Biomechanical Response of Implant Systems Placed in the Maxillary Posterior Region Under Various Conditions of Angulation, Bone Density, and Loading

Transcription

1 Biomechnicl Response of Implnt Systems Plced in the Mxillry Posterior Region Under Vrious Conditions of Angultion, Bone Density, nd Loding Chun-Li Lin, MS, PhD 1 /Jen-Chyn Wng, DDS, MS 2 /Lnce C. Rmp, DMD, PhD 3 /Perng-Ru Liu, DDS, MS, DMD 4 Purpose: The im of this study ws to determine the reltive contriution of chnges in implnt system, position, one type, nd loding condition on the iomechnicl response of single-unit implnt-supported restortion using nonliner 3-dimensionl finite element nlysis (3D FEA). Mterils nd Methods: FEA models of single-unit (crown) restortion supported y the Frilit-2 implnt nd MH-6 utment or the Strumnn stndrd implnt with the Strumnn solid utment were used. Ech system ws nlyzed y FEA with oth stright nd 20-degree ngled utments. Simulted implnt plcement ws performed in the mxillry premolr re with 3 vritions in implnt orienttion reltive to the residul ridge. Anlysis of ech orienttion ws conducted for ech of 4 one qulity types descried y Lekholm nd Zr, with lterl nd xil loding conditions imposed. The effect of ech vrile ws expressed s percentge of the totl sum of squres s computed using nlysis of vrince. Results: Lrger strin vlues were noted in corticl one with lterl force nd the Frilit-2 system. Bone strin incresed with decresing one density nd ws ffected primrily y one qulity. Implnt stress ws influenced minly y implnt position. Conclusions: Better stress/strin distriution is possile when implnts re plced long the xis of loding with multiple res of corticl contct. The Strumnn solid utment performed etter s force-trnsmission mechnism. INT J ORAL MAXILLOFAC IMPLANTS 2008;23:57 64 Key words: utment-implnt connection, iomechnics, one type, finite element nlysis, implnt plcement Orl rehilittion with osseointegrted implnts is n effective tretment for the replcement of teeth, with long-term clinicl studies reporting 95% survivl for mndiulr implnts nd 65% to 85% survivl for mxillry implnts. 1 3 Filure my result 1 Associte Professor, Deprtment of Mechnicl Engineering, Chng Gung University, To-yun, Tiwn. 2 Associte Professor nd Chir, Deprtment of Prosthodontics, Kohsiung Medicl University Fculty of Dentistry, nd Kohsiung Medicl University Hospitl, Kohsiung, Tiwn. 3 Associte Professor, Deprtment of Comprehensive Dentistry, University of Alm t Birminghm, School of Dentistry, Birminghm, Alm. 4 Associte Professor nd Chir, Deprtment of Comprehensive Dentistry, University of Alm t Birminghm, School of Dentistry, Birminghm, Alm. Correspondence to: Dr Jen-Chyn Wng, 100 Shih-Chun 1st Rod, Kohsiung City 807, Tiwn. Fx: E-mil: cguce@yhoo.com.tw from loss of osseointegrtion or component filure susequent to restortion nd my e relted to unfvorle loding or to high stress concentrtions. 4,5 Bone qulity is lso n importnt fctor, with more filures found in one of lower density. 6,7 Cliniclly, these fctors re difficult to investigte ecuse of limited informtion nd smple vrition. Idelly, the implnt should e surrounded y lyer of investing one with minimum thickness of 1 mm for optiml osseointegrtion. 8 A frequent rrier to optiml implnt plcement in the posterior mxill is the presence of ony irregulrities. The opertor my plce the implnt such tht loding will e directed down the long xis of the implnt, with the possile risk of decresed thickness of investing one. Alterntively, the implnt my e plced with n ngultion similr to tooth, thus incresing the likelihood of lterl loding. The influence of implnt ngultion on stress is mtter of dete. Some The Interntionl Journl of Orl & Mxillofcil Implnts 57

2 Tle 1 Simulted Implnt Components Used Implnt Dimeter Length Autment (mm) (mm) Autment connection Mnufcturer Frilit-2 (FRI) MH-6, stright nd Internlly hexed, Frident, Mnnheim, 20-degree ngled seprte utment screw Germny Strumnn (STR) Solid utment, stright One-piece Morse tper Strumnn, Bsel, nd 20-degree ngled with threded picl Switzerlnd terminus reserch hs demonstrted tht stress in the ngled implnt would increse 5-fold under lterl loding. 9,10 However, other investigtions hve shown tht the stress level incurred with the use of ngled utments, lthough elevted, remins within the physiologic limits of one nd produces cliniclly cceptle results. 11,12 Vritions in component design mong implnt systems my led to different stress/strin distriutions, thus ltering the trnsmission of forces to surrounding one. 2,13 Most 2-stge externl hexgon screw-type implnt systems employ utment screws tht cn rek, loosen, or ecome distorted ecuse of their smll dimeter or their design. 14 To void this prolem, implnt-utment joints with internl hexgons or octgons with incresed depths hve een proposed nd developed. 15,16 A 1-piece tper interference-fit utment design with threded picl terminus is nother option. 17 It remins to e investigted whether uneven strin concentrtions or screw distortion occur under lterl loding with this system nd which of these 2 mechnisms imprt greter stility to n implntsupported restortion. Finite elementl nlysis (FEA) is useful tool for investigting iomechnicl interctions of vrious designs. However, since relistic 3-dimensionl (3D) models of the implnt-supported prosthesis re complex, mny previous studies hve ltered only few prmeters nd hve filed to fully exploit the cpilities of FEA. 18,19 The im of this study ws to determine the reltive contriution of chnges in implnt system, position, one type, nd loding condition on the iomechnicl response of singleunit implnt-supported restortion using nonliner 3D FEA. MATERIALS AND METHODS Computerized tomogrphic imges of humn edentulous mxillry second premolr re exhiiting uccl one irregulrities were cquired. The size of the edentulous re used ws pproximtely 14 mm in the mesiodistl dimension nd 12 mm in the uccolingul dimension. Two types of implnts with their respective utments nd restortions (Tle 1) were simulted within the ony model (Fig 1) using component dimensions otined from previous study. 20 FEA solid models were constructed using Mimics (Mimics 6.1; Mterilise Softwre, Leuven, Belgium) nd ANSYS FEA softwre (ANSYS 8.0; ANSYS, Houston, PA). The mxillry second premolr crown restortion ws simulted y imging plster cst on scle of 1 to 5 with 4-xis lser scnner (3D Fmily Technology, Tipei, Tiwn). Twenty-four profiles in rdil direction from the centrl foss of the crown to the root pex were collected in 15-degree increments nd ssemled s virtul 3D wire-frme structure with Pro/Engineer (Pro/Engineer 2001; Prmetric Technology, Wlthm, MA). The solid crown model ws then generted with ANSYS nd ssemled with the utments to complete the simulted single-unit implnt-supported restortion solid models (Fig 1). The mesh models were generted using mpping pproch with 8- node iso-prmetric rick elements (solid 45). Nonliner frictionl contct elements (contct 49; defined s node to surfce) were used to simulte the dpttion etween the vrious components of ech implnt system (Fig 2). A friction coefficient vlue of 0.5 ws ssumed for ll contct surfces. 21 Ech implnt ws modeled t 3 positions within the ony segment. In the first position (P1), implnt plcement ws simulted within the residul ridge prllel to the frontl plne (Figs 1 nd 1d). In the second position (P2), implnt plcement ws similr to P1, ut there ws contct etween the implnt nd the uccl corticl plte in the middle third of the implnt ody (Figs 1 nd 1e). In the third position (P3), implnt plcement ws simulted within the residul ridge, with uccl ngultion of 20 degrees reltive to the frontl plne (Figs 1c nd 1f ). A 20-degree ngled utment ws simulted in the P3 position. Simultions were conducted of ech model (Fig 1) with 4 types of one. These one types followed the clssifiction of Lekholm nd Zr 22 s follows: (1) 58 Volume 23, Numer 1, 2008

3 c d e f Fig 1 Six solid models showing 2 implnt systems, Frilit-2 nd Strumnn, in 3 positions with fricted crowns: () Frilit-2 implnt in position 1 (FRI; P1); () Frilit-2 implnt in position 2 (FRI; P2); (c) Frilit-2 implnt in position P3 (FRI; P3); (d) Strumnn implnt in position 1 (STR; P1); (e) Strumnn implnt in position 2 (STR; P2); nd (f) Strumnn implnt in position 3 (STR; P3). Fig 2 3D FEA models of n implnt-supported prosthesis constructed for this study. () Frilit-2 (FRI) system, including the utment, utment screw, nd implnt. () Strumnn (STR) system, including the utment nd implnt. Tle 2 Mteril Properties Assigned to Mterils Simulted Young's modulus Possion's Mteril (MP) rtio References Corticl one 14, Dense treculr one 1, Low-density treculr one Gold lloy (prosthesis) 90, , 30 Titnium (implnt system) 110, , 31 Fig 3 Loding conditions pplied () AF force directed down the long xis of the crown. () LF concentrted force vector directed t 45-degree ngle reltive to the lingul cusp. entirely homogeneous compct one, (2) 1.5-mm lyer of corticl one ounding core of dense cncellous one, (3) 0.75-mm lyer of corticl one ounding core of dense cncellous one, nd (4) 0.75-mm lyer of corticl one ounding core of low-density cncellous one. Elstic properties used for one nd restortive mterils were otined from the literture (Tle 2). Lterl nd xil loding conditions (LF nd AF, respectively) were pplied to ech model (Fig 3). Loding condition LF simulted lterl 150-N force with concentrted force vector cting on the lingul cusp t 45-degree inclintion. This force ws simulted s pproching the cusp from the uccl direction. Loding condition AF simulted n xilly directed 150-N force cting on the centrl foss of the crown. 23 Exterior nodes t the mesil nd distl surfces of the lveolr one were fixed in ll directions s the oundry conditions for ll 48 models. Mximum von Mises strin for corticl nd cncellous one ws recorded, nd mximum von Mises stress ws recorded for ech implnt. 24,25 Effect of implnt position, one qulity, implnt system, nd loding condition on the mechnicl response were The Interntionl Journl of Orl & Mxillofcil Implnts 59

4 Tle 3 Strin ANOVA Min Effects for Corticl Bone Vrile df SS Men SS %TSS Position Bone qulity Implnt type Lod condition Totl nlyzed using nlysis of vrince (ANOVA; Minit 12.23; Minit, Stte College, PA). 26 However, ecuse these dt from FE nlyses hve generlly een found not to e normlly distriuted (n essentil prerequisite for ANOVA), it ws necessry to trnsform the dt prior to performing prmetric sttistics. Since miniml strin/stress vlues re preferle, the cquired dt were logrithmiclly trnsformed using the following eqution: n i = 10log 10 ( i 2 ) Tle 4 Strin ANOVA Min Effects for Cncellous Bone Vrile df SS Men SS %TSS Position Bone qulity Implnt type Lod condition Totl Tle 5 ANOVA Min Effects for Implnt Stress Vrile df SS Men SS %TSS Position Bone qulity Implnt type Lod condition Totl where n i ws the trnsformed dt nd i ws the mximum strin/stress otined from FEA. 24 RESULTS Rw dt for mximum von Mises strin (corticl nd cncellous one) nd stress (implnt) were recorded. Becuse these dt were not normlly distriuted, logrithmic trnsformtion ws pplied. A less negtive vlue in the trnsformed dt corresponds to lower strin/stress. The reltive contriution of ech effect (sum of squres [SS]) is expressed s percentge of the totl sum of squres (%TSS). SS nd %TSS re presented for corticl one strin (Tle 3), cncellous one strin (Tle 4), nd implnt stress (Tle 5). Figure 4 shows mgnitude plots for the comined effects of ech vrile for mximum strin Fig 4 Min effects of implnt position (P1, P2, or P3), one density (1 to 4), implnt type (STR or FRI), nd loding condition (AF or LF) t ech level for trnsformed mximum von Mises strin on () corticl one, (, fcing pge) cncellous one, nd (c, fcing pge) trnsformed mximum von Mises stress on the implnt P1 P2 P3 BD1 BD2 BD3 BD FRI STR LF AF 60 Volume 23, Numer 1, 2008

5 80 80 P1 P2 P3 BD1 BD2 BD3 BD FRI STR LF AF P1 P2 P3 BD1 BD2 BD3 BD c FRI STR LF AF in corticl one (Fig 4) nd cncellous one (Fig 4) nd for mximum stress in the implnt (Fig 4c). With respect to corticl one (Tle 3), loding condition ccounted for 55% of the vrition in strin mgnitude. Implnt type ccounted for 24% of the vrition, implnt position ccounted for 12% of the vrition, nd one qulity ccounted for 9% of the vrition. Figure 4 shows tht lterl force nd the FRI system showed incresed strin when compred with xil force nd the STR system, respectively. Implnt position ws not the mjor fctor ffecting strin in corticl one; however, the plot indicted tht P2 resulted in the lowest strin mong the 3 positions, followed y P1 nd P3. Strin in corticl one incresed with decresing one qulity. The Interntionl Journl of Orl & Mxillofcil Implnts 61

6 c d Fig 5 Strin distriutions of () the Frilit-2 (FRI) implnt system nd () the Strumnn (STR) implnt system plced in position 1 with one type 1 nd pplied lterl forces. Mximum strin is concentrted t the cervicl regions in corticl one. (c nd d) The sme systems plced in position 1 with one type 4 nd pplied lterl forces. Here, mximum strin is concentrted in cncellous one t the implnt pex. Fig 6 Stress concentrtion regions of the () Frilit-2 (FRI) utment screw nd () the Strumnn (STR) solid utment. Bone qulity (68%) ws the mjor fctor ffecting cncellous one strin, followed y loding condition (27%), implnt position (4%), nd implnt type (1%; Tle 4). Comined min effects plots showed incresing strin with decresing one qulity. Lterl force incresed strin when compred with xil force. Position nd implnt type hd less effect on cncellous one strin (Fig 4). Stress to the implnt ws determined primrily y implnt position (64%), followed y implnt type (31%), loding condition (5%), nd one qulity (0%) (Tle 5). Comined mgnitude plots showed tht the P2 position produced lower stress, followed y P1 nd P3 (Fig 4c). Also, the STR model reduced stress s compred to the FRI model. Loding condition nd one type demonstrted lmost no influence on implnt stress. Ares of strin/stress concentrtion were determined (Fig 5). Strin concentrtions in one were dependent on one qulity irrespective of loding condition nd implnt type. The strin distriutions in one types 1 to 3 were similr, with mximum strin concentrted t the cervicl regions in corticl one. The res of mximum strin with one type 4 were found in cncellous one round the pex of the implnt. Furthermore, stress concentrtion regions of the FRI models were found long the threds of the utment screw. In the STR models, stress concentrtion regions were found t the tpered end of the utment nd first 2 picl threds of the screw (Fig 6). DISCUSSION The successful use of dentl implnts hs een welldocumented, ut implnt filures re still unvoidle. 4,5,27,28 Implnt filures oserved fter prosthesis delivery re minly relted to iomechnicl complictions. The mechnisms responsile for iomechnicl implnt filure re not fully understood, owing to complictions from mny relted fctors, such s loding condition, prosthesis type, implnt design, implnt position, one type, nd mteril properties of the one-implnt interfce. 4 Unfortuntely, these iomechnicl spects re difficult to investigte using solely clinicl or experimentl pproches with limited informtion nd smple vritions. FEA hs een widely ccepted s complementry tool for understnding detiled mechnicl responses in iologic investigtions. However, little ttempt hs een mde to ssess model sensitivity to vrition in input prmeters or interctions. Amiguous results from FEA my occur ecuse of unrelistic ssumptions of interfcil conditions etween mterils nd components. 20,21 This study employed 3D FEA coupled with more relistic interfcil conditions (ie, employing frictionl surfce etween different components nd using vrile prmeters t different levels). A full fctoril procedure ws performed exploring every possile comintion of levels of ech fctor nd the min effect of ech level on mximum von Mises strins/stresses. 62 Volume 23, Numer 1, 2008

7 Strin hs een ccepted s one of the mechnicl signls tht stimultes remodeling of the one surrounding the implnt, nd von Mises stress hs een ccepted s the frcture criterion for metl mterils sed on elstic mechnics This in vitro investigtion recorded von Mises strin nd stress for one nd implnt, respectively, through FEA simultion to ssess multiple vriles tht ffect the success of n implnt-supported restortion. In ddition, ANOVA yielded the contriution of ech vrile to the totl sum of squres nd determined the fctor levels minimizing stress nd strin. The results indicted tht implnt position ws the primry influence on implnt stress; it lso contriuted to corticl one strin. The dvntge of the P2 position ws due to the fct tht forces could e trnsferred into supporting one y the cervicl corticl lyer nd uccl corticl contct (Fig 1). Implnt stress nd corticl one strin concentrtions were highest in the P3 position due to ending moment effect of the ngled utment. These effects indicte tht implnts should e plced long the direction of xil loding of the proposed prosthesis with multiple res of corticl contct to otin etter stress/strin distriution. Bone qulity ffected strin for oth cncellous (68%) nd corticl one (9%), with strin incresing s one qulity decresed. For one types 1, 2, nd 3, strin concentrtion regions were found t the cervicl res in corticl one, due to the higher elstic modulus of corticl one. With one type 4, strin incresed nd ws concentrted round the pex due to low one density. Concentrtion of mximum strin concentrted round the picl portion of the implnt my increse the risk of micromovement nd initil instility. When plcing implnts in sites of lower one density, the opertor is encourged to plce longer or wide-dimeter self-tpping implnts using conventionl drilling technique without countersinking or to use n osteotome technique without drilling. With the use of such osteocompressive procedures, one density nd primry stility of implnts my e improved. Extending the heling period prior to prosthesis friction my lso increse one density nd yield more fvorle force trnsmission. The implnt model tested ffected the strin found in corticl one nd the stress in the implnt. Men vlues were higher with the FRI model thn with the STR model (Figs 4 nd 4c). Stress concentrtion regions seen within the FRI model increse the possiility of mechnicl complictions such s screw loosening, rekge, or creep. With the STR model, stress concentrtion regions indicte tht the utment connection relies to greter extent on contct pressure nd frictionl resistnce of the Morse tper. This effect on the force trnsmission mechnism supports clinicl findings tht screw loosening occurs less frequently with the STR model. 17 Loding condition ffected one strin. The high percentge contriution found in corticl one ws due to the high elstic modulus of this mteril. Lterl loding produced ending moment tht significntly incresed the strin vlues found t cervicl res in corticl one nd round the implnt pex in cncellous one. Such high strin concentrtions induced y unfvorle loding suggest custive mechnism for mrginl one loss fter long-term dynmic loding. This finding supports the recommendtion to eliminte or minimize lterl occlusl contcts of posterior implnt-supported restortions. Whenever possile, fltter inclines should e developed on cusps, nd cusp-to-foss reltionship in mximum intercusption with no eccentric occlusl contct should e used. As mny nterior teeth nd implnts s possile should e used to distriute lterl forces if group function occlusl scheme is unvoidle in eccentric movement. Three-dimensionl nonliner FEA ws pplied in this study to investigte the reltive contriution of chnges in implnt system, position, one type, nd loding condition on the iomechnicl response of single-unit implnt-supported restortion. However, the present investigtion ws limited y the ssumptions mde regrding loding condition, mteril properties, nd implnt-one interfcil conditions. Lterl nd xil forces were exmined seprtely, wheres cliniclly, pplied forces re usully found to e comintion of oth. Liner elstic (homogeneous nd isotropic) properties for ll mterils were used due to numericl convergence considertions nd ecuse wide rnge of vlues exist for these properties in the literture. The implntone interfce ws ssumed to e fully osseointegrted, nd specil surfce modifictions (ie, the SLA surfce of the Strumnn implnt) were not considered. Therefore, the results provide only generl insight into the iomechnics of implnt loding under verge conditions. CONCLUSIONS The dt from this nonliner 3D FEA study led to severl conclusions of clinicl significnce: 1. The plcement of implnts long the direction of xil loding of the proposed prosthesis my promote etter stress/strin distriution. 2. The use of one condenstion methods during plcement my improve the initil stility of implnts. The Interntionl Journl of Orl & Mxillofcil Implnts 63

8 3. The STR model (Strumnn) my provide etter force trnsmission mechnism nd my decrese the risk of utment loosening nd screw frcture. 4. Estlishing n occlusl scheme to reduce lterl occlusl force is recommended. ACKNOWLEDGMENTS This reserch ws supported y grnt NSC E from the Ntionl Science Council, Tiwn. We would like to thnk Dr Wen-Jen Chng t the Deprtment of Industril Engineering nd Mngement, T-Hw Institute of Technology, for her ssistnce with the sttisticl nlysis. REFERENCES 1. Brånemrk P-I, Breine U, Adell R, et l. Intr-osseous nchorge of dentl prostheses I. Experimentl studies. Scnd J Plst Reconstr Surg 1969;3: Adell R, Lekholm U, Rockler B, et l. A 15-yer study of osseointegrted implnts in the tretment of the edentulous jw. Int J Orl Surg 1981;6: Zr GA. Introduction to osseointegrtion in clinicl dentistry. J Prosthet Dent 1983;49: Shin S, Cehreli MC,Ylcin E.The influence of functionl forces on the iomechnics of implnt-supported prostheses A review. J Dent 2002;30: Cehreli MC, Shin S, Akc K. Role of mechnicl environment nd implnt design on one tissue differentition: Current knowledge nd future contexts. J Dent 2004;32: Mrtinez H, Dvrpnh M, Missik P, Celletti R, Lzzr R. Optiml implnt stiliztion in low density one. Clin Orl Implnts Res 2001;12: Holmes DC, Loftus JT. Influence of one qulity on stress distriution for endosseous implnts. J Orl Implntol 1997;23: Clellnd NL, Gilt A, McGlumphy EA, Brntley WA. A photoelstic nd strin guge nlysis of ngled utments for n implnt system. Int J Orl Mxillofc Implnts 1993;8: Cny S, Hersek N, Akpinr I, Asik Z. Comprison of stress distriution round verticl nd ngled implnt with finite-element nlysis. Quintessence Int 1996;27: Clellnd NL, Lee JK, Bimenet OC, Brntley WA. A three-dimensionl finite element stress nlysis of ngled utments for n implnt plced in the nterior mxill. J Prosthet Dent 1995;4: Sethi A, Kus T, Sochor P, Axmnn-Krcmr D, Chnvz M. Evolution of the concept of ngulted utments in implnt dentistry: 14-yer clinicl dt. Implnt Dent 2002;11: Sklk R. Aspects of iomechnicl considertion. In: Brånemrk P-I, Zr GA, Alrektsson T (eds).tissue-integrted Prostheses: Osseointegrtion in Clinicl Dentistry. Chicgo: Quintessence, 1985: Hs R, Polk C, Furhuser R, Milth-Pokorny G, Dortudk O, Wtzek G. A long-term follow-up of 76 Brånemrk singletooth implnts. Clin Orl Implnts Res 2002;13: Schwrz MS. Mechnicl complictions of dentl implnts. Clin Orl Implnts Res 2000;11: Blfour A, O Brien GR. Comprtive study of ntirottionl single tooth utments. J Prosthet Dent 1995;73: Mollersten L, Lockowndt P, Linden LA. Comprison of strength nd filure mode of seven implnt systems: An in vitro test. J Prosthet Dent 1997;78: Levine RA, Clem DS, Wilson TG, Higginottom F, Sunders RL. A multicenter retrospective nlysis of the ITI implnt system used for single-tooth replcements: Results of loding for 2 yers. Int J Orl Mxillofc Implnts 1997;12: Lin CL, Lee HE, Wng CH, Chng KH. Interfcil stress nlysis etween posterior resin-onded ridge nd utments y finite element pproch. Comput Methods Progrms Biomed 2003;72: Lin CL, Hsu KW, Wu CH. Multi-fctoril retiner design nlysis of posterior resin-onded fixed prtil dentures: A finite element study. J Dent 2005;33: Lin CL, Wng JC, Kuo YC. Numericl simultion on the iomechnicl interctions of tooth/implnt-supported system under vrious occlusl forces with rigid/non-rigid connections. J Biomech 2006;39: Merz BR, Hunenrt S, Belser UC. Mechnics of the implnt-utment connection: An 8-degree tper compred to utt joint connection. Int J Orl Mxillofc Implnts 2000;15: Lekholm U, Zr GA. Ptient selection nd preprtion. In: Brånemrk P-I, Zr GA, Alrektsson T (eds).tissue-integrted Prostheses: Osseointegrtion in Clinicl Dentistry. Chicgo: Quintessence, 1985: Td S, Stegroiu R, Kitmur E, Miykw O, Kuskri H. Influence of implnt design nd one qulity on stress/strin distriution in one round implnts: A 3-dimensionl finite element nlysis. Int J Orl Mxillofc Implnts 2003;18: Frost HM.Wolff s lw nd one s structurl dpttions to mechnicl usge: An overview for clinicins. Angle Orthod 1994;64: Boresi AP, Schmidt RJ, Sideottom OM. Advnced mechnics of mterils. New York: John Wiley, 1993: Dr FH, Mekin JR, Aspden RM. Sttisticl methods in finite element nlysis. J Biomech 2002;35: Gross M, Lufer BZ. Splinting osseointegrted implnts nd nturl teeth in rehilittion of prtilly edentulous ptients. Prt I: Lortory nd clinicl studies. J Orl Rehil 1997;24: Becker CM, Kiser DA, Jones JD. Guidelines for splinting implnts. J Prosthet Dent 2000;84: Benzing UR, Gll H, Weer H. Biomechnicl spects of two different implnt-prosthetic concepts for edentulous mxille. Int J Orl Mxillofc Implnts 1995;10: Moff JP, Lugssy AA, Guckes AD, Gettlemn L. An evlution of nonprecious lloys for use with porcelin veneers. Prt I. Physicl properties. J Prosthet Dent 1973;30: vn Rossen IP, Brk LH, de Putter C, de Groot K. Stress soring elements in dentl implnts. J Prosthet Dent 1990;64: Frost HM.Wolff s lw nd one s structurl dpttions to mechnicl usge: An overview for clinicins. Angle Orthod 1994;64: Melll A, Wiskott HW, Botsis J, Scherrer SS, Belser UC. Stimulting effect of implnt loding on surrounding one. Comprison of three numericl models nd vlidtion y in vivo dt. Clin Orl Implnts Res 2004;15: Boresi AP, Shmidt RJ, Sideottom OM. Advnced Mechnics of Mterils. New York: John Wiley & Sons, 1993: Volume 23, Numer 1, 2008