# Effective Arterial Elastance Is Insensitive to Pulsatile Arterial LoadNovelty and Significance

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## Abstract

Effective arterial elastance (E_{A}) was proposed as a lumped parameter that incorporates pulsatile and resistive afterload and is increasingly being used in clinical studies. Theoretical modeling studies suggest that E_{A} is minimally affected by pulsatile load, but little human data are available. We assessed the relationship between E_{A} and arterial load determined noninvasively from central pressure–flow analyses among middle-aged adults in the general population (n=2367) and a diverse clinical population of older adults (n=193). In a separate study, we investigated the sensitivity of E_{A} to changes in pulsatile load induced by isometric exercise (n=73). The combination of systemic vascular resistance and heart rate predicted 95.6% and 97.8% of the variability in E_{A} among middle-aged and older adults, respectively. E_{A} demonstrated a quasi-perfect linear relationship with the ratio of systemic vascular resistance/heart period (middle-aged adults, *R*=0.972; older adults, *R*=0.99; *P*<0.0001). Aortic characteristic impedance, total arterial compliance, reflection magnitude, and timing accounted together for <1% of the variability in E_{A} in either middle-aged or older adults. Despite pronounced changes in pulsatile load induced by isometric exercise, changes in E_{A} were not independently associated with changes pulsatile load but were rather a nearly perfect linear function of the ratio of systemic vascular resistance/heart period (*R*=0.99; *P*<0.0001). Our findings demonstrate that E_{A} is simply a function of systemic vascular resistance and heart rate and is negligibly influenced by (and insensitive to) changes in pulsatile afterload in humans. Its current interpretation as a lumped parameter of pulsatile and resistive afterload should thus be reassessed.

- arterial load
- characteristic impedance
- effective arterial elastance
- total arterial compliance
- ventricular–arterial coupling
- wave reflections

## Introduction

Left ventricular (LV) afterload is an important determinant of normal cardiovascular function and a key pathophysiologic factor in various cardiac disease states. In the presence of a normal aortic valve, LV afterload corresponds to the mechanical load imposed by the systemic arterial tree (arterial load). Arterial load is influenced by arterial health and is a key determinant of LV systolic and diastolic function, LV remodeling, and the risk of heart disease.^{1–3}

Accurate physiological characterization of parameters of arterial load is crucial to interpreting human data related to ventricular–arterial interactions. Arterial load can be precisely and comprehensively characterized via analyses of aortic pressure–flow relationship. Aortic input impedance analyses obtained in this manner constitute the gold standard analytic method for the assessment of arterial load.^{1,4–7} Pressure–flow analyses allow the quantification of steady or resistive load as well as various components of pulsatile load.^{1,8} Early studies of aortic input impedance were performed using invasive measurements, but more recently, comprehensive noninvasive assessments of arterial load via pressure–flow analyses have been shown to be feasible in both clinical and epidemiological settings, using a combination of arterial tonometry and Doppler echocardiography. This noninvasive approach has provided significant insights into the role of arterial hemodynamics in normal aging, sex-related physiological differences,^{9,10} hypertension,^{11} obesity,^{12} diabetes mellitus,^{13} myocardial dysfunction,^{14} heart failure,^{2,15} and the hemodynamic effects of pharmacological interventions^{16,17} in humans.

Motivated by the need to represent arterial load in the pressure–volume plane, the determinants of the end-systolic pressure (P_{ES})–stroke volume (SV) relationship were assessed by Sunagawa et al.^{18,19} Making substantial simplifying assumptions about the arterial tree, the authors derived an equation that relates the slope of this relation to arterial properties and proposed that this slope (which they called effective arterial elastance [E_{A}]) is a lumped parameter of aortic input impedance, which captures relevant information about both pulsatile and resistive components of afterload. Although E_{A} is attractive because of its simplicity, there are various disadvantages of E_{A} as an index of arterial load. E_{A} is prominently influenced by heart rate (HR; a cardiac, rather than an arterial property)^{20,21} and its sensitivity to pulsatile load, as opposed to resistive load,^{20,21} has not been addressed properly. The latter issue has important implications, given the well-recognized importance of pulsatile LV load.^{1–3} Although little evidence exists on the sensitivity of E_{A} to pulsatile load, the view that it incorporates both resistive and pulsatile load is increasingly accepted. Modeling approaches suggest that E_{A} has little dependence on pulsatile load and depends largely on the ratio between systemic vascular resistance (SVR) and heart period (T), the latter being the inverse of HR.^{20} However, data in humans are scarce and limited to 2 small studies.^{21,22}

In this study, we aimed (1) to assess the relationship between E_{A} and indices of pulsatile and resistive arterial load obtained via central arterial pressure–flow analyses in a general population-based sample of middle-aged adults without clinically evident cardiovascular disease (substudy 1A) and in a diverse clinical population of older adults with suspected or established cardiovascular disease (substudy 1B) and (2) to assess the sensitivity of E_{A} to detect changes in specific parameters of arterial load in response to isometric exercise, an intervention with known pronounced effects on pulsatile load^{23} (substudy 2).

## Methods

### Study Population

#### Substudy 1

For the assessment of the relationship between E_{A} and specific indices of arterial load at rest, we investigated the following 2 populations:

Substudy 1A: The Asklepios study cohort, composed of 2524 men and women aged 35 to 55 years, without evidence of overt cardiovascular disease, sampled from the Belgian communities of Erpe-Mere and Nieuwerkerken, as previously described in detail.^{24,25} Complete echocardiographic and tonometry data for analyses of arterial load were available from 2368 subjects.

Substudy 1B: Given that pulsatile (rather than resistive) load may more prominently affect E_{A} in older age groups or those with cardiovascular disease, we also studied a population of older adults (n=193) with established or suspected cardiovascular disease, referred for a clinically indicated cardiac MRI examination at the Philadelphia Veterans Affairs Medical Center.

#### Substudy 2

To assess changes in response to isometric handgrip exercise, we enrolled adults aged 20 to 80 years. Subjects were studied at the echocardiography laboratories of the Hospital of the University of Pennsylvania and Philadelphia VA Medical Center. We excluded pregnant women, subjects with a personal or family history of hypertrophic cardiomyopathy or those with poor acoustic windows.

The corresponding institutional review boards or ethical committees approved all substudies, and all subjects provided written informed consent.

### Assessment of Proximal Aortic Inflow

Inflow to the proximal aorta was examined using Doppler echocardiography in all substudies, except for substudy 1B (which used MRI to measure aortic flow, as described below). Echocardiographic examinations were performed using a Vivid-7 ultrasound platform (Vingmed Ultrasound, Horten, Norway) as previously described.^{24,25} Instantaneous LV outflow tract velocities were measured form the apical 5-chamber view and multiplied by LV outflow tract cross-sectional area to obtain volume flow.

In substudy 1B, which enrolled patients referred for a cardiac MRI examination, we measured ascending aortic flow with phase-contrast MRI, using a 1.5-T Avanto or Espree system (Siemens Medical Solutions). A phase-contrast gradient echo pulse sequence with through-plane velocity encoding was applied during free-breathing using retrospective gating, in a plane perpendicular to the long axis of the ascending aorta at the level of the pulmonary artery bifurcation. Maximal velocity encoding was usually set at 150 cm/s but adjusted during the examination to avoid aliased velocity measurements. Other typical parameters were slice thickness 6 mm, matrix 192×192, and repetition time ≈10 ms. Images were analyzed using the freely available software Segment.^{26}

### Arterial Tonometry

Arterial tonometry was performed in the supine position, simultaneously with echocardiographic LV outflow tract interrogations or immediately after the MRI, using high-fidelity Millar applanation tonometers (SPT-301; Millar Instruments, Houston, TX) and dedicated acquisition platforms, either with a custom-made platform (Asklepios study)^{24,25} or using the Sphygmocor device (Atcor Medical, Sydney, Australia). Carotid pressure waveforms were calibrated with brachial diastolic and mean blood pressure; the latter was measured via numeric integration of the brachial tonometric pressure waveform in substudy 1A (Asklepios study)^{25} or measured with an oscillometric device (HP-78352c; Hewlett-Packard, Palo Alto, CA) in substudies 1B and 2. Carotid pressure waveforms were exported and further processed in an identical fashion in all cases, as described below.

### Pressure–Flow Analyses

Pressure (P) and flow (Q) velocity recordings were processed off-line using custom-designed software written in Matlab (The Mathworks, Natick, MA) as previously described.^{25,27} Proximal aortic characteristic impedance (Zc) was computed in the time domain as the slope of the early systolic pressure–flow relationship.^{2,25} As previously described in detail,^{25} the pressure wave was separated into its forward (Pf) and backward (Pb) traveling component (ie, the reflected wave)^{1,6,25,28,29}:

Reflection magnitude was defined as the ratio of the amplitudes of Pb and Pf (Pb/Pf). Reflected wave transit-time (RW_{TT}) was computed from wave separation analysis as the moment in time where Pb adds to Pf, as previously described.^{30} Total arterial compliance (TAC) was calculated via the pulse pressure method.^{31} Alternative analyses were performed with TAC computed by the area method.^{32} SVR was computed as mean aortic pressure divided by cardiac output. E_{A} was computed as the ratio of P_{ES} (ie, pressure at the dicrotic notch) to SV.^{19,20,22}

### Handgrip Exercise (Substudy 2)

For this substudy, after acquisitions of baseline pressure and flow measurements, subjects performed 3 maximal voluntary dominant forearm contractions with a Stoelting handgrip dynamometer (Stoelting, Wood Dale, IL). The force of contraction was averaged, and a submaximal target of 40% was used for a sustained handgrip effort until fatigue. Carotid tonometry and echocardiographic assessments of LV outflow tract flow were performed immediately before termination of the handgrip maneuver and used for pressure–flow analyses, as described above.

### Carotid–Femoral Pulse Wave Velocity Measurements

Because arterial load is strongly influenced by arterial stiffness, we also assessed the association between E_{A} and carotid–femoral pulse wave velocity (PWV; a well-established index of arterial stiffness) in substudies 1A and 1B. In substudy 1A (Asklepios study population), carotid–femoral PWV was calculated using the foot-to-foot method using carotid and femoral recordings as previously described.^{24,25} In substudy 1B, carotid–femoral PWV was calculated using the Sphygmocor PVx device (Atcor Medical, Sydney, Australia).

### Statistical Analyses

The relationship between E_{A} and specific indices of resistive (SVR) and pulsatile load (aortic Zc, TAC, reflection magnitude, and RW_{TT}) was analyzed using multivariable linear regression models in which E_{A} was the dependent variable, with specific indices of arterial load and HR included as independent variables. We assessed the amount of variability in E_{A} that is accounted for by SVR, HR, and indices of pulsatile load, by examining the *R*^{2} increase associated with the addition of all indices of pulsatile load (aortic Zc, TAC, reflection magnitude, and RW_{TT}) to a model containing HR and SVR. Because previous modeling studies suggest that E_{A} is a linear function of the SVR/heart period (the latter being the inverse of HR),^{20} we also built models in which this ratio replaced SVR and HR in the list of independent variables. For the experimental substudy, which studied the effects of isometric exercise, we used similar statistical methods to assess the amount of variability in the change in E_{A} that is accounted for by the change in individual indices of arterial load and HR, computed in all cases by subtracting the postintervention value from the resting value. Given that for any given heart rate, E_{A} is different from SVR only to the degree that P_{ES} is different than mean arterial pressure (MAP), we performed an alternative set of analyses assessing how pulsatile load affects the difference between P_{ES} and MAP.

Multi-colinearity of predictor variables was evaluated with variance inflation factors and condition indices and addressed with mean centering as needed. Statistical significance was defined as 2-tailed α<0.05. Statistical analyses were performed using SPSS for Mac v20 (SPSS Inc, Chicago, IL).

## Results

Table 1 shows important demographic and clinical characteristics of subjects included in each substudy.

### Relationship Between Arterial Load and E_{A} in Middle-Aged Adults

Table 2 shows regression models assessing the association between E_{A} and specific indices of arterial load among middle-aged adults (Asklepios study). In this population, SVR and HR predicted 95.6% of the variability in E_{A}. The ratio of SVR/heart period (SVR/T) was highly correlated with E_{A} (*R*=0.972; *R*^{2}=0.945). Table S1 in the online-only Data Supplement presents unadjusted correlations and *R*^{2} values between E_{A} and indices of pulsatile load. Correlations between SVR and indices of pulsatile load are also presented for comparison. It can be seen that the correlations between E_{A} and pulsatile load indices were weaker than the quasi-perfect correlation between E_{A} and either the SVR or the SVR/T ratio. It is also apparent that the magnitude of the correlations between E_{A} and indices of pulsatile load paralleled the magnitude of the correlations between SVR and indices of pulsatile load.

In a multivariate model containing SVR/T and all indices of pulsatile load as predictors of E_{A} (Table 2), SVR/T was the strongest predictor (standardized β=0.91; *P*<0.0001). A lower TAC and greater reflection magnitude were both weakly associated with a greater E_{A}. However, a longer RW_{TT} was also associated with a higher E_{A}. Aortic Zc was not independently associated with E_{A}. All indices of pulsatile load combined increased the model *R*^{2} by <0.01 (ie, they independently accounted for <1% of the variability in E_{A}, after accounting for SVR/T ratio). Adjustment for sex and exclusion of subjects taking vasoactive medications did not appreciably influence the observed associations (not shown).

### Relationship Between Arterial Load and E_{A} in Older Adults

Table 3 shows regression models assessing the association between E_{A} and specific indices of arterial load in older adults. In this population, SVR and HR predicted 97.8% of the variability in E_{A}, whereas the ratio SVR/T predicted 99% of the variability in E_{A}. Unadjusted correlations between E_{A} and pulsatile load indices were weaker and closely paralleled the magnitude of the correlations between SVR and indices of pulsatile load (Table S1).

In a multivariate model containing SVR/T and all indices of pulsatile load as predictors of E_{A}, SVR/T was the strongest predictor (standardized β=0.99; *P*<0.0001). A lower TAC and greater reflection magnitude were both weakly associated with an increase in E_{A}. However, a lower aortic Zc and a longer RW_{TT} (both of which indicate more favorable pulsatile loading) were also associated with a higher E_{A}. All indices of pulsatile load increased the model *R*^{2} by 0.002 (ie, they independently accounted for only 0.2% of the variability in E_{A}, after accounting for the SVR/T ratio). Results were similar when only subjects with a LV ejection fraction >45% were included (Table S2).

Adjustment for sex and vasoactive medications shown in Table 1 did not appreciably influence the observed associations (not shown).

### Relationship Between Changes in Arterial Load and Changes in E_{A} After Isometric Exercise

Table 4 shows changes associated with isometric exercise in substudy 2. Isometric exercise induced an increase in HR (+6.2 bpm; *P*<0.0001), an increase in SVR (+209 dyn·s/cm^{5}; *P*<0.0001), a reduction in TAC (−0.33 mL/mm Hg; *P*=0.002), an increase in proximal aortic Zc (+0.027; *P*=0.002), an increase in reflection magnitude (+0.04; *P*=0.001), and a shorter RW_{TT} (−12 ms; *P*<0.0001).

Table 5 shows regression models assessing the association between the change in E_{A} and the change in specific indices of arterial load in response to isometric exercise. The change in SVR and HR predicted 96.8% of the variability in the change in E_{A}. The change in the SVR/T was quasi-perfectly correlated with the change in E_{A} (*R*=0.99; *R*^{2}=0.978), as shown in Table 3 (model 2). Unadjusted correlations between the change in E_{A} and the change in indices of pulsatile load were much weaker and closely paralleled the magnitude of the correlations between the change in SVR and the change in indices of pulsatile load (Table S1).

In a multivariate model assessing the change in SVR/T and the change in all indices of pulsatile load as predictors of the change in E_{A} in response to isometric exercise, the change in SVR/T was the strongest predictor (standardized β=0.96; *P*<0.0001). A reduction in TAC and an increase in reflection magnitude in response to isometric handgrip exercise were both weakly associated with an increase in E_{A} (standardized β≤0.05 for both). The changes in all indices of pulsatile load combined accounted for an increase in the model *R*^{2} of 0.005 (ie, they independently accounted for only 0.5% of the variability in the change in E_{A}, after accounting for the change in SVR/T).

Adjustment for sex and vasoactive medications shown in Table 1 did not appreciably influence the observed associations (not shown).

### Analyses Using TAC Computed With the Area Method

Because the pulse pressure method variably underestimates arterial compliance relative to the area method, we performed additional analyses that included TAC computed with the area method (Tables S3–S5). Results from these regression models were similar to those obtained in models that used TAC computed with the pulse pressure method.

### Correlations Between Pulsatile Load and the Difference Between MAP and P_{ES}

We assessed the variability in P_{ES} that is accounted for by (1) MAP, (2) the difference between P_{ES} and MAP (P_{ES}−MAP) in the study populations. Among middle-aged adults (substudy 1A), MAP and (P_{ES}−MAP) accounted for 77.6% and 12.5% of the variability in P_{ES}, respectively. In older adults (substudy 1B), MAP and (P_{ES}−MAP) accounted for 88.2% and 11.8% of the variability of P_{ES}, respectively. Similarly, in substudy 2, the MAP change in response to handgrip exercise accounted for 89.6% of the variability in P_{ES} change, whereas the change in P_{ES}−MAP accounted for only 10.4% of the variability in P_{ES} change.

The main determinant of P_{ES}−MAP was HR, rather than pulsatile load (Table S6). Furthermore, P_{ES}−MAP was not significantly related to ascending aortic Zc in any substudy; although it increased with decreasing TAC, it also increased with a greater RW_{TT} (a favorable pattern of pulsatile load) among older adults.

All indices of pulsatile load together accounted for only 24% and 28% of the variability in P_{ES}−MAP among middle-aged adults and older adults, respectively. Similarly, in substudy 2, the change in all indices of pulsatile load together accounted for only 24% of the variability in the P_{ES}−MAP change.

In summary, pulsatile load accounted for a small proportion of the variability of P_{ES}−MAP, which in itself accounted for a small proportion of the variability in P_{ES}, because most of the latter variability was determined by MAP.

### Correlation Between E_{A} and Carotid–Femoral PWV

In regression models containing the SVR/T ratio and carotid–femoral PWV as predictors of E_{A}, the latter did not bear any independent relationship with E_{A}. In these analyses among middle-aged adults (substudy 1A), the standardized coefficient for SVR/T was 0.97 (*P*<0.0001), whereas the standardized coefficient for carotid–femoral PWV was <0.001 (*P*=0.95). Among older adults (substudy 1B), the standardized coefficient for SVR/T was 0.996 (*P*<0.0001), whereas the standardized coefficient for carotid–femoral PWV was −0.003 (*P*=0.66).

## 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:

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:

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 al^{20} 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 al^{22} 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 al^{21} 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 pressure^{43} 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 al^{44} 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}.

### Perspectives

Assessment of arterial load and ventricular–vascular coupling provides important physiological information and is increasingly used in clinical and epidemiological human research. Our study demonstrates that E_{A}, which has been interpreted as an index of integrated resistive and pulsatile arterial load, is insensitive to the latter and dependent almost entirely on the former, as well as on HR. Its current interpretation as a lumped parameter of pulsatile and resistive afterload should thus be reassessed. Comprehensive pressure–flow analyses provide a powerful alternative for the noninvasive assessment of arterial load.

## Sources of Funding

This research was funded by Fonds voor Wetenschappelijk Onderzoek Vlaanderen research grants G.0427.03 and FWO G.0838.10 (for the Asklepios Study) and 1R21AG043802-01 (J.A. Chirinos).

## Disclosures

None.

## Footnotes

The online-only Data Supplement is available with this article at http://hyper.ahajournals.org/lookup/suppl/doi:10.1161/HYPERTENSIONAHA.114.03696/-/DC1.

- Received May 12, 2014.
- Revision received May 27, 2014.
- Accepted July 8, 2014.

- © 2014 American Heart Association, Inc.

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# Novelty and Significance

### What Is New?

We characterized the influence of specific arterial properties on effective arterial elastance, currently regarded as a lumped parameter that incorporates pulsatile and resistive afterload.

We demonstrate that effective arterial elastance is merely a function of systemic vascular resistance and heart rate and is negligibly influenced by (and insensitive to) changes in pulsatile afterload in humans.

### What Is Relevant?

Arterial load is an important determinant of normal cardiovascular function and a key pathophysiologic factor in various cardiac disease states.

Accurate physiological characterization of parameters of arterial load is therefore crucial to interpreting human data related to ventricular–arterial interactions.

Pulsatile arterial load can be precisely and comprehensively characterized via analyses of aortic pressure–flow relationships.

Effective arterial elastance, in contrast, depends almost entirely on systemic vascular resistance and heart rate and has poor sensitivity to the human pathophysiological ranges of pulsatile afterload observed in vivo.

### Summary

Effective arterial elastance is merely a function of systemic vascular resistance and heart rate and is negligibly influenced by (and insensitive to) changes in pulsatile afterload in humans. Its current interpretation as a lumped parameter of pulsatile and resistive afterload should thus be reassessed.

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- Effective Arterial Elastance Is Insensitive to Pulsatile Arterial LoadNovelty and SignificanceJulio A. Chirinos, Ernst R. Rietzschel, Prithvi Shiva-Kumar, Marc L. De Buyzere, Payman Zamani, Tom Claessens, Salvatore Geraci, Prasad Konda, Dirk De Bacquer, Scott R. Akers, Thierry C. Gillebert and Patrick SegersHypertension. 2014;64:1022-1031, originally published July 28, 2014https://doi.org/10.1161/HYPERTENSIONAHA.114.03696
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- Effective Arterial Elastance Is Insensitive to Pulsatile Arterial LoadNovelty and SignificanceJulio A. Chirinos, Ernst R. Rietzschel, Prithvi Shiva-Kumar, Marc L. De Buyzere, Payman Zamani, Tom Claessens, Salvatore Geraci, Prasad Konda, Dirk De Bacquer, Scott R. Akers, Thierry C. Gillebert and Patrick SegersHypertension. 2014;64:1022-1031, originally published July 28, 2014https://doi.org/10.1161/HYPERTENSIONAHA.114.03696Permalink: