## Abstract

The clinical assessment of left ventricular (LV) systolic function during atrial fibrillation (AF) is unreliable and difficult because of beat-to-beat variability. We evaluated an index for the estimation of LV systolic function in AF that is based on the relationship between the preceding (R-R_{1}) and prepreceding (R-R_{2}) R-R intervals. LV Doppler stroke volume (SV), ejection fraction (EF), peak aortic flow rate (AoF) and the maximum value of the first derivative of the LV pressure curve (dP/d*t*
_{max}) were evaluated in 13 healthy open-chest dogs during triggered AF. All parameters showed a significantly strong positive linear relationship with the ratio of R-R_{1}/R-R_{2} (*r* = 0.65, 0.74, 0.75, and 0.70 for SV, EF, AoF, and dP/d*t*
_{max}, respectively). The calculated value of LV systolic parameters at R-R_{1}/R-R_{2} = 1 in the linear regression line showed a good relationship and an agreement with the measured average value of the parameter over all cardiac cycles (SV, 12.1 vs. 12.8 ml; EF, 49.6 vs. 51.2%; AoF, 1.37 vs. 1.48 l/min; and dP/d*t*
_{max}, 2,323 vs. 2,454 mmHg/s). Using the LV systolic parameters estimated at R-R_{1}/R-R_{2}= 1 in the linear regression line allows the LV contractile function to be accurately and reproducibly evaluated during AF and obviates the less-reliable process of averaging multiple cardiac cycles.

- preload
- afterload
- contractility
- R-R interval
- echocardiography
- left ventricular

atrial fibrillation(AF) is a major health problem that affects 0.9% of the population and is characterized classically by an irregularly irregular rhythm (9). The resultant effect of this irregularity is the absence of optimal left ventricular (LV) systolic function due to the loss of atrial booster-pump function as well as beat-to-beat changes in preload, afterload, and contractility (17). Yet another hemodynamic consequence of AF is the rapid ventricular rate, which further adversely affects LV function because preload and contractility diminish due to decreased filling time.

The beat-to-beat variation, which is the signature of AF, can be a detriment to the reliable and reproducible clinical assessment of LV systolic function (see Fig. 1,*top*). Owing to this variability, in clinical practice the standard protocol for obtaining an accurate assessment of LV function involves averaging a random number of consecutive cardiac cycles. In addition to being cumbersome, this process is suboptimal, because the averaged value is variable and dependent on a selected window of cardiac cycles (5). It is well appreciated that LV systolic function during AF varies depending on the preceding cardiac cycle lengths (3, 7, 12-14, 16, 23, 24, 26, 27). Nakamura and colleagues (22) reported a significant positive linear relationship between the maximum value of the first derivative of the LV pressure curve (dP/d*t*
_{max}) and the ratio of preceding (R-R_{1}) to prepreceding (R-R_{2}) R-R intervals (R-R_{1}/R-R_{2}). Recently Yamaguchi and co-workers (27) and Suzuki and colleagues (26) reported that the value of end-systolic LV maximum elastance (*E*
_{max}) at R-R_{1}/R-R_{2} = 1 in the linear regression line could estimate stable LV systolic function. Clinically it would be extremely valuable if LV systolic function could be accurately estimated using parameters that are noninvasively derived [such as Doppler stroke volume (SV) and ejection fraction (EF) from echocardiography] and validated [using peak aortic flow rate (AoF) and dP/d*t*
_{max}] and then the above index could be applied to relate the preceding and prepreceding R-R intervals.

The objectives of this study using an experimental canine AF model were to evaluate: *1*) the relationship between hemodynamic parameters (SV, EF, AoF, and dP/d*t*
_{max}) and the R-R_{1} and R-R_{2} intervals as well as the ratio of R-R_{1}/R-R_{2}; and *2*) whether the value of these LV systolic parameters at R-R_{1}/R-R_{2} = 1 in the linear regression line could estimate LV systolic function despite the potential influence by preload and afterload.

## METHODS

This study received institutional review and approval in accordance with the American Association for Accreditation of Laboratory Animal Care. A total of 13 healthy mongrel dogs weighing 25–35 kg were used in the present study. The dogs were placed in the supine position and were initially anesthetized with thiopental (20 mg/kg iv). Anesthesia was maintained with an inhalation mixture of oxygen and isoflurane (1.0–2.0%). The dogs were intubated with a cuffed endotracheal tube and ventilated with room air and oxygen through a Dräger SAV respirator (North American Dräger; Telford, PA), which was adjusted as needed to maintain normal arterial blood gases. Blood-gas values for the animals were maintained at a Po
_{2} of >80 mmHg, Pco
_{2}of 35–45 mmHg, and pH 7.35–7.45 via infusion with bicarbonate solutions and alteration of ventilation volume and rate. A median sternotomy was performed to expose the heart.

Quadripolar electrodes for recording and pacing were sutured to the right atrial (RA) appendage and the right ventricular (RV) apex. A bipolar plate electrode was sutured to the epicardial sinus node fat pad in the superior vena cava for delivery of vagal nerve stimulation to initiate and maintain AF (11). The pacing protocol was stored in a programmable stimulator Master-8. Surface electrocardiograms (ECGs; I, II, and III) and intracardiac ECGs (RV apex and RA appendage) were displayed continuously on a monitor, amplified, and digitally recorded on our laboratory recording system (EP Lab; Quinton Electrophysiology). AF was initiated by rapid-burst stimulation of the RA through the electrode sutured to the sinus node fat pad. Impulses were 1 ms in duration and were separated by a 50-ms interimpulse interval; typical amplitude was 2–5 V. Once the AF was initiated (usually after the first 5 s), the impulse was reduced to 50 μs, which was sufficient to produce stimulation of preganglionic vagal fibers to maintain AF.

A high-fidelity micromanometer catheter (Millar; Houston, TX) was inserted into the carotid artery and advanced such that the tip was near the LV apex for recording the LV pressure. Before the insertion, the catheter was soaked in warm saline for 30 min and zeroed to air. The LV dP/d*t*
_{max} was obtained from the LV pressure recording. The peak AoF was obtained by a transonic flow probe placed on the ascending aorta.

Epicardial echocardiography was performed using commercially available equipment, specifically, a Sequoia C512 ultrasound system (Acuson; Mountain View, CA) with a 3.5-MHz phased-array transducer. From the four-chamber view, the LV volumes at end diastole (EDV) and end systole (ESV) were calculated using the single-plane Simpson's rule. The LV EF was calculated by the formula EF = (EDV − ESV)/EDV × 100 (percent). The LV outflow tract velocity was recorded from the standard LV five-chamber view by placing the pulsed-wave Doppler sample volume at the LV outflow tract ∼1–2 cm below the aortic valve. The diameter of the LV outflow tract during midsystole was measured from the parasternal long-axis view. The Doppler SV was calculated as a product of the velocity-time integral of the LV outflow Doppler profile, and the LV outflow cross-sectional area was calculated from the LV outflow tract diameter (assuming a circular geometry).

After preamplification with a universal amplifier (Gould; Valley View, OH), the ECG data were digitized with 1-ms resolution using a 12-bit analog-to-digital converter (National Instruments; Austin, TX) interfaced with a Pentium 200-MHz computer running customized software developed in the LabVIEW graphical programming environment (National Instruments). All of the electrical and hemodynamic data were recorded into data-acquisition boards simultaneously with an echocardiogram during the baseline sinus rhythm and the triggered AF. The LV volumes and EF were measured from the videotape off-line for 10 consecutive cardiac cycles. These data were expressed as an average value ± SD. The differences in R-R intervals, LV volumes, and EF values between the two conditions were analyzed using Student's paired*t*-test.

Analysis of simultaneous electrical and hemodynamic data was performed within the LabVIEW environment. The LV systolic function was evaluated by pulsed-wave Doppler-derived SV and peak AoF in 11 of 13 dogs and the dP/d*t*
_{max} was used in all 13. We attempted to obtain each LV systolic parameter for >100 consecutive cardiac cycles, but the number of data points involving SV was <100 in 6 animals due to intermittent suboptimal Doppler signal quality. The R-R intervals were measured from the RV ECG. The R-R_{1} and R-R_{2} intervals for a given cardiac beat were measured with all LV systolic parameters during AF (see Fig. 1, *bottom*). The relationships between each LV systolic parameter at a given cardiac beat and the R-R_{1} interval, as well as the R-R_{1}/R-R_{2} ratio, were evaluated. The correlation coefficients were obtained by linear regression analysis. The value of each LV systolic parameter at R-R_{1}/R-R_{2} = 1 was calculated from the equation of linear regression line in the relationship between the parameter and the R-R_{1}/R-R_{2} ratio. Bland and Altman analysis (2) was applied to evaluate the relationship and agreement between the calculated values of each parameter at R-R_{1}/R-R_{2} = 1 in the linear regression line and the measured average value of each systolic parameter in all cardiac cycles. The difference in correlation coefficients in the relationship between R-R_{1} or the R-R_{1}/R-R_{2} ratio and each parameter was evaluated by a Fisher's *Z* transformation and a Student's paired *t*-test. Estimation of the LV EF during AF was again performed using the value at R-R_{1}/R-R_{2} = 1 in the linear regression line with a smaller sample of consecutive cardiac cycles (16–26 cycles) in 9 of 13 dogs. *P*< 0.05 was considered statistically significant.

## RESULTS

Compared with sinus rhythm, triggered AF caused significant shortening of the R-R interval (427 ± 81 vs. 341 ± 122 ms;*P* < 0.0001) and decreases in average EF (61 ± 9 vs. 51 ± 8%; *P* < 0.01), LV EDV (22 ± 6 vs. 14 ± 4 ml; *P* < 0.0001), and peak systolic LV pressure (140 ± 58 vs. 80 ± 21 mmHg; *P* < 0.0001).

All LV systolic parameters during AF showed a significant positive correlation with R-R_{1} intervals (*r* = 0.58, 0.58, 0.63, and 0.59 for SV, EF, AoF, and dP/d*t*
_{max}, respectively; see Fig.2, *left*) and the R-R_{1}/R-R_{2} ratio (*r* = 0.65, 0.74, 0.75, and 0.70 for SV, EF, AoF, and dP/d*t*
_{max}, respectively; see Fig. 2,*right*). However, the correlation coefficients were significantly greater for the relationship between the systolic parameters and the R-R_{1}/R-R_{2} ratio than for those between the parameters and the R-R_{1} interval alone (*P* < 0.05, 0.01, 0.001, and 0.01 for SV, EF, AoF, and dP/d*t*
_{max}, respectively). Interestingly, even when a relatively small number of cardiac cycles were used, LV EF and SV also showed a significant positive correlation with the R-R_{1}/R-R_{2} ratio (see Fig.3).

Tables1-4show the average values during the baseline sinus rhythm, the equation of the linear regression line (i.e., the relationship between the LV systolic parameters and the R-R_{1}/R-R_{2} ratio), and the calculated values of each parameter at R-R_{1}/R-R_{2} = 1 in the linear regression line, as well as the measured average value over all cardiac cycles during AF in each of the studied dogs. The calculated value of each LV systolic parameter at R-R_{1}/R-R_{2} = 1 in the linear regression line was quite similar to the measured average value over all cardiac cycles during AF (SV, 12.1 vs. 12.8 ml; AoF, 1.37 vs. 1.48 l/min; dP/d*t*
_{max}, 2,323 vs. 2,454 mmHg/s; EF, 49.6 vs. 51.2%). The Bland and Altman analysis showed a good relationship and agreement between the calculated and measured values of each LV systolic parameter (see Figs. 4 and5).

For each of the LV systolic functional parameters, both the calculated values at R-R_{1}/R-R_{2} = 1 in the linear regression line and the measured average values were significantly smaller during triggered AF than during baseline sinus rhythm (see Tables 1-4).

## DISCUSSION

As a result of beat-to-beat variation, it has traditionally been difficult to estimate LV systolic function in patients with AF. This problem applies to all measures of ventricular contractile function including noninvasively derived measures such as LV EF and SV as well as invasively obtained parameters such as dP/d*t*
_{max}. It would be useful to have an accurate and reproducible method available by which one could instantaneously estimate LV systolic function during AF in patients undergoing routine cardiac evaluations. In this study we demonstrated that impaired LV systolic function during AF could be accurately assessed by invasively derived peak AoF and dP/d*t*
_{max} and echo Doppler-derived SV and LV EF using the ratio of the preceding and prepreceding R-R intervals.

A positive correlation between the R-R_{1} interval and dP/d*t*
_{max}, Doppler SV, and LV outflow peak velocity was previously reported for AF (13, 16, 21). The beat-to-beat variations in blood pressure that are also characteristic of AF have been ascribed to time-dependent changes in ventricular filling acting via the Frank-Starling mechanism (1, 3, 8). Furthermore, Hardman and colleagues (13) reported that the interval-force relationship (mechanical restitution) is a significant determinant of the beat-to-beat variation that is typical of the LV contractile state during AF. This mechanical restitution phenomenon is a situation whereby a larger force development occurs after long intervals and smaller force occurs after short intervals (4,6).

A negative correlation between the R-R_{2} interval and measures of systolic function has also been reported for AF (12,14, 23). This inverse relationship between the prepreceding R-R interval and contractility (postextrasystolic potentiation) is a phenomenon responsible for stronger contractions after a cardiac cycle with a short coupling interval (14, 15, 20). Therefore, given the variability in cycle lengths, it is necessary to evaluate LV systolic function during AF by taking into account both mechanical restitution (dependent on the R-R_{1} interval) and postextrasystolic potentiation (dependent on the R-R_{2}interval).

*E*
_{max} is an index for evaluating LV systolic function that is considered to be relatively load independent (25-27). Yamaguchi and co-workers (27) reported that the *E*
_{max} at R-R_{1}/R-R_{2} = 1 in the linear regression line of the relationship between *E*
_{max} and the R-R_{1}/R-R_{2} ratio during AF could estimate resting LV systolic function. Unfortunately,*E*
_{max} is not a parameter that is clinically available and can be readily measured in a simple, routine, and noninvasive manner (18). Furthermore, there is a critical limitation for the use of this method in patients with AF due to the beat-to-beat variability observed in pressure-volume loops. Yamaguchi and colleagues (27) determined *E*
_{max}during irregular heart beats as the slope of the line connecting the left-upper corner of the pressure-volume loop of each cardiac cycle and a “predetermined” LV volume at which the peak isovolumic LV pressure was zero (*V*
_{0}). This was derived during regular pacing in an experimental canine model with the assumption that*V*
_{0} is constant during AF. Therefore, not only is this assumption flawed, but we cannot apply this methodology to the clinical setting where determination of *V*
_{0} is not feasible.

Conversely, the LV EF and Doppler SV obtained by echocardiography are widely available as noninvasive measures of LV function and dP/d*t*
_{max}, and peak AoF can be readily obtained in the catheterization laboratory and operating room. It would be clinically useful if the values of these LV systolic parameters at R-R_{1}/ R-R_{2} = 1 in the linear regression line could also estimate resting LV systolic function similar to the findings using *E*
_{max}.

In our study, >100 consecutive cardiac cycles were evaluated to obtain a reliable estimate of LV systolic function. This suggests that the calculated values obtained with R-R_{1}/R-R_{2} = 1 in the linear regression line, which showed a good agreement with the averaged values over all cardiac cycles, can be expected to reliably estimate LV systolic function during AF. Recently it was reported (5) that the optimal number of beats necessary for estimating LV systolic function during AF is at least 13. Notably, we have also observed a high correlation coefficient when a smaller number of cardiac cycles were evaluated for an estimation using the parameters (EF and Doppler SV) at R-R_{1}/R-R_{2} = 1 (see Fig. 3). We conclude therefore that it is possible to obtain an accurate and reliable estimated value at R-R_{1}/R-R_{2} = 1 in the linear regression line for the average LV systolic function during AF using a relatively small number of consecutive cardiac cycles.

Suzuki and colleagues (26) have recently presented a computer-simulation study in which they used equations proposed by Yue and co-workers (28) to describe ventricular contractility (measured as *E*
_{max}) during AF as a result of the combined action of mechanical restitution and postextrasystolic potentiation. These authors found that ventricular contractility of any given irregular beat could be reasonably predicted by the value of the R-R_{1}/R-R_{2} ratio for that beat. Moreover, it has been demonstrated that the value when the intervals are equal (R-R_{1} = R-R_{2}; hence R-R_{1}/R-R_{2} = 1) in the regression line closely estimates the average value of ventricular contractility.

In general, our results confirm the findings of Suzuki and colleagues (26) and extend that work by demonstrating that R-R_{1}/R-R_{2} = 1 can be used with the regression line to determine the average values for a number of important echocardiographic (EF and SV) and hemodynamic (dP/d*t*
_{max} and peak AoF) parameters. However, it should be noted that our results suggest the need for a cautious extrapolation of the computer-simulation results. The linear combination of the two mechanisms [as in the model of Suzuki and colleagues (24)] may not be true for a wide range of irregular R-R_{1} and R-R_{2} intervals. As shown in Figs. 2 and 3, there was a substantial scattering of data points for each of the measured physiological parameters when R-R_{1}/R-R_{2} = 1. This precludes the use of just any given pair of equal subsequent intervals.

The possible reason for the above restriction can be understood in the context of combined effects of restitution and potentiation. The potential potentiation and the time required for mechanical restitution might be variable in different individuals depending on pathophysiological conditions. The smallest degree of LV contractility (i.e., the minimum potentiation) can be realized when the longest duration of the prepreceding R-R interval and the shortest restitution time are combined. Furthermore, the greatest degree of contractility (i.e., maximum potentiation) could be produced when the shortest duration of the prepreceding R-R interval and the longest restitution time are combined. The correct estimation of the average physiological parameter principally requires substitution of R-R_{1}/ R-R_{2} = 1 in the regression line that is obtained on the basis of a large number of fibrillatory intervals. We have demonstrated, however, that in some cases the total number of observed fibrillatory intervals can be relatively small (see Fig. 3). Furthermore, the linear regression line could be determined by the maximum and minimum potential LV contractility in relation to the ratio of R-R_{1}/R-R_{2} because the value at R-R_{1}/ R-R_{2} = 1 in the linear regression line can be regarded as a mean LV contractility. In the clinical scenario, we speculate that the LV systolic value at *x*= 1 in the equation of the linear regression line (which could be drawn by connecting only extreme values at which the R-R_{1}/R-R_{2} ratio are maximum and minimum) may provide a reliable estimate of LV systolic function during AF.

Further studies are needed, however, to determine if a representative regression line can be produced with a limited number of observations.

There are some limitations in the present study. In measuring the beat-to-beat variability of each LV systolic parameter, it was necessary to include all values, even those approaching zero. Had we omitted those values, an R-R interval might have been misrepresented as being longer than it actually was. We only excluded beats appearing during the mechanical refractory period; otherwise, it would be impossible to obtain a reasonable correlation between LV systolic parameters and the R-R_{1}/R-R_{2} ratio. Another limitation was the use of healthy mongrel dogs in this experiment. We did not evaluate whether these relationships could also be observed in the pathological heart. However, other investigators have shown that LV SV variability during AF was not influenced by impaired LV systolic function (19), and interval-dependent potentiation of contractility was preserved in patients with depressed LV function (21). A validation study would be necessary to determine whether this index could be applied to depressed or failing hearts. In the present study, AF was acutely induced by burst stimulation of the right atrium and was perpetuated by vagal nerve stimulation in anesthetized open-chest dogs. The resultant ventricular response rate and depolarization sequence might be different in patients with chronic AF. An advantage of this model is that the cycle-length variability was random and not controlled. Clinical study may be necessary to determine whether these relationships are valid for naturally occurring AF. Finally, we evaluated relatively short R-R intervals in this study as was dictated by our AF model. This is because most animals in this triggered AF model manifested a rapid ventricular rate. If the R-R interval exceeded 600 ms, the curve might plateau with complete mechanical restitution, and the relation could be exponential (10). However, the relation was mostly linear when R-R intervals were short. Furthermore, the relationship between LV systolic function and the R-R_{1}/R-R_{2} ratio was more likely linear, and the correlation coefficient obtained by monoexponential fitting might not be significantly different from that by linear regression analysis (27). Therefore, the evaluation of LV systolic function using a linear regression line seems reasonable. Further study is needed to evaluate whether this index would remain true even with very slow ventricular rates.

The pulsed-wave Doppler SV and EF are used clinically and are more practical than the complex invasive method that is required to measure*E*
_{max}, AoF, and dP/d*t*
_{max}. Furthermore, both of these parameters have shown a significantly positive correlation with the R-R_{1}/R-R_{2} ratio even when a relatively small number of cardiac cycles was sampled. The typical practice of averaging LV systolic parameters is hindered in that it is time consuming and variable depending on the cardiac cycles selected. By contrast, obtaining a value of the LV systolic parameter at R-R_{1}/R-R_{2} = 1 in the linear regression line may provide a more accurate method for estimating resting LV systolic function during AF. Finally, although clinically useful and readily available parameters were tested, the implementation of this index, which relates preceding cardiac cycles, will require automated methods of sampling several cardiac cycles for it to become a clinically useful and practical tool. Methods currently commercially available on ultrasound equipment, such as on-line and real-time automated endocardial border-detection algorithms for determination of EF as well as automated Doppler signal envelope-detection methods, would allow data acquisition and output of a long consecutive series of cardiac cycles.

We conclude that measured parameters of LV systolic function during AF closely correlate with the ratio of the preceding and prepreceding R-R intervals. Using the LV systolic parameters calculated at R-R_{1}/R-R_{2} = 1 in the linear regression line allows LV contractile function to be accurately and reproducibly evaluated in AF, which obviates the less-reliable and cumbersome process of averaging multiple cardiac cycles.

## Acknowledgments

This work is supported in part by American Heart Assoication Grant AHA-9808489A (T. N. Mazgalev) and National Institutes of Health Grant RO1-HL-60833-01A1.

## Footnotes

Address for reprint requests and other correspondence: R. A. Grimm, Cardiovascular Imaging Center, Dept. of Cardiology, Desk F-15, Cleveland Clinic Foundation, 9500 Euclid Ave., Cleveland, OH 44195 (E-mail: grimmr{at}ccf.org).

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- Copyright © 2001 the American Physiological Society