The experimental setup has been described before [25]. Briefly, Landrace pigs (n = 59, 68 ± 1 kg) were fasted overnight with free access to water and sedated with 0.25–0.5 mg kg^− 1 midazolam (Midazolam „ERWO “5 mg/ml- ampoules, ERWO Pharma GmbH, Brunn am Gebirge, Austria) and 10–20 mg kg^− 1 ketamine (Ketasol 100 mg/ml, aniMedica GmbH, Senden-Bösensell, Germany). The animals were intubated and anaesthesia was continued with 1.0–2.0 Vol% sevoflurane (Sevorane®, Abbott GmbH, Vienna, Austria), 30–35 μg kg^− 1 h^− 1 fentanyl (Fentanyl-Janssen™, 0.1 mg ampoules, Janssen-Cilag Pharma, Vienna, Austria), 1–1.25 mg kg^− 1 h^− 1 midazolam, 3 mg kg^− 1 h^− 1 ketamine and 0.2 mg kg^− 1 h^− 1 pancuronium (Pancouronium bromide 2 mg/ml ampoules, Ratiopharm GmbH, Ulm, Germany). Pigs were ventilated (Julian, Draeger, Vienna, Austria) with an FiO₂ (Fraction of inspired oxygen) of 0.5, an I: E-ratio of 1:1.5, the positive end-expiratory pressure was set at 5 mmHg and a tidal volume (VT) of 10 ml kg^− 1. The respiratory rate was adjusted constantly to maintain an end-expiratory carbon dioxide partial pressure between 35 and 45 mmHg. Under fluoroscopic guidance, all animals were instrumented with a Swan-Ganz catheter (Edwards Lifesciences CCO connected to Vigilance I, Edwards Lifesciences, Irvine, CA, USA), and an LV conductance catheter (5F, 12 electrodes, 7 mm spacing, MPVS Ultra, Millar Instruments, Houston, Texas, USA). A 14-F sheath was introduced into the left femoral vein, and an intravascular cooling catheter connected to a cooling unit (Accutrol™ Catheter 14F and InnerCool RTx Endovascular System, Philips Healthcare, Vienna, Austria) was positioned with the tip at the level of the diaphragm in the inferior caval vein. The body core temperature was measured at the tip of the Swan-Ganz-catheter. After instrumentation, the animals were allowed to stabilize for 30–60 min.

The experimental protocols are summarized in Fig. 1 and have been described in detail before [21‐24].

Steady-state hemodynamics were obtained and averaged over three respiratory cycles. At each time point, volumetric conductance data were calibrated by measuring cardiac output (slope factor a) and hypertonic (10%) saline infusion (parallel volume) as described earlier [26, 27]. At the end of each experimental protocol anaesthetised and unconscious animals were euthanized by an injection of an 80 mmol potassium chloride bolus.

Details on data analysis have been described before [25]. Pressure-volume data and time intervals were analysed off-line by CircLab Software (custom made by P. Steendijk). End-diastole was defined as the time-point of zero crossing of LV dP/dt before its rapid upstroke. End-systole was defined as the time point of maximum pressure/volume ratio. CPO (W), LV SW min^− 1 (W), LV EF, RPP and TP were calculated by using the following equations:

All data are presented as mean ± standard deviation (SD). The correlations between LV SW and LV SW min^− 1 with CPO, LV EF, RPP, TP, LVP_max and LV dP/dt_max were assessed by linear regression analysis. The assumption of normality of residuals was checked by the Kolmogorov-Smirnov test as well as graphically by a probability plot. Data between groups before and after cardiac insult at different temperatures were analysed by two-way ANOVA (groups 1–3). A one-way ANOVA for repeated measurements was used to compare data within one group (group 4). Steady state data at different temperatures, before and during dobutamine infusion, were compared by two-way ANOVA for repeated measurements (group 5). Post-hoc testing was performed by Tukey’s test. Normality was demonstrated by the Shapiro-Wilks test or by visual inspection of normal probability plots. Nonnormally distributed variables were examined either by Kruskal-Wallis- or Friedman-Test. A p-value < 0.05 was considered significant. For statistical calculations, we used the software Sigmastat (Version 4.0, Systat Software, Inc) and SPSS (Version 23.0, IBM, Armonk, NY).

Systemic hemodynamics from the experimental protocols are summarized in Table 1. CO, LV SW min^− 1 and CPO spanned over a wide range of values, with the following means (ranges): CO 5.7 L min^− 1 (8.2 L min^− 1), CPO 0.94 W (1.75 W) and LV SW min^− 1 0.99 W (1.88 W).

In group 5 (DOB), CO and CPO decreased with cooling from hyperthermia to normothermia to MH and were increased by dobutamine at each temperature step (Table 1). In groups 1–4, CO was per se significantly lower during MH than during NT. CPO decreased significantly with the interventions in groups 1–4, but there was no significant difference between NT and MH.

Systemic vascular resistance increased with cooling from hyperthermia to MH and was decreased by dobutamine at each temperature step. Except for sevoflurane-induced myocardial depression, SVR was significantly higher during MH after each intervention.

CPO showed the best correlation with LV SW min^− 1 (Fig. 2; r² = 0.89; p < 0.001). LV EF did not correlate at all, neither with LV SW (Fig. 3a; r² = 0.02; p = 0.059) nor with LV SW min^− 1 (Fig. 3b; r² = 0.01; p = 0.259). Other common parameters of cardiac function showed a statistically significant but moderate correlation. RPP (Fig. 4a; r² = 0.67; p < 0.001) did correlate better than TP (Fig. 4b; r² = 0.54; p < 0.001) with LV SW min^− 1. LVP_max showed a similar correlation with LV SW (Fig. 5a; r² = 0.55; p < 0.001), but correlated worse with LV SW min^− 1 (Fig. 5b; r² = 0.47; p < 0.001). LV dP/dt_max showed the worst correlation with both LV SW (Fig. 5c; r² = 0.23; p < 0.001) and LV SW min^− 1 (Fig. 5d; r² = 0.28; p < 0.001). An additional file shows the correlations between CPO and LV SW min^− 1 of each individual experimental group (Additional file 1).

The correlation between CPO, as measured by pulmonary artery catheterization (PAC) and invasive arterial pressure, and LV SW min^− 1 measured via the invasive gold-standard (conductance method) has never been tested so far. Since pressure-volume analysis remains a time-consuming, complex and highly invasive measurement requiring additional equipment and expertise, the concept of deriving similar information by assessing CPO instead of LV SW is therefore quite attractive for the clinical practice. Being assessed as the product of cardiac output and mean aortic pressure and therefore combining the heart’s ability to create both pressure and flow, CPO describes the function of the heart as a hydraulic pump [13]. More precisely, hydraulic power in general consists of two components. The power expended to generate a steady (or non-pulsatile) flow is described as the mean external power, which is assessed as the product of mean arterial pressure and cardiac output. The energy used in producing the pulsatile component of flow and pressure is described as pulsatile power. The sum of both mean and pulsatile power results in the total external hydraulic power generated by the ventricle [33]. Hence, CPO is a measure of mean power, whereas LV SW is a measure of total energy imparted to the vasculature system including pulsatile power being assessed on a beat to beat basis. Under physiological conditions, the fraction of pulsatile power is about 10% of the total power generated by the left ventricle, while it rises with arterial hypertension, decreased distensibility of the proximal arteries and increases in heart rate [34‐36]. In the pulmonary circulation, pulsatile power can make up to 30% of total power [33, 37]. The ratio between pulsatile power and mean power can be regarded as a measure of the efficiency of ventricular-arterial coupling, while an increase of the pulsatile fraction indicates a decrease in efficiency [35]. Although CPO does not include information of pulsatile power, we could show here for the first time a strong correlation to LV SW min^− 1 under various inotropic states during acute heart failure. Of note, none of the experiments included LV output tract (LVOT) obstruction or aortic valve obstruction as well as severe stiffness of the aorta, which in turn would have increased LV SW min^− 1 without changing CPO.

As abovementioned, CPO was shown to be the best predictor of intrahospital mortality in patients with cardiogenic shock [12]. Furthermore, it allows an exact hemodynamic characterization of patients with acute congestive heart failure by plotting CPO with SVR [38] and it was shown to be the only parameter, when measured at baseline, with a significant prediction of recurring severe acute heart failure (manifested as frank pulmonary edema) within 24 h from hospitalization in the ICU setting [39]. However, the role of CPO has not been yet fully integrated into the clinical ICU routine, in part due to a lack of data supporting the use of PAC in patients with advanced heart failure. In a meta-analysis investigating 13 randomized controlled trials (RCT) on the impact of PAC on survival, Shah et al. [4] argued that the neutral effects of PAC might be based on unclear hemodynamic goals in combination with a lack of effective treatment strategies driven by the obtained hemodynamic measurements [2, 4]. We suggest here that CPO obtained via PAC is an excellent parameter to monitor cardiac performance in experimental conditions resembling critically-ill patients. Furthermore, recent data show the feasibility of a minimally invasive assessment of CPO and cardiac power integral [40‐43], opening new scenarios of CPO-based monitoring of critical patients without the need for PAC.

We could clearly show that LV EF does not reflect external cardiac work over a wide range of experimental inotropic states representative for patients during acute heart failure. In clinical practice, LV EF plays a major role in the diagnosis and treatment of heart failure, as a surrogate marker of cardiac remodelling [44] and reverse remodelling [45] or as a general predictor of outcome in heart failure with reduced LV EF [46, 47]. Nevertheless, our data imply that LV EF is not accurate enough in mirroring the function of the heart as a hydraulic pump under various conditions of acute heart failure and should be preferably interpreted within the hemodynamic context.

The rate pressure product and the triple product are both clinical indices of myocardial oxygen consumption and therefore regarded as indirect measures of cardiac work [48‐52]. Thus, we used these parameters as surrogates for LV SW min^− 1. In our findings, we confirm a correlation between both RPP and TP with LV SW min^− 1, with RPP having a better correlation than TP. The worse correlation of TP with LV SW min^− 1 could be explained by integrating LV dP/dt_max into the calculation which is known to be a preload, afterload and heart rate dependent measure of cardiac contractility [44, 53‐55]. Also, LV dP/dt_max itself correlated worst with LV SW and LV SW min^− 1.

Interestingly, LVP_max alone correlated as good as the TP with LV SW, emphasizing the potential role of estimating LV pressure as a measure of the actual work done by the left ventricle in specific subpopulations of cardiogenic shock patients, i.e. under left ventricular assistance.

The main limitation is the retrospective design of the study, meaning that the analysed data were not always part of the major outcome of the original studies. However, the quality of the original tracings has been reviewed by 2 independent investigators. Specific limitations related to the experimental setup from which these data were derived have been described earlier [21‐24]. Another limitation of the study is related to the fact that animals were investigated under general anaesthesia, in order to minimize the animals’ distress and to obtain stable hemodynamic conditions. Nevertheless, we believe the data to be representative enough for the translation to a clinical ICU setting. Furthermore, the study did not include experimental models of LVOT obstruction or increased stiffness of the aorta for modelling of patients with aortic stenosis or severe arteriosclerosis.