Uncertainty quantification of inflow boundary condition and proximal arterial stiffness-coupled effect on pulse wave propagation in a vascular network.

Abstract

This work aims at quantifying the effect of inherent uncertainties from cardiac output on the sensitivity of a human compliant arterial network response based on stochastic simulations of a reduced-order pulse wave propagation model. A simple pulsatile output form is used to reproduce the most relevant cardiac features with a minimum number of parameters associated with left ventricle dynamics. Another source of significant uncertainty is the spatial heterogeneity of the aortic compliance, which plays a key role in the propagation and damping of pulse waves generated at each cardiac cycle. A continuous representation of the aortic stiffness in the form of a generic random field of prescribed spatial correlation is then considered. Making use of a stochastic sparse pseudospectral method, we investigate the sensitivity of the pulse pressure and waves reflection magnitude over the arterial tree with respect to the different model uncertainties. Results indicate that uncertainties related to the shape and magnitude of the prescribed inlet flow in the proximal aorta can lead to potent variation of both the mean value and standard deviation of blood flow velocity and pressure dynamics due to the interaction of different wave propagation and reflection features. Lack of accurate knowledge in the stiffness properties of the aorta, resulting in uncertainty in the pulse wave velocity in that region, strongly modifies the statistical response, with a global increase in the variability of the quantities of interest and a spatial redistribution of the regions of higher sensitivity. These results will provide some guidance in clinical data acquisition and future coupling of arterial pulse wave propagation reduced-order model with more complex beating heart models.