Denis Chemla1, David Boulate2, Jason Weatherald3, Edmund M T Lau4, Pierre Attal5, Laurent Savale6, David Montani6, Elie Fadel2, Olaf Mercier2, Olivier Sitbon6, Marc Humbert6, Philippe Hervé7. 1. Service d'Explorations Fonctionnelles Multidisciplinaires Bi-site Antoine Béclère - Le Kremlin-Bicêtre, AP-HP, Le Kremlin-Bicêtre, France; Université Paris-Sud, Faculté de Médecine, Université Paris-Saclay, Le Kremlin-Bicêtre, France; INSERM UMR_S 999, Hôpital Marie Lannelongue, Le Plessis-Robinson, France. Electronic address: denis.chemla@aphp.fr. 2. Department of Thoracic and Vascular Surgery and Heart-Lung Transplantation, Marie Lannelongue Hospital, Le Plessis-Robinson, France. 3. Department of Medicine, University of Calgary, Division of Respirology, and Libin Cardiovascular Institue of Alberta, Calgary, Alberta, Canada. 4. Department of Respiratory Medicine, Royal Prince Alfred Hospital, University of Sydney, Missenden Road, Camperdown, Australia. 5. Department of Otolaryngology-Head and Neck Surgery, Shaare-Zedek Medical Center and Hebrew University Medical School, Jerusalem, Israel. 6. Université Paris-Sud, Faculté de Médecine, Université Paris-Saclay, Le Kremlin-Bicêtre, France; INSERM UMR_S 999, Hôpital Marie Lannelongue, Le Plessis-Robinson, France; Service de Pneumologie, Hôpital Bicêtre, AP-HP, Le Kremlin-Bicêtre, France. 7. INSERM UMR_S 999, Hôpital Marie Lannelongue, Le Plessis-Robinson, France; Department of Thoracic and Vascular Surgery and Heart-Lung Transplantation, Marie Lannelongue Hospital, Le Plessis-Robinson, France.
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 control patients. METHODS: In the first, theoretical part of the study, we discuss 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 among sPAP, mPAP, and dPAP. In the second part of the study, fluid-filled pressures were analyzed in 981 incident, untreated PAH and high-fidelity pressures were also analyzed in 44 historical control patients (mPAP range, 9-113 mm Hg). 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 control patients (normal distribution), mean sPAP/mPAP and mPAP/dPAP were 1.572 (97%Φ) and 1.470 (91%Φ), respectively. In both PAH and control patients, this was consistent with the Φ hypothesis, assuming < 1 mm Hg error in estimation of sPAP, mPAP, and dPAP on average. CONCLUSIONS: In PAH and in control patients, 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 pulmonary hypertension and warrant explanation.
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 control patients. METHODS: In the first, theoretical part of the study, we discuss 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 among sPAP, mPAP, and dPAP. In the second part of the study, fluid-filled pressures were analyzed in 981 incident, untreated PAH and high-fidelity pressures were also analyzed in 44 historical control patients (mPAP range, 9-113 mm Hg). 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 control patients (normal distribution), mean sPAP/mPAP and mPAP/dPAP were 1.572 (97%Φ) and 1.470 (91%Φ), respectively. In both PAH and control patients, this was consistent with the Φ hypothesis, assuming < 1 mm Hg error in estimation of sPAP, mPAP, and dPAP on average. CONCLUSIONS: In PAH and in control patients, 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 pulmonary hypertension and warrant explanation.