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1Department of Biomedical Engineering and 2Center for Nonlinear and Complex Systems, Duke University, and 3Division of Pediatric Cardiology, Department of Pediatrics, Duke University Medical Center, Durham, North Carolina
Submitted 11 June 2006 ; accepted in final form 17 November 2006
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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rate dependence; short-term memory; dynamic restitution curve; S1-S2 restitution curve; action potential duration
Often, the existence and the magnitude of spatial APD differences depend on the pacing rate. Thus electrical restitution, i.e., the relationship between APD and the preceding diastolic interval (DI), is the fundamental tool in investigating the stability of cardiac rhythm. Specifically, steepness of the APD restitution curve (RC) has been linked to arrhythmogenesis, with steeper curves associated with alternans, a pattern of alternating long and short APDs occurring at fast pacing rates (27). Even in a homogeneous tissue, different regions can alternate out of phase (discordant alternans), causing dispersion of repolarization, unidirectional block, and eventually reentry (10, 30, 34). Similarly, a single premature stimulus can cause dispersion of repolarization and initiate reentry (1, 21). Thus the onset of an arrhythmia can be precipitated by "functional" APD heterogeneities that occur because of purely dynamic processes. Intrinsic tissue heterogeneities can work synergistically with functional heterogeneities, greatly increasing vulnerability to arrhythmia (44). However, little is currently known about spatial heterogeneity of both transient and steady-state restitution.
To date, restitution has typically been characterized by the dynamic RC [which measures steady-state APD at fixed basic cycle lengths (BCL)] or by the S1-S2 RC (which measures APD following premature or postmature stimuli when pacing at a fixed BCL). The restitution portrait (RP) was developed as a tool for measuring and visualizing multiple aspects of APD restitution simultaneously (20). In addition to the dynamic RC and S1-S2 RC, the RP includes a transient response that arises from short-term cardiac memory. The short-term memory response (also called APD accommodation) is the slow monotonic change in APD following a sustained change in pacing rate. This response is a measure of the amount of memory present with respect to pacing history and occurs on a timescale of minutes (11, 20, 36, 45). It should be noted that this response is distinct from long-term memory changes that involve electrical remodeling and occur on timescales of hours or longer (37). The dynamic, S1-S2, and short-term memory responses, measured for a series of BCL and visualized simultaneously in a RP, give a comprehensive assessment of both transient and steady-state aspects of restitution.
Our study is the first measurement of the RP in the perfused mammalian ventricle in vitro; previously, the RP has been measured in superfused frog ventricular tissue (20) and isolated rabbit and guinea pig myocytes (40). Likewise, this is a first study that investigates spatial differences in the RP; previous studies either involved single cells (40) or were limited to only one or two microelectrode impalements (20). We differentiate in this study between heterogeneity of restitution that forms spatial patterns repeatable from animal to animal and heterogeneity with no consistent spatial patterns. The former is generally attributed to varying ion channel densities in different regions of tissue. The cause of the latter is not known, but many have studied such dispersion of restitution because the degree of dispersion is thought to affect rhythm stability (21, 25). This study focuses on the former: we use the RP to characterize repeatable gradients of restitution properties from apex to base in rabbit epicardium.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Experiments were performed on 14 adult New Zealand White rabbits (3.8 ± 0.5 kg), 6 female and 8 male, following a protocol approved by the Duke University Institutional Animal Care and Use Committee. Rabbits were premedicated with intramuscular ketamine (35 mg/kg) and xylazine (5 mg/kg) and then given intravenous heparin (800 U/kg) followed by thiopental sodium (20 mg/kg). Hearts were rapidly excised and submerged in cold, oxygenated high-potassium Tyrode solution containing (mM) 123 NaCl, 11 dextrose, 20 NaHCO3, 24 KCl, 1.0 NaH2PO4·H2O, 1.1 MgCl2·6H2O, and 1.8 CaCl2. The aorta was quickly cannulated and retrograde perfused with the same cold, high-potassium Tyrode solution. The right coronary artery was sutured closed, and the right ventricular free wall, both atria, and most of the septum were removed to isolate the left ventricular free wall (16). The atrioventricular node was cauterized.
The tissue was submerged in a heated bath and perfused with a 37–38°C oxygenated Tyrode solution identical to that described above but with 4.5 mM KCl. In 10 of 14 animals, the excitation-contraction uncoupler 2,3-butanedione monoxime (BDM, 15 mM) was added to the perfusate. A constant-flow perfusion system was used with no recirculation of perfusate. Perfusion pressure was maintained between 35 and 45 mmHg by adjusting the flow rate. Tissue equilibrated for 90 min.
Action Potential Recordings
In 10 of 14 animals, hearts were stained with the voltage-sensitive dye di-4-ANEPPS by perfusing with 50 ml of Tyrode solution containing 5 µM dye. Optical action potentials were recorded with up to six small-diameter optical fibers (105-µm core, numerical aperture = 0.22) placed against the epicardium. Excitation light from two 5-mW green lasers (532 nm) was coupled into the fibers, and fluorescence was collected from the tissue with the same fibers. A dichroic mirror was used to separate the two wavelengths of light (excitation and fluorescence). Fluorescence was long-pass filtered at 590 nm and detected with a photodiode. This optical recording system is described in more detail in previous publications (14, 31). The tissue ECG was recorded with two silver-silver chloride electrodes placed in the bath with positive and negative electrodes positioned near the apex and base, respectively. All signals were displayed continuously with LabView software (National Instruments, Austin, TX).
Optical signals and ECG were band-pass filtered from 0.1 to 500 Hz, digitized at 12-bit resolution, and sampled at a rate of 1 kHz per channel. Postprocessing was performed with MATLAB software (MathWorks, Natick, MA). Optical action potentials were digitally filtered with a 15-point median filter. The median filter was chosen because it accurately preserves the shape and timing of both upstroke and repolarization dynamics (46).
Microelectrode Recordings
In four animals, experiments were performed without the use of BDM. Action potentials were recorded from the epicardium with one to three floating microelectrodes (16). Microelectrode capacitance was offset with feedback through a driven shield set to 
80% of the ringing threshold. Data were low-pass filtered (500 Hz), digitized at 16-bit resolution, and sampled at 2 kHz. The pacing protocol and data analysis were the same as for optical recordings. Attempts were made to maintain impalement throughout the entire pacing protocol. However, for quality control, only action potentials with sharp upstrokes and amplitudes >70 mV were used for analysis.
Perturbed Downsweep Pacing Protocol
The tissue was paced epicardially from a bipolar electrode with 2-ms pulses at twice the diastolic threshold. Restitution properties were studied with a modified version of the perturbed downsweep protocol (PDP) previously described by Tolkacheva et al. (41) and implemented in pieces of bullfrog myocardium by Kalb et al. (20). In the PDP used by Kalb et al. (20), a downsweep in BCL was performed, with 60 s of pacing at each BCLn in the downsweep. After 60 s of pacing at each BCLn, single stimuli were applied at long and short coupling intervals of BCLL,S = BCLn ± 
(where is S2 perturbation size), with five stimuli at BCLn between the two. Twenty more stimuli were applied at BCLn before moving to BCLn+1 and repeating the above sequence.
The PDP was modified for our rabbit experiments to reduce the amount of continuous time spent pacing at short cycle lengths. This was done to reduce tissue hypoxia that could occur because of perfusion with a nonblood solution during a period of high metabolic demand. The PDP was divided into segments, called runs, each consisting of two decrements in BCL. Between runs the tissue was paced at a recovery cycle length, BCL0 = 1,000 ms, for a minimum of 2 min. A graphic outline of one run is shown in Fig. 1. Beginning at BCL0, cycle length was abruptly shortened to BCL1 and paced for 60 s. BCL was again decremented to BCL2 and paced for 60 s. One stimulus was applied at a long cycle length, BCLL = BCL2 + , followed by five stimuli at BCL2. Then 1 stimulus was applied at a short cycle length, BCLS = BCL2 – , followed by 20 stimuli at BCL2 before returning to BCL0. The S2 perturbation size was varied from 20 to 50 ms. Action potentials were recorded continuously during each run. Each modified PDP consisted of five to seven runs with different values of BCL1 and BCL2 in each run.
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Restitution properties were determined at three epicardial locations (apex, midventricle, base). In five animals, three PDPs were performed per animal with the stimulus located at the apex during one downsweep, the middle during another, and the base during another, as shown in Fig. 2A. The order of sites was changed for each animal. Action potentials were recorded at a single epicardial location within 3 mm of the stimulus. Within each PDP, the runs were not ordered with decrementing BCL, but were instead randomized. In another five animals, two PDPs were performed per animal with the stimulus located at the apex and base of the epicardium, as shown in Fig. 2B. The stimulus order was changed for each animal. Action potentials were recorded simultaneously from multiple epicardial sites grouped in three locations: apex, midventricle, and base. Within each PDP, the runs were performed in decrementing order. It was determined from the first five animals that randomization of the runs was not necessary.
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APD and DI were measured between the time of maximum upstroke velocity and 70% of repolarization. Pairs of APD and preceding DI (DIn, APDn+1) measured during the PDP were grouped into the three response types of the RP: the dynamic RC, the S1-S2 RC, and the short-term memory response.
The dynamic RC measures steady-state behavior over the range of cycle lengths that produce 1:1 (stimulus:response) rhythms. At each BCL1 and BCL2, the last ten (DIn, APDn+1) pairs after 60 s of pacing were averaged to obtain steady-state points (Fig. 1). All steady-state APDn+1 were plotted as a function of DIn to form the dynamic RC. The slope was determined by fitting the data to an exponential equation of the form:
 | (1) |
D is a constant. The S1-S2 RC measures the deviation from steady state in response to a single premature or postmature stimulus. In contrast to previous studies in which the slope was evaluated as a function of the S2 interval with the S1 interval fixed (9, 11, 12), we obtained the slope as a function of the S1 interval. Specifically, at each BCL2, a small section of the S1-S2 RC was formed from the steady-state response and the responses to BCLL and BCLS. These three (DIn, APDn+1) responses were fit to a straight line by least-squares linear regression. The slope was determined from the fitted line. Thus in this study the slope of the S1-S2 RC was evaluated at the steady state of each BCL (S1), and consequently reflects the stability of the steady-state responses to small perturbations in pacing rate.
The short-term memory response measures the transient response after a step change in BCL from steady state at a preceding BCL. This response is also referred to as the constant BCL response (20) or accommodation (43). Short-term memory responses were obtained from the full 60 s of pacing at each BCL1 and BCL2. The magnitude of the step change in BCL (
) was divided into two groups. A large step ( = 500–850 ms) was used for the transition from BCL0 to BCL1, and a small step ( = 50–100 ms) was used for the transition from BCL1 to BCL2. At each BCL1,2, the change in APD as a function of time was fit to an exponential of the form:
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is the time constant of short-term memory. Determination of APD Alternans
The presence of beat-to-beat alternation in APD, or alternans, was detected with a frequency spectrum analysis method similar to a method that is commonly used to detect T-wave alternans (15, 30). In contrast to T-wave alternans detection, which performs analysis on vectors of time-aligned voltage signals, this method uses vectors of APD (in units of ms) in order to detect only repolarization alternans and not conduction time alternans. Analysis was performed on overlapping epochs of 64 consecutive APDs recorded during BCL1 and BCL2 of each PDP. Within each epoch a power spectrum estimate was calculated from the discrete Fourier transform of the autocorrelation function of the vector of 64 APDs. The presence of alternans corresponds to a peak in the power spectrum at 0.5 cycles/beat. The total alternans power is found by subtracting the mean noise in an adjacent spectral band from the alternans peak. The alternans magnitude is equal to two times the square root of the total alternans power. The K-score was calculated as a statistical measure of the degree of alternation relative to the noise in an adjacent spectral band. Significant alternation was considered present if the total alternans power was greater than 3 standard deviations of the noise band and the alternans magnitude exceeded 4 ms. This detection algorithm was tested with a false signal containing noise, and a detection threshold of 4-ms alternans magnitude was determined. Persistent alternans was defined as significant alternation that persisted for the entire 60 s of pacing at BCL1,2. Transient alternans was defined as significant alternation in at least one but not all epochs during BCL1,2 pacing.
Statistical Analysis
Steady-state APD, RC slopes, and short-term memory time constants were compared across pacing and recording sites with a repeated-measures analysis of variance (ANOVA). Slopes of dynamic and S1-S2 RCs measured before 1:1 (normal) and 2:2 (alternans) responses were also compared with a repeated-measures ANOVA. Results with P < 0.05 were considered statistically significant. Values are given as least-squares means ± SE unless otherwise stated.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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In 10 animals, a total of 24 PDPs were performed. During each PDP, RPs were recorded from up to six epicardial sites. A total of 47 RPs were obtained. Figure 3 shows an example of one RP recorded from the midventricular region of the epicardium while the tissue was paced from a nearby midventricular site (see pacing protocol, Fig. 2A). In this case, alternans was not induced. Distinct restitution responses were present: response to steady-state pacing (dynamic RC), response to single premature and postmature paced beats (S1-S2 RC), and transient response following an abrupt change in cycle length (short-term memory).
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The short-term memory response elicited from a step change in BCL of size is represented by filled circles in Fig. 3. During the short-term memory response, there is an initial relatively large change in APD and DI in the first beat (analogous to an S1-S2 response), followed by a slow monotonic decrease in APD and increase in DI to reach steady state (see Fig. 6). Because APD and DI change only gradually during this response, these points fall on a line with a slope of –1 (20), although this is not immediately obvious in Fig. 3 because of the scale of the axes. In each run of the PDP, two short-term memory responses were observed, due to two step changes: BCL0 to BCL1 (large ) and BCL1 to BCL2 (small ). For visual clarity, only the latter response is shown in Fig. 3.
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Each component of the RP was compared among pacing and recording sites to investigate whether there were spatial differences in the restitution properties in the rabbit epicardium that were repeatable among animals.
Dynamic restitution. Steady-state APD did not depend significantly on pacing or recording site when pacing at a BCL of 1,000 ms or when pacing at shorter BCL. This means that there was no persistent APD gradient from apex to base across the rabbit epicardium and that there was no consistent relationship between pacing site and APD, or between distance from the pacing site and APD. However, the lack of any persistent spatial dependence of APD does not mean that APD was identical at all recording sites. Of the nine RPs in which multiple simultaneous recording sites were used, seven had statistically significant differences in steady-state APD at BCL = 1,000 ms, and four had statistically significant steady-state differences at BCL = 200 ms. However, these APD differences varied in magnitude and direction between animals. At BCL = 1,000 ms, the difference in steady-state APD between recording sites ranged from 0 to 27 ms on average.
In Fig. 4A, the slopes of all dynamic RCs (n = 33, all animals) are shown as a function of BCL. The dynamic RC slope increased as BCL was decreased from 1,000 to 140 ms. The mean maximum slope of the dynamic RC was 0.78 ± 0.11 (n = 33, all animals), and only 7 of 33 dynamic RCs had a maximum slope >1. Summary data for the maximum dynamic RC slope and steady-state APD are given in Table 1 as a function of recording and pacing sites. At all BCL tested, no significant differences in dynamic RC slope were found with respect to pacing site (see Fig. 5A) or recording site. Maximum dynamic RC slope also did not depend significantly on pacing site or recording site.
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In the first beat after a sustained step change in BCL, APD did not always decrease as expected. In both Fig. 6, A and B, when BCL was abruptly decreased, APD initially increased. In Fig. 3, the responses to small step changes in BCL also showed an initial increase in APD, such that the first APD of each short-term memory transient is longer than the previous steady-state APD. A prolonged initial APD was observed in 69.3% of the short-term memory responses to a large and in 16.3% of the responses to a small . This is consistent with the finding of negative S1-S2 RC slopes, although a quantitative comparison is not possible because the step changes in BCL for S1-S2 and short-term memory responses were not of equal size.
Short-term memory response.
Figure 6, A and B, show examples of short-term memory responses recorded from the apex, midventricle, and base from two different animals in response to large step changes in BCL. In Fig. 6A, the three responses were not measured simultaneously but were instead measured within a few millimeters of the pacing site, and the stimulus was moved for each recording (see Fig. 2A). In Fig. 6B, all three recordings were made simultaneously while the tissue was paced from the base (see Fig. 2B). There were significant spatial differences in the short-term memory response following a large step change in BCL. The mean time constant of the decay, , is plotted in Fig. 7 as a function of recording site. In Fig. 7A, the data are shown for pacing and recording from the same region. The time constant was significantly shorter in the midventricular region than in the apex (19.1 ± 1.1 vs. 26.5 ± 1.3 s; P < 0.01) or base (19.1 ± 1.1 vs. 23.5 ± 1.2 s; P = 0.03). In Fig. 7B, the data are shown for recordings at different distances from the pacing site. In this case, there were no significant differences in among recording sites. Interestingly, for the midventricle, was significantly shorter when pacing in the same region compared with pacing from the apex or base (19.6 ± 4.5 vs. 38.6 ± 3.5 s; P = 0.02). There were no significant differences in between the two experimental designs when recording in the apex or base regions. In the case of small step changes in BCL, there were no significant spatial differences in with respect to recording or pacing site.
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(s)] and is plotted as a function of BCL for large and small BCL step sizes (Fig. 8, A and B, respectively). In addition, was determined in units of number of stimuli [(#beats)] and is plotted for large and small BCL step sizes (Fig. 8, C and D, respectively). While there was a large standard deviation in at any given BCL, the mean (s) was approximately constant across BCL for both large and small step changes in BCL. With linear regression, the mean (s) following large BCL steps increased by only 2.6 s for every 100-ms decrease in BCL (slope = –0.026 ± 0.009 s/ms; P = 0.003 vs. zero). For small BCL step sizes, the change in (s) as a function of BCL was statistically insignificant [slope = –0.012 ± 0.007; P = not significant (NS) vs. zero]. In contrast, (#beats) clearly increased with decreasing BCL for both large (slope = –0.39 ± 0.04 beats/ms; P < 0.001 vs. zero) and small (slope = –0.32 ± 0.03 beats/ms; P < 0.001 vs. zero) BCL step changes. The time constant was also dependent on the size of the step change in BCL: was significantly longer (P < 0.001) after a large ( = 27.1 ± 0.9 s) than after a small ( = 20.2 ± 0.9 s).
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Alternans was observed in 7 of 10 animals and during 12 of 24 PDPs. A total of 18 RPs were measured that contained alternans. Figure 9 shows examples of action potentials recorded during a normal 1:1 response, alternans, and a more complex response, and Table 2 lists the corresponding slopes of the dynamic and S1-S2 RCs. The slopes are given at BCL immediately preceding the shortest BCL eliciting a 1:1 response and are compared with slopes immediately preceding 2:2 (alternans) and complex (all responses other than 1:1 and 2:2) responses. The slope of the dynamic RC was not significantly different preceding alternans and 1:1 responses (Table 2; P = NS), but it was significantly steeper preceding complex responses than preceding 1:1 responses (P < 0.01). The slope of the S1-S2 RC was steeper preceding alternans than preceding 1:1 responses (P < 0.01) and also steeper preceding complex responses than preceding 1:1 responses (P = 0.01). When recording at multiple epicardial sites (as in Fig. 2B), transient alternans and 1:1 responses often coexisted. At the longest BCL eliciting transient alternans, alternans always occurred at a measurement site that was farthest from the stimulus. When pacing from the apex alternans first occurred at the base (n = 3), and when pacing from the base alternans first occurred at the apex (n = 3). Alternans never occurred first at the midventricle. In each case, alternans only occurred closer to the stimulus when pacing at shorter BCL. In 8 of 18 RPs with alternans, a "bubble" of persistent alternans was seen, where stable 1:1 responses were observed at BCL both longer and shorter than the range of BCL with 2:2 responses.
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The potential impact of BDM on the RP was tested in preparations (n = 4) in which no BDM was used and action potentials were recorded with microelectrodes. Mean steady-state APD at BCL0 = 1,000 ms was 168.7 ± 5.1 ms, compared with 110.6 ± 2.9 ms in the experiments with BDM (see Table 1). At BCL = 200 ms, mean steady-state APD was 82.0 ± 3.0 ms, compared with 91.0 ± 3.2 ms for the experiments with BDM. The mean maximum dynamic RC slope was 0.95 ± 0.09, which was larger than the maximum slope with BDM (0.78 ± 0.11; Table 1). The mean maximum S1-S2 RC slope was 0.13 ± 0.03, which is indistinguishable from the maximum slope with BDM (0.13 ± 0.02; Table 1). The slope of the S1-S2 RC was larger when pacing at the apex (0.032 ± 0.012) than when pacing at the base (0.027 ± 0.011) and still larger when pacing at the midventricle (0.090 ± 0.012). While sample sizes were not large enough to determine whether these differences were statistically significant, the spatial trend in the data parallels the results with BDM.
The mean time constant of the short-term memory transient was larger after large step changes in BCL ( = 38.2 ± 3.3 s) than after small steps ( = 27.8 ± 2.8 s), which was also the case for the data measured with BDM. When recording close to the stimulus (experimental design of Fig. 2A), the time constants after large steps were 38.6 ± 7.1, 37.2 ± 7.8, and 39.0 ± 6.6 s for sites at the apex, midmyocardium, and base, respectively. The time constant was shortest at the midmyocardium, as also seen in Fig. 7A for the data with BDM. When recording at a distance from the stimulus (experimental design of Fig. 2B), the time constants after large steps were 36.4 ± 6.1, 37.7 ± 5.1, and 40.4 ± 5.7 s for recording at the apex, midmyocardium, and base, respectively. The trend is not exactly the same as the comparable data measured with BDM (Fig. 7B), but no significant spatial differences in time constants were present in the BDM data. Time constants measured in units of time (s) did not change significantly as a function of BCL. This is consistent with the data measured with BDM, in which the time constants were more dependent on BCL when measured in number of beats than when measured in units of time (Fig. 8).
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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This study has measured, for the first time, the restitution portrait in mammalian tissue. The RP in rabbit ventricular tissue had many features similar to those previously reported in frog ventricular tissue (20) and rabbit and guinea pig isolated myocytes (40). Each contained distinct restitution responses for the dynamic RC, S1-S2 RC, and short-term memory response. Quantitatively, both the frog and mammalian cells exhibited a larger dynamic range of APD and a steeper dynamic RC than did rabbit ventricle, but the slope of the S1-S2 RC was similar in all three studies (20, 40).
The S1-S2 RC exhibited both positive and negative slope values. A negative S1-S2 RC slope resulted when a premature S2 stimulus elicited an APD that was longer than the steady-state APD at the S1 interval. A similar behavior was seen in the initial response to a sustained change in pacing rate (also an S1-S2 response). This response type has been termed supernormal (6) and appears to be a prevalent response in rabbit epicardium. It can be elicited by both a small change in BCL (as in the S1-S2 RCs) and a large change in BCL but was more prevalent in response to a large change in BCL: APD initially increased in over half of the responses to large decrements in BCL. This response type is similar to biphasic S1-S2 RCs measured in the right ventricles of humans (11). In those patients, a full S1-S2 RC was measured for a fixed S1 value. These RCs had a local maximum around a DI of 50 ms and had negative slope for a range of DI >50 ms. A response of this type has also been observed in other species including dog (17), cat (5), and sheep (26).
Short-Term Memory
In the rabbit ventricle, the short-term memory transient followed an exponentially decaying time course with a mean time constant of 27.1 ± 0.9 s. Many other species have similar exponentially decaying transients. In humans, Franz et al. (11) reported that the time to reach steady state after an abrupt change in pacing rate was 2.6 ± 0.5 min. Time constants reported in guinea pig (45), canine (36), and frog (20) ranged from 20 to 70 s. In rabbit isolated myocytes, the time constant ranged from 30 to 50 s (40). These values are all remarkably similar considering the differences in species and preparations. Short-term memory has been attributed to slow changes in intracellular or extracellular ionic concentrations, but the exact mechanism is not clear. Miyata et al. (24) note that the time course of changes in extracellular potassium concentration after a change in pacing rate closely matches the time course of changes in APD. Williams et al. (45) presented evidence that the short-term memory time constant may be linked to the inward rectifier K+ current (IK1) and hypothesized that interspecies similarities are due to the ubiquitous nature of IK1.
We observed that the time constant of short-term memory [(s)] was independent of pacing rate. The time to reach steady-state APD did not depend on a specific number of action potentials, but rather on a specific length of time, regardless of pacing rate. In rabbit and guinea pig single cells, decreased linearly with decreasing BCL (40). The reason that is dependent on BCL in rabbit single cells and is independent of BCL in coupled rabbit tissue is not clear from these two studies. It may be related to handling of extracellular potassium in restricted (coupled tissue) versus nonrestricted (isolated cell) extracellular space. In our study, the time constant of short-term memory was dependent on the size of the step change in BCL; more time was needed to recover from a larger step change. This implies that the time constant may be related to the difference in steady-state APD at the two pacing rates.
Spatial Differences in Restitution Properties
Dynamic RC and S1-S2 RC. Spatial heterogeneity of restitution can be of two types: it can form spatial patterns that are repeatable from animal to animal, or it can have no consistent spatial patterns. We do not focus in great length on the latter because our limited number of recording sites prevents adequate measurement of epicardial dispersion of APD.
In this study, 78% of the RPs had significant spatial differences in steady-state APD at BCL = 1,000 ms, whereas 44% did at BCL = 200 ms. These data suggest that spatial differences in APD exist at steady state. However, these spatial differences did not form repeatable patterns. This study found no significant consistent spatial gradients of steady-state APD with respect to either pacing or recording site at either long or short BCL. Previous studies have found conflicting results on epicardial gradients of steady-state APD in the rabbit. Some have reported longer APDs at the apex than at the base (18), while others have reported longer APDs at the base than at the apex (23), and yet others have found no difference (48). We conclude that while some amount of heterogeneity may exist, there is little evidence in this study for a consistent pattern of differences in steady-state APD across the rabbit epicardium.
The dynamic RC and the S1-S2 RC did not have consistent spatial differences across the rabbit epicardium with respect to the recording site. Neither dynamic nor S1-S2 RCs, the most commonly used measures of restitution, were found to differ substantially in the three epicardial recording regions tested: apex, midventricle, and base. We conclude that the classic restitution measures (steady-state APD, slopes of dynamic and S1-S2 RCs) show little spatial dependence in the rabbit epicardium under normal conditions.
However, the slope of the S1-S2 RC was dependent on the pacing site. The slope was steeper when pacing from the apex than from the base. APD restitution is affected by both pacing location and direction of propagation (39). Electrotonic interactions are affected by stimulation because the stimulus current produces an electrotonic load imbalance near the stimulus site, which can prolong APD in the region local to the stimulus (22, 39). However, Sampson and Henriquez (39) showed that adding transmural heterogeneity into a simulated rabbit ventricle reduced steady-state APD prolongation near the stimulus compared with a homogeneous rabbit ventricle. This is in agreement with our finding that steady-state APD and dynamic RC slope did not differ significantly at the pacing site. The effect during non-steady-state pacing is not known. It is possible that electrotonic effects at the site of stimulation may impact transient responses (S1-S2, short-term memory) more than the steady-state response.
In addition, direction of propagation relative to fiber direction in anisotropic tissue has been shown to affect electrotonic interactions, conduction velocity, and APD (47). Previous studies have shown that APD is longer during longitudinal versus transverse propagation (13, 28). Fiber direction in the rabbit left ventricle varies significantly across the epicardium, and fiber direction is likely different in each of the three regions of interest in this study, apex, midventricle, and base (42). In the base and midventricle regions of the recording area the fiber direction runs predominantly along the long axis of the left ventricle, but the apical fiber direction is predominantly perpendicular to the long axis (42). The difference found in S1-S2 RC slope when the pacing site was moved implies that tissue heterogeneities exist, whether structural or functional, and the S1-S2 restitution response is affected differentially by the change in stimulus location and the change in the direction of propagation.
Short-term memory. The time to reach steady-state APD after an abrupt shortening of cycle length was found to have repeatable spatial heterogeneity in the rabbit epicardium. We found that the time constant of the short-term memory transient near the pacing site depended on epicardial location: it was significantly shorter in the midventricle than at the apex or base. However, the time constant measured farther from the pacing site was spatially uniform and did not depend on pacing site. The differences in time constant measured close to the stimulus may result from local differences in wave front propagation relative to fiber direction or from electrotonic effects near the site of stimulation, as discussed in the previous section. The differences may also be related to spatial heterogeneity of specific ion channel densities such as the apex-to-base gradients in the rapid and slow delayed rectifier K+ currents, IKr and IKs (7). Whether the heterogeneity is structural or functional in nature, its existence becomes apparent when the local electrical load is modified by the pacing stimulus.
Rosenbaum et al. (38) measured the first 25 beats after a change in cycle length from 500 to 300 ms in guinea pig and found that epicardial dispersion of repolarization decreased in the first 10 beats at the new cycle length and then increased. This transient change in dispersion may be due to spatial heterogeneity of the short-term memory time constant, although such heterogeneity has not been shown in guinea pig.
Alternans. We found that the dynamic RC slope was significantly less than unity immediately preceding alternans. In addition to having slope less than unity, the dynamic RC was also not significantly steeper preceding alternans than preceding 1:1 responses. Even though the S1-S2 RC remained shallower than the dynamic RC, and always less than unity, its slope was positively correlated with the onset of alternans. These findings confirm previous research that reported alternans in the presence of RC slope <1 (12, 35), in disagreement with the restitution criterion proposed by Nolasco and Dahlen (27). However, this restitution criterion is based on a one-dimensional concept of restitution, in which APD is strictly a function of the preceding DI. This relationship does not hold for tissue with memory, as evidenced by distinct dynamic, S1-S2, and constant BCL responses (8, 9, 20, 43). For tissue with memory, the alternans criteria take the form of a combination of slopes: the combination can be equal to 1, while individual slopes can be quite different from 1 (41). Others have suggested that APD restitution alone may not determine the onset of alternans; factors such as spatial heterogeneity of restitution (25), conduction velocity restitution (8, 10), or calcium cycling (12, 32) may also play a role.
Alternans was observed to form at the recording site most distant from the stimulus at a slower pacing rate and was seen in more proximal locations only after the rate had been increased. Both experiments and models have found this same behavior (8, 10). This phenomenon may be due to spatial gradients of restitution properties that are induced by pacing and boundary effects, although significant gradients distal to the stimulus were not observed.
Impact of BDM on Restitution Responses
In previous studies the electromechanical uncoupler BDM was shown to have the following effects on restitution: it decreases steady-state APD (4, 35), decreases the maximum slope of the dynamic restitution curve (4, 35), and can either decrease the amplitude of alternans (35) or decrease the occurrence of alternans (4). While most of the experiments presented here were performed with BDM, a small subset (n = 4) of the studies were performed in the absence of BDM. Qualitatively, the RPs with and without BDM were very similar. In both cases, the S1-S2 RCs were more shallow than the dynamic RC at all BCL. The short-term memory transients followed exponentially decaying time courses with similar time constants in both sets of experiments. Some quantitative differences were found in the restitution responses. First, at BCL = 1,000 ms steady-state APD was longer in preparations without BDM compared with those with BDM (168.7 ± 5.1 vs. 110.6 ± 2.9 ms). APD differences were much smaller between the two groups at short BCL. Second, the mean maximum dynamic RC slope was larger without BDM (0.95 ± 0.09) than with BDM (0.78 ± 0.11). Third, the time constants of the short-term memory transients were longer in experiments without the use of BDM (38.2 ± 3.3 s, large BCL step change) than in those with BDM (27.1 ± 0.9 s, large step changes). The changes seen in steady-state APD and dynamic RC slope confirm previous research (4, 35).
Other restitution properties remained unchanged. The mean maximum slope of the S1-S2 RC was unaffected by the use of BDM. Also, the behavior of the short-term memory time constant was consistent in both sets of experiments: the time constant was shorter after a smaller step change in BCL, and it was independent of the value of the BCL. We also investigated the spatial differences in restitution properties and found similar trends with and without BDM. Specifically, the S1-S2 RC was steeper when pacing from the apex than from the base. Also, when pacing and recording in the same epicardial region, the time constant was shorter at the midventricle than at the apex or the base.
Implications and Limitations
Two characteristics of the RP were found to have repeatable spatial heterogeneity with respect to the pacing site: the time constant of the short-term memory transient in response to local stimulation and the S1-S2 RC slope. The presence of these two transient spatial heterogeneities following a change in pacing rate may affect electrical stability at the onset of a tachycardia or during a series of rapid ectopic beats, both common precursors to ventricular fibrillation. Our results predict that the restitution response of tissue to tachycardia or ectopy may be different than the response to similarly timed sinus beats. Vulnerability may be affected by the location of origin of the abnormal beats. The mechanism for this would be twofold: the restitution properties near the site of origin of the beats may change depending on location, and the spatial dispersion of repolarization farther from the site of origin may also be altered, creating a period of higher vulnerability during the first few beats of ectopy or tachycardia.
The finding of these repeatable spatial heterogeneities of restitution (S1-S2 and short-term memory) also has implications for future research. With classic restitution measures (the dynamic and S1-S2 RCs), the transient heterogeneity of short-term memory would not have been discovered. This study illustrates the need for more complete characterization of the multiple aspects of restitution. The PDP and the RP are useful techniques for this purpose.
This study was limited by the fact that action potential recordings were only obtained from a maximum of six locations at a time. This type of experimental design can be useful in detecting gradients in restitution properties across different regions of tissue (16, 18, 19). However, detecting the dispersion of restitution properties within a smaller area of tissue, such as has been performed previously (21, 25), requires higher resolution and is therefore not possible with so few recording points. We must make the assumption that the differences within an epicardial region (apex, midventricle, or base) were of smaller magnitude than the gradients in restitution properties that might exist across regions. Comparisons of restitution properties measured with and without BDM were limited by the fact that the comparisons were not made in the same animals and also by the small number of animals (n = 4) in which BDM was not present. This study was also limited by the fact that APD was only recorded from the epicardium. Previous studies have shown that transmural gradients in steady-state APD exist at slow to moderate pacing rates (2, 16). Thus future work will involve transmural measurements of the RP, which would allow us to elucidate spatial differences in both steady-state and transient restitution responses.
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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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), S1-S2 RC data (+ and x), and short-term memory responses (
). BCL, basic cycle length; BCLL, long BCL; BCLS, short BCL.
