The pulmonary resistance-compliance relationship: Real or mathematical artifact?

Abstract

Pulmonary vascular resistance (PVR) and arterial compliance (PAC) have been reported to share an inverse hyperbolic relationship, with their product-the pulmonary vascular time constant (τ)-remaining more or less constant across disease states. However, PAC is often estimated as stroke volume (SV) divided by pulse pressure (PAC_clinical = SV/PP), introducing potential mathematical coupling with PVR, which is dependent on SV. This inherent relationship may artificially produce hyperbolic correlations. We conducted joint density analysis (JDA) and hemodynamic simulations using data from patients with pulmonary hypertension due to left-sided disease. PAC_clinical was calculated as SV/PAPP, and PVR as (PA_M - PCWP)/CO. Log-transformed values were analyzed to assess the PVR-PAC_clinical relationship. JDA demonstrated a strong inverse correlation between PVR and PAC_clinical (Spearman's R = -0.88, CI -0.92 to -0.82), increasing to -0.92 with bootstrapping. Hemodynamic simulations confirmed a first-order hyperbolic decay (PAC = τ_avg/PVR; r² = 0.86, p < 0.001). The relationship shifted downward with increasing PCWP. Our findings replicate the reported PVR-PAC_clinical relationship, highlighting its mathematical dependence. Further studies using more accurate PAC estimation methods are needed to determine whether this association is truly physiological or an artifact of calculation.