Discussion

We assessed the relationship between E_A and specific indices of arterial load determined from central pressure–flow analyses among middle-aged adults in the general population, as well as a diverse clinical population of older adults. We also investigated the sensitivity of E_A to changes in pulsatile load induced by isometric exercise. Our findings consistently demonstrate that E_A is a quasi-perfect function of SVR and HR (more specifically, of SVR/T), with weak, inconsistent and in some cases, erratic contributions from measures of pulsatile load such as aortic Zc, TAC, or wave reflection magnitude and timing. Similarly, despite pronounced changes in pulsatile load induced by isometric exercise, changes in E_A were a quasi-perfect linear function of the change in SVR/T and negligibly influenced by changes in pulsatile load. Our empirical findings demonstrate, in agreement with modeling studies,²⁰ that E_A depends almost entirely on SVR and HR and has poor sensitivity to the human pathophysiological ranges of pulsatile afterload observed in vivo.

The derivation of E_A as a summary index of arterial load was motivated by the appeal of expressing afterload by a linear P_ES–SV relationship, which can be expressed in the same units as LV end-systolic elastance. However, E_A does not represent the true physical arterial elastance (ie, the inverse of arterial compliance) nor does it depend purely on arterial properties. Defining arterial elastance as the ratio of P_ES/SV treats the arterial system as an elastic chamber in which pressure increases linearly from zero to P_ES as a result of the SV. However, in reality, arterial pressure pulsations hover around a nonzero mean pressure (which, in turn, depends on SVR and cardiac output). The P_ES/SV ratio (E_A) is therefore much different from true arterial elastance and profoundly influenced by SVR. It also follows that, to the degree that P_ES closely approximates MAP, E_A closely approximates SVR when the latter is expressed in elastance units (ie, normalized for time). This leads to the prediction that the SVR/T ratio (which depends purely on resistive load and HR, a cardiac property) is the main determinant of E_A. This can be expressed as follows: SVR equals the ratio of MAP to cardiac output, and the latter is in turn equivalent to the product of SV and HR:

(1)

where T is the cardiac time period (the inverse of HR). Therefore, to the degree that P_ES is similar to MAP, SVR/T ratio is similar to the ratio of P_ES to SV:

(2)

Despite the appealing nature of E_A as a single index that lumps resistive and pulsatile afterload, pulsatile load is in reality complex, time-varying, and impossible to characterize by a single number. The gold standard expression of arterial load is the aortic input impedance spectrum, which fully characterizes the mechanical load imparted by the vascular system downstream of the proximal aorta in the frequency domain. Several arterial functional indices can be derived from this impedance spectrum or from analogous analyses in the time domain.^6,29,33 A basic set of parameters that characterizes arterial load includes SVR and several indices of pulsatile load,^{1,2,6,7,29,33} including (1) proximal aortic Zc, (2) TAC, (3) reflection magnitude, and (4) reflected wave timing. The notion that E_A represents a lumped parameter of arterial load incorporating both resistive and pulsatile load originated from mathematical analyses by Sunagawa et al,¹⁹ in which the arterial system was represented by a 3-element Windkessel model consisting of aortic Zc, peripheral resistance (R), and arterial compliance (C). Important simplifying assumptions, which are usually overlooked in the literature, were undertaken in this derivation. Although when properly interpreted, the 3-element Windkessel model is an useful representation of the arterial tree, it does not explicitly account for wave conduction or reflections, thus neglecting the effects of reflected waves on LV afterload,^1,3,6,34,35 myocardial hypertrophy,^36–38 fibrosis,³⁶ dysfunction,^{1,14,34,39–42} and the risk of heart failure.³ More importantly, the derivation by Sunagawa et al assumed a square-shaped aortic pressure waveform in systole, rising instantaneously at the beginning of systole from the end-diastolic to the P_ES value, being subsequently completely flat until end-systole. This marked simplification thus ignores all pulsatile pressure phenomena occurring above P_ES, neglecting the effects of pulsatile load on the time-resolved systolic pressure profile. As originally acknowledged by Sunagawa et al,¹⁹ a relatively large error in this model occurs when the area under the pressure curve above P_ES increases, which occurs precisely in situations of increased pulsatile load (such as aging and arterial stiffening).¹ The nonphysiological square-shaped systolic pressure profile also neglects the variability in the slope of the early systolic pressure–flow relationship (which is governed by aortic Zc), at a time during which most of the pulse pressure is achieved and peak myocardial wall stress occurs.²⁷ Such profound limitations of E_A can also be inferred by analysis of the formula derived by Sunagawa et al (Equation S2) to express the arterial determinants of P_ES/SV (ie, E_A), as summarized in the online-only Data supplement. Briefly, careful analysis of this derivation reveals that the effect of compliance is negligible and the effect of proximal aortic Zc is reduced to a minuscule contribution to total resistance (which originates predominantly in the microvasculature), fully ignoring the important role of Zc in the pulsatile pressure–flow relationship. Taking into account straightforward algebraic considerations, this derivation actually shows that E_A closely approximates R/T.

In addition to the relatively simple analytic arguments discussed above, more complex modeling studies assessing the sensitivity of E_A to SVR and pulsatile load have been performed using a mathematical heart-arterial interaction model.²⁰ In such studies, Segers et al²⁰ demonstrated a strong linear relationship between E_A and SVR/T and showed that, within the human pathophysiologic ranges, this ratio was a much more important determinant of E_A than TAC.

The concept that E_A represents a lumped index of resistive and pulsatile load has gained widespread acceptance, with little in vivo data to support and despite the considerations and modeling studies mentioned above. To our knowledge, only 2 small studies assessing this issue in humans are available.^21,22 Kelly et al²² studied 9 men and 1 woman referred for cardiac catheterization. They performed arterial hemodynamic measurements before and after an acute preload reduction and in 7 cases, a pharmacological intervention. The authors assessed the relationship between the P_ES/SV ratio and the Sunagawa expression of E_A (Equation S2, discussed above). Not surprisingly, they demonstrated that this expression, which they called an input impedance measure of E_A, adequately predicted the P_ES/SV ratio. However, in such expression, the influence of pulsatile load had already been eliminated largely because of important nonphysiological simplifying assumptions mentioned above. Interestingly, in this study, E_A had an almost perfect linear relationship with SVR/T (R=0.98). However, the authors noted that E_A was systematically greater than SVR/T (the relationship thus differing from the line of identity) and interpreted this to be the result of the oscillatory load caused by reduced TAC, increased Zc and wave reflections, concluding that E_A better indexed the arterial load effects on the LV. Of note, although the authors derived indices of pulsatile load (aortic Zc, TAC, and wave reflections) from aortic input impedance spectra, they did not actually present relationships between these measures and E_A. Importantly, the quasi-perfect relationship between E_A and SVR/T was obtained using values of E_A and SVR/T from all measurements derived from their 10 study subjects at baseline and after various interventions. Not only was pulsatile load different between individuals at baseline, but markedly varied between measurements (TAC, for instance, increased by 75.6% after preload reduction and aortic Zc decreased by 44%, compared with baseline). Given that pulsatile load was highly variable, had it influenced E_A to any significant degree, it would have distorted the otherwise perfect relationship between SVR/T and E_A, rather than simply shift it from the line of identity, while maintaining its high coefficient of correlation. If one accepts that E_A truly integrates pulsatile load, shifting the SVR/T–E_A relationship from the line of identify while maintaining its nearly perfect correlation coefficient would imply that all these measurements were obtained under identical pulsatile load conditions (such that all points were shifted up by the same amount, thus preserving the high correlation), which was clearly not the case. The systematic difference between E_A and SVR/T thus cannot be interpreted as support of the sensitivity of the former to pulsatile load. Careful analysis of the study data indeed shows that the responsible factor for most of this difference was the use of LV pressure at the time of peak LV elastance, rather than actual end-systolic arterial pressure (dicrotic notch pressure), to compute E_A. Notably, LV pressure at the time of peak LV elastance was 15 mm Hg greater than actual arterial P_ES, leading to a systematic overestimation of E_A relative to SVR/T, because E_A is greater than SVR/T only to the degree that P_ES is greater than MAP.

In the only other study assessing the relationship between E_A and pulsatile load in humans, Chemla et al²¹ studied 66 subjects and demonstrated some sensitivity of E_A to TAC. However, in this study, TAC was estimated as SV/pulse pressure, which is affected by not only TAC but also SVR. Furthermore, the influence of other parameters of pulsatile load was not assessed. Our study addressed the influence of various indices of pulsatile load in middle-aged adults without established cardiovascular disease, as well as a clinical population of older individuals, thus encompassing a wide range of pathophysiologic values of pulsatile load. In addition, we assessed changes in E_A and various arterial parameters in response to an experimental intervention that induced pronounced effects on pulsatile arterial load. Despite marked changes in Zc, TAC, reflection magnitude, and timing in response to handgrip exercise, E_A changed in a quasi-perfect linear fashion with the SVR/T ratio, indicating that E_A is insensitive to, and does not adequately integrate, changes in pulsatile arterial load.

In addition to the direct computation of E_A based on a known value of P_ES, indirect approximations have been proposed when P_ES is unknown, such as assuming that P_ES equals 90% of systolic blood pressure⁴³ or directly approximating E_A using the following formula: (2×systolic blood pressure+diastolic blood pressure)/3 SV.²² To the degree that a directly measured E_A is an inadequate index to assess pulsatile load, any approximations will be similarly inadequate.

Our findings have implications for the interpretation of clinical studies addressing the relationship between arterial load and disease states or cardiac dysfunction. Weber et al⁴⁴ demonstrated that E_A was less useful than central pulse pressure or reflected wave amplitude to discriminate patients with heart failure with preserved ejection fraction from patients with other causes of exertional dyspnea. Similarly, among adults without established cardiovascular disease, measures of pulsatile load were more strongly related to diastolic mitral annular tissue velocities than E_A. Only specific measures of pulsatile load (such as aortic Zc and measures of wave reflections) independently predicted mitral annular velocities in that study.¹⁴ Furthermore, in a recent prospective study among patients with established heart failure and preserved ejection fraction, E_A failed to predict adverse outcomes.⁴⁵

Because E_A is used along with end-systolic LV elastance as an index of ventricular–arterial coupling, our findings imply that this paradigm does not properly assess the effects of pulsatile load on the heart. The pressure–volume paradigm characterizes only limited aspects of ventricular–arterial coupling (such as energetic efficiency and SV changes), which is a much broader concept. Indeed, although as shown here, pulsatile load does not significantly affect the P_ES/SV relationship (and thus the E_A/E_ES ratio), pulsatile load is clearly important because of its effects on LV fibrosis, dysfunction, and failure. The LV loading sequence, in particular, which is intrinsically neglected by the pressure–volume paradigm, is an important determinant of maladaptive remodeling, hypertrophy, diastolic dysfunction, and heart failure risk.^{1,34,36,37,40,46,47}

Our study should be interpreted in the context of its strengths and limitations. Strengths include the large sample size and the high degree of consistency in our findings across different substudies, as well as the assessment of resting arterial load indices and changes in response to a suitable intervention. For obvious practical and safety reasons, we performed noninvasive measurements rather than invasive measurements of central pressure. However, the same pressure signals were used to compute E_A and all parameters of pulsatile load; therefore, any measurement bias would have affected E_A and its determinants in parallel, thus not affecting our conclusions. In addition, the main advocated use of E_A is its simplicity for use as a noninvasive parameter of arterial load; accordingly, comprehensive assessments of pulsatile load were obtained from noninvasive measurements, which avoids potential advantages of invasively assessed pressure–flow relationships over noninvasively assessed E_A.