In simulation of cardiovascular processes and diseases patient-specific model parameters, such as constitutive properties, are usually not easy to obtain. Instead of using population mean values to perform "patient-specific" simulations, thereby neglecting the inter- and intra-patient variations present in these parameters, these uncertainties have to be considered in the computational assessment. However, due to limited computational resources and several shortcomings of traditional uncertainty quantification approaches, parametric uncertainties, modeled as random fields, have not yet been considered in patient-specific, nonlinear, large-scale, and complex biomechanical applications. Hence, the purpose of this study is twofold. First, we present an uncertainty quantification framework based on multi-fidelity sampling and Bayesian formulations. The key feature of the presented method is the ability to rigorously exploit and incorporate information from an approximate, low fidelity model. Most importantly, response statistics of the corresponding high fidelity model can be computed accurately even if the low fidelity model provides only a very poor approximation. The approach merely requires that the low fidelity model and the corresponding high fidelity model share a similar stochastic structure, i.e., dependence on the random input. This results in a tremendous flexibility in choice of the approximate model. The flexibility and capabilities of the framework are demonstrated by performing uncertainty quantification using two patient-specific, large-scale, nonlinear finite element models of abdominal aortic aneurysms. One constitutive parameter of the aneurysmatic arterial wall is modeled as a univariate three-dimensional, non-Gaussian random field, thereby taking into account inter-patient as well as intra-patient variations of this parameter. We use direct Monte Carlo to evaluate the proposed method and found excellent agreement with this reference solution. Additionally, the employed approach results in a tremendous reduction of computational costs, rendering uncertainty quantification with complex patient-specific nonlinear biomechanical models practical for the first time. Second, we also analyze the impact of the uncertainty in the input parameter on mechanical quantities typically related to abdominal aortic aneurysm rupture potential such as von Mises stress, von Mises strain and strain energy. Thus, providing first estimates on the variability of these mechanical quantities due to an uncertain constitutive parameter, and revealing the potential error made by assuming population averaged mean values in patient-specific simulations of abdominal aortic aneurysms. Moreover, the influence of correlation length of the random field is investigated in a parameter study using MC.

Multiple patient-specific parameters, such as wall thickness, wall strength, and constitutive properties, are required for the computational assessment of abdominal aortic aneurysm (AAA) rupture risk. Unfortunately, many of these quantities are not easily accessible and could only be determined by invasive procedures, rendering a computational rupture risk assessment obsolete. This study investigates two different approaches to predict these quantities using regression models in combination with a multitude of noninvasively accessible, explanatory variables. We have gathered a large dataset comprising tensile tests performed with AAA specimens and supplementary patient information based on blood analysis, the patients medical history, and geometric features of the AAAs. Using this unique database, we harness the capability of state-of-the-art Bayesian regression techniques to infer probabilistic models for multiple quantities of interest. After a brief presentation of our experimental results, we show that we can effectively reduce the predictive uncertainty in the assessment of several patient-specific parameters, most importantly in thickness and failure strength of the AAA wall. Thereby, the more elaborate Bayesian regression approach based on Gaussian processes consistently outperforms standard linear regression. Moreover, our study contains a comparison to a previously proposed model for the wall strength.

If computational models are ever to be used in high-stakes decision making in clinical practice, the use of personalized models and predictive simulation techniques is a must. This entails rigorous quantification of uncertainties as well as harnessing available patient-specific data to the greatest extent possible. Although researchers are beginning to realize that taking uncertainty in model input parameters into account is a necessity, the predominantly used probabilistic description for these uncertain parameters is based on elementary random variable models. In this work, we set out for a comparison of different probabilistic models for uncertain input parameters using the example of an uncertain wall thickness in finite element models of abdominal aortic aneurysms. We provide the first comparison between a random variable and a random field model for the aortic wall and investigate the impact on the probability distribution of the computed peak wall stress. Moreover, we show that the uncertainty about the prevailing peak wall stress can be reduced if noninvasively available, patient-specific data are harnessed for the construction of the probabilistic wall thickness model.

The present results indicate that in AAA, increased locally acting biomechanical conditions (stress and strain) involve increased synthesis of collagen and proteoglycans with increased failure tension. These findings confirm the presence of adaptive biological processes to maintain the mechanical stability of AAA wall.

Growth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

The aim of this paper is to give an overview of different multifidelity uncertainty quantification (UQ) schemes. Therefore, different views on multifidelity UQ approaches from a frequentist, Bayesian, and possibilistic perspective are provided and recent developments are discussed. Differences as well as similarities between the methods are highlighted and strategies to construct low‐fidelity models are explained. In addition, two state‐of‐the‐art examples to showcase the capabilities of these methods and the tremendous reduction of computational costs that can be achieved when using these approaches are provided.

Our results show for the first time that gene expressions of destabilizing factors within AAA tissue might be correlated to geometric and mechanical properties of the AAA wall. However, we found no influence of local mechanical conditions on gene expression of these factors. Therefore, these preliminary results are still ambiguous.

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