Surgical simulators present a safe and potentially effective method for surgical training, and can also be used in pre- and intra-operative surgical planning. Realistic modeling of medical interventions involving tool-tissue interactions has been considered to be a key requirement in the development of high-fidelity simulators and planners. The soft-tissue constitutive laws, organ geometry and boundary conditions imposed by the connective tissues surrounding the organ, and the shape of the surgical tool interacting with the organ are some of the factors that govern the accuracy of medical intervention planning.

This thesis is divided into three parts. First, we compare the accuracy of linear and nonlinear constitutive laws for tissue. An important consequence of nonlinear models is the Poynting effect, in which shearing of tissue results in normal force; this effect is not seen in a linear elastic model. The magnitude of the normal force for myocardial tissue is shown to be larger than the human contact force discrimination threshold. Further, in order to investigate and quantify the role of the Poynting effect on material discrimination, we perform a multidimensional scaling study. Second, we consider the effects of organ geometry and boundary constraints in needle path planning. Using medical images and tissue mechanical properties, we develop a model of the prostate and surrounding organs. We show that, for needle procedures such as biopsy or brachytherapy, organ geometry and boundary constraints have more impact on target motion than tissue material parameters. Finally, we investigate the effects surgical tool shape on the accuracy of medical intervention planning. We consider the specific case of robotic needle steering, in which asymmetry of a bevel-tip needle results in the needle naturally bending when it is inserted into soft tissue. We present an analytical and finite element (FE) model for the loads developed at the bevel tip during needle-tissue interaction. The analytical model explains trends observed in the experiments. We incorporated physical parameters (rupture toughness and nonlinear material elasticity) into the FE model that included both contact and cohesive zone models to simulate tissue cleavage. The model shows that the tip forces are sensitive to the rupture toughness. In order to model the mechanics of deflection of the needle, we use an energy-based formulation that incorporates tissue-specific parameters such as rupture toughness, nonlinear material elasticity, and interaction stiffness, and needle geometric and material properties. Simulation results follow similar trends (deflection and radius of curvature) to those observed in macroscopic experimental studies of a robot-driven needle interacting with gels.