −60 mV, defining the beginning of the DI.

Figure 4

Behavior of IBI(x) in the LR-I model fiber during (A) the S1S2 protocol and (B) the alternant pacing protocol, in normal [K⁺]_o (left panels) and decreased [K⁺]_o (right panels). The BCLs are the same as those for which restitution curves are presented in Fig. 2. Similar to Fig. 1, open circles (on the right side of the plots) indicate a stable point, shaded circles an unstable point, and dotted circles approximate the stable alternating state. The dotted shaded lines represent exponential functions with length constants calculated according to Eqs. 2 and 4 with Λ_S1S2 = 8.1 cm for normal [K⁺]_o and −28.9 cm for low [K⁺]_o (in A), and Λ_alt = 1.4 cm for normal [K⁺]_o and −5.9 cm for low [K⁺]_o (in B), respectively.

Figure 5

Behavior of ΔIBI(x), Λ_S1S2, and Λ_alt in cultured cardiomyocyte strands. (A) ΔIBI(x) in one preparation during the S1S2 protocol, in normal [K⁺]_o (left) and decreased [K⁺]_o (right). Same format as in Fig. 4A. The vertical markers correspond to the positions of operational electrodes. The dotted shaded curves are exponential fits to the data. (B) A_even(x) and A_odd(x) from the same preparation during alternant pacing. Same format as in panel A and Fig. 4 B. (C) (Top) Summary of Λ_S1S2 and Λ_alt values (represented as their reciprocals 1/Λ) as a function of γ/c^∗2 (according to Eqs. 2 and 4) for all preparations (n = 9). Vertical lines connect data points corresponding to the same preparation in the same [K⁺]_o. The oblique solid line corresponds to Λ_S1S2 = c^∗2/γ (Eq. 2) and the dashed line to Λ_S1S2 = c^∗2/2γ (Eq. 4 with α = 0). (Bottom) Corresponding ratios Λ_alt/Λ_S1S2, and values of α according to Eq. 4.

Figure 6

Analysis of conduction, CV restitution, and interbeat intervals in a heterogeneous cardiomyocyte strand. (A) Steady-state activation profile during pacing at BCL = 125 ms in normal [K⁺]_o. Data points correspond to operational electrodes. The arrow denotes a segment in which conduction was depressed (between x = 4.8 and 5.06 cm). (B) S1S2 CV restitution curves established globally for the entire strand and for the depressed segment, in normal [K⁺]_o (left) and decreased [K⁺]_o (right). The curves represent exponential fits to the data. (C) Deviation of the interbeat interval from BCL as a function of distance during S1S2 protocols (ΔS1S2(x), solid) and during the alternant pacing protocol (A_even(x) and A_odd(x), bold shaded traces) in normal [K⁺]_o. The vertical markers correspond to the positions of operational electrodes. (D) Same as panel C, but in decreased [K⁺]_o.