Uncertainty quantification and sensitivity analysis during the development and validation of numerical artery models

Abstract

Increasing age and cardiovascular diseases lead to stiffening of the vasculature. Knowledge about an individual’s arterial stiffness gives insights into the current state of the cardiovascular system and it is considered to be a valuable diagnostic index. However, arterial stiffness cannot be measured directly. Numerical modelling based on measurements of flow and deformation in an individual’s artery enable an indirect means. Our research aims to develop a method to estimate the local arterial stiffness of an artery from non-invasive measurements through inverse modelling. Experimental measurement limitations and the unmeasurable nature of model input parameters lead to uncertainties in the model prediction. Uncertainty quantification and sensitivity analysis (UQSA) inform about how the model prediction is influenced by these uncertainties. Due to the computational expenses of 3D fluid-structure interaction (FSI) models, we reduced the model’s complexity to a 1D model. To verify the 3D-FSI implementation and validate the 1D implementation we performed simulated inflation tests and compared the results with analytical theory. 3D-FSI simulations were performed and compared to the 1D-model predictions for different simplification assumptions. To quantify the impact of uncertainties in input data, polynomial chaos expansion for UQSA was applied to the 1D-model. This analysis revealed the model input parameters which lead to the highest variability in model prediction. UQSA showed that variations in the Young’s modulus and the lumen radius lead to the largest variability in the 1D-model prediction. Thus, we focused in the validation process on the comparison between the the arterial wall behaviour between the 1D and the 3D-FSI model.