The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms

Abstract

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.

Fast uncertainty quantification of activation sequences in patient‐specific cardiac electrophysiology meeting clinical time constraints

“…The key aspect for applying multifidelity methods is therefore the availability of fast low‐fidelity models. Typical examples are the following: • A mathematical model of expert opinions or empirical evidence . In this case, the challenge is to create a model that in analytic form can make use of the full stochastic input and to quantify its effect on the output. • Surrogate models, fitting data generated by the high‐fidelity model at a small number of given input samples .…”

Multifidelity approaches for uncertainty quantification

“…Perhaps more importantly, other Bayesian regression approaches are easier to implement or third party libraries or packages can be used, facilitating the setup of a BMFMC framework. GPs are one example and state‐of‐the‐art results have been obtained with both techniques.7, In addition, the use of GPs as a regression approach facilitates a comparison between the BMFMC approach and multifidelity GP emulators, which will follow in the next section.…”

“…Since the wall thickness is modeled as random field, the thickness becomes a function of spatial location, here denoted by , and a number of random variables collectively denoted as x . The realizations of the random field are computed with a series expansion approach, as described in Biehler and Wall, which leads to a stochastic dimension of 5520. We adjust the geometry of the models at run‐time using a custom‐made algorithm in our research code.…”

“…GPs are one example and state-of-the-art results have been obtained with both techniques. [7,48] In addition, the use of GPs as a regression approach facilitates a comparison between the BMFMC approach and multifidelity GP emulators, which will follow in the next section.…”

Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

“…By adopting a stochastic framework, model parameters are sampled from appropriate probability distributions which are either assumed, relying on existing literature and clinical data, or assimilated from available patient-specific data.Recently, UQ has gained traction in the field of cardiovascular modeling, primarily utilizing UQ techniques centered around a single model complexity, primarily three-dimensional computational fluid dynamics (CFD) simulations or lower complexity one-dimensional models. Recent studies have investigated the impact of geometry and boundary condition parameters on coronary fractional flow reserve [28], demonstrated a multi-resolution approach to quantify boundary condition uncertainties [29] and in conjugation with random fields [30] for coronary artery bypass grafts, and performed stochastic collocation in a one-dimensional arterial network [31], along with others [32][33][34][35][36][37][38][39].Several challenges arise when quantifying uncertainty in cardiovascular simulations. First, there are typically multiple sources of uncertainty to account for and propagate through the model.…”