ORIGINAL ARTICLE

Dynamic simulation of the self-tapping insertionprocess of orthodontic microimplants intocortical bone with a 3-dimensional finite elementmethod

Wonjae Yu,a Hyo-Sang Park,b Hee-Moon Kyung,b and Oh-Won Kwonb

Daegu, Korea

FromUniveaAssobProfeThe aucts oReprinSchooKoreaSubm0889-Copyrhttp:/

834

Introduction: The aim of this study was to evaluate the stress state in the cortical bone around an orthodonticmicroimplant during and after the insertion surgery. Methods: The self-tapping insertion of an orthodonticmicroimplant into 1-mm-thick cortical bone containing a predrilled hole was simulated by using a 3-dimensional finite element method. The entire insertion surgery was replicated by a total of 3601 calculationsteps: ie, the first 3600 dynamic steps analyzing the insertion process and an additional static step foranalyzing the residual stress state after insertion. Four microimplants were experimentally inserted into rabbittibiae to measure the insertion torques and compare themwith the finite element analysis results.Results:Rea-sonable agreement was observed between the experimentally measured and the finite element calculatedtorques, confirming the validity of our finite element simulation, which showed that high stresses can developin the interfacial bone during microimplant insertion. Hoop stresses above the ultimate tensile strength and radialstresses above the ultimate compressive strength of cortical bone developed in the bone. Furthermore, residualradial stresses higher than the critical threshold stress to trigger pathologic bone resorption were observed afterinsertion. These high insertion-related stresses implied that it is not the orthodontic force or the timing of itsapplication, but the insertion conditions that can determine the bone’s response to the microimplant and itsclinical prognosis. Conclusions: This in-vitro finite element analysis showed that, during the self-tappinginsertion of orthodontic microimplants, stresses high enough to fracture cortical bone can develop. After theself-tapping insertion, the radial stresses calculated at the interfacial bone were higher than the thresholdvalue to trigger pathologic bone resorption. (Am J Orthod Dentofacial Orthop 2012;142:834-41)

Overload is identified as a major risk factor for thefailure of orthodontic microimplant treatment.Since stresses or strains higher than a certain

threshold can trigger pathologic changes in thebone,1,2 an overloaded implant, either an orthodonticmicroimplant or a dental implant, is prone to lose itsosseous support and loosen, and it might fail if thesituation is left unaddressed.3,4

the Department of Orthodontics, School of Dentistry, Kyungpook Nationalrsity, Daegu, Korea.ciate professor.ssor.uthors report no commercial, proprietary, or financial interest in the prod-r companies described in this article.t requests to: Hee-Moon Kyung, Department of Orthodontics, Dentall, Kyungpook National University, 188-1, Sam Duk 2Ga, Jung Gu, Daegu,, 700-412; e-mail, hmkyung@knu.ac.kr.itted, March 2012; revised and accepted, August 2012.5406/$36.00ight � 2012 by the American Association of Orthodontists./dx.doi.org/10.1016/j.ajodo.2012.08.016

A number of studies, experimental and numeric, havealready been carried out to investigate the effects of mi-croimplant size: length and diameter,5 shape and de-sign,6,7 insertion angle and characteristics of theimplant bed bone,7,8 and the presence or distance ofadjacent teeth9 on the bone stresses. Unfortunately,however, most of these studies have focused exclusivelyon the effect of orthodontic forces. Stresses from an-other important source—those caused by the placementof the microimplant—have generally been ignored.

Stresses created at the point of insertion might needmore attention because, although strong primary stabil-ity is a prerequisite for the clinical success of a microim-plant, a tight fit between the microimplant and the bonecan create high stresses at the interface. The immediateor early loading protocol used routinely in microimplanttherapy will not allow sufficient time for bone to relievethese insertion stresses by remodeling or other relaxationmechanisms. Therefore, it is quite likely that the

Yu et al 835

interfacial bone is subjected to a certain level of residualstress before orthodontic forces are applied.

Recent experimental studies have shown that the in-sertion stresses by themselves—ie, before the applicationof force to the microimplant—are high enough to causecracks in bone.10,11 This suggests that biomechanicalanalysis should take into account the insertion stressesas well as those from the orthodontic forces.Accordingly, this study was designed to evaluate thestresses developing in the cortical bone duringmicroimplant placement. The primary goal was to testwhether a finite element simulation can reliablyreplicate the dynamic self-tapping insertion procedure.

MATERIAL AND METHODS

The geometries of microimplants (AbsoAnchorSH1312-07; Dentos, Daegu, Korea) and a cortical boneplate, shown in Figure 1, were created by using a com-puter-aided design program (Autodesk Inventor, SanRafael, Calif). The microimplant has a slightly taperedbody (diameters, 1.3 mm at the cervix and 1.2 mm atthe apex). Its shaft, 6.5 mm in length, has a V-shaped,0.25-mm-high machined thread on the surface. By re-ferring to a previous study, we designed a coin-shapedbone specimen, 1 mm thick and 2.6 mm in diameter,containing a through-thickness predrilled hole of 0.9mm in diameter.12 To minimize the finite element modelsize, cancellous bone was not included in the analysis.

With the DEFORM 3-dimensional program (version6.1; Scientific Forming Technologies, Columbus, Ohio),the finite element simulation was designed to resembleclinical practice as closely as possible. As shown inFigure 1, the microimplant was initially placed abovethe bone with its center line collinear with that of thehole. It was then moved down along the line until its api-cal threads came into contact with the hole wall. Thefinite element simulation of the self-tapping insertionwas then started under displacement-controlled condi-tions. The microimplant was programmed to rotateand advance into the hole continuously, at a rotationspeed of 30 rpm and an advancement speed of 0.25mm per second; therefore, every 2 seconds, the microim-plant rotated 1 turn and advanced 0.5 mm downward:ie, the pitch of the microimplant’s thread. A total of3600 calculation steps were used to simulate the 10turns and 5 mm of advancement of the microimplantinto the hole. After this, the displacement condition im-posed on the microimplant was removed (which repli-cated the detachment of the insertion driver from themicroimplant’s head), and the final residual stress statewas calculated.

The 3-dimensional mesh of the bone specimen con-sisted of approximately 45,000 4-node tetrahedron

American Journal of Orthodontics and Dentofacial Orthoped

elements. A finer mesh was used around the hole, wherethe interaction between the microimplant and bonemainly occurs. The element size within 0.25 mm fromthe hole wall was one fifth of those without, as shownin Figure 1, B. The initial mesh, however, was subjectedto continuous changes, since an automatic remeshingscheme was used to accommodate the deformation ofthe interfacial bone in accordance with the microimplantinsertion. All nodes on the outer perimeter of the bonewere clamped as geometric boundary conditions. The ki-netic friction coefficient between the microimplant andthe bone during the insertion was assumed to be con-stant at 0.1.

Large deformation of the interfacial bone wasexpected during microimplant insertion, inducingstresses above the yield strength of the cortical bone.Therefore, not only elastic but also plastic material be-havior should be considered. Due to the lack of literaturereporting the elasto-plastic properties of the human jawcortical bone, leg bone data were taken from the litera-ture.13 The use of leg cortical bone data can be justifiedbecause of the close similarity in the elastic modulus be-tween the leg bones (16.8 GPa; Fig 2) and jaw bonesused in several implant studies; it was in the range of13.7 to 20 GPa.14-16 Figure 2 shows the graphic stress-strain relationship that was reconstructed and used inthis study. The ultimate strength (138.76 MPa) shownin Figure 2 was the tensile strength. The compressivestrength was set to 198.22 MPa, 30% higher than thetensile strength based on previous studies.17,18

To predict the postoperative response of the interfa-cial bone, the critical threshold stress was defined as–67.37 MPa. This corresponds to –4000 microstrainsthat has been described as the threshold strain1,2 totrigger pathologic bone resorption.3

The titanium alloy (Ti-6Al-4V) microimplant wasmodeled as a rigid material to allow for faster calcula-tions on the assumption that deformations in the micro-implant would be insignificant compared with those inthe interfacial bones.

To verify the validity of our finite element simulation,an animal experiment was conducted. The tibialmiddiaphysis of a mature white rabbit, 12 months old,weighing approximately 3.0 kg, was used to provide cor-tical bone of a similar quality to that used in the finiteelement analysis. The experimental protocol was ap-proved by the Animal Care Committee of the School ofDentistry at Kyungpook National University in Korea.

Two microimplants were inserted into each of bothtibiae with the self-tapping method (left, sites 1 and 2;right, sites 3 and 4). Pilot holes were drilled at a right an-gle to the bone surface with a 0.9-mm drill bit at 500rpm under external saline irrigation to minimize the

ics December 2012 � Vol 142 � Issue 6

Fig 1. Analysis model: A, geometry and dimensions (in millimeters) of the orthodontic microimplantand bone specimen; B, finite element mesh of bone.

836 Yu et al

risk of thermal damage. The microimplants were thendriven into the holes at 30 rpm with a surgical engine(Elcomed SA-200C; W&H Dentalwerk BuermoosGmbH, Buermoos, Austria). With a built-in torque meter,the insertion torque was recorded throughout the inser-tion process with a sampling time of 0.125 second andan accuracy of .001 Ncm. Four more orthodontic micro-implants (2 in each tibia) were inserted with the self-drilling method for another study, which is not describedhere. All surgeries were performed by an experienced or-thodontist.

After insertion, the microimplants were driven out,and the tibiae were cut into pieces so that each piecehad 1 implantation site. The bone thickness was thenmeasured with a caliper.

RESULTS

The bone thicknesses measured at the 4 implant siteswere 1.10 mm (sites 1 and 2), 0.95 mm (site 3), and1.15 mm (site 4). At site 4, a macroscopic crack runningacross the hole was found, so the torque data recordedthere were discarded. Figure 3 shows the torque valuesmeasured at the other 3 sites together with one calcu-lated by the finite element simulation. Reasonableagreement between the measured and calculated valueswas observed.

Figures 4 and 5 show the radial and hoop stressesdeveloping in the interfacial bone during microimplantinsertion. For an easy examination, stresses in thecross-section (cut by the y-z plane) of the bone specimenare shown. The radial stress (Fig 4) is the stress

December 2012 � Vol 142 � Issue 6 American

component that developed as a direct result of the mi-croimplant’s thread pressing the pilot-hole wall. Onthe other hand, the hoop stress (Fig 5) is the stress com-ponent acting in a tangential direction around the holeas a result of the diameter differences between themicroimplant and the hole. In Figures 4 and 5, eithercompressive or tensile ultimate strength of the corticalbone was selected as the cutoff value: red, where stressesexceed the ultimate compressive strength; and blue,where stresses exceed the ultimate tensile strength. Allparts of Figures 4 and 5 represent a typical stage ofmicroimplant placement. Overall, the radial stresses arecompressive or neutral (Fig 4), whereas the hoop stressesare tensile (Fig 5).

A large amount of bone deformation was observedeasily on the upper and lower faces of the corticalbone where the bone materials, being less constrained,can deform more freely. The highest radial stresses(red), above the ultimate compressive strength of bone,occur near the thread tips (Fig 4), indicating that the in-terfacial bone here can crush during microimplant inser-tion. On the other hand, the radial stresses near thevalleys of the threads are minimal, althoughmuch defor-mation takes place there.

The hoop stresses shown in Figure 5 are quite differ-ent from the radial stresses. Except for the initial tran-sient period when the interfacial bone, compressed bythe microimplant threads, started to deform, the hoopstresses in all succeeding stages are tensile, as high asor higher than the tensile ultimate strength of bone. Un-like the radial stresses, the highest hoop stresses are not

Journal of Orthodontics and Dentofacial Orthopedics

Fig 2. Elasto-plastic stress-strain relationship of cortical bone reconstructed from Burstein et al.13

(*)Compressive threshold strain1; (**)tensile threshold strain2 for pathologic bone remodeling.

Fig 3. Comparison of the measured and the finite element method calculated insertion torque values.

Yu et al 837

contained in the localized areas. Instead, all interfacialbones, near the thread tips and valleys alike, are subjectto high hoop stresses.

Figure 6 shows the residual radial stresses after themicroimplant has been inserted. Instead of the ultimatestrength, the cutoff stress used here was –67.36 MPa—ie,the critical threshold stress for pathologic bone resorp-tion. It shows that bones near the thread tips are subjectto stresses higher than the critical threshold stress.

American Journal of Orthodontics and Dentofacial Orthoped

DISCUSSION

The interfacial bone was expected to undergo largedeformations during the insertion of the microim-plant.16 Thus, a sophisticated nonlinear elasto-plasticmodel was needed to assess the entire range of stressesin bone: both below and above the yield stress. A rela-tively simple rigid plastic model can be used for qualita-tive analysis.12 This model treats bone as a rigid material

ics December 2012 � Vol 142 � Issue 6

Fig 4. The radial stress distributions in the interfacial bone during the insertion process of an orthodon-tic microimplant: A, initial; B, 2 turns; C, 4 turns; D, 6 turns; E, 8 turns; F, 10 turns.

838 Yu et al

below the yield stress and calculates only the plasticstresses (or strains), ignoring stresses generated in theelastic domain. The analysis burden thus could be re-duced. However, for bone, elastic stresses are important.As shown in Figure 2, the critical threshold stresses totrigger pathologic resorption of bone, a key parameterin the prediction of the postinsertion response of the in-terfacial bone, are within the elastic range.

So far, limited attempts have been made to quantifythe stresses induced during microimplant placement.The lack of evaluation methodologies or instrumentsto measure the stresses in the narrow interfacial bonehas forced the use of an indirect measurement such asinsertion torque. Insertion torque is a product of the in-sertion resistance when the microimplant is beingscrewed in; since this resistance is proportional to theamount of bone compression or radial stress, it can be

December 2012 � Vol 142 � Issue 6 American

used as a reference to monitor the insertion stress.Some researchers proposed a clinical guideline for theinsertion torque to maximize the survivability of micro-implants.19 However, the insertion torque is a functionof many other factors including implant size, surfacecondition, thread design, bone quality, and so on; there-fore, it cannot be correlated to localized stresses directlyor accurately.

As shown in Figures 4 and 5, the width of theinterfacial bone subjected to higher insertion stresses isabout as narrow as the microimplant radius. Becauseof this limited space and the acutely changing stress pro-file thereon, direct measurement of stress would be dif-ficult. Therefore, we chose insertion torque as theparameter to validate the finite element simulation.

The friction coefficient of 0.1 between the microim-plant and the cortical bone used in our finite element

Journal of Orthodontics and Dentofacial Orthopedics

Fig 5. The hoop-stress distributions in the interfacial bone at each insertion stage: A, initial; B, 2 turns;C, 4 turns; D, 6 turns; E, 8 turns; F, 10 turns.

Yu et al 839

simulation is a rather low value compared with valuesused in other studies. Although experimentally mea-sured friction data between titanium alloy microim-plants and cortical bone are lacking, a frictioncoefficient from 0.1 to 0.6 has been used in orthopedicimplant studies: ie, between the titanium alloy implantand the cortical bone.20,21 In studies of dentalimplants with roughened surfaces, 0.1 to 0.3 has beenused: 0.3 when bone is dense and intact,22 and 0.1when bone is less intact or when osseointegration is in-complete.23,24 The use of a low-friction coefficient inthis study, however, might be justified, since our micro-implants had a smooth surface, with the lubricating ef-fect of saline solution during insertion, and the frictionduring insertion occurred under kinetic conditions. Theagreement between the measured and calculated torquevalues (Fig 3) might also support the use of a low-

American Journal of Orthodontics and Dentofacial Orthoped

friction coefficient between the microimplant and thecortical bone.

Apart from the friction coefficient, some simplifyingassumptions used in this study could have affected theaccuracy of the finite element analysis. The cutting bladecould have had an effect; the AbsoAnchor SH1312-07model has cutting blades at its tip so that the pilot-hole wall could be cut to form thread grooves in thebeginning stage of insertion. Ignoring this additional os-teotomy could have resulted in overestimation of the in-sertion stresses. Another factor that should bementionedis the postfailure behavior of the bone. As shown inFigure 5, as soon as half the length of the microimplantwas inserted, the hoop stresses in the entire interfacialbone were high enough to cause bone fractures. Cracks,if they occur as observed in previous experimental stud-ies, might significantly lower the rigidity of the interfacial

ics December 2012 � Vol 142 � Issue 6

Fig 6. The residual radial stress distribution in the interfa-cial bone after orthodontic microimplant insertion.

840 Yu et al

bone and thus the stresses thereon.10,11 In this study, theinterfacial bone was assumed to retain the plasticstiffness even when stresses reached the ultimatestrength. This assumption, which was used to improvethe stability of the numeric calculation, could haveresulted in a higher stress state, especially hoop stressescompared with reality. On the other hand, the areaunder the risk of compressive failure because of highradial stress was restricted to a relatively narrow regionnear the thread tips of the microimplants (Fig 4). Hence,the error in the distribution of the radial stress might berelatively low. The error associated with torque calcula-tions could also be minor, since torque is proportionalnot to hoop but to radial stresses.

As expected, high stresses developed in the interfacialbone during the insertion of the microimplant. Interfa-cial bone stresses, especially hoop stresses, rose abovethe ultimate strength of the cortical bone during the in-sertion process (Fig 5). This indicates that, even when theright size of drill is used for predrilling, there is still a sub-stantial risk of damaging and breaking the interfacialbone during the insertion surgery, as observed in theprevious studies.10,11 Seemingly more important,however, the postinsertion stresses near the thread tipareas were higher than the critical threshold stressesfor pathologic bone resorption (Fig 6). This indicatesthat the interfacial bones, especially those contactingthe threads, are likely to undergo pathologic changesat least for a certain period of time after insertion, dete-riorating the stability of the microimplant in the bone.The postinsertion hoop stresses were not included inthe evaluation. Because of the possibility of bone frac-ture as a result of the high hoop stresses during insertion,the accuracy of the postinsertion hoop-stress calculationcannot be guaranteed.

As compared with the level of stresses induced duringand after insertion, stresses produced by orthodonticforces appear to be much lower. Although various levels

December 2012 � Vol 142 � Issue 6 American

of stress have been reported for microimplants of differ-ent sizes, a quantitative finite element study reportedthat a peak stress of approximately 8 MPa is inducedin the cortical bone by an orthodontic force of 200 cNapplied to the same microimplant model used in thisstudy.25 Because of the marked differences betweenthe stress levels caused by the 2 sources, the stressesadded by the orthodontic force after microimplant inser-tion seem to be almost meaningless. This implies that itis not the orthodontic force or the timing of its applica-tion, but the insertion conditions that determine thebone’s response to microimplants and the prognosis oftherapy with microimplants.

CONCLUSIONS

The self-tapping insertion process of orthodonticmicroimplants was successfully simulated by the 3-dimensional finite element method. Within the limita-tions of this in-vitro finite element study, the followingconclusions were drawn.

1. The interfacial bone stresses—both radial and hoopstresses—induced during the self-tapping insertionprocess were high enough to cause a fracture,even though a pilot hole was drilled by using theright size of drill bit.

2. After the self-tapping insertion, the radial stressescalculated at the interfacial bone near the threadtips of the orthodontic microimplant were higherthan the threshold value to trigger pathologicbone changes.

REFERENCES

1. Frost HM. Bone's mechanostat: a 2003 update. Anat Rec A DiscovMol Cell Evol Biol 2003;275A:1081-101.

2. Pattin CA, Caler WE, Cater DR. Cyclic mechanical property degra-dation during fatigue loading of cortical bone. J Biomech 1996;29:69-79.

3. Sugiura T, Horiuchi K, Sugimura M, Tsutsumi S. Evaluation ofthreshold stress for bone resorption around screws based onin vivo strain measurement of miniplate. J Musculoskelet NeuronalInteract 2000;1:165-70.

4. van Staden RC, Guan H, Johnson NW, Loo YC, Meredith N. Step-wise analysis of the dental implant insertion process using the fi-nite element technique. Clin Oral Implants Res 2008;19:303-13.

5. Jiang L, Kong L, Li T, Gu Z, Hou R, Duan Y. Optimal selections oforthodontic mini-implant diameter and length by biomechanicalconsideration: a three-dimensional finite element analysis. AdvEng Software 2009;40:1124-30.

6. Nalbantgil D, Tozlu M, Ozdemir F, Oztoprak MO, Arun T. FEManalysis of a new miniplate: stress distribution on the plate, screwsand the bone. Eur J Dent 2012;6:9-15.

7. Suzuki A, Masuda T, Takahashi I, Deguchi T, Suzuki O, Takano-Yamamoto T. Changes in stress distribution of orthodontic minis-crews and surrounding bone evaluated by 3-dimensional finiteelement analysis. Am J Orthod Dentofacial Orthop 2011;140:e273-80.

Journal of Orthodontics and Dentofacial Orthopedics

Yu et al 841

8. Jasmine MI, Yezdani AA, Tajir F, Venu RM. Analysis of stress inbone and microimplants during en-masse retraction of maxillaryand mandibular anterior teeth with different insertion angula-tions: a 3-dimensional finite element analysis study. Am J OrthodDentofacial Orthop 2012;141:71-80.

9. Motoyoshi M, Ueno S, Okazaki K, Shimizu N. Bone stress fora mini-implant close to the roots of adjacent teeth—3D finite ele-ment analysis. Int J Oral Maxillofac Surg 2009;38:363-8.

10. Wawrzinek C, Sommer T, Fischer-Brandies H. Microdamage in cor-tical bone due to the overtightening of orthodontic microscrews.J Orofac Orthop 2008;69:121-34.

11. Lee NK, Baek SH. Effects of the diameter and shape of orthodonticmini-implants on microdamage to the cortical bone. Am J OrthodDentofacial Orthop 2010;138:8.e1-8.

12. Nam O, Yu W, Kyung HM. Cortical bone strain during the place-ment of orthodontic microimplant studied by 3D finite elementanalysis. Korean J Orthod 2008;38:228-39.

13. Burstein AH, Reilly DT, Martens M. Aging of bone tissue: mechan-ical properties. J Bone Joint Surg Am 1976;58:82-6.

14. Meijer HJ, Starmans FJ, Steen WH, Bosman F. Location of im-plants in the interforaminal region of the mandible and the con-sequences for the design of the superstructure. J Oral Rehabil1994;21:47-56.

15. Lewinstein I, Banks-Sills L, Eliasi R. A finite element analysis ofa new system (IL) for supporting an implant-retained cantileverprosthesis. Int J Oral Maxillofac Implants 1995;10:355-66.

16. Menicucci G,Mossolov A,Mozzati M, Lorenzetti M, Preti G. Tooth-implant connection: some biomechanical aspects based on finiteelement analyses. Clin Oral Implants Res 2002;13:334-41.

American Journal of Orthodontics and Dentofacial Orthoped

17. Reilly DT, Burstein AH. The elastic and ultimate properties of com-pact bone tissue. J Biomech 1975;8:393-405.

18. Ayers RA, Miller MR, Simske SJ, Norrdin RW. Correlation of flexuralstructural properties with bone physical properties: a four speciessurvey. Biomed Sci Instrum 1996;32:251-60.

19. Motoyoshi M, Hirabayashi M, Uemuram M, Shimizu N. Recom-mended placement torque when tightening an orthodonticmini-implant. Clin Oral Implants Res 2006;17:109-14.

20. Viceconti M, Muccini R, Bernakiewicz M, Baleani M, Cristofolini L.Large sliding contact elements accurately predict levels of bone-implant micromotion relevant to osseointegration. J Biomech2000;33:1611-8.

21. Wehner T, Penzkofer R, Augat P, Claes L, Simon U. Improvement ofthe shear fixation stability of intramedullary nailing. Clin Biomech2011;26:147-51.

22. Bardyn T, G�edet P, Hallermann W, B€uchler P. Prediction of dentalimplant torque with a fast and automatic finite element analysis:a pilot study. Oral Surg Oral Med Oral Pathol Oral Radiol Endod2010;109:594-603.

23. Lin D, Li Q, Li W, Ichim I, Swain M. Evaluation of dental implantinduced bone remodelling by using a 2D finite element model.Proceedings of the 5th Australasian Congress on Applied Mechan-ics (ACAM 2007), 2007 Dec 10-12, Brisbane, Australia, p. 301-6.

24. Atieh M, Shahmiri RA. The evaluation of optimal taper of immedi-ately loaded wide-diameter implants: a finite element analysis.J Oral Implantol 2011 Sep 9 [Epub ahead of print].

25. Yu WJ, Kyung HM. A quantitative evaluation of cortical bonestresses influenced by diameter of orthodontic micro-implant.J Korean Res Soc Dent Mater 2007;34:75-87.

ics December 2012 � Vol 142 � Issue 6