Parameter inference in a computational model of haemodynamics in pulmonary hypertension

Figure 1.. Data processing. Dynamic data from the right atrium (RA), right ventricle (RV) and main pulmonary artery (PA) for each patient are digitized from right heart catheterization recordings and used for model calibration.

Figure 2.. Model schematic. Follows an electrical circuit analogue. The model has eight compartments: the systemic and pulmonary arteries and veins, two atria and two ventricles. Each compartment is modelled as compliant and is separated by a resistor element. The right atrium, right ventricle and pulmonary arteries (red boxes) have both dynamic and static data. The pulmonary veins and systemic arteries have only static data. RHC, right heart catheterization; CO, cardiac output.

Figure 3.. Heart chamber elastance function. Representative elastance function for the atrial (red) and ventricular (blue) heart chambers. Timing parameters are shown above their respective phases of the cardiac cycle. Note that ventricular isovolumic contraction occurs while the atrium is still relaxing.

Figure 4.. Sensitivity analysis. Parameter ranking based on a local sensitivity analysis using either r1 (a) or r2 (b). Each patient is plotted by a different colour. The parameter order is based on median sensitivity across all patients. Average first order (Si) and total order (STi) Sobol’ indices using either r1 or r2 (c). Average parameter ranking based on (STi) magnitude for either residual are shown in (d). The horizontal dashed lines separate influential (above) and non-influential (below) parameters. Green boxes highlight parameters used for r1 and red boxes are additional parameters included in r2.

Figure 5.. Multi-start Inference. For each patient, each subset is tested for identifiability using eight randomized starting guesses within ±20% of the nominal value. Coefficient of variance (CoV) for the final parameter sets using (a) r1 or (b) r2 provide a CoV below 10%.

Figure 6.. Changes in parameters due to PH. Box and whisker plots showing quantiles and outliers for the estimated parameters. Results show the relative difference from the normotensive parameters.

Figure 7.. Hyperbolic Rp-Cpa relationship. Optimal values of Rp and Cpa for the normotensive (black) and PH (red) patients. The best-fit curve is given by Cpa = 0.6518/(0.1005 + Rp), and is similar to previous findings using isolated Windkessel models [44]. A PVR ≥ 3 Wood units (3 WU=0.18, mmHg s ml−1) is considered in the PH range (dashed line).

Figure 8.. Optimal model predictions. (a) Optimal model fits for pressure, pi (mmHg) and cardiac output, CO (l min−1) using either r1 (dotted line) or r2 (solid line) compared with the data for patient 7. (b) simulated pressure-volume loops in the ventricles and atria using residual 1 (dotted line) and residual 2 (solid line) for the dataset from patient 7.

Figure 9.. Simulated pressure–volume loops. Pressure–volume loops in the normotensive (norm) and all nine PH patients are contrasted. Model predictions include (a) left atrial, (b), right atrial, (c) left ventricular and (d) right ventricular pressure–volume loops.

Figure 10.. Output uncertainty. Uncertainty in the model outputs for pressure, pi (mmHg) and cardiac output, CO (l min−1) using either r1 (a) or r2 (b) for the quantity of interest.