Animation and Simulation Techniques for VR-Training Systems in Endoscopic Surgery

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Animation and Simulation Techniques for VR-Training

Systems in Endoscopic Surgery

Çakmak H. K., Kühnapfel U.

Forschungszentrum Karlsruhe GmbH, Institut für Angewandte Informatik Postfach 3640, 76021 Karlsruhe, Germany

Email: cakmak@iai.fzk.de http://www-kismet.iai.fzk.de

Abstract

We present new animation and simulation techniques to improve the visual realism of virtual reality (VR) based training systems for minimally invasive surgery (MIS). This paper describes the Karlsruhe Training System for Endoscopic Surgery and focuses on the need of animation and simulation methods for realistic visual effects to increase the acceptance of VR-based training systems by surgeons. In detail, interactive modeling and simulation of soft tissue is presented and basic surgical interaction modules are introduced. The remainder of the paper describes a new method for simulating irrigation and suction, new simulation and animation methods for hemodynamics (pulse, bleeding), organ motility, smoke and fluids.

1 Introduction

Minimally invasive surgery (MIS) has taken over an important role as a new opera-tion technique since it’s introducopera-tion a few decades ago. Endoscopic instruments and a camera are inserted into the body of the patient through natural and artificial orifices of the body and surgical procedures are carried out. Compared with the advantages for the patient, the surgeon has to deal with difficult conditions during the surgical operation. In contrast to classical surgery the direct view to the operation area and the contact with the patient is missing. Moreover the surgeon has to learn the handling of the instruments for minimally invasive surgery in order to perform surgical operations with a high level of precision. This can be overcome only by intensive training. Tra-ditional training methods like the pelvi-trainer lack realistic anatomical features. The enormous computing power of nowadays computer systems and the combination of new simulation methods with virtual reality (VR) techniques enable the development of interactive VR-based training systems for minimally invasive surgery. The realism of the simulation is important for the acceptance of a simulator beside the real-time capability and the variety of possible surgical interactions. This comprises the realistic modeling, the natural behaviour of virtual objects during an interaction with plausible visual and haptic consequences.

In this paper new animation and simulation methods for improving the visual realism of surgical training systems are introduced. In section 2 a brief overview of current training systems for minimally invasive surgery is given and the necessary compo-nents for a realistic training simulator are discussed. In section 3 the Karlsruhe Endo-scopic Training System is described in detail and the new modeling tool KisMo for creating realistic surgical simulation scenarios with deformable organ models is pre-sented. Section 4 gives an overview of surgical interaction modules in the training system. Also a new animation method for coagulation smoke and a simulation method

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for irrigation and suction are introduced. In section 5 the new concept of actively deforming objects is introduced. One approach is the simulation of the pulse com-bined with arterial bleeding and it’s stopping by application of clips. Another method enables the animation of organ motility. The paper finishes with conclusions and a short list of current developments.

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3 The Karlsruhe Endoscopic Training System

At the Forschungszentrum Karlsruhe KISMET (Kinematik Simulation, Monitoring and Off-Line Programming Environment for Telerobotics) has been developed as a visualisation and simulation system [Küh91]. The most significant features of KIS-MET are geometrical and kinematical modeling, a hierarchical data concept, multi-body-dynamics, support of haptic devices, multiple levels of detail, various rendering modes (polyhedron, NURBS, volume rendering) and stereo-viewing. Because of these capabilities, KISMET was found to be an ideal simulation system for computer aided surgery. The software has been improved and a realistic user interface has been built to create a realistic training system for minimally invasive surgery.

3.1 System overview

The realistic user interface (Figs. 1,2) consists of a mechano-electrical box (artificial human body) with a set of MIS-instruments and foot-switches to control interactions (simulation reset, instrument and camera change, lighting). Thus the trainee surgeon interacts in usual manner by manipulating the instruments. The movements of the instruments are measured by means of a PC-based joint angle measurement device. The PC provides up to 48 analog 12-Bit input channels for the instruments and 32 Bits digital input for the foot-switches. The position data is measured by potentiome-ters hinged at the instruments degrees of freedom. On request of the graphics work-station the sensor data is transmitted via asynchronous RS-232 connection (38.400Bit/s), the maximum response time delay is less than 20 ms for one data block. The sensor data is used to render models of surgical instruments and to generate a synthetic view of the operation site in dependence of the endoscopic camera position. The surgical scene is specified in a hierarchical model-database, in which the geome-try of the objects, the kinematics of the instruments and the elastodynamical behav-iour of deformable objects are defined. Deformable objects form the foundation of the surgical simulation. Their behaviour is defined by physical characteristics like mass, stiffness and damping. Real-time collision algorithms enable the trainee surgeon to manipulate deformable objects using the physical instrument set and perform virtual interactions like grasping, cutting, clipping and coagulation.

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Fig. 1. The MIS-Trainer Fig. 2. The realistic user interface of the MIS-training system 3.2 Simulation of deformable objects

Object deformation is simulated using a mass-spring model. Mass knots on the object surface and inner mass knots are connected with each other by virtual springs and damping elements. The equation of motion for the spatial nodal net is solved by the Lagrange equation of motion, which is an ordinary differential equation (ODE) sec-ond order. g u F u u i i n i j j j i ext i i i i d k m m + = −

∑

i − ≠ =0 , ₍₁₎

Here ni is the number of virtual springs connected to the mass knot mi, ki,j the spring

constant for the virtual spring between the mass knots mi and mj, Fext the external

force acting on the mass knot mi, di the damping and g the gravitational constant. The

velocity vi and the position ui of the mass knot mi are calculated by splitting the ODE

second order into two ODEs first order and numerical integration over the time with h as the integration time step and Bi the bounding matrix, which indicates whether the

velocity and position of a mass knot are updated or not.

          − − − ⋅ ⋅ + =

∑

≠ = + k i i i k i n i j j j i ext i i k i k i k m d m h i v g u F B v v 0 , 1 ₍₂₎

The position of a mass knot is calculated as follows:

1 1 + + ₌ ₊ k i k i k i u hv u (3)

For a realistic deformation behaviour of the objects, the spring constants, mass and damping factors have to be chosen properly. The non-linear and anisotropic behaviour of real tissue has been measured in vivo with tension and compression tests [Maa99]. The stress-strain curves for various organs have been recorded and approximated by polynomials third degree, which were used to set up the spring constants correctly.

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Medical image data (CT, MR, VisibleHuman) Modeling aid Elasticity measurement of living tissue Elasticity-parameters _Splin em od elin g Volume Rendering Moveable orthogonal texture slices

P rocedural Te xt ures

KisMo

3D-Geometry 3D-Mass-Spring-Net Object Connectivity Actively deforming Objects

(ADO) Model-/Material-Texture-database Internal format

KISMET

Simulation Visualisation Simulation-scenario

3.3 Modeling of realistic surgical scenarios

The new software tool KisMo (Kismet Modeller) has been created for realistic mod-eling of simulation scenarios with deformable objects. The concept of the modmod-eling software is shown in the following figure.

Fig. 3. The concept of the modeling software KisMo

KisMo has been designed for efficient generation of surgical simulation scenarios with deformable objects models. Spline-surface modeling and flexible pipe modeling are the basic modeling techniques used in KisMo. Three predefined object types (flat, pipe, ball) are interactively modified to get the desired object shape. Medical image data (CT, MRI, Visible Human), which is visualised with texture-based, real-time volume rendering techniques [Fra95] and moveable texture slices, serves as a model-ing aid to approximate the position and shape of individual patient organs. The meas-ured material properties (knot mass, damping and spring constants) are assigned to each object within a user-interface (see Fig. 4-left), whereas each geometry vertex of an object is interpreted as a mass knot and the edges as springs between the mass knots. An object with multiple layers is modelled by scaling copies of the object and connecting layer knots with other knots on the neighbouring layers using virtual springs, so that volumetric elements are created (see Fig. 4-right).

Another important feature in KisMo is the possibility to create procedural textures for organ surfaces. Many organs have a characteristic, non-uniform surface color with thin arterial and venous vessel trees. Two well known methods in computer graphics have been combined to achieve the typical appearance of organ textures: Turbulence functions and Lindenmayer-Systems (L-Systems). The turbulence function introduced by Perlin [Per85] has been modified, so that the noise field, which serves as a basis for the turbulence function, is filled with pixel-values of a user defined image. The user can determine the basic color of the texture with the sample image, but due to the random choice of pixels out of the sample, the final texture color is different at each recalculation. L-Systems are well known to produce tree-like structures [PL90]

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be-cause of their self repeating nature. Figure 4-right shows the artificial surface texture mapped onto a stomach model, which has an outer and inner layer connected with each other to form a volumetric object layer.

Organ models are connected with each other at their mass knots with a nearest-neighbour approach and form organ model groups, which can be combined to create the final surgical simulation scene. Additionally each model, texture and elastody-namic material data can be archived in an internal database for reuse or modification to create different training scenarios. The specification of actively deforming objects (ADO) is also done in KisMo, which will be introduced in section 5.

Fig. 4. Modeling the uterus of the visible female (left) and a procedural texture for a two-layer, actively deforming stomach model (right) with KisMo

KisMo has been used to model a realistic simulation scene for endoscopic surgery training in gynaecology (GYN-Trainer). The simulation scene contains 21 elastody-namic objects with 2.751 mass knots, which are connected by 10.942 virtual springs. The following table gives an overview of the objects, the images in Fig. 5 show an exterior and an endoscopic view of the simulation scene for gynaecology.

Model name Objs Knots Springs

Uterus 1 339 1328 Ovaries 2 230 864 Fallop. Tubes 2 408 1462 Ligaments 2 358 1376 Arterial tree 6 594 2508 Venous tree 7 675 2844 Intestines 1 147 560 Total 21 2.751 10.942

Table: Objects in the gynaecology simulation scene

Fig. 5. Simulation scene for gynaecology with endo-scopic instruments (exterior/interior view)

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The gynaecology simulation scene consists of 15.182 vertices and 6.966 textured polygons and enables a frame rate of 11 frames per second on a SGI Octane with two R10000 processors (250 MHz) and a frame rate of 6 frames per second on an Inter-graph PC with two Pentium-II XEON processors (400 MHz). One processor is used for the elastodynamic simulation and calculates the position data of the object knots (producer) for the second processor, which makes use of them to render the objects (consumer).

4 Realistic simulation of surgical procedures

In this section we will introduce basic and advanced interaction modules together with animation methods for realistic visual effects for surgical interactions.

4.1 Basic surgical interactions

Basic surgical interaction modules for grasping, setting of clips, cutting and coagula-tion have been realised and described in [KKK96] for the Karlsruhe MIS-Training System. Collision detection between instruments and organ models is carried out by simplification of the instrument geometry and using hierarchical collision tests with mass knots of deformable objects. Collisions of deformable objects with each other are prevented by setting up virtual springs between their mass knots. Grasping virtual soft tissue causes object deformation by pushing object knots along the instrument effectors and shaft. In dependence of the knot displacement the forces in the nodal net are calculated and transmitted to a haptic input device if present. Is the amount of force acting on a mass knot bigger than a threshold value, so the object topology is changed by duplicating mass knots and springs properly to simulate tearing apart of the virtual soft tissue. Topology change of an object is also done during a cut or co-agulation. The application of clips defines constraints for the interacting mass knots. Figure 6 shows a surgical intervention at the uterus (grasping, cutting) and Figure 7 shows a simulation of sterilisation by application of two clips and dissection of the fallopian tube.

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4.2 Animation of steam and smoke for coagulation

Coagulation is used for operative damage of tissue and to prevent or stop bleeding. The smoke animation is based on Perlin’s turbulence function [Per85] to create a volume block with a smoke density distribution. The volume block is mirrored verti-cally in order to achive a smooth transition while shifting vertical texture coordinates for animation of the rising smoke during the visualisation of the volume block with the 3-d texture rendering technique [Fra95]. The texture slices are cut of the volume block perpendicular to the viewing direction and mapped onto polygons, which form together a cone and are rendered back-to-front with blending. Figure 8 shows three types of different smoke created by manipulating the color tables of the texture.

Fig. 8. Animated, volume rendered smoke

types with varying colors/transparencies Fig. 9. Coagulation with smoke animation andsteaming up of endoscopic lens The animation of smoke with 3d-texture based volume rendering technique requires a special 3d-texture memory, which is not available on every computer. A new, more general animation method was developed, in which the texture coordinate shifting is replaced by the texture slice shifting technique combined with the Billboard-technique [McR98]. The texture slices are mapped onto circles, which are hang up along a time dependent animated spline curve with increasing size along the curve. Additionally the circles are scaled dependent on the viewing angle to the smoke geo-metry and the circle index, in order to give the illusion of a thin smoke column sprea-ding out to the sides during smoke rise. The transparency of each circle is increasing from the center to the corners of each circle and from bottom to top along the anima-ted hermite-spline curve at the circle centers.

The steaming up of the endoscopic lens is also animated, as an effect of the steam generated during the burning of virtual tissue. In dependence of the density of the 3d smoke texture and the coagulation duration, an appropriate texture, which is mapped onto a polygon in front of the virtual endoscopic camera, gets visible by decreasing the polygon transparency gradually (see Fig. 9).

4.3 Simulation of irrigation and suction

A new interaction module is surgical irrigation and suction. The jet of water is simu-lated with a particle system introduced in [Ree83]. The initial velocity and amount of particles are calculated from real data of surgical instruments for irrigation. Particles

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are generated by activating the irrigation instrument and move according to the New-ton’s laws of motion (see Fig. 10). Sophisticated collision algorithms use hierarchical collision tests with bounding boxes and bounding spheres to recognise collisions of particles with deformable objects, whereas the real-time property of the simulation is kept. The impacting particles on soft objects cause an object deformation. The force acting on an object knot is calculated from the loss of kinetic energy of a particle during the repel at the soft object. The loss of kinetic energy is transmitted to the object’s mass-spring-net. The external force acting on the object knot due to particle impact is defined as follows:

) ( 2 2 new old old old ext m k v v v v F = ⋅ ⋅ ⋅ − (4)

Here vold is the velocity of a particle before impact and vnew after impact, m the mass

of the particle and k the spring constant at the collided object knot. The particle ve-locity vnew after an impact is calculated with the tangential vT and normal vN

compo-nent of vold, the normal vector on the object surface, an user-defined elasticity factor ε

and a friction factor µ as follows:

N T

new v v

v =(1−µ)⋅ −ε⋅ (5)

Splashing effects are achieved by generating new particles after a particle collision. The accumulated particles form a pool, which is realised by a deformable flat object. With the knowledge of the irrigation amount, the increase of the pool height is calcu-lated. Wave effects on the pool surface are simulated by applying external forces onto the mass-spring-surface according to formula (4) after particle collision. Other meth-ods are manipulating the texture coordinates or geometry coordinates with a time dependent mathematical function. The

pool surface is textured with a static image of the simulation scene and ren-dered transparently giving the impres-sion of reflectance of the simulation scene on the pool surface. Redrawing the scene with a mirror transformation matrix for the scene reflectance is not suited for the real-time application. Further, air bubbles are created during irrigation and simulated using a particle system with Lennard-Jones forces act-ing between the particles and the pool surface [AT90]. The accumulated fluid is removed by activating the virtual suction instrument, whose suction per-formance is based on real instrument data.

5 Actively Deforming Objects

The new concept of actively deforming objects (ADO) enables to liven up passive deforming objects and so to animate human physiology. In this paper two methods are Fig. 10. Simulation of irrigation with motion-blurred particles, splashing, object deformation

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T TT i ii m mm e ee

introduced. The first method enables the visual simulation of hemodynamics, the second method enables to animate organ motility.

5.1 Visual Simulation of hemodynamics

The visual simulation of hemodynamics covers the modeling of an arterial vessel tree, simulation of pulse combined with arterial bleeding after an injury and it’s stopping.

5.1.1 Modeling of an arterial vessel tree and simulation of pulse

The arterial and venous vessel tree is modeled with KisMo using spline curves for interconnected pipes. The vessel hierarchy is stored in the simulation database for a correct propagation of the pulse. The user can determine the heart beat rate and so the rate of generation of new pulse waves. For

each vessel the mean pulse velocity and the forces, which are acting on the vessel walls, are specified. Medical literature is used for speci-fying the correct pulse velocities in each ves-sel. In dependence of the pulse velocity and the simulation time, the positions of the two force waves, which are travelling along the vessel hierarchy, are determined. The first force wave applies forces onto the vessel walls, the second wave removes the forces in the next simulation step at the same spot (see Fig. 11). The direc-tion of the force vectors are calculated at the beginning of the simulation for each object knot: they point from the pipe axis to the object knots on the pipe surface. Note that force waves are duplicated at bifurcations for correct propagation (see Fig. 12). Problems arise, if the heart beat rate is chosen too big and the pulse velocity too small. That means, that a new pulse wave has to be initiated, while other waves are still propagating. In this case, all propagating pulse waves are deleted and a new pulse wave is initiated at the top of the vessel tree hierarchy. In an optimal simulation all surface knots, which are grouped in knot rings,

would be affected by the force waves. This is not always possible, because the time step between two calls of the pulse simulation may be too big, the pulse velocity may be chosen too big or the knot rings may have unequal distances to each other along the pipe axis. A solution for this is to apply forces to groups of knot rings.

5.1.2 Particle Simulation for arterial bleeding

Correct values for various blood vessel properties are given in medical books like in [Mil89], e.g. the blood flow in the aorta is Q=83 ml/s, the average velocity of blood is |vm|= 20 cm/s with the aorta radius r=12 mm. Based on these data, a particle based

Fig. 11. Pulse wave propagation in an arterial vessel model

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F0,ado

F1,ado

simulation for arterial bleeding after an injury of an artery has been developed. After a cut into a vessel, the corresponding object knots are registered. If the propagating pulse wave arrives at the cut, the pulse wave propagation is stopped at that spot and an amount of particles with a certain initial velocity are generated, which move due to gravitational forces (see Fig. 13). The amount of particles is calculated on the blood flow in the vessel and the varying volumes of the particle spheres (the maximum particle radius is specified in the simulation data-base). Implicit surfaces have been also tested for rendering instead of particle spheres, but were found as not suitable for a real time application. The accumulated blood forms a pool inside the virtual body, which has to be irrigated and removed. The color and transparency of the pool is calculated from the amount of water and blood particles.

Stopping of the bleeding is realised by application of virtual clips. Knots which are clipped are registered and the propagation of the pulse wave is stopped when a clipped object knot is reached. When a clip is set correctly, no object knots, which are marked as cut, are reached and as a consequence no blood particles are generated - the arterial bleeding gets stopped.

Fig. 12. Propagation of pulse waves and dupli-cation at bifurdupli-cations

Fig. 13. Particle based simulation of arterial bleeding after cutting into an artery

5.2 Animation of organ motility

Many surgical training systems focus on the correct behaviour of deformable ob-jects, which react as passive objects to an interaction and don’t take into account the importance of active organ motion, which is essential for the visual realism of a training system. We introduce two meth-ods for animating organ motility. The first method allows to animate periodic motion like the intestinal and stomach motion

with mathematical functions like sin(t,ki), which is dependent on the time (t) and knot

position (ki). Periodical functions are used to generate external forces Fi,ado for a

de-formable object with ni surface knots. Two force types are overlapped to generate the

final object motion. For each object knot ring F0,ado is acting radial from the object

Fig. 14. Animation of organ motility with external forces on deformable objects

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axis to the surface knots effecting an inflating and deflating motion, F1,ado is acting

longitudinal, causing a motion of knot rings along the object axis (see Fig. 14). The directions ui of the force vectors are initialised once at the beginning of the session

and the amplitude Ai, wave speed wSi, wave direction wDi, frequency fri and a

fre-quency disturbance frDi for eliminating the motion regularity are specified in the

simulation database. Also the amplitude Ai is randomly generated based on the

speci-fied mean (∆pi,mean) and variance (∆pi,var) value for the impulse with the simulation

step h and the sign-function with a random value argument. With the total simulation time t, the external forces are defined as:

(

)

_           ⋅ + ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ = fr frD rand n k wD wS t A k t i i i i i i i i i i,ado(, ) u sin 2π F (6)

(

rand

)

h

Ai = ⋅ ∆ i,mean+sgnrand⋅∆ i,var⋅

1

p

p (7)

The second method is similar, where only time dependent, non-periodical, external forces like F0,ado are generated, which cause impulsive contraction and dilatation

mo-tion at specified posimo-tions. For this, the amount and direcmo-tion of the forces and the constant or varying time step (by stating a mean and variance value) for each knot ring are specified. A huge palette of simple organ motion can be animated realistically with these methods.

Conclusion

We have presented the Karlsruhe Endoscopic Surgery Trainer for minimally invasive surgery in gynaecology. New extensions to the system have been introduced like new interaction modules (irrigation, suction) combined with new animation and simulation methods for visual enhancement of the simulation system (smoke, fluids, pulse, bleeding) for a widespread acceptance of VR-based surgical training systems for surgeons’s education and training. These methods have been applied to a new simula-tion scenario for surgical training in gynaecology, which has been created with the new modeling tool KisMo. Current developments are simulation of suturing and liga-tion as new surgical interacliga-tions, performance measurement, tutoring systems and embedding the training system into a multimedia environment.

Acknowledgements

We acknowledge the medical advice of Mrs. Prof. L. Mettler (University Kiel-Germany, Section for Gynaecology) and Prof. G. Buess (University Tübingen-Germany, Minimal Invasive Surgery) and their teams.

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Animation and Simulation Techniques for VR-Training Systems in Endoscopic Surgery