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The asymmetry of a bevel-tip needle results in the needle naturally bending when it is inserted into soft tissue. In this study we present a mechanics-based model that calculates the deflection of the needle embedded in an elastic medium. Microscopic observations for several needle-gel interactions were used to characterize the interactions at the bevel tip and along the needle shaft. The model design was guided by microscopic observations of several needle-gel interactions. The energy-based model formulation 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 different kinds of gels. These results contribute to a mechanics-based model of robotic needle steering, extending previous work on kinematic models.
Misra et al. (2009) studied this question.