INTRODUCTION

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ACCURATE ASSESSMENT AND MONITORING of heart function is one of the major determinants for the effective diagnosis and treatment of congestive heart failure (9, 31, 33). The demand for more specific and better measurements of various aspects of cardiac performance is also growing with an increasing complexity of therapeutic options.

The relationship between left ventricular (LV) stroke work (SW) and end-diastolic volume (EDV) [termed the preload recruitable SW relationship (PRSW)] is highly linear and reproducible and can be quantified by the slope (M_w) and x-intercept (V_w) in the equation SW = M_w × (EDV  V_w). M_w is recognized as a load-insensitive index of contractile function (10). A flat slope indicates that increased preload produces relatively little increase in SW because of reduced contractility (10). The relationship takes preload and afterload into account and is applicable in a wide variety of cardiac diseases (8, 13, 17, 25). One major limitation to the wide clinical application of PRSW is the requirement for manipulation of LV pressure and volume over a range of preload. To overcome this, a novel technique was developed recently in healthy canines to estimate PRSW from steady-state measurements (16). The rationale underlying this single-beat technique is the allometric hypothesis (16). Allometry is the pattern of covariation among several morphological traits or between measures of size and shape (22). Whereas the allometric hypothesis may be applicable to the normal human heart, it may not be applicable to the remodeled heart due to cardiomyopathy or previous myocardial infarction. Although this single-beat technique has the potential to be used noninvasively for routine practice, it must be critically validated in humans with healthy and diseased hearts.

Therefore, the purposes of the present study were 1) to compare the M_w calculated from the standard multiple-beat approach with the M_w estimated from the single-beat technique (SBM_w) in invasive conditions; and 2) to compare the M_w calculated from the standard multiple-beat approach invasively with the SBM_w derived from completely noninvasive conditions.

	METHODS

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Study population. Forty-five adults referred for diagnostic catheterization (36 men and 9 women) participated in this study. All patients provided informed consent, and the Institutional Review Board of Taipei Veteran General Hospital approved the study protocol. Patients with aortic stenosis or LV outflow obstruction were excluded. Primary indications for cardiac catheterization were chest pain or heart failure. Clinical diagnoses included normal coronary artery anatomy and LV ejection fraction (n = 15), hypertensive cardiovascular disease (n = 10), coronary artery disease (n = 16), hypertrophic cardiomyopathy (n = 3), and constrictive pericarditis (n = 1). A summary of the patient characteristics is provided in Table 1. Among these, eight patients with coronary artery disease had obvious regional wall motion abnormalities of the LV defined by both transthoracic echocardiography and left ventriculography. Their clinical characteristics are summarized in Table 2.

Study protocol. Patients underwent routine right and left heart catheterization, coronary arteriography, and left ventriculography. A 6-Fr multielectrode conductance-micromanometer catheter (SSD-767 and SSD-768, Millar) was then placed into the LV, with the pigtail tip advanced to the ventricular apex. Acute preload reduction was produced in all subjects by temporarily impeding inferior vena cava inflow with a large occlusion balloon catheter (17-205, Boston Scientific) (7). In addition to rest data, intravenous dobutamine (5 and 10 µg · kg¹ · min¹, respectively) was administrated to induce changes of contractility. Dobutamine infusion was withheld in patients with intolerable discomfort, systolic blood pressure (BP) >180 mmHg, or procedure time >1 h at the end of the rest study. In total, 12 dobutamine studies were collected from 8 patients (4 patients had regional wall motion abnormalities). All pressure and volume signals were digitized at 500 Hz using custom data-acquisition display software and analyzed off-line. Details of the invasive pressure-volume analysis have been previously reported (4, 20).

M_w estimation algorithm. The PRSW relationship was determined by linear regression analysis of SW and EDV from multiple beats obtained during each vena caval occlusion, according to the equation

(1)

By rearranging Eq. 1, M_w is given by the equation

(2)

Previous studies have demonstrated that V_w remains essentially constant within an individual, regardless of any short-term change of loading or inotropic conditions (8, 10, 17, 25). Therefore, it is apparent from Eq. 2 that M_w can be calculated from a baseline beat (SW_B and EDV_B) once the value of V_w is known for the individual subject. Karunanithi et al. (16) assumed, on the basis of allometric principles (11, 22, 26, 32), that the ratio of the volume within the epicardial shell corresponding to V_w (V_w,epi) to the volume within the epicardial shell corresponding to EDV_B (EDV_B,epi) is relatively constant (k). Therefore

(3)

Expressing this ratio in terms of chamber volume yields

(4)

where LV_wall is the wall volume. By rearranging Eq. 4

(5)

Substituting for V_w in Eq. 2 yields the following equation for SBM_w

(6)

Because LV mass equals LV_wall times 1.05 (specific gravity of the heart muscle) (21), the LV_wall was estimated from the echocardiography-derived LV mass. The empirical V_w,epi-to-EDV_B,epi ratio k for each individual was calculated from V_w, EDV_B, and LV_wall accordingly. V_w was determined from multiple beats during preload reduction (10). To apply the single-beat technique noninvasively, SW was estimated as the product of Doppler-derived SV and the oscillometrically derived mean systemic BP (23).

Statistical analysis. All hemodynamic data are expressed as means ± SD. Linear regression was performed to examine the correlations between individually calculated k values from multiple-loop data and other variables, including age, height, body weight, systolic BP, ejection fraction, EDV, and LV mass. The agreement between M_w and SBM_w was examined using Bland-Altman analysis (1). Similar analyses were done in subgroups of large and small LV volume or large and small mass. The agreement of changes of SBM_w and M_w induced by intravenous dobutamine infusion was also examined with univariate linear regression. Statistical significance was reported at P < 0.05.

	RESULTS

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Characteristics of the ratio of the epicardial shell volumes. Similar to reported canine data, in which the average k value was 0.72 ± 0.01 (16), the k value calculated from individual patients varied in the range of 0.66-0.81 with a mean of 0.72 ± 0.04. There was no significant correlation between the individual k value and age (Fig. 1A), height, body weight, body mass index, steady-state systolic BP (Fig. 1B), EDV_B (Fig. 1C), or ejection fraction. On the other hand, the individual k value was significantly correlated with LV mass in the regression equation individual k value = 0.0004 × LV mass + 0.6408 [r = 0.60, SE of the estimate (SEE) = 0.0316, P < 0.001; Fig. 1D]. The relationship between LV mass and the k value was preserved in patients with regional wall motion abnormalities (Fig. 1D, open symbols). On the basis of the regression equation, LV mass was used to estimate individual k values for calculating SBM_w.

View larger version (31K): [in this window] [in a new window]   Fig. 1.   Relations between individual ratios of epicardial shell volumes at zero stroke work (unstressed volume) and during steady state (stressed volume) (k values) derived from multiple-beat pressure-volume data and age (A), systolic blood pressure (SBP; B), left ventricular (LV) end-diastolic volume (LVEDV; C), and LV mass (D) in patients with various heart diseases. , Patients without regional wall motion abnormalities; , patients with significant regional wall motion abnormalities. SEE, SE of the estimate. Solid line, linear regression.

Estimation of M_w by SBM_w in the steady state. On the basis of a constant k of 0.7 (16), SBM_w predicted M_w well (M_w = 0.88 × SBM_w + 24.15, r = 0.88, SEE = 16.94, P < 0.0001; Fig. 2A), and Bland-Altman analysis demonstrated that all points of difference were within 2SD of the mean difference except for two outliers (Fig. 2C). The absolute differences for these two outliers were 53.4 and 48.4 erg · cm³ · 10³, respectively. The first patient was a 61-yr-old female with hypertrophic cardiomyopathy and hypertension, whose LV mass was 283.0 g. The second patient was 65-yr-old male with hypertensive cardiovascular disease and concentric LV hypertrophy, whose LV mass was 284.1 g. When the k value was estimated from the individual LV mass, the prediction improved slightly (M_w = 0.89 × SBM_w + 15.55, r = 0.93, SEE = 13.58, P < 0.0001; Fig. 2B). Bland-Altman analysis revealed only one outlier outside the 2SD boundary, who was a 68-yr-old female with hypertensive cardiovascular disease, Type 2 diabetes mellitus, and concentric LV hypertrophy (LV mass = 198.3 g; Fig. 2D).

View larger version (32K): [in this window] [in a new window]   Fig. 2.   A: linear regression (solid line) and 95% confidence intervals (dotted lines) of reference slope of the preload recruitable stroke work relationship (Mw) vs. constant k-derived single-beat Mw (SBMw) for 45 subjects during steady status. B: linear regression (solid line) and 95% confidence intervals (dotted lines) of reference Mw vs. estimated k-derived SBMw in the same condition. C and D: Bland-Altman plots of Mw vs. constant k-derived SBMw (C) and estimated k-derived SBMw (D). Means (solid lines) and the 2SD difference (dotted lines) are shown. , Patients without regional wall motion abnormalities; , patients with significant regional wall motion abnormalities.

Responses of SBM_w to intravenous dobutamine. To further test the robustness of the single-beat technique, changes in SBM_w induced by intravenous dobutamine infusion in 12 studies were compared with changes in M_w. Absolute changes in SBM_w before and after dobutamine infusion correlated significantly with M_w using either a constant k (M_w = 0.57 × SBM_w + 24.53, r = 0.84, SEE = 13.76, P = 0.0007; Fig. 3A) or an estimated k (M_w = 0.55 × SBM_w + 21.65, r = 0.82, SEE = 14.47, P = 0.0011; Fig. 3B).

View larger version (18K): [in this window] [in a new window]   Fig. 3.   Absolute changes in SBMw before and after dobutamine infusion correlate well with changes in Mw using either a constant k (A) or an estimated k (B). Solid lines, linear regression; dotted lines, 95% confidence intervals; , patients without regional wall motion abnormalities; , patients with significant regional wall motion abnormalities.

Noninvasive SBM_w estimation. The calculation of SBM_w requires the estimation or measurement of SW_B, EDV_B, and LV_wall, and all can be derived noninvasively. According to our invasive data, SW_B calculated directly from the pressure-volume loop was highly significantly correlated with the estimation from the product of mean aortic systolic BP and SV: SW_{B(loop area)} = 1.0 × SW_{B(mean BP × SV)} + 403 (SEE = 518, r = 0.98, P < 0.001). Therefore, noninvasive SW_B was estimated from the product of mean brachial arterial pressure and echocardiographically derived SV (23). However, because the noninvasive examination was performed ~1 h before the cardiac catheterization, the correlations between the invasive and noninvasive measurements of the pressure, volume, and estimated SW_B were significant but less satisfactory: EDV_(invasive) = 0.83 × EDV_{(noninvasive)} + 20.8 (SEE = 24.8, r = 0.64, P < 0.001); systolic BP_(invasive) = 0.92 × systolic BP_{(noninvasive)} + 14.0 (SEE = 7.1, r = 0.94, P = 0.002); and SW_B(invasive) = 0.76 × SW_{B(noninvasive)} + 2,131 (SEE = 1,983, r = 0.73, P < 0.001). Subsequently, noninvasively derived SBM_w correlated significantly with invasively derived M_w (M_w = 0.63 × SBM_w + 53.68, r = 0.66, SEE = 27.21, P < 0.0001) using a constant k (Fig. 4, A and C). With the use of an estimated k, the predicted power of noninvasively derived SBM_w improved slightly (M_w = 0.68 × SBM_w + 43.16, r = 0.71, SEE = 25.25, P < 0.0001; Fig. 4, B and D).

View larger version (33K): [in this window] [in a new window]   Fig. 4.   A and B: linear regression (solid lines) and 95% confidence intervals (dotted lines) of invasive Mw vs. noninvasive SBMw using a constant k of 0.7 (A) or an estimated k (B) for 45 subjects during steady status. C and D: Bland-Altman plots of Mw vs. constant k-derived SBMw (C) and estimated k-derived SBMw (D). Means (solid lines) and the 2SD difference (dotted lines) are shown. , Patients without regional wall motion abnormalities; , patients with significant regional wall motion abnormalities.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

In this study, we demonstrated that it is feasible to use a single steady-state heart beat to estimate M_w of the PRSW relationship in humans with various heart diseases, including patients with significantly remodeled hearts. In addition, we found that the k value, the ratio of the epicardial shell volumes at zero SW (unstressed volume) and during steady state (stressed volume), varied significantly with the LV mass. Therefore, the single-beat technique can further be improved with the use of a k value estimated from the LV mass instead of a constant of 0.7 (16). We also demonstrated that the modified technique has the potential for noninvasive application in routine clinical practice.

The anatomic and physiological basis of the k value. The underlying rationale for the calculation of SBM_w is the allometric hypothesis (16). According to this theory, within all species of animals the size of each organ bears a specific allometry exponent to body weight (11, 12, 32). On the basis of the allometry theory, the ratio of V_w,epi to EDV_B,epi (unstressed volume to stressed volume) was assumed to be a constant k, and this assumption appeared to be valid in healthy canines (16). In the current study, we found that k values in patients with diseased or healthy hearts varied in a narrow range, whereas the mean k value (0.72) was essentially the same as that in healthy canines. Furthermore, the variation of k values could be predicted from the LV mass in the patients. The relationship between LV mass and k was preserved even in patients with significant LV remodeling, i.e., with dilated LV volume, LV hypertrophy, or regional wall motion abnormalities due to previous myocardial infarction.

Impact of LV mass, EDV, and regional wall motion abnormality on the SBM_w technique. Cardiomegaly and LV hypertrophy are consequences of progressive heart failure and LV remodeling. Regional wall motion abnormality is a frequent consequence of previous myocardial infarction. It might be anticipated that the allometric theory is not valid in patients with enlarged heart sizes. According to Eq. 4, it is expected that the k value would increase with an increase in LV mass if EDV_B and V_w were held constant. Our data were consistent in that patients with larger LV mass or smaller EDV tended to have greater k values. However, because the variation of k values with LV mass or chamber size was small, the SBM_w technique remained valid in patients with wide ranges of LV mass (92-365 g) or EDV (52-215 ml), using either a constant k or an estimated k value. In patients with regional wall motion abnormalities, k values were within the same range, and the relations with the LV mass were preserved (Fig. 1D, open symbols).

Noninvasive applications of the SBM_w technique. The single-beat technique was the foundation for the potential wide application of PRSW in clinical practice. According to Eq. 6, the calculation of SBM_w requires measurements of SW_B, EDV_B, and LV mass, all of which can be derived from noninvasive echocardiography and brachial BP measuring. In the current study, noninvasively derived SBM_w was significantly related to invasively derived SBM_w using either a constant k or an estimated k. The correlation coefficients were slightly lower than those from the invasive studies. This less satisfactory result was most likely due to the fact that the echocardiographic examination was performed 1 h earlier than the catheterization. It is reasonable to assume that the echocardiographic measurements and oscillometric brachial BPs obtained during the cardiac catheterization should yield better results. However, we were reluctant to do so because the lengthened catheterization time might risk the patients' safety.

Other single-beat techniques for assessment of LV contractility. In addition to M_w, the slope (E_es) of the end-systolic pressure-volume relationship (ESPVR) is also a recognized as a load-insensitive index of LV contractility. We (3) have developed and validated a novel single-beat technique to estimate E_es noninvasively. Because M_w and E_es describe LV performance in different perspectives, the availability of both techniques should provide a more comprehensive evaluation of LV performance. The PRSW relationship is highly linear and relative afterload independent (5, 10, 19, 24, 25); the ESPVR, however, is less linear than the PRSW relationship (2, 18). The range of change of the PRSW relationship is less than that of the ESPVR when the contractility changes (25). The PRSW relationship is not a pure systolic contractility index but rather integrates both systolic and diastolic properties (19, 25). Therefore, the PRSW relation can be considered as a measure of integrated pump function and the ESPVR as systolic function. Because of the different hemodynamic characteristics, it would be ideal to have both M_w and E_es to enhance clinical interpretation. Although the theories behind the single-beat technique for estimating E_es and M_w are quite different, both parameters can be obtained during the same echocardiographic examination, and this should facilitate the clinical application of both techniques.