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.

Online parameter estimation for surgical needle steering model.

Estimation of the system parameters, given noisy input/output data, is a major field in control and signal processing. Many different estimation methods have been proposed in recent years. Among various methods, Extended Kalman Filtering (EKF) is very useful for estimating the parameters of a nonlinear and time-varying system. Moreover, it can remove the effects of noises to achieve significantly improved results. Our task here is to estimate the coefficients in a spring-beam-damper needle steering model. This kind of spring-damper model has been adopted by many researchers in studying the tissue deformation. One difficulty in using such model is to estimate the spring and damper coefficients. Here, we proposed an online parameter estimator using EKF to solve this problem. The detailed design is presented in this paper. Computer simulations and physical experiments have revealed that the simulator can estimate the parameters accurately with fast convergent speed and improve the model efficacy.