Animals were premedicated with an intramuscular dose of xylazine (10 mg⋅kg^–1) and ketamine (40 mg⋅kg^–1). Then they were tracheotomized and their lungs mechanically ventilated in volume-controlled mode (Servo 900c, Siemens-Elema, Solna, Sweden), with 8 ml⋅kg^–1 of tidal volume, positive end-expiratory pressure of 0 cmH₂O, an inspiration to expiration ratio of 1:2, inspired oxygen fraction of 0.6, and a respiratory rate of 35–40 breaths⋅min^–1 adjusted to maintain an end-tidal CO₂ between 35 and 45 mmHg. The right internal jugular vein was catheterized for continuous sedation with ketamine (10–40 mg⋅kg^–1⋅h^–1) and midazolam (1–3 mg⋅kg^–1⋅h^–1). The muscular blockade was maintained with a rocuronium bromide infusion (0.6–1.2 mg⋅kg^–1⋅h^–1) (Quesenberry and Carpenter, 2012). Adequacy of anesthesia before neuromuscular blockade and through the experiment was evaluated by the absence of any significant blood pressure and/or heart rate change in response to an external noxious stimulus. A Ringers lactate solution (6 ml⋅kg^–1⋅h^–1) was administered as a maintenance fluid therapy. Animal temperature was continuously monitored by a rectal probe and maintained between 38 and 40°; using a heating pad. A 22G sterile polyethylene catheter was introduced into the right femoral artery and connected to a pressure transducer (TruWave, Edwards Lifesciences LLC, Irvine, CA, United States) zeroed against atmospheric pressure. Optimal damping of the arterial waveform was checked by a square wave test. The left femoral vein was used to administer vasoactive drugs and fluid bolus.

A pediatric esophageal Doppler probe (KDP72; CardioQ Combi, Deltex Medical, Chichester, United Kingdom) was introduced into the esophagus until obtaining the best outline and maximal peak velocity of aortic blood waveform. Cardiac output (CO) was calculated using the minute distance of aortic blood flow, which represents the distance traveled by a column of blood in 1 min and is calculated by the Doppler system as the product of HR and the velocity-time integral of the aortic flow waveform. The peak velocity and maximum acceleration of blood flow were used as indexes of the left ventricular systolic function (Sabbah et al., 1986; Wallmeyer et al., 1988). The arterial pressure signal was transferred from the multi-parametric monitor (S/5, Datex-Ohmeda, Helsinki, Finland) to the Doppler system and automatically synchronized with the aortic blood flow waveform for pressure-flow analysis.

A 3-element Windkessel model was used for characterizing the arterial system (Westerhof et al., 2009), consisting of systemic vascular resistance [SVR = mean arterial pressure (MAP)/CO]; arterial compliance (C_art = stroke volume / arterial pulse pressure) (Remington et al., 1948) and characteristic impedance (Zc). Zc represents the arterial input impedance in the absence of arterial wave reflections (Nichols and O’Rourke, 2005). Assuming that arterial reflections are negligible during early systole (Milnor, 1989; Nichols and O’Rourke, 2005), Zc was estimated as the slope of the early ejection pressure-flow relationship, using the ratio between the maximum of the first derivate of pressure and flow (Li, 1986; Lucas et al., 1988).

The effective arterial elastance (Ea) was used as a lumped parameter of arterial load accounting for both mean and pulsatile components (Kelly et al., 1992a):

E ⁢ a = R T / [ t s + τ × ( 1 - e - t ⁢ d ⁢ / ⁢ τ ) ]

Where R_T is the total mean vascular resistance (SVR + Zc), t_s and t_d are systolic and diastolic periods, respectively, and τ the diastolic time constant (τ = SVR × C_art) (Kelly et al., 1992a).

PPV was calculated as the percentage changes in arterial pulse pressure during a ventilatory cycle as [(PPmax – PPmin)/(PPmax + PPmin)/2] × 100, where PPmax and PPmin represent the maximal and minimal arterial pulse pressure, respectively. The calculation of SVV was performed similarly. SVmax and SVmin were calculated by integrating the systolic component of aortic blood flow waveform, whereas PPV was derived from the femoral arterial pressure waveform. PPV and SVV values were simultaneously analyzed and averaged during 1 min using a custom Excel macro (Microsoft Corporation, Redmond, WA, United States) (Figure 1). Ea_dyn was calculated as beat-to-beat PPV/SVV averaged during 1 min (Monge Garcia et al., 2011).

Left ventricular energetics were analyzed from the instantaneous pressure and flow recordings. Aortic blood flow and femoral arterial pressure waveforms were recorded simultaneously during at least 20 s at 180 Hz and ensemble-averaged, foot-to-foot aligned using the maximum of the second derivative (Vardoulis et al., 2013), and interpolated to the duration of the cardiac cycle to provide a representative waveform for analysis. An illustrative example of the signal processing is shown in Figure 2. The contribution of kinetic energy was considered negligible and not included in the analysis (Milnor, 1989).

The left ventricular (LV) total power (Ẇ_tot) transferred to the systemic circulation was calculated as the time-averaged integral of the instantaneous product of blood pressure (P) by flow (Q) during the whole cardiac period (T):

W . t ⁢ o ⁢ t = 1 T ⁢ ∫ 0 T P ⁢ ( t ) ⁢ Q ⁢ ( t ) ⁢ d t

The product of mean pressure by mean flow, or steady power (Ẇ_std), corresponds to the energy maintaining forward blood flow and represents the fraction of Ẇ_tot useful for organ perfusion (O’Rourke, 1967; Milnor, 1989; Cholley and Le Gall, 2016).

W . s ⁢ t ⁢ d = P ¯ × Q ¯

The oscillatory power (Ẇ_osc) refers to the energy lost in pulsatile phenomena due to cardiac contractions:

W . o ⁢ s ⁢ c = W . t ⁢ o ⁢ t - W . s ⁢ t ⁢ d

The oscillatory power fraction (%Osc) represents the portion of Ẇ_tot wasted in oscillatory power and quantifies the efficiency with which the external mechanical power was transferred into useful work from the LV to the arterial system (O’Rourke, 1967; Berger et al., 1995; Cholley and Le Gall, 2016). Therefore, the lower the %Osc, the more efficiently LV external work is delivered to the arterial system and converted into useful work for creating blood flow. %Osc has been used as a measure of the optimization of ventriculo-arterial coupling (O’Rourke, 1967; Cholley and Le Gall, 2016).

% O s c = W . o ⁢ s ⁢ c W . t ⁢ o ⁢ t × 100

We also calculated the LV power necessary for generating one unit cardiac output for a given arterial load, as the energy efficiency ratio (EER) (Berger et al., 1995; Grignola et al., 2007):

E ⁢ E ⁢ R = W . t ⁢ o ⁢ t ⁢ a ⁢ l / C ⁢ O

Therefore, the lower the EER, the lower the energy required for generating blood flow for a given LV afterload.

After completion of the surgical procedures, animals were allowed to stabilize MAP and HR (variation < 5%) at least for 10 minutes. After that, they were assigned using a computer-generated random sequence to three groups (6 animals each): a sham-operated group (SHAM), a septic group (EDX), and a septic group with hemodynamic resuscitation (EDX-R). In septic animals, a purified lipopolysaccharide (LPS) prepared from Escherichia coli serotype 055:B5 (Sigma Chemical, St. Louis, MO) was intravenously infused over 10 min through the femoral vein (1 mg⋅kg^–1 diluted in normal saline for a total volume of 8 ml, and flushed by 2 ml of normal saline to ensure a complete delivery). The dose and rate of LPS administration were previously established on a pilot experiment with 8 animals, in which the dose was varied from 1 to 2 mg⋅kg^–1. SHAM animals received an equivalent amount of normal saline. Three hours after LPS infusion, animals in the EDX-R group received a fluid bolus of 20 ml⋅kg^–1 for 10 min. A norepinephrine infusion started at 0.25 mcg⋅kg^–1⋅min^–1 was started after fluid administration if MAP was below the baseline level. Norepinephrine was increased by 0.10 mcg⋅kg^–1⋅min^–1 every 3 min until reaching a MAP value similar to the baseline level (±5% deviation). Hemodynamic measurements, aortic blood flow, and arterial pressure waveforms were recorded a least during 1 min at baseline and every hour up to 4 h after LPS or placebo administration. In EDX-R animals, measurements after fluid bolus (post-infusion) and norepinephrine infusion (which corresponds to 4 h after LPS infusion) were also obtained. After completion of the study protocol, animals were euthanized using a lethal dose of intravenous potassium chloride under deep anesthesia. Animal death was confirmed by verification of the absence of blood flow and arterial pressure tracings. A schematic description of the study protocol is shown in Figure 3.

Data are expressed as the mean ± SD or median (25th to 75th interquartile). The normality of data was checked by the Shapiro Wilk test. Differences between groups at baseline were performed using a one-way analysis of variance (ANOVA), and differences over time were assessed by two-way mixed ANOVA for repeated measurements. The Greenhouse–Geisser correction was used when the Mauchly test detected violation of sphericity. Whenever a significant interaction was found, pairwise comparison between groups was performed using a one-way ANOVA with the Tukey-Kramer test. Mixed-effect regression analyses were used to evaluate the relationship between Ea_dyn (the dependent variable) and arterial load, cardiac function variables, cardiac energetics, and indexes of cardiovascular efficiency (%Osc and EER) in septic shock animals (EDX and EDX-R groups). Models were constructed using individual animals and experimental groups as subjects for random factors, and experimental stages as repeated measurements with a heterogeneous first-order autoregressive covariance structure. This allowed us to consider the correlation between subjects and non-constant variability over time, which are not considered by the standard linear regression analysis. Model selection was based on the corrected Akaike’s Information Criteria, in which lower scores indicate superior fit (Fitzmaurice et al., 2011). Model parameters were estimated via the restricted maximum likelihood method, and the estimated fixed effect of each parameter quantified by using estimated value and standard error (SE). A P < 0.05 was considered statistically significant. All statistical analyses were two-tailed and performed using MedCalc Statistical Software version 19.1 (MedCalc Software bvba, Ostend, Belgium¹; 2019) and SPPS (SPSS 21, SPPS Inc., Chicago, IL).

There were no significant differences between groups in all studied variables at baseline. The infusion of LPS resulted in a hyperdynamic hemodynamic profile with a progressive increase in CO secondary to a positive chronotropic response, a significant reduction in mean arterial pressure (35%), and a decreased arterial load (Table 1). This phenomenon was characterized by a progressive flattening of the pressure-flow relationship (Figure 4). Systolic function, as assessed by peak velocity of aortic blood flow, significantly increased in endotoxic shock animals. Although all experimental groups showed a significant decrease in the evolution of arterial load, the group and time interaction analysis showed that the changes in C and Zc were more pronounced in the EDX group when compared with the SHAM animals (Table 2). LPS reduced Ẇ_osc and slightly Ẇ_tot, but did not affect Ẇ_std, which resulted in a better cardiovascular efficiency according to a lower Ẇ_osc/Ẇ_tot ratio (%Osc) and EER (Figures 5, 6).

The effects of hemodynamic resuscitation in the EDX-R group are summarized in Table 3. Fluid bolus increased CO and MAP by 19 and 18%, respectively, although MAP remained significantly lower than the baseline value (58 ± 8 vs. 45 ± 4 mmHg; p = 0.011). Norepinephrine was therefore required in all EDX-R animals to restore MAP to a similar value that baseline levels (58 ± 8 vs. 59 ± 5 mmHg; p = 0.504). Overall, hemodynamic resuscitation resulted in a higher cardiac energetic cost and lower cardiovascular efficiency (higher EER and %Osc).

Figure 7 shows the development of Ea_dyn, PPV, and SVV among different experimental groups. Ea_dyn increased in both EDX and EDX-R groups because of a significant increase in PPV but decreased in EDX-R animals after fluid administration (Table 3). The time course of Ea_dyn did not reach statistical significance in SHAM animals.

When analyzing the relationship of different variables of arterial load, cardiac function, cardiac energetics, and cardiovascular efficiency indexes on Eadyn on endotoxic septic animals (EDX and EDX-R), the linear-mixed regression analysis revealed that Ea_dyn were related to both arterial and cardiac factors (Table 4). The overall impact of LV afterload, as assessed by Ea, was inversely associated with Ea_dyn (estimate: −1.082; 95% confidence interval (CI): −1.417 to −0.748; p < 0.001), being Zc the only component of arterial load associated to Ea_dyn (Table 4). On the other hand, among cardiac function variables, only heart rate was positively related to Ea_dyn. When a linear-mixed model was used with Zc and HR as fixed effects and Ea_dyn as the dependent variable, their association with Ea_dyn remained significant, and the coefficient of determination between predicted values and Ea_dyn was r² = 0.67.

The relationship between cardiac energetics and Ea_dyn in septic shock animals (EDX and EDX-R) is shown in Table 4. Although no significant association between Ea_dyn and Ẇ_tot was found (estimate: 0.003; 95%CI: −0.003 to 0.011; p = 0.279), its components Ẇ_std and Ẇ_osc were independently associated: while Ẇ_std was positively associated with Ea_dyn, Ẇ_osc did so negatively. Ea_dyn was also related to both estimates of cardiovascular efficiency: %Osc and EER. Accordingly, the better the efficiency (i.e., the lower EER and %Osc), the higher the Ea_dyn.

We found that heart rate and Zc, which represent the pulsatile component of the LV hydraulic workload (Milnor, 1989), were the main variables associated to Ea_dyn in septic animals. Moreover, when considering only HR and Zc, 67% of the actual Ea_dyn values could be predicted in the septic animals. However, considering that these two variables cannot account for all the Ea_dyn values, we cannot exclude that other factors not contemplated in our arterial load and cardiac function assessment may have impacted the observed Ea_dyn.

These findings corroborate previous results about the compound nature of Ea_dyn and the impact of both cardiac and arterial factors (Monge Garcia et al., 2020). While net changes in Ea, a net measure of LV afterload, were negatively associated with Ea_dyn, variations in heart rate did so positively (Monge Garcia et al., 2017; de Courson et al., 2019). Our results also confirm earlier observations about the impact of endotoxic septic shock on the PPV/SVV relationship. In a model of LPS-induced pneumonia in mechanically ventilated rats, Cherpanath et al. (2014) observed that the ratio PPV/SVV was higher in LPS-treated compared with untreated rats. Septic animals also showed a significant decrease in arterial tone, as reflected by an increase in net arterial compliance (Cherpanath et al., 2014). This study, together with our previous observations about the impact of changes in arterial load (Monge Garcia et al., 2017), support the notion that Ea_dyn does not represent a real measure of central arterial tone nor an index of the arterial stiffness, and that the concept of Ea_dyn as a variable describing LV afterload should be avoided (Monge Garcia et al., 2020).

The force that pumps blood from the heart to the peripheral circulation is determined by an energy gradient that comprises a kinetic, gravitational, and a potential element (Burton, 1972). During a contraction, the heart works increasing potential energy and, in a much smaller proportion, kinetic energy. This work is distributed to the systemic circulation generating the energy gradient that drives blood flow through to the systemic circulation and delivers adequate transport for oxygen and nutrients to the tissues. In turn, the hydraulic work generated by the ventricle can be divided into two components: steady and oscillatory work. While Ẇ_std represents the work per unit time that effectively contributes to blood flow and peripheral perfusion, Ẇ_osc represents the unavoidable consequence of the pulsatile nature of the heart’s activity and is considered “wasted” energy (Milnor, 1989). An efficient cardiovascular system would then minimize the oscillatory component of LV mechanical work. The ratio Ẇ_osc/Ẇ_tot (i.e., %Osc) becomes then a sort of index of the efficiency of the LV mechanical power dissipation in the arterial system (O’Rourke, 1967). Moreover, as the ability of the heart as a pump depends not only on the myocardial performance but also on the physical properties of the arterial system, %Osc represents also a measure of the efficiency of the matching between the heart and the arterial system (O’Rourke, 1967; Milnor, 1989).

While in normal conditions Ẇ_osc accounts only about 10% of the total LV mechanical work (O’Rourke, 1967; Nichols et al., 1986), which manifests the optimal efficiency of the arterial system for buffering cardiac pulsations, factors altering arterial load or heart rate are known to affect this balance (O’Rourke, 1967; Cox, 1974). In our study, the overall %Osc at baseline was 11 ± 2%, similar to that reported in previous animal studies (O’Rourke, 1967; Cholley et al., 1995). While in SHAM animals %Osc remained unchanged, it significantly decreased during LPS infusion and increased after hemodynamic resuscitation. These modifications agree with the known relationship between Zc and HR and %Osc. Previous studies have shown that, when Zc decreases or heart rate increases, %Osc decreases (O’Rourke, 1967; Cox, 1974; Nichols et al., 1977; Laskey et al., 1985). In our study, septic animals showed a progressive and significant decrease in Zc and increased heart rate. Not surprisingly, these same factors were the main determinants of the Ea_dyn changes in septic animals. As Ea_dyn was directly related to Ẇ_std but inversely to Ẇ_osc, Ea_dyn reflects then not only the net LV mechanical work but how this work is generated. Therefore, changes in Osc% and EER were inversely associated with Ea_dyn variations. Accordingly, when cardiovascular efficiency increases, so does the Ea_dyn (Monge Garcia et al., 2020).

Our results differ from those reported by Cholley et al. (1995) in a similar study. These authors found that a lower dose of LPS (600 μg⋅kg^–1) resulted in a hypodynamic hemodynamic profile characterized by low cardiac output, arterial hypotension, and increased %Osc. Septic shock was also associated with a lower heart rate and higher Zc resulting from the aortic smooth muscle contraction and aortic wall edema. These discrepancies may likely reflect differences in the experimental setup, the dose of LPS, and the anesthetic regimen used (pentobarbital vs. ketamine and midazolam). However, even if our results differ in how LPS affects hemodynamics, both are coheren t on the physiological mechanisms and how these factors are known to affect %Osc (O’Rourke, 1967; Cox, 1974; Nichols et al., 1977; Kelly et al., 1992b).

Ventriculo-arterial uncoupling and impaired LV efficiency is a frequent phenomenon in septic shock (Yan et al., 2017; Guarracino et al., 2019; Pinsky and Guarracino, 2020). The assessment of ventriculo-arterial coupling in these patients may help to determine the underlying mechanism of cardiovascular failure and to predict the effectiveness of the hemodynamic therapies (Guarracino et al., 2019). Therefore, considering the crucial role of ventriculo-arterial coupling and LV efficiency in septic shock, the continuous assessment of Ea_dyn as an index for monitoring cardiovascular mechanical efficiency becomes therefore evident. However, the clinical usefulness of Ea_dyn as an easily measured bedside tool for monitoring VAC and LV efficiency requires further validation.

Our evaluation of the cardiovascular efficiency was based on the analysis of the instantaneous arterial pressure-aortic blood flow relationship (Milnor, 1989). This analysis, however, does not represent the actual LV mechanical efficiency since it does not consider myocardial oxygen consumption (Suga et al., 1981). Moreover, because of our simplified assessment of LV performance, we cannot determine the actual impact of LPS on myocardial performance, which would have required the invasive measurements of LV volume and pressure. However, we have recently demonstrated that Ea_dyn is significantly related to ventriculo-arterial coupling and LV efficiency using the data obtained from the LV pressure-volume analysis by the classical conductance catheter technique (Monge Garcia et al., 2018). Our current results agree with the observations made in this study. Nevertheless, even if LPS infusion was associated with an improved transfer of the power from the LV to the arterial system, we cannot confirm that this condition was only related to a better myocardial contractility. As LPS can alter not only LV contractility but also loading conditions (Pinsky and Rico, 2000; Jianhui et al., 2010), the decreased arterial load in septic animals may have played an essential role in the improved power transfer efficiency (O’Rourke, 1967). A low %Osc indicates therefore that, for a given LV myocardial performance, the arterial load was relatively lower. Thus, even if %Osc does not directly describe the ventricular-arterial coupling variables, it represents an index of the efficiency of the cardiovascular system (Berger et al., 1995; Cholley and Le Gall, 2016).