Compliance boundary conditions for simulating deformations in a limited target region

Patient-specific models in medical procedures are often limited to a relatively small region of interest due either to computational concerns or to the fact that only a part of anatomy could be observed in the input medical images. Thus, for deformable planning or training simulations, boundary conditions at the borders of such models are necessitated. Zero-displacement or -force constraints at outer boundaries are commonly used, with the assumption that the selected region is large enough to minimize effects on the deformable behavior inside the region of interest. This may, however, still result in errors and does require superfluous elements to extend models. In this work, a mixed boundary condition type, called compliance boundary condition, is proposed to constrain model boundaries. Different techniques to define and estimate these boundary constraints are studied with simulation experiments. Results are presented for palpation on 2D and 3D phantoms and needle insertion to a male pelvic anatomical model.