Automated model discovery for muscle using constitutive recurrent neural networks

Area of Science:

• Computational mechanics
• Biomaterials science
• Machine learning in engineering

Background:

• Soft biological tissues exhibit complex mechanical behavior, with stiffness dependent on both deformation and deformation rate.
• Traditional modeling involves selecting and fitting parameters of time-dependent constitutive models to experimental data.
• Existing machine learning methods, like feed-forward neural networks, excel at modeling hyperelasticity but struggle with the history-dependent nature of viscoelasticity.

Purpose of the Study:

• To develop a novel machine learning framework capable of simultaneously discovering constitutive models and parameters for viscoelastic soft tissues.
• To integrate hyperelastic and viscoelastic modeling using a hybrid neural network architecture inspired by quasi-linear viscoelasticity.
• To validate the model's performance against established methods using experimental data from passive skeletal muscle.

Main Methods:

• A hybrid neural network architecture combining a feed-forward network for hyperelastic response and a recurrent neural network for viscous response was developed.
• The network was trained using unconfined compression relaxation experimental data from passive skeletal muscle.
• The discovered model was compared against a Neo-Hookean Standard Linear Solid model, an advanced mechanics-based model, and a vanilla recurrent neural network.

Main Results:

• The novel constitutive recurrent neural network successfully discovered a Mooney-Rivlin type energy function and a Prony-series type relaxation function.
• The discovered model demonstrated superior prediction accuracy on unseen data compared to the Neo-Hookean Standard Linear Solid and vanilla recurrent neural network.
• The model satisfies basic physical principles and generalizes well, even with limited experimental data.

Conclusions:

• Constitutive recurrent neural networks offer a powerful, data-driven approach for autonomously discovering accurate models and parameters for soft viscoelastic tissues.
• This rheologically-informed network architecture effectively captures both time-independent and time-dependent mechanical behaviors.
• The developed framework advances the modeling of biological tissue mechanics, offering a robust alternative to traditional methods.