Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model

TL;DR

This study develops a stochastic modeling approach to quantify uncertainties in arterial wall parameters within blood flow simulations, highlighting the impact of viscoelastic properties and validating against patient data.

Contribution

It introduces a novel uncertainty quantification framework for viscoelastic parameters in arterial hemodynamics using spectral stochastic collocation methods.

Findings

Pressure waveform predictions are highly sensitive to viscosity uncertainties.

The methodology's predictions align well with in-vivo patient data.

Viscoelastic modeling significantly affects pressure variability estimates.

Abstract

This work aims at identifying and quantifying uncertainties related to elastic and viscoelastic parameters, which characterize the arterial wall behavior, in one-dimensional modeling of the human arterial hemodynamics. The chosen uncertain parameters are modeled as random Gaussian-distributed variables, making stochastic the system of governing equations. The proposed methodology is initially validated on a model equation, presenting a thorough convergence study which confirms the spectral accuracy of the stochastic collocation method and the second-order accuracy of the IMEX finite volume scheme chosen to solve the mathematical model. Then, univariate and multivariate uncertain quantification analyses are applied to the a-FSI blood flow model, concerning baseline and patient-specific single-artery test cases. A different sensitivity is depicted when comparing the variability of flow rate and velocity waveforms to the variability of pressure and area, the latter ones resulting much more sensitive to the parametric uncertainties underlying the mechanical characterization of vessel walls. Simulations performed considering both the simple elastic and the more realistic viscoelastic constitutive law show that the great uncertainty of the viscosity parameter plays a major role in the prediction of pressure waveforms, enlarging the confidence interval of this variable. In-vivo recorded patient-specific pressure data falls within the confidence interval of the output obtained with the proposed methodology and expectations of the computed pressures are comparable to the recorded waveforms.