The complexity of most surgical models has not allowed interactive simulations on standard computers. We propose a new framework to finely control the resolution of the models. This allows us to dynamically concentrate the computational force where it is most needed. Given the geometrical model of an object to simulate, we first compute a bounding box and then recursively subdivide it where needed. The cells of this octree structure are labelled with mechanical properties based on material parameters and fill rate. An efficient physical simulation is then performed using hierarchical hexaedral finite elements. The object surface is used for rendering and to apply boundary conditions. Compared with traditional finite element approaches, our method dramatically simplifies the task of volume meshing and increases the propagation of the deformations.