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 uni-axial extension test of the pathological aortic wall, solved with the finite-element (FE) 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 inter-lamellar elastic fibers. Then to assess the uncertainty in the output stress distribution due to this 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 FE analysis. The results show that the neural network is able to predict the stress distribution of the FE analysis while significantly reducing the computational time. In addition, it provides the probability for exceeding critical stresses within the aortic wall, which could allow for the prediction of delamination or fatal rupture.

arXiv commentPreprint. 55 pages, 8 figures

References in corpus (15)

• Automated Design of Deep Learning Methods for Biomedical Image Segmentation
• Variational Inference: A Review for Statisticians
• A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges
• Domain Adaptation for Medical Image Analysis: A Survey
• Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
• PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain
• The importance of transparency and reproducibility in artificial intelligence research
• Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification
• Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
• 3D Convolutional Encoder-Decoder Network for Low-Dose CT via Transfer Learning from a 2D Trained Network
• A Comparison of Optimization Algorithms for Deep Learning
• Simulation of hyperelastic materials in real-time using Deep Learning
• Deep learning-based surrogate model for 3-D patient-specific computational fluid dynamics
• Numerical Simulation of Non-Gaussian Random Fields with Prescribed Correlation Structure
• Numerical Simulation of Non-Gaussian Random Fields with Prescribed Marginal Distributions and Cross-Correlation Structure II: Multivariate Random Fields

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