COLOSCOPY SIMULATION: TOWARDS ENDOSCOPES IMPROVEMENT Christofer Kühl ENSAM, 151 boulevard de l’hôpital, 75013 Paris, France, +33144246417, [email protected]

Georges Dumont IRISA/INRIA, SIAMES Project, Campus de Beaulieu, 35042 Rennes cédex, France, +33299842574, [email protected]

Abstract: Minimally invasive surgery progresses have allowed to greatly decrease patient suffering. A way to improve these techniques is to use active tools, which could adapt to the inspected environment. The development of these tools is very complex. So simulation methods can be significantly helpful in order to produce the most suitable tools while limiting the quantity of physical prototypes. We work on the design of a simulator for virtual coloscopy. Besides the virtual prototyping aspect for new active endoscopic devices, we can also use it as a training simulator once the device is designed. To do so, we have to address the simulation process of the colon. This article is mainly devoted to the description of the chosen models for the colon behaviour, which are used for the simulator. Some experimental results are presented which confirm the validity of the different choices. To finish, sigmoid untwisting operation is presented as a benchmark test to prove the efficiency of the simulator.

Keywords: coloscopy, simulation, mechanical law, active endoscope 1 Introduction In the medical field, a strong demand is expressed by the surgeons to realize less invasive inspection and operation devices. An answer to this problem is given by the micro robotics systems, which will enable the operating gesture to be assisted thanks to active endoscopes realization. The CNRS demonstrator "micro inspect intra tube" demand gave us the opportunity to develop collaboration between various organisms: - The LRP (Laboratoire de Robotique de Paris 6) for the conception of an endoscope with distributed SMA (Shape Memory Alloy) actuators; - The ENS (Ecole Normale Supérieure de Cachan – Antenne de Bretagne) and the IRISA (Institut de Recherche en Informatique et Systèmes Aléatoires) for the development of a simulator aimed at optimizing the developed prototypes. The project is led by the idea of creating an active endoscope, and developing methods to optimise this endoscope, for three main characteristics: the geometry, the actuators and the command [Dumont02a]. 1

Figure 1: Schematic view of the active endoscope The proposed endoscope is constituted of a stiff polyarticulated structure (see Figure 1), actuated by means of SMA springs. Its tubular structure allows the passage of optical fibre and tools. It is wrapped up in an elastomer sheath to protect the patient from the mechanical structure [Szewczyk99]. During the realization of the endoscope physical prototype, a simulator is simultaneously developed, aiming at the virtual test of this new tool, and this before it is physically built [Dumont02b]. In this intend, we have proposed a model representing the endoscope, on one hand, and, on the other hand, we develop a model representing the colon. Only this model is focussed in this paper. The idea of using a physically based virtual environment is also developed in [Meseure03] for example. In the next section, we present how we represent the colon behaviour. It is based on a spline model of the geometrical part and on a dynamical simulation. One special attention is devoted to the mesenteric ligament action. Two different contact models are then presented. The first concerns the contact between the active endoscope end the colon, the second concerns the self-collision of the colon. The third section briefly presents experimental results associated with the developed model. These experiments allow us to identify the behavioural law to use for the colon. Fourth part is devoted to simulation results, particularly in showing sigmoid untwisting operation, which is identified as a key point in coloscopy. To conclude, perspectives of this work are set out. 2 Colon modelling The colon is the terminal part of the gastro-intestinal system. It is connected to the small intestine by the cæcum. Mesenteric ligaments sustain the ascending and descending part of the colon. The transversal colon and the sigmoid are not linked to any part of the body. The sigmoid is generally buckled. It is very different from one patient to another. Living tissues have mechanical properties which are essentially non linear. For this reason, models coming from linear elasticity are generally insufficient. Phenomena such as non-linearity, anisotropy, heterogeneity, viscoelasticity, viscoplasticity have to be considered during modelling.

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Lot of models have been proposed for soft tissues, from the association of mass-springdamper [Fung93], to finite element models responding to viscoelastic behaviour laws [Delingette98]. Considering the particular geometry of the colon: longilineal and tubular, the choice has

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Caecum Ascending colon Hepatic angle Transverse colon Splenic angle Descending colon Sigmoid

Figure 2: Anatomy of the colon been made to base our movement description on a spline representing the average line of the intestine (locus of cross-section centres of the colon). This has been inspired by work on dynamic animation of deformable objects in large displacements. This work has been developed in textile industry [Remion00], and is based on movement description through splines. Moreover, a very similar model for simulating the small intestine in laparoscopy is proposed in [France02, France04] or in [Raghupathi04] where a special attention is dedicated to the mesentery actions. 2.1 Modelling through spline This distributed approach allows us to generalise the Ikuta model [Ikuta01]. He proposes to consider the movement of circle series representing the intestine wall. But this allows only a discrete approach of the problem. Using splines let us distribute mass and different interactions. These splines are defined as 1-dimensional parametric functional combinations of a common set of n 3D control points qi , i  0,n. A point on such an object is referenced by its spline number j  0, np and its parametric position on this spline p  0,1. Its absolute 3D position is given by the position function of its spline, built upon a set of blending j functions  bi p: 

Mj :





p



0,1  3 M j  p   bij pqi

(1)

i

Knowing control points position allows us to define the configuration of the intestine average line, and then by distributing circles along this line, to define the colon wall configuration. Catmull-Rom splines were chosen [Catmull74].

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colon wall

control points

qn1

q2 q1

qn  2

q0

spline

Figure 2: Colon geometrical modelling 2.2 Mechanical behaviour Dynamic behaviour of this curve is given by Lagrangian equations:





d K K E (2) q, qÝ,t    q, qÝ,t   Qi   i  0,nand   x, y, z   dt qÝi qi qi where K denotes the kinetic energy function of the curve, Qi the power rating of the other external forces in the virtual movement instilled by qi , and E the potential energy of the   external forces deriving from a potential. 

 a mechanical behaviour for the colon. Each one of these terms is calculated by proposing   d K K Ý with M il   (  blj pbij pdp) (3) q, qÝ,t    q, qÝ,t   MqÝ   p 0,1   Ý dt qi qi j0,np where M is the colon mass matrix. Knowing  , colon mass density per unit length, and choosing one of the interpolation methods, allows calculating completely this mass matrix. Notice this matrix is constant. That means it is calculated and inversed before simulation, and  at each calculation step, which permits to have very fast then does not need any re-evaluation   simulation.

2.3 Mesenteric ligaments action The intestine is supposed to be hung up to the body by a set of springs-dampers, so corresponding to a Voigt model (this model was proposed in [Menciassi01]). These lifters are supposed to be linearly distributed.Their contribution to Lagrangian equations is:

Wmesentery  K q t   q0  CqÝ t  with K il  and Cil 



 (

j0,np

 (

j0,np

 

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p0,1

p0,1

kblj pbij pdp)

cblj pbij pdp)

(4) (5)

where k represents the mesentery stiffness density per unit length, and c represents its vicosity density per unit length.



k



c



2.4 Colon deformation energy

The colon is a very soft organ, which has almost no resistance to flexion and torsion. This is the reason why our model just has tension stiffness, with viscoelastic behaviour. To represent it, a Voigt model is displayed between two consecutive control points. tension spring

k tension ctension Figure 4: Colon deformation energy modelling Their contribution to Lagrangian equations is: Wdef   Edk q t q t  EdcqÝ t  (6)



where Ed k corresponds to the elastic term of the deformation energy, and Edc corresponds to the viscous term. It is important to notice that Ed k depends on spline configuration, and needs to be updated at each calculation step. 2.5 Contact model    2.5.1

Endocopecolon contact

Considering that the endoscope is especially long, and of complex geometry, its surface is represented by a set of interaction points. Each endoscope segment is cut in p slices, on which are located n interaction points I ik .



  5

l

I 12

d

I 21 I1n

I11

1st slice

I p1 pth slice

2nd slice

Figure 5: Interaction point disposition To estimate contact forces between the endoscope and the colon, the distance between each interaction point I ik and the spline is calculated by scanning the whole spline. This distance is defined by the nearest point on the spline M j p to I ik . This distance is then compared to the colon radius at M j p. If this distance is greater than the radius, an interaction occurs. A contact viscoelastic force is then applied at M j p and I ik by the  reaction principle:    (7) F  kwalldist.n  fwall v.n.n  where kwall and fwall are the mechanical coefficients of the viscoelastic model, dist represents the penetration depth, and n the contact normal.



  In particular configurations, colon happens to be in contact with itself (for example in the case of sigmoid  loop). To manage with these self-collisions, a method based on use of spheres, as proposed in [Davanne02], has been chosen. These spheres are distributed along the spline with the same radius than the circular sections at this point. Intersections between spheres correspond to the self-collision cases for which viscoelastic forces are applied. Notice  that intersections research goes very fast because it is only linked to the relative position of spheres centres and their radius. Be aware that no force should be developed between neighbour spheres. 2.5.2 

Self-collisions 

Neighbour spheres Intersecting

 spheres F

 F Figure 6: Interaction spheres

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2.6 Graphic display The simulator graphic interface is based on functionalities of OpenGL library, which allows managing creation of geometrical primitives, scene point of view, lighting or even texture veneering on objects. So the fastest method is used to construct intestine surface. It consists in drawing circles along the spline centred on it and located in the orthogonal plan.

 n

circle

j

circle

j 1

Pi , j

M

 b

 t

Pi , j 1

Pi1, j

qn1

Pi1, j 1

qn Figure 7: Frenet reference system - Wall meshing Then circles are joined with facets in order to reconstruct the intestine surface. The observation position and direction allow to chose between an onboard view and a global one, with functionalities such as translation, rotation or zoom. 3 Experimental results In the previous section, the models to describe colon behaviour have been presented. The colon was considered as a deformable solid in large displacement. A large number of parameters emerged from this model. Experiments on pig colon have been made to identify these parameters, pig intestine being chosen for its great likeness with human one. Be aware that manipulations have been made ex vivo, which gives us only an idea of order of magnitude of the parameters. So, the colon mass density per unit length has been identified:

  0, 4kg.m1

(8)

The model stiffness ktension of the deformation energy model was identified by using a test bench for tension. 



7

colon

Colon stiffness 12

180m m

force sensor

Force (N)

10

8

6

4

Sample 1 2

Sample 2 0

displacement sensor

0

0, 02

0, 04

0, 06

0, 08

0, 1

0, 12

displacem ent (m )

Figure 8: Experimental device – Experimental results The measures gave us this result:

dF (9)  892  51Nm 1 / m d where  corresponds to the colon lengthening. Notice that this is a mass density per unit length. The non-linear behaviour of the living tissues can be here easily recognized. ktension 



4 Results  To test the simulator quality, the sigmoid untwisting [Macrae] has been reproduced. The main part of the examination is done when the endoscopic device is withdrawed. The medical practitioner try to reach the ileocolic valve: this part is very delicate because the practitioner has to align the endoscope with the colon in order to continue to progress. Furthermore, the colic angles are very difficult to cross. The final point is the crossing of the sigmoid colon.

Figure 9: method to untwist the sigmoid colon The technique consists in rolling up the endoscopic device into the sigmoid. Then the practitioner unrolls the buckle by rotating the endoscopic device and by withdrawing it. The sigmoid is untwisted and the rest of the inspection is more easily done.

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t  0s

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t  2s

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t  8s

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t  6s

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t 10s

t 18s

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t  4s

t 12s

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t  20s

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t 16s

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t  22s

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t  26s

t  24s

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t  28s

Figure 10: Sigmoid untwisting   The figure above (figure 10) shows that this operation can be reproduced thanks to the developed simulator. So it can be used as a training tool.

In the same way, the texture veneering and the onboard view functionality makes it possible to get a realistic image, comparable to the one obtained with a camera located at the distal part of the endoscope.

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Figure 11: View on board 5 Conclusion A simulator in developing process will give the opportunity to reproduce coloscopy. First results confirm the validity of the chosen method, based on a dynamic approach of splines. An experimental approach has been made to check the validity of the chosen models. However, this approach has to be extended in order to identify all the parameters of the mechanical model, notably the contact ones (nowadays, these parameters are adjusted for a realistic animation). The development of this simulator is part of a larger process, which consists in designing an active tool for endoscopy. So it is associated with a set of models for the simulation of endoscope behaviour [Dumont04]. The complete simulation should allow determining the best driving strategy to obtain an automatic progression of the endoscope, minimizing endoscope-colon interactions and consequently reducing patient suffering.

Figure 12: Command based on a multi-agent approach

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Figure 12 presents the first results obtained with a multi-agent approach, which allows limiting contacts, by automatic conformation of the active endoscope, the fine control of the model is a work in progress. To finish, the whole simulator is used to optimise the endoscope design as developed in [Kühl02]. References [Catmull74] Catmull R., Rom R., « A class of local interpolating splines », Computer aided geometric design, Academic Press, 1974. [Davanne02] Davanne J., Meseure P., Chaillou C., « Stable haptic interaction in a dynamic virtual environment », IEEE/RSJ International Conference on Intelligent Robots and Systems, 2002. [Delingette98] Ackerman M.J., « Toward realistic soft-tissue modelling in medical simulation », Proceedings of the IEEE, Vol. 86, No. 3, pp. 512-523, 1998. [Dumont02a] Dumont G., Kühl C., Bidaud P., « Simulating And Optimizing Active Endoscope Prototypes», Proceedings of ISR2002 (International Symposium on Robotics), Sweden, 2002. [Dumont02b] Dumont G., Kühl C., Andrade G., « A dynamical simulator for designing active endoscopes », Proceedings of the 5th World Congress on Computational Mechanics, WCCM V, Austria, 2002. [Dumont04] Dumont G., Kühl C., « Mixed beam model to calculate the behaviour of shape memory alloy spring actuators », Proceedings of IDMME’04 : 5th International Conference on Integrated Design and Manufacturing in Mechanical Engineering, Bath, GB, 2004. [France02] France L., Angelidis A., Meseure P., Cani M.P., Lenoir J., Faure F., Chaillou C., « Implicit representations of the human intestines for surgery simulations », MS4CMS’02: Modelisation and Simulation for Computer-aided Medicine and Surgery, ESAIM Proceedings, Vol. 12, pp. 42-47, 2002 [France04] France L., Lenoir J., Angelidis A., Meseure P., Cani M-P., Faure F., Chaillou C., « A Layered Model of a Virtual Human Intestine for Surgery Simulation », Medical Images Analysis, Elsevier Sciences, 2004. [Fung93] Fung Y.C., « Biomechanics, Mechanical properties of living tissues, Second edition », Springer, 1993. [Kühl02] Kühl C., Dumont G., « Virtual endoscopy: from simulation to optimization of an active endoscope », MS4CMS’02: Modelisation and Simulation for Computer-aided Medicine and Surgery, ESAIM Proceedings, Vol. 12, pp. 84-93, 2002. [Ikuta01] Ikuta K., Iritani K., Fukuyama J., « Mobile virtual endsocope system with haptic and visual information for non-invasive inspection training », Proceedings of the 2001 IEEE, International Conference on Robotics and Automation, Seoul, pp. 2037-2044, 2001. [Macrae] Macrae F., « Adult diagnostic colonoscopy », Endosurgery, colon and rectum [Menciassi01] Menciassi A., Park J.H., Lee S., Gorini S., Dario P., Park J.O., « Robotic solutions and mechanisms for a semi-autonomous endoscope », IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1379-1384, 2002. [Meseure03] Meseure P., Davanne J., Hilde L., Lenoir J., France L., Triquet F., Chaillou C., « A Physically-Based Virtual Environment dedicated to Surgical Simulation », International Symposium on Surgery Simulation and Soft Tissue Modeling (IS4TM), 2003. [Raghupathi04], Raghupathi L., Grisoni L., Faure F., Marchal D., Cani M.-P., Chaillou C., « An Intestine Surgery Simulator: Real-Time Collision Processing and Visualization », IEEE Transactions on Visualization and Computer Graphics, vol. 10, num. 6, pp. 708-716, Nov-Dec 2004. [Remion00] Remion Y., Nourrit J.M., Nocent O., « Dynamic Animation of N-dimensional Deformable Objects » , WSCG Proceedings, Plzen, Czech Republic, pp. 147-154, 2000. [Szewczyk99] Scewczyk J., Troisfontaine N., Bidaud P., « An active tubular polyarticulated microsystem for flexible endoscopes », Proceedings of IARP : International Workshop on Micro Robots, Micro Machines and Systems, 1999.

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