Abstract

We propose a framework for assessing closed loop effects from vasodilator treatment for pulmonary hypertension (PH), i.e. high blood pressure in the lungs, a serious and potentially fatal disorder. PH is diagnosed using invasive right heart catheterization (RHC) and typically treated by administrating vasodilators, i.e. drugs that dilate pulmonary arteries causing the pulmonary arterial pressure to decrease. Closed loop effects occur when an intervention, e.g. treatment administration, based on predictions from a calibrated model affects the initial assumptions of the model, e.g. the patient's physiology, however the model cannot be re-calibrated. That might be due to calibration requiring exposing the patient to invasive treatments, such as RHC. We apply a 1D fluid dynamic mathematical model with structured tree boundary condition, which predicts pressure and flow for a given pulmonary arterial network and parameters. The complexity of the model leads to challenging problems related to parameter identifiability. Our first contribution is proposing a framework integrating mathematical modelling, data availability at initial vs. follow-up visits, and statistical uncertainty quantification (UQ). Second, we demonstrate how to select subsets of parameters to be inferred at different visits that are practically identifiable, influential, and clinically relevant. The selection is informed by the results from numerical optimization, sensitivity analysis, and parameter interpretability. Third, we design an UQ study in which deterministic model outputs are perturbed by realistic noise. In contrast to previous studies using IID perturbations, we use non-stationary Gaussian processes fitted to empirical mouse data. This corrects for the mismatch between the model and the data. In our frequentist approach we infer the parameters for multiple perturbed datasets covering a broad range of physiological profiles. Follow-up results show that we recover the general patterns of the true pressure signals and match the systolic and diastolic values. We correctly predict PH for 76% of the datasets.