Flexible multibody modeling of a surgical instrument inside an endoscope

The implementation of flexible instruments in surgery necessitates high motion and force fidelity and good controllability of the tip. However, the positional accuracy and the force transmission of these instruments are jeopardized by the friction, the clearance, and the inherent compliance of the instrument. The surgical instrument is modeled as a series of interconnected spatial beam elements. The endoscope is modeled as a rigid curved tube. The stiffness, damping, and friction are defined in order to calculate the interaction between the instrument and the tube. The effects of various parameters on the motion and force transmission behavior were studied for the axially-loaded and no-load cases. The simulation results showed a deviation of 1.8% in the estimation of input force compared with the analytical capstan equation. The experimental results showed a deviation on the order of 1.0%. The developed flexible multibody model is able to demonstrate the characteristic behavior of the flexible instrument for both the translational and rotational input motion for a given set of parameters. The developed model will help us to study the effects of various parameters on the motion and force transmission of the instrumen

Improved Force Transmission of a Flexible Surgical Instrument by Combining Input Motion

The force transmission of a flexible instrument through an endoscope is considerably deteriorated due to friction between the contacting surfaces. Friction force along the axial direction can be reduced by combining the translational motion input with rotation. A ratio ζ is defined to measure the reduction in the friction force along the axial direction due to the combined motion input at the proximal end of the instrument. An analytical formula is derived that shows the reduction in the friction force for the combined motion input. A flexible multibody model was setup and various simulations were performed with different motion inputs. The simulation result showed a reduction of 80% in the value of ζ in accordance with the analytical result for the given velocity ratio. Several experiments were performed with constant translational motion input combined with constant and sinusoidal rotational motion input. A maximum reduction of 84% is obtained in the value of ζ against a reduction of 89% calculated analytically. The knowledge of force transmission with a combination of motions can be used to increase the force fidelity of a flexible instrument in applications like robotic surgery with a flexible instrumen

Design of an Experimental Set-Up to Study the Behavior of a Flexible Surgical Instrument Inside an Endoscope

The success of flexible instruments in surgery requires high motion and force fidelity and controllability of the tip. However, the friction and the limited stiffness of such instruments limit the motion and force transmission of the instrument. In a previous study, we developed a flexible multibody model of a surgical instrument inside an endoscope in order to study the effect of the friction, bending and rotational stiffness of the instrument and clearance on the motion hysteresis and the force transmission. In this paper, we present the design and evaluation of an experimental setup for the validation of the flexible multibody model and the characterization of the instruments. A modular design was conceived based on three key functionalities: the actuation from the proximal end, the displacement measurement of the distal end, and the measurement of the interaction force. The exactly constrained actuation module achieves independent translation and rotation of the proximal end. The axial displacement and the rotation of the distal end are measured contactless via a specifically designed air bearing guided cam through laser displacement sensors. The errors in the static measurement are 15 μm in translation and 0.15 deg in rotation. Six 1-DOF load cell modules using flexures measure the interaction forces and moments with an error of 0.8% and 2.5%, respectively. The achieved specifications allow for the measurement of the characteristic behavior of the instrument inside a curved rigid tube and the validation of the flexible multibody model