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Department of Physiology, University of Bern, Bern, Switzerland
Submitted 21 July 2006 ; accepted in final form 30 November 2006
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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tachyarrhythmia; microelectrode arrays; conduction velocity; conduction block; mathematical modeling; integrative electrophysiology; cell culture; ventricular myocytes
If heart rate is abruptly accelerated, an increase in the probability of unidirectional conduction block (UCB) to occur at structural discontinuities will increase the likelihood of reentry initiation. After the onset of reentry, an increased probability of block may contribute to either wave break formation or termination of reentry. Moreover, changes in conduction velocity (CV) will have a direct impact on the stability of circus movement by modulating head-tail interactions (29). Therefore, the dynamics of CV and of the probability of block consecutively to an abrupt increase in heart rate are decisive in determining the initiation or the spontaneous termination of reentry.
Numerous studies have explored the rate-dependent behavior of the cardiac action potential (AP) at the single-cell level and the rate dependence of propagation at the tissue level. However, there is still a need to better link the experimental observations at the cellular level to those at the tissue level to gain a deeper understanding of ionic mechanisms underlying the rate-dependent dynamics of cardiac conduction. Most previous investigations have been carried out in tissue fragments, in intact tissue (7, 65), or in cardiac patients (15, 19), in which effects of tissue anisotropy, wave front curvature, tissue discontinuities, and disease status on conduction properties play an additional role. Furthermore, most studies have focused on the dependence of conduction characteristics on pacing rate at steady state or on the prematurity of single impulses (7, 15), and only a few studies have addressed the transient dynamics of CV or UCB upon changes in pacing rate (65).
In the present study, we used patterned cardiomyocyte cultures, a technique permitting control of tissue architecture, to examine the dynamics of CV in cell strands and UCB across tissue expansions during rapid pacing. In simulations of conduction, we assessed the underlying ionic processes. We have shown that conduction characteristics can follow different and even opposite evolutions, depending on the interplay between changes in AP duration (APD), rate-dependent changes of intracellular Na+ ([Na+]i) and Ca2+ concentrations ([Ca2+]i), postrepolarization refractoriness, and discontinuities in tissue structure.
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MATERIALS AND METHODS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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60 min. Pacing and recording. As shown in Fig. 1, the preparations were stimulated using platinum-coated dipoles with biphasic voltage pulses of opposite polarity (amplitude: 0.5–2.5 V, duration of each phase: 2 ms). The preparations were paced for 1 min at a basic cycle length (BCL) of 500 ms. The cycle length (CL) was then reduced to a given test CL for a period of 1 min. Finally, pacing at the initial BCL was resumed for 1 min. This protocol was repeated after a resting period of 5–10 min for different test CLs (in steps of 10 ms). Only experiments with continuous 1:1 stimulus capture during the entire protocol and in which CV was stable after the first minute of pacing at a BCL of 500 ms were used for further analysis.
Extracellular unipolar electrograms were recorded from rows of 12 indium-tin oxide microelectrodes (spacing: 0.5 mm) and sampled at 10 kHz. Activation times were defined at the occurrence of the minimum of the first derivative of the extracellular electrograms (30).
In the strands (width: 100–150 µm), CV was computed by linear regression of activation times recorded along the preparation. Only strands in which conduction was uniform (r > 0.999) were used. The combination of patterned growth techniques and multisite extracellular recordings obtained using MEAs permitted an accurate beat-to-beat assessment of CV in cardiac tissue structures with a controlled geometry and during pacing protocols lasting several minutes. This would not have been feasible with the use of optical mapping techniques because of the significant phototoxic damage exerted by voltage-sensitive dyes after prolonged illumination (54).
Across tissue expansions (150-µm-wide strands expanding into rectangular monolayers), the conduction delay was quantified as previously described (Ref. 50; further details in RESULTS). In case of block, the fraction of blocked impulses was calculated from the conduction ratio (e.g., a 5:4 conduction ratio corresponds to 20% of blocked impulses).
Additional experiments were performed with expansions of 40-, 60-, and 80-µm-wide strands. These preparations were paced on the side of the strand for 1-min periods at a BCL of 1,000 ms, followed by 1-min periods at the shortest CL at which UCB occurred within the first 30 s. Because it was not possible to adequately align strands with a width <100 µm with the microelectrodes, these preparations were grown on glass substrates. The capture of the stimuli and the success or failure of conduction across the expansions were assessed via identification of contractions in digital video recordings (30 frames/s) by using principal component analysis of the video signal from 5 x 5-pixel regions 300–400 µm before the expansion and immediately after the expansion, respectively. This approach is similar to that described by Hwang et al. (24), who used video signal analysis to monitor contractions and infer conduction patterns in cardiac cell cultures.
Optical AP recordings. To evaluate the effect of an abrupt change in pacing rate on APD, we performed optical AP recordings as described previously (51) in disk-shaped monolayer cultures (diameter: 8 mm) grown on glass substrates. The cultures were stained with the voltage-sensitive dye di-8-ANEPPS and superfused with HBSS at 36°C. The preparations were paced using a protocol analogous to that described above. The emitted fluorescence was recorded using a custom-made tandem-lens macroscope (Rodenstock, Dübendorf, Switzerland; f = 50 mm) and a fast CMOS camera (MiCAM Ultima; SciMedia, Irvine, CA; acquisition rate: 1 kHz; 100 x 100 pixels, corresponding to an area of 1 x 1 cm of the preparation). To minimize distortion of APs by motion artifacts and to maximize the signal-to-noise ratio (peak to peak: 5.6 ± 1.5 for the raw signal from individual pixels), we selected a region of interest along an activation isochrone over which the signal was integrated. After integration, the signal-to-noise ratio was 24.7 ± 6.6 (peak to peak). However, this low ratio still precluded an accurate determination of APD at 95% of repolarization (APD95) because of the slow rate of final repolarization. We observed that the precision of APD95 determination was not significantly increased by filtering the signal (a 100-Hz low-pass filter was used) and that the determination of APD at 50% of repolarization (APD50) was less sensitive to noise and filtering. Therefore, APD was measured at 50% of repolarization.
We noted that the phototoxic damage exerted by the dye induces a progressive prolongation of APD. This photodynamic effect also progresses during the periods between successive illuminations. Therefore, recordings were limited to the second last and last APs at the end of a 1-min period of pacing at a BCL of 500 ms and to the subsequent premature impulse delivered after a coupling interval of 250 ms. Only recordings from preparations that had not been illuminated before were used.
To optically establish CV and APD restitution curves over the range of CLs used in MEA experiments, we performed additional experiments in patterned 600-µm-wide strands grown on glass substrates, using a microscopic recording system as described previously (51). The cultures were stained and superfused in the same way as in the experiments with disk-shaped monolayers. The strands were paced using a protocol analogous to that used in the experiments with the MEAs (1 min of pacing at a BCL of 500 ms, followed by an abrupt transition to pacing at a test CL). Optical signals of the last AP at the end of the pacing period at a BCL of 500 ms and the subsequent premature impulse were collected using a x20 objective (Fluar; Carl Zeiss, Feldbach, Switzerland) with 4 rows of 19 optical fibers. The mapped region was changed to another strand or strand segment for each recording, ensuring that no recording was obtained from a region illuminated twice. To avoid movement artifacts, which are prominent in microscopic recordings, we added the excitation-contraction uncoupler cytochalasin D (20 µmol/l; Sigma-Aldrich) to the superfusion solution. Previous studies have shown that this agent can be used for optical mapping of cardiac APs without affecting APD, APD restitution, or CV (33, 74). Control recordings of propagating APs with and without cytochalasin D confirmed that this uncoupler did not significantly affect AP parameters in our cultures. APD was measured at 50% of repolarization.
Modeling of conduction.
The Pandit-Clark-Giles-Demir (PCGD) model of the adult rat left epicardial ventricular myocyte (45) without EGTA buffer was used to simulate conduction in strands of 61 cells and in strands merging into an expansion. We observed that the original model exhibits early afterdepolarizations at pacing rates >2 Hz due to insufficient inactivation and excessive reactivation of the L-type Ca2+ current (ICa,L). Therefore, we modified the equation for the time constant of the ICa,L inactivation gate f11 as follows to accelerate its kinetics at potentials greater than –15 mV:
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This modification (involving the second term of the equation) results in lower and monotonically decreasing values of 
f11 at potentials greater than –15 mV instead of increasing values of f11 with voltage in the original formulation [see 
Fig. 3C in Pandit et al. (45)]. This modification is in agreement with the results of Berjukow et al. (2) showing that the time constant of the decay of ICa,L does not exhibit an increase at potentials greater than –15 mV. Furthermore, based on a study by Stengl et al. (66) showing that the time constant of the rapid inactivation gate of the transient outward current (Ito) in the rat is <35 ms at positive membrane potentials, we reduced the time constant of its fast inactivation gate by 5%.
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95% repolarization). The initial conditions were obtained from a cell that was kept at rest until all ion concentrations had reached steady state. Thus the initial conditions for modeling of conduction were analogous to the initial conditions in our in vitro experiments, in which the pacing protocol was initiated in preparations that had remained quiescent for several minutes.
Statistics. Values are given as means ± SD; n represents the number of distinct preparations used. Data were compared using analysis of variance or the Student's t-test, where appropriate. P < 0.05 was considered significant.
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RESULTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Each strand was first paced for 1 min at a basic cycle length (BCL) of 500 ms. Subsequently, CL was abruptly reduced to a given test CL during 1 min. Thereafter, pacing at a BCL of 500 ms was resumed. This protocol was repeated with different test CLs, decreasing in steps of 10 ms. For each strand, we determined two values of test CL, termed "short CL" (SCL) and "critical CL" (CCL): SCL was defined as the CL that decreased CV slightly by 1–3 cm/s; CCL was defined as the shortest CL able to maintain 1:1 capture during the entire protocol. For all experiments (n = 10), SCL was 281 ± 27 ms and CCL amounted to 189 ± 35 ms. The fact that CCL was much longer than APD (APD95 is in the range of 100–150 ms at a BCL of 500 ms; see Fig. 4) suggests the presence of postrepolarization refractoriness (20).
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The changes described in Fig. 2A were consistently observed in all 10 experiments, as shown in Fig. 2B. During pacing at CCL, the minimum CV was reached after 4–15 s. Recovery of CV to the level present before rapid pacing was observed in all experiments.
Computation of rate-dependent dynamics of the velocity of continuous propagation. A modeling study of the rate dependence of continuous propagation was conducted to gain mechanistic insights into the CL-dependent temporal behavior of CV. In a strand of normally coupled cells formulated using the PCGD model, we evaluated the involvement of depolarizing Na+ current (INa), intracellular accumulation of Na+, and rate-dependent changes of APD on CV. The strand was stimulated in a manner analogous to the experiments shown in Fig. 2.
The behavior of CV and related critical model parameters are shown in Fig. 3. The model reproduced closely the changes in CV observed experimentally during rapid pacing (Fig. 3A). Specifically, CV during pacing at SCL exhibited the initial rapid decrease. However, in the model, CV continued to decrease, although at a much lower rate. Pacing at CCL induced a biphasic behavior of CV consisting of an initial decrease during the first 13 s, followed by a subsequent increase. Near the end of pacing at CCL, CV slightly decreased again. These dynamics were correlated to the behavior of peak INa. Changes in INa directly determined the evolution of CV during pacing at both SCL and CCL. This confirmed the well-known role of INa in continuous propagation (52, 58).
The model study allowed us to discern an initial and a delayed mechanism for the changes in INa. The initial rapid decrease of INa and CV occurred during the first 4 s at SCL and the first 13 s at CCL, respectively. It was related to an increase in APD caused by a decrease in the transient outward current, Ito. AP prolongation then led to a decreased availability of INa, as visualized by the decrease in the product of the inactivation gating variables h x j, a parameter that characterizes recovery of INa from inactivation. The delayed changes in peak INa and, accordingly, in CV occurred after the initial rapid decrease of INa during the rest of the rapid pacing period. They were due to intracellular Na+ accumulation (which decreased the Na+ Nernst potential, ENa; not shown) and accelerated Na+/K+ pumping. In the case of pacing at SCL, the dominating effect of the increase in [Na+]i was to decrease ENa, peak INa, and, thus, CV. In the case of pacing at CCL, the acceleration of the Na+/K+ pump by increasing [Na+]i led to a shortening of APD. This shortening enhanced the recovery of INa from inactivation and produced a larger peak INa despite the decreased transmembrane Na+ gradient and ENa. The intracellular accumulation of Na+ finally led to a decreased driving force for INa by further diminishing ENa and, consequently, to a last stage (last 30 s of rapid pacing) during which CV resumed to decrease.
ICa,L exhibited rate-dependent dynamics similar to the behavior of INa. The increasing Ca2+ in the subsarcolemmal compartment during rapid pacing did not result in a significant Ca2+-based inactivation of ICa,L (not shown). Furthermore, because the reversal potential of ICa,L is constant in the PCGD model formulation (+65 mV), the changes in ICa,L could not be explained by changes in the transmembrane [Ca2+] gradient. Thus the rate-dependent changes in peak ICa,L were predominantly determined by its voltage-dependent recovery kinetics, which, in turn, were mainly influenced by APD.
The minimal diastolic potential (MDP) exhibited a slight rate-dependent increase from –80.4 mV at a BCL of 500 ms to –79 mV at SCL and –77 mV at CCL. Because the kinetics of the slow inactivation gate j are strongly voltage dependent in this range (the corresponding values of j are 87, 103, and 133 ms), the slight increase of MDP contributed to slow INa recovery at high pacing frequencies and thus to postrepolarization refractoriness (5, 46).
To further explain the effect of postrepolarization refractoriness on conduction dynamics, we performed the simulation shown in Fig. 3A at a CCL of 170 ms with j scaled by a factor 0.3 (not shown). In the control simulation, CV decreased (49%) from 39.0 cm/s before rapid pacing to the minimal value of 19.8 cm/s during rapid pacing. When j was scaled by 0.3 (i.e., 3.3 times faster recovery of INa), CV decreased by a smaller extent (29%). The dynamics of APD differed only minimally. Thus postrepolarization refractoriness due to a large j potentiated the influence of APD prolongation on CV during rapid pacing.
The interdependence of CV, INa, APD, and repolarizing Na+/K+ pump current on [Na+]i was verified by resetting [Na+]i to the nominal model value after each beat in the computer model. In this situation, as shown in Fig. 3B, only the initial Ito-dependent decrease of CV and APD was present, whereas the subsequent changes in model parameters during rapid pacing were not observed.
As indicated by vertical lines and markers in Fig. 3A, the level to which [Na+]i was reset in Fig. 3B was reached after 40 s at SCL and 30 s at CCL, respectively, in free-running [Na+]i control simulations. At these time points, model parameters (circles in Fig. 3A) had the same values as those at steady state during [Na+]i resetting. To verify the dependence of model parameters on [Na+]i, we carried out the resetting simulations of Fig. 3B at different values of [Na+]i (9, 10, and 12 mmol/l; not shown). The changes presented in Fig. 3B were larger at smaller [Na+]i. However, the steady-state level of model parameters always corresponded to the values observed in the free-running [Na+]i control simulations at the time point when [Na+]i reached the resetting value. This indicates that beyond the initial phase of rapid changes governed by Ito adaptation, the evolution of model parameters was essentially determined by [Na+]i. Furthermore, this explains the overshoot of APD at CCL and the undershoot of CV in Fig. 3A relative to that in Fig. 3B, which occurred at a time point (13 s) when [Na+]i had not yet reached the value at which it was reset in Fig. 3B.
Experimental investigation of the behavior of APD at the transition to rapid pacing. To evaluate the effect of an abrupt change in pacing rate on APD, we obtained optical AP recordings in monolayer cultures, as shown in Fig. 4. The optical signal was recorded for the second last and last APs at the end of a 1-min pacing period at a BCL of 500 ms, as well as for the first premature impulse introduced at a coupling interval of 250 ms. Figure 4A shows three frames (at intervals of 5 ms) during concentric wave front propagation in one preparation (CV = 35 cm/s). Figure 4B shows the optical signal, integrated over the region of interest marked along the wave front in the second frame of Fig. 4A. The duration of the three APs was 57, 57, and 61 ms, respectively. As shown in Fig. 4C, in a total of five preparations, APD was not statistically different between the second last and the last impulse during pacing at a CL of 500 ms. In contrast, APD of the premature impulse was significantly longer by 6%. This prolongation was in the same range as that observed in the simulations for the first AP during rapid pacing (see Fig. 3).
Comparative investigation of CV and APD restitution curves in the cultures and in the PCGD model. It is well known that APD and CV restitution play an essential role in determining the dynamics of conduction in cardiac tissue (47). To examine the behavior of the experimental preparations and the PCGD model in terms of restitution properties, we compared CV restitution curves based on the experiments shown in Fig. 2B to CV restitution curves obtained from the PCGD model strand. In addition, optical recordings of APs in patterned strands were conducted to construct CV and APD restitution curves for the first premature impulse at CLs in the range of those used in the experiments with MEAs.
Figure 5A depicts experimental CV restitution curves (as a function of CL) for 1) the first impulse during rapid pacing (corresponding to a classic S1S2 restitution protocol), 2) at the time of the minimal CV during the first 15 s of rapid pacing (point b in Fig. 2), and 3) at the end of the 1-min rapid pacing train (point c in Fig. 2). The corresponding CV restitution curves of the PCGD model, presented in Fig. 5B, were similar to the experimental data in Fig. 5A. CV restitution was characterized by a slow recovery of CV extending over >100 ms, compatible with slow INa recovery and postrepolarization refractoriness. Moreover, the restitution curves obtained after a prolonged period of pacing [also called "dynamic restitution" (26, 67)] were steeper than the curves obtained for the S1S2 protocol, reflecting the mono- or biphasic adaptation of CV as shown in Figs. 2 and 3.
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Interestingly, the APD restitution curve (Fig. 5D) was multiphasic. APD increased (to 104.0 ± 3.0% of the control value, n = 12, P < 0.05) when CL was decreased from 500 to 300 ms and increased further at a CL of 250 ms (to 107.0 ± 2.8%, n = 6, P < 0.05). APD then decreased when CL was shortened <250 ms, but APD nevertheless remained longer than the reference value at the BCL of 500 ms. At all test CLs, APD of the premature impulse was significantly longer than APD at a BCL of 500 ms (n 5, P < 0.05). This confirms our observation in monolayer cultures that APD is prolonged at the onset of rapid pacing (see Fig. 4) over the range of CLs used in the MEA experiments. Moreover, the APD increase observed at a CL of 250 ms was similar and not statistically different from the increase observed in the monolayers in the absence of cytochalasin D (Fig. 4), supporting the notion that this agent does not alter the electrophysiology of the cultured cells.
APD restitution curves were established for the PCGD model and are shown in Fig. 5E. The slopes of the APD restitution curves were negative over the entire range of CLs tested. In both the experiments and the model, the fact that APD was longer at all CLs compared with control values at a BCL of 500 ms (associated with the existence of negative slopes in the APD restitution curves) is therefore in accordance with AP prolongation upon the transition to a faster pacing. This behavior of APD is characteristic for our preparations and for the PCGD model (as illustrated further in Fig. 5F) and was observed previously in rat cardiomyocytes (59, 60, 62, 71, 72). In the model, APD of the first premature impulse increased by 10% at a CL of 250 ms, which is comparable to the 6% increase observed in the optical experiments with monolayers and patterned strands (Figs. 4 and 5D, respectively).
Theoretical investigation of the effects of intracellular Ca2+ accumulation and ICa,L on rate-dependent changes of CV. It has been suggested that the rise in intracellular [Ca2+] during tachyarrhythmias may contribute to slow conduction (35, 64). To evaluate the function of intracellular Ca2+ homeostatic mechanisms in modulating continuous conduction, we explored the role played by Ca2+ accumulation in the model by resetting the [Ca2+] in all cell compartments to the end-diastolic values after 1 min of pacing at a BCL of 500 ms. This permitted us to pinpoint the effects of intracellular Ca2+ accumulation particularly after the onset of rapid pacing. The strand was stimulated using the pacing protocol with CCL (170 ms, as in Fig. 3). As shown in Fig. 6A, [Ca2+] resetting led to a less pronounced increase of APD during rapid pacing. This was caused by enhanced reverse-mode function of the Na+/Ca2+ exchanger due to increasing [Na+]i (which was not reset) during rapid pacing. In addition to the increasing repolarizing Na+/K+ pump current (INaK), the enhanced outward Na+/Ca2+ exchange current (INaCa) reduced the prolongation of APD. The resulting longer diastolic intervals permitted a more complete recovery of INa, leading to a less prominent decrease of CV. The biphasic behavior of APD and CV at CCL was abolished. After the initial rapid decrease of CV due to the initial APD prolongation, CV continued to decrease slowly. This slow decrease was due to decreasing ENa linked to increasing [Na+]i. The shorter diastolic intervals favored recovery of ICa,L from inactivation as well, resulting in an increased peak ICa,L. However, the net effect on APD was dominated by the increasing INaK and the enhanced outward INaCa.
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Rate dependence of conduction in a discontinuous structure. Discontinuous propagation in cardiac tissue is caused by the specific arrangement of myocyte bundles and tissue layers in the atria and ventricles. The common denominator of discontinuous propagation across sites of changing tissue geometry such as tissue expansions (18, 50, 53, 54, 70), isthmuses (6), and pivot points (21) is the mismatch between the depolarizing source current supplied by the front of the propagating AP and the electrical load downstream. To study the influence of a site of source-to-load mismatch on conduction during changes in the frequency of excitation, we assessed propagation across abrupt tissue expansions (cell strands merging into rectangular monolayers) in patterned growth cultures, using a pacing protocol analogous to the linear structures described above.
In a first series of experiments, we tested the rate dependence of propagation across expansions of strands with a relatively large width of 150 µm. As shown in a previous experimental and computational studies, this strand width produces a low degree of source-to-load mismatch (18). Figure 7, A and B, depicts the behavior of the conduction delay across the expansion in one experiment during pacing at SCL and CCL (in these experiments, CCL was defined as the shortest CL still permitting 1:1 conduction across the expansion). Similar to the changes of CV in linear strands (Fig. 2), the changes of the conduction delay across the expansion during SCL and CCL followed distinct rate-dependent behaviors. Whereas pacing at SCL induced a monotonic increase of the conduction delay from 1.2 to 1.7 ms, pacing at CCL produced a delay that initially increased to 3.2 ms and subsequently decreased to 2.5 ms. In a total of five experiments, these changes were qualitatively similar (Fig. 7C).
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Computation of UCB at a site of source-to-load mismatch. We used the PCGD model to numerically simulate propagation in a cell strand merging into a monolayer (Fig. 10A). The strand was paced at a BCL of 500 ms for 1 min before and after a 60-s test period at a CL of 180 ms. Conduction across the expansion was successful during the first 7 s of rapid pacing. Subsequently, propagation was characterized by a Wenckebach-like periodicity with a monotonically increasing fraction of blocked impulses (Fig. 10, B and C). During the entire pacing period, intracellular Na+ continued to accumulate, explaining the progression of UCB in a way analogous to the conduction slowing in linear strands (see Fig. 3). The role of intracellular Na+ accumulation in determining the progression of UCB was verified by resetting [Na+]i to the nominal model value (10.74 mmol/l) after each beat in the computer model (not shown). This intervention prevented the decrease of ENa and the increase of INaK and INaCa, and it resulted in a complete abolishment of UCB progression. The first blocked impulse occurred after 3 s of rapid pacing, and the degree of block remained constant for the entire minute of rapid pacing with a conduction ratio of 7:6. This ratio was similar to that in the control simulation (Fig. 10) at the moment when [Na+]i reached the resetting value. This suggests that intracellular Na+ accumulation is a major determinant not only of the dynamics of continuous propagation (as presented in Fig. 3) but also of the degree of block across tissue discontinuities.
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DISCUSSION |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Effects of an abrupt increase in pacing rate on CV and APD. Our recordings using extracellular MEAs show that upon an abrupt increase in pacing rate, CV initially decreases beat by beat. The optical recordings indicate that an abrupt acceleration of pacing is associated with a prolongation of APD. The modeling results suggest that a beat-to-beat increase in APD at the onset of rapid pacing might be the mechanism underlying the initial phase of conduction slowing, mediated by a progressive shortening of diastolic intervals and reduced INa recovery. In addition, postrepolarization refractoriness linked to the rate-dependent increase of the minimal diastolic potential contributed to the initial conduction slowing by decreasing INa availability.
APD prolongation has been demonstrated to occur in adult rat cardiomyocytes at fast pacing rates (59, 60, 62, 71), and experimental evidence for a rate-dependent APD prolongation in cultured neonatal rat ventricular myocytes was shown by Wickenden et al. (72) using patch-clamp recordings. In the rat, the relative contribution to repolarization of Ito among other K+ currents is prominent (23, 59), and recovery of Ito from inactivation exhibits time constants that can extend to several hundreds of milliseconds (36, 68). Therefore, during rapid pacing, peak Ito is bound to decrease and results in APD prolongation. This incomplete recovery from inactivation of Ito was shown previously to be the major mechanism underlying the rate-dependent APD prolongation in cultured neonatal rat myocytes (72).
In agreement with these results obtained in single cells, a prolongation of APD was observed in our multicellular preparations as well and was reproduced in our simulations using the PCGD model, in which the initial APD prolongation was dominated by the kinetics of Ito. This suggests that the PCGD rat ventricular cell model represents an adequate tool for the study of rate-dependent phenomena in cultures of neonatal rat ventricular myocytes.
It may be argued that in many other species (e.g., guinea pig, human), the changes of CV upon the transition to a rapid rate may be different, because APD shortens (19, 73) due to the predominance of delayed rectifier K+ currents (IKr, IKs) in repolarization. These currents significantly increase when the diastolic interval is shortened. Indeed, in simulations using the Luo-Rudy dynamic model of the guinea pig ventricular cell (17, 37) instead of the PCGD model, we observed that CV of the first impulse during rapid pacing was slower and that its APD was considerably shorter because of the incomplete deactivation of IKs. The following diastolic interval thus became long enough to let INa recover almost fully for the second and the subsequent impulses, which propagated at a velocity almost identical to that before rapid pacing (not shown). After prolonged pacing leading to intracellular accumulation of Na+ and a corresponding decrease of ENa, CV and APD then decreased monotonically in accordance with the observations of Spach et al. (64) in canine ventricular preparations. The species-related difference in APD accommodation to changes in pacing rate also is reflected by the studies of Kalb et al. (26) in bullfrog ventricular tissue and Tolkacheva et al. (67) in isolated guinea pig and rabbit ventriculocytes, in which APD decreased during pacing at short CLs.
The behavior of APD described in the present work differs from that observed in the studies of Bursac and Tung (4), Entcheva et al. (16), and Derksen et al. (12) using cultures of neonatal rat ventricular myocytes. In the studies of Bursac and Tung and those of Entcheva et al., shortening of APD was observed at the end of 1-min periods of pacing at increasing rates, and Derksen et al. observed, using an S1S2 pacing protocol, that APD was shorter for premature impulses. These electrophysiological dissimilarities indicate that there were substantial differences in the electrophysiological properties of the cells and/or the experimental conditions used in these studies. In particular, the age of the animals from which the cells were obtained and the age of the cultures at the time of experiments were different compared with the present study. Functional modifications of the electrical function of cardiac cells in culture with age, linked to a different degree of expression of ion channels, have been described previously (22, 27, 72), and it is possible that differences in the ages of animals and cultures may have resulted in different electrical phenotypes.
An additional explanation for these dissimilarities is the possible difference in the myofibroblast content of the preparations. As shown recently, electrotonic interactions between intrinsically present myofibroblasts and cardiomyocytes depolarize the latter and thus decrease dV/dtmax and CV (40). These interactions are likely to affect not only the currents underlying the AP upstroke but also other transmembrane currents, which can lead to distinct electrophysiological features.
In contrast to these differences in the cell culture models, it is noteworthy that the APD restitution curve of our preparations is very similar to the curves presented by Schouten and ter Keurs (56) and by Dumitrescu et al. (14) for intact adult rat ventricular myocardium. This similarity suggests that under our culture and experimental conditions, APD in our in vitro model behaves in a manner comparable to that observed in intact adult tissue and that our findings may therefore be extrapolated to the heart of the adult animal. This comparative review of results obtained in single cells and in cell cultures therefore demonstrates that both preparation procedures and experimental conditions play a critical role in defining the electrical behavior of cardiac tissue.
As shown experimentally and theoretically in this study and also as suggested by the patch-clamp measurements of Derksen et al. (12) showing a slow recovery of depolarizing current for premature impulses, neonatal rat ventricular tissue is characterized by a high degree of postrepolarization refractoriness due to a slow recovery of INa from inactivation. Thus modulation of CV occurs at CLs significantly longer than the APD and over a range of CLs that is wider than the range of rate-dependent APD variations. Although postrepolarization refractoriness is not a property of normal cardiac tissue of large mammals and was not observed by Bélichard et al. (1) in adult rat ventricular tissue, it has been implicated as a major arrhythmogenic factor during acute myocardial ischemia (8).
Delayed changes in CV and APD. Abrupt transitions to rapid excitation at CLs close to the refractory period induced a further change in CV that was related to an increase in [Na+]i. The effects of intracellular Na+ overload consequent to rapid pacing on APD were studied earlier by Faber and Rudy (17). Their results show that Na+ accumulation can lead to APD shortening due to a progressive increase of INaK and INaCa. In the theoretical part of our study, intracellular Na+ accumulation and the associated increase of INaK and INaCa was the prevalent mechanism underlying the delayed APD shortening and the seemingly paradoxical acceleration of conduction.
Rate dependence of UCB on ion accumulation and Na+/K+ pump function. Success of propagation across sites of source-to-load mismatch depends on the source current generated principally by INa and, to a smaller extent, by ICa,L (50, 70). In this study, the dependence of the source current INa on an abrupt change in rate can be explained by two mechanisms with opposing effects. The balance between these two processes explains why the degree of UCB decreased in the presence of relatively low degrees of source-to-load mismatch (Fig. 9, left) and increased in the presence of high degrees of mismatch (Fig. 9, right). Both mechanisms are caused by rate-dependent intracellular Na+ accumulation. In the first case, the progressive shortening the APD caused by the increase in INaK and outward INaCa produces removal of INa inactivation. In the second case, intracellular Na+ accumulation leads to a decreased electrochemical Na+ gradient and a decrease in INa.
Importantly, successful propagation at a site of source-to-load mismatch is frequency dependent (6). Obviously, the subcritical pacing CL for induction of UCB was shorter in the case of a low than in the case of a high degree of mismatch in our experiments (Fig. 9A). At the lower degree of mismatch associated with shorter subcritical CLs, the decrease of the level of UCB suggests that the effect of intracellular Na+ accumulation to shorten the APD prevailed over the effect to decrease INa via a decreased driving force. The resulting progressive increase of INa was responsible for the observed recovery of propagation. At the higher degree of mismatch associated with longer subcritical CLs, the decreasing electrochemical gradient prevailed and explained the progression of block.
Our findings demonstrate that the relation between rate and success of propagation is modulated by the degree of source-to-load mismatch, which may lead to opposite rate-dependent dynamics of UCB. Moreover, the results show that intracellular Na+ accumulation and the Na+/K+ pumping during rapid activity add another level of complexity to the intricate interplay among ion channel function, tissue structure, and ionic homeostasis underlying rate-dependent conduction dynamics. Furthermore, the dynamics of UCB that we describe also may apply to other types of geometries that exhibit source-to-load mismatch, e.g., isthmuses and pivot points (6, 21), since the biophysical mechanisms of propagation in such geometries share close similarities with the tissue expansions used in this study (29).
It has been shown that in the presence of large conduction delays (e.g., in cardiac tissue with reduced gap-junctional coupling or across-tissue discontinuities), ICa,L contributes to the success of propagation in addition to INa (50, 58, 70). In accordance with these studies, block of ICa,L precipitated conduction block across simulated expansions. Intracellular Ca2+ accumulation at rapid pacing rates also may decrease the driving force of ICa,L (a mechanism not incorporated in the PCGD model) and cause more prominent Ca2+-based inactivation of this current. Therefore, the decrease of ICa,L during rapid pacing also may influence the rate-dependent dynamics of the degree of UCB across sites of source-to-load mismatch.
Finally, it is important to mention that Na+ accumulation in cardiac cells at rapid pacing rates has been observed in different experimental settings and in different species (13, 69). This phenomenon is reproduced not only by the PCGD model but also by the Luo-Rudy model (17, 37), and it is likely to be present in other mathematical models of cardiac cells incorporating dynamic changes in [Na+]i [e.g., Courtemanche et al. (9); Iyer et al. (25)]. Whereas APD prolongation and the biphasic behavior of APD or CV may be species specific, Na+ and Ca2+ accumulation together with changes in refractoriness and their effects on INa, CV, and UCB during rapid activity are likely to be a feature affecting all species.
In conclusion, intracellular Na+ and Ca2+ accumulation and postrepolarization refractoriness are likely to play an important role in the modulation of the degree of UCB at discontinuities in structurally nonuniform cardiac tissue as found, for example, at junctions between Purkinje fibers and the ventricular myocardium (39, 44), at the border zones of infarct scars (11), in fibrotic myocardium (63), and in the atrioventricular node (38, 48).
Study limitations. Because the observed phenomena are linked to the ion channel repertoire specific to the rat, they cannot be directly extrapolated to other species. However, under circumstances where the role of Ito in repolarization becomes important (e.g., in the Brugada syndrome, see below), the mechanisms that we discuss may nevertheless be involved in other species as well.
In our simulations, the rate-dependent increase of [Na+]i closely corresponds to the increase measured in the adult rat ventricular cell (13). The possibility cannot be excluded, however, that the ion accumulation in neonatal rat cardiomyocyte cultures follows different dynamics. More insight could be obtained from measurements of [Na+] and [Ca2+] using, for example, fluorescent indicators. Furthermore, APD measured in our optical experiments differs quantitatively from the APD of the modeled cells. This difference is expected with regard to the fact that the experiments were performed in neonatal rat ventricular tissue, whereas for simulations of conduction, we used the PCGD model of the adult rat ventricular cell, which has a shorter AP. As shown in previous studies, ion channels typical for the rat ventricular cell exhibit different levels of expression during ontogenesis, which affects quantitatively APD and the rate dependence of APD of cardiomyocytes at different ages (27, 72).
Finally, in intact tissue, K+ can affect conduction by accumulating in the restricted extracellular space (32, 41). In the cultures, such a restricted space is present between the cardiomyocytes and the growth substrate. In the simulations, we did not take into account extracellular K+ changes. However, the correspondence between experimental and theoretical results suggests that the effects of extracellular K+ accumulation were presumably minimal.
Implications for arrhythmogenesis. The beginning of a tachyarrhythmia leads to a sudden increase of excitation rate. The feedback resulting from rate-dependent variations of CV may then contribute to the highly complex dynamics of CL and excitation patterns. Furthermore, within diseased myocardium, UCB at structural discontinuities may influence the spatiotemporal characteristics of reentry and lead to the fractionation of wave fronts. This may contribute to initiation or maintenance of fibrillatory conduction and fibrillation.
As shown in the present study, rapid pacing influences both CV and the probability of UCB. In conjunction, these two factors will determine the incidence of reentry initiation. In discontinuous tissue structures [e.g., an anatomically defined circuit incorporating a site of source-to-load mismatch (49)], the highest incidence rate is expected to occur when 1) conduction is slowest and 2) the probability of UCB is highest. In our experimental settings, this combination is obtained after 5–10 s of subcritical rapid pacing (cf. Fig. 2, critical CL) in the presence of a structural discontinuity exhibiting a moderate degree of source-to-load mismatch (cf. Fig. 9, left). In this example, CV would accelerate again beyond 10 s of rapid pacing and the probability of conduction block would decrease, thus diminishing the probability of reentry to occur.
Our findings suggest that the interaction among a rapid change in rate, APD, and propagation depends in a complex way on the expression and function of ion channels, known to be different in distinct regions of the heart, among species, and among cardiac pathological settings. It may be speculated, for example, under what circumstances the role of Ito may become important in other species. For example, the density of Ito is prominent in the right ventricular epicardium, contributing to the pathogenesis of the Brugada syndrome (61). It was shown in a canine model of Brugada syndrome and drug-induced long QT syndrome that the epicardial AP can undergo a considerable Ito-mediated prolongation at the transition from low to high pacing rates (3, 75). Furthermore, the biphasic rate-dependent dynamics of APD in our modeling study were very similar to those reported in a genetic mouse model of the long QT3 syndrome (43). Therefore, one might envision that during a tachyarrhythmic event in these syndromes, APD, CV and UCB might follow dynamics similar to those that we currently report.
Finally, our results may be applicable to the function of the atrioventricular node during supraventricular tachyarrhythmias. It is generally accepted that cardiac glycosides increase the degree of AV nodal block via enhancement of vagal tone (42). Our observations suggest that reduction of Na+/K+ pumping by cardiac glycosides also may increase the degree of block by modifying the intracellular ion balance. Moreover, our study suggests that cardiac glycosides, apart from the well established arrhythmogenic effects related to intracellular Ca2+ overload, may increase the risk of ventricular reentrant arrhythmias via intracellular Na+ accumulation.
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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), at the time of the minimal CV during the first 15 s of rapid pacing (
), and at the end of the 1-min rapid pacing train (
) in experiments with microelectrode arrays (MEAs). CV was normalized to CV at the end of the first minute of pacing at a BCL of 500 ms. B: corresponding CV restitution curves in the PCGD model. C: CV restitution curve for the first impulse during rapid pacing in optical mapping experiments. D: APD restitution curve for the first impulse during rapid pacing in optical experiments. E: APD restitution curves in the PCGD model, corresponding to A and B. F: AP prolongation upon the transition to rapid pacing at a CL of 250 ms in the PCGD model. The first 4 APs are depicted (1–4).
