(D-131) Pulmonary Hemodynamic Simulation and Uncertainty Quantification using Surrogate Modeling

Introduction:: The pulmonary circulation is a high-flow, low-pressure system under normal cardiovascular conditions. However, common diseases such as left-heart failure produce a malicious biomechanical environment that alters pulmonary vascular and right heart function. A common complication is elevated pulmonary blood pressure, i.e., pulmonary hypertension, which can only be diagnosed via invasive right heart catheterization, typically months to years after disease onset. Tools that can link both pulmonary vascular structure from imaging data and dynamic hemodynamic measurements from catheterization or echocardiography will assist in diagnostics and early detection. Patient-specific hemodynamics models are one such tool, but typically accrue a high computational cost and simulation uncertainty. Hence, we use a polynomial chaos expansion (PCE) to capture uncertainties in an arteriovenous circulation model and develop a robust, efficient surrogate that can be run within seconds.


Materials and Methods:: The computational model links the large arteries and veins to an empirical, bifurcating microcirculation. There are 15 large pulmonary arteries and 12 large pulmonary veins, described by length, radii, and their connectivity, as documented in a prior study by Mynard et al. [1]. The bifurcating arterial and venous trees are connected using the structured tree model, as implemented by Bartolo et al. [2], which links the arteriovenous circulations via an admittance matrix. Blood flow in the large vessels is described by a one-dimensional mass conservation and momentum balance equation. The dynamics of the vessel walls are dictated by a linear elastic pressure-area relationship. A flow profile is prescribed as a boundary condition for the arteries while a left atrial pressure waveform is coupled to the outflow of the four large pulmonary veins.

We assume that the effective blood vessel stiffness is constant in the large arteries (k_A), large veins (k_V), and microcirculation (k_MV), that the radii scaling in the microcirculation (α, β, and r_min) are consistent in the arteriolar and venular compartments, and that the length-to-radius ratio in the arterial (l_rr^A) and venous (l_rr^V) microcirculation are distinct. In total, there are two large vessel stiffness parameters, one microcirculation stiffness, and five parameters describing the microcirculation geometry. Briefly, we use PCEs to calculate variance-based sensitivity indices for blood pressure (P), flow (Q), wall shear stress (WSS), and cyclic stretch (CS). In addition, we use the PCE as an efficient surrogate model for predicting hemodynamics.

Results, Conclusions, and Discussions:: We calculate the predictive uncertainty with respect to several hemodynamic outputs across the large arteries and veins. Uncertainty in the Main Pulmonary Artery (MPA) flow and pulmonary venous pressure is minimal since they are used as boundary conditions. As shown in Figure 1(a), the MPA pressure standard deviation (red) at diastole is 15 mmHg, whereas the systolic standard deviation is nearly 30 mmHg. The left superior pulmonary vein shows a similar flow uncertainty, with larger standard deviations during peak flow rates in Figure 1(b). Uncertainty in WSS in the MPA and left superior vein are shown in Figure 1(c-d). Arterial CS varied from 5-15%, whereas venous CS was consistently less than 2%. Sobol’ indices indicate that radii scaling parameters α and β are the most influential on P, Q, and WSS in the arteries and veins, as well as arterial CS, shown in Figure 2(b). The venous stiffness, k_V, is the most influential on venous CS. To test the accuracy of the PCE as a surrogate, we considered five out of sample pressure profiles as test data. The coefficient of determination (R²) was above 0.99 across all test datasets.



We utilize PCE as an efficient surrogate for calculating output uncertainty and model sensitivity. Whereas previous studies focus on single predictions of biomechanical stimuli such as WSS and CS, we investigated the plausible range of values that could be simulated in an arteriovenous hemodynamics model. Our results show that the branching of the microvasculature contributes the most to output uncertainty. This parallels our current understanding of pulmonary hypertension progression, as the pulmonary microvasculature is typically the first to undergo vascular remodeling. Our model has the potential to serve as a patient-specific tool, hence quantifying uncertainty in the parameter-to-output pipeline is necessary as the field moves towards in-silico medicine. Lastly, we show that PCEs can be used as an efficient surrogate model, thus reducing computation time from several minutes to less than a second. The uncertainties in WSS and CS provide a necessary range of values for conducting in-vitro endothelial cell shear and stretch experiments.




Acknowledgements (Optional): : This study was supported by the National Institutes of Health NIBIB grants R01HL154624 (NCC) and R01HL147590 (NCC). The project described was supported by the National Center for Research Resources and the National Center for Advancing Translational Sciences, National Institutes of Health, through Grant TL1 TR001415 (MJC). The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

References (Optional): : [1] Mynard, Jonathan P., Smolich. Joseph J. "One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation." Annals of biomedical engineering 43 (2015): 1443-1460.

[2] Bartolo, Michelle A., Qureshi, Muhammad U., Colebank, Mitchel J, Chesler, Naomi C., Olufsen, Mette S. "Numerical predictions of shear stress and cyclic stretch in pulmonary hypertension due to left heart failure." Biomechanics and Modeling in Mechanobiology 21.1 (2022): 363-381.