Unsupervised full-field Bayesian inference of orthotropic hyperelasticity from a single biaxial test: a myocardial case study

2025-10-10

AI Summary

Traditional multimodal tissue mechanical testing requires multiple specimens and complex loading protocols, rendering constitutive parameter identification susceptible to inter-specimen variability and operator-induced damage. To address this, we propose an unsupervised, full-field Bayesian inference framework based on a single non-uniform biaxial stretch experiment. This work pioneers the integration of the EUCLID method with Bayesian statistics for automated constitutive discovery and uncertainty quantification in orthotropic hyperelastic materials—such as myocardial tissue. The framework synergistically combines 3D continuum mechanics modeling, unsupervised machine learning, and full-field deformation field analysis, enabling robust parameter inversion from a single experimental dataset alone. Validation across multiple noise levels demonstrates high fidelity between inferred parameters and ground truth, accompanied by rigorous credibility intervals. The approach significantly enhances robustness, reproducibility, and experimental efficiency in soft tissue biomechanics.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Fully capturing this behavior in traditional homogenized tissue testing requires the excitation of multiple deformation modes, i.e. combined triaxial shear tests and biaxial stretch tests. Inherently, such multimodal experimental protocols necessitate multiple tissue samples and extensive sample manipulations. Intrinsic inter-sample variability and manipulation-induced tissue damage might have an adverse effect on the inversely identified tissue behavior. In this work, we aim to overcome this gap by focusing our attention to the use of heterogeneous deformation profiles in a parameter estimation problem. More specifically, we adapt EUCLID, an unsupervised method for the automated discovery of constitutive models, towards the purpose of parameter identification for highly nonlinear, orthotropic constitutive models using a Bayesian inference approach and three-dimensional continuum elements. We showcase its strength to quantitatively infer, with varying noise levels, the material model parameters of synthetic myocardial tissue slabs from a single heterogeneous biaxial stretch test. This method shows good agreement with the ground-truth simulations and with corresponding credibility intervals. Our work highlights the potential for characterizing highly nonlinear and orthotropic material models from a single biaxial stretch test with uncertainty quantification.

Problem

• Inferring orthotropic hyperelasticity from single biaxial tests using Bayesian inference
• Overcoming multi-sample variability in traditional tissue mechanical testing
• Quantifying material parameters with uncertainty from heterogeneous deformation profiles

Innovation

• Bayesian inference for orthotropic hyperelasticity identification
• Unsupervised parameter discovery from single biaxial test
• Full-field heterogeneous deformation profiles enable characterization