Flexible Needle–Tissue Interaction Modeling With Depth-Varying Mean Parameter: Preliminary Study

Flexible needle steering has aroused a lot of research interest in recent years. It has the potential to correct targeting errors, which may be caused by needle bending, tissue deformation, or error in insertion angle. In addition, control and planning based on a steering model can guide the needle to some areas that are currently not amenable to needles because of obstacles, such as bone or sensitive tissues. Thus, there is a clear motivation for needle steering. In this paper, a spring-beam-damper model is proposed to describe the dynamics during the needle-tissue contact procedure. Considering tissue inhomogeneity, depth-varying mean parameters are proposed to calculate the spring and damper effects. Local polynomial approximations in finite depth segments are adopted to estimate the unknown depth-varying mean parameters. Based on this approach, an online parameter estimator has been designed using the modified least-square method with a forgetting factor. Some preliminary experiments have been carried out to verify the steering model with the online parameter estimator. The details are given in this paper. Finally, conclusions and future studies are given at the end.