# Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate

arXiv: https://arxiv.org/abs/2202.10244 · HTML: https://mlsanity.com/paper/2202.10244/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 134 references that are in the map.
- First posted on arXiv 21 Feb 2022.

## Builds on (most cited first, 30 of 32)

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- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
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- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Domain Adaptation for Medical Image Analysis: A Survey](https://mlsanity.com/paper/2102.09508/) (2021)
- [Embracing Imperfect Datasets: A Review of Deep Learning Solutions for Medical Image Segmentation](https://mlsanity.com/paper/1908.10454/) (2019)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [The One Hundred Layers Tiramisu: Fully Convolutional DenseNets for Semantic Segmentation](https://mlsanity.com/paper/1611.09326/) (2016)
- [Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification](https://mlsanity.com/paper/1802.00850/) (2018)
- [Optimization for deep learning: theory and algorithms](https://mlsanity.com/paper/1912.08957/) (2019)
- [3D Convolutional Encoder-Decoder Network for Low-Dose CT via Transfer Learning from a 2D Trained Network](https://mlsanity.com/paper/1802.05656/) (2018)
- [Deep Learning for Computational Chemistry](https://mlsanity.com/paper/1701.04503/) (2017)
- [Simulation of hyperelastic materials in real-time using Deep Learning](https://mlsanity.com/paper/1904.06197/) (2019)
- [A Review of Deep Learning with Special Emphasis on Architectures, Applications and Recent Trends](https://mlsanity.com/paper/1905.13294/) (2019)
- [A Comparison of Optimization Algorithms for Deep Learning](https://mlsanity.com/paper/2007.14166/) (2020)

## Built on by (most cited first, 2 of 2)

- [A connection between probability, physics and neural networks](https://mlsanity.com/paper/2209.12737/) (2022)
- [Stochastic PDE representation of random fields for large-scale Gaussian process regression and statistical finite element analysis](https://mlsanity.com/paper/2305.13879/) (2023)

## Abstract (arXiv)

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.