Beam-inside-beam contact: Mechanical simulations of slender medical instruments inside the human body

This contribution presents a rapid computational framework to mechanically simulate the insertion of a slender medical instrument in a tubular structure such as an artery, the cochlea or another slender instrument.

Beams are employed to rapidly simulate the mechanical behaviour of the medical instrument and the tubular structure. However, the framework's novelty is its capability to handle the mechanical contact between an inner beam (representing the medical instrument) embedded in a hollow outer beam (representing the tubular structure). This "beam-inside-beam" contact framework, which forces two beams to remain embedded, is the first of its kind since existing contact frameworks for beams are "beam-to-beam" approaches, i.e. they repel beams from each other. Furthermore, we propose contact kinematics such that not only instruments and tubes with circular cross-sections can be considered, but also those with elliptical cross-sections. This provides flexibility for the optimization of patient-specific instruments.

The results demonstrate that the framework's robustness is substantial, because only a few increments per simulation and a few iterations per increment are required, even though large deformations, large rotations and large curvature changes of both the instrument and tubular structure occur. The stability of the framework remains high even if the modulus of the inner tube is thousand times larger than that of the outer tube. A mesh convergence study furthermore exposes that a relatively small number of elements is required to accurately approach the reference solution.

The framework's high simulation speed originates from the exploitation of the rigidity of the beams' cross-sections to quantify the exclusion between the inner and the hollow outer beam. This rigidity limits the accuracy of the framework at the same time, but this is unavoidable since simulation accuracy and simulation speed are two competing interests. Hence, the framework is particularly attractive if simulation speed is preferred over accuracy.