Computer-based training system for cataract surgery

Jeremie Dequidt, Hadrien Courtecuisse, Olivier Comas, Jeremie Allard,

Christian Duriez, Stephane Cotin, Elodie Dumortier, Olivier Wavreille,

Jean-Francois Rouland

To cite this version:

Jeremie Dequidt, Hadrien Courtecuisse, Olivier Comas, Jeremie Allard, Christian Duriez,et al.. Computer-based training system for cataract surgery. Transactions of the So-ciety for Modeling and Simulation International, SAGE, 2013, <http://is.gd/2Mihj1>.<10.1177/0037549713495753>. <hal-00855821>

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https://hal.inria.fr/hal-00855821

Submitted on 30 Aug 2013

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Computer-Based Training System For Cataract Surgery

Jeremie Dequidt∗1,2,3, Hadrien Courtecuisse1, Olivier Comas1, Jeremie Allard1,2,3,

Christian Duriez1,2,3, Stephane Cotin1,2,3, Elodie Dumortier4,5, Olivier Wavreille4,5 and

Jean-Francois Rouland4,5

1Shacra(INRIA Lille - Nord Europe / INRIA Nancy - Grand Est / LIFL)2LIFL, CNRS UMR8022

3University of Lille 14CHRU Lille, Hopital Claude Huriez

5Ophtalmologie, INSERM U86

August 30, 2013

Received: Dec. 16 2012, Revised: Apr. 12 2013, Ac-cepted: Apr. 22 2013

Abstract

This paper describes a single simulation frameworkto perform interactive cataract surgery simulations.Contributions includes advanced bio-mechanicalmodels and intensive use of modern graphics hard-ware to provide fast computation times. Surgical de-vices are replicated and located in a real-time thanksto infra-red tracking. Combination of a high-fidelitysimulation and actual surgical tools are able to im-prove surgeon immersion while training. Preliminarytests have been performed by experienced ophthal-mologists to qualitatively assess the face-validity ofthe simulator and the faithfulness of the behavior ofthe anatomical structures as well as the interactionswith the surgical tools.

∗E-mail address: jeremie.dequidt@inria.fr Contact address: Ba-timent INRIA A, 40 avenue Halley, 59650 Villeneuve d’Ascq,France. Phone number: +33 359.577.881. Fax number: +33359.577.850

Keywords: Cataract surgery simulation, real-timebiomechanical models, training environment

1 Introduction

Cataract surgery has made important advances overthe past twenty years, and every year, more than fivemillion people in the United States and in Europeundergo cataract surgery. This procedure is howevercomplex to perform as it requires good hand-eyecoordination as well as accurate microscopic manip-ulations of surgical instruments. Therefore a longtraining period is mandatory to acquire these nec-essary skills. Current method of training are basedon companionship and this apprenticeship modeldepends on the availability of the instructor and po-tentially exposes patients to complications due tothe inexperience of the operator. In this context, re-cent reports have demonstrated the advantages andadded value of computer-based simulation over con-ventional training [1]. Therefore, new training simu-lation systems for cataract surgery have been recentlydeveloped. Typically, these simulators offer a combi-

1

nation of simulation software that aims at reproduc-ing some parts of the cataract surgery procedure andhardware devices that allow the surgeons for realisticinteraction with the simulation. For instance, [2] pro-pose a Mass-Spring mechanical model of the capsulein order to simulate the capsulorhexis, whereas [3]and [4] focus on the phacoemulsification step usingdedicated strategy to remove tetrahedrons from avolumetric mesh. Some other works have combinedmultiple cataract surgery steps in their simulatorslike [5] or [6]. Regarding interaction devices, someset-ups are based on 6DOF tracking systems that canpossibly provide force feedbacks [6] or CCD-basedoptical tracking system like in EYESI simulator 1.

Simulators can provide almost limitless opportu-nity to practice and achieve surgical proficiency ina controlled and safe environment. However, if thetraining scenario is scripted in the simulator, like ina video game, then the benefit is limited. Hence, wethink that the student must have the possibility to errand when it happens, it shall not be the end of thescenario. In such case, the novice must also learn torecover from the mistakes. To allow for such freedomin the simulation, the design of the software mustrely on a physics-based simulation. If the behaviorof the anatomical structures is guided by accuratedeformable models, if the interactions between sur-gical tools and organs rely on accurate contact andfriction laws, then it is possible to allow for a realisticsimulation whatever the action of the user is. Obvi-ously, the biomechanical model accuracy can not takeprecedence over the constraint of real-time execution:the motions of the user must quasi-immediately betransferred in the simulation. But the computationalpower available on today’s CPUs and GPUs allowsfor attractive compromises between accuracy andcomputation time.

This paper presents our recent works in the field ofcataract surgery simulator. Our main objectives arethe following:

(a) be able to train on the three most important stepsof the procedure: capsulorhexis, phacoemulsifi-cation, and intra-ocular lens injection which has

1http://www.vrmagic.com/simulators/eyesi-surgery-simulator/eyesi-cataract/

not, to our knowledge, been treated previously

(b) develop advanced models based on biomechan-ics that can be easily parametrized using materialproperties and that can be computed quickly

(c) have a working environment and devices as closeas possible to real operating rooms.

The rest of this article is divided as follows: sec-tion 2 provides a brief overview of our system, andeach important step of the simulation is detailed inthe following sections (e.g. the phacoemulsificationin section 3, the capsulorhexis in section 4 and theintra-ocular lens implant in section 5). The section 6is about the approach we use to make interactionsnatural to cataract surgeons.

2 Overview & Contributions

Training system: The training system described inthis chapter is based on a computer-based simula-tor and a environment close to an actual operatingroom. The environment consists in a microscopewhere stereo glasses have been fixed in order to ren-der the virtual scene in 3D, a full-body mannequinwhere replaceable silicon eyes that support cataractsurgery may be inserted. Monitors are also availablein the room to provide additional informations (likevital constants) or feedbacks. This serves a pedagogicpurpose because it increases the feeling of immer-sion while allowing to train and memorize the realprocedure with the same devices (microscope, ped-als...) and the same surgical tools design using rapidprototyping. The tools are tracked in real-time andtheir 3D position is used to feed our real-time simu-lation. Figure 1 illustrates the various componentsthat are part of the training system and how their areconnected.

Real-time simulation: The computer-based simu-lation has been developed using SOFA2 which is anopen-source framework targeted at interactive med-ical simulation. SOFA provides a set of tools suchas detection algorithms, GPU optimizations, linear

2http://www.sofa-framework.org

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FEM... that offers a good trade-off between accuracyand computational cost. For improved realism, oursimulation of cataract surgery relies on geometricallynon-linear finite element models (FEM) using tetrahe-dral elements for the lens, and triangular elements forthe capsule. Both models derive from Hooke’s lawand are based on a co-rotational method [7]. The dif-ferent models have been created by a 3D artist basedon anatomy handbooks. Mechanical properties areparametrized using values reported in the literature[8], and use an implicit integration scheme to enforcerobustness of the deformation process. While thisallows realistic and interactive deformation of thecapsule and lens, additional information needs to beintroduced to enable realistic tearing: the principaldirection of fibers within the soft tissue. As many bi-ological soft tissues are composite fibrous materials,the orientation of these fibers highly influences the di-rection of propagation of the tear in the tissue. It alsointroduces anisotropy in the model. State-of-the artcomputer graphics techniques (like Volume Render-ing) are implemented in order to achieve convincingvisible rendering of the human eye.

Figure 1: Functional view and picture of the training system.The system relies on devices used in real procedures(microscope, pedals...), replicas of surgical tools thatare tracked in real-time and on a simulation enginethat renders a realistic and interactive simulation ofcataract surgery.

3 Lens model and phacoemulsifi-cation

This section presents the volume model used for mod-eling the deformations and the motions of the lensand also the interaction model developped for thephacoemulsificator.

The behavior of the lens is based on finite ele-ment modeling that allows for simulating differentrigidities given the age and the pathology of the pa-tient: typical stiffness values reported in the literaturerange from 1kPA (20-year old human) to 5 kPA (over60 year old person) [9].The fragmentation and aspira-tion of the lens is performed in 3D and in real-time byusing the phacoemulsificator’s pedal which activatesa local change in the geometry and behavior of thelens volumetric model. New algorithms and modelshave been developed to obtain this fast simulationcomputation without sacrificing realism.

3.1 Related Work

Many works focused on modeling the deformationof soft tissues. If we focus on real-time algorithms,mass-spring networks [10] is one of the most popu-lar methods, mainly because of their simplicity andefficiency. Their main drawback appear in the dif-ficulty to model specific material laws and parame-ters. However a recent work by [11] has shown thatit is possible to compute springs stiffness on trian-gular and tetrahedral meshes relating to St Venant-Kirchhoff materials.

To model biomechanical behaviors more precisely,one can instead use Finite Element Models (FEM).This approach is more computationally intensive,and was initially used interactively by relying onpreprocessing [12, 13], limiting the approach to lin-ear small deformations without topological changes.To remove these limitations, [7] introduced the co-rotational formulation, which relies on linear elasticmaterial but non-linear geometric deformations bycomputing a local rigid rotation for each element.

3

3.2 Tools and Methods

3.2.1 Deformable Lens Model

The deformable lens is modelled using a co-rotationalFEM formulation with linear elasticity. It is repre-sented by a tetrahedral mesh that can be tessellatedto produce small elements (see Figure 2(b)). Wechose an implicit time integration scheme in order toachieve large time-steps and provide a stable simula-tion even when subjected to challenging interactions.We use the approach detailed in [14], where the result-ing system of equations is solved iteratively using aConjugate Gradient solver implemented on the GPU.

(a) (b) (c)

Figure 2: Tessellation algorithm that can dynamically refinetetrahedra (a). Two-levels tetrahedral topology forlens phacoemulsification (b).

One important aspect of this method is that themechanical matrix of the full system is not explicitlycomputed, but matrix-vector products are insteadparallelized directly over the mesh elements. Thisallows to easily change the topology of this mesh, asis necessary in this application to implement the in-teractions with the phacoemulsifier explained below.

3.2.2 Interactions with the Phacoemulsifier

The phacoemulsifier proposes two modes of interac-tions to the surgeon:

Aspiration: when activated, liquids from the eye arepumped into the instrument, creating a forcepushing the lens toward the tip of the pha-coemulsifier.

Fragmentation: A probe at the tip vibrate at about40,000 cycles per second, creating ultrasonicwaves that break up the lens into small pieces

that are sucked into the instrument by the aspi-ration and removed from the eye.

The aspiration aspect is handled by defining a spher-ical volume around the type and finding parts of thelens within it. When the aspiration is activated, anartificial force is added to pull the enclosed particlestoward the tip. When fragmentation is also activated,we remove tetrahedral elements from the geometri-calmodel of the lens.The removed elements shouldbe as fine as possible to provide an accurate visualfeedback to the surgeon. However, the mechanicalmesh need to be relatively coarse to maintain goodperformances. To solve this issue, we use a finer tes-sellated mesh for rendering and interactions with theinstrument. This is done by splitting each tetrahe-dron in the simulation mesh into 8 smaller tetrahedra(Fig. 2(a)). Therefore finer elements are removed dueto aspiration. And if the 8 finer elements of a coarsetetrahedron are removed, the coarse tetrahedron isalso removed in order to mechanically take into ac-count the loss of matter in the lens. This allows theuse of a relatively coarse mechanical mesh (Fig. 2(b))while using a more detailed visual mesh (Fig. 2(c))for the rendering.

3.2.3 Semi-Opaque Volume Rendering

The cristalline lens is opacified by the cataract, but itis not completely opaque. During phacoemulsifica-tion, the quantity of light that is bouncing back fromthe retina through the lens is an important visual cuefor the surgeon to guide his action. To reproducethis effect, we rely on a volume rendering techniquecalled Projected Tetrahedra as implemented by [15].Each tetrahedron in the visual mesh is sent to thegraphics card as input to complex shaders that ren-der their contributions taking into account the lightdissipation along the depth of the tetrahedra at eachpixel.

3.3 Results

Figure 3 shows the resulting simulation of the pha-coemulsification step. The lens is deformed when

4

Figure 3: Three screenshots of the phacoemulsification simula-tion. Local fragmentation of the lens create a cross-likepattern on the lens.

in contact with the instrument and can thus be ro-tated by the surgeon to create a cross-like carvingusing local fragmentation and aspiration through thetip of the phacoemulsifier. This step is implementedby removing elements from a visual mesh that istessellated at a finer resolution than the underlyingmechanical mesh. This method is rather simple anddo not suffer from the stability issues of other ap-proaches based on local remeshing. The removal ofthese small elements progressively allows more andmore light to pass through the lens. This effect is im-plemented through an advanced volume renderingtechnique. It is an important visual cue that the sur-geon must learn to use in order to ensure not pushingthe instrument too low within the eye, which can leadto puncturing the underlying membrane. The 3000tetrahedra of the lens model are simulated and ren-dered on 2.4 GHz processor with a standard graphiccard. Simulation performance is of 80 fps with anintegration time-step of 0.01 seconds.

4 Lens capsule model and capsu-lorhexis

In this section, we focus on Continuous CurvilinearCapsulorhexis, a technique used to create a circularopening in the lens capsule. Once a small initial inci-sion has been made, this technique relies essentiallyon the application of shear and stretch forces to cre-ate the opening. When performed correctly, the con-tinuous curvilinear capsulorhexis creates a smoothopening, reducing the risk of tear when forces areapplied to the capsule during surgery. The main riskwith the continuous curvilinear capsulorhexis is toeither create an opening that is too large or to create

an edge that could promote a tear proceeding out-wards. From a simulation and training standpoint,it is essential that the model of deformation and tearof the capsule is realistic. In [16] and [4] the lens cap-sule is modeled by a mass-spring network based ona triangular mesh. The main issue with these modelsis that they rely on discrete methods which requirespecific mesh structures (e.g. radial and concentricsprings with different stiffnesses) to reproduce theanisotropic properties of the capsule. Also, whensimulating the capsulorhexis, complex re-meshingtechniques are required to maintain a similar meshstructure. The approach presented in this sectionrelies on a continuous model based on elasticity the-ory for which specific fiber directions can be defined.This allows real-time anisotropic soft tissue deforma-tion as well as realistic tearing simulation.

4.1 Tools and Methods

Using a finite element technique, one can no longerrely on the mesh topology to specify preferred di-rections of anisotropy. The approach presented hererelies on a continuous model based on elasticity the-ory for which specific fiber directions can be defined(see 4.2). The underlying finite element model canhandle geometrically non-linear anisotropic deforma-tions at interactive rates. This model is combinedwith a novel technique for determining the fracturedirection, which can be propagated along existingedges of the topology or across existing faces by us-ing a remeshing algorithm [17].

In our approach, we propose to model the de-formation and tearing of thin soft tissue (such asmembranes, capsules, etc.) by using a transverselyisotropic elastic model. The model is based on a co-rotational finite element method formulation, usingtriangular elements on which a specific fiber direc-tions can be defined (see Figure 4). During defor-mation of the tissue, this fiber orientation, and theprincipal strain direction on the element are usedto determine the tear propagation. Tearing or frac-ture within an element only occurs when a thresholdis reached, which is computed using an eigenvaluedecomposition of the strain tensor in each element.If the largest eigenvalue is above a given threshold

5

(in our experiments, the value is tuned accordingto the feedbacks provided by the surgeon), the ele-ment is identified as ”breakable” and the eigenvectorassociated with this eigenvalue corresponds to theprincipal strain direction (see figure 4). Since tearingtends to propagate from an already fractured loca-tion, we also account for the history of tear locationand direction in the overall computation of the cur-rent tear direction. Topological changes on the FEMmesh are performed at each time step. Each trian-gle in the neighborhood of the current tear locationwhich strain is above our threshold will be re-meshed.This local re-meshing subdivides a triangle into newtriangles. There is no particular requirement on thelocal re-meshing besides avoiding very small trian-gles which lead to ill-conditioned systems.

Figure 4: From left to right: tearing propagation throughout thetissue. Fibers (not visible on the meshes since they aredefined per triangles) are oriented with a 45 degreeangle, and forces are applied outward, on the left andright sides of the square mesh. Our fracture criteriais represented as the shaded area. One can see on theleft image how the anisotropy affects the deformationof the tissue, and on the rightmost images how thefracture direction depends on the previous fracturedirection, as well as fiber direction. The square mesh iscomposed of 1,500 triangles. Anisotropic deformation,fracture and remeshing are performed in real-time.

4.2 Anisotropic Soft Tissue Model

As many biological soft tissues are composite fibrousmaterials, additional information needs to be intro-duced to enable realistic tearing: the principal di-rection of fibers within the soft tissue. Indeed, theorientation of these fibers highly influences the direc-tion of propagation of the tear in the tissue. It alsointroduces anisotropy in the model. The proposed

model for describing deformation and tearing of thinsoft tissue (such as membranes, capsules, etc.) relieson a transversely isotropic FEM formulation using tri-angular elements, in which a specific fiber directioncan be defined on each element. The fiber directionon each element, called θ, is defined with respect to alocal (co-rotational) reference frame (x, y). This localframe of reference is in turn defined with respect to aglobal frame of reference (X,Y) via a rigid transforma-tion. The frame defined by the fiber is named (F,T),where F is along the fiber, and T is the transverse(orthogonal) direction (see Figure 5). This leads tothe following definition of the anisotropic materialstiffness matrix of an element: σx

σyτxy

=1

1− νFνT

K11 K12 K13K21 K22 K23K31 K32 K33

εxεy

γxy

K11 = c4EF + s4ET + 2c2s2(νTEF + 2GF)K22 = s4EF + c4ET + 2c2s2(νTEF + 2GF)K33 = c2s2(EF + ET − 2νTEF) + (c2 − s2)GF)K12 = c2s2(EF + ET − 4GF) + (c4 + s4)νTEF)K13 = −cs[c2EF − s2ET − (c2 − s2)(νTEF + 2GF)]K23 = −cs[s2EF − c2ET + (c2 − s2)(νTEF + 2GF)]

where c = cosθ, s = sinθ, GF = EF/(1 + νF) andνT/ET = νF/EF. Since we are dealing with the sim-ulation of fracture and tearing, topological changeswill occur. To numerically handle these changes inan optimal way, we use an iterative solver (conjugategradient) for which there is no need to perform anymatrix assembly [18].

Figure 5: Global reference frame (X,Y,Z), local frame (x,y), andframe (F,T,N) based on fiber orientation.

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4.3 Tearing Criterion

Although a significant amount of work exists in thefield of finite element modeling for the simulationof fractures (see [19, 20] for instance), little has beendone in the area of interactive medical simulation.Principal difficulties come from the real-time simu-lation requirement, and the need to account for thepresence of fibers (previous work essentially dealwith isotropic materials). In general, tearing or frac-ture occurs when a certain stress threshold is reached.For isotropic materials, this threshold is the samein every direction, and a fracture criterion can bedetermined using an eigenvalue decomposition ofthe stress tensor in each element [21]. If the largesteigenvalue is above the given threshold, the elementis then fractured along a direction perpendicular tothe eigenvector associated to the principal stress di-rection. This is however not applicable in the caseof anisotropic materials, as the presence of fibersleads to preferred fracture directions. Also, the stressthreshold is generally not identical along the fiberand transverse directions. Fracture occurs when thestress along the fiber or transverse to the fiber ishigher to arbitrary threshold (σF and σT) e.g. whenσF > σF or σT > σT and we propose the followingmeasure of the fracture condition, i.e. tearing occursif:

c(d, σ, f, p) > 1 (1)

where d is the potential direction of propagation ofthe fracture, σ = (σxσyτxy) is the stress tensor, f isthe fiber direction, and p is the previous fracture di-rection (useful to avoid backtracking suddenly whenwe are continuing from an existing fracture, as oth-erwise the stress and fiber directions are undirected).This criterion is typically evaluated at the tip of apre-existing fracture or at the center of each poten-tially fracturing element. In this work we proposea first formulation of the fracture criteria, based onthe stress threshold in each direction σ. This criterionincludes a parameter limiting the angle between theprevious and next directions of propagation to be atmost θP:

c(D, σ, f, p) =σD⊥σd⊥

H ((d · p)− cos θP)

with d⊥ = d× n(2)

where H is the Heaviside step function: H(a− b) ={0 if a < b, 1 if a ≥ b}. The stress along a directionu can be computed by the coordinate transformationformula, using the angle θu between u and the x axisof the local frame of reference:

σu = cos2 θu σx + sin2 θu σy + 2 sin θu cos θu τxy (3)

As illustrated in Eq. 1, anisotropic materials are typ-ically characterized by two stress thresholds, σF inthe direction of the fibers, and σT in the transverse di-rection. It is not clear what this threshold is for otherdirections. In our approach, we interpolate betweenσF and σT based on the angle between u and the fiberdirection. To favor directions that are close to the fiberdirection, it is useful to specify a peek function witha controllable steepness. This is achieved through auser-defined power α in the interpolation factor:

σu = σT + (σL − σT)

(1− 2

πcos−1 (|u · f|)

)α

(4)

With this formulation, the criterion along the fiberand transverse directions match the original condi-tions given by the anisotropic model.

Locally refining the mesh and lowering thetimestep would allow a precise evaluation of thestress at the time of fracture [21]. A single direc-tion will reach the threshold, thus a single candi-date will be selected for fracturing. However, if thesimulation needs to meet real-time constraints, thissolution might prove prohibitive. Therefore, we pro-pose the following approximations. First, in the caseof linear materials, the computed stress inside eachelement does not precisely represent the real ma-terial stress, unless very fine meshes are used. Toapproximate the stress σ at the tip of the fracture,we propose to compute a weighted average of thestress inside each element in the neighborhood of thepoint of interest. Second, if large timesteps are used,several points and directions can reach the fracturethreshold at the end of the timestep. To avoid sub-stepping, which would be incompatible with real-time simulations, we propose the following heuris-tic: we choose as the fracture direction the directiondfracture where the criterion c(d, σ, f, p) is maximum,i.e. c(dfracture, σ, f, p) = max c(d, σ, f, p). For the

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special case of an isotropic fracture criterion (σF = σTand θσ = 90o), the solution can be computed by eigen-value decomposition of the stress tensor. Thus, ouralgorithm is equivalent to the maximum principal stresscriterion for the special case of isotropic materials. Forgeneral anisotropic surfaces, an exhaustive search onall the directions within the triangles connected tothe fracture tip can be used, as the evaluation of ourcriterion can be implemented very efficiently.

4.4 Tearing Propagation

Once the fracture direction has been determined,topological changes need to be applied to the finiteelement mesh to describe fracture propagation. Atthis point, there are two possible strategies. In thecase where the initial mesh is sufficiently fine, or ifthe edges are oriented along the fiber or transverse di-rection, it is possible to restrict the potential fracturedirection to an existing edge. This solution is simpleto implement, and the simulation cost as well as thequality of the initial mesh is preserved (as no newelement is created). However the resulting fracturewill be highly dependent on the original mesh. Fora precise, mesh-independent, tearing propagation, itis necessary to allow for arbitrary fracture directions.Once the fracture direction dfracture has been deter-mined, triangles need to be split to create new edgesalong the fracture direction. Particular care must betaken to avoid creating degenerated triangles whichwould otherwise negatively impact the computationof the finite element model. This issue is addressedusing the work of [21].

4.5 Results

Figure 6 illustrates the tearing and deformation mod-els in the context of a simulation of capsulorhexis.The membrane of the lens capsule is modeled as ananisotropic material with material properties similarto the actual lens capsule, and we use a co-rotationalfinite element formulation to numerically solve theproblem. Anisotropy is produced by concentric fibers(radially spaced every 0.5mm) that are defined onthe mesh to describe the actual structure of the lens

capsule. An implicit integration scheme is used to en-force robustness of the deformation process. Withthis approach, realistic deformations can be com-puted in real-time, and tearing of the membrane canbe simulated (see Fig. 6). The results clearly showqualitative realistic deformations accounting for theanisotropic nature of the tissue, and fracture propa-gation that depends on the fiber direction.

(a) Visualization of the opening into the lens capsule

(b) Visualization of the opening into the lens capsule

Figure 6: Simulation of capsulorhexis, a technique used to cre-ate a circular opening in the lens capsule. This tech-nique relies essentially on the application of shear andstretch forces to propagate a fracture throughout themembrane. Top (a): the mesh used to support the com-putation of the deformation and topological changes.Bottom (b): final result as seen in the training system.

5 Intra-ocular Lens Implantation

At last, the injection of the artificial lens and its de-ployment in the capsule in real time is performedby simulating the intra ocular lens deformation andinteraction within the capsule. The artificial lens ismodeled using finite element shells and allows real-istic reproduction of the mechanical behavior duringthe exit of the injector [22, 23]. The simulation also ac-counts for a physics-based modeling of the contacts

8

of the implant with the injector and the capsule wallsas well as self-contacts (contact of the implant on it-self). In the following, the model used to describethe implant is explained and the obtained results arepresented.

5.1 Related Work

There are two main difficulties related to the simula-tion of the intra-ocular lens implantation. The firstone is to model the complex deformation (essentiallydue to bending) of the lens, and the second consistsin modeling the contacts between the lens implantand the injector or the lens capsule. The deforma-tion of thin structures whose volume is negligiblecompared to their surface area (like intra-ocular im-plants) is fairly challenging. In fact, very few modelshave been proposed in the field of medical simulationfor simulating, in real-time, the deformation of thinstructures. To allow for an interactive simulation,a computationally efficient formulation is needed.Our finite element procedure was largely developedbased on physical understanding without the use ofmathematical shell theories. Indeed, our shell FEMwas obtained by simply superimposing a plane stressand bending energies. Although we use a simpleshell formulation, our model allows large displace-ments nevertheless through the use of a co-rotationalframework. Co-rotational approaches have been suc-cessfully applied to real-time simulation over the lastfew years [7]. They offer a good trade-off betweencomputational efficiency and accuracy by allowingsmall deformations but large displacements

5.2 Tools and methods

The approach used to model the complex deforma-tions of the implant during its insertion in the lenscapsule is based on the use of triangular shell ele-ments and a co-rotational formulation. The combina-tion of both leads to an accurate, yet computationallyefficient, shell finite element method featuring bothmembrane and bending energies. In addition, thepolynomial shape functions employed to computeinternal forces in our FEM formulation are also usedto process contacts and interactions with the curved

triangles. The benefits of our approach (fast compu-tation and possible interactions with other objects)allow us to successfully simulate the complex stepof the insertion and deployment of the intra-ocularimplant.

5.2.1 Geometrical model of the implant

To simulate the insertion and deployment of an intra-ocular lens, we first created a triangulation of the lenssurface. Particular care was given to the mesh, toensure that areas where large stresses occur contain ahigher density of elements (see Fig. 7). This was done

Figure 7: An actual intra-ocular implant (courtesy of Alcon)and the triangular mesh used in our simulations. No-tice the higher density of elements in areas where largedeformations will take place.

by noting the constraints applied by the surgeon tothe haptics while inserting the implant within theinjection device. During this stage, the haptics arefolded onto the implant body, leading to high stressesat the junctions. The lens mesh contains 743 trianglesand 473 nodes. Models of the injection device andthe entire eye anatomy were also created. Physicalparameters of the lens implant have been providedby the manufacturer Alcon. Thus, for the implant wespecified a Young’s modulus of 1MPa, a Poisson’sratio of 0.42 and its mass density was set to 1.2g/cm3.

The first difficulty is to obtain the folded geometryof the lens within the injection device. This step isnot important for the training process and does notneed to be interactive. Indeed the surgeon does notalways have to prepare the implant as some injectiondevices are readily available with a folded implantalready in place. We simulate the folding processby first folding the haptics onto the implant bodyby applying forces on the haptics while maintainingthe body fixed. While still exerting the forces on thehaptics, the body was then rolled around them to

9

obtain the shape described in figure 8. The foldedimplant was then placed into the injection device.

Figure 8: Intermediary steps of the intra-ocular implant foldingand fully folded implant ready to be placed into theinjection device.

5.2.2 Mechanical model of the implant

As mentioned earlier, we propose to define a trian-gular shell element by combining a two-dimensionalin-plane membrane energy, with an off-plane energyfor describing bending and twist. In the followingwe detail the bending stiffness computation in orderto present the polynomial shape functions that areused in the shell model.

To calculate the stiffness matrix for the transverse

Figure 9: The different degrees of freedom u of a triangular thinplate in bending.

deflections and rotations shown on Fig. 9, the deflec-tion uz is computed using a polynomial interpolation:

uz = c1 + c2x + c3y + c4x2 + c5xy+c6y2 + c7x3 + c8xy2 + c9y3 (5)

where c1, . . . , c9 are constants. Using a third-degreepolynomial expression allows us to reach a greaterprecision for both the computation of the bendingenergy and the interpolation within the surface of theshell. Let us define the vector u = {u1u2 . . . u9} ofthe displacements and slopes at the three corners ofthe triangular plate using the following notations:

u1 = (uz)x1,y1

u2 =(

∂uz∂y

)x1,y1

u3 = −(

∂uz∂x

)x1,y1

(6)

and so on for the two other vertices and we can derivea matrix C such as u = Cc where c = {c1c2 . . . c9}.We can then calculate the strains from the flat-platetheory using:

exx = −z∂2uz

∂x2 eyy = −z∂2uz

∂y2 exy = −2z∂2uz

∂x∂y(7)

Symbolically this may be expressed as e = Dcwhere D derives from (5) and (7). Noting thatc = C−1u, we have e = DC−1u = bu where thestrain-displacement matrix b = DC−1. The stiffnessmatrix Ke for an element is then obtained from:

Ke =∫

vbTχbdV where χ is the material matrix .

(8)The stiffness matrix in the global frame is eventuallyobtained using the rotation matrix of the element.

5.2.3 Mechanical interactions with the curved sur-face of shells

The practical interest of modelling complex be-haviours such as bending and twisting would re-main fairly low for medical simulation if contactsand constraints were not handled properly. Indeed,the simulation of the injection consists in pushing

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the intra-ocular implant within the injection deviceinto the lens capsule. During these stages of the sim-ulation, complex contacts occur and consist of selfcollisions of the lens as well as collisions betweenthe lens and the injector and later with the capsule.Obviously the contacts do not always occur onto thevertices of the triangles, they often occur onto thecurved surface of the shell. In our case the difficultyof handling contacts comes from different sources.First the collision detection must be carried out withthe curved surface of shell elements as opposed to theclassic detection on plane triangles. Then the forceapplied onto any given point of the curved surfaceneeds to be mapped onto the 3 vertices.

Firstly, in order to detect the collision with the bentsurface, we have chosen the subdivision approach.We sample the flat surface of each element by recur-sively dividing each triangle into four smaller onesand the deflection of each new vertex is computedusing (5) according to the displacements and slopesat the three vertices of the triangular element. Thisprocess of subdivision has two benefits. It allows usto render each shell as a curved triangle (Fig. 10 (a)and (b)) and to detect any collision with the curvedsurface of the shell using any of the classic collisiondetection algorithms working on flat triangles.

Figure 10: (a) The triangle formed by the three vertices of theshell has been recursively subdivided 3 times andthe deflection of each new vertex was computed ac-cording to the same deflection function used in ourshell FEM. (b) Sampling the actual surface of theshell allows more accurate rendering and collisiondetection. (c) The shape function is used to distributean external force F onto the triangle nodes.

Secondly, once a collision has been detected, itmust be processed by distributing the normal com-ponent of the force applied to the bent surface into a

force and a torque at each of the three nodes (Fig. 10(c)). This process is carried out by merely invertingour shell FEM formulation.

In a nutshell, the same polynomial interpolationfunction (5) chosen to compute the bending energyin our FEM formulation is also useful for handlingthe curved surface of our shells (regarding both vi-sualisation and interactions with other objects). Asadhesions between the haptics and the body is oftenobserved in surgery, friction also needs to be takeninto account in the contact response process. To solvethe contacts we use the contact warping method pro-posed by Saupin et al. [24] as it offers an efficient wayto compute physically correct contact responses inthe case of co-rotational models.

5.2.4 Simulation results

Results of our simulation are illustrated in figure11. We can notice the progressive deployment ofthe implant when it exits the injector. The shape ofthe intra-ocular lens remains very close to that of areal one during all stages of the simulation: withinthe injector, during the ejection phase, and when inplace within the capsule. Due to the high stiffnessand low mass of the lens, a direct sparse solver wasused at each time step (dt = 0.01 s) rather than aniterative solver, resulting in a more accurate and morestable simulation, to the detriment of computationtimes (about 5 FPS for the complete simulation, andabout 10 FPS for the deformation only, on a 2.4 GHzprocessor).

6 Interaction Devices

The way of interacting with the computer-based sim-ulator is important especially if the system targetsteaching and practising purposes. Moreover accu-racy and stability of the interaction system is essentialin a medical context. Our proposition combines repli-cas of real surgical tools as well as fast and robust 3Dtracking to accurately track the manipulations of thesurgeon.

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Figure 11: Three steps of the simulation of the intra-ocular lensimplant injection and its deployment within the lenscapsule. Top: images from a real cataract surgery,courtesy of Dr. Tarek Youssef, ophtalmologist inCanada. Below: our simulation of the implant’s de-ployment.

6.1 Related Work

The use of a stylus attached to an articulated armallows good precision and force feedback and is apopular interaction device for computer-based simu-lations [6, 3]. However it can hardly handle multipletools and interaction modality (a stylus with a sin-gle button) is quite far from cataract surgery tools.Optical tracking offers a bigger workspace but mayrequire time-consuming algorithms to provide 3Dtracking of tools [16].

6.2 Methods

Our approach is based on infra-red optical trackingwhich combines the benefits of optical tracking withfast algorithms. Indeed the image segmentation isfaster because only the reflective markers need to bedetected. The rest of this section describes how thetracking is done and connected with the simulationengine.

Real surgical tools could have been used to interactwith the simulation, however they suffer from twoimportant drawbacks. First they are exepensive andsecond they are metal-based which makes the track-ing more difficult and lower the accuracy (diffusereflection area may appear on the images). There-fore, the use of replicas of surgical tools based onpolyamide (nylon) was made. They were first mod-

elled using standard CAD software and then werebuilt using fast prototyping. Figure 12 shows thecomparison between some of the real surgical toolsand the ones used in our simulation. Reflective mark-ers may disturb the clinician, especially for graspingtasks, but the markers are carefully placed to limitdisturbance.

Figure 12: Examples of tools used in cataract surgery and theones we built for interacting with the simulation.From left to right: the phaco chopper, the phacoemul-sification handpiece and the capsulorhexis forceps.

6.3 Robust 3D Tracking

Figure 13: Overview of our setup: mannequin and microscopewhere 6 infrared cameras are attached. These camerasallow to track in real-time the motion of the surgicaltools.

Our setup includes 6 infra-red cameras that tar-gets the area around the eye. Two cameras may besufficient to provide a 3D tracking but this is not a ro-bust set-up. Indeed, intensive manipulations in thatarea may completely or partially hide instrumentspreventing the real-time tracking to work. With 6cameras, the operative area is well covered and dur-ing any step of the procedure at least two cameras

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are able to track the instruments. The setup is shownon figure 13. The redundancy involved with the 6cameras make the calibration more time-consumingbut once it has been performed, the tracking algo-rithm is able to provide 3D position of markers inreal time. We are also using a feature proposed byTracking Tools3 software which allows to track rigidbodies. Each rigid body is defined as a set of reflec-tive markers and the distance between markers donot change over time and the tracking is then moresimple. 3 markers may be sufficient to define a 3D po-sition but again for robustness issues, we introduceredundancy by placing 4 markers on the instrument.Using different signatures (e.g. the way markers areplaced on the tools), we can manage to track sev-eral tools simultaneously (see figure 14) which is aprerequisite for several steps of the cataract surgeryprocedure.

For a better balance of the computation powerneeded to run our simulation system, two computersare used. The first one, which does not require largecomputational resources, is connected to the cam-eras and runs the tracking software while the secondone runs the simulation engine. The two computersshared tracking informations by using the VRPN li-brary 4 which is a lightweight and low-latency client-server protocol dedicated to virtual reality applica-tions. The simulation engine is therefore on a singlecomputer (with high-performance graphics cards)and can provide fast response to user inputs.

7 Conclusion

The results presented in the previous sections de-scribed original contributions which, combined in asingle simulation framework, allow to perform in-teractive cataract surgery simulations. These con-tributions rely on advanced bio-mechanical modelsand intensive use of modern graphics hardware toprovide fast computation times. Moreover, surgi-cal devices, that are tracked in real-time thanks toinfra-red cameras, have been reproduced in order

3http://www.naturalpoint.com/optitrack/products/tracking-tools/

4http://www.cs.unc.edu/Research/vrpn/

Figure 14: Screenshots of the tracking of surgical tools. Withthe reflective markers, the tracking system is ableto compute the 3D position of the tool in real-timeand using different marker signatures, we can man-age to detect several tools simultaneously withoutambiguity.

to faithfully mimic the operating room environmentand the actual procedures. Preliminary tests havebeen performed by experienced ophthalmologists toqualitatively look at the realism of the simulation andthe faithfulness of the interactions with the surgicaltools.

As these feedbacks were positive a double-blindexperiment is conducted among ophthalmologist in-terns to assess the effectiveness of simulation trainingcompared to current companionship training meth-ods. This experiment is based on the following pro-tocol: first, a common metric system has to be definein order to provide a common ground to evaluatesurgeons performance in a real procedure or in a sim-ulated procedure; second, the comparison of perfor-mance between interns that were exclusively trainedon simulators will be confronted with interns thatwere trained according to companionship method.

The common ground used to measure surgeonsperformance during cataract surgery is based on [25]and is an objective performance rating tool derivedfrom the Objective Structured Assessment of Techni-cal Skill (OSATS) [26]. OSATS has also been validatedfor other surgical specialities. The work of Saleh et.al. on OSACSS (Objective Structured Assessment ofCataract Surgical Skill) exhibits construct validity andis therefore a valuable tool to assess the surgical skillof trainees [25]. OSACSS is based on a set of 20 mea-surements or observations that can be programmedinto the simulation engine. For instance, indices in-

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clude Eye Positioned Centrally Within Microscope View,Iris Protection or Capsulorhexis: Formation and CircularCompletion and can be easily translated into computerinstructions. All of these criteria are based on geo-metric criteria, contact analysis (pressure on somefragile anatomical structures) or procedure step com-pletion. The experiment has started where a series oftrainees practice in the virtual environment and areevaluated by both experts and the simulator. Scoreswill be compared and we do expect that the simula-tion provides scores that are close to those grant bythe expert surgeons.

Once this step is achieved settling that our simula-tion provides comparable and objective scores thatassess skills in cataract surgery, future works willrequire a second and longer experiment. This exper-iment will be conducted to determine the possibleoutcomes of the simulator and if practicing in ourvirtual environment is a viable training method thatis complementary to companionship training.

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deformation with cutting and haptic feedback.Progress in Biophysics and Molecular Biology, 103(2-3):159–168, December 2010. Special Issue on SoftTissue Modelling.

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[16] Roger Webster, Joseph Sassani, Rod Shenk, MattHarris, Jesse Gerber, Aaron Benson, John Blu-menstock, Chad Billman, and Randy Haluck.Simulating the continuous curvilinear capsu-lorhexis procedure during cataract surgery onthe eyesi system. Stud Health Technol Inform,111:592–5, Jan 2005.

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8 Authors’ biographies

• Jeremie Dequidt completed a Ph.D. thesis inComputer Science at the University of Lille 1 in2005. As a post-doctoral fellow he joined the Sim-Group at CIMIT (Boston, MA) and then INRIAAlcove team, working on interventional radiol-ogy simulations. Since september 2008, he isan Assistant Professor in Computer Science atPolytech’Lille. He also is a member of the In-ria research-team Shacra. His research worksinclude collision detection and response, me-chanical / geometric / adaptive modeling andexperimental validation of the simulations.

• Hadrien Courtecuisse is a research engineer atIHU Strasbourg. He received his Ph.D. in com-puter science from Lille University in 2011. He

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works in the field of real-time medical simula-tion since 2008. His research interests includefinite element methods, GPU parallel processingusing CUDA, Sparse Linear Algebra, Collisiondetection, and modelisation of the interactionswith soft bodies.

• Olivier Comas is a research associate at Na-tional Research Council Canada. He receivedhis Ph.D. in computer science from Lille Uni-versity in 2010 and his M.S. in medical imageprocessing and robotics from Strasbourg Univer-sity in 2006. He works in the field of real-timemedical simulation since 2006. His research in-terests include include finite element methodsand GPU parallel processing using CUDA.

• Jeremie Allard received a PhD degree in Com-puter Science from University of Grenoble in2005. Then, he got a postdoctoral position at theCIMIT SimGroup in Boston. He joined INRIA in2007 where he gets a research scientist position.His research interests include new highly paral-lel architectures such as GPUs in the context ofinteractive simulations for medical applications.

• Christian Duriez received a PhD degree inrobotics from University of Evry in 2004 for aresearch work done at CEA Robotics lab on hap-tic rendering of collision between deformablesolids. Then, he got a postdoctoral position atthe CIMIT SimGroup in Boston. He arrived atINRIA in 2006 where he gets a research scientistposition. His research work concerns finite ele-ment methods computed in real-time, robot con-trol by simulation, contact modeling and hapticrendering.

• Stephane Cotin joined INRIA in 2007 to hold aposition of Research Director. Since January 2010he also leads the SHACRA group, a multidisci-plinary team of scientists involved in the fieldon medical simulation. He also manages thedevelopment of a Large Scale Initiative on Medi-cal Simulation, a collaborative research programinvolving scientists from six different teams. Be-fore joining INRIA, he was Research Lead for

the Medical Simulation Group at CIMIT, wherehe managed a team of 12 permanent researchersand post-doctoral fellows. His main researchinterests are in physics-based simulation, real-time simulation of soft-tissue deformations, andmedical applications of this research.

• Elodie Dumortier is a Senior Registrar of theUniversities and a Medical Assistant at the Hos-pitals of Lille. Her research focuses on the val-idation of simulation to train cataract surgeryprocedures.

• Olivier Wavreille is a Senior Registrar of theUniversities and a Medical Assistant at the Hos-pitals of Lille. His research focuses on the palpe-bral portion of the lacrimal gland and on the tearfilm.

• Jean-Francois Rouland is a University Profes-sor at University of Lille and is also the Headof Ophthalmology Department in Lille Hospital.He is also the General Secretary of the French So-ciety of Glaucoma Expert of the French Ministryof Health.

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