INTRODUCTION

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LEFT VENTRICULAR CONTRACTILITY is commonly defined by the end-systolic pressure-volume relationship (ESPVR) (15, 16, 24). In the right ventricle (RV), the concept of ESPVR is also valid (8, 20) but it is difficult to apply in practice. The major problem is the difficulty in measuring instantaneous RV volume in vivo. In 1988, Kass (13) summarized the limitations of available methods and mentioned the potential of conductance volumetry. Although not completely validated for measurement of instantaneous volume, conductance has been used repeatedly to generate pressure-volume loops in animals and humans (34). The method remains difficult and time consuming and is therefore predominantly used as a research tool (31). A second problem may be the identification of end systole on triangle-shaped RV pressure-volume curves. Several investigators (9, 20) determined ESPVR from end-ejection pressures and volumes, but end ejection and end systole are known to occur at different times in the RV. Finally, the ESPVR is generally obtained during a transient change in preload or afterload, but such maneuvers may affect sympathetic tone and myocardial contractility and may not be acceptable in patients.

We therefore propose a method to assess right ventricular ESPVR without measuring instantaneous RV volume and without changing preload or afterload (Fig. 1). Part of this method has been validated for the left ventricle (26, 27). It assumes that the ESPVR is the same in ejecting and isovolumic beats, and that the maximal pressure of an isovolumic beat (P_max) can be extrapolated from normal ejecting beats. We investigated whether RV P_max can also be predicted from normal ejecting beats to determine ESPVR and to derive RV end-systolic elastance (E_es), pulmonary artery effective elastance (E_a), and ventricular-arterial coupling efficiency as the E_es-to-E_a ratio (E_es/E_a). We further investigated whether E_es reflects RV contractile changes induced by dobutamine and propranolol, and whether it is affected by changes in RV preload or afterload.

View larger version (10K): [in this window] [in a new window]   Fig. 1.   Principle of single-beat end-systolic pressure-volume relationship (ESPVR) determination. The ESPVR is assumed linear and afterload independent. Trace ABCDA is the pressure-volume curve of a normal ejecting beat, with end diastole in point A and end-systole in point C. In a traditional approach, a progressive increase of afterload at same preload yields the end-systolic points I, J, and K, and the ESPVR is defined as the CIJK line. In the present approach, the computed maximal pressure of an isovolumic beat at same preload (ABLBA) yields the end-systolic point L, and ESPVR is defined as the CL line.

	METHODS

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Preparation. The experiments were done in accordance with the "Guiding Principles in the Care and Use of Animals" approved by the American Physiological Society. Details of our preparation have been published previously (4). Briefly, 28 mongrel dogs (mean wt 24 kg) were anesthetized with sufentanil (10 µg/kg iv) and -chloralose (80 mg/kg iv), followed by infusions of sufentanil (1 µg · kg¹ · h¹) and -chloralose (20 mg · kg¹ · h¹), and ventilated with 40% O₂ and 5 cmH₂O end-expiratory pressure. RV pressure was monitored with a micromanometer catheter (Millar Instruments; Houston, TX) and instantaneous pulmonary blood flow with a transit-time ultrasonic flow probe (Transonic Systems; Ithaca, NY). Cardiac output and RV ejection fraction were measured with a fast-response thermodilution pulmonary artery catheter (Baxter-Edwards; Irvine, CA) (30). A clamp was placed around the pulmonary artery upstream from the flow probe, ~1 cm away from the pulmonary valve. The chest was closed but no attempt was made to restore negative pleural pressure. Hypoxic pulmonary vasoconstriction was enhanced by aspirin (20 mg/kg iv) (4).

Protocol. In the first part of the study, flow and pressures were recorded during several beats before and during the first beat after the proximal pulmonary artery was clamped (Fig. 2). In each dog, the procedure was repeated at each combination of normal or low preload and normal or high afterload with normal or low or high myocardial contractility (12 combinations). Preload was decreased by inflating a balloon in the inferior vena cava to reduce venous return. Afterload was increased by reducing the inspired oxygen to 10% to cause hypoxic pulmonary vasoconstriction. Contractility was increased by dobutamine (5-10 µg · kg¹ · min¹ iv) and decreased by propranolol (1 mg/kg iv). In the second part of the study, flow and pressures were recorded to determine ESPVR and to assess RV contractility and coupling efficiency. Contractility, preload, and afterload were modified by the same procedures as before. Because we found flow reduction and hypoxia to cause sympathetic stimulation, we also increased the afterload by constricting the proximal pulmonary artery and assessed the effects of flow reduction, hypoxia, and constriction before and after - and -adrenergic blockade with phentolamine (2 mg/kg iv + 50 µg · kg¹ · h¹) and propranolol (2 mg/kg iv) (4).

View larger version (21K): [in this window] [in a new window]   Fig. 2.   Example of proximal pulmonary arterial (PA) clamping procedure. The beat recorded just after the clamping is isovolumic, as verified by the absence of flow in the artery, and begins at the same end-diastolic volume and pressure (press) as the normal ejecting beats. RV, right ventricular.

Data analysis. Ventricular and arterial components of coupling, E_es and E_a, were determined from about five signal-averaged consecutive beats. First, RV end-diastolic volume was calculated as the ratio of stroke volume to ejection fraction (end-diastolic volume does not affect E_es or E_a; see DISCUSSION). The decrease of RV volume during systole was computed by integration of the instantaneous pulmonary arterial flow, assuming that blood flowing through the proximal pulmonary artery was ejected from the RV. Second, the RV pressure-volume loop (limited to isovolumic contraction, ejection and isovolumic relaxation) was constructed from instantaneous RV pressure and volume. Third, P_max was determined by fitting the equation P = a + b · sin (c · t + d), where P is pressure and t is time, to RV pressure values before the maximal first derivative of pressure development over time (dP/dt) and after minimal dP/dt (Fig. 3, left) (26). Coefficients a-d were computed by a least-square nonlinear fitting routine by using the Levenberg-Marquardt procedure. P_max was obtained as P_max = a + 2 b. Fourth, the ESPVR line was drawn from P_max down and tangent to the pressure-volume curve, i.e., from predicted isovolumic beat end systole to actual ejecting beat end systole (Fig. 3, right) (27). The arterial effective elastance line was drawn from end systole to end diastole. Fifth, E_es was computed as the slope of the ESPVR line, and E_a as the absolute slope of the arterial elastance line (17).

View larger version (21K): [in this window] [in a new window]   Fig. 3.   Determination of ventricular end-systolic elastance (Ees) and arterial effective elastance (Ea). Left: end-systolic pressure of an isovolumic beat is computed by sine wave extrapolation from the ejecting beat by using pressure values recorded before maximal first derivative of pressure development over time (dP/dt) and after minimal dP/dt. Right: this maximal RV pressure of isovolumic beats (Pmax) value is drawn on the RV pressure-volume diagram. The ESPVR line is drawn from Pmax down and tangent to the pressure-volume curve, i.e., from predicted isovolumic beat end systole to actual ejecting beat end systole (defined by the contact point of pressure-volume curve and ESPVR line). The effective arterial elastance line is drawn from end systole to end diastole. Ees is the slope of the ESPVR line, and Ea is the absolute slope of the arterial elastance line.

Statistics. Results are expressed as means ± SE. Predicted and observed values were compared by correlation analysis. Changes in contractility, preload, and afterload were tested by analysis of variance and analysis of contrasts. P values <0.05 were accepted as indicating statistical significance.

	RESULTS

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P_max prediction. Observed P_max values were obtained in 136 of the 144 instances. Failures were related to premature beats triggered by the clamping procedure. Predicted P_max values were obtained in 114 instances. Failures were mainly related to RV pressure tracing artifacts due to catheter knocking against the ventricular wall at low preload or during dobutamine infusion. The automated fitting procedure failed in eight instances. Overall, 106 pairs of values were available for correlation analysis. In each dog, a strong correlation was observed between observed and predicted P_max (r = 0.98 ± 0.02, P < 0.001). Regression lines had intercepts of 1 ± 2 mmHg and slopes of 0.87 ± 0.06 (Fig. 4). Predicted P_max thus consistently overestimated observed P_max by ~15%.

View larger version (16K): [in this window] [in a new window]   Fig. 4.   Example of correlation between Pmax, measured when the pulmonary artery is clamped, and predicted by nonlinear extrapolation from normal ejecting beats. The correlation is remarkably linear (R = 0.99). The predicted Pmax overestimates measured Pmax by ~15%.

Baseline and inotropic changes. Baseline hemodynamics and blood gas values were normal (Table 1). E_es was 1.1 ± 0.1 mmHg/ml, E_a was 0.8 ± 0.1 mmHg/ml, and E_es/E_a was 1.6 ± 0.4. Dobutamine increased cardiac output and systemic arterial pressure. It increased E_es to 2.0 ± 0.2 mmHg/ml, did not affect E_a, and increased E_es/E_a to 2.5 ± 0.5. Propranolol did not change cardiac output and decreased systemic arterial pressure. It did not affect E_es or E_a significantly, but decreased E_es/E_a to 0.9 ± 0.2. 

Preload and afterload changes. Venous return reduction decreased cardiac output and all intravascular pressures and increased heart rate (Table 2). It did not affect E_es, increased E_a from 0.6 ± 0.1 to 1.3 ± 0.2 mmHg/ml, and decreased E_es/E_a from 2.0 ± 0.3 to 1.1 ± 0.2 mmHg/ml. E_es tended to increase in dogs with moderate hypotension and tachycardia due to baroreceptor-induced adrenergic stimulation. It tended to decrease in dogs with severe hypotension and tachycardia, possibly due to decreased coronary flow. After adrenergic blockade, venous return reduction still decreased cardiac output and pressures, but no longer had an effect on heart rate, E_es, E_a, or E_es/E_a. Hypoxia increased pulmonary arterial pressure and cardiac output (Table 3). It increased E_es from 1.0 ± 0.1 to 1.3 ± 0.2 mmHg/ml and E_a from 0.7 ± 0.1 to 1.1 ± 0.2 mmHg/ml and did not affect E_es/E_a. After adrenergic blockade, hypoxia still increased E_es, but decreased E_es/E_a from 1.4 ± 0.2 to 1.1 ± 0.1 mmHg/ml. Pulmonary artery constriction increased pulmonary arterial pressure and decreased cardiac output (Table 4). It increased E_es from 1.2 ± 0.2 to 2.0 ± 0.4 mmHg/ml and E_a from 1.0 ± 0.1 to 2.6 ± 0.5 mmHg/ml and decreased E_es/E_a from 1.6 ± 0.5 to 0.9 ± 0.1. After adrenergic blockade, constriction still increased E_es and decreased E_es/E_a.

	DISCUSSION

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RV pressure-volume curves. Right ventricular pressure-volume curves and ESPVR were first reported by Maughan et al. (20), in an isolated heart preparation and with a method avoiding any assumption of ventricular shape. Compared with the left ventricle, the authors noted the lower pressures, the triangular shape of the curves, and the time lag between end systole and end ejection (20). Later, ESPVR and maximal elastance were determined in vivo from pressure-volume curves obtained by cineradiography, radionuclide ventriculography, and sonomicrometry. These methods, however, were limited by geometrical assumptions, sampling frequency, and/or amount of needed calculations (13). More recent studies were done with conductance volumetry in animals (10, 11, 19, 31) and humans (3, 33). The method is not easy to apply in the RV and remains predominantly used as a research tool (31). We determined RV volume changes by integrating flow measured in the proximal pulmonary artery with a widely validated ultrasonic method. As seen in Fig. 3, the resulting pressure-volume curves are quite comparable to those reported by Maughan et al. (20).

ESPVR afterload independence. In the left ventricle, afterload independence of ESPVR was initially reported by Suga et al. (25) and confirmed by Maughan et al. (21) using linear ESPVR. In subsequent studies, ESPVR was commonly found linear (2, 7, 14, 23), but sometimes found curvilinear with a decreased slope at high preload (7, 14, 18) or at high afterload (23, 28). Noda et al. (23) reported that curvilinearity was small, particularly if afterload changes were of limited amplitude. Kass et al. (14) concluded that despite curvilinearity, E_es determined throughout limited load ranges could accurately assess inotropic state. Taking curvilinearity into account, Van der Velde et al. (28) found only nonsignificant effects of afterload on ESPVR slope. Accordingly, the authors (1, 27) who investigated the myocardial contractility with methods assuming ESPVR afterload independence reported significant and consistent results in patients. All of the above-mentioned studies involved the left ventricle. In the RV, the afterload independence of ESPVR has been investigated only by Maughan et al. (20) using isolated hearts and linear ESPVR. ESPVR slopes in isovolumic beats were found to be once flatter (2.26 vs. 2.60 mmHg/ml) and once steeper (2.68 vs. 2.50 mmHg/ml) than in ejecting beats. Recalculations from their individual data (20, Table 2) show similar end-systolic pressures in ejecting and isovolumic beats at end-systolic volumes of 40 ml (83 ± 7 vs. 85 ± 7 mmHg) and 60 ml (135 ± 11 vs. 138 ± 11 mmHg). This result suggests that RV ESPVR is the same for ejecting and isovolumic beats, and thus is afterload independent in the investigated volume ranges.

P_max prediction. In isolated hearts, Sunagawa et al. (26) determined by Fourier analysis that the pressure-time relationship of a left ventricular isovolumic beat is very close to a sine wave. Accordingly, they found a good correlation between P_max observed during an isovolumic beat and P_max predicted by sine wave extrapolation from the isovolumic parts of an ejecting beat. The same assumption could be incorrect in the RV, due to its crescent shape and its asynchrone contraction pattern, or not be true in vivo due to ventricular interdependence or pericardial constraint. We therefore verified the assumption for the in vivo RV with the use of ejecting and isovolumic beats beginning at the same end-diastolic volume. We found excellent individual correlations between observed and predicted P_max (r = 0.98 ± 0.02). Predicted P_max overestimated observed P_max, a finding that we had anticipated. The lower P_max during our "isovolumic" beats was attributed to the pulmonary valve opening and to minimal ejection from the RV into the pulmonary artery up toward the clamping device. In this situation, observed P_max should be lower than predicted P_max, and the difference should increase in proportion to the generated ventricular pressure. This is exactly what we observed. These results suggest that predicted P_max is very close to the P_max of a true isovolumic beat. The single-beat method used in the left ventricle (27) can thus also be used in the RV to determine the ESPVR and assess the inotropic state.

Baseline and inotropic changes. Baseline RV E_es values were ~1.1 mmHg/ml, in keeping with values of 1.2 mmHg/ml reported in dogs with sonomicrometry (12). E_a was ~0.7 mmHg/ml, reflecting the low pulmonary arterial pressure and resistance. E_es/E_a was ~2, which is remarkably similar to the values reported for left ventricular-aortic coupling (6, 15). According to Burkhoff et al. (5), E_es/E_a values of 2 are associated with a maximal ratio between mechanical work production and myocardial oxygen consumption. Our results thus confirm that the RV is optimally matched to its afterload in the normal state. They also confirm that intrinsic mechanical properties of the right and left ventricles are similar, and that the apparent differences result from the much lower RV afterload (5, 8). Dobutamine increased E_es and E_es/E_a, whereas propranolol decreased E_es/E_a. The absence of effect of propranolol on E_es indicates a low sympathetic tone, probably resulting from the anesthesia, normal blood volume and normal aortic pressure (in view of the decrease in E_es/E_a, the absence of changes in E_es and E_a could also result from a type 2 error due to a large individual variability). We conclude that our method adequately detects dobutamine-induced inotropic changes, and thus can be used to assess RV contractility.

Preload and afterload changes. Venous return reduction increased E_a, due to the increase in pulmonary vascular resistance and impedance (4). E_es remained unaffected, due to variable individual effects of adrenergic stimulation. Accordingly, adrenergic blockade inhibited all effects of venous return on E_es and E_es/E_a. Active (hypoxic) vasoconstriction and passive (mechanical) arterial constriction increased E_a. They also increased E_es, possibly due to adrenergic stimulation. However, both of them still increased E_es after adrenergic blockade. Such an adrenergic-unrelated E_es response to increased afterload is quite consistent with homeometric autoregulation or Anrep effect (22). Recent studies (10, 19) reported RV homeometric autoregulation in animals with increased afterload due to respiratory distress syndrome or to pulmonary arterial occlusion. The Anrep effect is mediated by changes in intracellular calcium sensitivity and concentration and is unaffected by propranolol but inhibited by verapamil (29, 32). We therefore tried to prevent the E_es response by verapamil, but additional verapamil depressed contractility so much that pulmonary arterial constriction resulted in rapid death. Contractility-unrelated effects of afterload on E_es therefore cannot be completely excluded, but our results are entirely consistent with the assumption that single-beat-derived E_es is a load-independent index of RV contractility in clinically relevant ranges of preload and afterload.

Perspectives. To our knowledge, the present method is the first permitting assessment of RV contractility and RV arterial coupling without measuring RV volume or modifying preload or afterload. We used actual RV end-diastolic volume in our calculations, but any arbitrary value can be used without affecting E_es or E_a (see Fig. 3). Pulmonary arterial velocity and flow can be obtained by noninvasive Doppler and magnetic resonance techniques. The present method is thus already applicable to patients during right heart catheterization. When Doppler techniques will be able to generate RV pressure signals of sufficient quality, as they do for the left ventricle, the present method will be applicable to patients in a completely noninvasive way.