  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.
