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Recurrent neural network to predict hyperelastic constitutive behaviors of the skeletal muscle

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Abstract

Hyperelastic constitutive laws have been commonly used to model the passive behavior of the human skeletal muscle. Despite many efforts, the use of accurate finite element formulations of hyperelastic constitutive laws is still time-consuming for a real-time medical simulation system. The objective of the present study was to develop a deep learning model to predict the hyperelastic constitutive behaviors of the skeletal muscle toward a fast estimation of the muscle tissue stress.

A finite element (FE) model of the right psoas muscle was developed. Neo-Hookean and Mooney-Rivlin laws were used. A tensile test was performed with an applied body force. A learning database was built from this model using an automatic probabilistic generation process. A long-short term memory (LSTM) neural network was implemented to predict the stress evolution of the skeletal muscle tissue. A hyperparameter tuning process was conducted. Root mean square error (RMSE) and associated relative error was quantified to evaluate the precision of the predictive capacity of the developed deep learning model. Pearson correlation coefficients (R) was also computed.

The nodal displacements and the maximal stresses range from 70 to 227 mm and from 2.79 to 5.61 MPa for Neo-Hookean and Monney-Rivlin laws, respectively. Regarding the LSTM predictions, the RMSE ranges from 224.3 ± 3.9 Pa (8%) to 227.5 \(\pm\) 5.7 Pa (4%) for Neo-Hookean and Monney-Rivlin laws, respectively. Pearson correlation coefficients (R) of 0.78 \(\pm\) 0.02 and 0.77 \(\pm\) 0.02 were obtained for Neo-Hookean and Monney-Rivlin laws, respectively.

The present study showed that, for the first time, the use of a deep learning model can reproduce the time-series behaviors of the complex FE formulations for skeletal muscle modeling. In particular, the use of a LSTM neural network leads to a fast and accurate surrogate model for the in silico prediction of the hyperelastic constitutive behaviors of the skeletal muscle. As perspectives, the developed deep learning model will be integrated into a real-time medical simulation of the skeletal muscle for prosthetic socket design and childbirth simulator.

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Funding

This present study was funded by the Métropole Européenne de Lille (MEL) and the I-SITE ULNE (Université Lille Nord Europe).

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  1. Univ. Lille, CNRS, Centrale Lille, UMR 9013, LaMcube, Laboratoire de Mécanique, Multiphysique, Multiéchelle, 59655, Villeneuve d’Ascq Cedex, F-59000, Lille, France

    Abbass Ballit & Tien-Tuan Dao

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Correspondence to Tien-Tuan Dao.

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Ballit, A., Dao, TT. Recurrent neural network to predict hyperelastic constitutive behaviors of the skeletal muscle. Med Biol Eng Comput 60, 1177–1185 (2022). https://doi.org/10.1007/s11517-022-02541-z

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