A novel model for insertion of a flexible rod into a three-dimensional channel - Liu, Jiajun (Nanyang Technological University, 2023)
Many medical procedures, like colonoscopy and catheterization, have to insert medical instruments into the lumen, which can be generalized as inserting an elastic rod into a curved channel. A model accurately representing the insertion process would significantly benefit the structural design and control of these medical instruments. However, the evolving contact locations and forces make the development of such a model challenging. The finite element method has tradeoffs between efficiency and accuracy. Existing contact pattern based models neglected friction and treated tip states as known, which oversimplifies the problem. Moreover, calculating the normal vector from channel to rod consumes significant computational power in these existing models. This thesis aims to model the quasistatic insertion process with friction, promoting fast and accurate computation of the mechanics involved to address those issues mentioned. The rod was segmented based on how it contacts the channel. These segments were modeled by the classical theory of elasticity. A set of ordinary differential equations was derived for normal vector calculation. The contact location and external forces were generated by optimizing the proposed rod model. The proposed models were validated on two- and three-dimensional channels. The contact types and locations during the insertion in a two-dimensional channel were observed and compared with the simulation. The maximum root mean square error of the insertion forces was 0.055 N in the two-dimensional test cases and 0.018 N in the three-dimensional test cases. The proposed model can yield the evolving interactions between the rod and channel during the insertion efficiently, paving the way for the rational design, actuation, simulation, and control of flexible instruments and robots.