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Implicit Representations of the Human Intestines for Surgery Simulation
Laure France, Alexis Angelidis, Philippe Meseure, Marie-Paule Cani, Julien Lenoir, François Faure, Christophe Chaillou
To cite this version:
Laure France, Alexis Angelidis, Philippe Meseure, Marie-Paule Cani, Julien Lenoir, et al.. Implicit
Representations of the Human Intestines for Surgery Simulation. Modelling and Simulation for
Computer-aided Medicine and Surgery, MS4CMS, Nov 2002, Rocquencourt, France. �inria-00517243�
Simulations
Laure France 1
Alexis Angelidis 2
PhilippeMeseure 1
Marie-Paule Cani 2
Julien Lenoir 1
Francois Faure 2
Christophe Chaillou 1
1
LIFL,Universite LilleI, Villeneuve d'Ascq
[Laure.FrancejPhilippe.MeseurejJulien.LenoirjChristophe.Chaillou]@li.fr
2
iMAGIS-GRAVIR, INRIA Rh^one-Alpes, Montbonnot
[Alexis.AngelidisjMarie-Paule.CanijFrancois.Faure]@imag.fr
Abstract
Inthispaper,weproposeamodelingoftheintestinesbyimplicitsurfacesforabdominalsurgerysimula-
tion. ThediÆcultyofsuchasimulationcomesfromtheanimationoftheintestines. Asamatteroffact,the
intestines areaverylong tubethatis notisotropicallyelastic, andthat bendsoveritselfatvariousspots,
creatingmultipleself-contacts.
We usea multiple component modelfor the intestines: Therst component is amechanicalmodelof
their axis; the second component is aspecicsphere-based modelto managecollisions and self-collisions;
and the third component is a skinning model to dene their volume. This paper focuses on the better
representation for skinning the intestines. We compare two implicit models: Surfaces dened by point-
skeletons andconvolutionsurfaces.
A direct applicationof this simulation is the training of a typical surgical gesture to move apart the
intestinesinordertoreachcertainareasoftheabdomen.
Keywords: Surgicalsimulation,virtualreality,implicitsurfaces,real-timecomputation,applicationto
medicaldomain.
Resume
Danscetarticle,nousproposonsunemodelisationdesintestinsparsurfacesimplicitespourlasimulation
dechirurgieabdominale. La diÆculted'unetellesimulationprovientdel'animationdesintestins. Eneet,
lesintestinssontuntreslongtubequin'estpaselastiquedemaniereisotrope,etquiserepliesurlui-m^eme
endenombreuxendroits,creantdemultiplesauto-contacts.
Nousutilisonsunmodeleaplusieurscomposantspourlesintestins: lepremiercomposantestunmodele
mecaniquereduit aleur axe; le deuxiemecomposant estun modelespeciquebase surdes spheres pour
gererlescollisions etauto-collisions ;etletroisiemecomposantestunmodeled'habillagepourdenirleur
volume. Cet article sefocalisesurlameilleurerepresentationpourhabiller les intestins. Nous comparons
deuxmodelesimplicites:les surfacesdeniespardessquelettesponctuelsetlessurfacesdeconvolution.
Uneapplicationdirectedecettesimulationestl'apprentissaged'ungestechirurgicalcaracteristiquepour
rassemblerlesintestinsandedegagercertaineszonesdel'abdomen.
Mots cles: Simulationchirurgicale, realitevirtuelle, surfacesimplicites,calculstemps-reel,application
audomainemedical.
1 Introduction
Laparoscopicsurgeryisasurgicaltechniquethatusesacameraandsurgicaltoolsinsertedintothebodyvia
smallincisions. Thistechniqueleadstounusualworkingconditionsthatrequiremanyrehearsals. Thetraining
thencouldbeperformedonasimulator. Surgeonswouldlearnthesurgicalgesturesonphysicallybasedvirtual
organsthatreacttotheiractions.
Some endoscopic simulators exist, usually consisting in simulating the interaction of surgical tools with
a single organ. Dynamic virtual organs have already been modeled, such as the liver [5, 10, 12, 16] or the
ofverydeformableobjectsthatareincontactin variousspots andmayundergoverylargedisplacements.
The goal of our simulator is to clearan area to treat, by pushing/pulling and maintainingthe intestines
in another place of the abdominal cavity. Indeed, this clearing stage is needed before surgeries such as the
gallbladderremovalorcolontumors. However,thisactionrisesseveralchallenges: Largedisplacements,contacts
andself-collisions.
Wedevelopedarstmodeloftheintestinesin[13],composedofthreecomponents: Amechanicalmodelto
denetheirphysicalbehavior;amodelforself-collisionsbetweentheirparts andcollisionswithotherobjects;
andaskinningmodelto representand displaytheirshape. However,theskinningmodelbasedonparametric
generalizedcylinderswasnotsatisfying,sinceitcouldresultinsurfacediscontinuitiesinhighly curvedregions
andinvolumeloss.
In this paper, we addressthis problem byusing implicit surfaces,known for representingquite naturally
organicshapes[2]. Indeed, theyfollowaskeletonin anintuitive wayregardlessofitsdeformation. Moreover,
this representation allows thegeneration of contact between surfaces [6]. Lately, implicitsurfaces were even
adaptedtolevelsofdetail(LOD)bytaking intoaccountmulti-resolutionaspects[1].
Thepaperisorganizedasfollows: Section2reviewsourthreecomponentmodelfortheintestines. Sections
3and4presentthetwoalternativeskinningmodelsanddiscusstheirabilitytomodeltheintestines. Section5
concludesanddiscussessomefuture work.
2 A three component model for the intestines
Wewantto simulatetheevolutionof thebehaviorand thevisual aspectof theintestinesunder theaction
ofsurgicaltools,andto returnanappropriatehapticfeedbackviatheuserinterface. Tosimulatethephysical
behavior of the intestines, we use a mechanical model that animates their virtual skeleton. The intestines
skeleton can be represented asa curve with mechanical properties. Next, since the intestines may undergo
self-collisionsand collisions with their environment and some surgical tools, we use a detectionmodel based
onthemechanicalmodelto computethese collisionsand theirresponse. Finally,weprovideaskinningmodel
in orderto representanddisplaytheshapeoftheintestines (butwith nomechanicsat this level). Webriey
presentour rstmodel (furtherdetails canbefound in[13])and discussthe awsof theparametricskinning
modelweused.
2.1 MechanicalModel
WeuseacubicCatmull-Rom[9]segmentedsplinetodenetheintestinesaxis(theirskeleton). Thisdenition
allowstheusertocontroltheshapeofthesplinejust bymodifyingthecontrolpoints. Inorder toanimatethe
spline,weuseaLagrangianformalisminspiredfrom[17]. This formalismtakesinto accountthecontinuity of
theobjectandthusenablesacontinuousmassdistributionalongthecurve. Moreover,itallowsexternalactions
and/orconstraintstooccuranywherealongthespline.
The formulation of the equations leadsto the resolution of a systemof the form MA = B, namely the
resolutionof A=M 1
B, withM thegeneralizedmassmatrix, Athe accelerationof thedegreesof freedom
(the control points), and B the forces. It waspointedout that M is a diagonalblock matrixwith identical
diagonalblocksM. M is asymmetric, time-independent matrix,allowingthe pre-computationof theinverse
matrix, yielding in a faster resolution of the equation system. Besides, we take benetof the locality of the
Catmull-Romspline: For anycubic spline, the matrixM is band. Finally, the system resolution complexity
becomes O(n). Once thissystem solved,weget theaccelerationofthe degreesof freedom. Weuse aRunge-
Kuttaintegrationschemetoestimatethenewvelocitiesandnewpositions ofthecontrolpoints.
2.2 Collision/Self-collisionModel
Ourcollisiondetectionmethodusesanapproximationoftheobjectshapebyboundingspheres. A3Dgrid
thatdiscretizesthespaceisusedtospeeduptheprocess: Collisionsonlyneedtobeperformedbetweenspheres
belongingtoasamevoxel. Thisprocessisiteratedforeachsphereaddedtothegrid. Sincethepenaltymethods
arewellsuitedtodeformableobjects,theyareusedforcollisionresponse(see[11]formoredetails).
uniformlyaccordingtotheparametricabscissa(seeFigure1). Whenasurgicaltoolinteractswiththeintestines,
the intestines spheres ensure the detection of the collision and provide penalty forces as reaction response,
yieldinginthemovementand/ordeformationoftheintestinesandinforcesreturnedbythefeedbackdevice.
Neighbor spheres
Self-collision
Figure 1: Spheredistributionalongtheintestinesaxis.
Self-collisionsbetweenintestinesfoldsaremanagedbyusingthesamemethod. Nevertheless,inthedetected
collisions,wemustdiscardthespheresthatareneighborsalongtheintestinesaxis(seeFigure1).
2.3 Skinning Model
Themechanicalmodelrunsat100Hzormore,independentlyfromtheskinningmodel,displayedat25Hz.
Ateachdisplaystep(thatmaybelargerthanthesimulationstep),askinningoftheintestinesmustbegenerated.
Itmustdependupontheposition andtheplacementoftheirskeleton. Inotherwords,theskeletondescribing
thegeneralmotionoftheobject,theskinninghastofollowit,providingtheresultingshapeoftheobject.
Dierent methodsexist to deneavolume, someofthem aremoreadapted toatubular volume basedon
alinearskeleton. Theideais to createa volume delimited byasurfacearoundthe skeleton. Inourprevious
model[13], wedenedtheintestines surfaceasaparametricsurfacearoundthediscreteskeletonbasedonthe
splinepoints,atadistancerepresentingtheintestinesradius. Thisrepresentationallowedaninteractivedisplay.
Nevertheless,it suersfrom twomajordrawbacks: First,theresultingshapeisimperfect forhigh curvatures,
andsuersfromtangentandvolumediscontinuities;second,there isnodirectmethodtodeformitinorderto
modelexactcontactbetweensurfaces.
On theother hand, implicit surfaces particularly suit organicshapes, since theycontrol a volume around
theskeleton,enablingrealisticcurvedshapesandgeometriccontactbetweensurfaces[7]. Theremainderofthe
articlepresentstwomethodsbasedonimplicitsurfacesforthedisplayoftheintestines.
3 Implicit Intestines using Point-Skeletons
3.1 Method
An implicit surfaceisdened by theset of pointssuchthat the valueofa giveneld function f forthese
pointsP equalsto a given valuee, namelythe iso-value,for which the iso-surfaceis drawn: f(P)=e. The
evaluation of theeld function for anypointallowsastraightforwarddetectionof theinterior/exteriorof the
object. Thischeckingsimpliesthecollisiondetectionbetweenobjects,andthustheblendingcontrol.
One possibility to generate an implicit surface from a skeleton is to use distance surfaces [4]. Distance
surfacescomputetheeld valueat agivenpoint P fromits distanceto itsclosestpointontheskeleton. The
blendingof severalskeletonscontributionsisdirectly performedbysummingtheireld values. Thistechnique
thensuppressessurfacefoldsatthejointofskeletons,but maycreatebulges[3].
Wedenetheintestinessurfaceasanimplicitsurfacegeneratedbydiscretepoint-skeletonspositionedalong
thespline. Thestrengthoftheireldvalueistunedaccordingtotheradiusoftheintestines(seeFigure2(a)).
Duringtheanimation,theskeletonshapevariesasthesplinepointsmove. However,iftwopointsoftheelastic
spline are too far from each other, there is no moreblending between them, thus separatingthe objectinto
twoparts. In order to avoidthese topology changes, the numberof sampling points mustchange during the
simulation. This is done by adaptivelyplacing spheresalongthe curve at intervalswhich rangeis afunction
of the spline segment length and the radius of the spheres. Next, we use areal-time implementation of the
marchingcubesalgorithmproposedby[19]forthevisualizationoftheimplicitsurface.
Theblendingpropertyoftheimplicitsurfaceensuresacontinuousshapefortheintestinesmodel(seeFigure
2(b)). However,itisparticularlydiÆculttoprovideaconstantradius. Indeed,thevariationofthenumberof
skeletonsleadstouctuationsofthe geometry(thiscouldrepresentthespasmsofthe intestines,but wewant
tocontrolthem). Moreover,caremust betaken toavoidblendingbetweennon-consecutiveparts. Itrequires
theuseoftheblendinggraph. Unfortunately,inourimplementation,theblendingcontrolcannotbedoneata
suÆcientratedueto themarchingcubemethodto displaythesurface.
qi
qj
(a)Model. (b)Interactivedisplay.
Figure2: Implicitintestinesusingpoint-skeletons.
4 Implicit Intestines generated by a Convolution Surface
4.1 Method
In order to avoidthe aws of avarying numberof point-skeletons, we must use thewhole skeleton curve
orat least alinearapproximationof this curveto generatethe intestines geometry. Onepossibility is to use
convolutionsurfaces [3], andto representtheshapeasaset ofconnectedconvolutionsegment-skeletons. This
representation avoids bulges on the surface that coats the segments, and allows the number of segments to
changeateachtimestepwithoutcreatingjumps ontheimplicitsurfacegeometry,aslongasnewlyintroduced
verticesaresmoothlytranslated.
Forasingleconvolutionsegment-skeleton, theeldvalueatapointP isthesumofthecontribution ofall
thepoint-skeletonsalongthesegment. Thisintegralhasaclosed-formsolutionforvariouspoint-skeletonkernel
functions[8,15,18]. Thesolutionproposedin[8]isthefastest,anditsexpressionis:
f(P)= sin
1 sin
2
d 2
(P;H)
(4.1)
withd(P;H)thedistancebetweenP anditsprojectionH ontheskeletonsegment,
1 and
2
thesignedangles
betweenthis axisofprojectionandthelineslinkingP totheextremitiesoftheskeletonsegment.
A straightforwardwayof modeling asmoothcomplexsurfacewouldthen consist in summingallthe indi-
vidual eld contributionsof the simple segment-skeletons. This would nothowever preventthe surfacefrom
blendingbetweennon-consecutiveparts. Therefore, weusethecontrolledblendingtechniquedevelopedin [1],
thatrstneedstodescribethesamplingoftheimplicitsurface.
Todisplaythesurfacesatinteractiverate,weusetheseed-basedmethodof[8]whichtakesbenetfromthe
temporalcoherence. Seedsmigratetowardsthesurfaceaccordingtotheiso-surface. Initially,theystartfromthe
skeleton,andintheremainderofthesimulation,theystartfromtheirpreviouspositions. Thediscretizationof
thesurfacetriangulationisadaptive,allowingthesurfacetoberenderedatdierentlevelsofdetail. Toproduce
theadaptivesampling, aroughpolygonizationisinitially attachedto afew samplingpoints,andthen rened
recursivelybyauniform subdivision untilacertaincriterionissatised.
assigns to every point P
i 2 IR
3
on the surface a parameter u
i
along the skeleton, which corresponds to the
attachedpointof theseedaxis. A localportion ofthe skeleton aroundu
i
is usedto computef(P
i
),which is
aneighborhood of constant size D around u
i
. The eld value is then computed exactlyas before, with the
exception that only the useful partof the skeleton is considered in this case. A constrain on D is D < 2R
(Ris theintestinesradius),sincetwopointsonthesurfaceseparatedbyadistancegreaterthan2R mustnot
inuenceeachother.
4.2 Results
With this model, thevisual rendering of theintestines is satisfying: There is no blending, and no bulges
created(seeFigure 3(b)). However,the computation timeis stilltooslowifwe wantane discretization of
thesurfaceobject.
j i
j i
j i
D u
u P
P D
(a)Model. (b)Displayofintestinesonlyanimatedwithgravity.
Figure3: Implicitintestinesgeneratedbyasubdivisioncurve.
5 Conclusion
Inthispaper,wepresentedamethodtosimulate atinteractiveratetheintestinesin theabdominal cavity,
for surgical training purposes. The intestines are very deformable objects, and during a surgery, they may
undergolargedisplacementsand multiple interactions. Theintestinesmodelisbasedonaskeletondened by
aspline tocomputeitsmechanicalmotionfromtheLagrangeformalism. Collisionspheresarethenusedfora
fastcollisiondetection,providingreal-timefeedbackviathehapticdevice. Thepaperfocusedontheskinningof
thismodel. Itcomparedtwoimplicitsolutionsthatoerquitegoodresultsintermsofvisualeectsconcerning
the movements and deformations of the intestines. We showed that this skinning by implicit surfaces may
be attractivein the context of a surgical simulator. Theintroduction of adaptive implicit surfaces based on
convolutionisinterestingsincetheanimationcouldbedisplayedatdierentlevelsofdetailtoobtaininteractive
ratewhatevertheworkstation.
Currently, only the discretization of the surface triangulation is adaptive. A future work could consist
in dynamically adapting the discretization of the skeleton according to the varying curvature. It could be
interestingto dealwith bothaspects in order to tune theparameters to obtaincomputations anddisplay in
real-time. Moreover, it could be possible to add the contact surfaces presented in [1] so that the contact is
betterhandled. Ontheother hand,self-collisionscouldbedetectedmoreprecisely bytakingintoaccountthe
informationprovidedbytheimplicitsurface.
ThisworkissupportedbyINRIA(FrenchNationalInstituteforResearchinComputerScienceandControl)
aspartof the ARC SCI (research action forIntestines SurgerySimulator). The authors would like to thank
people ofIRCAD(French DigestiveCancerResearchInstitute)fortheirconstructivediscussions.
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