  This paper presents a survey of the state-of-the-art deformable models
studied in the literature concerning soft tissue deformable modeling for
interactive surgical simulation. It first introduces the challenges of surgical
simulation, followed by discussions and analyses on the deformable models,
which are classified into three categories: the heuristic modeling methodology,
continuum-mechanical methodology, and other methodologies. It also examines
linear and nonlinear deformable modeling, model internal forces, and numerical
time integrations, together with modeling of soft tissue anisotropy,
viscoelasticity, and compressibility. Finally, various issues in the existing
deformable models are discussed to outline the remaining challenges of
deformable models in surgical simulation.
