Golden Ratio and the Proportionality Between Pulmonary Pressure Components in Pulmonary Arterial Hypertension
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".