  Engineering simulations using boundary-value partial differential equations
often implicitly assume that the uncertainty in the location of the boundary
has a negligible impact on the output of the simulation. In this work, we
develop a novel method for describing the geometric uncertainty in
image-derived models and use a naive method for subsequently quantifying a
simulation's sensitivity to that uncertainty. A Gaussian random field is
constructed to represent the space of possible geometries, based on
image-derived quantities such as pixel size, which can then be used to probe
the simulation's output space. The algorithm is demonstrated with examples from
biomechanics where patient-specific geometries are often segmented from
low-resolution, three-dimensional images. These examples show the method's wide
applicability with examples using linear elasticity and fluid dynamics. We show
that important biomechanical outputs of these example simulations, namely
maximum principal stress and wall shear stress, can be highly sensitive to
realistic uncertainties in geometry.
