Golden Ratio and the Proportionality Between Pulmonary Pressure Components in Pulmonary Arterial Hypertension

Abstract Background The golden ratio (Phi, Φ = 1.618) is a proportion that has been found in many phenomena in nature including the cardiovascular field. We tested the hypothesis that the systolic over mean pulmonary artery pressure ratio (sPAP/mPAP) and the mean over diastolic pressure ratio (mPAP/dPAP) may match Φ in patients with pulmonary arterial hypertension (PAH) and in controls. METHODS In the first, theoretical part of the study, we discussed why our hypothesis is consistent with three known hemodynamic features of the pulmonary circulation: (1) the 0.61 slope of the mPAP vs sPAP relationship, (2) pulmonary artery pulse pressure and mPAP have an almost 1:1 ratio, and (3) the proportional relationship between sPAP, mPAP and dPAP. In the second part, fluid-filled pressures were analyzed in 981 incident, untreated PAH and high-fidelity pressures were also analysed in 44 historical controls (mPAP range 9-113 mmHg). Results In PAH (non-normal distribution), median values of sPAP/mPAP and mPAP/dPAP were 1.591 (98%Φ) and 1.559 (96%Φ), respectively. In controls (normal distribution), mean sPAP/dPAP and mPAP/dPAP were 1.572 (97%Φ) and 1.470 (91%Φ). In both PAH and controls, this was consistent with the Φ hypothesis assuming Conclusions In PAH and in controls, the fluctuations in sPAP and dPAP around mPAP exhibited a constant scaling factor matched to Φ. This remarkable property allows linkage of various empirical observations on pulmonary hemodynamics that were hitherto apparently unrelated. These findings warrant further confirmation in other types of PH and warrant explanation.