Lumped‐parameter models of the pulmonary vasculature during the progression of pulmonary arterial hypertension

A longitudinal study of monocrotaline‐induced pulmonary arterial hypertension (PAH) was carried out in Sprague‐Dawley rats to investigate the changes in impedance (comprising resistance and compliance) produced by elevated blood pressure. Using invasively measured blood flow as an input, blood pressure was predicted using 3‐ and 4‐element Windkessel (3WK, 4WK) type lumped‐parameter models. Resistance, compliance, and inductance model parameters were obtained for the five different treatment groups via least‐squares errors. The treated animals reached levels of hypertension, where blood pressure increased two folds from control to chronic stage of PAH (mean pressure went from 24 ± 5 to 44 ± 6 mmHg, P < 0.0001) but blood flow remained overall unaffected. Like blood pressure, the wave‐reflection coefficient significantly increased at the advanced stage of PAH (0.26 ± 0.09 to 0.52 ± 0.09, P < 0.0002). Our modeling efforts revealed that resistances and compliance changed during the disease progression, where changes in compliance occur before the changes in resistance. However, resistance and compliance are not directly inversely related. As PAH develops, resistances increase nonlinearly (R (d) exponentially and R at a slower rate) while compliance linearly decreases. And while 3WK and 4WK models capture the pressure‐flow relation in the pulmonary vasculature during PAH, results from Akaike Information Criterion and sensitivity analysis allow us to conclude that the 3WK is the most robust and accurate model for this system. Ninety‐five percent confidence intervals of the predicted model parameters are included for the population studied. This work establishes insight into the complex remodeling process occurring in PAH.