  Biomechanical models often need to describe very complex systems, organs or
diseases, and hence also include a large number of parameters. One of the
attractive features of physics-based models is that in those models (most)
parameters have a clear physical meaning. Nevertheless, the determination of
these parameters is often very elaborate and costly and shows a large scatter
within the population. Hence, it is essential to identify the most important
parameter for a particular problem at hand. In order to distinguish parameters
which have a significant influence on a specific model output from
non-influential parameters, we use sensitivity analysis, in particular the
Sobol method as a global variance-based method. However, the Sobol method
requires a large number of model evaluations, which is prohibitive for
computationally expensive models. We therefore employ Gaussian processes as a
metamodel for the underlying full model. Metamodelling introduces further
uncertainty, which we also quantify. We demonstrate the approach by applying it
to two different problems: nanoparticle-mediated drug delivery in a multiphase
tumour-growth model, and arterial growth and remodelling. Even relatively small
numbers of evaluations of the full model suffice to identify the influential
parameters in both cases and to separate them from non-influential parameters.
The approach also allows the quantification of higher-order interaction
effects. We thus show that a variance-based global sensitivity analysis is
feasible for computationally expensive biomechanical models. Different aspects
of sensitivity analysis are covered including a transparent declaration of the
uncertainties involved in the estimation process. Such a global sensitivity
analysis not only helps to massively reduce costs for experimental
determination of parameters but is also highly beneficial for inverse analysis
of such complex models.
