Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural network

Abstract

Aortic dissection progresses via delamination of the medial layer of the wall. Notwithstanding the complexity of this process, insight has been gleaned by studying in vitro and in silico the progression of dissection driven by quasistatic pressurization of the intramural space by fluid injection, which demonstrates that the differential propensity of dissection can be affected by spatial distributions of structurally significant interlamellar struts that connect adjacent elastic lamellae. In particular, diverse histological microstructures may lead to differential mechanical behavior during dissection, including the pressure-volume relationship of the injected fluid and the displacement field between adjacent lamellae. In this study, we develop a data-driven surrogate model for the delamination process for differential strut distributions using DeepONet, a new operator-regression neural network. The surrogate model is trained to predict the pressure-volume curve of the injected fluid and the damage progression field of the wall given a spatial distribution of struts, with in silico data generated with a phase-field finite element model. The results show that DeepONet can provide accurate predictions for diverse strut distributions, indicating that this composite branch-trunk neural network can effectively extract the underlying functional relationship between distinctive microstructures and their mechanical properties. More broadly,

A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data

“…Next, we provide an introduction to the vanilla 2 DeepONet. Although vanilla DeepONet has demonstrated good performance in diverse applications [20,40,41,42,43,44,45,46,47], here, we propose several extensions of DeepONet to achieve better accuracy and faster training.…”

“…In our dataset, the Reynolds number of the domain of integration spans from 1800 2 to 2322 2 , and the problem was solved for 59 different perturbation frequencies in the range [100, 125] with arbitrarily sampled phase. Moreover, the input function is defined on a mesh with resolution (20,47), and the output function is on a mesh with resolution (111, 47). Because the output functions in the dataset differ in amplitudes by more than two orders of magnitude, a weighted MSE is used, where each loss term is weighted by the the amplitude of each function.…”

“…A better strategy to compute the POD modes for problems with multiple scales need to be developed in the future. For FNO, because the input and outputs functions have different mesh resolution, we first use a linear interpolation to interpolate the input function from (20,47) to (111,47). FNO performs better than POD-DeepONet, but is much worse than DeepONet with Fourier features.…”

Analyses of internal structures and defects in materials using physics-informed neural networks

“…Emerging research reveals the profound untapped potential of physics-based, multidisciplinary, deep learning approaches with unprecedented opportunities for scientific and engineering advances in molecular analysis (4), design of materials with improved properties and performance (5,6) in structural and functional applications, and unique pathways for the characterization of properties of materials (7)(8)(9)(10)(11). To further realize this potential, broadly applicable methodologies in the area of NNs are needed to address a variety of issues that underpin deep learning analyses, governed by physical laws and guided by mathematical formulations.…”