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J Am Coll Cardiol, 2001; 38:2028-2034 © 2001 by the American College of Cardiology Foundation |
a Division of Cardiology, Taipei Veterans General Hospital, Taipei, Taiwan, R.O.C. Taiwan
b National Yang-Ming University, Taipei, Taiwan, R.O.C. Taiwan
c Division of Cardiology, Department of Internal Medicine, The Johns Hopkins Medical Institutions, Baltimore, Maryland, USA
Manuscript received March 9, 2001; revised manuscript received July 25, 2001, accepted August 20, 2001.
* Reprint requests and correspondence: Dr. David A. Kass, Halsted 500, Division of Cardiology, Johns Hopkins Medical Institutions, Baltimore, Maryland 21287 USA.
dkass{at}bme.jhu.edu
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Abstract |
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BACKGROUND: Left ventricular end-systolic elastance is a major determinant of cardiac systolic function and ventricular-arterial interaction. However, its use in heart failure assessment and management is limited by lack of a simple means to measure it noninvasively. This study presents a new noninvasive method and validates it against invasively measured Ees.
METHODS: Left ventricular end-systolic elastance was calculated by a modified single-beat method employing systolic (Ps) and diastolic (Pd) arm-cuff pressures, echo-Doppler stroke volume (SV), echo-derived ejection fraction (EF) and an estimated normalized ventricular elastance at arterial end-diastole (ENd): Ees(sb) = [Pd – (ENd(est) x Ps x 0.9)[/(ENd(est) x SV). The ENd was estimated from a group-averaged value adjusted for individual contractile/loading effects; Ees(sb) estimates were compared with invasively measured values in 43 patients with varying cardiovascular disorders, with additional data recorded after inotropic stimulation (n = 18, dobutamine 5 to 10 µg/kg per min). Investigators performing noninvasive analysis were blinded to the invasive results.
RESULTS: Combined baseline and dobutamine-stimulated Ees ranged 0.4 to 8.4 mm Hg/ml and was well predicted by Ees(sb) over the full range: 
(r = 0.91, SEE = 0.64, p < 0.00001, n = 72). Absolute change in Ees(sb) before and after dobutamine also correlated well with invasive measures: 
(r = 0.88, p < 0.00001). Repeated measures of Ees(sb) over two months in a separate group of patients (n = 7) yielded a coefficient of variation of 20.3 ± 6%.
CONCLUSIONS: The Ees can be reliably estimated from simple noninvasive measurements. This approach should broaden the clinical applicability of this useful parameter for assessing systolic function, therapeutic response and ventricular-arterial interaction.
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Routine approaches for assessing left ventricular (LV) function are based largely on image-analysis or right-heart monitoring. Both are useful yet provide limited information specific to the LV, and neither indexes ventricular-arterial interactions, which can be crucial for optimizing chronic therapy (6–9). The end-systolic pressure-volume relation (ESPVR) and its slope (Ees) have proven very useful in this regard since Ees is a major determinant of LV systolic performance and heart interaction with the systemic vasculature (8–13). However, Ees determination has generally required invasively measured LV pressure and volumes recorded over a range of cardiac loading. This has hampered the broader application of this parameter to clinical heart failure diagnosis and management.
Several approaches have been proposed for estimating Ees without loading interventions (14–16), and these are generally referred to as single-beat methods (Ees(sb)). For example, based on similarities between the amplitude and time-normalized human LV time-varying elastance curves during early isovolumic contraction, we reported that Ees could be estimated from steady-state data (15). This approach has been since applied to other species as well (17). Subsequent studies (16) improved on this approach by individually adjusting the normalized elastance curve to compensate for load and contractility dependencies.
A strength of these particular methods (14,16) is their potential to be used noninvasively. While this has already been attempted (18), there are no data validating the noninvasive approach by comparing it with directly measured (multiple-cycle derived) invasive Ees. In this study, we developed a modified noninvasive method for Ees(sb) and verified this method by comparisons with results obtained from invasive (multiple-beat) analysis.
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Methods |
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Additional studies were obtained by noninvasive method in seven subjects with vascular stiffening and normal heart function (placebo arm of pharmacologic study) to test measurement reproducibility over time. All patients provided informed consent, and the relevant institutional review board for each respective institution approved the protocol(s).
Study protocol
Patients underwent routine coronary angiography, left ventriculography and right heart catheterization. A 7F multielectrode conductance/micromanometer catheter was then placed into the LV, with the pigtail tip advanced to the ventricular apex. Left ventricular volumes were recorded using a stimulator-microprocessor (Sigma V, CardioDynamics, the Netherlands) and calibrated to match thermodilution-derived stroke volume (SV) and contrast ventriculogram-derived EF. Echocardiograms were performed (Agilent, Sonos-5500, Palo Alto, California) using a wide-band frequency-fusion phase-array transducer. Brachial systolic (Ps) and diastolic (Pd) blood pressures were obtained with an oscillometric blood pressure monitor. End-systolic pressure (Pes) was estimated from Ps x 0.9 (19). This was further tested in 17 subjects in whom concomitant brachial cuff pressure and invasive data were measured, yielding a linear relation with slope 1.01, p < 0.0001, r = 0.75. Left ventricular outflow tract diameter was measured at the base of the aortic leaflets in a parasternal long-axis view from which cross-sectional area was determined. Stroke volume was measured from proximal aorta pulse-wave Doppler-flow (apical five-chamber view) and aortic cross-sectional area (20). A standard method was used to calculate LV EF from two-dimensional guided M-mode echocardiographic data (21).
In addition to rest data, noninvasive and invasive assessments were made in 18 patients before and after varying contractility by dobutamine (5 to 10 µg/kg per min, intravenous). Comparisons were simultaneous in five studies and sequential (separated by 1 to 2 h) in the others. A total of 29 prepost dobutamine comparisons were obtained (two doses in most patients).
Ees(sb) estimation algorithm
The algorithm for Ees(sb) assumed a linear end-systolic pressure-volume relation in the measured data range and a constant volume axis intercept of the end-systolic pressure volume relation (V0). Using pressures and volumes determined during midisovolumic contraction (td) and at end-systole (tes), two values of LV elastance were derived: 
and 
. Their ratio ENd (Ed/Ees) was the time and amplitude normalized time varying elastance at time td. We found that values of ENd were conserved during the isovolumic period in humans despite diverse cardiac disease, heart function and arterial load. Thus, knowledge of td meant that ENd and, thereby, Ees and V0 could be derived (14).
The prior study of Senzaki et al. (14) sampled pressures and volumes at several time points during isovolumic contraction (i.e., multiple values of td). This was easily achieved since both signals were measured invasively, and the final Ees estimate averaged separate calculations. For noninvasive analysis, however, a single pressure-volume point is used, timed at the onset of ejection (end of the isovolumic period). By substituting arterial diastolic pressure for end-isovolumic LV pressure and arterial systolic pressure for LV end-systolic pressure, one obtains (see Appendix for details):
 | (1) |
where Ved and Ves are end-diastolic and end-systolic volumes, SV is stroke volume, ENd is the normalized elastance value at the onset of ejection and Pd and Pes are arterial diastolic and end-systolic pressures, respectively.
The accuracy of equation 1 is dependent on the reliability of the measured data and the value chosen for ENd. Our prior study employed high-fidelity pressure/volume signals to yield accurate timing for ENd determination and early isovolumic contraction data to minimize intrapatient variability about the group-averaged normalized LV elastance at the onset of ejection (ENd(avg)) value. For noninvasive application, ENd occurs at the onset of ejection, increasing individual load/contractile-dependent deviations from the population average. To reduce this variance, we developed an approach similar to that of Shishido et al. (16) using a regression model to improve the individual noninvasive estimated normalized LV elastance at the onset of ejection (ENd(est)) for each patient, based on noninvasive measures of systolic function (EF) and arterial load (ratio of arterial diastolic to systolic pressure).
The ENd(est) regression-model was based on data obtained in 23 completely separate and previously recorded studies in which invasive aortic pressure and LV pressure-volume data were concomitantly measured. An individual time-varying elastance function was calculated from rest steady-state data, with V0 in this calculation based on multicycle ESPVR analysis as previously described (14). This curve was normalized by amplitude and time, and its value at the upstroke of aortic pressure determined. This served as the "gold standard" value for ENd. The ENd(est) was obtained from a group-averaged normalized elastance curve value at this same time td (ENd(avg)), baseline EF and the ratio of arterial diastolic to systolic pressure (Pd/Pes), given by:
 | (2) |
where ENd(avg) is given by a seven-term polynomial function:
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.
where ai are (0.35695, –7.2266, 74.249, –307.39, 684.54, –856.92, 571.95, –159.1) for i = 0 to 7, respectively. The value of tNd was determined by the ratio of pre-ejection period (R wave 
flow-onset) to total systolic period (R-wave end-flow), with the time at onset and termination of flow defined noninvasively from the aortic Doppler waveform. Each factor in equation 2 was a significant independent contributor to the regression. Figure 1 compares ENd(est) with directly measured ENd. The regression yielded an overall r = 0.88 and p < 0.00001, with a SEE about 10% the mean. The Ees(sb) was then derived by combining equations 1 and 2:
 | (3) |
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Results |
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(r = 0.81, SEE = 0.50, p < 0.0001). The mean difference was 0.03 mm Hg/ml (95% confidence interval: –0.14 0.19), that is, no systematic bias, and 80% of the estimate errors fell below 0.6 mm Hg. Figure 3C shows combined baseline and postdobutamine data, extending the range of Ees comparisons nearly twofold and improving the strength of the overall correlation. The regression SEE was 0.64, with the mean error of 0.43 ± 0.5 (again with no bias) and with about 75% of the estimates falling within 0.6 mm Hg/ml of the measured value.
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(r = 0.88, SEE = 0.67, p < 0.0001).
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Discussion |
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The correlations between measured and estimated Ees(sb) values at rest and with acute contractility change were generally good, and there was reasonable repeated-measurement reproducibility over time. It is important in this regard to consider the accuracy of the new estimation method relative to likely clinical applications. The majority (between 75% to 80%) of absolute discrepancies between Ees(sb) and the invasive "goal-standard" value were smaller than 0.6 mm Hg/ml (consistent with SEE from regression analysis). The Ees typically ranges near 2.0 mm Hg/ml in normal hearts (13), <1.0 mm Hg/ml in dilated failing hearts (12) and about 4.0 mm Hg/ml in hypertrophied hearts (22). Thus, an absolute error of 0.6 mm Hg should be adequate to correctly identify most patients within these populations. The 20% variability observed with repeated measures suggests that Ees(sb) estimates are unlikely to cross between disease groups by pure chance. However, it also indicates that moderate changes are likely needed for the new method to detect real alterations in Ees(sb) over time or with interventions.
Comparison with other single-beat analysis methods. Several prior studies have reported methods for estimating Ees from single-beat data. Most commonly, the Pes/Ves ratio is calculated. However, the assumption that the ESPVR passes through the origin in humans results in consistent overestimation of true Ees and substantially greater prediction variance (Fig. 5) (14). Kameyama et al. (9) used a more complex noninvasive analysis to estimate Ees based on pressure-cuff calibrated subclavian artery pulse tracings, echocardiography imaging and load interventions. This approach, and recent adaptations employing acoustic quantification methodology (23), remain limited by a need for varying load, which can result in unreliable image quantitation during the loading change. Other efforts to assess Ees involve curve fitting to the pressure waveform (15), an approach that seems less reliable than the Ees(sb) method (14) and is not translatable to noninvasive analysis.
Recently, Shishido et al. (16) proposed a bilinear approximation to the normalized time varying elastance curve (rising phase only) and found this simple fit provided a reliable estimate of Ees in anesthetized dogs. Central to their determination was individual estimation of the point at which the first linear approximation to rising elastance transited to the second, an inflection occurring at or near the onset of ejection. Rather than being independent of loading or contractile conditions, the inflection point had sensitivities that could be predicted from EF. Lack of a stable inflection point might seem to counter our prior clinical study (14) in which the elastance waveform was fairly well conserved during early systole. However, this earlier invasive analysis relied on data measured during the pre-ejection isovolumic period, when load and contractile effects on the elastance curve were minimal. In contrast, the method of Shishido et al. (16) as well as the present method relied on data measured solely at the onset of ejection, where these factors are more influential. Equation 2 in this study was developed independently yet concurrently with the approach of Shishido et al. (16) and serves the same purpose as their regression model to individualize a bilinear elastance. One noteworthy difference was that this study developed the model from an independent patient group and then applied this to a separate study population.
The new Ees(sb) method should also be contrasted to a recently described single-beat determination of preload recruitable stroke work (24). Preload recruitable stroke work is a useful systolic parameter that typically displays greater stability to varying loading over Ees and other indexes, and the recent study by Karunanithi and Feneley (24) extended this index to single-beat analysis. However, determination required invasive pressure and volume data, and it is unclear how easily or well this can be extended to noninvasive testing. Furthermore, it is more difficult to assess ventricular-arterial interaction with preload recruitable stroke work as opposed to Ees, which is an advantage for the latter in predicting systemic pressure responses to afterload or preload reduction therapy (11,13).
Study limitations
Technical limitations in the catheterization laboratory precluded simultaneous noninvasive/invasive analysis in many subjects, and those studies in which this was achieved still may not have optimized echo-Doppler imaging. However, this should have introduced greater scatter in our comparison data, not less. This study also did not evaluate the load-sensitivity of Ees(sb) but, rather, focused on the correlation between this parameter and directly measured invasive data. Prior invasive investigations of the Ees(sb) method have demonstrated the lack of loading influences (14).
As with many prior studies, the current invasive analysis frequently yielded an apparent negative V0 intercept for the ESPVR measured in the physiologic data range. This is not a unique feature of conductance catheter analysis, as similar findings have been reported in various mammalian species regardless of the volume method used and previously discussed (14) and is mostly related to nonlinear behavior of the ESPVR at highly reduced load. Importantly, the behavior of the ESVPR in the physiologic loading range defines the relevant hemodynamic responses; so Ees assessed in this range is most important. The new noninvasive algorithm was designed to estimate this operational Ees value, regardless of whether it predicted a negative (i.e., nonphysiologic) V0 based on a purely linear extrapolation.
Conclusions
Left ventricular end-systolic elastance can be estimated from easily obtained noninvasive parameters, and the values obtained are generally well correlated with directly measured data. Besides its implications regarding contractile strength, Ees values also help clarify integrated cardiovascular responses to altered vascular loading (8,11–13,25). In this important sense, it should be useful for assessing the efficacy of heart failure therapies and targeting the type of treatment most likely to prove beneficial.
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APPENDIX |
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TopAbstractMethodsResultsDiscussionAPPENDIXReferences |
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 | (A1) |
and for the onset of ventricular ejection point is:
 | (A2) |
Since by definition, 
, equation A2 can be rewritten as:
 | (A3) |
Rearranging equation A1 and combining it with equation A3 yields:
 | (A4) |
which is then solved for Ees:
 | (A5) |
Left ventricular volume at the onset of ejection (Vd) is very close to the LV end-diastolic volume, so stroke volume (SV) can substitute for (Vd – Ves). The Pes is approximated by the product of brachial systolic pressure Ps x 0.9. Substitution of these variables in equation A5 yields equation 1 in the Methods section.
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Footnotes |
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References |
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Ees) induced by dobutamine determined by noninvasive estimation versus the directly assessed value derived from invasive pressure-volume loops. The noninvasive method provided a good estimate of 