This paper is concerned with deriving a dynamic model of a moderately flexible needle inserted into soft tissue, where the model's output is the needle deflection. The main advantages of the proposed dynamic modeling approach are that the presented model structure involves parameters that are all measurable or identifiable by simple experiments and that it considers the same inputs that are currently used in the clinical practice of manual needle insertion. Conventional manual needle insertion suffers from the fact that flexible needles bend during insertion and their trajectories often vary from those planned, resulting in positioning errors. Enhancement of needle insertion accuracy via robot-assisted needle steering has received significant attention in the past decade. A common assumption in previous research has been that the needle behavior during insertion can be adequately described by static models relating the needle's forces and torques to its deflection. For closed-loop control purposes, however, a dynamic model of the flexible needle in soft tissue is desired. In this paper, we propose a Lagrangian-based dynamic model for the coupled needle/tissue system, and analyze the response of the dynamic system. Steerability (controllability) analysis is also performed, which is only possible with a dynamic model. The proposed dynamic model can serve as a cornerstone of future research into designing dynamics-based control strategies for closed-loop needle steering in soft tissue aimed at minimizing position error.
Dynamical modeling and controllability analysis of a flexible needle in soft tissue