Stochastic modeling of inhomogeneities in the aortic wall and uncertainty quantification using a Bayesian encoder–decoder surrogate

Abstract

Inhomogeneities in the aortic wall can lead to localized stress accumulations, possibly initiating dissection. In many cases, a dissection results from pathological changes such as fragmentation or loss of elastic fibers. But it has been shown that even the healthy aortic wall has an inherent heterogeneous microstructure. Some parts of the aorta are particularly susceptible to the development of inhomogeneities due to pathological changes, however, the distribution in the aortic wall and the spatial extent, such as size, shape and type, are difficult to predict. Motivated by this observation, we describe the heterogeneous distribution of elastic fiber degradation in the dissected aortic wall using a stochastic constitutive model. For this purpose, random field realizations, which model the stochastic distribution of degraded elastic fibers, are generated over a non-equidistant grid. The random field then serves as input for a uniaxial extension test of the pathological aortic wall, solved with the finite element method. To include the microstructure of the dissected aortic wall, a constitutive model developed in a previous study is applied, which also includes an approach to model the degradation of interlamellar elastic fibers. To then assess the uncertainty in the output stress distribution due to the proposed stochastic constitutive model, a convolutional neural network, specifically a Bayesian encoder–decoder, was used as a surrogate model that maps the random input fields to the output stress distribution obtained from the finite element analysis. The results show that the neural network is able to predict the stress distribution of the finite element analysis while also significantly reducing the computational time. In addition, this provides the probability for exceeding certain rupture stresses within the aortic wall, which could allow for the prediction of delamination or fatal rupture.