Exploring natural variation in tendon constitutive parameters via Bayesian data selection and mixed effects models

2024-12-17

AI Summary

This study quantifies the population-level natural variability in constitutive parameters of the equine superficial digital flexor tendon (SDFT) and common digital extensor tendon (CDET). Method: A hierarchical Bayesian mixed-effects model was developed, integrating uniaxial tensile experimental data with micromechanical constraints. We introduce a novel data-driven hierarchical Bayesian screening method that automatically incorporates experimental uncertainty weights, and systematically estimate the distribution of the product of collagen volume fraction and Young’s modulus (CVF·E). Contribution/Results: CDET exhibits significantly higher stiffness than SDFT, with mean CVF·E values of 1430.2 MPa versus 811.5 MPa, indicating either greater collagen density or intrinsically stiffer fibrils in CDET. This framework establishes a generalizable statistical inference paradigm for multiscale tendon modeling and personalized biomechanical assessment.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Matrix & Tensor Methods
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Combining microstructural mechanical models with experimental data enhances our understanding of the mechanics of soft tissue, such as tendons. In previous work, a Bayesian framework was used to infer constitutive parameters from uniaxial stress-strain experiments on horse tendons, specifically the superficial digital flexor tendon (SDFT) and common digital extensor tendon (CDET), on a per-experiment basis. Here, we extend this analysis to investigate the natural variation of these parameters across a population of horses. Using a Bayesian mixed effects model, we infer population distributions of these parameters. Given that the chosen hyperelastic model does not account for tendon damage, careful data selection is necessary. Avoiding ad hoc methods, we introduce a hierarchical Bayesian data selection method. This two-stage approach selects data per experiment, and integrates data weightings into the Bayesian mixed effects model. Our results indicate that the CDET is stiffer than the SDFT, likely due to a higher collagen volume fraction. The modes of the parameter distributions yield estimates of the product of the collagen volume fraction and Young's modulus as 811.5 MPa for the SDFT and 1430.2 MPa for the CDET. This suggests that positional tendons have stiffer collagen fibrils and/or higher collagen volume density than energy-storing tendons.

Problem

• Investigating natural variation in tendon constitutive parameters across horse populations
• Developing Bayesian mixed effects models for population parameter distributions
• Implementing hierarchical data selection to avoid tendon damage effects

Innovation

• Bayesian mixed effects model for population analysis
• Hierarchical Bayesian data selection method
• Microstructural mechanical models with experimental data