3-d Multibody Modeling of a Flexible Surgical Instrument inside an Endoscope

Modern surgical procedures involve flexible instruments for both diagnostic and therapeutic purposes. 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 and clearance inside the endoscope, and the compliance of the instrument. The objective of this paper is to set up a 3-D flexible multibody model for a surgical instrument inside an endoscope to study its translational and rotational behavior. The 3-D model incorporates all the deformations—axial, torsion, and bending— due to its interaction with the surroundings. The interaction due to the contact is defined along the normal and tangential direction at the contact point. The wall stiffness and damping are defined in the normal direction. Friction is defined along the tangential direction. The calculation of the interaction force and moment is explained with an example. Various simulations were performed to study the behavior of the instrument inside a curved rigid tube. The simulations for the insertion into a 3-D tube defined in a plane were compared for both 2-D and 3-D model. The simulation results from the 3-D ∗Address all correspondence to this author. Tel.: +31 53 489 5442. Fax: +31 53 489 3631. Email: [email protected] model give the same results as the 2-D model. A simulation was carried out for the insertion in a 3-D tube using the 3-D model and the total interaction force on the instrument was analyzed. A 3-D multibody model was set up for the simulation of fine rotation. A motion hysteresis of 5◦ was observed for the chosen configuration. The 3-D multibody model is able to demonstrate the characteristic behavior of the flexible instrument under different scenarios. Both translational and rotational behavior of the instrument can be characterized for the given set of parameters. The developed model will help us to study the effect of various parameters on the motion and force transmission of the instrument. INTRODUCTION Minimally Invasive Surgery (MIS) has greatly reduced the unnecessary damage and trauma to healthy tissues, leading to faster recovery, reduced infection rates, and reduced postoperative complications. Most of the limitations imposed by the conventional laparoscopic system are well addressed by the surgical robotic system by increasing dexterity, restoring proper hand–eye coordination and an ergonomic working position, and improving visualization [1, 2]. Furthermore, the ability of inte1 Copyright c © 2012 by ASME grating and interfacing with various technologies has expanded the horizon of these robotic systems. The state-of-the-art robotic surgery systems employ rigid instruments [3]. However, with conventional colonoscopy and with the emergence of Natural Orifice Transluminal Endoscopic Surgery (NOTES) and Single Incision Laparoscopic Surgery (SILS) procedures, the use of flexible instruments is inevitable. These flexible instruments are fed through access channels provided in the endoscope or endoscopic platform. The instrument tip is remotely controlled. The inherent flexibility of the instrument, coupled with the friction inside the endoscope channel and the convoluted shape of the endoscope inside the body, makes the control of the instrument tip difficult and cumbersome. As the flexible endoscopy continues to evolve more into a therapeutic tool and as the endoscopic procedures are becoming more invasive, the surgical instruments require complex manipulations [4,5]. The instrument tip needs to deliver motion and force with a required precision and accuracy. The motion and force transmission of these instruments are critical for achieving good surgical outcomes. In an endoscope-like surgical system, the instrument is controlled from the proximal end. Nonlinearities are introduced in motion transmission by the friction forces between the instrument and the access channel. Moreover, the shape of the endoscope changes depending on the location of the surgical site. There will be a change in the force/torque delivered which is dependent on the friction properties and the shape of the contacting surfaces. Since it is difficult to place the sensors at the distal end of the instrument, the actual position and the force delivered at the instrument tip are difficult to estimate and control. This makes the control of the instrument tip difficult and challenging. A thorough understanding of the flexible instrument behavior inside the access channel of the endoscope can lead to a proper design of the controller and eventually can lead to the automatic control of the instrument tip for the desired motion or force. This also leads to the design of the instruments not only for the functionality but also for the control. In our previous study [6, 7], we described the flexible multibody model to study the sliding behavior of the flexible instrument inside a curved endoscope in the presence of friction. A 2-D flexible multibody model was set up to study the effect of friction and bending stiffness of the instrument on motion hysteresis. However, the model was limited to planar cases and the model can address only the translational behavior. In a previous study [8], the motion of a slender and flexible beam in a rigid tube was considered. A 3-D flexible multibody model is required to address the dynamic behavior in rotation and translation. The objective of this paper is to set up a 3-D flexible multibody model to study both the translational and rotational behavior of the instrument in a 3-D environment. The flexible instrument is modeled as a series of interconnected two-noded spatial beam elements. The endoscope is modeled as a curved rigid tube of uniform circular cross-section. The shape of the curved rigid tube is defined by the center line of the tube using spatial geometric curves. The wall stiffness and damping is defined along the normal direction of the tube. The friction is defined in the tangential plane. The interaction forces are defined at the nodes of the instrument model. The axial, bending and rotational stiffnesses are defined along with the mass and inertia properties of the instrument. The calculation of interaction forces are explained subsequently. Simulations are performed for 2-D and 3-D cases and the results are compared. In this paper, an endoscope refers to a flexible endoscope typically used for the examination of gastrointestinal tract, for example, during colonoscopy and gastroscopy procedures. However, the endoscope is modeled as a rigid curved tube. The instrument refers to the flexible instrument used for biopsy or for simple surgical procedures, which is fed through the access channel of the endoscope. The proximal end of the instrument is the base end from where the surgeon manipulates the instrument. The distal end is the tip of the instrument which interacts with the tissue directly. The model of the flexible instrument and of the endoscope are explained in detail in the following section. The contact model and the calculation of interaction forces are explained subsequently. Various simulations were performed to study the behavior of the instrument. The simulation results are discussed thereafter. MODELING OF A FLEXIBLE SURGICAL INSTRUMENT The surgical instrument is modeled as a series of interconnected two-noded spatial beam elements. The endoscope is modeled as a rigid tube of uniform circular cross-section. The shape of the rigid tube is defined by a center line of the tube using spatial geometric curves. The contact between the beam and the tube is defined at the nodes of the beam elements. A computer program SPACAR [9] is used for the modeling and simulation of the flexible surgical instrument. SPACAR is a modeling and simulation tool for multibody dynamic analysis of planar and spatial mechanisms with rigid and flexible elements. A Flexible Surgical Instrument As Flexible Beam The model of the flexible instrument together with the model of the tube is shown in Fig. 1. The origin of the global frame, O, is situated at the beginning of the tube and the initial tangential direction is the X-axis. The encircled number, n ©, represents the nth beam element. The nodes are represented by the numbers. The surgical instrument is modeled as a series of interconnected flexible beam elements as available in the SPACAR program. Each beam element has a node at either end. The beam element has six degrees of freedom defined at each node—three 2 Copyright c © 2012 by ASME