Inflinclchaelem

Shiming Liu, DD

aDoctoral student, Department of PbProfessor, Department of ProsthodcProfessor, Department of ProsthododProfessor, Department of MechaniceAssociate Professor, Department of

The Journal of Prosthetic

uence of occlusal contact and cuspination on the biomechanicalracter of a maxillary premolar: A finiteent analysis

S,a Yuhua Liu, DDS,b Jun Xu, DDS,c

Qiguo Rong, PhD,d and Shaoxia Pan, DDSe

Peking University School and Hospital of Stomatology, Beijing, China;Peking University, Beijing, China

Statement of problem. Restoring teeth with large amounts of dentin loss is challenging, especially for posterior teethwith high cusps. However, strategies for reducing the lateral forces are based on clinical experience instead of thanscientific evidence.

Purpose. The purpose of this study was to analyze the biomechanical characteristics of maxillary premolars with differentferrule configurations and to investigate the influence of occlusal contact and cusp inclination on stress distribution withthe finite element method.

Material and methods. Five numerical casts of a maxillary premolar were generated; each adopted 1 of the 5 coronal dentinconfigurations: i (access cavity with 4-mm dentin height) and ii to v (2-mm complete ferrule, 2-mm facial ferrule, 2-mmpalatal ferrule, 2-mm proximal ferrule, and restored with a post and core, respectively). Both gold-alloy and glass-fiber postswere modeled. An oblique load of 200 N was applied to the top, middle, and bottom of the 45-degree facial cusps. Thecusp inclination was remodeled to 60 degrees, followed by the application of a 200-N load to the top. The values ofthe maximum principal stress and von Mises stress were calculated to assess overload risk.

Results. When the top of 45-degree facial cusps was loaded, the maximum local stress concentration on dentin was foundin teeth with a facial ferrule and restored with a gold-alloy post. When the middle of 45-degree facial cusps were loaded, theprincipal stresses of teeth with a complete ferrule, palatal ferrule, and proximal ferrule were similar to those of the accesscavity teeth. In contrast, the principal stress of a tooth with a facial ferrule was close to that of the access cavity toothafter remodeling the facial inclination to 60 degrees.

Conclusions. Maxillary premolars with only facial dentin remaining show higher local stress on root dentin. Altering theloading position and reducing the facial cusp inclination can reduce local stresses. (J Prosthet Dent 2014;112:1238-1245)

Clinical ImplicationsNumerical calculations indicate that the ability of post-and-core restoredteeth to withstand occlusal forces may be inferior to that of vital teeth.For a maxillary premolar with extensive defects, a risk of overloadingarises when it bears an oblique load; appropriate occlusal design wouldimprove biomechanical behavior and greatly reduce this risk.

The restoration of endodonticallytreated teeth is challenging when a largeamount of dentin has been lost. Thelongevity of these teeth depends mainly

rosthodonontics, Pekntics, Pekal EngineeProsthod

Dentis

on the remaining hard dental tissue.The ability of the restoration with aferrule to bind the remaining toothstructure together is believed to be the

tics, Peking University School and Hospital ofing University School and Hospital of Stomatoing University School and Hospital of Stomatoring, Peking University.ontics, Peking University School and Hospital o

try

key to long-term stability and is essen-tial for a post-and-core restoration.1

In vitro studies have found that1.5- to 2-mm ferrule height is ideal1-3

Stomatology.logy.logy.

f Stomatology.

Liu et al

1 Maxillary premolars with different coronal dentin config-urations and loading protocols.

November 2014 1239

and check that the resistance of recon-structed teeth is directly related tothe amount of remaining sound hardtooth.4,5 Both the amount of toothstructure loss and the position of cor-onal defects are associated with theloading resistance of the teeth. Theresults of proximal caries, trauma, orocclusal overload often make it difficultto achieve a complete “all around”dental ferrule. A nonuniform ferrulemay have a negative influence on thefracture resistance of post-and-corerestored teeth, although this is still su-perior to the nonferrule scenario.6,7

According to some in vitro studies, thelocation of sound tooth structure that

Table I. Geometric properties and load

Group

CrownHeight(mm)

RootLength(mm)

CoronDentiHeigh(mm

Access cavity 8 13 4

Complete ferrule 8 13 2

Palatal ferrule 8 13 2

Facial ferrule 8 13 2

Proximal ferrule 8 13 2

Liu et al

provides resistance to occlusal forces isprobably more important than havingcircumferential axial wall dentin.6-8

When limited coronal dentin re-mains so that a standard ferrule is notpossible, the risk of tooth fractureand restoration debonding is muchhigher.5-7,9,10 In group function situa-tions, this is worse for maxillary pre-molars, which, because of their highcusps, are exposed to repeated obliqueocclusion forces that are translated intohigh lateral forces.11 Therefore, whenprosthetic treatment is planned forsuch teeth, attention should be focusedon protecting the damaged teeth fromhigh functional loads to avoid failures.

steps of 5 teeth analyzed

alnt)

Post Length (mm)

Above theFerrule (h1)

In theRoot (h2)

45-DegreeCuspTop

d d O

2 10 O

2 10 O

2 10 O

2 10 O

Results of a number of studies indicatethat the occlusal design should bemodified for teeth with substantialdentin loss to protect the supportingunits and the restoration from over-load.12 Researchers recommend mini-mizing the lateral forces to reduce therisk of fatigue fracture.13 However, theway in which lateral forces should bereduced and the extent of this reductionremains to be determined.

Therefore, the purpose of thisstudy was to analyze, by means of 3-dimensional (3D) linear-elasticity finiteelement simulations, the biomechanicalcharacter and dentin fracture risk of 4post-and-coreerestored maxillary pre-molars with either complete or partialferrules. To investigate the influence ofocclusal contact position on stress dis-tribution in dentin, 3D casts weredesigned with different loading posi-tions on the facial cusps to simulate theocclusal adjustment procedure thatwould be carried out clinically. The in-fluence of facial cusp inclination alsowas examined.

MATERIAL AND METHODS

The geometry of a maxillary pre-molar was obtained by scanning anacrylic resin tooth replica. The 3D castwas reconstructed by using modelingsoftware (UG NX 6.0; Ansys). Five 3Dcasts were created based on this initialcast to simulate maxillary premolarswith different coronal dentin config-urations (Fig. 1, Table I) as follows: i,pulpless tooth with access cavity and

Load Steps

45-DegreeCuspMiddle

45-DegreeCusp

Bottom

60-DegreeCusp

Bottom

d d d

O O O

O O O

O O O

O O O

Table II. Material properties

MaterialsYoung

Modulus (E) (GPa)PoissonRatio (n) Reference No.

Dentin 18.6 0.31 18

Crown (ceramic) 380 0.25 18

Gold-alloy post 93.0 0.33 18

Glass-fiber post 40.0/11.0 0.26/0.32 18

Core composite resin 6.9E-4 0.30 19

Gutta percha 0.14 0.40 14

Cortical bone 13.7 0.30 20

Trabecular bone 1.37 0.30 20

Periodontal ligament 6.89E-5 0. 45 21

1240 Volume 112 Issue 5

4 mm remaining coronal dentin (AC);ii, pulpless tooth with 2-mm completeferrule (360 degree) (CF); iii, pulplesstooth with 2-mm palatal ferrule (180-degree) (PaF); iv, pulpless tooth with2-mm facial ferrule (180-degree) (FF);and v, pulpless tooth with 2-mmproximal ferrule (180-degree) (PrF).All the casts were developed with 0.2-mm periodontal ligament and bone

2 Von Mises stress contours of teeth witrestored teeth.

The Journal of Prosthetic Dentis

block. The AC cast tooth was restoredwith a single complete crown, andthe others, ii to v, were restored witha post and core and a completecrown. Modeled posts consisted ofgold alloy or glass fiber and wereassumed to be perfectly bonded to theroot dentin. The complete crown wasceramic, with a 45-degree facial cuspinclination.

h different ferrules. A, Gold-alloy-post res

try

The 3D casts were imported intoa finite element software package(ANSYA Workbench 10.0; Ansys). Allthe materials were presumed to belinearly elastic, homogeneous, andisotropic, except for the glass-fiberposts, which were modeled as trans-versally isotropic (Table II). Three-dimensional meshes were createdthrough 10-node tetrahedral elementswith quadratic displacement shapefunctions and 3 degrees of freedom pernode. The mean mesh size was ap-proximately 0.2 mm, and the bottomsection of the bone block was assumedto be fixed. The casts included approx-imately 210 000 elements and 290 000nodes.

To evaluate the influence of occlusalcontact and cusp inclination on toothbehavior, 2 load steps were separatelyprocessed. First, a 200-N oblique staticload was applied to all the teeth (i-v).The load was angled at 45 degreeswith respect to the occlusal plane andapplied to the top of the facial cusps.

tored teeth. B, Glass-fiber-post

Liu et al

100

80

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von

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es S

tres

s (M

Pa)

AC CF PF FF PrF

Coronal Root Apex Shoulder A

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Coronal Root Apex Shoulder B3 Von Mises stress measured at shoulder, crown, andapex of teeth. A, Gold-alloy-post restored teeth. B, Glass-fiber-post restored teeth.

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Au Post

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Composite Resin

4 Von Mises stress measured at post and core. A,Gold-alloy-post. B, Glass-fiber-post and composite resin.

November 2014 1241

Liu et al

Second, for the post-and-core restoredteeth (ii-v), the same 200-N load wasapplied to the middle and bottom ofthe facial cusps. After that, the facialcusp inclination of the complete crownwas remodeled from 45 to 60 degrees,with the 200-N load applied to thetop of a 60 degrees facial cusp (Fig. 1,Table I). The resulting stress fields ofthe post-and-core restored teeth werecompared with that of the completecrown restored tooth (AC). The peakvalues of von Mises stress (svM) andmaximal principal stress (smax) wereused to quantify the local risk of fractureat the dentin. The interface of the dentinand restoration were analyzed to deter-mine the potential for bonding failure.

RESULTS

The von Mises stress distributionswere computed for the 4 premolarsrestored with either a gold-alloy or aglass-fiber post, and the results are re-ported in Figures 2, 3, which graphicallycompare the von Mises values at theshoulder, the coronal root, and theapex for all test configurations. The ACtooth induced the highest von Misesstress at the shoulder (approximately78 MPa). Stress concentration waslocated at the apex of the gold-alloyrestored teeth, and the highest vonMises stress was observed in the FFtooth (approximately 94 MPa). Whenthe glass-fiber restored teeth wereanalyzed, the stress values at the apexwere lower than those of the gold-alloyrestored teeth. The von Mises stressinduced at the shoulder of the CF tooth(approximately 70 MPa) was greaterthan that for the other 3 glass-fiberrestored teeth. The von Mises stressesmeasured for post-and-core materialsare presented in Figure 4. The FF toothinduced the highest stress in the gold-alloy post, approximately 374 MPa.The stress values in the glass-fiber postwere approximately 31 to 34 MPa,whereas the stresses at the compositeresin ranged from 32 MPa (PF) to 48MPa (PrF).

A comparison of the peak andaverage values of the maximal principal

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AAverage Peak

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5 Maximal principal stress measured at dentin. A, Gold-alloy-post restored teeth. B, Glass-fiber-post restored teeth.

1242 Volume 112 Issue 5

stress measured at the dentin of all testteeth is presented in Figure 5. The peakand the average maximal principalstress of the AC tooth were approxi-mately 61 MPa and 33 MPa. The peakstresses induced by the gold-alloy postrestored teeth ranged from 59 MPa(CF) to 68 MPa (FF). Average stressvalues ranged from 43 MPa (PF) to 49MPa (FF) in gold-alloy restored teeth;approximately 24% to 33% higher thanthe AC tooth. With a glass-fiber post,the peak maximal principal stresseswere approximately 57 MPa, 7% lowerthan the AC tooth. Average stressvalues ranged from 37 MPa (CF) to 40MPa (PF, FF, PrF), approximately 11%to 18% higher than that for the ACtooth. The maximal principal stressdistributions at the dentin underdifferent loading patterns are presentedin Figure 6. Compared with loading onthe top of a 45-degree facial cusp,stress was reduced for the gold-alloyand glass-fiber post restorations when

The Journal of Prosthetic Dentis

the middle or bottom was loaded andthe cusp inclination was reduced.

The peak and average values ofprincipal stress under different loadingpatterns are compared in Figure 7. Thepeak value of the maximal principalstress at the AC tooth was assumed toequate to the ultimate dentin strengthand the average stress to the fatiguestrength. When the top of a 45-degreecusp was loaded, the tensile limits ofthe dentin were exceeded for all thegold-alloy restored teeth. When themiddle was loaded, the peak principalstresses were reduced by approximately17% to 20%, and the average stresseswere reduced by approximately 15%to 19%. The tensile limits were onlyreached for the FF tooth. Whenloading occurred on the bottom of a45-degree cusp or the top of a 60-degree cusp, the peak stresses werereduced by approximately 29% to 34%,and the average stresses were reducedby approximately 31% to 33%. All test

try

teeth had lower stress values than theAC tooth.

As for the glass-fiber restored teeth,the tensile limits of dentin were excee-ded when the top of a 45-degree cuspwas loaded. When the middle wasloaded, the peak stress values werereduced by approximately 14% to 15%,and the average stress values declinedapproximately 15% to 25%. All testteeth induced lower stresses than theAC tooth, and the CF tooth exhibitedthe lowest stress among all 4 teeth.With loading on the bottom of a45-degree cusp or the top of a 60-degree cusp, the peak and averagevalues of the maximal principal stresseswere reduced by approximately 38%to 43%.

The von Mises stress measured atthe composite resin and glass-fiber postunder different loading patterns are re-ported in Figure 8. Stresses introducedat the composite resin were reduced byapproximately 12% with loading on themiddle of a 45-degree cusp, and by 25to 29% with loading on the bottom orwhen the cusp angle was 60 degrees.Stresses at the glass-fiber post withloading on the middle of a 45-degreecusp were approximately 10% lowerthan those exerted by loading at the topand were 23% lower when loading onthe bottom or when the cusp angle was60 degrees.

DISCUSSION

This study investigated the me-chanical behavior of restored teeth withextensive coronal dentin loss and theinfluence of occlusal design on stressdistribution. The mechanical charac-teristics of teeth with different ferruleconfigurations and post materials wereexamined. Simulations with gold-alloyposts found that stress concentrationin the remaining dentin was higher inthe tooth with a facial ferrule than inthose with other ferrule configurations.The results of the current study, that thegold-alloy PF and CF teeth found thelowest stress when loaded on the top ofa 45-degree cusp, are consistent withprevious observations,7,8 which may be

Liu et al

6 Maximal principal stress contours of palatal ferrule tooth under different loading procedures. A,Gold-alloy-post restored teeth. B, Glass-fiber-post restored teeth. 1. Load on top of 45-degree cusp; 2. Loadon middle of 45-degree cusp; 3. Load on bottom of 45-degree cusp; 4. Load on top of 60-degree cusp.

November 2014 1243

related to the position of the coronaldefect because the oblique forces onthe maxillary premolars were applied onthe palatal side and directed toward thebuccal side.

For teeth with glass-fiber posts,the principal stresses in the remainingdentin were more homogeneous. Ac-cording to some studies, this may bedue to the similar elastic moduli of thedentin and the glass-fiber post.14 Theinfluence of occlusal contact and cuspinclination also was analyzed, and thepartial ferrule effect was taken intoaccount. The maximal principal stresswas gradually decreased as the loadingposition moved from the top to thebottom of the cusps and as the facialcusp inclination was reduced. Whenthe loading force was applied to the

Liu et al

middle and bottom of the facial cusp,the main oblique torque graduallyreduced. The peak and average prin-cipal stresses for the AC cast, whenloaded on the top, can be consideredas “safe levels”; for gold-alloy casts,when loaded on the top of the cusps,high principal stresses at the root re-gion were found to be risk indicatorsfor root fracture. Loading at the mid-dle of the cusps effectively reduced thepeak and the average stresses to safelevels for the CF, PaF, and PrF castsbut not for the FF cast.

When the glass-fiber post was used,the peak von Mises stress value on thecomposite resin core ranged from 32to 48 MPa when loaded on the topof 45-degree cusps; based on previousstudies, this indicates a cohesive failure

risk.15,16 When loaded on the middleof the cusps, all glass-fiber casts hadless principal stress than the AC castand less von Mises stress occurred inthe glass-fiber post. In addition to theloading position, increasing the cuspangle also reduced the tensile stress.The lever arm of the oblique load wasreduced when the facial cusp anglewas 60 degrees, and there was a sub-stantial decrease in tensile stress in theapical root region. In the simulationswith gold-alloy posts, the root dentinfound lower stress concentrationcompared with that of the AC tooth,regardless of the position of the partialferrule.

To improve the mechanical stabilityand long-term success of post-and-corerestorations, modifying the occlusal

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7 Maximal principal stress (peak and average values) measured at dentin for differentloading procedure. A, Gold-alloy-post restored teeth. B, Glass-fiber-post restored teeth.

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8 Von Mises stress measured on composite resin and glass-fiber-post under differentloading procedures. A, Peak stress measured on composite resin. B, Peak stressmeasured on glass-fiber-post.

1244 Volume 112 Issue 5

The Journal of Prosthetic Dentistry Liu et al

November 2014 1245

design of maxillary premolars withlarge-scale tissue loss has many ad-vantages, as found by this numericalsimulation. First, for teeth with limitedcoronal dentin at the loading location,it was important to lower the obliqueforces by reducing the lateral occlusalcontact area and by preventing contacton the top of the facial cusp, thusprotecting the remaining dentin fromfracture. Second, when teeth have acoronal defect where the load isapplied, for instance, the maxillarypremolars with palatal dentin loss andno ferrule, the risk of restoration failureand root fracture should be considered.The overloading risk at the apex dentincannot be improved unless the obliqueload is only applied to the bottom of ahigh facial cusp or to a low cusp. Eventhough the tooth is restored with aglass-fiber post and a composite resincore, it is difficult to guarantee suffi-cient adhesive strength and the long-term stability of the restoration.

Two limitations of this studyshould be addressed in future work.First, the mechanical behavior of theperiodontal ligament would be betterdescribed by an elastic anisotropicnonlinear discrete cast, according tothe orientation and assignment of fi-bers.17 Second, the perfect bondinginterface disregards the different de-gree of bonding between the restora-tion material and the dentin. Thecementation layer should be analyzedto establish the influence of this factoron stress distribution.

CONCLUSIONS

Maxillary premolar casts haddifferent biomechanical characteristicsfor different ferrule configurations.When the tooth had only a facial ferrule

Liu et al

left above the gingiva and was restoredwith a gold-alloy post, it exhibited thehighest local stress on root dentin.These stress levels indicate a substantialrisk of overloading in such situations.By loading on the middle or bottom ofthe facial cusp and by reducing facialcusp inclination, local stress concen-tration can be reduced.

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14. Arjau-Escribano A, Sancho-Bru JL, Forner-Navarro L, Rodriguez-Cervantes PJ, Perez-Gonzalez A, Sanchez-Marin FT. Influence ofprefabricated post material on restored teeth:fracture strength and stress distribution.Oper Dent 2006;31:47-54.

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16. Aksornmuang J, Foxton RM, Nakajima M,Tagami J. Microtensile bond strength of adual-cure resin core material to glass andquartz fiber posts. J Dent 2004;32:443-50.

17. Franco M, Marco M, Giuseppe V.Mechanical behavior of endodonticrestorations with multiple prefabricatedposts: a finite-element approach. J Biomech2007;40:2386-98.

18. Pegoretti A, Fambri L, Zappini G,Bianchetti M. Finite element analysis of aglass fibre reinforced composite endodonticpost. Biomaterials 2002;23:2667-82.

19. Okamato K, Ino T, Iwase N, Shimizu E,Suzuki M, Satoh G, et al. Three-dimensionalfinite element analysis of stress distributionin composite resin cores with fiber postsof varying diameters. Dent Mater J 2008;27:49-55.

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21. Ruse ND. Propagation of erroneous datafor the modulus of elasticity of periodontalligament and guttapercha in FEM/FEApapers: a story of broken links. Dent Mater2008;24:1717-9.

Corresponding author:Dr Yuhua LiuPeking University School and Hospital ofStomatologyNo. 22 Zhongguancun Nandajie, Haidian DistrictBeijing, 100081PR CHINAE-mail: lyhdentist@163.com

Copyright ª 2014 by the Editorial Council forThe Journal of Prosthetic Dentistry.