Bayesian inference on a microstructural, hyperelastic model of tendon deformation

TL;DR

This paper develops a Bayesian framework to estimate and quantify uncertainty in microstructural hyperelastic models of tendon deformation, linking tissue microscale parameters to macroscopic mechanical behavior.

Contribution

It introduces a Bayesian approach with adaptive MCMC for parameter inference in a microstructural tendon model, addressing uncertainty in tissue parameters.

Findings

Posterior distributions align with previous measurements.

Quantifies uncertainty in tissue parameters for individual tendons.

Framework applicable to other soft tissues.

Abstract

Microstructural models of soft tissue deformation are important in applications including artificial tissue design and surgical planning. The basis of these models, and their advantage over their phenomenological counterparts, is that they incorporate parameters that are directly linked to the tissue's microscale structure and constitutive behaviour and can therefore be used to predict the effects of structural changes to the tissue. Although studies have attempted to determine such parameters using diverse, state-of-the-art, experimental techniques, values ranging over several orders of magnitude have been reported, leading to uncertainty in the true parameter values and creating a need for models that can handle such uncertainty. We derive a microstructural, hyperelastic model for transversely isotropic soft tissues and use it to model the mechanical behaviour of tendons. To account for parameter uncertainty, we employ a Bayesian approach and apply an adaptive Markov chain Monte Carlo algorithm to determine posterior probability distributions for the model parameters. The obtained posterior distributions are consistent with parameter measurements previously reported and enable us to quantify the uncertainty in their values for each tendon sample that was modelled. This approach could serve as a prototype for quantifying parameter uncertainty in other soft tissues.