Application of Bayesian statistics to tendon mechanical models to quantify uncertainty of mechanical model parameters. #

James Casey, Jessica Forsyth, Tom Shearer, Simon Cotter

15:50 Monday in 3Q68.

Part of the Cell and tissue mechanics session.

Abstract #

Tendons are a type of soft tissue that have a strong nonlinear stress response to input strain. Mechanical models that describe tendon deformation largely use the continuum framework to formulate a hyperelastic stress-strain relationship. Tendons have a hierarchical collagenous microstructure, and the collagen fibres present are predominantly known to cause anisotropy and nonlinearity on the macro scale.

Because of the nonlinearity and high variability between different types of tendon tissues, value of model parameters corresponding to mechanical properties of tendons, such as the Young’s modulus and shear modulus, have been reported over many orders of magnitude. A precise knowledge of these parameters is crucial to fields such as injury modelling and computer-aided surgery. As such, a modelling framework for soft tissues that can quantify this uncertainty will shed light on the variability of soft tissues on the individual, and population, levels. We aim to quantify the uncertainty in the model parameters using the Bayesian framework, alongside a microstructural model for tendon deformation. Furthermore, we wish to understand the natural variation of these parameters on a population level, using mixed effects models. Markov chain Monte Carlo (MCMC) methods allow us to sample from the arising probability distributions, which we apply to data produced from tensile testing of tendons.