Pulmonary vascular resistance and compliance stay inversely related during treatment of pulmonary hypertension

Abstract

Introduction

Pulmonary hypertension (PH) is characterized by an increased right ventricular (RV) afterload. Although, the RV initially may adapt to this afterload, most patients eventually die from heart failure. Since new therapies aimed at reducing RV afterload have been introduced in the last decade, it is important to gain insight in the factors that contribute to RV afterload and how they are affected by therapy.

In clinical practice, changes in RV afterload after therapy are most often described as changes in pulmonary vascular resistance. For example, in clinical trials on new therapies, pulmonary vascular resistance is often used as a secondary^1,2 or even primary³ endpoint. However, while resistance relates to steady load (ratio of mean pressure and mean flow), flow is obviously pulsatile. Since arterial compliance relates to oscillatory load, compliance may be a haemodynamic parameter of equal importance as resistance. However, to our knowledge the long-term effects of therapy on compliance in PH have not been studied yet. Mahapatra et al.⁴ showed that compliance is a strong predictor of mortality, but they did not study the changes in compliance after therapy. Weinberg et al.⁵ studied changes in compliance, but they studied acute effects only.

The product of resistance (R) and compliance (C) is called the RC-time because it has the unit of time. It characterizes the decay of pulmonary artery pressure in diastole.⁶ In a previous study, we have shown that the RC-time is the same in patients with and without PH,⁷ implying that R and C are inversely related: patients with a large R have a small C and patients with a small R have a large C. We hypothesized that the RC-time remains the same during therapy for PH. As shown in Figure 1, patients with severe PH (high R at baseline) will then require a much larger decrease in R than patients with mild PH (low R at baseline) in order to obtain the same increase in C. Therefore, it may be expected that patients show more haemodynamic improvement when their decrease in R is accompanied by an increase in C than when R decreases alone. In this study, we determined both R and C twice during therapy and related changes in cardiac index with changes in R and C.

Figure 1

The consequence of a constant RC-time τ during therapy for patients A and B. At baseline, patient A has a low resistance R (mild PH) and patient B a high resistance (severe PH). If the RC-time is constant, patients will always move along the dashed line and a change in resistance ΔR will be accompanied by a change in compliance ΔC. If the resistance R of both patients decreases with the same amount ΔR, patient A will improve much more in compliance than patient B. Thus, patient A will improve substantially in both steady and pulsatile afterload, while patient B will improve in steady afterload only.

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Methods

Patients and measurements

We included all consecutive patients with pulmonary arterial hypertension (PAH) or inoperable chronic thromboembolic pulmonary hypertension (CTEPH) who had undergone two right-heart catheterizations between October 2003 and June 2006 and who were treated for PH. The distribution of diagnoses is shown in Table 1. The CTEPH patients had a history of pulmonary embolism and an abnormal pulmonary angiogram. Their operability was evaluated according to the recommended criteria.^8–10 All patients suspected of PH were evaluated according to a standard diagnostic protocol.¹¹ PAH is confirmed if a mean pulmonary artery pressure >25 mmHg and a pulmonary capillary wedge pressure <15 mmHg at rest is found. On a regular basis or if the clinical occasion calls for it, patients undergo a follow-up right-heart catheterization for assessment of treatment effectiveness. The first of the two catheterizations could either be a baseline (before disease-specific treatment) or a follow-up catheterization.

To prevent selection bias for a specific treatment, we included patients on a wide variety of regimens (Table 2). In addition, many patients went through one or more regimen changes between the two catheterizations. The institutional ethics committee approved the study and all patients gave informed consent.

Pressure was measured during right-heart catheterization (PAH) or during pulmonary angiography (CTEPH). Cardiac output was measured using the Fick principle or thermodilution. If possible, pulmonary capillary wedge pressure (or left-ventricular end-diastolic pressure) was measured. If wedge pressure could only be measured during one of the two catheterizations or during a third catheterization not longer than 1 year ago, wedge pressure was assumed equal to the latter. If a reliable wedge pressure was not available, a value of 10 mmHg was assumed. In 19 patients, pressure and ECG were digitally recorded using a PowerLab data acquisition system (ADInstruments) for comparison of the RC-time estimation methods.

RC-time

R was calculated as the ratio of mean pulmonary artery pressure and mean flow and C as the ratio of stroke volume and pulse pressure. For the RC-time τ it then holds that

with T the heart period, mPAP mean pulmonary artery pressure, PCWP the pulmonary capillary wedge pressure, and PP the pulmonary artery pulse pressure. To test the validity of this formula, τ was also estimated from the pulmonary artery pressure in the subset of patients with a digitally recorded pressure. A mono-exponential function was fit to the diastolic pulmonary artery pressure of an ensemble-averaged cardiac cycle.^6,7 The function was fit by linear regression of the logarithm of the diastolic pressure (from 50 ms after the start of diastole to 50 ms before the end; asymptotic pressure equal to PCWP). These analyses were done with MATLAB 7.0, R14 (The MathWorks, Natick, MA, USA).

Statistical methods

Values of catheterization 1 and 2 were compared with a paired Student’s t-test (two-tailed). Delta’s (Δ) were calculated as the value at catheterization 2 minus the value at catheterization 1 and average absolute changes as the average of the absolute value of the delta’s. Different regression models were used to explain the changes in cardiac index (ΔCI). First, ΔR and ΔC were used separately as univariate predictors. Subsequently, the model with ΔR as predictor was stepwise extended with ΔC and ΔR·ΔC (interaction term) as predictors. These models were compared using the F test and the standardized regression coefficients. Besides ΔR and ΔC, the length of the arrow (vector) λ that connects the first and second RC-pair of a patient (Figure 1)

was used as a predictor. In case of improvement in R during therapy (ΔR negative), λ was assigned a positive sign and otherwise a negative sign.

Because both the dependent and the independent variables in the regression models are derived from common measurements, regression and correlation may be biased due to mathematical coupling.¹² We corrected mathematical coupling with the method of Stratton et al.¹² for univariate regression and the SIMEX method¹³ for multivariate regression. Differences with P < 0.05 were regarded as statistically significant (two-tailed testing). Values are presented as mean±SD. Statistical analysis was done with SPSS 12.0.1 for Windows (SPSS, Chicago, IL, USA) and correction for mathematical coupling with MATLAB.

Results

Patient characteristics

Our study population consisted of 17 men and 45 women, aged 47.8 ± 15.1 years at catheterization 1 (range 21.2–78.6 years). Fifty-two patients were diagnosed with PAH and 10 patients with inoperable CTEPH. The time between the two catheterizations was 1.1 ± 0.4 years (range 50–748 days). Table 3 summarizes the haemodynamic data. Most of the haemodynamic variables changed significantly during the period between the catheterizations (P < 0.01). On average, we did not find a change in right atrial pressure and heart rate. The average absolute change was 3.1 ± 2.5 mmHg in right atrial pressure and 9.8 ± 8.8 b.p.m. in heart rate.

RC-time

Bland–Altman analysis of the two estimation methods for τ revealed an average difference of –0.05 ± 0.10 s, indicating that the simple formula underestimates τ with respect to the average of the simple formula and τ estimated with the exponential fit (Figure 2). Since, the former is the product of two validated estimation methods (R, the ratio of pressure and flow, and C, the ratio of stroke volume and pulse pressure) and since it enables estimation of τ in a larger cohort of patients, we judged the agreement acceptable.

Figure 2

Bland–Altman analysis of the agreement between τ estimated from the simple formula and from the exponential fit. The dashed lines denote the limits of agreement and the dotted lines the corresponding 95% confidence intervals.

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On average, the RC-time did not change significantly during the period between the two catheterizations: τ₁ = 0.61 ± 0.15 s and τ₂ = 0.59 ± 0.16 s. Although many patients showed a change in τ (average absolute change 0.11 ± 0.09 s or 19 ± 16%, Figure 3), the average difference was not statistically significant (paired Student’s t-test: P = 0.320; 95% confidence interval of differences: –0.017 to 0.053 s).

Figure 3

The RC-time τ measured during the catheterizations 1 and 2. Squares with errorbar denote mean±SD.

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We investigated whether the heterogeneity of the population concealed possible different behaviour of subgroups. Subgroups were defined on the basis of moment of catheterization 1 (either before or during disease-specific treatment) and diagnosis (idiopathic PAH or CTEPH). In none of the subgroups, a significant change in τ was found (Table 4).

Figure 4 (left panel) relates C and R at the time of catheterizations 1 and 2. An arrow connects data of individual patients. Apparently, during the course of the disease, patients follow the hyperbola that results from a constant RC-time (Figure 1). This is further illustrated in Figure 4 (right panel) where the changes in R and C are plotted as vectors from the origin. The majority of the vectors end in the top-left or bottom-right quadrants indicating that if R decreases, C increases and vice versa. These vectors correspond with a movement tangential to the hyperbola of the left panel, whereas vectors in the top-right and bottom-left quadrants correspond to a (somewhat paradoxical) perpendicular movement. We conclude that for the population as a whole, the RC-time does not change between the two catheterizations.

Figure 4

Left: compliance C vs. resistance R at catheterizations 1 and 2. The circles denote catheterization 1 and the arrows point to catheterization 2. The grey line is the hyperbola C=τ/R. Note that most arrows start and end in the vicinity of the curve. Right: ΔR and ΔC represented as a vector from the origin, indicating the change in both R and C between catheterizations 1 and 2.

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Haemodynamic changes

Linear regression with changes in cardiac index ΔCI as dependent variable and changes in load in terms of ΔR, ΔC, and λ yielded the results shown in Table 5 and Figure 5. The regression coefficients are corrected for mathematical coupling. Correction did not significantly affect the regression slope nor did it decrease the correlation coefficients. Since correlation coefficients can be problematic (e.g. >1) after correction for mathematical coupling,¹² we report the R² before correction. Changes in CI are much better explained by ΔC (R² = 0.67), and even better by ΔR and ΔC combined or by λ (R² = 0.74 and 0.70, respectively) than by ΔR alone (R² = 0.37, Figure 5).

Figure 5

Linear regression with ΔCI as dependent variable and change in resistance ΔR, change in compliance ΔC and vector length λ. λ, a combined measure of ΔR and ΔC, best explains changes in CI.

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Discussion

No change in RC-time

We found that the RC-time, the product of pulmonary vascular resistance R, and pulmonary arterial compliance C, does not change significantly in patients treated for PH. This implies that R and C are inversely related, which agrees with our hypothesis (Figure 1). This is best illustrated in a plot of C vs. R, where most of the data are in close vicinity of the hyperbola (Figure 4, left panel).

We deliberately introduced heterogeneity in the study in four ways. First, patients with many forms of PH were included. Our study covered both the categories (categories 1 and 4) of the WHO classification of PH¹⁰ that are currently targets of PH-specific treatment. Second, a wide variety of treatment regimens (Table 2) was included and many patients went through a regimen change during the study period. Thus, we prevented bias for a specific therapy. Third, the time between the two catheterizations was not fixed, resulting in a variety of periods (range 50–748 days). Thus, we also prevented bias for a specific duration. Fourth, patients were included with either the first of the two catheterizations at baseline (before disease-specific treatment) or at follow-up. Since we did not find significant changes in this heterogeneous group of patients nor in more homogeneous subgroups, we conclude that the inverse coupling of R and C is a basic phenomenon. Our finding of a nearly constant RC-time during therapy is in line with what we and others have found for patients at baseline.^7,14,15

We used the length of the vector (with a sign) that connects the data of the first and the second catheterization (with a positive sign corresponding to a decrease in R) to relate changes in the ‘RC-plane’ with cardiac index. This vector length λ accounts for changes in both resistance and compliance, and thus comprehensively summarizes a patient’s improvement or decline in both steady and pulsatile afterload. For a patient with severe PH in whom R decreases much but C changes little, and for a patient with mild PH in whom R decreases little but C increases more, a similar value for λ may be found. Since its ability to predict changes in CI is about the same as that of the multiple regression model of ΔR and ΔC, λ may be an important clinical parameter.

Haemodynamic consequences

The inverse coupling of R and C has direct and important haemodynamic consequences. In mild PH, the decrease in R is accompanied by a substantial increase in C, while in severe PH, the increase in C is negligible (Figure 1). This may explain the clinical observation that patients with mild PH (moderately increased R) often show a greater haemodynamic improvement after therapy than patients with severe PH (strongly increased R), even if their R decreases by the same amount.¹⁶

If R and C are inversely related, the contribution of C to RV afterload is as important as the contribution of R. This is confirmed by the strong correlations of ΔCI with ΔC alone (R² = 0.67) and with ΔR and ΔC combined (R² = 0.74, Figure 5). The strong correlations cannot be explained by mathematical coupling due to the common measurements on which the dependent and independent variable are based. At first sight, it may be surprising that ΔC even better predicts changes in CI than ΔR. However, under the assumption of a constant RC-time τ, it can be shown that ΔC can be expressed in terms of R and ΔR

If ΔC is predicted with this formula (thus using R and ΔR only), the same correlation with ΔCI is found as in case of the measured ΔC (Figure 6).

Figure 6

Linear regression of ΔCI with ΔC predicted from ΔR under the assumption that RC-time τ is constant. Note the similarity in slope, intercept, and goodness-of-fit (R²) with the middle panel of Figure 5.

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CI is one of the few haemodynamic parameters with significant prognostic value¹⁷ and also one of the few that correlate with functional measures.¹⁸ Although λ correlates strongly with changes in CI, it should be appreciated that both reflect different things. CI is the result of the complex interaction of heart and arterial system. Thus, CI is determined by both the characteristics of the vascular bed and the heart. If the heart starts failing, the state of the vascular bed may be unaltered but CI will decrease. If, on the other hand, the arterial system changes due to progression of the disease, the state of the heart may be unaltered but CI will again decrease. In contrast, λ only reflects changes in the vascular bed. Therefore, its clinical relevance resides in its specificity for the vascular bed and its apparent ability to describe changes in RV afterload better than changes in either R or C. It should be noted that as a consequence λ not necessarily reflects changes in the functional status of the patient, since these are the result of an even far more complex interaction.

Clinical importance of compliance

Since pulmonary vascular resistance is mainly determined by the small peripheral arteries and arterioles and PH most often is caused by small vessel disease, most of the attention has been paid to the study of the role of small vessels in PH. Pulmonary arterial compliance, on the other hand, is generally believed to be determined by the large vessels and has, consequently, been studied to a much lesser extent. However, most PH-patients die from RV failure and, as our study shows, compliance strongly contributes to RV afterload. Therefore, our present study suggests that in clinical studies more attention should be paid to changes in arterial compliance.

In the research on ventricular afterload, the contribution of arterial compliance has been gaining importance, especially in the study of systemic hypertension.¹⁹ Recent studies indicate that compliance may be of similar importance in PH. Muthurangu et al.¹⁵ assessed pulmonary arterial compliance in 17 patients suspected of PH or congenital heart disease using MR-guided cardiac catheterization. Mahapatra et al.,⁴ in a study with 104 PH-patients, have shown that invasively assessed arterial compliance is a strong predictor of survival. Furthermore, Jardim et al.²⁰ have shown that non-invasively assessed pulmonary artery distensibility is significantly higher in PAH patients responding to an acute vasodilator and Gan et al.²¹ have shown that pulmonary artery stiffness is also a strong predictor of survival.

Our present study is to our knowledge not only the first to report on the long-term effects of disease-specific therapy on pulmonary arterial compliance in PH, but also the first to provide a clue as to why pulmonary arterial compliance is a strong predictor of survival. This is best illustrated in the plot of C vs. R (Figures1 and 4). With R and C remaining inversely related during development of the disease, a patient who is developing PH will start in the upper left region of the curve and will move from left to right along the curve (instead of, as is shown, from right to left). Then, a small increase in resistance will be accompanied by a substantial decrease in compliance. Thus, an inverse relationship implies that loss of pulmonary arterial compliance is an early sign of PH. This may explain why compliance is a strong predictor of survival. Furthermore, because measures of pulmonary arterial compliance can be assessed non-invasively, this provides a new perspective on screening of patients suspected of PH.

Limitations

In a number of patients, wedge pressure data were incomplete. In some patients, it was measured during an earlier catheterization and included in the study, in some it could not be measured reliably, and in a few patients referred to our hospital for treatment right-heart catheterization data were incomplete. In the CTEPH-patients, pressure was measured during angiography with a catheter other than a balloon-tipped catheter. In all patients, but especially in the patients without a reliable or even absent wedge pressure measurement, left-sided heart disease was excluded by means of an extensive echo and MRI protocol. In case of incomplete data, we assumed that the wedge pressure remains constant in time or we assumed a reference value. In either case, this is a safer assumption (in terms of accuracy of R) than assuming a wedge pressure of zero. This allowed inclusion of the wedge pressure in the analyses, but we also carried out our analyses by leaving out wedge pressures. Although the numerical values changed, the statistical results were similar (same correlations and levels of significance). Therefore, we assume that the inaccuracies in the wedge pressure play a minor role in the study.

C, estimated as the ratio of stroke volume and pulse pressure, is regarded a rather crude estimate of arterial compliance.^6,22 However, we⁷ and Segers et al.²³ have shown that it, despite overestimating compliance, correlates well with other compliance estimation methods. The ratio of stroke volume and pulse pressure is attractive for clinical application because it can be calculated from standard clinical measurements.

The two estimation methods for τ agreed only moderately (limits of agreement –0.25 and 0.15 s). Theoretically, the exponential fit would be the preferred method, but it is not very accurate in practice, mainly due to its dependence on the part of diastolic pressure curve that is chosen for the fit. Although we optimized circumstances by automating the procedures as much as possible, the fit was not optimal in all cases. Therefore, it may be questioned which of the two methods is most inaccurate. The simple estimator is the product of two well-validated parameters and might even be the most accurate of the two.

In the definition of λ, the terms under the square root sign are quantities of different physical dimensions. If one of the terms is thought to contain a weight factor with value equal to 1 and the correct dimension, this problem is resolved. It must, however, be noted that this factor should have a different value when R and C are expressed in other units. Therefore, it may be better to standardize R and C by a (reference) population mean and standard deviation. The fit of CI vs. this standardized λ would decrease slightly (R² = 0.67).

Conclusion

In conclusion, this study shows that pulmonary vascular resistance and compliance remain inversely related during therapy for PH. As a consequence, cardiac index improves more when a resistance decrease is accompanied by a compliance increase (as in mild PH) than when resistance alone decreases (as in severe PH). Furthermore, an inverse relation implies that early in the disease a compliance decrease is larger and more easily observed than a resistance increase.

Conflict of interest: J.W.L., N.W., T.J.C.F., C.T.J.G., K.M.M., F.G.v.d.B.: none declared. A.B.: lectures for Actelion (2005 and 2006, € 500 per year) and Encysive (2006, € 700), advisory boards of GlaxoSmithKline (2006, € 1200) and Pfizer (2005, € 700), unrestricted educational grant from GlaxoSmithKline (€ 25.000). A.V.N.: lecture for Actelion (2003, € 1000).

Funding

Netherlands Heart Foundation (NHS2003B274 to J.W.L.); Netherlands Organization for Scientific Research (Mozaïek 017.001.154 to C.T.G.).

References