<p>Significant research efforts have been focused on modeling the interaction between surgical needles and soft tissues which can be used to measure the deflection of a bevel-tip needle inside soft tissue. The development of such a model, which predicts the steering behavior of the needle during needle-tissue interactions, could improve the performance of many percutaneous needle-based procedures. In the current work, we use the dynamic Euler-Bernoulli beam theory to develop an analytical model to predict the deflection of the needle. In the Euler–Bernoulli thin beam theory (beams in which the length is much larger than the depth with an aspect ratio of, at least, 10:1), the rotation of cross-sections of the beam is neglected compared to the translation and the angular distortion due to shear is considered negligible compared to the bending deformation, this will allow us to model the needle as an Euler-Bernoulli cantilever beam which is moving along its longitudinal axis and undergoing various external loads. These external loads are the result of the interaction between the tissue and the needle during insertion and they can be modeled as the following: a tissue cutting force acting at the needle’s beveled tip modeled as a concentrated force, and needle-tissue interaction forces acting along the needle length which include: (i) tissue reaction forces as the result of its deformation caused by needle bending and modeled as a transverse distributed load; and (ii) friction forces between the needle shaft and the tissue modeled by an axially distributed load tangent to the needle shaft. From Euler-Bernoulli beam elastic foundation theory we can develop the governing equation of motion for the translating needle inside the tissue and under the external forces described previously. In the early models, we assumed: (i) the deflection of the needle is small compared to its length; (ii) the needle is a long and thin cantilever beam with a constant cross-section clamped from one side and free on the other side; and (iii) the tissue is homogeneous. With these assumptions and by using the governing equation and the proper boundary conditions we derive the mathematical expression for the transverse displacement of the needle (the needle deflection) and predict the steering behavior of the needle. The accuracy of the analytical predictions offered by the model is verified by comparing them to the experimental data. Our ongoing work is to improve this analytical model by expanding the model assumptions of having constant cross-section needles to more complicated shape needle and modifying the model parameters (a homogeneous tissue) to make this model suitable for studying the deflection mechanics of bioinspired surgical needles in order to predict the steering behavior of these needles during insertion into multi-layered tissues.</p>

An Analytical Model for Predicting the Deflection of Hollow Surgical Needle in Soft Tissue

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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