Proceedings of the 25"' Annual International Conference of the IEEE EMBS Cancun. Mexico * September 17-21,2003

Computer Simulation of Prostate Resection for Surgery Training

M. A. Padilla Castaiieda, F. Arambula Cosio Image and Vision Lab., CCADET, UNAM, P.O. Box 70-186, MCxico, D.F., 04510

Abstract- During a Transurethral Resection of the Prostate (TURP), a surgeon removes the inner prostate tissue that obstructs the urinary flow. In this minimally invasive procedure, the novice surgeons must perform hundreds of training sessions before acquiring the skills needed. In this paper we present a three-dimensional (3D) computer model of the prostate for TURP simulation. The prostate model is designed to he the hasis of a computer simulator for TURP training. The model was built from a set of ultrasound images with a technique that constructs a 3D volumetric mesh of the prostate shape. We used a set of ultrasound images with the prostate contour automatically annotated, using a point distribution model of the prostate which is adjusted by a genetic algorithm. A mass-spring method is used to model tissue deformation due to surgical tool interaction. The model simulates, in real-time: resections; tissue deformations and the cavity produced by the user as the surgical procedure progresses.

Keywords-Deformable models, Prostate, Prostatectomy, Surgery simulation, Surgery training systems.

I. INTRODUCTION

Transurethral resection of the prostate (TURF') is the modem standard procedure to treat urinary blockage due to an enlarged prostate gland, as a minimally invasive surgical procedure it offers significant advantages such as reduced patient trauma, and short recovery periods. However, the procedure restricts the movements of the surgeon, provides limited visibility of the operating site, and requires well- developed orientation skills using only the monocular view of the endoscope. A modem training altemative consists of the development of computer training systems that help the urology residents to acquire the skills in shorter periods of time, with less risk for the patients, and in an economically suitable manner.

The development of surgery training systems involves the construction of deformable models that simulate tissue cutting and tissue deformation due to the interaction with the surgical instruments. The two main groups for real time simulation of tissue deformation are models based on the finite element method (FEM) and models based on mass- spring systems.

Finite element methods use realistic mechanical models based on continuum mechanics applied over a discretisation of the entire object into volume elements. Systems based on FEM provide accurate, off-line, patient specific results, like the prototype reported by Koch et al. [I]. Bro-Nielsen [2] simplifies the system equations with a technique called

condensation, unfortunately the method is still slow for even simple tissue cutting operations.

On mass-spring systems, the object mesh is considered as a set of nodal 'masses interconnected with their neighbours by springs. Deformations occur as a result of the intemal energy produced by the springs and extemal forces applied on the body. Miss-spring models seem better suited for surgery training applications, that do not need very accurate deformations, but require a physical behaviour with enough visual realism, like the works reported in [ 3 ] , [4].

In this paper we present a 3D computer model of the prostate that simulates, in real time, tissue resections and deformations. The model forms the basis for the development of a real time computer simulator for TURP training. The prostate model was built from a set of ultrasound images, automatically annotated with a point distribution model (PDM) adjusted by a genetic algorithm (GA). The deformable behaviour of the prostate is modelled with the mass-spring method. Resections are modelled through the removal of nodes and geometrical elements from the volumetric mesh. Gomes et al. [ 5 ] reported a training system for TURP, which focus on monitoring the surgery progress with positional feedback, but does not include a prostate model that simulates real time physical behavior.

11. METHODOLOGY

A. Physical model for TURP simulation

The physical behaviour of the prostate is modelled using the mass-spring method. In this method the continuous domain R of the defoimable object is approximated by a geometrical discretisation R', where R' consists of a mesh formed by an arrangement of geometrical elements of smaller size, the vertex and edges of every geometrical element represents nodes and links between them on the mesh. In this way, objects reflect 8 dynamical nature, by associating physical characteristics like mass, stiffness and damping, to nodes and links. Every node represents a mass point that is interconnected with its neighbours by springs (links) and which moves in a viscous medium. The dynamic system is determined by the discretised Lagrange equation of motion (1).

0-7803-7789-3/03/$17.00 02003 IEEE 1152

where: mi is the mass of the node i in the mesh, at Cartesian coordinates x i ; y i is the damping coefficient of the node i (viscosity of the medium); gi is the intemal elastic force vector; and fi represents all the extemal forces acting on the node i .

Deformations result l?om the internal elastic energy produced by the spring arrangement and the extemal forces applied on the object surface. Typically, mass-spring systems use simplified linear elasticity models where the intemal elastic forces acting on the node i are given by (2).

where: p is the stiffness coefficient of the spring connecting node i and j for all the neighbors in N(i) ; x, is the current position of node i; xi is the current position of node j ; and

B. Geometric model of the prostate

is the spring length at rest position.

To reconstruct the three-dimensional shape of the prostate, the mesh generation method uses a set of transverse, transurethral, ultrasound images, separated by intervals of 5mm along the main axis of the gland. All images were automatically annotated (Fig. I), using a point distribution model (PDM) adjusted by a genetic algorithm. The genetic algorithm optimizes the shape and pose parameters of the PDM of the prostate, through minimization of an error function that measures the error between a model instance and the gray level information of the ultrasound image [6].

Each of the contours of the prostate was sampled in a radial manner, taking as the origin the centre of the transurethral ultrasound transducer. The number of samples is determined by the size of the sampling angle a, which is the control parameter of the mesh generation method. The same procedure is applied to the contour of the prostatic urethra (inner duct) forming a set of cross-sections C with both capsule (outer perimeter) and urethra samples (Fig. 2.a).

(a) (b) Fig I . Transurethral ullrasound imagcs with the pm~tate contour^

automatically annatatcd (a) At Smm from the bladder neck (b) At 1 S m m

(4 (b) Fig 2 . 3 0 shape mesh gencration of the prosme. (a) Radial sampling of a

prostatc cross-section with sampling angle a. @) 3D surface mesh intcrpolated from the transurethral ultrasound cross-sections.

Since it is not possible to identify the prostatic urethra from ultrasound images, we drew an approximate urethra contour on each of the ultrasound images. In this manner, the sampled points of every cross-section c$ (with the capsule and the urethra contours) in C, represent the control points of the prostate shape. In order to control the uniformity of the mesh, we calculated the average length ( I ) of all the segments mi and m’ij in C, that join the control points mi and mi of the capsule, and the control point m’i and m’, of the urethra, respectively.

The next step is to transform the prostate shape C, typically composed by 5 to 12 cross-section images (separated at 5mm), into the new shape C* now composed by n target cross-sections separated by the average distance I , previously calculated. C* is generated using cubic spline interpolation over the control points of C (Fig 2.b). To model the prostate as a solid body, the algorithm also interpolates, for every cross-section cs, in C*, k internal sampled contours from the capsule to the urethra (Fig 3).

Again, the number of k inner contours depends on the I value. Finally, the last step is to arrange the solid body of the prostate as a mass-spring mesh of lattice form, where every node v y k in the body is linked with at most 6 adjacent nodes ( w + ; ~ , & vji+l.b vjj,k+;, vi+lj+l.b v;+li,k+l and v,+;~+; ,x+I ) . Figure 4 illustrates the arrangement of the 3D mesh as a mass-spring system. Additional geometric volume elements of the form of a pentahedron ( VEI and VE,) are constructed (Fig. 4). As we will show in section ll.C, the form of these volume elements is useful for simulating tissue resection operations.

gcncration of the prostatc

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Fig. 4. Volumc dements of thc 3 D mass-spring mcsh of the prostatc.

C. Tissue resection simulafion

The basic tissue removal mechanism during TURP is the resection or vaporization of small tissue chips. Tissue resection during TURP modifies significantly the shape of the prostate. The urologist produces a cavity inside the obstructed urethra, by resecting the adenomatous tissue until the capsule is reached. For tissue resection simulation we use an approach, inspired in [7], that take advantage of the mass-spring mesh arrangement described in section ILB, based on pentahedral volume elements.

After a collision between the prostate body and the resection element of the resectoscope occurs, the contact node v, of the mesh is detected. Then, it is determined the list L of volume elements on the vicinity of v,, that are under of the cutting radius c, (typically 3mm to 5mm ) which must be removed from the mesh. After that, every volume element in L and its mechanical elements are removed from the mesh. When a spring s is being removed, the force fc, needed to fully compress the spring s is calculated and added to the resection force fh of its i-adjacent nodes. When a node m has no more links, the node is removed, and its force fr, is added to the frk forces of his old &neighbors. In this way, after a resection occurs, every node j around the resected zone, posses a compression force fr, that is progressively determined and used as extemal force in (1). The local effect of resection is the deformation of the tissue surrounding the resection zone, as a result of the contribution-of the resection forces of all the elements removed from the mesh. The global result of all resections and the corresponding local tissue deformations is the slight collapse of theremaining inner tissue.

111. RESULTS

The model described was implemented in C using the OpenGL libraries for rendering, on a SUN BLADE 2000 workstation (with one processor at 1 Ghz), without specialized graphics hardware.

The slides on Fig. 5 show a simulated resection of the prostate model. The figure presents a prostate with an urethra, almost completely obstructed by the tissue that has

. .

Fig. 5. Cavity produced mar the urethra after some rcscctions. After cvcry resection the tissue deforms, and a f m some tissue reseclions arc pcrformcd

(top Icfl to bottom right) the prostate slightly collapses.

grown in excess (top left slide) The slides also show the removing process of the adenoma. It can be observed the cavity produced after several tissue resections from the obstructed urethra, and .the progressive collapse of the inner tissue.

In Table 1 is shown the average processing rate (frames/s) without display for meshes generated with a sampling angle a fiom 7 to 11 degrees and a cutting radius c, of 5". Processing rates in Table 1 include collision

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detection operations, geometric mesh modifications and tissue deformation after resection. It can be observed that:the response rate increases from 11 to 25 Hz as the complexity of the mesh is reduced (increased sampling angle a) .

TABLE I AWRAGE PROCESSING RATE NEEDED TO UPDATE THE MODEL AFrER

RESECTION USING A Ca OF 5MM.

a(deg) Processing rate (Hz) 7 11.27 8 12.32 9 13.91 IO 19.84 11 25.50

The model is able to reproduce tissue resections of different sizes, depending on the cutting radius of the resectoscope. Along with resections, the model simulates in real-time tissue deformations and the global collapse of the prostate capsule as the resection of the adenoma progresses.

ACKNOWLEDGMENT

The authors are grateful to Dr. Jorge Mirquez from the Image and Vision Lab. at CCADET, U", and to Dr. Alejandro Sinchez, Urology specialist from Clinic. No. 26 of the Mexican Institute of Social Security (IMSS), for their useful comments and insight provided on the subjects of 3D- meshes and TURF'.

IV. DISCUSSION REFERENCES

The results show that the model is well suited for real time interactions during resection simulation: in the worst case, the response rate without display is higher than the 10 Hz (IO frames/s) recommended as the minimum for visual realism. Unfortunately, a display rate of 8 frmes/s approx. was observed for a sampling angle of 8 deg., this is below the 10 frameds recommended. However significantly higher frame rates should be possible with the use of graphics acceleration hardware since the processing time of the model alone (Table 1) would allow for more than 12 framesh at a sampling angle of 8 deg.

not seem mandatory for TURP simulation since the prostate tissue is very soft to resection and vaporisation, and the surgical guidance is mainly through feedback' A passive mechanical interface with position encoders and working volume restrictions is being developed.

In the short term, it looks difficult to obtain biomechanical studies of the prostate that allow physical validation of the model. Fortunately, for a prostatectomy training system, a model that visually behaves well is enough. For this reason, we are collaborating with an urologist to determine the right mechanical properties of the model, which provide visual realism.

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[2] Bro-Nielaen, M., "Finite Element Modelling in Surgcry Simulation", Proceedings afthe IEEE, Vol. 86, No. 3, pp. 490-503, March 1998.

[3] Ktihnapfel, U,, Cakmak H.K., M d , H., "Endoscopic surgcry training using vimal reality and deformable tissue simulation", Computers and Graphics, 24, pp. 671 -682, 2000.

Stephanides, M., "Rcal-Time Simulation of Deformable Objects Tools and Application". Computer Animation 2001, Seoul, Korea. November 7-8,2001,

Computer Assisted TrainingIMonitoring System for N R P Struchtrc and Design", IEEE Trans. On Information Technology in Biomed., Vol. 3, No. 4, pp. 242-250, 1999. Admbula Cosio, F., Davies, B.L., "Automatcd prostatc recognition: a key process for clinically effective robotic prostatcctomy", Medical & Biological Engineering & Computing. Val. 37, No. 2, pp. 236-243, March 1999. Catin S., Delingette H., Ayachc N., "A hybrid elastic model for real time cutting, dcfomtions, and force feedback far surgery training and simuIatim,.l Thc Visual Computer, 16, pp3.437-452,2000.

[dl Brown, I., Sorkin, S . , BNYnS, C., Latombe, J.C., Montgomery, K.

In opinion of experts in urology, haptic feedback does [SI Games, M.P.s.F., B m t , A.R.w., Timoncy, A.G., Davies, B.L., -A

[6]

[7]

V. CONCLUSION

We have reported a computer model of the prostate that is the basis for the development of a real-time virtual reality simulator for TURP training.. The prostate model is constructed from a set of ultrasound images which are automatically annotated. A 3D volumetric mesh of the prostate is constructed through sampling of the set of annotated contours. The method allows to control the visual realism of the 3D mesh with appropriate time response, by varying its sampling parameter a (radial sampling angle).

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