Deformation Modeling of a Flexible Instrument Using a Bézier Curve

Abstract

Flexible instruments are extensively used in medical applications. Manipulation of these instruments is challenging and troublesome. To study the behavior of these instruments, different modeling approaches like finite element, Cosserat rod, and differential geometry have been used. In this paper, an alternate modeling approach using Bézier curve is proposed to understand large deformation in a flexible instrument. The shape is represented by a Bézier curve. The deformation includes extension, flexure, and torsion in the instrument. Strain energy and geometric constraints are formulated using Bézier control points. The shape of the deformed instrument under the given constraints is obtained by minimizing the total strain energy. Nonlinear constrained optimization is used for the minimization to find the deformed shape. The proposed method is applied for large elastic deformation in three-dimensional space. Loop formation is observed and validated with the experimental results. The proposed method will help in understanding the mechanics of a flexible instrument. Looping is a common problem during colonoscopy. The developed model will help in developing strategies for the safe introduction of these instruments inside the body for performing diagnostic and surgical interventions.