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.

The effects of clinically‐derived parametric data uncertainty in patient‐specific coronary simulations with deformable walls

“…19,20 In this context, several one-dimensional cardiovascular models, assuming blood as a Newtonian fluid and fully developed, axisymmetric flow inside a cylindrical vessel have been employed previously to demonstrate successful integration of UQ in cardiovascular modeling. Taking advantage of the low computational cost of one-dimensional hemodynamic models, several studies discussed the effect of variability in constitutive model parameters, 21 arterial wall stiffness, inlet velocity, 22 geometry, resistance, and pressure, 23 and assessment of global sensitivity. One-dimensional models are however limited when one wishes to understand and quantify realistic flow patterns and local flow features.…”

Reduced‐order modeling of hemodynamics across macroscopic through mesoscopic circulation scales

“…Inspired by earlier approaches, [ 17,18 ] authors of the present document have decided to capitalize on the numerical solver documented in our previous studies and inherited for the case of convectiondominated macroscale arteries. [ 5,7 ] Instead of domain-decomposing the network, in order to select most efficient numerical schemes depending on flow regimes, we have instead treated the network as a whole and computationally improved our solver to handle the various blood flow scales of our system. As explained later, much efforts have been dedicated to time-stepping tuning and memory constraints originating from the microcirculation.…”

“…One-dimensional ROM are commonly used to simulate convection-dominated blood flow for which pulse waves propagate in large elastic arteries. [ 21,6,7 ] They rely on a fluid-structure interaction mathematical framework that is much simplified when assumptions of Newtonian properties, linear elasticity (and to some extent nonlinear viscoelasticity) and homogeneous geometry are made for the blood fluid, the vessel walls mechanical response and the circulation network, respectively. They predict hemodynamic quantities with satisfactory accuracy and their low computational cost enables the simulation of broad arterial networks.…”

Computational Model for the Generalised Dispersion of Synovial Fluid

“…The generalized dispersion model is very useful and valid for all time, for examples of biomedical engineering, namely coronary artery diseases [CAD] and synovial joints [12]. In CAD The suspended particles may execute microcirculation in dispersing through the endothelium.…”