Parametric Eyeball Model for Interactive Simulation of Ophthalmologic Surgery

Transcription

1 Parametric Eyeball Moel for Interactive Simulation of Ophthalmologic Surgery Yiyu Cai*, Chee-Kong Chui, Yaoping Wang, Zhenlan Wang, James H. Anerson 3 School of MPE, Nanyang Technological University, Singapore Biomeical Lab, Kent Rige Digital Labs, Singapore Johns Hopkins University School of Meicine, Marylan 05, USA myycai@ntu.eu.sg Abstract. In this paper, we escribe a parametric eyeball moeling system for real-time simulation of eye surgery. A knowlege-base approach is use to parametrically moel the ophthalmologic structures. Together with the parametric eye moeling an the integration of patient-specific isease images, the ophthalmologic knowlege atabases of eye iseases, eye material properties, an eye surgical instruments an proceures can help to provie better maneuverability an more realistic scenarios for eye surgical simulation. A customize Finite Element Metho (FEM) is evelope to analyze the eformation of the eyeball an the interactions between the bio-structures an the instruments in the surgery simulation. A phantom haptic an force feeback virtual environment is use for real-time interactive ophthalmologic surgical simulation.. Introuction Eye iseases are among the most common an rapily growing public health concerns. Eye surgery involves very eicate proceures, an new techniques an evice are being constantly introuce to the ophthalmology community [-]. The complications of ophthalmologic iseases, however, often pose ifficulties for surgeons to make both timely an accurate critical ecisions. Subsequently, very intensive training is require for ophthalmologic professionals in orer to provie high quality stanar surgical services. Computer eye surgical simulation has been evelope to provie better training for the ophthalmologic stuents or junior eye surgeons. Hanna et al reporte their simulation work of arcuate keratomomy for astigmatism [3-4]. Sagar et al built an eye surgical simulator within a virtual reality environment [5-6]. Bio-mechanical stuies for eye anatomy an pathology play a vital role in eye surgical simulation [7-0]. In this work, we aim to evelop a more realistic eye surgical simulator. Patientspecific eye iseases will be consiere with the simulation. This information is further enhance by the knowlege atabase proviing typical information an scenario in eye iseases, isease eye material properties an eye surgery instruments an proceures. The work focuses on the Asian populations. A parametric eyeball W. Niessen an M. Viergever (Es.): MICCAI 00, LNCS 08, pp , 00. Springer-Verlag Berlin Heielberg 00

2 466 Y. Cai et al. moel incluing the cornea, lens, sclera, retina, an choroi, etc, are evelope with the capability of 3D variational change of the ophthalmology. A customize computational engine using FEM metho is provies real-time analysis for eformation an interaction in eye surgery. The graphical simulation is seamlessly integrate with the FEM base physical moeling on the avance OpenGL architecture an virtual haptic environment.. Parametric Eyeball Moeling Using Ophthalmologic Knowlege Guiance. Ophthalmologic Knowlege Base Our online survey on eye isease was conucte in Singapore recently that shows about 80% of the 68 voting people have myopia (Figure ). There is also a tren in the average age of the onset of pupils iagnose with eye iseases. Eye surgery is becoming more common an popular. Traitionally, eye surgery trainees practice using animal eyeballs. There approach presnts problems. First, animals on't suffer from the same isease as humans. Next, animal eyeballs are not reusable an if a mistake is mae, the eyeball must be iscare an a new one use. Also, there are ifferences in terms of ophthalmologic anatomy an pathology between ifferent races, sex, age, etc. We are builing an ophthalmologic knowlege atabase for Asian races. The ata is obtaine from publishe literature, public omain eye isease ata, an interviews incluing online survey. Typical ata inclue () Asian eye iseases; () Asian eye biomechanical material property; an (3) Eye surgical instrument an proceures. The knowlege atabase will capture various eye iseases for the Asian population (Figure ). The eye isease atabase captures information of geometry an pathology. The eye material property atabase keeps biomechanical values such as Young's an Shear's moules for various parts of the bio-structure. The eye instrument an proceure atabase inclue typical surgical evices an proceures use for a particular operation. With such an ophthalmologic knowlege atabase, simulation of ifferent eye isease scenario becomes feasible. Figure. Online survey on eye isease in Singapore

3 Parametric Eyeball Moel for Interactive Simulation of Ophthalmologic Surgery 467 Eye Diseases Eye Material Properties Eye Instruments & Proceures Figure. Ophthalmologic Knowlege Database. Parametric Eyeball Moeling We moel the eyeball parametrically. This allows variational change of eyeball geometry an anatomy. The cornea is transparent, an resembles a little watchglass [7-8]. In the anterior aspect, the cornea is transversely ellipsoi, whereas its posterior aspect is circular. Looke from in front, the cornea is elliptical. From the behin, the cornea appears circular. This ifference is ue to the fact that the sclera an conjunctiva overlap the cornea anteriorly more above an below than laterally. Ieally, the cornea forms part of the surface of a sphere. In isease conition such as astigmatism, it is more curve in the vertical than in the horizontal meriian. The sclera forms the posterior opaque approximately five-sixths of the fibrous tunic of the eye. Its anterior portion is visible, an constitutes the white of the eye. The sclera is thickest behin an graually becomes thinner when trace forwars. The choroi is firmly attache to the margin of the optic nerve, an slightly place at the points where vessels an nerves enter it. The lens of the eye is a transparent biconvex boy of crystalline appearance place between the iris an the vitreous. Its axial iameter varies markely with accommoation. Like all lenses, that of the eye presents two surfaces: anterior an posterior, an a borer where these surfaces meet, known as the equator. The anterior surface is the segment of a sphere. Figure 3 illustrates the eyeball moel represente in a polygonal moe. Iniviual parts of the eyeball are parametrically represente an variation of the geometry is possible. With the ophthalmologic knowlege atabase, the parametric moele eyeballs can provie high fielity platforms for eye surgical simulation..3 Patient-Specific Image Registration To improve the realism of eye surgery simulation, it is high important to integrate patient-specific eye isease information into the simulator. Ophthalmologic images are embee insie the 3D parametric moel using the atlas-base image alignment algorithm [-]. A uniform polar coorinate system of the eyeball is use in the process. A texture mapping technique is applie to match the ophthalmologic images an the eyeball structure. Alignment of the ophthalmologic image with the eyeball uner the guiance of eye atlas is thus turne into an optimization task.

4 468 Y. Cai et al. With patient specific ophthalmologic images embee into the 3D eyeball moel, visualization of abnormal eyeball structure can be performe. Figure 4 illustrates the visual fiel of a glaucoma eye isease. Figure 3. Parametric representation of eyeball moel Figure 4. Visualization of eye abnormal 3. FEM-Base Physical Moeling for Eye Surgery We are eveloping a computer-base simulator for eye surgery to help meical stuents an junior ophthalmologists impeove their surgical skills. We have built a physical base moel with finite element metho to simulate the real movement of bio-structures in response to the manipulation of the instruments uring the surgical proceure. The visco-elasticity biomechanics is aopte to escribe the eformation of the bio-structures [3-5]. In the 3D ocular moel, we have consiere the following structures: () Cornea, () Lens, (3) Sclera, (4) Chorois, an Iris, (5) Retina, (6) Muscles. All the structures are parametrically moele with reference to the ophthalmologic knowlege base. Emphasis, however, will be place upon the cornea, lens, an chorois since these are the primary structures involve in common practices. In the following sections, we escribe the bio-mechanical moeling of instruments an eye bio-structures. 3. Movement of Instrument It is note that the elasticity of all the instruments in practices are much harer then all the bio-structures involve in the operation. It is assume that a rigi structure with six-egree of freeom is use to represent the instruments. The movements of the instruments are then the sum of rigi boy isplacements as R = R R, R, R, R, R, R ) () ( x y z θ ρ ω

5 Parametric Eyeball Moel for Interactive Simulation of Ophthalmologic Surgery 469 where R x, R y an R z are the coorinates of the en of the instruments at the global space. R θ, R ρ an Rω represent the two rotations of the tip of the instruments with respect to the axis of the global system an a rotation with regar to its logistical axis. 3. Governing Equation of Deformation of Biostructures From stuies, 90% of corneal thickness is forme by the stroma. We assume that this controls the majority of the biomechanical behavior of the cornea an mainly consists of water (78%) an layere protein fibres (6%), which provies strength, elasticity an form. Ieally, it is assume as the visco-elasticity material in the eformation analysis. A visco-elastic material is one which exhibits properties of both viscous fluis an elastic solis. Many materials exhibit properties of elastic an viscous behavior epenent on stress. Examples inclue metals an Bingham plastics. However, viscoelasticity escribes a material which exhibits a combination of viscous an elastic behavior simultaneously. Visco-elastic materials can appear to be either soli or liqui, epening on whether the ominant property is elastic or viscous. Viscoelasticity is common among macromolecular materials an is often the result of molecular entaglement between macromolecules. Visco-elastic materials are characterize by two particular behaviors: Creep an Stress Relaxation. When a suen loa is applie, there is an initial rapi extension but instea of having a fixe extension as with an elastic soli, it continues to exten with time. When the loa is remove, there is an initial rapi contraction that quickly slows own. Conversely, the stress require to maintain constant strain ecreases with time. This is known as stress relaxation. An the eformation problem we encountere here is a multi-structures stress relaxation problem. 3.3 FEM Formulation We consier the FEM analysis of this multi-structures stress relaxation problem. The materials here is a time-epenent "flow" occurrence ue to the intervention of the instruments. The given equation can be given as, using Hamilton's principle, F ( x, t) = i t t 0 Lt = t t 0 ( Π Λ) t Where the Lagrangian function L is efine in terms of the potential energy ( Π ) an the Kinetic energy ( Λ ). The calculation of Π can be mae: v T T Π = B DB v (3) 0 where T = [ xyz, xyz,!, Nx Ny Nz (4) ] ()

6 470 Y. Cai et al. ix, iy, iz are the isplacements at x,y,z irections at i th FEM noe. B is the stanar strain matrix an D is the material matrix. Π can be further written as where Π = Κ = v 0 T Κ B T DB v Κ is the stiffness matrix of the bio-structures. The kinetic energy Λ can be given as v Λ = ( 0 ) v t ρ is the mass ensity of the iniviual material. Our problem here is a First-orer problem as where (5) (6) ρ (7) Κ + Κ = Q (8) = t an these erivatives can be replace by finite ifference approximations. In the Crank-Nicokon scheme, a time-stepping technique, n + + = n + = n n where is the finite step length. Hence the recurrence relation is obtaine as ( Κ + Κ ) ) n+ = Q + ( Κ Κ n+ It is implemente, for consistency, equation (0) shoul be use for Q. An using backwar ifference for () giving ( Κ + Κ ) n+ = Qn+ + Κ n n (9) (0) () () (3) In this case, the isplacement increments are calculate using the equilibrium iteration. 4. Virtual Reality Supporte Eye Surgical Simulation We evelope a computer-base simulator for eye surgery with the parametric eyeball moel to help meical stuents an ophthalmologists improving their surgical skills.

7 Parametric Eyeball Moel for Interactive Simulation of Ophthalmologic Surgery 47 Figure 5(a) is an image of the renere eyeball moel. Figures 5(b) is a snapshot of the graphical user interface. It shows the interaction between the evice an the cornea surface of the eyeball moele. User can feel the force feeback on the evice via the force feeback evice (PHANToM) in our simulation environment shown in Figure 6. (a) Figure 5. (a) Eyeball moel (b) Snapshot of graphical user interface of simulator (b) Figure 6. Eye surgical simulation environment The simulation system provies irect interaction with patient-specific moel an volumetric ata set while elivering haptic feeback to the user. A real-time volume renering technique base on ray casting, trilinear interpolation, an per-sample graient estimation algorithms was employe to visualize the patient-specific volume ata. Our physical-base eyeball moel an the associate FEM analysis provie the realistic haptic renering. User feels the force through the PHANToM. With the guiance of see-able an magnifie internal eyeball 3D representations of the patientspecific ata, a trainee can easily interact with the abnormal eye structures such as slightly cutting some cornea with a virtual scalpel. In Figure 6, a user is manipulating the PHANToM to interact with a patient s eyeball volume MRI ata sets uner the assistance of a variety of virtual tools.

8 47 Y. Cai et al. 5. Conclusion To meet the nees of training for ophthalmological professionals, a prototype for eye surgery simulation is escribe using the physical-base parametric eyeball moel. It enables simplifie eye surgery simulation in a real-time moe an with an easy-to-use feature. Future works inclues builing up more accurate an realistic eye moels. More evices an eye surgical operations will be evelope. In orer to allow users to realistically operate the simulate tools, appropriate han-eye co-orination will be enhance through continue application of virtual reality technologies. Acknowlegements Support of this research evelopment by National Science an Technology Boar of Singapore is gratefully acknowlege. The project is partially sponsore by the Nanyang Technological University (SDS 5/000). Reference [] Mann, I. C., Culture, Race, Climate an Eye Disease : An Introuction to The Stuy of Geographical Ophthalmology, Springfiel, Ill. : Thomas, 966. [] Lim A. S. M., Ophthalmology, Singapore Society of Ophthalmology, Singapore, 98. [3] Hanna, K. D., Jouve, F. E., Waring III, G. O., an Ciarlet, P. G., Computer simulation of arcuate an raial incisions involving the corneoscleral limbus, Eye, 989, No. 3, pp [4] Hanna, K. D., Jouve, F. E., Waring III, G. O., an Ciarlet, P. G., Computer simulation of arcuate an keratotomy for astigmatism, Refractive & Corneal Surgery, Vol. 8, March/April 989, pp [5] Sagar, M. A., Bullivant, D., Mallinson, G. D., Hunter, P. J., an Hunter, I. W., A virtual environment an moel of the eye for surgical simulation, Proceeings of SIGGRAPH Annual Computer Graphics Conference 994, Orlano, Floria, July 4-9, pp [6] Hunter, I. W., Doukogiou, D., Lafontaine, S. R., Charette, P. G., Jones, L. A., Sagar, M. A., Mallinson, G. D., an Hunter, P. J., A teleoperate microsurgical robot an associate virtual environment for eye surgery, Presence, Vol., No. 4, MIT, Fall 993, pp [7] Davson, H., The Eye, Acaemic Press, Cincinnati, New York, USA, 984. [8] Spencer W. H., Ophthalmic Pathology, W.B. Sauners Co., Philaelphia, 996. [9] Duane, T. D. an Jaeger E. A., Biomeical Founations of Ophthalmology, Harper & Row, Philaelphia, PA, 986. [0] Freberg, T. R. an Lace, J. W., A comparison of the elastic properties of human chorois an sclera, Experiment Eye Research, Vol. 47, 988, pp [] Richar, K. an Parrish II, Bascom Palmer Eye Institute's Atlas of Ophthalmology, Philaelphia, PA, Current Meicine, 999. [] Perkins, E. S., An Atlas of Diseases of the Eye, Churchill Livingstone, Einburgh, 987. [3] van Alphen, G. W. H. M., an Graebel, W. P., Elasticity of tissues involve in accommoation, Vision Research, Vol. 3, No. 7/8, 99, pp [4] Gallagher R. H., et al, Finite Elements In Biomechanics, Wiley, New York, USA, 98. [5] Pinsky, P. M., an Datye, D. V., A microstructureally-base finite element moel of the incise human cornea, Bio-mechanics, Vol. 4, No. 0, 99, pp