A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues From Digital Image Correlation...

Area of Science:

• Computational mechanics
• Biomaterials science
• Machine learning in engineering

Background:

• Biological tissue modeling traditionally relies on constitutive models, which require prior knowledge of material microstructure and specific model forms.
• Predicting tissue behavior under novel loading conditions remains a challenge for conventional approaches.

Purpose of the Study:

• To develop and evaluate a data-driven workflow for biological tissue modeling using neural operator learning.
• To compare the predictive performance of the data-driven approach against traditional finite element analysis with constitutive models.
• To enhance the generalizability of the data-driven model through physics-guided learning.

Main Methods:

• Construction of a material database from digital image correlation (DIC) measurements of porcine tricuspid valve tissue under biaxial stretching.
• Development of a neural operator learning model to predict displacement fields from loading inputs.
• Implementation of a physics-guided neural operator learning model incorporating partial physics constraints.

Main Results:

• The data-driven neural operator model demonstrated superior predictive performance (approximately one order of magnitude better) compared to conventional constitutive models on in-distribution data.
• The initial neural operator model showed reduced effectiveness on out-of-distribution loading ratios.
• Physics-guided neural operator learning improved extrapolative performance, particularly in the small-deformation regime.

Conclusions:

• Data-driven approaches, especially when augmented with sufficient data or partial physics constraints, offer a more effective alternative to traditional constitutive modeling for biological materials.
• Neural operator learning shows promise for modeling complex material responses without explicit microstructural information.
• Physics-guided machine learning can enhance the robustness and generalizability of data-driven models in computational mechanics.