INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

VENTRICULAR CONTRACTILITY is usually derived from a series of pressure-volume (P-V) loops that are measured during progressively altered cardiac loading conditions. It has been shown that the slope of the end-systolic P-V relation, which is also called the end-systolic or maximal elastance (E_es; Refs. 17, 18), reflects ventricular contractility independent of preload and afterload. Although E_es was first applied to the left ventricle, this index has also been validated for the right ventricle (5). Measuring E_es requires invasive techniques because simultaneous pressure and volume measurements are needed as well as the alteration of loading conditions. Hence its assessment is usually restricted to experimental settings and small-scale studies.

To obviate the need for measurement of P-V loops, hydraulic power has been proposed as an alternative way to quantify left ventricular (LV) contractility (2). For the left ventricle, hydraulic power is calculated as the instantaneous product of aortic pressure and flow during steady-state conditions to yield power () as a function of time (10). Maximal power (_max) is the maximal value of this curve (6, 8). An important limitation of _max as an index of contractility is its preload dependency (6). However, it has been shown for the left ventricle that _max can be corrected for this preload dependency by dividing _max by the LV end-diastolic volume (V) with a -value of 2 (6, 14). The index _max/V is usually referred to as the preload-adjusted _max (PAMP).

The aim of this study was to validate PAMP as an index for right ventricular (RV) contractility. To do so, we calculated PAMP and E_es in mongrel dogs at baseline and after dobutamine infusion. Although the inotropic effect of dobutamine was clearly demonstated by E_es, this was not the case for PAMP. To elucidate the apparent discrepancy between these indices of ventricular contractility, we used the experimental data to assess the parameters of a mathematical heart arterial interaction model. Computer simulations revealed a nonlinear relationship between the intercept of the end-systolic P-V relationship (V_d) and the -coefficient that should ideally be used to adjust for preload, with the value of 2 being valid only when V_d equals zero. Based on the mathematical model simulations, we propose a correction of PAMP (PAMP_c) that takes into account this V_d dependency. It is then verified whether PAMP_c allows us to detect the effects of inotropic interventions in the animal experiments.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Experimental Protocol

Ten healthy mongrel dogs (body wt 18-24 kg) were included in this study. After the dogs were premedicated with ketamine hydrochloride (10 mg/kg im; Ketalar) and piritramide (1 mg/kg im; Dipidolor, Janssen Pharmaceutica), anesthesia was induced with pentobarbital sodium (10 mg/kg iv; Nembutal). Endotracheal intubation was performed, and the lungs were mechanically ventilated with a 50% mixture of oxygen in air. Anesthesia was maintained with a continuous infusion of pentobarbital sodium (1 mg/kg) and piritramide (1 mg/kg). Arterial blood gases were measured at regular intervals, and ventilation was adjusted accordingly to maintain normocapnia. Normothermia was maintained by means of a heating mattress.

A fluid-filled catheter was inserted into the descending aorta via the right femoral artery to monitor systemic blood pressure and obtain samples for blood-gas analysis. Via a midline sternotomy, the inferior vena cava was dissected, and a band was placed around it for controlled alterations of RV preload. The heart was suspended in a pericardial cradle. The main pulmonary artery (PA) was dissected free from the aorta, and a 16- or 18-mm perivascular flow probe was placed around it and connected to an electromagnetic blood-flow meter (Skalar; Delft, The Netherlands) to provide continuous display of cardiac output. PA pressure (P_PA) and right atrial pressure were measured with fluid-filled catheters inserted through purse-string sutures in the RV outflow tract and right auricle, respectively. A 5-Fr microtipped pressure-transducer catheter (Millar Instruments; Houston, TX) and a 5-Fr dual-field conductance catheter (Millar Instruments) were inserted into the right ventricle through small stab wounds in the RV outflow tract. The correct position of the conductance catheter was determined by palpation and confirmed by observation of pressure and segmental volume signals with appropriate phase relationships. In all animals, all five conductance-catheter segments were located within the ventricle and used for analysis. The conductance catheter was connected to a volumetric system (Sigma 5, CD Leycom/CardioDynamics; Zoetermeer, The Netherlands), which was also used to measure blood resistivity. Parallel conductance was determined for each experimental condition by the rapid injection of 7 ml of 10% saline solution into the right atrium (1). For each animal, the -calibration factor was assessed as the ratio of stroke volume (SV) measured with the conductance catheter (SV_cond) and the PA flow probe (SV_flow) during steady-state conditions at baseline and was assumed to remain constant throughout the measurements. The correlation between SV_cond and SV_flow was 0.94 (P = 0.0003). Average SV_cond/SV_flow, i.e., the -calibration factor, was 1.18 ± 0.22 with a range of 0.75-1.38.

Data were recorded with the open chest and pericardium at steady-state baseline conditions and during transient vena cava occlusion that was induced via a band around the inferior vena cava for ~10 s. All data were measured with the ventilation suspended at end expiration. After hemodynamic data values had returned to baseline, all measurements (steady state and vena cava occlusion) were repeated during infusion of dobutamine (5-10 µg · kg¹ · min¹ iv) with the measurements starting at least 15 min after the onset of the infusion.

Data were measured at a sample rate of 250 Hz and stored on hard disk for subsequent analysis using customized software written in Matlab (Mathworks). Individual cardiac cycles were identified using the first minimum that preceded peak RV dP/dt, i.e., the onset of RV isovolumic contraction.

Experimental Data Analysis

Steady-state data. Steady-state data were averaged over at least five cycles and yielded one cardiac cycle of RV pressure and volume, P_PA, and PA flow (_PA) data. Heart rate (HR) was obtained from the duration of the average cardiac cycle. Systolic and diastolic pressure and mean P_PA values (SBP, DBP, and MAP, respectively) were calculated from P_PA. SV was calculated as the area under the flow curve, and cardiac output (CO) was obtained from HR and SV. RV V_ed was defined as the maximum value of the calibrated conductance-catheter signal. RV pressure at the onset of RV isovolumic contraction was used as the end-diastolic pressure (P_ed). _max was calculated as the maximum of the instantaneous product of P_PA and _PA. PAMP was calculated as _max/V.

Vena cava occlusion data. Five to ten successive beats were selected from the P-V loops measured during vena cava occlusion. Stroke work (SW) was calculated for each cycle as the area enclosed by the PV loop. The slope of the linear regression equation (M_w) on the V_ed-SW data yielded preload-recruitable SW. To calculate the slope (E_es) and intercept (V_d) of the end-systolic points in the P-V plane, we used an iterative method to identify these end-systolic points. We first calculated elastance [E(t)] as P_RV/(V_RV  V_d), where P_RV and V_RV were RV pressure and volume, respectively. V_d was given the initial value of zero. The points in the P-V plane that corresponded to maximal E(t) for each cycle were identified as the end-systolic points. Linear regression analysis on these points yielded a first estimate of E_es and a new estimate of V_d. This procedure was repeated with the resulting V_d values until successive values for V_d did not differ by >0.1%. For all data, convergence was reached within 3 or 4 iterations.

Heart Arterial Interaction Model

Model description. The heart arterial interaction model allows the calculation of RV pressure and volume as well as P_PA and PA flow (Fig. 1). RV function is described by a time-varying elastance function, whereas the arterial load is represented by a four-element, lumped-parameter windkessel model (16). The pulmonary arterial model parameters are total peripheral resistance (R), total arterial compliance (C), total inertance (L), and PA characteristic impedance (Z₀). Cardiac parameters are E_es, V_d, the slope of the diastolic P-V relationship (E_min) and RV end-diastolic pressure (P_ed), HR, and the time to reach maximal elastance (t_Ees). Tricuspid and pulmonary valves are simulated as frictionless, perfectly closing devices that allow forward flow only.

View larger version (7K): [in this window] [in a new window]   Fig. 1.   Electrical analog representation of the heart arterial interaction model. Cardiac function is modeled by a time-varying elastance function E(t) and the pulmonary arterial system by a four-element windkessel model consisting of total peripheral resistance (R), total arterial compliance (C), total inertance (L), and pulmonary artery (PA) characteristic impedance (Z0).

Assessing cardiac and arterial model parameters. In the computer model, E(t) is implemented in a normalized form [E_N(t_N)], i.e., it is normalized with respect to E_es and t_Ees (13, 17). We first calculated such an average RV E_N(t_N) from 25 P-V loops measured in 6 dogs during baseline conditions. For each simulation, RV function is fully determined by the actual E(t) value calculated from E_N(t_N) and E_es, t_Ees, E_min, HR, P_ed, and V_d values.

Model Simulations: Steady-State Data and Vena Cava Occlusion

For each animal and each condition, P_RV, V_RV, P_PA, and _PA were calculated with the reference parameter set and with four lower values of P_ed (in steps of 0.5 mmHg) to simulate the effect of reduced preload (i.e., V_ed reduction due to vena cava occlusion) over the same range as measured in the animals. For each cycle, _max was calculated and plotted as a function of V_ed. Similar to the animal experimental data, a power law of the form P_max = V was fitted through these points.

Impact of V_d on PAMP

Statistical Analysis

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Experimental Data Analysis

View larger version (25K): [in this window] [in a new window]   Fig. 2.   Effects of pharmacological inotropic stimulation on systolic blood pressure (SBP, A), cardiac output (CO, B), right ventricular (RV) end-diastolic volume (Ved, C), slope (Ees, D), and intercept (Vd, E) of the end-systolic pressure-volume (P-V) relationship and on the slope (Mw) of the preload-recruitable stroke-work relation. Means and SD values ( and error bars, respectively) are indicated; +P < 0.05; #P < 0.001, inotropic (INO) stimulation vs. baseline (BL).

View larger version (11K): [in this window] [in a new window]   Fig. 3.   Effects of inotropic stimulation on preload-adjusted maximal power (PAMP) calculated as max/V (A) and inotropic stimulation on corrected PAMP (PAMPc) calculated as max/(Ved  Vd)2 (B). Means and SD values ( and error bars, respectively) are indicated.

Model Simulations

View larger version (12K): [in this window] [in a new window]   Fig. 4.   Relationship between measured and estimated PA stroke volume (SV, A), systolic blood pressure (SBP, B), and diastolic blood pressure (DBP, C). Lines of regression and perfect agreement are indicated (solid and dashed lines, respectively).

Impact of V_d on PAMP

View larger version (12K): [in this window] [in a new window]   Fig. 5.   A: relationship between Vd and -power coefficient as derived from the computer simulations (solid line, fitted exponential curve). B: relationship between Vd and -power coefficient for the experimental data (solid line, exponential curve that was fitted through computer-simulation data). Dashed lines, points where Vd = 0 and  = 2.

View larger version (13K): [in this window] [in a new window]   Fig. 6.   A: relationship between max and RV Ved for computer-simulated data from dog 7. Fitting an exponential relationship through these data, -coefficients are 1.73 and 2.27 at baseline and inotropic stimulation, respectively. B: plotting the same data as a function of Ved  Vd,  becomes ~2.

Figure 3 also shows that PAMP_c was higher in the inotropic stimulation group than in the baseline group. The correlation between E_es and PAMP is weak (r = 0.36; not significant) in contrast to the correlation between E_es and PAMP_c (r = 0.88; P < 0.001; Fig. 7).

View larger version (11K): [in this window] [in a new window]   Fig. 7.   Relationship between Ees of the P-V relationship and the standard (A) and corrected (B) formulations of PAMP.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

We have applied two indices known to reflect LV contractility (i.e., E_es and PAMP) to the right ventricle. Pharmacological inotropic stimulation yielded the anticipated increase in E_es but not PAMP. A parameter study on a computer model that simulated heart arterial interaction revealed that V_d, the intercept of the end-systolic P-V relation, determines the -power coefficient that should be used to correct _max for preload. The value  = 2 [as proposed by Kass and co-workers (6)] only applies when V_d is negligible. Using computer simulations as well as experimental data, we have shown that this problem is overcome when _max is corrected as _max/(V_ed  V_d)², an index that we have indicated as PAMP_c.

In this open-chest, open-pericardium experimental study, inotropic stimulation led to an increase in P_PA and a borderline increase in CO. It was shown earlier (5) that when afterload is constant, E_es reflects changes in RV performance, which is confirmed by our results. In our study, there was a trend toward an increased total pulmonary vascular resistance (P = 0.08) and decreased pulmonary vascular compliance (P = 0.09), i.e., an increased afterload. These effects may explain the trend toward an increased RV end-diastolic volume.

To our knowledge, PAMP has not previously been studied in the right ventricle. Our data demonstrate that PAMP, defined as _max/V, is not an accurate index of RV contractility. The concept of PAMP is based on the observation that the power-law relationship _max = V_ed² can be fitted through _max  V_ed data points obtained under altered loading conditions. Optimal preload correction is then obtained by dividing _max by V, and  is a measure of contractility. It is important, however, that for a generally applicable index of contractility, the coefficient used in the index (i.e., ) is constant and independent of physiological variables. In both our experimental data and computer simulations, the -factor (usually assumed to be 2) was not constant but varied with V_d (range, 0.98-3.89). As a consequence, _max/V cannot be used as such to quantify contractility; in some cases (when V_d < 0), the factor 2 will be too high, whereas in other cases (when V_d > 0), it will be too low. The -V_d relationship can be expressed as  = 2.008e^0.0216V_d}. It is only when V_d = 0 that the -value approximates 2.

Supposing that V_d is known, one could think of correcting _max by dividing by V, with the -coefficient calculated as 2.008e^0.0216V_d. This approach, however, does not work. For example, in Fig. 6 (dog 7), using the optimal value for the -value, _max/V = 0.322 at baseline and _max/V = 0.086; i.e., a lower -value is found during inotropic stimulation. A more consistent approach is to plot _max as a function of V_ed  V_d. Doing so, the optimal value for the -coefficient becomes constant with the computer simulations yielding an average value of 1.99 ± 0.06 (range, 1.85-2.17). Therefore, when PAMP is modified as _max/(V_ed  V_d), the V_d dependency of the -factor disappears: the -value is indeed approximately constant, and the formula is generally applicable with  = 2. For the same example of Fig. 6, _max/(V_ed  V_d)² becomes 0.090 at baseline and 0.331 during inotropic stimulation, respectively, which is consistent with the anticipated effect of inotropic stimulation. This corrected PAMP is indicated as PAMP_c. Application on the experimental data revealed a significant difference between baseline and inotropic stimulation. Furthermore, in contrast to PAMP, PAMP_c shows an excellent correlation with E_es (r = 0.88; P < 0.001).

At present, we do not have the necessary experimental data to study PAMP and the relationship of the -value with V_d for the left ventricle. However, model simulations with parameters for the LV and systemic arterial system (data not shown) revealed the same tendency. Note, however, that a nonconstant -coefficient for the left ventricle was earlier reported by Kass and co-workers (11). They proposed to use  = 1 for the normal left ventricle, whereas  = 2 should be more appropriate for dilated ventricles. This finding is in line with our data, as it can be assumed that in the normal left ventricle V_d is small (and may even be negative), whereas with LV enlargement, V_d shifts to the right and requires higher -values.

In our study, the increase in E_es was accompanied by a trend toward rightward shifts of V_ed and the intercept of the end-systolic P-V relation. Variation of RV V_d over the cardiac cycle was reported by several authors (3, 5, 9), but a rightward shift in V_d with dobutamine infusion has to our knowledge not been documented for the right ventricle. RV volumes were measured with a conductance catheter, which is an indirect technique whereby the measured signals require calibration (parallel conductance and -slope factor) to obtain volumes. As such, the observed rightward shifts in V_ed and V_d may be due to physiological phenomena induced by dobutamine infusion and the borderline increase in RV afterload but also to variations or measurement errors in parallel conductance or -value. In this study, the -value was higher than reported in other studies (4, 15), where transit-time flow probes were used as a reference (on the order of 0.7-0.8). We may thus have underestimated absolute volumes. At the same time, however, this discrepancy illustrates the difficulties in measuring absolute volumes with the conductance-catheter technique and explains our rationale for investigating indices for RV contractility based on hydraulic power. Unfortunately, these indices require correction for preload, which is approximated as RV end-diastolic volume. As such, they cannot be fully uncoupled from volume measurements and the inherent measuring uncertainties. The sensitivity to measuring errors in absolute volumes is particularly problematic when PAMP is calculated as _max/V, because 1) small volume changes are squared, and 2) the -factor is not constant and equal to 2 but instead varies with V_d. By using _max/(V_ed  V_d)², these important limitations are attenuated, as volume shifts due to changes or erroneous measurement of parallel conductance have the same effect on V_d and V_ed (and thus do not affect V_ed  V_d), and the -factor is approximately constant and equal to 2. By plotting _max as a function of V_ed  V_d, V_d can be seen as a "correction volume," and the exact position of the P-V loop on the volume axis is less important for calculating PAMP. Within the linearized time-varying elastance concept, V_d is the theoretical volume (derived from linear extrapolation) for which the ventricle does not generate any pressure. It is only when filled to volumes higher than V_d that the ventricle generates pressure. Therefore, within the linear time-varying elastance concept, V_ed  V_d is perhaps a more appropriate marker of ventricular preload.

PAMP is potentially advantageous over E_es to characterize ventricular contractility, as its calculation does not require multiple P-V loops recorded under altered loading conditions. Moreover, for the left ventricle, _max can be computed from noninvasively measured arterial pressure (tonometry) and flow (Doppler echocardiography) (7). With a noninvasive estimate of V_ed, PAMP would be a noninvasive measure of LV contractility. Our data, however, indicate that _max is best corrected for preload using (V_ed  V_d)². Because V_d can only be determined from multiple P-V loops measured under altered loading conditions, the measurement of PAMP requires steady-state pressure and flow in the PA as well as RV P-V loops measured during caval vein occlusion. One can therefore only conclude that E_es is easier to obtain than corrected PAMP and that there is no simple index for LV or RV contractility based on one single (P-V loop) measurement during steady-state conditions.

This study is partly based on computer simulations where RV function is characterized by a time-varying elastance model, whereas the pulmonary arterial system is represented by a four-element windkessel model. The model was developed for LV heart arterial interaction studies and was validated using LV and aortic experimental data (12). Application of the model to the right ventricle is subject to some limitations. With the four-element windkessel model, we were able to fit the low-frequency (<5th harmonic) contents of the impedance spectra derived from measured P_PA and _PA, but the model often failed to accurately match the higher harmonics. Owing to this limitation, the model can predict low-frequency information such as SBP or DBP, SV, or maximal _PA, but the waveforms are poorly predicted. Another limitation is the use of the time-varying elastance concept for the right ventricle. Several authors (3, 9) reported an increase in the slope and a leftward shift of the intercept of the P-V relationship during RV contraction. In the experimental data analysis as well as the computer simulations, we assumed constant V_d. These computer-model limitations, however, do not affect the outcome of this study. All observations based on the computer-model simulations were confirmed by the experimental data and vice versa, although often with more scatter in the experimental data. Besides the above-mentioned computer-model limitations, the higher scatter is also due to the fact that simulated interventions are based on varying a single condition (e.g., filling pressure), which is an idealized situation that is virtually impossible to achieve in vivo. We also acknowledge that our experimental model has a number of potential limitations. First, it is relatively invasive, and pentobarbital sodium may have a negative inotropic effect. However, the latter should not have any influence on our results, because inotropic state was modulated in the experimental protocol. Second, the presence of an open chest and pericardium may have caused larger volume changes than a closed chest/closed pericardium setting, but we would not expect this to influence our main observation that V_d is required for an adequate correction of PAMP. Finally, the experimental data do not allow for assessment of the sensitivity of PAMP_c to HR or afterload changes. The present findings therefore cannot automatically be transposed to normal human beings; further studies in closed chest/closed pericardium conditions are required to validate our observations.

In summary, experimental data showed that in contrast to E_es, PAMP could not quantify the hemodynamic effect of inotropic stimulation of the right ventricle. This is due to the rightward shift in V_d, the intercept of the end-systolic P-V relation, and to the fact that _max should be adjusted for preload by dividing it by (V_ed  V_d)². Therefore, correct computation of PAMP requires data measured under altered loading conditions. This restriction limits the clinical value of PAMP for characterizing RV contractility.