Technical Brief

Bridging Finite Element and Machine Learning Modeling: Stress Prediction of Arterial Walls in Atherosclerosis

[+] Author and Article Information
Ali Madani

Molecular Cell Biomechanics Laboratory,
Department of Bioengineering,
University of California,
Berkeley, CA 94720;
Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720

Ahmed Bakhaty, Yara Mubarak

Molecular Cell Biomechanics Laboratory,
Department of Bioengineering,
University of California,
Berkeley, CA 94720;
Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720;
Department of Civil Engineering,
University of California,
Berkeley, CA 94720

Jiwon Kim

Molecular Cell Biomechanics Laboratory,
Department of Bioengineering,
University of California,
Berkeley, CA 94720;
Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720;
Department of Electrical Engineering and Computer Science,
University of California,
Berkeley, CA 94720

Mohammad R. K. Mofrad

Molecular Cell Biomechanics Laboratory,
Department of Bioengineering,
University of California,
Berkeley, CA 94720;
Department of Mechanical Engineering,
University of California,
208A Stanley Hall #1762,
Berkeley, CA 94720-1762;
Molecular Biophysics and Integrative Bioimaging Division,
Lawrence Berkeley National Lab,
Berkeley, CA 94720
e-mail: mofrad@berkeley.edu

1Corresponding author.

Manuscript received December 4, 2018; final manuscript received March 23, 2019; published online May 6, 2019. Assoc. Editor: Seungik Baek.

J Biomech Eng 141(8), 084502 (May 06, 2019) (9 pages) Paper No: BIO-18-1518; doi: 10.1115/1.4043290 History: Received December 04, 2018; Revised March 23, 2019

Finite element and machine learning modeling are two predictive paradigms that have rarely been bridged. In this study, we develop a parametric model to generate arterial geometries and accumulate a database of 12,172 2D finite element simulations modeling the hyperelastic behavior and resulting stress distribution. The arterial wall composition mimics vessels in atherosclerosis–a complex cardiovascular disease and one of the leading causes of death globally. We formulate the training data to predict the maximum von Mises stress, which could indicate risk of plaque rupture. Trained deep learning models are able to accurately predict the max von Mises stress within 9.86% error on a held-out test set. The deep neural networks outperform alternative prediction models and performance scales with amount of training data. Lastly, we examine the importance of contributing features on stress value and location prediction to gain intuitions on the underlying process. Moreover, deep neural networks can capture the functional mapping described by the finite element method, which has far-reaching implications for real-time and multiscale prediction tasks in biomechanics.

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Grahic Jump Location
Fig. 1

Prediction of atherosclerotic vessel stress with machine learning (ML) models trained on finite element method FEM simulation data: (a) mechanistic and statistical methods can be used for various continuum mechanics problems, (b) atherosclerosis can cause the buildup of plaque in blood vessels as shown, (c) an example idealized geometry of a 2D cross section of an atherosclerotic vessel with vessel wall, fibrous plaque, lipid pool, calcium deposit, and lumen structures defined. Geometries are randomly generated to create a database of FEM simulations, and (d) an example stress distribution generated by utilizing FEM. The input and output information are utilized to train ML models for prediction tasks such as maximum von Mises stress.

Grahic Jump Location
Fig. 2

Model architecture of five approaches taken for training a supervised deep learning model. Approach number ranges from 1 to 5 from top to bottom. Left-half darkly shaded boxes/circles (or red coloring) denotes input data fed to network. Right-half darkly shaded boxes/circles (or blue coloring) denotes output data used for loss calculation.

Grahic Jump Location
Fig. 3

Deep learning can accurately predict physiologically relevant indicators (maximum von Mises stress and location) for a given vessel geometry and pressure: (a) training and validation loss over 35 epochs displaying convergence and behavior of model training, (b) normalized maximum von Mises stress values for the held-out test set and predictions by the ML model, (c) 2D heat map of coordinate location of maximum von Mises stress over all the held-out test set samples, (d) 2D heat map of predicted locations of maximum von Mises stress on the held-out test set

Grahic Jump Location
Fig. 4

Comparative studies on varying baseline models and training dataset size: (a) deep learning model outperforms other baseline and machine learning strategies and (b) varying amounts of data are utilized for training the same model to examine performance versus data size



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