Finite element analysis of miniscrew implants used for ... · Finite element analysis of miniscrew implants used for orthodontic anchorage ... In general, the stress induced on cancellous

ORIGINAL ARTICLE

Finite element analysis of miniscrew implantsused for orthodontic anchorage

Te-Chun Liu,a Chih-Han Chang,b Tung-Yiu Wong,c and Jia-Kuang Liuc

Tainan, Taiwan, ROC

aPostgChengbProfeTainacAssosity Hicine.The aucts oSuppo2320-ReprinKungjkliu@Subm0889-Copyrdoi:10

468

Introduction: The miniscrew has been developed and effectively used as orthodontic anchorage, but currentstudies of its usage are insufficient to provide information about the underlying mechanical mechanisms. Theaim of this study was to investigate the roles of bone quality, loading conditions, screw effects, and implanteddepth on the biomechanics of an orthodontic miniscrew system by using finite element analysis. Methods: A3-dimensional model with a bone block integrated with a miniscrew was constructed to simulate variouscortex thicknesses, cancellous bone densities, force magnitudes and directions, screw diameters andlengths, and implanted depths of miniscrews.Results: Both stress and displacement increased with decreasingcortex thickness, whereas cancellous bone density played a minor role in the mechanical response. These 2indexes were linearly proportional to the force magnitude and produced the highest values when the forcewas perpendicular to the long axis of the miniscrew. A wider screw provided superior mechanical advantages.The exposed length of the miniscrew was the real factor affecting mechanical performance. Conclusions: Thescrew diameter was the dominant factor for minscrew mechanical responses. Both bone stress and screw dis-placement decreased with increasing screw diameter and cortex thickness, and decreasing exposed length ofthe screw, force magnitude, and oblique loading direction. (Am J Orthod Dentofacial Orthop 2012;141:468-76)

Anchorage control plays a crucial role in ortho-dontic treatment. It can maximize desired toothmovement and minimize undesired side ef-

fects.1 To obtain stronger anchorage, the orthodonticminiscrew was developed and has been used effectivelyas orthodontic anchorage for various types of toothmovement.2-5 Compared with conventional dentalimplants used for orthodontic anchorage, theorthodontic miniscrew, as a temporary mini-implant, of-fers many advantages, such as easier surgical procedure,less trauma during insertion and removal, minimal ana-tomic limitations, immediate loading after implantation,

raduate student, Institute of Oral Medicine, College of Medicine, NationalKung University, Tainan, Taiwan, ROC.ssor, Institute of Biomedical Engineering, National Cheng Kung University,n, Taiwan, ROC.ciate professor, Department of Stomatology, National Cheng Kung Univer-ospital, College of Medicine and Institute of Oral Medicine, College of Med-

uthors report no commercial, proprietary, or financial interest in the prod-r companies described in this article.rted by the National Science Council, Taiwan, ROC, under grants NSC 93-B-006-067 and NSC 94-2320-B-006-023.t requests to: Jia-Kuang Liu, Department of Stomatology, National ChengUniversity Hospital, 138 Sheng-Li Rd, Tainan 704, Taiwan, ROC; e-mail,mail.ncku.edu.tw.itted, January 2011; revised and accepted, November 2011.5406/$36.00ight � 2012 by the American Association of Orthodontists..1016/j.ajodo.2011.11.012

and lower costs.6-8 However, some clinical studies havereported a relatively high failure rate in miniscrewsused for orthodontic anchorage. Factors identified ascausing failure include inflammation, infection,nonkeratinized implant sites, and small miniscrews.9-14

Because of the nature of the orthodontic miniscrew,load transfer, and small size, biomechanical factors havebeen investigated in many studies. Previous studies haveevaluated the stability of miniscrew anchorage systemswith mechanical experiments, histomorphometric stud-ies, and finite element simulations of the roles of screwgeometry, bone quality, implantation conditions, andloading effects. Many suggestions were provided to in-crease the stability, such as using conical-shapedscrews,15 including abutment,16 preventing cervicalthreading,17 using screws with a wide diameter,15 apply-ing screws with a length of 9 mm,18 achieving bicorticalor partial osseointegration,19 implanting in cortical bonemore than 1-mm thick, 20-22 mplanting in high-densitybone,23 exploiting drill-free miniscrews,24 insertion with60� to 70� of angulation,25 securing with 5 to 10 Ncminsertion torque,26 and tilting the load in a buccal direc-tion.27 However, most of these suggestions were pro-vided without the support of mechanical reasoning.These outcomes could depend on the model or methodand should be applied with caution. Without a thoroughunderstanding of the biomechanical rationale of the

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Liu et al 469

orthodontic miniscrew, no reliable guidelines can beprovided for its clinical usage. The aim of this studywas therefore to investigate the roles of bone quality,loading conditions, screw size, and implanted depth onorthodontic miniscrews by using finite element analysis.The hypothesis was that, with the full field of mechanicalresponses and the precise control of parameters in finiteelement analysis, it is possible to determine the underly-ing biomechanical mechanism of miniscrews and thusprovide reliable usage guidelines.

MATERIAL AND METHODS

A 3-dimensional bone block model integrated witha miniscrew was constructed with a computer-aided de-sign program (SolidWorks; Dassault Syst�emes Solid-Works, Concord, Mass) to simulate a miniscrewimplanted in bone as an orthodontic anchorage unit.The bone block, consisting of cortical and cancellousbones, was simplified to dimensions of 20 mm in lengthand width, and 15 mm in height for evaluation. Theminiscrew geometry was based on the MONDEAL system(MONDEAL Medical Systems, Muhlheim, Germany): ie,the screw thread profile was an isosceles triangle 0.4mm in height and 0.16 mm along the base (Fig 1, A).The thread pitch was 1.0 mm. These thread dimensionswere fixed in all screw designs in this study. The modelwas meshed automatically with 10-node tetrahedralsolid elements (Fig 1, B). The interface between the cor-tex and the cancellous bone was assumed to be fullybonded; ie, the elements were continuous, sharing thesame nodes along the interface. A node-to-node contactcondition was given on the interface between the mini-screw and the bone block to imitate a stage without os-seointergration.

All materials in the model were homogeneous, isotro-pic, and linearly elastic. Theminiscrewwas assumed to bepure titanium with a Young’s modulus of 110 GPa anda Poisson’s ratio of 0.35.28 For healthy bone quality,the Young’s moduli of the cortical and cancellous boneswere 14 GPa28 and 1.3 GPa,18 respectively, and the Pois-son’s ratios were 0.3 for both. The static load along the x-axis was applied to the head of the miniscrew andperpendicular to its long axis to simulate the orthodonticforce. For the nodes located on the 5 exterior surfaces ofthe bone block, all but the superior surface where theminiscrew entered was constrained in all degrees of free-dom to simulate the boundary condition (Fig 1, B). Thenodal solution of the von Mises stress in the bone andthe displacement of the miniscrew were calculated foreach model with the finite element analysis program.

To justify the effect of bone quality on stress gener-ation, 4 cortex thicknesses—0.5, 1.2, 2.0, and 3.0 mm—

and 4 types of cancellous bone density with values

American Journal of Orthodontics and Dentofacial Orthoped

that were normal and 1/2, 1/4, and 1/8 of Young’s mod-ulus (1.3 GPa, and 650, 325, and 162.5 Mpa) of normalcancellous bone were studied. To determine the loadingeffect, 3 force magnitudes (2, 4, and 6 N) and force di-rections (60�, 90� and 120�) to mimic various clinicalconditions were investigated. Force direction was de-fined as the angle between the loading direction andthe long axis of the miniscrew, and a force direction of90� was the force perpendicular to the long axis of theminiscrew (Fig 2).

To determine the screw size effect, 3 screw (outer) di-ameters (1.2, 1.5, and 2.0 mm) and 5 screw lengths (7-15mm at 2-mm intervals) were investigated. The screwlength was measured including the screw head, whichhad a 2-mm height for all screw models. To provide in-formation on how deep a screw should be implanted,various screw depths (screw length in the bone block)were modeled. For each screw length, the implanteddepth started at 2 mm and increased in 2-mm incre-ments until the exposed screw length (screw segmentabove the bone block) was 3 mm (including the screwhead). For instance, the model with a 13-mm screwlength would be implanted in the bone block at 2, 4,6, 8, and 10 mm.

RESULTS

Figure 3 shows the peak vonMises stress on the mini-screw and the surrounding bone under 2 N, 90� force.Both compressive and tensile stresses were identifiedon 2 sides of theminiscrew, and the peak vonMises stresson the miniscrew was concentrated near the entrancepoint to the cortical bone, which represented a pivotpoint of the bending (Fig 3, A). For cortical bone, thepeak stress was located on the compression side of theentrance point because of the contact between the mini-screw and the cortex (Fig 3,B). The peak stress on cancel-lous bone was concentrated, again, at the entrance pointof the miniscrew, but this time on the screw’s tensile side,because of the seesaw effect (Fig 3, C).

In general, the stress induced on cancellous bone ismuch lower than that on the cortex. In addition, themost commonly identified structure failure in miniscrewanchorage systems is screw loosening. Therefore, onlycortex stress was examined in this study. The maximumdisplacement was always located at the top of the mini-screw head in all models and also evaluated for stabilityjustification. For comparison among various factors inthe following analyses, a bonemodel with a cortex thick-ness of 2 mm and a normal cancellous bone density im-planted with a miniscrew 2 mm in diameter and 13 mmin length embedded at a depth of 8 mm under 2 N, 90�

loading was defined as the base model. The result from

ics April 2012 � Vol 141 � Issue 4

Fig 1. A, The dimensions of the base miniscrew model; B, the whole structure is meshed, loaded, andconstrained.

Fig 2. Various force directions applied to the head of theminiscrew.

470 Liu et al

the base model was set as 1, and the resulting data wereexpressed as ratios of values to the base model in the fol-lowing figures.

The peak von Mises stress on the cortex increased asthe cortex thickness decreased from 3.0 to 0.5 mm underthe same loading conditions. However, these stress in-creases were mild, less than 10%, except when the cortexthickness was reduced from 1.2 to 0.5 mm, which in-duced a significant stress increase of 20% to 25% for dif-ferent densities of cancellous bone. On the other hand,the density of the cancellous bone had a minor effecton the cortex bone stress, no matter how thick the cortexwas. Coupling these 2 bone factors, cortex thickness andcancellous bone density, comparisons of the peak vonMises stress on the cortex are summarized in Figure 4,A. In the base model, when the Young’s modulus of can-cellous bone was reduced to one eighth of normal, thepeak von Mises stress on the cortex increased by only3%. However, if the cortex thickness and Young’s mod-ulus of cancellous bone were reduced simultaneously to0.5 mm and one eighth of normal, respectively, the peakvon Mises stress increased by 34%.

The maximum displacement, occurring at the mini-screw head as stated above, was always located at thetop of the miniscrew head in all models under all loadingconditions. The tendencies of maximum displacement ofthe miniscrews related to cortex thickness and cancel-lous bone density were similar to the results of thepeak von Mises stresses on the cortex. The displacementresults of the coupling effects of cortex thickness and

April 2012 � Vol 141 � Issue 4 American

cancellous bone density are summarized in Figure 4, B.In the base model, when the Young’s modulus of cancel-lous bone decreased to one eighth of normal, the max-imum displacement of the miniscrews increased byonly 4%. However, if the cortex thickness and theYoung’s modulus of cancellous bone were reducedsimultaneously to 0.5 mm and one eighth of normal,respectively, the maximum displacement of the mini-screw increased by 27%.

Journal of Orthodontics and Dentofacial Orthopedics

Fig 3. The stress contour plots of the sectioned base model (only the portion near the miniscrew, thehigh-stress region, is shown):A, the vonMises stress distribution on theminiscrew (the displacement isenlarged 150 times); B, the von Mises stress distribution on cortical bone (the miniscrew has been re-moved from the structure);C, the von Mises stress distribution on cancellous bone (miniscrew and cor-tex have been removed) (left side, compressive side; right side, tensile side).

Liu et al 471

Increasing the force magnitude resulted in a higherpeak von Mises stress on the cortex, and the peak stresswas linearly proportional to the force magnitude. A forcedirection of 90� showed a higher peak von Mises stressthan force directions of 60� and 120�, and the peakvon Mises stress values for 60� and 120� were almostthe same. If the peak von Mises stress value from thebase model was set as 1, those from force directions of60� and 120� decreased by 13% and 15%, respectively.Figure 5, A, summarizes the effects of force factors onthe peak von Mises stress on the cortex.

The results of the force effects related to the maximumdisplacement of theminiscrews were also similar to the re-sults from the peak vonMises stress on the cortex. Increas-ing the force magnitude resulted in greater displacementof the miniscrew, and the maximum displacement of theminiscrews was also linearly proportional to the forcemagnitude. A force direction of 90� showed the highestmaximum displacement in the miniscrews, whereas thevalues from 60� and 120� were almost same. If the max-imum displacement from the base model was set as 1,those from force directions of 60� and 120� decreasedby 14% and 12%, respectively. Figure 5, B, shows theforce effects on maximum miniscrew displacement.


The miniscrew size and implanted depth effects onthe maximum von Mises stress of the cortex were alsoexamined. The maximum von Mises stress on the cortexincreased significantly as the diameter of the miniscrewdecreased. For example, as the miniscrew diameter de-creased from 2.0 to 1.2 mm, the maximum von Misesstress increased more than 30 times. With the samemini-screw, the maximum von Mises stress on the cortex de-creased as the implanted depth increased. But as theimplant length increased, under the same implanteddepth, the maximum von Mises stress on the cortex in-creased. Close examination of the results showed thatthe exposed screw length (screw length above the cortexor total screw length minus the implanted depth) was thedominant factor. For the same screw diameter, the vonMises stress was almost the same when the exposedscrew length was the same, no matter how long thescrew was and how deep the screw was implanted. Togive an overview of the results of miniscrew effects,the maximum von Mises stress values on the cortexwere plotted against the miniscrew diameter, length,and exposed length, as shown in Figure 6. The trendof the maximum displacement of the miniscrew relatedto the miniscrew effects was similar to that of the


Fig 4. Bone effects with: A, the peak von Mises stress on the cortex; and B, the maximum displace-ment of the miniscrews.

472 Liu et al

maximum von Mises stress in bone related to the mini-screw effects.

DISCUSSION

Finite element models

Because of its mechanical nature, it is important tounderstand themechanical rationale of miniscrew usage.But it would be difficult to determine the underlying bio-mechanical mechanisms for miniscrew applicationsthrough an experimental approach because of the limited


measureable mechanical index, imprecise parametercontrol, and the large variations among samples. Onthe other hand, finite element analysis provides a moremanageable and flexible approach for the evaluation ofdental biomechanics than the experimental approach.29

Based on their numeric origin, the investigated parame-ters can be controlled more precisely, andmanymechan-ical indexes can be examined at any location on themodel to reflect the rationale of a mechanical response.However, the reliability of finite element analysis de-pends on the mesh model. In this study, the mesh models


Fig 5. Force effects with: A, the peak von Mises stress on the cortex; and B, the maximum displace-ment of the miniscrews.

Liu et al 473

contained roughly 80,000 to 110,000 nodes and 55,000to 80,000 elements, depending on the model conditions.The convergent criteria were set with a change in theglobal strain energy of less than 2%, and the elementstrain energy error was less than 5%.

This study had some limitations in the simulation.First, the geometry of the bone block was simplified toa rectangular block, and the material properties were as-sumed to be homogeneous. No soft tissue was simulated,although its impact would have been minor. Second, the


miniscrew was implanted in the bone block in a perfectcondition, perpendicular to the bone surface. Finally,the interface between the bone and the miniscrew waspure frictionless contact. However, these simplificationsshould affect the quantitative values of the simulations,not the underlying mechanical mechanism.

Bone effects related to stress

Previous finite element analysis studies found thatcortex thickness determines the overall load transfer


Fig 6. Miniscrew effects (diameter, length, and exposed length) with themaximum vonMises stress onthe cortex.

474 Liu et al

from miniscrew to bone, and the density of cancellousbone plays only a minor role in resisting this force.20,27

The results from our study were similar to previousfindings. There were 2 reasons for this. First, corticalbone with a higher Young’s modulus resists moredeformation and sustains higher loads than doescancellous bone. Second, the bending mode, asidentified in the miniscrew stress, has more effect at thebase support region, as justified by the concentratedhigh base stress in the entrance region of the cortex inFigure 3, B, than the rest of the embedded region,a straighter and less bent region. This could also explainthe cortex thickness effect. When the cortex was thickerthan 1.2 mm, the high base stress was distributed, andthe stress demonstrated only a mild change as the cortexthickness changed. But as the cortex thickness was re-duced to 0.5 mm, it was not enough to spread the basestress from bending, and therefore the peak stress in-creased more significantly. Although models with cortexthicknesses between 1.2 and 0.5 mm were not evaluatedin this study, other studies have suggested that a corticalbone thickness of 1 mm improves the success rate ofminiscrews; this is reasonable, based on the thicknesseffects in this study.20-22

When considering the effect of bone quality on stressdistribution, bone strains could reach values associatedwith the pathologic overload window only for thin


cortical bone (\0.5 mm) with low-density trabecularbone. For medium- and high-density trabecular bone,this danger is not present, since bone strains always oc-cur within mild overload or adapted windows.20 In thisstudy, when the cortex thickness was 0.5 mm, the peakstress increased with both low-density (162.5 Mpa)and high-density (1.3 GPa) Young’s modulus cancellousbone. Therefore, cortex thickness was a determining fac-tor of bone quality for miniscrew stability.

Thicker cortical bone increases the primary stabilitybut might decrease the secondary stability because ofexcessive bone compression if the site is not adequatelyprepared.30 Primary stability means the initial stabilityimmediately after insertion of an implant, and secondarystability indicates gains after osseointegration.31 Pri-mary stability is important during the healing and re-modeling period, especially when the implant isimmediately loaded. Secondary stability is responsiblefor implant success after the healing period and duringmost of the loading period. For increased stability ofthe miniscrew, no predrilling is required for 0.5 to 1.5-mm cortical bone, perforation of cortical bone witha 1-mm round bur is used for 1.5 to 2.5-mm corticalbone, and 4-mm long predrilling is recommended forcorticol bone more than 2.5 mm thick.30,31 In thisstudy, primary stability between the miniscrew and thebone block was simulated. If secondary stability was


Liu et al 475

simulated, the interface between the miniscrew and thebone block was assumed to be fully bonded. Thesituation would be complicated, so we did notsimulate secondary stability in this study.

Force effects related to stress

The simulated outcomes, stress and displacement,were almost linearly proportional to the force magnitudein our study, even though a nonlinear contact interfacewas present in the model. These results were reasonableand predictable, because the material properties in allcomponents were assumed to be linearly elastic, andthe contact interface provided insignificant nonlineareffects because of the small force applied. Nevertheless,the 6-N model had 3 times the stress in bone comparedwith the 2-N model, so a higher initial load should beavoided. This possibly agrees with other studies thatfound no detectable mobility or loosening of miniscrewswhen applying a light to moderate initial force.18,32,33

The peak von Mises stress on the cortex of theminiscrews had the greatest values with a force directionof 90� in this study. This force direction was a purebending load, whereas the force directions of 60� and120� were bending plus axial loading. A bending loadinduced much higher stress than an axial load. There-fore, bone stress was mainly affected by the bendingcomponent of force, a force component perpendicularto the screw axis. This supports the results derivedfrom S€utpideler et al,34 who conducted finite elementanalysis to evaluate the effects of the applied force angleon supporting bone. They concluded that, once the forcedeviated from vertical, it induced a horizontal compo-nent that increased the stress on bone, and further in-creasing the deviation angle significantly increased thestress. Barbier et al35 emphasized the importance of pre-venting or minimizing horizontal force on implants intheir finite element analysis. Another finite elementanalysis study also stated that, with a load tilted in a buc-cal direction of 45� to a mimiscrew, the stresses were re-duced by 35%.27 This could also be extrapolated for theminiscrew system in our study. If we tilted the horizontalload direction by 30�, it could reduce stress by 15%.

Screw effects related to stress

Previous studies found that wider miniscrews hadbetter stability, but observations of miniscrew lengthwere inconsistent.15,27 This could again be easilyexplained by the bending mode of the loaded miniscrew.Under bending, based on the second moment of inertiaof a cylinder, the peak stress is inversely proportional tothe third power of the diameter. Therefore, the miniscrewdiameter was the dominant factor in governing the stress


values of the structure among all investigated factors inthis study. Increasing the miniscrew diameter was themost effective way to reduce the peak stress.

Some studies evaluated the miniscrew-length effectand had inconsistent or inconclusive results.18,27 Thereason was that the screw length itself was not thedominant factor under the bending mode. The exposedlength, the level arm of the bending moment, was thereal factor influencing stress and displacement.Therefore, both screw length and implanted depth ofthe miniscrew should be considered. A longerminiscrew might not be able to provide extra stability ifit cannot be implanted deeply enough to reduce thelever arm. However, in this study, the minimumimplanted depth was 3 mm, which was 1 mm over thecortex. Further reducing the implanted depth mightprovide insufficient support to resist bending.

CONCLUSIONS

Three conclusions can be derived from this study: (1)the quality of cancellous bone is not cruical for mini-screw stability as long as a minimum cortex thickness,1.2 mm in this study, can be achieved; (2) to reducethe biomechanical risk in miniscrew applications, the im-plant site and the orientation of the miniscrew should bearranged to minimize the bend effect, reducing the forcecomponent perpendicular to the screw axis; and (3)a wider miniscrew is helpful, but a long screw could beharmful if it causes a long exposed length.

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Finite element analysis of miniscrew implants used for ... · Finite element analysis of miniscrew implants used for orthodontic anchorage ... In general, the stress induced on cancellous

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