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Bone stress and strain after use of a miniplate for molar protraction and uprighting: A 3-dimensional nite element analysis Lucila Zimmermann Largura, a Marco Andr e Argenta, b Maur ıcio Tatsuei Sakima, c Elisa Souza Camargo, d Odilon Guariza-Filho, d and Orlando Motohiro Tanaka e Curitiba, Paran a, and Araraquara, S~ ao Paulo, Brazil, and St Louis, Mo Introduction: The aim of this study was to use the nite element method to evaluate the distribution of stresses and strains on the local bone tissue adjacent to the miniplate used for anchorage of orthodontic forces. Methods: A 3-dimensional model composed of a hemimandible and teeth was constructed using dental computed tomographic images, in which we assembled a miniplate with xation screws. The uprighting and mesial movements of the mandibular second molar that was anchored with the miniplate were simulated. The miniplate was loaded with horizontal forces of 2, 5, and 15 N. A moment of 11.77 N$mm was also applied. The stress and strain distributions were analyzed, and their correlations with the bone remodeling criteria and miniplate stability were assessed. Results: When orthodontic loads were applied, peak bone strain remained within the range of bone homeostasis (100-1500 m strain) with a balance between bone formation and resorption. The maximum deformation was found to be 1035 m strain with a force of 5 N. At a force of 15 N, bone resorption was observed in the region of the screws. Conclusions: We observed more stress concentration around the screws than in the cancellous bone. The levels of stress and strain increased when the force was increased but remained within physiologic levels. The anchorage system of miniplate and screws could withstand the orthodontic forces, which did not affect the stability of the miniplate. (Am J Orthod Dentofacial Orthop 2014;146:198-206) T emporary skeletal anchorage devices, such as palatal implants, mini-implants, and miniplates, have been incorporated into orthodontic treat- ment, thereby expanding the limits of tooth movement, especially in uncooperative patients and those with many missing teeth or a complex malocclusion. 1,2 The miniplates introduced by Umemori et al 3 are anchorage devices that are indicated for the treatment of severe malocclusion and large tooth movements, such as in molar intrusion or retraction, for which anchorage control can be difcult. 4 The success rate of miniplates is well above 90%; however, failure of the miniplate system leads to miniplate mobility and conse- quently early miniplate removal. 5,6 Surgical trauma, local inammation, some specic anatomic structures close to the miniplate, and insufcient bone density are some factors related to miniplate failure. 5-7 The loss of miniplate stability can also be due to biomechanical problems and the effects of stress generated by the applied forces around the screws. 8 In plates used for osteosynthesis, the loss of screws was associated with high levels of stress at the screw- bone interface, which indicates a relationship between stress or strain and bone resorption around the screws. 9 With respect to dental implants, a direct relationship ex- ists between bone resorption and loading; however, very high or very low levels of strain lead to a negative balance in bone remodeling. 1 Using miniplates for anchorage results in a load that seems to be a central aspect of the device's stability because the magnitude a Postgraduate student, Graduate Program in Orthodontics, School of Health and Biosience, Pontif ıcia Universidade Cat olica do Paran a, Curitiba, Paran a, Brazil. b Adjunct professor, Graduate Program in Numerical Methods, Department of Civil Engineering, Federal University of Paran a, Curitiba, Paran a, Brazil. c Professor, Department of Orthodontics, School of Dentistry, University of S~ ao Paulo, Araraquara, S~ ao Paulo, Brazil. d Full professor, Graduate Program in Orthodontics, School of Health and Biosience, Pontif ıcia Universidade Cat olica do Paran a, Curitiba, Paran a, Brazil. e Professor, Graduate Program in Orthodontics, School of Health and Biosience, Pontif ıcia Universidade Cat olica do Paran a, Curitiba, Paran a, Brazil; postdoctoral fellow, Center for Advanced Dental Education, Saint Louis University, St Louis, Mo. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conicts of Interest, and none were reported. Address correspondence to: Orlando Motohiro Tanaka, Pontif ıcia Universidade Cat olica do Paran a, Rua Imaculada Conceic ¸ ~ ao, 1155, Bairro Prado Velho, CEP: 80.215-901, Curitiba, Paran a, Brazil; e-mail, [email protected]. Submitted, March 2013; revised and accepted, April 2014. 0889-5406/$36.00 Copyright Ó 2014 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.04.022 198 ORIGINAL ARTICLE

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  • ORIGINAL ARTICLEBone stress and strain after use of a miniplatefor molar protraction and uprighting: A3-dimensional finite element analysisLucila Zimmermann Largura,a Marco Andre Argenta,b Maurcio Tatsuei Sakima,c Elisa Souza Camargo,d

    Odilon Guariza-Filho,d and Orlando Motohiro Tanakae

    Curitiba, Parana, and Araraquara, S~ao Paulo, Brazil, and St Louis, MoaPostgBiosiebAdjuCivil EcProfePaulodFullBiosieeProfePontifellowSt LouAll auPotenAddreCatoli80.21Subm0889-Copyrhttp:/

    198Introduction: The aim of this study was to use the finite element method to evaluate the distribution of stressesand strains on the local bone tissue adjacent to theminiplate used for anchorage of orthodontic forces.Methods:A 3-dimensional model composed of a hemimandible and teeth was constructed using dental computedtomographic images, in which we assembled a miniplate with fixation screws. The uprighting and mesialmovements of the mandibular second molar that was anchored with the miniplate were simulated. Theminiplate was loaded with horizontal forces of 2, 5, and 15 N. A moment of 11.77 N$mm was also applied.The stress and strain distributions were analyzed, and their correlations with the bone remodeling criteria andminiplate stability were assessed. Results: When orthodontic loads were applied, peak bone strain remainedwithin the range of bone homeostasis (100-1500 m strain) with a balance between bone formation and resorption.The maximum deformation was found to be 1035 m strain with a force of 5 N. At a force of 15 N, bone resorptionwas observed in the region of the screws. Conclusions: We observed more stress concentration around thescrews than in the cancellous bone. The levels of stress and strain increased when the force was increasedbut remained within physiologic levels. The anchorage system of miniplate and screws could withstandthe orthodontic forces, which did not affect the stability of the miniplate. (Am J Orthod Dentofacial Orthop2014;146:198-206)Temporary skeletal anchorage devices, such aspalatal implants, mini-implants, and miniplates,have been incorporated into orthodontic treat-ment, thereby expanding the limits of tooth movement,especially in uncooperative patients and those withmany missing teeth or a complex malocclusion.1,2raduate student, Graduate Program in Orthodontics, School of Health andnce, Pontifcia Universidade Catolica do Parana, Curitiba, Parana, Brazil.nct professor, Graduate Program in Numerical Methods, Department ofngineering, Federal University of Parana, Curitiba, Parana, Brazil.ssor, Department of Orthodontics, School of Dentistry, University of S~ao, Araraquara, S~ao Paulo, Brazil.professor, Graduate Program in Orthodontics, School of Health andnce, Pontifcia Universidade Catolica do Parana, Curitiba, Parana, Brazil.ssor, Graduate Program in Orthodontics, School of Health and Biosience,fcia Universidade Catolica do Parana, Curitiba, Parana, Brazil; postdoctoral, Center for Advanced Dental Education, Saint Louis University,is, Mo.thors have completed and submitted the ICMJE Form for Disclosure oftial Conflicts of Interest, and none were reported.ss correspondence to: Orlando Motohiro Tanaka, Pontifcia Universidadeca do Parana, Rua Imaculada Conceic~ao, 1155, Bairro Prado Velho, CEP:5-901, Curitiba, Parana, Brazil; e-mail, [email protected], March 2013; revised and accepted, April 2014.5406/$36.00ight 2014 by the American Association of Orthodontists./dx.doi.org/10.1016/j.ajodo.2014.04.022The miniplates introduced by Umemori et al3 areanchorage devices that are indicated for the treatmentof severe malocclusion and large tooth movements,such as in molar intrusion or retraction, for whichanchorage control can be difficult.4 The success rate ofminiplates is well above 90%; however, failure of theminiplate system leads to miniplate mobility and conse-quently early miniplate removal.5,6 Surgical trauma,local inflammation, some specific anatomic structuresclose to the miniplate, and insufficient bone densityare some factors related to miniplate failure.5-7 Theloss of miniplate stability can also be due tobiomechanical problems and the effects of stressgenerated by the applied forces around the screws.8

    In plates used for osteosynthesis, the loss of screwswas associated with high levels of stress at the screw-bone interface, which indicates a relationship betweenstress or strain and bone resorption around the screws.9

    With respect to dental implants, a direct relationship ex-ists between bone resorption and loading; however, veryhigh or very low levels of strain lead to a negativebalance in bone remodeling.1 Using miniplates foranchorage results in a load that seems to be a centralaspect of the device's stability because the magnitude

    Delta:1_given nameDelta:1_surnameDelta:1_given nameDelta:1_surnameDelta:1_given nameDelta:1_surnamemailto:[email protected]://dx.doi.org/10.1016/j.ajodo.2014.04.022

  • Largura et al 199of the increase in strength leads to increased tensions inthe region of the screws.10

    Few studies have evaluated the influence of ortho-dontic forces on the biomechanical behavior of bone tis-sues around miniplates. This is critical because a positiveeffect on local loading of bone turnover might induce anexcessive bone response and result in difficulty inremoving the miniplate, whereas a negative effect mightreduce its stability.7,11

    Therefore, the aim of this study was to use the finiteelement method to simulate the stress and the deforma-tion that occur in the bone adjacent to the miniplatewhen loads are applied.

    MATERIAL AND METHODS

    A 3-dimensional (3D) model of the mandible and theteeth was reconstructed from dental computed tomo-graphic images obtained from the DICOM-image repos-itory (www.osirix-viewer.com/datasets). The geometricmodel was created in the format using software (version4.7; Simpleware, Exeter, United Kingdom), and it wasexported to the SolidWorks software (version 11.0; Das-sault Systemes, Waltham, Mass; http://www.solidworks.com/sw/183_ENU_HTML.htm). The stereolithographycomputer-aided design was transformed into a solidmodel, and the miniplate and screws (SAO; RAHOS,S~ao Paulo, Brazil; http://rahos.com.br/) were inserted(Fig 1). The final 3D model was composed of a hemi-mandible, an L-shaped titanium miniplate (1 mm thick),and 3 titanium screws (2 mm in diameter, 5 mm inlength). The hemimandible was composed of teeth(dentin, enamel, and periodontal ligament), cancellousbone, and cortical bone (2.3 mm thick). The model wasexported to ANSYS software (version 12.1; SwansonAnalysis, Pittsburgh, Pa) for the finite element analysis.

    All materials were considered to be isotropic and ho-mogeneous with linear elastic mechanical behavior. Thisapproach allowed a qualitative evaluation of the results,which was the aim of this study.12 The modulus of elas-ticity and the Poisson coefficient of the materials used inthe simulationtitanium, cortical bone, cancellousbone, enamel, dentin, and periodontal ligamentwereobtained from the literature and are listed in Table I.13-16

    The contact between the screws and the holes of theminiplate, the contact between the screws and the bone,and the contact between the teeth and the bone wereconsidered to be perfect. Simulation was performedwith the contact element type bonded, which doesnot allow sliding or separation between the faces. Thecontour regions were set to prevent interference withthe region of interest from the simulation. The mandiblewas fixed in the head of the mandible and the lower pos-terior region of the mandibular body.American Journal of Orthodontics and Dentofacial OrthopedThemechanical model is shown in Figure 2. The finiteelement mesh consisted of 573,066 nodes and9,645,858 elements. The elements used to recreate thematerials were the quadratic tetrahedral type definedby 10 nodes with 3 degrees of freedom at each node,represented in the x-, y-, and z-axes.

    The loading was performed to simulate the mesialmovements and the uprighting of the mandibular sec-ond molar (Fig 3). The following 6 load conditionswere simulated.

    Load 1: load of 2 N, representing orthodontic force inthe anteroposterior direction, was applied at the end ofthe miniplate and the bracket of the mandibular sec-ondmolar, simulatingmesial movement of that molar.Load 2: load of 5 N, representing orthopedic force inthe anteroposterior direction, was applied at the edgeof the miniplate and the bracket of the mandibularsecond molar.Load 3: a 11.77-N$mm (1200 gf.mm) moment wasapplied in the clockwise direction to the edge of theminiplate, thereby generating a counterclockwisemovement of the mandibular second molar. Theapplication of this load simulates the uprightingmovement of the second molar.Load 4: a 2-N anteroposterior force and an 11.77-N$mmmoment were applied to the edge of the mini-plate and to the mandibular second molar bracket.The application of this load causes simultaneousmesial movement and uprighting of the mandibularsecond molar.Load 5: an anteroposterior load of 5 N and an 11.77-N$mmmoment were applied at the edge of the mini-plate and to the mandibular second molar.Load 6: a 15-N anteroposterior force was applied tothe edge of the miniplate to achieve the level of forcethat would induce bone deformities with levels above3000 m strain.

    The area next to the miniplate was selected as the re-gion of interest in this study. The following analyseswere performed: (1) maximum principal deformationsin bone (1, traction), (2) minimum principal deforma-tions in bone (3, compression), (3) maximum principalstress in bone (s1, traction), and (4) minimum principalstress on the bone (s3, compression).

    RESULTS

    The stresses (in MPa) and strains (in m strain) occur-ring in the bone tissues were calculated and presented ina range of colors. Different colors represent differentlevels of strain and stress on the element analyzed. Redrepresents the maximum amount of stress (tension)and the maximum deformation (compression); blueics August 2014 Vol 146 Issue 2

    http://www.osirix-viewer.com/datasetshttp://www.solidworks.com/sw/183_ENU_HTML.htmhttp://www.solidworks.com/sw/183_ENU_HTML.htmhttp://rahos.com.br/

  • Fig 1. A, Tomographic slice; B, 3D model reconstructed from dental computed tomographic images;C, the miniplate; D, cortical bone with screws inserted (Solidworks).

    Table I. Mechanical proprieties of the materials usedfor the finite element analysis

    MaterialElastic modulus (E)

    (MPa)Poisson

    coefficient (v)Cortical bone 13800 0.26Cancellous bone 345 0.31Enamel 84100 0.20Dentin 18600 0.31Periodontal ligament 0.68 0.49Titanium 96000 0.36Steel 193000 0.31

    200 Largura et alrepresents the minimum amount of pressure (compres-sion) and the minimum deformation (tensile). Positiveor negative values in the voltage range indicate tensionor compression, respectively (Table II).

    The distribution of the maximum principal strains(loads 1-5) can be seen in Figure 4. Figures 5 and 6show the distributions of the maximum principalAugust 2014 Vol 146 Issue 2 Americanstresses and strains, respectively, during traction andin compression at load 1. Upon analysis of loads 1 to5, the maximum tensile strain was found at 1026 mstrain when the force applied was 5 N (load 2).During compression, the peak was found to be1035.3 m strain, also with force of 5 N. Load 6 wasexposed to a force of 15 N when the strain exceededphysiologic limits (m strain 3000), as shown inFigure 7.17

    The peak strain and stress in the bone tissue duringtraction and compression in loads 1 to 6 are shown inTable II. When comparing load 1 (2N) and load 5 (5N),we found that the levels of strain increased by approxi-mately 200% when the force increased by 2.5 times. Thelevels of strains and stresses were reduced when themoment was inserted. Compared with load 1, the defor-mation of load 4 was decreased by 0.46%, and strainsaccounted for 82.29%. Compared with load 2, the defor-mation of load 5 was decreased by 85.85%, and strainsaccounted for 86.11%.Journal of Orthodontics and Dentofacial Orthopedics

  • Fig 2. Finite element mesh.

    Fig 3. I, Mechanical model representing an anteroposterior load; II,mechanical model representing aclockwise moment:A, fixed support 1;B, fixed support 2;C, anteroposterior load;D, its reaction; E andF, binary forces representing a clockwise moment; G and H, its reaction.

    Largura et al 201The analysis of strain showed that the distribution ofdeformation was not uniform throughout the regionswhere the screws were analyzed. Some regions showedlow levels of deformation (\100 m strain).

    DISCUSSION

    The analysis of the stresses and principal strains sec-ondary to tension and in compression showed that theAmerican Journal of Orthodontics and Dentofacial Orthopedhighest stress occurred in the cortical bone. This resultis prevalent in many finite element analyses that haveinvestigated implants and mini-implants. This factmost likely indicates that the cortical thicknessinfluences the stability of the screw, which has beenobserved in studies with mini-implants,18-21 and thatthe variation of the density of trabecular bone has lessinterference.20,22,23 In this study, cortical thickness wasics August 2014 Vol 146 Issue 2

  • Fig 4. Maximum principal strain (stretching): A, load 1;B, load 2; C, load 3; D, load 4; E, load 5.

    Table II. Maximum principal strain (1), minimumprincipal strain (3), maximum principal stress (s1),minimum principal stress (s3) in the bone

    Load

    Maximumprincipalstrain

    (m strain)

    Minimumprincipal strain

    (m strain)

    Maximumprincipal

    stress (MPa)

    Minimumprincipal

    stress (MPa)1 527.3 522.9 6.55 7.192 1026.1 1035.3 14.41 14.973 303.7 303.4 3.81 4.124 434.6 424.6 5.39 5.395 881.0 879.4 12.4 12.656 3100.2 3208.5 43.46 45.72

    202 Largura et almodeled on the anatomy provided by tomography andtherefore could not be changed. Other models can beconstructed to assess this variation, including theimpact of cortical thickness on the screw stability.

    Evaluations of tensile and compressive zones haveshown similar behavior in both cases; this is consistentwith other studies investigating anchorage that haveused experimental implants,1,24 mini-implants,25,26

    and miniplates.7,11 However, a change was observed inthe distribution of the deformations. Duringcompression, a higher concentration of deformationsoccurred at the closest point of application of theforce screws; during traction, the highestconcentration of deformations occurred in the middleof the screw. The farthest screw received little forceduring both traction and compression, and therefore itwas not included in the analysis.

    The analysis of loads 1 and 5 showed that the stressesand strains were reduced when the moment was applied.The deformation in load 4 was reduced to 82.46% of thedeformation in load 1, and strains accounted for82.29%. The deformation of load 5 was reduced to85.85% of the deformation in load 2, and strains ac-counted for 86.11%. These results indicate that onestrength of the binary system is that it balances theforces and reduces the stresses transmitted to thebone, resulting in lower voltages when the moment isapplied.

    Analysis of loads 1 and 5 showed that the stresses andstrains increased by approximately 200% when themagnitude of the force increased by 2.5 times. Huanget al10 reported similar results when evaluating the effectof force on bone around the mounting screws throughfinite elements. They concluded that the magnitude ofthe force plays the most important role in bone responseand plaque stability, because tensions rose by 200%when the magnitude of the force tripled. However, anal-ysis of vonMises stress, which does not allow relating thedata to the criteria of bone remodeling, was performed.August 2014 Vol 146 Issue 2 AmericanThe von Mises criterion is a measure used to predictthe failure of ductile materials, such as metal, whenthe last resistance in traction coincides with the ultimatestrength in compression; this does not occur withbone.27,28 This method is frequently used in studiesreporting numeric analyses of stresses in biologictissues, and it reports the magnitude of the equivalentdeformation, but it is not suited for this analysis.29

    We analyzed the principal strain by comparing thepeak values of deformation in the reference valuesreported in the literature on bone adaptation.9,17 Weconcluded that although the levels of deformationJournal of Orthodontics and Dentofacial Orthopedics

  • Fig 5. A,Maximum principal strain (stretching), load 1; B,maximum principal stress (traction), load 1.

    Fig 6. A, Minimum principal strain (shortening), load 1; B, minimum principal stress (compression),load 1.

    Fig 7. A,Maximumprincipal strain (stretching), load 6;B,minimum principal strain (shortening), load 6.

    Largura et al 203increased with increasing force, the levels ofdeformation appear to remain at fairly safe levels onbone adaptation, indicating that forces of 5 N do notaffect the local bone response and stability of theminiplate. Although the analysis of biologic materialsis an approximation of reality, according to thissimulation, it would require 15 N to induce bone lossin the bone site (above m strain 3000). The data alsoAmerican Journal of Orthodontics and Dentofacial Orthopedsuggest that loading the miniplate does not inducebone formation because the deformation does notreach peak levels and thus enter the physiologic rangeof overload that would stimulate bone formation.17

    Few published experimental studies have reportedthe stability of orthodontic force with miniplates andlocal bone remodeling. Comparing the data from ournumeric analysis with data from histologic studiesics August 2014 Vol 146 Issue 2

  • 204 Largura et alindicates that the data regarding the stability of mini-plates are similar. Daimaruya et al30 conducted experi-ments in dogs to evaluate the effects of the intrusionand the degree of osseointegration of the molar screwand found that in both groups, the miniplates remainedstable throughout the experimental period independentof whether they were charged or uncharged. This findingindicates that loading did not influence the stability ofthe miniplates; this confirms the results of our study.

    Cornelis et al7 performed another experimental studyin dogs to evaluate the reaction to orthodontic forces ofthe bone around the screws. Both screws used in the sta-ble miniplates had good bone-screw contact, whereasone or both of the screws used in the mobile miniplatesdid not. The screws that did not have good bone-screwcontact showed no particular distribution in terms oftime, location, or load. No significant difference wasfound in the amount of bone-screw contact betweenthe loaded and unloaded screws; this indicates thatbone healing is not affected by the application of ortho-dontic forces. Cornelis et al11 also performed a study indogs to assess whether the application of orthodonticforces affects miniplate stability by evaluating bonemineral density around the screws. They reported thatminiplate stability was not affected by the load becausethe success rate did not vary between the loaded andunloaded miniplates.

    Similar results were observed in studies with ortho-dontic dental implants under load; they showed thatdental implants can be used as anchorage withoutcompromising their stability.1,24,31 Previous studieshave shown that mini-implants can be used foranchoring because loads used in orthodontics do notaffect the stability of these devices.26,32-36

    Our study showed that forces between 2 and 5 Ngenerate physiologic levels of deformation, and theyneither stimulate local bone resorption nor are stimulifor bone formation. This result suggests that when os-seointegration occurs at some screw, or when bone isfound covering a miniplate at removal, the phenomenonis caused by the influence of another factor, not themagnitude of the force. This finding is consistent withanimal studies demonstrating that osseointegrationoccurred in the same uncharged miniplates; this indi-cates that osseointegration is an adaptive time-dependent phenomenon that occurs when titanium isimplanted in the bone.7,20 The results of experimentalstudies on implants and mini-implants for anchorageare similar, indicating that the magnitude of orthodonticforces does not favorably influence bone remodel-ing.25,33,35,36 Several studies have shown thatosseointegration appears to be an adaptive biologictime-dependent phenomenon.1,25,26,32August 2014 Vol 146 Issue 2 AmericanOur simulation results showed wide variations in thelevels of strength and strain. In some bone regions, thestrain levels were below 100 m strain, classified in theliterature as levels leading to bone resorption.17 Thisresult could indicate that miniplate stability mighthave been compromised because of the absence of astimulus. Melsen and Lang1 and Cattaneo et al37 corre-lated the experimental data using finite element analysisand observed bone disuse regions, adapted bone re-gions, and bone formation regions around dentalimplants without compromising stability. A wide varia-tion in the amount of bone-screw contact at the inter-face (range, 2.2%-100%) has also been described inexperiments with mini-implants.25,36

    The study of miniplates by Cornelis et al7 reported1% to 77% bone-screw contact at the interface. Howev-er, Deguchi et al33 observed that approximately 5%bone-screw contact is sufficient for the screws to resistorthodontic forces. Luzi et al25 observed that mini-implants with 3% bone-screw contact resisted ortho-dontic forces successfully. Finally, Cornelis et al7,11

    confirmed that the miniplates remained stable withonly 1% bone-screw contact. Therefore, we suggestthat the bone disuse regions observed in our study(\100 m strain) do not affect miniplate stability. Accord-ingly, we can posit that miniplate mobility might berelated to other factors, such as local inflammation,surgical trauma, or insufficient bone density, with noinfluence of loading, as suggested by this simulationdata.4,5,7

    The finite element method is sensitive to both pa-rameters used to model the materials and the criteriaused to interpret the results. Therefore, the results ofnumeric simulations are an approximation of what oc-curs in reality, and the data from these analysesshould be used to direct clinical procedures and newresearch. However, more complex finite elementmodels are being developed with increasingly sophis-ticated computer programs, thereby making the finiteelement method a promising research tool for under-standing the biomechanical aspects of biologicsciences.

    CONCLUSIONS

    Based on the methodology and the approximationsin this 3D finite element analysis, we concluded thefollowing.

    1. The anchorage system with miniplate-supportedorthodontic forces does not influence the mini-plate's stability.

    2. The levels of strain and stress were reduced whenthe moments were inserted.Journal of Orthodontics and Dentofacial Orthopedics

  • Largura et al 2053. The strain showed that the distribution of deforma-tion was not uniform throughout the region of thescrew.

    4. The finite element method is a viable tool for assess-ing the distribution of stresses and strains on thelocal bone tissue adjacent to the miniplate usedfor orthodontic anchorage.REFERENCES

    1. Melsen B, Lang NP. Biological reactions of alveolar bone to ortho-dontic loading of oral implants. Clin Oral Implants Res 2001;12:144-52.

    2. Roberts-Harry D, Sandy J. Orthodontics. Part 9: anchorage controland distal movement. Br Dent J 2004;196:255-63.

    3. Umemori M, Sugawara J, Mitani H, Nagasaka H, Kawamura H.Skeletal anchorage system for open-bite correction. Am J OrthodDentofacial Orthop 1999;115:166-74.

    4. Chen YJ, Chang HH, Huang CY, Hung HC, Lai EH, Yao CC. A retro-spective analysis of the failure rate of three different orthodonticskeletal anchorage systems. Clin Oral Implants Res 2007;18:768-75.

    5. De Clerck EE, Swennen GR. Success rate of miniplate anchorage forbone anchored maxillary protraction. Angle Orthod 2011;81:1010-3.

    6. Kuroda S, Sugawara Y, Deguchi T, Kyung HM, Takano-Yamamoto T. Clinical use of miniscrew implants as orthodonticanchorage: success rates and postoperative discomfort. Am JOrthod Dentofacial Orthop 2007;131:9-15.

    7. Cornelis MA, Vandergugten S, Mahy P, De Clerck HJ, Lengele B,D'Hoore W, et al. Orthodontic loading of titanium miniplates indogs: microradiographic and histological evaluation. Clin OralImplants Res 2008;19:1054-62.

    8. Veziroglu F, Uckan S, Ozden UA, Arman A. Stability of zygomaticplate-screw orthodontic anchorage system: a finite element anal-ysis. Angle Orthod 2008;78:902-7.

    9. 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.

    10. Huang YW, Chang CH, Wong TY, Liu JK. Bone stress when mini-plates are used for orthodontic anchorage: finite element analysis.Am J Orthod Dentofacial Orthop 2012;142:466-72.

    11. Cornelis MA, Mahy P, Devogelaer JP, De Clerck HJ, Nyssen-Behets C. Does orthodontic loading influence bonemineral densityaround titanium miniplates? An experimental study in dogs.Orthod Craniofac Res 2010;13:21-7.

    12. Argenta MA, Gebert AP, Filho ES, Felizari BA, Hecke MB. Meth-odology for numerical simulation of trabecular bone structuresmechanical behavior. Comput Modeling Eng Sci 2011;79:159-82.

    13. Cattaneo PM, Dalstra M, Melsen B. The finite element method: atool to study orthodontic tooth movement. J Dent Res 2005;84:428-33.

    14. Knox J, Jones ML, Hubsch P, Middleton J, Kralj B. An evaluation ofthe stresses generated in a bonded orthodontic attachment bythree different load cases using the Finite Element Method ofstress analysis. J Orthod 2000;27:39-46.

    15. Toms SR, Eberhardt AW. A nonlinear finite element analysis of theperiodontal ligament under orthodontic tooth loading. Am JOrthod Dentofacial Orthop 2003;123:657-65.American Journal of Orthodontics and Dentofacial Orthoped16. Poppe M, Bourauel C, Jager A. Determination of the elasticity pa-rameters of the human periodontal ligament and the location ofthe center of resistance of single-rooted teeth a study of autopsyspecimens and their conversion into finite element models. J Oro-fac Orthop 2002;63:358-70.

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

    18. Baumgaertel S. Quantitative investigation of palatal bone depthand cortical bone thickness for mini-implant placement in adults.Am J Orthod Dentofacial Orthop 2009;136:104-8.

    19. Baumgaertel S, Hans MG. Buccal cortical bone thickness for mini-implant placement. Am J Orthod Dentofacial Orthop 2009;136:230-5.

    20. Stahl E, Keilig L, Abdelgader I, Jager A, Bourauel C. Numerical an-alyses of biomechanical behavior of various orthodontic anchorageimplants. J Orofac Orthop 2009;70:115-27.

    21. Motoyoshi M, Inaba M, Ono A, Ueno S, Shimizu N. The effect ofcortical bone thickness on the stability of orthodontic mini-implants and on the stress distribution in surrounding bone. IntJ Oral Maxillofac Surg 2009;38:13-8.

    22. Chatzigianni A, Keilig L, Duschner H, Gotz H, Eliades T,Bourauel C. Comparative analysis of numerical and experimentaldata of orthodontic mini-implants. Eur J Orthod 2011;33:468-75.

    23. 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.

    24. Oyonarte R, Pilliar RM, Deporter D, Woodside DG. Peri-implantbone response to orthodontic loading: part 1. A histomorphomet-ric study of the effects of implant surface design. Am J OrthodDentofacial Orthop 2005;128:173-81.

    25. Luzi C, Verna C, Melsen B. Immediate loading of orthodontic mini-implants: a histomorphometric evaluation of tissue reaction. Eur JOrthod 2009;31:21-9.

    26. Melsen B, Costa A. Immediate loading of implants used for ortho-dontic anchorage. Clin Orthod Res 2000;3:23-8.

    27. Doblare M, Garcia JM. On the modelling bone tissue fracture andhealing of the bone tissue. Acta Cient Venez 2003;54:58-75.

    28. Viecilli RF, Katona TR, Chen J, Hartsfield JK Jr, Roberts WE. Three-dimensional mechanical environment of orthodontic tooth move-ment and root resorption. Am J Orthod Dentofacial Orthop 2008;133:791.e11-26.

    29. Limbert G, van Lierde C, Muraru OL, Walboomers XF, Frank M,Hansson S, et al. Trabecular bone strains around a dental implantand associated micromotionsa micro-CT-based three-dimen-sional finite element study. J Biomech 2010;43:1251-61.

    30. Daimaruya T, Nagasaka H, Umemori M, Sugawara J, Mitani H. Theinfluences of molar intrusion on the inferior alveolar neurovascularbundle and root using the skeletal anchorage system in dogs.Angle Orthod 2001;71:60-70.

    31. Roberts WE, Helm FR, Marshall KJ, Gongloff RK. Rigid endosseousimplants for orthodontic and orthopedic anchorage. Angle Orthod1989;59:247-56.

    32. Buchter A, Wiechmann D, Gaertner C, Hendrik M, Vogeler M,Wiesmann HP, et al. Load-related bone modelling at the interfaceof orthodontic micro-implants. Clin Oral Implants Res 2006;17:714-22.

    33. Deguchi T, Takano-Yamamoto T, Kanomi R, Hartsfield JK Jr,Roberts WE, Garetto LP. The use of small titanium screws fororthodontic anchorage. J Dent Res 2003;82:377-81.

    34. Freire JN, Silva NR, Gil JN, Magini RS, Coelho PG. Histomorpho-logic and histomophometric evaluation of immediately and earlyics August 2014 Vol 146 Issue 2

    http://refhub.elsevier.com/S0889-5406(14)00476-4/sref1http://refhub.elsevier.com/S0889-5406(14)00476-4/sref1http://refhub.elsevier.com/S0889-5406(14)00476-4/sref1http://refhub.elsevier.com/S0889-5406(14)00476-4/sref2http://refhub.elsevier.com/S0889-5406(14)00476-4/sref2http://refhub.elsevier.com/S0889-5406(14)00476-4/sref3http://refhub.elsevier.com/S0889-5406(14)00476-4/sref3http://refhub.elsevier.com/S0889-5406(14)00476-4/sref3http://refhub.elsevier.com/S0889-5406(14)00476-4/sref4http://refhub.elsevier.com/S0889-5406(14)00476-4/sref4http://refhub.elsevier.com/S0889-5406(14)00476-4/sref4http://refhub.elsevier.com/S0889-5406(14)00476-4/sref4http://refhub.elsevier.com/S0889-5406(14)00476-4/sref5http://refhub.elsevier.com/S0889-5406(14)00476-4/sref5http://refhub.elsevier.com/S0889-5406(14)00476-4/sref5http://refhub.elsevier.com/S0889-5406(14)00476-4/sref6http://refhub.elsevier.com/S0889-5406(14)00476-4/sref6http://refhub.elsevier.com/S0889-5406(14)00476-4/sref6http://refhub.elsevier.com/S0889-5406(14)00476-4/sref6http://refhub.elsevier.com/S0889-5406(14)00476-4/sref7http://refhub.elsevier.com/S0889-5406(14)00476-4/sref7http://refhub.elsevier.com/S0889-5406(14)00476-4/sref7http://refhub.elsevier.com/S0889-5406(14)00476-4/sref7http://refhub.elsevier.com/S0889-5406(14)00476-4/sref8http://refhub.elsevier.com/S0889-5406(14)00476-4/sref8http://refhub.elsevier.com/S0889-5406(14)00476-4/sref8http://refhub.elsevier.com/S0889-5406(14)00476-4/sref9http://refhub.elsevier.com/S0889-5406(14)00476-4/sref9http://refhub.elsevier.com/S0889-5406(14)00476-4/sref9http://refhub.elsevier.com/S0889-5406(14)00476-4/sref9http://refhub.elsevier.com/S0889-5406(14)00476-4/sref10http://refhub.elsevier.com/S0889-5406(14)00476-4/sref10http://refhub.elsevier.com/S0889-5406(14)00476-4/sref10http://refhub.elsevier.com/S0889-5406(14)00476-4/sref11http://refhub.elsevier.com/S0889-5406(14)00476-4/sref11http://refhub.elsevier.com/S0889-5406(14)00476-4/sref11http://refhub.elsevier.com/S0889-5406(14)00476-4/sref11http://refhub.elsevier.com/S0889-5406(14)00476-4/sref12http://refhub.elsevier.com/S0889-5406(14)00476-4/sref12http://refhub.elsevier.com/S0889-5406(14)00476-4/sref12http://refhub.elsevier.com/S0889-5406(14)00476-4/sref12http://refhub.elsevier.com/S0889-5406(14)00476-4/sref13http://refhub.elsevier.com/S0889-5406(14)00476-4/sref13http://refhub.elsevier.com/S0889-5406(14)00476-4/sref13http://refhub.elsevier.com/S0889-5406(14)00476-4/sref14http://refhub.elsevier.com/S0889-5406(14)00476-4/sref14http://refhub.elsevier.com/S0889-5406(14)00476-4/sref14http://refhub.elsevier.com/S0889-5406(14)00476-4/sref14http://refhub.elsevier.com/S0889-5406(14)00476-4/sref15http://refhub.elsevier.com/S0889-5406(14)00476-4/sref15http://refhub.elsevier.com/S0889-5406(14)00476-4/sref15http://refhub.elsevier.com/S0889-5406(14)00476-4/sref16http://refhub.elsevier.com/S0889-5406(14)00476-4/sref16http://refhub.elsevier.com/S0889-5406(14)00476-4/sref16http://refhub.elsevier.com/S0889-5406(14)00476-4/sref16http://refhub.elsevier.com/S0889-5406(14)00476-4/sref16http://refhub.elsevier.com/S0889-5406(14)00476-4/sref16http://refhub.elsevier.com/S0889-5406(14)00476-4/sref17http://refhub.elsevier.com/S0889-5406(14)00476-4/sref17http://refhub.elsevier.com/S0889-5406(14)00476-4/sref18http://refhub.elsevier.com/S0889-5406(14)00476-4/sref18http://refhub.elsevier.com/S0889-5406(14)00476-4/sref18http://refhub.elsevier.com/S0889-5406(14)00476-4/sref19http://refhub.elsevier.com/S0889-5406(14)00476-4/sref19http://refhub.elsevier.com/S0889-5406(14)00476-4/sref19http://refhub.elsevier.com/S0889-5406(14)00476-4/sref20http://refhub.elsevier.com/S0889-5406(14)00476-4/sref20http://refhub.elsevier.com/S0889-5406(14)00476-4/sref20http://refhub.elsevier.com/S0889-5406(14)00476-4/sref20http://refhub.elsevier.com/S0889-5406(14)00476-4/sref21http://refhub.elsevier.com/S0889-5406(14)00476-4/sref21http://refhub.elsevier.com/S0889-5406(14)00476-4/sref21http://refhub.elsevier.com/S0889-5406(14)00476-4/sref21http://refhub.elsevier.com/S0889-5406(14)00476-4/sref22http://refhub.elsevier.com/S0889-5406(14)00476-4/sref22http://refhub.elsevier.com/S0889-5406(14)00476-4/sref22http://refhub.elsevier.com/S0889-5406(14)00476-4/sref23http://refhub.elsevier.com/S0889-5406(14)00476-4/sref23http://refhub.elsevier.com/S0889-5406(14)00476-4/sref23http://refhub.elsevier.com/S0889-5406(14)00476-4/sref23http://refhub.elsevier.com/S0889-5406(14)00476-4/sref23http://refhub.elsevier.com/S0889-5406(14)00476-4/sref24http://refhub.elsevier.com/S0889-5406(14)00476-4/sref24http://refhub.elsevier.com/S0889-5406(14)00476-4/sref24http://refhub.elsevier.com/S0889-5406(14)00476-4/sref24http://refhub.elsevier.com/S0889-5406(14)00476-4/sref25http://refhub.elsevier.com/S0889-5406(14)00476-4/sref25http://refhub.elsevier.com/S0889-5406(14)00476-4/sref25http://refhub.elsevier.com/S0889-5406(14)00476-4/sref26http://refhub.elsevier.com/S0889-5406(14)00476-4/sref26http://refhub.elsevier.com/S0889-5406(14)00476-4/sref27http://refhub.elsevier.com/S0889-5406(14)00476-4/sref27http://refhub.elsevier.com/S0889-5406(14)00476-4/sref28http://refhub.elsevier.com/S0889-5406(14)00476-4/sref28http://refhub.elsevier.com/S0889-5406(14)00476-4/sref28http://refhub.elsevier.com/S0889-5406(14)00476-4/sref28http://refhub.elsevier.com/S0889-5406(14)00476-4/sref29http://refhub.elsevier.com/S0889-5406(14)00476-4/sref29http://refhub.elsevier.com/S0889-5406(14)00476-4/sref29http://refhub.elsevier.com/S0889-5406(14)00476-4/sref29http://refhub.elsevier.com/S0889-5406(14)00476-4/sref30http://refhub.elsevier.com/S0889-5406(14)00476-4/sref30http://refhub.elsevier.com/S0889-5406(14)00476-4/sref30http://refhub.elsevier.com/S0889-5406(14)00476-4/sref30http://refhub.elsevier.com/S0889-5406(14)00476-4/sref31http://refhub.elsevier.com/S0889-5406(14)00476-4/sref31http://refhub.elsevier.com/S0889-5406(14)00476-4/sref31http://refhub.elsevier.com/S0889-5406(14)00476-4/sref32http://refhub.elsevier.com/S0889-5406(14)00476-4/sref32http://refhub.elsevier.com/S0889-5406(14)00476-4/sref32http://refhub.elsevier.com/S0889-5406(14)00476-4/sref32http://refhub.elsevier.com/S0889-5406(14)00476-4/sref33http://refhub.elsevier.com/S0889-5406(14)00476-4/sref33http://refhub.elsevier.com/S0889-5406(14)00476-4/sref33http://refhub.elsevier.com/S0889-5406(14)00476-4/sref34http://refhub.elsevier.com/S0889-5406(14)00476-4/sref34

  • 206 Largura et alloaded mini-implants for orthodontic anchorage. Am J OrthodDentofacial Orthop 2007;131:704.e1-9.

    35. Ohmae M, Saito S, Morohashi T, Seki K, Qu H, Kanomi R, et al. Aclinical and histological evaluation of titanium mini-implants asanchors for orthodontic intrusion in the beagle dog. Am J OrthodDentofacial Orthop 2001;119:489-97.August 2014 Vol 146 Issue 2 American36. Woods PW, Buschang PH, Owens SE, Rossouw PE, Opperman LA.The effect of force, timing, and location on bone-to-implantcontact of miniscrew implants. Eur J Orthod 2009;31:232-40.

    37. Cattaneo PM, Dalstra M, Melsen B. Analysis of stress and strainaround orthodontically loaded implants: an animal study. IntJ Oral Maxillofac Implants 2007;22:213-25.Journal of Orthodontics and Dentofacial Orthopedics

    http://refhub.elsevier.com/S0889-5406(14)00476-4/sref34http://refhub.elsevier.com/S0889-5406(14)00476-4/sref34http://refhub.elsevier.com/S0889-5406(14)00476-4/sref35http://refhub.elsevier.com/S0889-5406(14)00476-4/sref35http://refhub.elsevier.com/S0889-5406(14)00476-4/sref35http://refhub.elsevier.com/S0889-5406(14)00476-4/sref35http://refhub.elsevier.com/S0889-5406(14)00476-4/sref36http://refhub.elsevier.com/S0889-5406(14)00476-4/sref36http://refhub.elsevier.com/S0889-5406(14)00476-4/sref36http://refhub.elsevier.com/S0889-5406(14)00476-4/sref37http://refhub.elsevier.com/S0889-5406(14)00476-4/sref37http://refhub.elsevier.com/S0889-5406(14)00476-4/sref37

    Bone stress and strain after use of a miniplate for molar protraction and uprighting: A 3-dimensional finite element analysisMaterial and methodsResultsDiscussionConclusionsReferences