Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 2: multiple extrasystoles - PubMed (original) (raw)
Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 2: multiple extrasystoles
Zhilin Qu et al. Biophys J. 2006.
Abstract
Unidirectional conduction block of premature extrasystoles can lead to initiation of cardiac reentry, causing lethal arrhythmias including ventricular fibrillation. Multiple extrasystoles are often more effective at inducing unidirectional conduction block and reentry than a single extrasystole. Since the substrate for conduction block is spatial dispersion of refractoriness, in this study we investigate how the first extrasystole modulates this dispersion to influence the "vulnerable window" for conduction block by subsequent extrasystoles, particularly in relation to action potential duration restitution and conduction velocity restitution properties. Using a kinematic model to represent wavefront-waveback interactions and simulations with the Luo-Rudy model in a one-dimensional cable of cardiac cells, we show that in homogeneous tissue, a premature extrasystole can create a large dispersion of refractoriness leading to conduction block of a subsequent extrasystole. In heterogeneous tissue, however, a premature extrasystole can either reduce or enhance the dispersion of refractoriness depending on its propagation direction with respect to the previous beat. With multiple extrasystoles at random coupling intervals, vulnerability to conduction block is proportional to their number. In general, steep action potential duration restitution and broad conduction velocity restitution promote dispersion of refractoriness in response to multiple extrasystoles, and thus enhance vulnerability to conduction block. These restitution properties also promote spatially discordant alternans, a setting which is particularly prone to conduction block. The equivalent dispersion of refractoriness created dynamically in homogeneous tissue by spatially discordant alternans is more likely to cause conduction block than a comparable degree of preexisting dispersion in heterogeneous tissue.
Figures
FIGURE 1
(A) Schematic illustration of the S1 and S2 beats in a 1D space. S1 is always applied at x = 0, but S2 is applied in location l, which stimulates two opposite propagating waves (the S2 wave and S2* wave). θ is the wavefront velocity and Θ is the waveback velocity. (B) CV versus previous DI for normal (□) and 5-fold slowed (○) Na+ channel recovery, which are fit by Eq. 4 (line). (C) APD versus previous DI. The data are fit by Eq. 7 (solid line). The dashed line is an APD restitution curve by letting α = 0 and β = 0.4 in Eq. 7, which is a shallower APD restitution curve.
FIGURE 2
Induction of dispersion of refractoriness by a premature extrasystole in homogeneous tissue from the kinematic model (Eq. 3). Two cases were studied: all three stimuli were applied at the same end of the cable (A_–_C) and the S1 was applied at one end, but the S2 and S3 applied at the other end (D_–_F). (A) APD distribution in space (_a_2 versus x) of the S2 wave for normal (solid line) and fivefold-slowed (dashed line) Na+ channel recovery. _a_2 was obtained using with _d_1(x) solved from Eq. 8. (B) Vulnerable window (shaded area) for S3 for different S1S2 coupling interval (Δ_T_S1S2) obtained by numerically solving Eqs. 3–7 together for normal Na+ channel recovery. (C) w versus α (a parameter controls the slope of APD restitution curve in Eq. 7, as shown in Fig. 1 C) for normal (▪) and fivefold-slowed (□) Na+ channel recovery. w was calculated for the minimum S1S2 interval (Δ_T_S1S2 = 211 ms) that S2 propagates successfully. (D_–_F) Same as A_–_C but for S1 being applied at one end and S2 and S3 applied at the other end of the cable. w in F was calculated at Δ_T_S1S2 = 283 ms for normal Na+ channel recovery. “S2 failure” in B and E indicates the S1S2 interval is too short for S2 to stimulate the S2 wave. In numerical simulation, conduction block was considered to occur if _d_2(x) < _d_c at any location x.
FIGURE 3
Induction of dispersion of refractoriness and conduction block in homogeneous 1D cable of the LR1 model. The S1 was applied at one end whereas S2 and S3 were applied at the other end. (A) APD gradient induced by S2 for normal Na+ recovery with Δ_T_S1S2 = 280 ms (solid line) and for fivefold-slowed Na+ channel recovery with Δ_T_S1S2 = 287 ms (dashed line). (B) Vulnerable window (shaded area) of conduction block of the S3 beat for different S1S2 coupling intervals with normal Na+ channel recovery. “S2 failure” indicates an S1S2 interval is too short for S2 to stimulate the S2 waves. (C) Vulnerable window size w versus the induced maximum APD difference Δ_a_ for normal Na+ channel recovery (▪) and slowed Na+ channel recovery (□). Data were obtained from different S1S2 coupling intervals.
FIGURE 4
Modulation of dispersion of refractoriness and induction of reentry in a heterogeneous 1D cable using the LR1 model. (A) APD distribution in space of the S2 beat for different S1S2 coupling intervals (from top to bottom, Δ_T_S1S2 = 600 ms, 400 ms, 300 ms, and 250 ms) when S1, S2, and S3 were applied at the same end of the cable for an ascending APD gradient generated using Eq. 2. (B) Vulnerable window of conduction block of the S3 beat for different S1S2 coupling interval for the case as in A. The shaded area marked “S2 wave block” is the vulnerable window of conduction block of the S2 wave. “S2 failure” indicates the S1S2 interval is too short for S2 to stimulate the S2 waves. (C) APD distribution in space of the S2 beat for different S1S2 coupling interval (from top to bottom, Δ_T_S1S2 = 600 ms, 400 ms, 300 ms, and 270 ms) when S1 was applied in one end and S2 and S3 were applied at the other end of the cable for a descending APD gradient generated using Eq. 2 by exchanging the and
values. (D) Vulnerable window of conduction block of the S3 beat for different S1S2 coupling interval for the case as in C. “S2 failure” indicates the S1S2 interval is too short for S2 to stimulate the S2 waves. (E) APD distribution in space of the S2 beat for different S1S2 coupling intervals (from top to bottom, Δ_T_S1S2 = 600 ms, 270 ms, and 250 ms) when S1 and S2 were applied at the same end of the cable for a descending APD gradient as in C. (F) APD distribution in space of the S2 beat for different S1S2 coupling interval (from top to bottom, Δ_T_S1S2 = 600 ms, 340 ms, and 312 ms) when S1 was applied in one end and S2 was applied at the other end of the cable for an ascending APD gradient as in A.
FIGURE 5
Induction of dispersion of refractoriness by multiple extrasystoles in homogeneous 1D cable from the kinematic model (Eq. 3). (A) APD distribution in space for the S1, S2, S3, and S4 beats, which were applied at the same end of the cable. Δ_T_S1S2 = 211 ms, Δ_T_S2S3 = 65 ms, and Δ_T_S3S4 = 125 ms. (B) The vulnerable window w (shaded area) for the S5 beat versus the S3S4 interval for Δ_T_S1S2 = 211 ms and Δ_T_S2S3 = 65 ms. Inset shows w for Δ_T_S1S2 = 211 ms and Δ_T_S2S3 = 200 ms.
FIGURE 6
Induction of dispersion of refractoriness by multiple extrasystoles in homogeneous 1D cable of the LR1 model. Shown are APD distributions for the S1, S2, S3, and S4 beats, which were applied at the same end of the cable. (A) Normal Na+ channel recovery. Δ_T_S1S2 = 220 ms, Δ_T_S2S3 = 100 ms, and Δ_T_S3S4 = 150 ms. (B) Fivefold slowed Na+ channel recovery. Δ_T_S1S2 = 230 ms, Δ_T_S2S3 = 110 ms, and Δ_T_S3S4 = 170 ms.
FIGURE 7
Vulnerability to conduction block caused by multiple random extrasystoles. (A) The percentage of the simulations that conduction block occurred versus the number of random extrasystole applied for normal (▪) and fivefold-slowed (□) Na+ channel recovery in a homogeneous 1D cable by numerically solving Eq. 17. The stimulus was given when _d_n(0) > _d_0 with _d_0 = d_c + 60_ξ. ξ is a random number uniformly distributed between [0,1]. Conduction block is considered to occur when _d_n(x) < _d_c at any location _x_ and for any beat number _n_. Eqs. 4 and 7 were used. The total number of simulations for each data point is 2000 and the percentage is calculated as the portion of the 2000 simulations in which conduction block was observed. (_B_) The percentage of simulations in which conduction block occurs versus _α_ (Eq. 7) by numerically solving Eq. 17. The number of random stimuli is nine. (_C_) The percentage of the simulations that conduction block occurred versus number of random extrasystoles applied for normal (▪) and fivefold-slowed (□) Na+ channel recovery in a homogeneous 1D cable of the LR1 model. All extrasystoles were applied at the same end of the homogeneous cable. Control parameters were used. The extrasystole was given when _d_n(0) > _d_0 with _d_0 = _d_c + 60 ξ. The percentage was calculated as the number of simulations in which conduction block occurs against the total simulations for each random extrasystoles case. The total number of simulations for each case is 500.
FIGURE 8
Induction of dispersion of refractoriness and conduction block due to spatially discordant alternans in homogenous 1D cable. Control parameters were used except for the j gate of the Na+ channel. (A) APD distribution in space for two consecutive beats for PCL = 175 ms in the case of normal Na+ channel recovery. (B) APD distribution in space for two consecutive beats for PCL = 200 ms in the case of fivefold-slowed Na+ channel recovery. (C) The induced refractory barrier Δ_a_ (solid symbols) by discordant APD alternans and vulnerable window w (open symbols) for the S2 wave versus PCL for normal (triangles) and slowed (squares) Na+ channel recovery. Δ_a_ was defined as the APD difference between a minimum and its neighboring maximum in one beat (the beat marked by the open circles was used). (D) w versus Δ_a_ for the case of slowed Na+ channel recovery. The vulnerability to conduction block was examined by a S2 stimulus after a 30 beats APD alternans. The APD distribution in A and B was for 29th beat (•) and 30th beat (○).
FIGURE 9
Vulnerable windows for different S1 wavefront velocities, but the same spatial APD gradient, with normal and fivefold-slowed Na+ channel recovery. (Solid bar) Obtained by solving Eq. 3 with constant S1 wavefront velocity, i.e., . (Shaded bar) Obtained by solving Eq. 3 with S1 wavefront velocity varies as in the discordant alternans, i.e.,
. (Open bar) From LR1 model in homogeneous 1D cable. Normal recovery: the spatial APD distribution of the S1 beat is
, which was fit from the 30th beat (for x = 0–24 mm) of the discordant alternans shown in Fig. 8 A.
in which
was fit from the 29th beat (for x = 0–24 mm) in Fig. 8 A. PCL = 175 ms. Fivefold slowed recovery: the spatial APD distribution of the S1 beat is
, which was fit from the 30th beat (for x = 0–22 mm) of the discordant alternans shown in Fig. 8 B.
in which
was fit from the 29th beat (for x = 0–22 mm) in Fig. 8 B. PCL = 200 ms. Note that during discordant alternans, the cycle length CL(x) is not constant in space but varies, however, in a magnitude much smaller than APD; therefore, it is reasonable for us to calculate _d_1(x) using PCL instead of CL(x).
References
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