The quest to develop and validate an index that facilitates the surveillance of left ventricular function and the determination of the optimal time for intervention in patients with aortic stenosis is evident in the recently published literature15. Lee et al. studied subclinical ventricular deterioration in aortic stenosis (cardiac magnetic resonance study (CMR))16. One of the study's rationales is the reduced sensitivity of the left ventricular ejection fraction (LVEF) as a marker of myocardial damage. LVEF has inherent limitations irrespective of the method and modality employed. On the other hand, the European Society of Cardiology (ESC) recommends early intervention in patients with asymptomatic severe aortic stenosis and an LV EF < 50%17. A decrease in LVEF is a late marker and is usually suggestive of advanced myocardial damage, which might be irreversible in some patients16.
Pressure‒volume loop indices, namely, the LV elastance (Ees), are considered the gold standard for assessing LV function3. The invasive nature of such procedures limits their clinical utility. While several noninvasive methods for single-beat estimates of Ees have been developed and utilised in clinical practice, none have been validated for aortic stenosis.12
The Achilles heel in the noninvasive assessment of Ees is twofold: the measurement of LV ESP (LV end-systolic pressure) and the measurement of V0 (the maximal LV volume at which pressure is still zero).
Estimation of LV end-systolic pressure:
One of the main challenges in aortic stenosis is the estimation of noninvasive LV ESP.12 LV ESP in patients with no trans-aortic valve gradient, as developed by Kelly et al., is estimated as LV ESP = 0.9 × SBP, where SBP is the brachial systolic blood pressure measured by a mercury sphygmomanometer.10,18
Kelly et al. studied ten patients (simultaneously invasive and noninvasive studies) in an attempt to calculate arterial elastance (Ea). They showed an accurate prediction of LV ESP using correlation; they did not gauge the agreement between the two methods. They also assessed another formula, LV ESP ≈ (SBP × 2 + DBP)/3, to estimate LV ESP. Both formulas had similar accuracies for predicting the LV ESP (r2 = 0.97 and 0.96, respectively).18 Researchers such as Chen et al. and Kim et al. accepted this assumption (LV ESP = 0.9 × SBP) and used it in their single-beat estimates of Ees(sb).7,8
Tanoue et al. substituted LV ESP with MAP and showed a strong correlation between invasive and noninvasive Ees in an animal model of 24 mongrel dogs.6 However, correlation does not always mean that there is agreement between the two methods. Moreover, the substitution of LV ESP with MAP has not been validated in humans. Chemla et al. showed that LV ESP strongly correlates with SBP but is less strongly correlated with MAP.19 As such, this particular formula (MAP/ESV) has not been widely used in noninvasive studies for measuring Ees. Bombardini et al., in their noninvasive studies, substituted LV ESP with systolic blood pressure (noninvasive Ees(sb) = SBP/ESV).12,13
In aortic stenosis, the above assumptions fall short due to the presence of a gradient across the stenotic aortic valve (AV), i.e., the substitution of the LV ESP with a derivative of the brachial SBP would underestimate the LV ESP and, as a result, the Ees(sb). Yamashita et al. (coauthored by Tanoue) recognised this flaw among patients with aortic stenosis and substituted MAP with the "corrected MAP".11 The corrected MAP incorporated the AV peak gradient as measured by TTE.11 However, this assumption has not been validated in humans or in the context of AS. On the other hand, Bombardini et al. recommended the addition of the pressure drop to the brachial systolic blood pressure to estimate LV ESP.12
In this study, we showed that invasive LV ESP had the best agreement with Kelly's method for LV ESP when substituted with SBP (LV ESP = 0.9 × SBP). As a substitute, SBP had the smallest mean difference and the closest correlation coefficient to zero. The other methods (MAP, corrected MAP and the Bombardini suggestion) had weak agreement with the LV ESP, as evidenced by one sample t test and the Wilcoxon test.
Estimation of V0:
To calculate the ESPVR, V0, which is the maximal volume at which the pressure is still zero (the ESPVR volume axis intercept), should be measured (estimated). It is considered constant and load independent. V0 cannot be directly measured in clinical practice, but it can be estimated once the slope of the ESPVR (Ees) is known.7 Assuming that Ees is linear, two points from the regression line that represents Ees will be sufficient to estimate Ees (the slope) and, hence, V0.20 To generate these two points, researchers in the past altered the LV loading conditions with inferior vena cava (IVC) occlusion and repeated the PV loop measurements. The two measures of Ees (at normal loading conditions and reduced loading conditions) constituted the two points required to estimate Ees (the slope of change in the ESPVR). However, the above assumption is not entirely correct because ESPVR is nonlinear under high contractile states and low loading conditions.7 In large mammals, it is typically concave.21 Considering that the ESPVR is nonlinear under many conditions, V0 becomes load dependent. Chen et al., in their study to develop a single-beat estimate of Ees, and Maurer et al., in an echocardiography-based noninvasive survey, reported a negative V0.7,22
Nonetheless, the above assumptions have been generally accepted. The generated indices of contractility were still accurate, sensitive and reproducible. Chen et al. also wrote in their study: "importantly, the behaviour of the ESPVR in the physiologic loading range defines the relevant haemodynamic responses; so Ees assessed in this range is most important".7
Single-beat estimates of Ees generate a single figure of Ees. Researchers such as Shishido et al., Chen et al., and Kim et al. have attempted to account for this fact.5,7,8 The formulas used were based on time-varying elastance [E(t)] during the isovolumic contraction phase and ejection phase.9 As such, the need for two Ees estimates at two different loading conditions has been negated. Shishido et al. then used the following formula to estimate V0: V0(sb) = end systolic volume (Ves) – end systolic pressure (Pes)/Ees(sb).5 The simplified single-beat estimate of Ees, such as Ees(sb) = 0.9 × SBP/ESV, assumes V0 = zero. In this study, to simplify the research protocol to include otherwise lengthy and risky procedures, we measured the invasive ESPVR as Ees = ESP/ESV, i.e., we assumed V0 = zero.
The agreement between invasive Ees and noninvasive Ees(sb):
The single-beat estimate of Ees (Ees(sb)) formulas can be divided into two groups: the group that attempts to measure V0 and assumes that LV ESP = 0.9 × SBP, such as (Shishido, Chen and Kim), and the second group that assumes that V0 = zero but substitutes for LV ESP differently (Kelly, Tanoue, Yamashita and Bombardini).
Chowdhury et al. studied the agreement between invasively measured Ees and noninvasive Ees(sb) among children.3 Their research methodology mandated vena cava balloon occlusion. They compared four different methods of estimating Ees(sb): Chen, Kim, Shishido and Tanoue. Notably, they calculated Tanoue Ees as "Ees(sb4) = 0.9 × SBP/ESV". In their original publication, Tanoue et al. used the MAP as a substitute for the LV ESP, not 0.9 × SBP. They concluded the following: Chen's, Shishido's and Kim's methods overestimated the true Ees, and only the following formula, Ees(sb) = 0.9 × SBP/ESV, had good agreement with invasive Ees. Notably, patients with LV outflow obstruction, including patients with severe AS, were excluded.
In 2014, Yotti et al. studied 27 patients with various loading conditions (eight patients with dilated cardiomyopathy, ten normal EF patients and nine patients with end-stage liver failure). Their research methodology also mandated vena cava balloon occlusion. They concluded that Chen's method (r2 = -0.05, p > 0.05) failed to correlate with invasive Ees, while Kelly's method (Ees = 0.9 × SBP/ESV) had only a poor correlation (r2 = 0.38, p < 0.05).23
Kelly's method (Ees(sb) = 0.9 × SBP/ESV) and the SBP method (Ees(sb) = SBP/ESV) had the best agreement with the invasive Ees (allowing for the abovementioned assumptions). The methods that fell into group one had poor agreement with invasive Ees. Likewise, the methods that assumed V0 = zero (group two) but attempted to account for the gradient across the AV also showed poor agreement compared to Kelly's method.
It seems that a simplified formula, such as Ees(sb) = 0.9 × SBP/ESV or Ees(sb) = SBP/ESV, has the best agreement with the invasively measured Ees. The above conclusion holds true regardless of the method used to estimate the invasive Ees (with or without load variation) or the studied clinical condition, including severe AS. The number of assumptions made to assemble these complex formulas is likely the reason behind these findings.
As Chen et al. suggested, ultimately, the sensitivity and specificity of a specific index determine its clinical utility. All being equal, it is the simplest method that should be used.