Determination of the Target Ventricular Rate

Abstract

In a pilot study, we determined the target ventricular rate of patients with atrial fibrillation by evaluating their ventriculoarterial coupling.

Eleven patients with atrial fibrillation were studied. We recorded M-mode echocardiograms and radial artery blood pressure simultaneously. The left ventricular end-systolic pressure-volume ratio (Emax) and effective arterial elastance (Ea) were calculated for each beat, and the relationship of the preceding R-R interval (pRR) to Emax and Ea was evaluated. There was a significant positive correlation between pRR and Emax, and a significant negative correlation between pRR and Ea in all patients. The pRR that produced maximal stroke work was determined at the point of Emax=Ea, and the pRR that achieved maximal mechanical efficiency was determined at the point of 2Ea=Emax. By evaluating ventriculoarterial coupling in these patients who had atrial fibrillation, we were able to determine that the range between the 2 pRR intervals was the range of the optimal ventricular rate. A narrower range of the 2 pRR intervals was observed in patients with dilated cardiomyopathy than in the patients with no underlying cardiac disease.

We conclude that it may be possible to determine the optimal ventricular rate in patients with atrial fibrillation by evaluating ventriculoarterial coupling. (Tex Heart Inst J 2002;29:100–4)

Although good ventricular rate control is frequently set forth as a goal of therapy for patients with atrial fibrillation (AF), a method for determining the target ventricular rate in these patients has not been established and remains an important unresolved problem. ^1–3 It is not clear whether target ventricular rate differs in the presence or absence of underlying cardiac disease.

In the mid-1980s, an analysis of ventricular efficiency by means of ventriculoarterial coupling was proposed by Sunagawa and co-authors ^4,5 and Burkhoff and Sagawa. ⁶ In accordance with this method, left ventricular properties are quantified by using the slope (Ees) and volume (Vo) axis intercept of the linear end-systolic pressure-volume relationship. ⁶ Similarly, ventricular afterload is represented by the effective arterial elastance (Ea), ⁶ which is also quantified by using the slope of the relationship between the end-systolic pressure and stroke volume. By means of this analysis, Asanoi and colleagues ⁷ established that a relationship exists between stroke volume, ventricular contractility, preload, and afterload. We considered the possibility of applying the results of such analysis to the control of ventricular rate in patients with AF, and we conducted a pilot study.

The purpose of this pilot study was to estimate the optimal ventricular rate in patients with AF by study of ventriculoarterial coupling and to investigate whether this optimal rate is different in the presence of left ventricular insufficiency.

Patients and Methods

Eleven patients with chronic AF were divided into 2 groups: 7 with no underlying cardiac disease (lone-AF group), and the other 4 with dilated cardiomyopathy (DCM group). There was no significant difference in age between the 2 groups (Table I). The severity of cardiac dysfunction ranged from New York Heart Association class II to class III, and 2-dimensional echocardiography revealed diffuse hypokinesis of left ventricular wall motion in all 4 DCM patients. Patients with regional wall motion abnormalities, mitral regurgitation, and aortic valve stenosis were excluded from this study. No subjects in the lone-AF group received medication. All subjects in the DCM group were treated with diuretic agents and digitalis; in addition, 3 were treated with a vasodilator and 2 with an angiotensin-converting enzyme inhibitor.

Table I. Clinical Characteristics of the Patients

Using a Toshiba SSH-160A ultrasonoscope (Tokyo, Japan) with a 3.75-MHz transducer, we performed 2-dimensional, targeted, M-mode echocardiography of the left ventricular cavity; simultaneously, we recorded radial artery pressure (Jentow, Colin Electronics CBM-7000; Tokyo, Japan). All subjects gave their informed consent after receiving a detailed explanation of the procedures and their possible clinical benefits. All data were recorded by means of a Toshiba LSR-100A line scan recorder, which simultaneously recorded a lead-II electrocardiogram (ECG) and phonocardiogram at a paper speed of 50 mm/sec (Fig. 1). The left ventricular end-diastolic diameter was obtained at the peak of the R wave of the ECG, and the end-systolic diameter was obtained at the initial component of the 2nd heart sound. Left ventricular end-diastolic volume (LVEDV) and end-systolic volume (LVESV) were determined using the formula of Teichholz and colleagues, ⁸ and stroke volume (SV) was obtained by using the formula SV = LVEDV – LVESV. Left ventricular end-systolic pressure (LVESP) was approximated from the systolic component of the dicrotic pressure reading at the radial artery. The left ventricular end-systolic pressure-volume ratio (Emax) and effective arterial resistance (Ea) ⁷ were calculated using the following formulae: Emax = LVESP/LVESV and Ea = ESP/SV. Because Emax and Ea vary from beat to beat in patients with AF, we calculated Emax and Ea for each of 15 to 20 consecutive beats, then evaluated the relationship between the preceding R-R interval (pRR) and Emax or Ea.

Fig. 1 A simultaneous recording of an echocardiogram (ECG) and a phonocardiogram (PCG), this last for radial artery pressure.

DBP = diastolic blood pressure; ESP = end-systolic pressure; LVDd = left ventricular dimension (end-diastolic); LVDs = left ventricular dimension (end-systolic); SBP = systolic blood pressure

Results

Relation of Preceding R-R Interval to Emax or Ea.

In all patients, there was a significant positive correlation between pRR and Emax, and a significant negative correlation between pRR and Ea. Figure 2 shows an example of these relationships in a DCM patient. There was a close correlation (r=0.815) between the pRR-Emax and the pRR-Ea (r=−0.702). Individual data on the regression coefficients of the pRR-Emax relation and pRR-Ea relation are listed in Table II.

Fig. 2 Correlation between preceding R-R interval and Emax or Ea in a patient from the dilated cardiomyopathy group. There is a positive correlation between pRR and Emax (r=0.815, left panel) and a negative correlation between pRR and Ea (r=−0.702, right panel).

Ea = effective arterial elastance; Emax = left ventricular end-systolic pressure-volume ratio; pRR = preceding R-R interval

Table II. Regression Coefficients in 11 Patients, Showing Relation of pRR to Emax and Relation of pRR to Ea

Determination of Optimal Ventricular Rate in Patients with AF.

When the regression line of the pRR-Emax relationship was superimposed on that of the pRR-Ea relationship in the same pRR axis, the pRR that produced maximal stroke work was determined by the abscissa of the intersection between these 2 regression lines (Emax=Ea); similarly, the pRR that achieved maximal mechanical efficiency was determined by the abscissa of the intersection between 2Ea=Emax. The range between these 2 pRR intervals was considered the range of the optimal ventricular rate in evaluating ventriculoarterial coupling in patients with AF (Fig. 3). Individual data on the pRR intervals where Emax=Ea and Emax=2Ea, and on the range between these 2 pRR intervals, appear in Table III.

Fig. 3 Determination of optimal ventricular rate in patients with atrial fibrillation. The regression pRR and Emax can be superimposed on the regression line between pRR and Ea in the same pRR axis. The pRR that produces maximal stroke work is determined by the abscissa of the intersection between these 2 regression lines (Emax=Ea), and the pRR that achieves maximal mechanical efficiency is measured as the abscissa of 2Ea=Emax. The range between the 2 pRR intervals is considered the range of the optimal ventricular rate.

Ea = effective arterial elastance; Emax = left ventricular endsystolic pressure-volume ratio; pRR = preceding R-R interval

Table III. Individual Data of Optimal Heart Rate

Comparison of Target Ventricular Rate between Lone-AF and DCM Patients.

We compared the lone-AF patients with the DCM patients in regard to the 2 pRR intervals and the range between them. Between the 2 groups, there were no significant differences in either of the pRR intervals. However, the range between the 2 pRR intervals was significantly narrower in the DCM group (Fig. 4).

Fig. 4 Optimal ventricular rate in patients with atrial fibrillation. There are no significant differences between the 2 groups in either of the pRR intervals (left panel: pRR where Emax=Ea, center panel: pRR where Emax=2Ea). The range between the 2pRR intervals (right panel) is significantly narrower in the DCM group than in the LAF group.

DCM = dilated cardiomyopathy group; Ea = effective arterial elastance; Emax = left ventricular end-systolic pressure-volume ratio; LAF = lone-atrial fibrillation group; pRR = preceding R-R interval

Discussion

In patients with AF, hemodynamic disturbance is caused by the loss of atrial systole and by an inappropriately rapid and irregular ventricular rhythm. The rapid ventricular rate decreases diastolic filling and the left ventricular stroke volume. Therefore, control of the ventricular rate is an important issue in the management of patients with AF. ^1–3 However, no one has ever established what the ‘controlled’ rate should be. Bigger ⁹ recommends maintaining the ventricular rate at 50 to 90 beats/min at rest, while Storstein ¹⁰ suggests an even narrower range of 60 to 80 beats/min. Rawles ³ has reported that because atrial contraction is estimated to contribute to stroke volume by 20% to 50%, the ventricular rate in AF needs to be 20% to 50% higher than in sinus rhythm, to maintain a normal cardiac output. In all of these reports, the primary purpose for the control of the ventricular rate was to maintain normal cardiac output or stroke volume. The control of the ventricular rate has never been discussed from the viewpoint of ventricular efficiency.

Evaluating ventricular efficiency on the basis of ventriculoarterial coupling has been proposed by Sunagawa and colleagues ^4,5 and Burkhoff and Sagawa. ⁶ As mentioned earlier, left ventricular properties are quantified by using the slope (Ees) and volume (Vo) axis intercept of the linear end-systolic pressure-volume relationship, and ventricular afterload is represented by the effective arterial elastance (Ea) ⁶—also quantified by using the slope of the relationship between the end-systolic pressure and stroke volume.

Optimal ventriculoarterial coupling is achieved (that is, stroke work from a given end-diastolic volume is maximum), when Ees=Ea; and ventricular mechanical efficiency is optimized when Ees=2Ea. ^5,6,11 Using a physiologically loaded canine heart, Sunagawa's group ^4,5 experimentally demonstrated that left ventricular external work reaches its maximum when Ees=Ea. Burkhoff and Sagawa ⁶ showed that maximal mechanical efficiency is, in theory, attained when Ees=2Ea. Asanoi and coworkers ⁷ showed that Ees is nearly equal to 2Ea in subjects with normal ejection fractions (60% or more), and that Ees is nearly equal to Ea in subjects with moderately depressed ejection fractions (40%–59%).

In subjects with normal sinus rhythm, the Ea/Emax ratio is determined by ventricular contractility and the effective arterial elastance. Since preload, afterload, and ventricular contractility vary from beat to beat in patients with AF, ¹¹ Ees and Ea are not constant. However, Ees and Ea are considered to be influenced by cardiac cycle length, because they are derived from the pressure-volume relationship. In the present study, we used the left ventricular end-systolic pressure-volume ratio (Emax) as a parameter of left ventricular contractility, ^12,13 we used the end-systolic pressure-stroke volume ratio instead of Ea, ¹⁴ and we evaluated the relation of preceding R-R intervals (pRR) with both Emax and Ea.

In all patients, there was a significant positive correlation between pRR and Emax, and a significant negative correlation between pRR and Ea. These results suggest that optimal ventriculoarterial coupling can be determined by examining pRR in patients with AF. Therefore, we used a new method for determining optimal ventricular rate in patients with AF: in the same pRR axis, we superimposed the regression line of pRR-Emax on the regression line of pRR-Ea. In this manner, the pRR that produces the maximal stroke work is determined by the intersection of the abscissa between the 2 regression lines (Emax=Ea), and the pRR that produces maximal mechanical efficiency is determined by the intersection of the abscissa of 2Ea=Emax. By evaluating ventriculoarterial coupling in patients with AF, we found the range of the optimal ventricular rate to be the range between the 2 pRR intervals. In the present study, the target ventricular rate is the heart rate that achieves optimal coupling between the left ventricle and the arterial system.

Optimal ventricular rate may not be the same in the presence of underlying cardiac disease. In comparing pRR intervals in the lone-AF group with those in the DCM group, we found no significant differences between the groups, but the range between the 2 pRR intervals was significantly narrower in the DCM group. These results suggest that target ventricular rate is different in AF patients with underlying cardiac disease, and that changes in heart rate can easily cause failure of ventriculoarterial coupling in patients with DCM.

Study Limitations.

In this study, stroke volume was determined by using the formula of Teichholz and associates. ⁸ These investigators obtained measurements by M-mode echocardiography, which is inherently limited in its ability to measure left ventricular chamber size or stroke volume in patients with regional wall motion abnormalities. Therefore, we excluded from our study all patients with regional wall motion abnormalities, such as those caused by myocardial infarction.

In this study, measurements were not taken during exercise. Therefore, we have not excluded the effects of changes in autonomic tone caused by exercise.

The small number of cases analyzed in the present study is a weakness only partly offset by the novelty of what we have done: never before has the target ventricular rate in patients with AF been established by evaluating ventricular efficiency on the basis of ventriculoarterial coupling.

Clinical Implication.

Determination of the optimal ventricular rate by the evaluation of ventriculoarterial coupling as we have proposed might be useful in rate management by drug therapy (such as verapamil administration) or by pacemaker implantation.

Conclusion

In conclusion, this pilot study suggests that it is possible to determine the optimal ventricular rate in patients with AF through study of ventriculoarterial coupling. The range of optimal ventricular rates revealed in this manner is narrower in patients with dilated cardiomyopathy than in those with no underlying cardiac disease.