The sine transform is the sine qua non of the pulmonary and systemic pressure relationship

Assessment of therapeutic interventions in patients with pulmonary arterial hypertension (PAH) suffers from several commonly encountered limitations: (1) patient studies are often too small and short-term to provide definitive conclusions, (2) there is a lack of a universal set of metrics to adequately assess therapy and (3) while clinical treatments focus on management of symptoms, there remain many cases of early loss of life in a seemingly arbitrary distribution. Here we provide a unified approach to assess right and left pressure relationships in PAH and pulmonary hypertension (PH) patients by developing linear models informed by the observation of Suga and Sugawa that pressure generation in the ventricle (right or left) approximately follows a single lobe of a sinusoid. We sought to identify a set of cardiovascular variables that either linearly or via a sine transformation related to systolic pulmonary arterial pressure (PAPs) and systemic systolic blood pressure (SBP). Importantly, both right and left cardiovascular variables are included in each linear model. Using non-invasively obtained cardiovascular magnetic resonance (CMR) image metrics the approach was successfully applied to model PAPs in PAH patients with an r(2) of 0.89 (p < 0.05) and SBP with an r(2) of 0.74 (p < 0.05). Further, the approach clarified the relationships that exist between PAPs and SBP separately for PAH and PH patients, and these relationships were used to distinguish PAH vs. PH patients with good accuracy (68%, p < 0.05). An important feature of the linear models is that they demonstrate that right and left ventricular conditions interact to generate PAPs and SBP in PAH patients, even in the absence of left-sided disease. The models predicted a theoretical right ventricular pulsatile reserve that in PAH patients was shown to be predictive of the 6 min walk distance (r(2) = 0.45, p < 0.05). The linear models indicate a physically plausible mode of interaction between right and left ventricles and provides a means of assessing right and left cardiac status as they relate to PAPs and SBP. The linear models have potential to allow assessment of the detailed physiologic effects of therapy in PAH and PH patients and may thus permit cross-over of knowledge between PH and PAH clinical trials.