Analogous to the charging of capacitors, a significant proportion of the right ventricular SV ‘charges’ the reservoir volume and increases pressure in the compliant pulmonary arteries in systole, which discharges during diastole. Total pulmonary arterial capacitance (C) defines this relationship between volume and pressure as the increase in blood volume (ΔV) in the arterial system that produces a unit increase in arterial transmural pressure. In practice, C is difficult to measure because direct measurement of ΔV is not possible due to the continuous outflow from the arterial system. Therefore, the ratio of SV/PP has been used to determine C, accepting that this equation overestimates the true C.

Rearranging this equation:

$$R \, \times \, SV \, = \, RC \, \times \, PP$$

RC is related to pulmonary arterial wedge pressure (PAWP) as previously described by Tedford et al. [4] and Lankhaar et al. [5, 6]: RC = - 0.0063 × PAWP + 0.46.

Therefore,

$$SV \, = \, \left( \right) \, \times \, PP/R,$$

Or

$$SV \, = \, \left( \right) \, \times \, PP/ \, \left( \right),$$

to derive SV in ml.

Based on this equation, SV is predominantly related to PP and R. Changes in absolute levels of PAWP have a modest effect on absolute SV. For example, at a constant R of 2.0WU and PP of 20 mmHg, doubling PAWP from 12 to 24 mmHg is associated with a decrease in SV from 64 to 51 ml. However, at PAWP of 12 mmHg and PP of 20 mmHg, SV increases from 64 to 85 ml if PVR is reduced from 2.0 to 1.5 WU.

In the absence of significant changes in R, PP is predominantly related to absolute SV. We hypothesized that changes in PP can be used to track changes in SV and CO in acute settings where R is unchanged.

This is a retrospective study that included consecutive patients who underwent orthotopic heart transplantation from two centers from 2019 to 2022. Patients who underwent post-transplant mechanical circulatory support were excluded (n = 43). Hemodynamic data from pulmonary artery catheterization were collected at two separate time points: immediately following admission into intensive care unit post-heart transplantation (T0) and at 6 h thereafter (T6) were used. Fully anonymized data were collected as part of the evaluation of post-transplant management and approved by our institution, University Hospitals Birmingham NHS Foundation Trust (CARMS-18295). Patient consent was not needed, and this study complies with the ethical framework outlined by the NHS Health Research Authority.

This study has two parts: Firstly, we tested the agreement between the calculator-derived SV (i.e., calculator SV) and the SV derived from conventional thermodilution CO (i.e., thermodilution SV) studies at T0.

Secondly, we simulated the condition where repeat thermodilution and wedge studies were not available, so the pulmonary vascular resistance was assumed to be unchanged from baseline. For this simulation, we used baseline (T0) R to ‘calibrate’ the calculator and pulmonary artery diastolic pressure (PADP) at T6 to replace PAWP at T6. The calculator SV using these assumptions were compared against the ‘true’ thermodilution SV.

All data were analyzed for normality with histograms and the Shapiro–Wilk test. Normally distributed data are expressed as mean and standard deviation and non-parametric data are expressed as median and interquartile range (IQR). The Mann–Whitney U test was employed to compare non-parametric data. A p < 0.05 was considered statistically significant.

Correlation and linear regression analyses were performed comparing the calculator-derived SV and the thermodilution-derived SV and SV index (SVi, indexed to body surface area). The calculator SV were adjusted based on the coefficient and constant. The differences, percentage change, and mean between the calculator and thermodilution-derived SV were then calculated and Bland–Altman plots were constructed. The percentage error (i.e., accuracy), derived by the Bland–Altman analysis, is the difference in the measured value from the reference method.

There is inherent error in cardiac output measurements by thermodilution (limits of precision of ± 10–20%). When comparing the current calculator against this reference method (thermodilution), the limits of agreement will inevitably be larger than the limits of precision of the reference method (combining the errors of the test and reference methods). On the basis of an analysis of 25 studies, Critchley et al. [7] suggested that a value of up to 30% is considered clinically acceptable, and this is the limit that we have adopted in this study.

Pearson correlation was performed comparing the raw calculator SV with CO-derived SV and the coefficient and constant yielded was used to adjust the raw calculator SV data. All statistical analyses were performed on IBM SPSS Statistics for Mac, Version 29.0. IBM Corp., Armonk, NY, USA.