Empiric Pulmonary Arterial Compliance Reflects the Resistance‐Compliance Relationship and Predicts Mortality in Pulmonary Hypertension

ABSTRACT

The resistance–compliance (RC) relationship between pulmonary vascular resistance (PVR) and pulmonary arterial compliance (PAC) provides an integrative measure of global right ventricular (RV) afterload. However, debate persists regarding the clinical utility of PAC calculated using the empiric formula (PAC_empiric), and the ideal method for calculating PAC. We analysed haemodynamic and pulmonary pressure waveform data from 156 patients with pulmonary hypertension (PH). PAC was calculated using three methods: PAC_empiric, as well as two established waveform analysis methods, area‐under‐the‐curve (PAC_AUC), and diastolic decay (PAC_DD). Generalized linear mixed models were used to evaluate the relationship between PVR and PAC across these three methods. Model performance was assessed using Akaike and Bayesian Information Criteria (AIC/BIC). The diagnostic performance of each method was evaluated using ROC analysis. Cox regression was applied to assess the association with long term mortality. All three PAC methods demonstrated a strong inverse hyperbolic correlation with PVR. PAC_empiric provided stronger model performance (AIC −504.3; R² = 0.968), and best discriminated PH subtypes (AUC = 0.91), outperforming PAC_AUC (AUC = 0.88) and PAC_DD (AUC = 0.75). PAC_empiric was also a stronger predictor of mortality than PAC_AUC, PAC_DD or PVR (c‐statistic = 0.747, compared to 0.737, 0.709 and 0.741 respectively). PAC_empiric is a robust and accessible method for assessing the pulsatile component of RV loading. This study supports its use as a physiologically meaningful parameter that together with PVR provides a comprehensive estimation of global RV afterload.

Abbreviations

AUC

area under the curve

BSA

body surface area

DD

diastolic decay

mPAP

mean pulmonary arterial pressure

PAC

pulmonary arterial compliance

PH

pulmonary hypertension

PP

pulse pressure

PVR

pulmonary vascular resistance

RC

resistance‐compliance

ROC

receiver operating characteristic

RV

right ventricle

SV

stroke volume

WU

Wood units

1. Introduction

The right ventricle (RV) is a low‐pressure chamber, and precise assessment of its afterload from the pulmonary circulation is therefore central to understanding RV function. Clinically, mean pulmonary arterial pressure (mPAP) and pulmonary vascular resistance (PVR) are commonly used to estimate RV afterload. However, these measures do not account for the load generated by pulsatile pulmonary flow. Pulsatile flow is well‐established as a significant proportion of RV load, however due to complexity in its measurement, is usually excluded from RV routine afterload assessment [1].

Pulmonary arterial compliance (PAC) is one metric that reflects this pulsatile load, and in combination with PVR, can describe the total, or global RV afterload. There is a well‐documented inverse‐hyperbolic relationship between PVR and PAC, such that increases in resistance are incremental until the compliance is saturated, resulting in exponential increases in PVR. This resistance‐compliance(RC) relationship governs the interaction between PVR and PAC and provides a framework for summarizing the global RV load as a function of both these parameters [2, 3, 4, 5, 6, 7, 8]. A integrative parameter, the RC time, calculated as the product of PVR and PAC, has been widely described, and while previously considered to be a constant [4, 5], has more recently been shown to vary in across different PH groups [6, 7, 9, 10, 11, 12].

Despite its utility in characterizing the stage and severity of pulmonary vascular disease [13], PAC has not been widely clinically adopted, partly due to ongoing debate regarding the ideal method for its calculation. PAC is most often estimated using the empiric formula (PAC_empiric = SV/PP), and while this is most practical for clinical use, analysis of pulmonary waveforms may provide a more physiologically accurate assessment of compliance and better capture the dynamic and regional properties of the pulmonary vasculature [14, 15] Waveform‐analysis methods for calculating PAC include the area‐under‐the‐curve (PAC_AUC) and diastolic decay (PAC_DD) methods [16, 17], however while these methods may improve accuracy they are technically more complex, sensitive to error in the setting of artefact or poor waveform quality, and require additional software for their calculation, making them less suited for routine clinical use. From this perspective, PAC_empiric would therefore be preferable if PAC were to be more widely implemented into clinical practice, however to further inform this, few direct comparisons have been conducted between the PAC calculation methods [18].

With the aim of broadening the clinical adoption of PAC alongside PVR to characterise global RV afterload, this study evaluates the ability of the three PAC calculation methods, alongside PVR, to characterize the RC relationship, and assesses their diagnostic and prognostic utility. Using mathematical modelling, this study: 1) demonstrates the RC relationship using each of the PAC calculation methods, 2) compares the strength of the relationship between PVR and PAC, for each of the PAC calculation methods; 3) investigates the ability of the PAC calculation methods to distinguish between PH subtypes, as well as their association with mortality; and 4) investigates the association of the RC time with prognosis.

2. Methods

We retrospectively analyzed 1017 routine right heart catheterization (RHC) studies performed between 2021 and 2024. Indications included suspected or monitoring of pulmonary hypertension (PH), heart failure with preserved and reduced ejection fraction, pre‐heart or lung transplant assessment, and investigation for dyspnea of unknown origin. Pulmonary pressures and waveforms were obtained using a fluid filled catheter. Cardiac output (CO) was obtained using the thermodilution method, and SV calculated by dividing by heart rate. Measurements were repeated until three values were obtained within 10% of one another, and averaged. Where there was significant variability, or in the presence of severe tricuspid regurgitation, the estimated Fick method was used. PVR was calculated by the standard equation (the difference in mean pulmonary pressure and wedge pressure, divided by CO). PAC_empiric was calculated using SV divided by pulse pressure (PP). Where pulmonary pressure waveforms were available, and of sufficient quality for analysis, PAC_AUC and PAC_DD were derived from pressure waveform analysis, using methods that have previously been described [16, 17]. For comparison of PAC methods, the data set was limited to those cases with available data for all three PAC calculation methods (n = 156). Demographic and clinical data were recorded at the time of RHC, and mortality data, to the end of April 2025, was obtained from medical records. To reflect real‐world data, cases were only excluded if haemodynamic values were unfeasible. Local ethics committee approval was obtained.

2.1. Statistical Analysis

Statistical analysis was conducted in R Studio version 4.4.1. Generalized linear mixed models with a gamma distribution and inverse link function were used to model PAC as a function of PVR. Model fit was evaluated using residual plots, as well as Akaike information criterion (AIC) and Bayesian information criterion (BIC), with lower numbers indicating better model fit, as well as ANOVA and pseudo‐R² statistics where applicable. For PAC method comparison, cohorts were restricted to cases with a complete PAC data set across all three PAC calculation methods. Agreement between PAC estimation methods was evaluated by pairwise linear regression with residual plots and Bland–Altman analysis, reporting mean bias and 95% limits of agreement. Adjusted models including age and body surface area (BSA) were also created due to their known influence on PAC. Interaction models evaluated the individual contributions of SV and inverse PP. The diagnostic performance of each PAC calculation method was evaluated using receiver operating characteristic (ROC) analysis, with comparison using a Delong test statistic, with significance level 0.05. Cox regression was applied to determine the association between mortality and PAC in adjusted and unadjusted models. Due to moderate collinearity consistent with their known physiological relationship, PVR and PAC were analyzed in separate models. Cox regression analysis was also performed for RC time (PAC × PVR), to determine whether this lumped parameter exhibited a similar prognostic utility as its components. A complete description of the modelling used in this analysis is included in the Supplement.

3. Results

Results from 1089 RHC were obtained for all patients undergoing clinically indicated RHC at a single center. 72 cases were subsequently excluded due to incomplete or unfeasible data (19 CO; 21 PP, 11 heart rate, 10 PCWP, and 11 biologically unfeasible values), leaving 1017 cases with complete baseline pressure data (Figure 1). The mean PAC_empiric in this cohort was 2.98 ± 1.90 mL/mmHg (Table S1). Subsets with available pressure waveform data for PAC_AUC and PAC_DD included 222 and 156 patients, respectively, and the cohort was therefore limited to 156 cases for comparison of the three PAC calculation methods (Table 1). Compared to the full cohort, this subset was younger (58 ± 17 vs. 62 ± 17 years; p  =  0.001), had fewer cases of post‐capillary PH (7% vs. 21%; p  =  0.003), and more pre‐capillary PH (42% vs. 28%; p  =  0.002), however there were no significant differences between mean haemodynamic parameters (Table S1). In this cohort (n = 156), the mean PAC_empiric (2.92 ± 1.78) did not significantly differ from PAC_AUC (2.76 ± 1.91; p = 0.053) or PAC_DD (2.65 ± 2.84; p = 0.26). Mortality data was available for 152 of 156 patients, with 4 lost to follow‐up. In total 30 (19.7%) patients died during the mean follow‐up period of 1079 ± 315 days. Pairwise comparisons of PAC_empiric, PAC_AUC and PAC_DD was performed to show agreement between methods. Scatterplots with regression lines and residual analyses demonstrated only moderate correlations between methods (R² 0.39–0.48). Bland–Altman analysis revealed that PAC_AUC was systematically higher than PAC_empiric (bias +2.4; 95% LoA −3.7 to 8.5) and higher than PAC_DD (bias +2.9; 95% LoA −3.3 to 9.1). In contrast, PAC_DD_and PAC_empiric showed the closest agreement, with minimal bias (−0.4; 95% LoA −3.2 to 2.3). These findings indicate that while the methods are correlated, they are not interchangeable, with PAC_DD most closely approximating PAC_empiric (Supporting Figure S11 and Table S9).

Figure 1.

Study exclusions. Pulmonary arterial compliance (PAC) was calculable for all 1017 in the cohort using the empiric formula (PAC_empiric). For 795 cases, raw pulmonary pressure waveforms were not available, leaving 222 cases for which the PAC could be calculated by the area‐under the curve method (PAC_AUC) and 156 cases using the diastolic decay method (PAC_DD). PAC_AUC, pulmonary arterial compliance, using the area‐under‐the‐curve method; PAC_DD, pulmonary arterial compliance, using the diastolic decay method; PAC_empiric, pulmonary arterial compliance, using the empiric formula; PCWP, pulmonary capillary wedge pressure.

Table 1.

Baseline demographics and characteristics in the comparison cohort (n = 156).

	Characteristic (mean ± SD)
Age (years)	58.2 ± 17
Gender (female), n (%)	89 (57)
Pulmonary Hypertension Category (n (%))
Pre‐capillary	66 (42)
Isolated post‐capillary	11 (7)
Combined pre‐and post‐capillary	45 (29)
Normal	26 (17)
Borderline*	8 (5)
BMI (kg.m−2)	28.3 ± 6.6
BSA (m2)	1.9 ± 0.3
Heart rate (bpm)	76 ± 15
SPAP (mmHg)	55 ± 23
DPAP (mmHg)	24 ± 10
mPAP (mmHg)	35 ± 14
PCWP (mmHg)	16 ± 7
CO (L/min)	5.4 ± 1.9
PVR (WU)	3.9 ± 2.7
PVR (mmHg.s. mL−1)	0.24 ± 0.16
PACempiric (mL. mmHg−1)	2.98 ± 1.78
PACAUC (mL. mmHg−1)	2.76 ± 1.91
PACDD (mL. mmHg−1)	2.65 ± 2.84

Abbreviations: AUC, area under the curve; BMI, body mass index; bpm, beats per minute; BSA, body surface area; CO, cardiac output; DD, diastolic decay; DPAP, diastolic pulmonary arterial pressure; mPAP, mean pulmonary arterial pressure; PAC, pulmonary arterial compliance; PVR, pulmonary vascular resistance; SPAP, systolic pulmonary arterial pressure; WU, Wood units.

^*(mPAP 20‐25, PCWP < 15 mmHg; PVR < 2.0).

3.1. The Effect of PAC Methods on the Resistance‐Compliance Relationship

All three PAC methods demonstrated statistically significant inverse hyperbolic relationships with PVR (Table 2). PAC_empiric was significantly associated with PVR, (${\beta }_1$ = 1.48; 95% CI: 1.39–1.57, z = 31.6, p < 0.0001); ${\mathit{PAC}}_{\mathit{empiric}}=\frac{1}{0.13+1.48\bullet \mathit{PVR}}$ (Figures 2a, S1, and S2). PAC_AUC demonstrated a similar but slightly weaker association, (${\beta }_1$ = 1.13; 95% CI: 0.96–1.29, z = 13.39, p < 0.0001; ${\mathit{PAC}}_{\mathit{AUC}}=\frac{1}{0.20+1.13\bullet \mathit{PVR}}$, Figure 2b and S3), as did PAC_DD (${\beta }_1$ = 0.81; 95% CI: 0.49–1.13, z = 5.03, p < 0.0001; ${\mathit{PAC}}_{\mathit{DD}}=\frac{1}{0.26+0.81\bullet \mathit{PVR}}$; Figures 2c and S4). Model comparisons were conducted within the cohort where all three PAC calculation methods were available (n = 156), and showed that PAC_empiric provided a superior model fit (AIC −504.3; BIC −487.3) compared to PAC_AUC (AIC −397.6; BIC −380.5) and PAC_DD (AIC −136.0; BIC −123.3) (Table 3a). Te independent contributions of SV and inverse PP were modelled. SV and 1/PP were both significantly associated with PVR; however, SV explained only 33.3% of the model variance (R² = 0.333), whereas 1/PP explained 86.8% (R² = 0.868). Including both terms in a multivariate model improved model fit, yet PAC_empiric still demonstrated a stronger association with PVR than either component individually or combined, yielding the highest R² (0.968) (Tables 3b and 4; Figures S7–S10).

Table 2.

Model coefficients and confidence intervals for the relationship between PAC and PVR^*.

Method	Intercept $\mathit{(}\mathit{\beta }$ 0)	PVR coefficient (${\mathit{\beta }}_{\mathbf{1}}$)	Z score	95% CI	Sample size
PACempiric	0.13	1.48	31.62	1.39–1.57	1017
PACAUC	0.19	1.13	13.39	0.96–1.29	222
PACDD	0.26	0.81	5.03	0.49–1.13	156

Abbreviations: PAC_AUC, pulmonary arterial compliance, calculated using the area under the curve method; PAC_DD, pulmonary arterial compliance, calculated using the diastolic decay method; PAC_empiric, pulmonary arterial compliance, calculated by stroke volume/pulmonary pulse pressure; PVR, pulmonary vascular resistance.

^*Models used a gamma distribution with an inverse link function.

Figure 2.

The inverse hyperbolic relationship between pulmonary compliance and resistance persists across three PAC calculation methods. (a) using PAC_empiric to calculate compliance; ${\text{PAC}}_{\text{empiric}}=\frac{1}{0.13+1.48·\text{PVR}}$; (${\mathrm{\beta }}_1$ = 1.48; 95% CI: 1.39–1.57, z = 31.6, p < 0.0001); (b) Using the area under the curve method to calculate compliance; ${\text{PAC}}_{\text{AUC}}=\frac{1}{0.19+1.13·\text{PVR}}$; (${\mathrm{\beta }}_1$ = 1.13; 95% CI: 0.96–1.29, z = 13.39). (c) Using the diastolic decay method to calculate compliance; ${\text{PAC}}_{\text{DD}}=\frac{1}{0.26+0.81·\text{PVR}}$; (${\mathrm{\beta }}_1$ = 0.81; 95% CI: 0.49–1.13, z = 5.03, p < 0.0001). AUC, area under the curve; DD, diastolic decay; PAC, pulmonary arterial compliance; PVR, pulmonary vascular resistance; red line representing the relationship ${\text{PAC}}_{\text{empiric}}$ = 1/(β₀ + β₁. PVR); confidence intervals represented by grey bands.

Table 3a.

Model comparison statistics for PAC methods; (n = 156).

Model	AIC	BIC
PACempiric	−504.3	−487.3
PACAUC	−397.6	−380.5
PACDD	−136.0	−123.3

Abbreviations: AIC, Akaike Information Criterion; AUC, area under the curve; BIC, Bayesian Information Criterion; DD, diastolic decay; PAC, pulmonary arterial compliance.

Table 3b.

Model comparison statistics for component analysis for PAC_empiric (n = 1017).

Model	AIC	BIC	Pseudo‐R2	Likelihood ratio test*
SV	−1678.2	−1658.5	0.333	—
Inverse PP	−1910.1	−1890.5	0.868	χ2 = 435.09; df = 1; p < 0.0001
SV + inverse PP	−2111.3	−2086.6	0.962	χ2 = 203.11; df = 1; p < 0.0001
PACempiric	−2185.1	−2165.4	0.968	—

Abbreviations: AIC, Akaike Information Criterion; AUC, area under the curve; BIC, Bayesian Information Criterion; DD; diastolic decay; PAC, pulmonary arterial compliance; PP, pulmonary pulse pressure; PVR, pulmonary vascular resistance; SV, stroke volume.

^*Comparison to SV model; PAC_empiric model is not nested, and cannot be compared by likelihood ratios.

Table 4.

Model summary statistics for models of stroke volume and inverse pulse pressure with PVR; (n = 1017).

Model	Intercept $(\beta$ 0)	PVR coefficient (${\beta }_1$)	95% CI	p value
SV	2.07	0.07	0.06–0.08	< 0.0001
Inverse PP	0.63	131.23	118.22–144.25	< 0.0001
SV + inverse PP	−2.89	SV: 0.06	SV: 0.05–0.07	< 0.0001
		1/PP: 125.72	1/PP: 115.29–136.16	< 0.0001
PACempiric	0.53	2.18	2.03–2.34	< 0.0001

Abbreviations: PAC, pulmonary arterial compliance; PP, pulmonary pulse pressure; PVR, pulmonary vascular resistance; SV, stroke volume.

In univariate analyses, age and BSA were significantly associated with PAC_empiric (Table S2). PAC_AUC and PAC_DD were significantly associated with age, but not BSA. In adjusted models, PAC_empiric remained independently associated with PVR ${(\mathit{PAC}}_{\mathit{empiric}}=\frac{1}{0.17+1.35\bullet \mathit{PVR}}$, ${\beta }_1$ = 1.35; 95% CI: 1.27–1.43, z = 34.6, p < 0.0001; Figures 3 and S5), as did PAC_AUC and PAC_DD (Tables S3–S5). Model fit was significantly improved by the addition of BSA and age, (χ² = 97.73; df = 2; p < 0.0001; Figures S5 and S6), however the marginal increase in pseudo‐R ² (from 0.968 to 0.974) suggested that age and BSA contribute to less than 1% of the variance in these models.

Figure 3.

Empiric pulmonary compliance to resistance, adjusted for age and BSA. ${\text{PAC}}_{\text{empiric}}=\frac{1}{0.27+1.43·\text{PVR}}$, (${\mathrm{\beta }}_1$ = 1.43; 95% CI: 1.34–1.51, z = 32.3, p < 0.0001). PAC, pulmonary arterial compliance; PVR, pulmonary vascular resistance; red line representing the relationship ${\text{PAC}}_{\text{empiric}}$ = 1/(β₀ + β₁. PVR); confidence intervals represented by grey bands.

3.2. Diagnostic and Prognostic Performance of PAC

The diagnostic performance of the three PAC methods was evaluated by ROC analysis, discriminating pre‐ versus post‐capillary PH. PAC_empiric showed numerically superior performance compared to PAC_AUC and PAC_DD (AUC = 0.91; 0.88; 0.75, respectively; Table 5; Figure 4), however the performance of PAC_empiric was only statistically superior to PAC_DD.

Table 5.

Receiver operating characteristics for PAC calculation methods; (n = 156).

Method	AUC, PH diagnosis (95% CI)	p value*
PACempiric	0.91 (0.83–0.98)	—
PACAUC	0.88 (0.81–0.96)	0.487
PACDD	0.75 (0.63–0.87)	0.003

Abbreviations: AUC, area under the curve; CI, confidence interval; DD, diastolic decay.

^*Compared to PAC_empiric.

Figure 4.

ROC analysis curves for the comparison of diagnostic performance between PAC_empiric, PAC_AUC, and PAC_DD for pulmonary hypertension (n = 156).

Univariable Cox regression analyses demonstrated that age, BMI, pulmonary pulse pressure (PP), systolic (SPAP) and mPAP, SV, and PVR were each significantly associated with mortality (Table S6). All models met the proportional hazards assumption. Age, identified as the strongest clinical and statistical predictor, was included as a covariate in multivariable models.

Both PAC_empiric and PVR were independently associated with mortality. Higher PAC_empiric was associated with reduced mortality risk (HR = 0.60, 95% CI: 0.42–0.86; p = 0.005), and PVR showed a strong positive association with mortality (HR = 10.19, 95% CI: 1.96–52.9; p = 0.006). Kaplan–Meier survival curves stratified by tertiles of PAC_empiric and PVR, and adjusted for age are shown in Figures 5 and 6. While there was moderate collinearity between PAC_empiric and PVR, in a combined model, PAC_empiric remained a significant mortality predictor, while PVR did not (Table S7).

Figure 5.

Kaplan–Meier survival curves stratified by tertiles of empiric pulmonary arterial compliance (PAC_empiric), adjusted for age. Patients in the lowest tertile of PAC had significantly lower survival compared to those in the mid and high tertiles (p = 0.005), demonstrating the prognostic value of PAC_empiric in identifying patients at elevated mortality risk. Tertile 1: PAC_empiric = 0.54–1.90; Tertile 2: PAC_empiric = 1.91–3.28; Tertile 3: PAC_empiric = 3.29–10.23.

Figure 6.

Kaplan–Meier survival curves stratified by tertiles of pulmonary vascular resistance. Patients in the highest tertile of PVR had significantly reduced survival compared to those in the mid and low tertiles (p = 0.0004), supporting PVR as an independent predictor of mortality. Tertile 1: PVR = 0.03–0.13; tertile 2: PVR = 0.14–0.26; tertile 3: PVR = 0.26–0.89.

PAC_AUC and PAC_DD were also assessed using univariable Cox models (Table S8). Similarly to PAC_empiric, PAC_AUC and PAC_DD were both significantly associated with reduced mortality. Again, similarly to PAC_empiric, in models adjusted for age (Table 6), PAC_AUC remained a significant predictor of mortality, while PAC_DD did not (Figure 7). PAC_empiric exhibited the strongest discriminatory capacity of the three calculation methods (c‐statistic = 0.713).

Table 6.

Cox regression analyses for mortality, predicted by PAC methods and age.

Model	Coefficient	HR	95% CI	p value	Concordance	Sample size
Model: PACempiric
PACempiric	−0.507	0.60	0.42, 0.86	0.005	0.747	152
Age	0.042	1.04	1.01, 1.07	0.002	0.747	152
Model: PACAUC
PACAUC	−0.405	0.67	0.47, 0.94	0.021	0.737	152
Age	0.044	1.05	1.02, 1.07	< 0.001	0.737	152
Model: PACDD
PACDD	−0.287	0.75	0.53, 1.06	0.107	0.709	152
Age	0.043	1.04	1.02, 1.07	0.002	0.709	152

Abbreviations: AUC, area under the curve; CI, confidence interval; DD, diastolic decay; HR, hazard ratio; PAC, pulmonary arterial compliance (mL. mmHg⁻¹).

Figure 7.

Hazard ratios for mortality associated with methods of estimating pulmonary arterial compliance (PAC). Cox proportional hazards models were adjusted for age. PAC_empiric and PAC_AUC were significantly associated with mortality. Error bars represent 95% confidence intervals.

Finally, RC time (PAC × PVR) was computed using each PAC method and analyzed in age‐adjusted Cox models. None of the RC time variants were significantly associated with mortality (Table S8), although age remained consistently predictive, suggesting that combining PAC and PVR into a single parameter attenuated their individual predictive abilities.

4. Discussion

We applied statistical modelling of real‐world pulmonary haemodynamic and waveform data in a comparison of PAC calculation methods to address existing uncertainties surrounding the PAC calculation method, which have limited its broader clinical application. Although PAC_empiric has been shown to predict mortality in some cohorts [13], its accuracy compared to waveform analysis methods has been questioned, and few comparisons of waveform calculation methods have previously been conducted.

In summary, all three PAC calculation methods demonstrated the well‐recognised inverse hyperbolic RC relationship with PVR. This is well‐established across PH phenotypes, and provides a physiologically grounded framework for quantifying global RV afterload [6, 7, 9, 10, 11, 12]. The findings from this study support the ability of each method to estimate the PAC within this framework, however. PAC_empiric provided superior model performance, in that it most strongly modelled an inverse hyperbolic relationship with PVR. Pairwise residual and Bland–Altman analyses showed that the three approaches to estimating PAC are only moderately correlated and not directly interchangeable. Notably, PAC_DD showed the closest agreement with PAC_empiric, whereas PAC_AUC consistently overestimated compliance relative to both alternative methods. This systematic difference likely reflects the underlying assumptions of the area‐under‐the‐curve approach, which may amplify apparent compliance when pressure decay is prolonged. These findings highlight that methodological choice can meaningfully influence PAC values and should be carefully considered when comparing results across studies.

Related to this, any concerns that the relationship between PAC_empiric and PVR may be artefactual due to mathematical interaction between their equations were not supported. While this has been raised previously [19], overwhelmingly, evidence supports the physiological relationship between PAC and PVR [5, 6, 20]. When SV and 1/PP were modelled independently, neither variable alone, nor their combination, explained the observed relationship as effectively as their ratio (PAC_empiric), which retained the strongest association with PVR. Analyses showed that the SV term shared between PAC_empiric and PVR accounted for only one‐third of the RC relationship, and while the inverse PP explained a large component of the RC relationship, there was additional improvement after taking the ratio of the terms. This further supports the physiological basis of the RC relationship, which is in line with models of vascular function. As vascular distensibility diminishes, PAC declines even before a marked rise in resistance is observed. This is consistent with vascular mechanics and Poiseuille's law, which predict a nonlinear increase in resistance following an early loss of compliance [21]. The early steep decline in PAC with modest increases in PVR, observed here and in prior studies, underscores this concept [2, 3, 4, 5, 6, 7, 8], and these findings support that PAC_empiric can be applied in conjunction with PVR as a valid and robust model for estimating global RV afterload.

PAC_empiric also provided more accurate diagnostic and prognostic performance than the waveform analysis methods, particularly in distinguishing PH subtypes. With regard to mortality, PAC_empiric was the most robust compliance‐based predictor, and PVR remained less predictive than PAC_empiric, including in multivariate modelling. Interestingly, RC time (PAC × PVR), despite its theoretical appeal as an integrated vascular function metric, showed no significant relationship with survival. The likely explanation is that RC time conflates the individual contributions of PAC and PVR. For example, a patient with high compliance and low resistance may have the same RC time as a patient with poor compliance and high resistance, despite these patients having markedly different hemodynamic profiles, and associated clinical risks and prognoses. This highlights a key limitation of composite parameters in that while they may reflect underlying physiology, they can also mask clinically relevant variation by collapsing opposing effects into a single neutral value, and in effect, RC time may obscure important prognostic differences that are retained when PAC and PVR are modelled independently. This finding suggests that although there is a predictable relationship between PAC and PVR, their individual contributions to prognosis are not interchangeable and should therefore be evaluated separately, including when assessing mortality risk.

Finally, although waveform analysis methods may yield more precise estimates of PAC [17], our results indicate that they do not offer significant advantages in modelling the RC relationship, nor in discriminating between PH groups or predicting mortality. PAC_empiric is more clinically feasible to obtain than waveform analysis methods, and while this cannot be the primary reason for selecting one calculation method over another, considering that PAC_empiric can be justly utilised with PVR to estimate the pulsatile and resistive components of RV afterload, the ease of its clinical use is also an advantage.

In summary, PAC_empiric is not only a physiologically meaningful index of pulsatile load but also the most practical method for clinical use. In conjunction with PVR, it allows a combined assessment of resistive and pulsatile components of RV afterload, offering a tool to comprehensively characterise the haemodynamic function of the pulmonary circulation and RV afterload in PH.

4.1. Limitations

Waveform data required for PAC_AUC and PAC_DD calculations were only available in a subset of the cohort, which may introduce selection bias. Although baseline haemodynamic parameters were similar between subgroups, the PAC_DD cohort had a significantly lower proportion of post‐capillary PH and a higher proportion of pre‐capillary PH cases. At low PVR we observed more variability in the data, and while this may be a result of the sample size, future investigation into the behavior of the RC relationship at lower or normal PVR is warranted.

5. Conclusion

This study demonstrates that PAC_empiric reflects the established inverse hyperbolic relationship with PVR, outperforming waveform‐derived methods in characterising the global RV afterload within this framework, as well as being a stronger discriminator of PH and predictor of mortality. Theoretical concerns regarding mathematical interaction between PAC_empiric and PVR were not supported, reinforcing the validity of assessing these both parameters to gain a more comprehensive picture of global RV loading in both research and clinical settings.

Author Contributions

Hannah Kempton: data collection, data analysis, manuscript preparation. Nick Olsen: statistical support and analysis development. Katherine Kearney: data collection and scientific development. Christopher S. Hayward: supervision and scientific development. David W. Muller: supervision and editing. Audrey Adji: data collection and analysis, including waveform analysis.

Ethics Statement

Local ethics committee approval was obtained for this project as per local protocols.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting Figure S1: Diagnostic plots using simulated Dunn‐Smyth residuals from the DHARMa package1 for the relationship between PAC_empiric and PVR. Supporting Figure S2: Diagnostic plots for the above model were re‐examined following exclusion of the top 25 observations. Supporting Figure S3: Diagnostic plots using simulated Dunn‐Smyth residuals from the DHARMa package 1 for the relationship between PAC_AUC and PVR (A) Quantile‐quantile plot of uniform residuals showing observed vs. expected values. Supporting Figure S4: Pearson residuals for the relationship between PAC_DD and PVR. Supporting Figure S5: Diagnostic plots using simulated Dunn‐Smyth residuals from the DHARMa package 1 for the model of the relationship between PAC_empiric and PVR, adjusted for age and BSA. Supporting Figure S6: Diagnostic plots using simulated Dunn‐Smyth residuals from the DHARMa package 1 for the model of PAC_AUC and PVR, adjusted for age and BSA. Supporting Figure S7: Pearson residuals for the model of PAC_DD and PVR, adjusted for age and BSA. Supporting Figure S8: Pearson residuals for Model for SV and PVR. Supporting Figure S9: Pearson residuals for the model assessing inverse pulse pressure as a predictor of PVR. Supporting Figure S10: Pearson residual diagnostics for the model assessing stroke volume and inverse pulse pressure as predictors of pulmonary vascular resistance. Supporting Figure S11: Pearson residual diagnostics for the model assessing PAC_empiric as a predictor of pulmonary vascular resistance. Supporting Figure S12: Pairwise comparison of pulmonary arterial compliance (PAC) estimates. Supporting Table S1: Comparison of baseline statistics for three PAC calculation methods. Supporting Table S2: Unadjusted analyses for age and BSA in predicting PAC_empiric (n = 1017). Supporting Table S3: Results of the multivariate model for PAC_empiric; (n = 1017). Supporting Table S4: Outcome of adjusted model for pulmonary compliance by area under the curve; (n = 222). Supporting Table S5: Outcome of adjusted model for PAC_DD; (n = 156). Supporting Table S6: Cox regression analyses for mortality and co‐variates; (n = 152). Supporting Table S7: Cox regression analysis for mortality, predicted by PAC_empiric and PVR; (n = 156). Supporting Table S8: Univariate cox regression analysis for mortality, predicted by PAC methods. Supporting Table S9: Cox regression analyses for mortality, predicted by RC time* and age. Supporting Table S10: Pairwise agreement between PAC estimation methods

Kempton H., Olsen N., Kearney K., Hayward C. S., Muller D. W., and Adji A., “Empiric Pulmonary Arterial Compliance Reflects the Resistance‐Compliance Relationship and Predicts Mortality in Pulmonary Hypertension,” Pulmonary Circulation 15 (2025): 1‐11, 10.1002/pul2.70184.