Derivation of Stroke Volume from Pulmonary Artery Pressures

Determination of blood flow, i.e., stroke volume (SV) and cardiac output (CO), is an integral part of hemodynamic monitoring in intensive care medicine. Despite the availability of less- or non-invasive technologies, intermittent CO monitoring (thermodilution) using the pulmonary artery catheter (PAC) remains the most widely used modality [1] in critically ill patients with circulatory shock. However, the intermittent nature of CO measurement is a limitation, especially in rapidly changing hemodynamic conditions, such as during dynamic tests of preload responsiveness (e.g., passive leg raising) and therapeutic interventions such as fluid or vasopressor administration.

‘Continuous’ pulmonary artery thermodilution measures CO without the need for intermittent manual indicator injection (e.g., intermittent thermal filament heating). However, in practice, ‘continuous’ CO measurements are intermittent averaged values (averaging improves the signal-to-noise ratio but causes a delay of several minutes). The agreement with intermittent thermodilution is modest [2] and catheters are expensive.

Pulmonary artery pulse pressure (PP) is directly related to SV, a relationship that is modified by pulmonary vascular resistance (R). The purpose of this study was to develop a SV calculator from PP to allow continuous monitoring of SV and CO from PP based on this relationship between PP and SV. We evaluated this calculator in a cohort of patients who underwent heart transplantation. From our previous study [3], we noted no significant changes in R from admission into intensive care unit post-heart transplantation (T0) to 6 h post-admission into the intensive care unit (T6). On this basis, we hypothesized that PP can be used to track SV changes from T0 to T6.

This study included 169 patients who underwent orthotopic heart transplantation from two centers from 2019 to 2022 (Table 1). Hemodynamic data at T0 and T6 are displayed in Table 2. The median thermodilution-derived SV was 47.9 ml (37.5–61.0 ml) and the median calculated SV was 87.4 ml (66.1, 110.1). Calculator SV correlated with thermodilution-derived SV at T0 (r = 0.920, p < 0.001, coefficient of 0.539 and the constant of 2.06) (Fig. 1). After applying the coefficient and constant to the calculator SV, the adjusted median calculator SV was 49.1 (37.4, 63.1) ml. There was no significant difference between the adjusted calculator SV compared with the CO-derived SV (49.1 ml (37.4, 63.1) vs. 48 ml (37, 62.8), p = 0.780).

The median difference at T0 between the adjusted calculator SV and thermodilution-derived SV was  – 0.052 ml (– 4.12, 4.46), the median percentage change was  – 0.078% (– 8.86, 11.6). The difference between the calculator SV and thermodilution-derived SV was not statistically significant (mean  – 0.04, SD: 7.97, p = 0.944). The absolute difference between the adjusted calculator SV and the CO-derived SV at T0 was plotted against the mean on Bland–Altman plot [Fig. 2, the red line denoting the mean difference of  – 0.043 ml and the black lines representing the 95% confidence interval (95% CI  – 15.6 to 15.6)]. The mean percentage change between the adjusted calculator SV and thermodilution-derived SV was 1.83% and 95% CI (– 27.2 to 30.8) (Fig. 3).

For indexed stroke volume (stroke volume index, SVi), the median thermodilution-derived SVi was 28.1 ml (19.7, 38.7) and the median calculator SVi was 51.2 ml (34.7, 71.2). Correlation and linear regression analysis showed strong correlation with R² of 0.911, and a coefficient and constant of 0.552 and 0.6, respectively. The adjusted calculator SVi median was 28.9 ml (19.7, 39.9) compared to the CO-derived SVi of 28.1 ml (19.7, 38.7), and there was no significant difference p = 0.781. Bland–Altman plots for SVi are displayed in Figs. 2b and 3b. Over 95% of the calculator SV were within the 30% limit of agreement with thermodilution-derived SV.

Stroke volume was calculated at T6, adjusted using the same coefficients and constants as above and compared to thermodilution-derived SV, using the simulated conditions where repeat pulmonary vascular resistance measurements were not available. Using the R at baseline (T0) to ‘calibrate’ the calculator and PADP at T6 (instead of PAWP at T6), we found no significant difference between the thermodilution-derived SV vs. the calculator SV at T6: 47.7 ml (37.6, 58.9) vs. 46.4 ml (33.2, 59.6), p = 0.251. The median thermodilution-derived SVi was 27.7 ml (19.5, 35.9) compared to the median adjusted calculator SVi of 26.1 ml (17.7, 37.7) and this was also not statistically significant p = 0.203; suggesting that once ‘calibrated’ at baseline, PP can be used to derive SV at T6. The Bland–Altman plots for T6 are displayed in Figs. 4 and 5. With these assumptions under simulated conditions, there appeared to be greater scatter (about 25% exceeded the 30% limit of agreement), especially at higher SV.

In this study, we have shown that in a cohort of patients who underwent heart transplantation, our calculator once ‘calibrated’ from baseline pulmonary vascular resistance, can track SV from PP within a 6-h interval with an acceptable level of agreement between the calculator-derived and thermodilution-derived SV. Over 95% of the calculator SV were within the 30% limit of agreement with thermodilution-derived SV in an cohort of patients who underwent heart transplantation. There was greater scatter (lower agreement) under the simulated conditions, especially at higher SV.

There are limitations to all CO monitoring devices and technology. The main limitation of calculator-derived (other than the invasiveness of PAC) is the inherent assumptions. Firstly, the pulmonary artery capacitance is calculated as a simple ratio of SV to PP, which overestimates true capacitance. Secondly, the RC time constant reported by Tedford et al. is derived from simple regression of hemodynamic data from a large, mixed cohort of patients. Nonetheless, this simple calculator appears to perform within acceptable limits. We further evaluated this calculator using published data. For example, taking pooled data from 47 publications [8] that described 72 individually evaluated populations comprising of 1187 subjects, the calculator-derived SV of 91 ml is close to the reported mean SV of 96 ml.

Potential applications include the assessment of SV response to intravenous fluid administration or inotropes, both are common interventions in (cardiac) intensive care units. Rapid intravenous fluid administration such as fluid challenges do not appear to have a significant effect on pulmonary vascular resistance. For example, the study by Fujimoto et al. [9] showed no significant changes in pulmonary vascular resistance with rapid saline infusions of 10–15 ml/kg in individuals without heart failure and 0.3–1.0 l of normal saline in patients with heart failure. Similarly, Andersen et al. [10] reported no significant change in pulmonary vascular resistance with fluid administration in patients with heart failure. Indeed, our calculator-derived SV also appears to operate within acceptable limits compared to the hemodynamic data reported by Andersen et al. (Supplementary Material).

One caveat is that the increase in PAWP could confound the relationship between PP and SV. An increase in PAWP would increase PP, even if SV is unchanged. There are two mitigating factors. Firstly, the effect of PAWP on PP and absolute calculator SV is modest. Secondly, PADP can be used to approximate PAWP in most cases in the absence of pulmonary vascular disease. Thus, once ‘calibrated’ with baseline pulmonary vascular resistance and using PADP, the changes in SV in response to fluid administration could be quantified:to derive SV in ml.

Our data suggest that these assumptions reduced the agreement between calculator SV and thermodilution SV (about 25% exceeded the 30% limit of agreement), but was acceptable in the majority of patients within the first 6 h of heart transplantation. It is likely that a more selected use of this calculator (identifying conditions where these assumptions are valid) would improve the level of agreement.

Aside from the calculator, the physiologic considerations also allow the following ‘rules-of-thumb’ to be applied:

This study has notable limitations. First, we have only evaluated this calculator in patients who have had heart transplantations. The application of this calculator to other patients would need further study. Secondly, the measurements were not standardized. It is possible that standardization of PP measurement (e.g., during expiratory phase) may improve agreement between the calculator- and thermodilution-derived SVi and CO. Thirdly, we have evaluated a 6-h window early post-transplant, as we have previously shown that pulmonary vascular resistance did not change significantly over this time interval. It is possible that the window may be extended in the absence of any significant changes in ventilatory parameters that could alter pulmonary vascular resistance. Alternatively, this calculator may be used to complement intermittent thermodilution studies (e.g., six-hourly) to derive R to ‘re-calibrate’ the calculator. Finally, although there was general agreement between calculator SV and thermodilution SV under simulated conditions at T6, the level of agreement was poorer and there were individuals with clinically significant deviations; implying that these assumptions are not valid in some patients. Future studies are needed to further examine the use of this calculator.

We describe a calculator to derive SV from PP, as an adjunct to aid continuous hemodynamic monitoring following heart transplantation. Once ‘calibrated’ from baseline pulmonary vascular resistance, this calculator may be used to track SV from PP within a 6-h interval with acceptable level of agreement with thermodilution-derived SV in a selected group of patients.