## Abstract

During ventricular fibrillation (VF) only 39% of the variation in action potential duration (APD) is accounted for by the previous diastolic interval [DI_{(n−1)}], i.e., restitution, and the previous APD [APD_{(n−1)}], i.e., memory. We tested the hypothesis that a characteristic of the AP upstroke, the maximum rate of depolarization (*V̇*_{max}), also helps account for its APD. A floating microelectrode was used to make transmembrane recordings at 16,000 samples/s from the anterior left ventricular wall during four 20-s episodes of VF in each of six pigs. *V̇*_{max}, time from *V̇*_{max} to 60% repolarization (APD_{60}), and DI were calculated throughout all episodes. Stepwise linear regression was used to determine how well each APD_{60} (APD_{60n}) was predicted by *V̇*_{max} of that AP, the four previous DIs (*n*−1, *n* − 2, *n* − 3, *n* − 4), and the three previous APD_{60}s (*n*−1, *n* − 2, *n* − 3). *V̇*_{max} entered in the regression equation significantly more often (86% of VF episodes) than either APD_{(n−1)} (47% of episodes) or DI_{(n−1)} (58% of episodes). When these three variables entered first or second, their coefficients were almost always positive, consistent with a longer APD associated with *1*) a larger *V̇*_{max}, *2*) a longer APD_{(n−1)}, and *3*) a longer DI_{(n−1)}. *R*^{2} of the regression for all entered variables was 0.51 ± 0.01 (mean ± SD). During the first 20 s of VF in swine, *V̇*_{max} is a more important determinant of APD than the previous DI (restitution) or the previous APD (memory). All variables together account for only one-half of APD variation during VF.

- electrophysiology

much experimental evidence indicates that early ventricular fibrillation (VF) is maintained by reentry (23, 24). Restitution properties and cardiac memory both have been hypothesized to be important factors in the creation of reentry through their effects on action potential (AP) duration (APD) and the refractory period (6, 10). The restitution hypothesis of VF states that the slope of the diastolic interval (DI) restitution curve is the main determinant of wave break that is responsible for the maintenance of VF (18, 31). In general, a long DI leads to a long APD and a short DI leads to a short APD, so that the coefficient relating these two variables is positive (5, 7). If the slope of this restitution relationship is >1, then a small change in DI leads to a greater change in APD, which leads to a greater change in DI, etc., until the DI is so short that the tissue is still in its refractory period and block occurs. In addition to restitution, cardiac memory is also important during VF (16). Cardiac memory is the phenomenon in which not just the previous DI [DI_{(n−1)}] but also the previous APD [APD_{(n−1)}], as well as the DIs and APDs of even earlier cycles, influence the present APD [APD_{(n)}] and the refractory period (8, 26). Because of cardiac memory, a long APD_{(n−1)} leads to a long APD_{(n)} while a short APD_{(n−1)} leads to a short APD_{(n)}, so that the coefficient relating these two variables is also positive.

We previously showed (16) that neither DI_{(n−1)} nor APD_{(n−1)} was linearly correlated with APD_{(n)} during early VF in the right ventricle of pigs. However, when we included both variables as well as other variables in a stepwise linear regression analysis to predict APD_{(n)}, we found a high incidence and a positive coefficient of DI_{(n−1)} in the regression equation, indicating that restitution is important in determining APD during VF, as well as a high incidence and positive coefficient of APD_{(n−1)}, indicating that cardiac memory is equally important. The fact that these variables are related to APD_{(n)} in a multiple regression but not in a single regression indicates that DI_{(n−1)} and APD_{(n−1)} are related to APD_{(n)} but that the interaction of these and other variables obscures these relationships. However, restitution and memory together only accounted for a mean of 39% of the variability of APD in the regression equation (16). Therefore, factors other than restitution and memory are also important in determining APD during VF. Indeed, these other factors account for 61% of APD variability and so are more important than restitution and memory together.

Voltage-gated Na^{+} channels are transmembrane proteins responsible for the rapid upstroke of the cardiac AP and therefore underlie impulse conduction and conduction velocity (CV) through much of the myocardium (4, 13). The Na^{+} channels responsible for the rapid upstroke of the AP have been shown to be responsible for the late Na^{+} conductance in the maintenance of the AP plateau (35) so that they may influence APD. The Na^{+} channels have also been shown to be active during early VF (33). The maximum upstroke of the AP (*V̇*_{max}) and amplitude of the upstroke of the AP (APA) are indexes of Na^{+} channel activity (9, 19).

The purpose of this study was to test the hypothesis that these correlates of Na^{+} channel activity, *V̇*_{max} and APA, are related to APD during early VF. We tested this hypothesis by determining whether *V̇*_{max} and APA in addition to and independently of DI_{(n−1)} and APD_{(n−1)} account for part of the APD variability during early VF by making microelectrode recordings on the left ventricular epicardium of the intact pig heart in vivo.

## METHODS

Animals were managed in accordance with the American Heart Association guidelines on research animal use (1), and the protocol was approved by the University of Alabama at Birmingham Institutional Animal Care and Use Committee.

#### Animal preparation.

Six 32- to 40-kg pigs were injected intramuscularly with Telazol (4.4 mg/kg), xylazine (2.2 mg/kg), and atropine (0.04 mg/kg) for anesthetic induction. Anesthesia was maintained with isoflurane in 100% oxygen by inhalation. Core body temperature, arterial blood pressure, arterial blood gases, ECG lead II, and serum electrolytes were monitored and maintained within normal ranges throughout the study.

The heart was exposed through a median sternotomy and supported in a pericardial sling. An Ag-AgCl reference electrode for the intracellular recording electrode was sutured to the inside of the chest. A catheter (model 6942, Sprint, Medtronic) with a 479-mm^{2} surface area electrode in the right ventricle and a 766-mm^{2} surface area electrode in the superior vena cava were inserted for defibrillation. Warm saline at 38°C was dripped on the heart surface throughout the study to keep the epicardium warm.

#### Signal recordings.

For intracellular recordings, a conventional microelectrode (tip resistance 10–30 MΩ, filled with 3 M KCl) was mounted on a 30-μm Ag-AgCl spiral wire to allow the microelectrode to follow cardiac motion (16, 34). APs were recorded from the anterior left ventricle with DC coupling as the difference in voltage between the intracellular microelectrode and the extracellular Ag-AgCl reference electrode. The signal was passed through a high-impedance capacitance-compensation preamplifier (model 773, WP Instruments) and was recorded by a mapping system that sampled at 16 kHz and stored the data on 8-mm data cartridge tapes (Exabyte) for off-line analysis (16). The signals were filtered between 0.5 (high pass) and 4,000 (low pass) Hz.

#### Experimental protocol.

APs during sinus rhythm and VF were continuously monitored and recorded with the mapping system. Sinus APs were considered to be stable when they met the following criteria: *1*) a flat baseline between each AP, *2*) a sharp upstroke during phase 0, *3*) an amplitude >100 mV, and *4*) clearly formed phases 1, 2, 3, and 4. APD and *V̇*_{max} were calculated for the last four sinus beats before VF onset, and the average values were computed. After APs were stable for >10 beats during sinus rhythm, VF was induced by stimulating the right ventricle with a 9-V battery for 1 s. VF episodes were induced five to eight times in each animal to ensure four episodes with stable microelectrode recordings. We excluded from analysis episodes with morphologically distorted APs caused by unstable lodging of the microelectrode in the cell. After induction, each VF episode was recorded for 20 s before a defibrillation shock was delivered.

We also made APD and *V̇*_{max} restitution measurements during pacing in two animals. Pacing stimuli were delivered at twice diastolic threshold to the right ventricle. Trains of 30 S1 were repeated at the intervals described below. Pacing started at 300 ms and was decreased to 200 ms by 50-ms steps. The pacing interval was reduced in 10-ms steps from 200 ms to an interval that induced VF or lost 1:1 capture. To capture during shorter pacing intervals, the S1-S1 interval was initially 300 ms, then decreased in 10-ms steps to the target interval, and thereafter kept at the target interval for 30 beats (16). We measured the APD and *V̇*_{max} from the last beat of each pacing cycle to construct the APD and *V̇*_{max} restitution curves.

#### Data analysis.

To eliminate electrotonic signals that did not represent a true AP, APDs during VF were limited to those with an APA >40 mV and a *V̇*_{max} >5 V/s, as has been done by others (20, 32). Because of the rapid activation rates during VF, complete repolarization rarely occurred. APD_{60} was measured as the time interval from *V̇*_{max} until 60% repolarization based on the APA of each individual AP during VF (Fig. 1) (20). We previously (16) compared the APD_{60} measured at a constant voltage with the APD measured by the above method, and a significant correlation was found. DI was taken as the time interval from the end of APD_{60} to *V̇*_{max} of the next APD.

We calculated the first derivative of each sample during the upstroke of each AP, using a 5-point parabolic fit. The maximum first derivative was defined as the *V̇*_{max} for that particular AP.

#### Statistical analysis.

Statistical analysis of *V̇*_{max}, APA, APD, and DI during different periods of VF was performed with Repeated Measures (SPSS). As presented below, *V̇*_{max} and APA were highly correlated. Therefore, we chose just one of them, *V̇*_{max}, to use in the linear regression to predict APD_{(n)}. Stepwise linear regression (8) was used to determine how well each APD_{60} (APD_{60n}) could be predicted by the *V̇*_{max} of that AP as well as the four previous DIs (*n*−1, *n* − 2, *n* − 3, *n* − 4) and the three previous APD_{60}s (*n*−1, *n* − 2, *n* − 3) (SAS, SAS Institute). APD_{(n)} was the dependent variable, and *V̇*_{max(n)} and the previous three APDs (*n*−1, *n* − 2, *n* − 3) and four DIs (*n*−1, *n* − 2, *n* − 3, and *n* − 4) were independent variables. The forward stepwise procedure first found the single regressor that could best account for APD_{(n)} in a least-squares sense. It then found the next best regressor and continued to add in additional variables in order of increasing significance. The significance threshold for entering a variable was 0.25. The procedure was performed on four successive 5-s segments. Data are reported as means ± SD. The coefficient of variation of cycle length (CL), DI, and APD was compared with paired *t*-test. A value of *P* < 0.05 was considered statistically significant.

## RESULTS

The restitution relations for APD and *V̇*_{max} obtained during the pacing protocol were both well fit by an exponential function (Fig. 2*A*). Figure 2*B* shows that *V̇*_{max} decreased as the pacing cycle length decreased in the same animal as in Fig. 2*A*. However, consistent with our previous findings from the right ventricle (16), the plot of DI vs. APD during the first 20 s of VF formed a scattered cluster of points (*R*^{2} = 0.005; Fig. 3*A*). There was a weak linear relationship between DI and *V̇*_{max} (*R*^{2} = 0.21; Fig. 3*B*), indicating that there was a tendency for a larger *V̇*_{max} to be followed by a larger DI and vice versa. There was also a weak linear relationship between APD_{60(n−1)} and APD_{(n)} (*R*^{2} = 0.23; Fig. 3*C*), indicating that a larger APD tended to be followed by a larger APD during VF. There was no linear relationship between APD_{60(n−1)} and *V̇*_{max} (*R*^{2} = 0.06; Fig. 3*D*), indicating that there was no tendency for a longer APD to be followed by a larger *V̇*_{max}.

During sinus rhythm, APD_{60} was 326 ± 6 ms, APA was 108 ± 7 mV, and *V̇*_{max} was 117 ± 9 V/s. During the first 20 s of VF, CL was 125 ± 14 ms, DI was 30 ± 12 ms, and APD_{60} was 95 ± 16 ms. Thus the coefficient of variation in CL (11%) was significantly less than that of DI (40%) and APD (17%, *P* < 0.001). APA was 56 ± 10 mV, and *V̇*_{max} was 45 ± 31 V/s. APA and *V̇*_{max} were highly correlated during the first 20 s of VF (*R*^{2} = 0.92; Fig. 4).

Of the eight variables in the stepwise linear regression procedure, 5.5 ± 1.3 entered the equation to predict APD_{(n)} during VF (Table 1). *V̇*_{max} entered the equation to predict APD_{(n)} in 86% of the 5-s VF segments, with 90% of the coefficients positive. *V̇*_{max} was the first or second variable entered into the regression equation in 75% of the 5-s VF segments. DI_{(n−1)} was included in the equation second most frequently (58% of episodes), while APD_{(n−1)} was entered third most frequently (47% of episodes). DI_{(n−1)} and APD_{(n−1)} were the first or second entered in the regression equation in 35% and 26% of VF episodes, respectively. The coefficient of the variable in the equation was positive in 61% of the 5-s VF segments for DI_{(n−1)} and in 72% of the segments for APD_{(n−1)}.

In contrast, the coefficients were negative for DI_{(n − 2)} and APD_{(n − 2)} in >50% of the VF segments in which they entered the regression equation (Table 1). The coefficients were again positive for DI_{(n − 3)} and APD_{(n − 3)} in >50% of segments and then negative for DI_{(n − 4)} in >50% of segments. The mean ± SD of the *R*^{2} of the regression for all intervals was 0.51 ± 0.01.

To allow comparison with our previous study (16), in which we recorded from the right ventricle and digitized the microelectrode recording at a rate of only 2 KHz, we performed the stepwise linear regression procedure over the entire 20-s VF episodes without including *V̇*_{max}, but using only the seven previous DIs and APDs to predict APD_{(n)} during VF. Of these seven variables, 4.1 ± 1.2 entered the equation. Consistent with the data for the right ventricle (16), the two variables that appeared most frequently in the regression equation were APD_{(n−1)}, which entered for 97% of the VF segments, and DI_{(n−1)}, which entered for 75% of the segments (Table 2). The coefficients for the *n*−1, *n* − 2, and *n* − 3 variables alternated in sign for >50% of entered VF segments, similar to the findings from the right ventricle (16) as well as to the findings from the left ventricle when *V̇*_{max} was included in the regression procedure. The *R*^{2} of the regression for all segments was 0.30 ± 0.13.

To help determine the reason why multiple stepwise linear regression showed that DI and APD were related to the next APD but univariate linear regression did not, we examined the relationship of DI to the previous APD during the first 20 s of VF. These two variables were not independent. Instead, there was a negative relationship between DI and its preceding APD (*R*^{2} = 0.56; Fig. 5), so that a larger APD was usually followed by a shorter DI and vice versa, which is consistent with the smaller percent SD in CL, i.e., the sum of APD and DI, than in APD or DI.

## DISCUSSION

Our data indicate the following. *1*) *V̇*_{max} is a more important determinant of APD than are the previous DI and the previous APD during the first 20 s of VF in the pig. *2*) Consistent with our previous findings in the right ventricle (16), the data recorded from the left ventricle also show that both restitution and memory are significantly related to APD during this period of VF. *3*) The positive coefficients in the regression equation for the preceding *V̇*_{max}, APD, and DI are consistent with a longer APD preceded by a larger *V̇*_{max}, a longer previous APD (memory), and a longer previous DI (restitution). (4) Because CL varies less than APD or DI, APD is better correlated with the following DI than the previous DI (restitution).

#### Repolarization alternans and VF.

Cardiac electrical alternans has been recognized as a precursor to VF both experimentally and clinically (22, 27, 28). Over the past decade, many studies have investigated the mechanisms responsible for alternans and, on the basis of results from in vitro studies, much emphasis has been placed on the slope of the APD restitution curve as one of the main factors responsible for the induction of VF (12, 22, 25). However, most of the studies in which alternans was observed did not involve VF but used rapid pacing, in which the direction of wave front propagation and the activation rate were constant so that the effects of cardiac memory were constant.

During VF, there are many wave front collisions and fractionations (14), the activation rate frequently changes (15), and ischemia progresses continuously. The same cell at different times is activated by wave fronts that come from different directions at different rates. In this situation in which the effects of memory are changing, we found in this and our previous study that a linear univariate correlation between the APD and the previous DI, as predicted by the restitution hypothesis for VF, does not exist. While our previous in vivo study (16) demonstrated that memory in addition to APD restitution correlated with APD on the right ventricular epicardium, the two factors together predicted only 39% of the APD. Our findings from the left ventricular epicardium in the present study were similar: restitution and memory accounted for only 30% of the variation in APD.

#### V̇_{max} of action potential during VF.

Na^{+} channel activity is still maintained during the early stages of VF (33). *V̇*_{max} is determined by the rate at which Na^{+} enters the cytosol (11, 19). Abnormal elevation of intracellular Na^{+} has been observed in myocytes during VF and ischemia (11, 29). The rapid activation rate during VF increases the rates of Na^{+} and Ca^{2+} influx to such an extent that the Na^{+}-K^{+} pump and the Na^{+}/Ca^{2+} exchanger are unable to restore the ionic concentrations to normal levels and the APD is shortened (9, 30). Elevated intracellular Na^{+} concentration reduces the transmembrane Na^{+} gradient, resulting in deceased *V̇*_{max} and thus slowed conduction (11, 17). Thus *V̇*_{max} may be related to CV and may influence APD during VF. However, a simulation by Faber and Rudy (11) demonstrated that a significant decrease in *V̇*_{max} only occurred when the intracellular Na^{+} concentration was greater than ∼14 mM, with very little change at lower concentrations. The very fast rate during the first 20 s of VF might not be sufficient to cause this amount of change in Na^{+}; however, the global ischemia caused by the loss of coronary perfusion during VF would be expected to accelerate Na^{+} accumulation (21).

The membrane potential immediately before stimulation (the takeoff potential) is an important determinant of Na^{+} channel opening and so also affects APA and *V̇*_{max}. In the working myocardial cell at a normal resting potential of −85 mV, strong depolarizing stimuli generate large APs with rapid upstrokes. (3). However, if the cell is partially depolarized before stimulation, the same stimulus produces a smaller, more slowly rising AP because the preexisting depolarization inactivates Na^{+} channels (19). When depolarization closes the h gates of Na^{+} channels and the cell is in its relative refractory period, evoked APs have a slow *V̇*_{max}, are of low amplitude, and conduct slowly (19). These factors may explain why Zhou et al. (33) found a significant negative correlation between the takeoff potential and *V̇*_{max} during early VF. The correlation between *V̇*_{max} and APD does not necessarily mean that the variations in *V̇*_{max} are the direct cause of variations in APD. The cause may be variations in the takeoff potential or some other variable such as the state of the slow Ca^{2+} channels. The work of Akiyama (2) as well as Zhou et al. (33) suggests that VF action potentials are maintained by slow Ca^{2+} channel currents as well as Na^{+} channel currents.

When *V̇*_{max} was added to the stepwise linear regression, the contributions of the previous DI and the previous APD to the APD decreased. This finding suggests that some of the effect of the previous DI and APD on the APD is also present in the *V̇*_{max}. This is consistent with the univariate correlation between the previous DI (*R*^{2} = 0.21) and the previous APD (*R*^{2} = 0.06) with *V̇*_{max}. However, even with the addition of *V̇*_{max} to the regression equation, all of the factors together could only account for 51% of the variation in APD. Therefore, other factors, such as wave front direction, wave front curvature, electrotonus, and cardiac anatomy may also influence APD independent of *V̇*_{max}, restitution, and memory.

It is intriguing that although there was almost no univariate linear correlation between the APD and the previous DI (restitution), there was a significant correlation (*R*^{2} = 0.56) between the APD and the next DI. This relationship occurred because the CL, i.e., the sum of the APD and the next DI, varied less with a SD of 11% of the mean than did the DI with a SD of 40% of the mean or the APD with a SD of 17% of the mean.

#### Limitations.

One limitation is that we had to expose the epicardium to air to obtain recordings of the transmembrane potential. This procedure might have influenced the results of the study. However, we attempted to minimize cooling of the epicardium by dripping warm saline on it.

We only recorded and analyzed 20 s of VF in this study. Other investigators have shown that the Na^{+} channel deactivates and the slow Ca^{2+} current plays an increasing role in the action potential dynamics at later stages of VF (2). Therefore, the relationship between *V̇*_{max} and APD during later stages of VF may be different from that during early VF, and these differences should be investigated in future studies.

## GRANTS

This work was supported in part by National Heart, Lung, and Blood Institute Grants HL-085370, HL-066256, and HL-28429 and an American Heart Association Scientist Development Grant.

## Acknowledgments

We thank Frank Vance and Reuben Collins for their assistance in the animal preparation. We also acknowledge Kate Sreenan for assistance with manuscript preparation.

## Footnotes

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- Copyright © 2007 by the American Physiological Society