Probabilistic noninvasive prediction of wall properties of abdominal aortic aneurysms using Bayesian regression

Abstract

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.

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

“…The simpler approach models the constitutive parameters as a spatially constant random variable, which follows a prescribed probability distribution, while thus neglecting spatial variability. A lognormal distribution was found to provide a good description to experimental measurements of the thickness . Another way of stating this is that the wall thickness abides by a lognormal distribution where μ t and σ t denote the mean and standard deviation of the normal distribution.…”

“…For this material, a bulk modulus with ν =0.49 was used and η =−2. According to the results by Biehler et al, which are based on 218 uniaxial tensile test samples from 80 patients, the following values were chosen for the constitutive parameters α =0.121 MPa and β =2.98 MPa. While the constitutive parameters of ILT and AAA wall are also afflicted with considerable uncertainties, the restriction to an uncertain wall thickness is made in this work for ease of exposition.…”

“…Intrapatient variability is shown by squares in the same color, which indicate measurements from specimens that were excised from the same patient. Taken from Biehler et al…”

“…Subsequently, the procedure for the estimation of the correlation length is explained. Model A is a lognormal random field model based on fitting a Gaussian distribution to study population thickness measurements of the logarithm of the wall thickness, ie, the data shown in Figure . The resulting lognormal random field has a spatially constant mean function, ie, m ( x ; θ m )=0.4434.…”

Challenges of order reduction techniques for problems involving polymorphic uncertainty

“…The parameters as well as the type of probability distribution is typically inferred from ex‐vivo data or elicited from experts. Another option is to use probabilistic machine learning techniques to predict parameter distributions from noninvasively available data . In order to propagate the uncertainty through the model efficiently, we use a Gaussian process‐based surrogate model which is trained on a set of 200 optimal Latin Hyper Cube training samples.…”