Nonholonomic Modeling of Needle Steering
International Journal of Robotics Research
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During needle-based procedures, transitions between tissue layers often involve puncture events that produce substantial deformation and tend to drive the needle off course. In this paper, we analyze the mechanics of these rupture events corresponding to unstable crack propagation during the insertion of a sharp needle in an inhomogeneous tissue. The force-deflection curve of the needle prior to a rupture event is modeled by a nonlinear viscoelastic Kelvin model and a stress analysis is used to predict the relationship between rupture force and needle velocity. The model predicts that the force-deflection response of the needle is steeper and the tissue absorbs less energy when the needle moves faster. The force of rupture also decreases for faster insertion under certain conditions. The observed properties are sufficient to show that maximizing needle velocity minimizes tissue deformation and damage, and consequently, results in less needle insertion position error. The model predicts that tissue deformation and absorbed energy asymptotically approach lower bounds as velocity increases. Experiments with porcine cardiac tissue confirm the analytical predictions.