Three-dimensional modeling and finite element …...Three-dimensional modeling and ﬁnite element analysis in treatment planning for orthodontic tooth movement Hussein H. Ammar,a

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Three-dimensional modeling and finite elementanalysis in treatment planning for orthodontictooth movement

Hussein H. Ammar,a Peter Ngan,b Richard J. Crout,c Victor H. Mucino,a and Osama M. Mukdadid

Morgantown, WVa

FromaGradneerinbProfecProfedAssisCollegspiratThe aucts oSuppoReprinspace26506Subm0889-Copyrdoi:10

Introduction: The objective of this study was to demonstrate the potential of 3-dimensional modeling and finiteelement analysis as clinical tools in treatment planning for orthodontic tooth movement. High stresses in boneand miniscrew implants under load can cause fractures and trauma for orthodontic patients, and treatmentsare typically planned by using clinical experience or simple 2-dimensional radiographs.Methods: Anatomicallyaccurate 3-dimensional models reconstructed from cone-beam computed tomography scans were used tosimulate the retraction of a single-rooted mandibular canine with a miniscrew placed as skeletal anchorage.Detailed stress distributions in the implant and peri-implant bone were found, in addition to the effect of theorthodontic bracket hook length and the angulation of retraction force on stress response in the periodontalligament (PDL). Results: The numeric results showed that the equivalent von Mises stress on the miniscrewunder a 200-cN tangential load reached 42 MPa at the first thread recession, whereas von Mises stress inthe peri-implant bone only reached 11 MPa below the neck. High tightening loads of 200 N$mm of torsionand 460 cN of axial compression resulted in much greater bone and implant von Mises stresses thantangential loading, exceeding the yield strengths of the titanium alloy and the cortical bone. Increasing thehook length on the orthodontic bracket effectively reduced the canine PDL stress from 80 kPa with no hookto 22 kPa with a hook 7 mm long. Angulating the force apically downward from 0� to 30� had a lesssignificant effect on the PDL stress profile and initial canine deflection. The results suggest that stresses onminiscrew implants under load are sensitive to changes in diameter. Overtightening a miniscrew afterplacement might be a more likely cause of fracture failure and bone trauma than application of tangentialorthodontic force. The reduction of stress along the PDL as a result of increasing the bracket hook lengthmight account for steadier tooth translation by force application closer to the center of resistance of a single-rooted canine. The relatively minor effect of force angulation on the PDL response suggests that the verticalplacement of miniscrews in keratinized or nonkeratinized tissue might not significantly affect orthodontic toothmovement. Conclusions: This model can be adapted as a patient-specific clinical orthodontic tool forplanning movement of 1 tooth or several teeth. (Am J Orthod Dentofacial Orthop 2011;139:e59-e71)

Anchorage is an important consideration for or-thodontists and is often an essential componentin treatment planning. Of particular clinical

West Virginia University, Morgantown.uate Research Assistant, Department of Mechanical and Aerospace Engi-g, College of Engineering and Mineral Resources.ssor and chair, Department of Orthodontics, College of Dentistry.ssor, Department of Periodontics, College of Dentistry.tant professor, Department of Mechanical and Aerospace Engineering,e of Engineering and Mineral Resources, Center for Cardiovascular and Re-ory Sciences, West Virginia School of Medcine.uthors report no commercial, proprietary, or financial interest in the prod-r companies described in this article.rted by grants from NIDCR 1R21DE019561 and WV PSCoR.t requests to: Osama M. Mukdadi, Department of Mechanical and Aero-Engineering, PO Box 6106, West Virginia University, Morgantown, WV-6106; e-mail, [email protected], March 2010; revised and accepted, September 2010.5406/$36.00ight � 2011 by the American Association of Orthodontists..1016/j.ajodo.2010.09.020

value is the situation in which absolute anchorage is re-quired for retraction of anterior teeth or protraction ofposterior teeth. Such anchorage can be provided extra-orally with headgear or intraorally by using adjacentteeth or dental implants. The advantage of intraoral an-chorage is reduced patient compliance for treatment.1,2

This is an important factor, considering that 19% oforthodontic visits in 2004 were by children under 12years of age, and nearly 77% were by minors less than18.3 Adults can also be averse to the use of headgearfor esthetic or professional reasons.

Temporary skeletal anchorage devices such as mini-screw implants have become increasingly popular inorthodontic tooth movement because of their biocom-patibility, small size, and placement versatility. Figure 1shows the placement of miniscrews between the rootsof the mandibular second premolars and first permanent

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mailto:[email protected]

Fig 1. Clinical orthodontic example of canine retractionwith miniscrew anchorage attached by elastics to thehook for space closure without forward movement of theposterior molars.

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molars to retract the anterior canines without forwardmovement of the posterior molars. Miniscrews providethe optionof early or immediate loadingwithout a lengthyinitial latency period.4 Other advantages include place-ment versatility because of the relatively small diameterof the endosseus body1,5 and relatively simpleprocedures for placement and removal.2 The smooth sur-face and minimal osseointegration reduce torsional resis-tance.6 Miniscrews can be placed between teeth withsufficient bone density and root clearance, giving ortho-dontists a variety of placement options.7 However, inter-ference with the root or periodontal ligament (PDL) cancause significant anchorage loss and mobility or patienttrauma.8 Heightened stresses in peri-implant bone fromorthodontic loading, miniscrew orientation, surroundingbone quality and quantity, or miniscrew design might re-sult in soft-tissue inflammation, microfractures in thebone or implant, or bone resorption.8,9 Such failurescan compromise anchorage stability and increase therisk of pain or injury. Low stresses in bone at placementcan also result in low primary stability of the implant orbone atrophy.10 High torque might also cause bone dam-age or miniscrew fracture, requiring corrective surgery.8

Currently, the planning of miniscrew placement islimited to the use of clinical judgment in addition to2-dimensional panoramic radiographs.11 The use of dig-ital radiography can overcome some problems of imagedistortions resulting from magnification or image noiseand reflections, but stress and strain distributions underorthodontic force application cannot be determined.11

Modern medical imaging, modeling, and finite element(FE) analysis solutions can provide powerful tools for op-timizing 3-dimensional (3D) morphology from radio-graphic scans and determining stress and deflectiondistributions for complex anatomic geometries such asbone. Previous FE studies on miniscrews have used arti-ficial, nonspecific bone-block geometries, finding criti-cal stress areas and the effects of miniscrew length,diameter, and cortical bone thickness on stress re-sponse.12 Motoyoshi et al13 performed nonspecific sim-ulations to test the effects of thread pitch and abutmentattachment on miniscrew stresses. Pollei et al14 con-ducted FE analyses of miniscrews on various commercialimplant designs with patient-specific bone geometry,defining a rigidly bonded implant-bone contact for lin-ear simulation. Gracco et al15 performed nonspecific 2-dimensional FE simulations of a miniscrew with varyinglengths and degrees of osseointegration, reporting thatstresses decreased with greater osseointegration. MostFE studies focused solely on simulations with either min-iscrews12-15 or teeth16-19 from different, isolatedmodels. The objective of this study was to determinethe stress profile on the miniscrew implant and peri-

January 2011 � Vol 139 � Issue 1 American

implant bone caused by both a tangential orthodonticforce and tightening loads by using 3D modeling andFE analysis. In addition, the effects of orthodonticbracket hook length and force angulation on resultingstress response of the canine PDL were determined.The long-term goal was to determine the potential of3D modeling and FE analysis in treatment planning forpatient-specific tooth movements.

MATERIAL AND METHODS

Figure 2 shows the procedures for 3D modeling andFE analysis in planning for patient-specific tooth move-ment with a miniscrew. First, a cone-beam computed to-mography (CBCT) scan of a patient’s maxilla andmandible was acquired in vivo. Images with a squarepixel size of 0.41 mm and a total size of 512 pixels persquare were used. A total of 128 layered slices were savedin DICOM format with a 21-cm field of view and im-ported into Mimics software (version 12.1, Materialise,Plymouth, Mich). The voxel size was approximately0.41 3 0.41 3 0.6 mm with a maximum smoothing er-ror of half of this voxel volume. A global threshold wasdefined to isolate bone from soft tissues. Then automaticsegmentation operations were performed on the mor-phology to reduce noise and artifacts. The mandibularleft canine was isolated with its root for treatment by us-ing local thresholding on the CBCT images. Scaling andBoolean operations were then carried out to model thePDL as a thin enclosure around the root with an averagethickness of approximately 0.3 mm. Models weresmoothed before the Boolean subtractions to ensurean even fit. One miniscrew implant design was chosenas anchorage for retraction of the mandibular canine

Journal of Orthodontics and Dentofacial Orthopedics

Fig 2. The approach for 3D patient-specific model reconstruction and FE simulation of tooth, PDL, andminiscrew from in-vivo CBCT scans. One patient scan and 1 miniscrew design were studied.

Table I. Elastic material properties of anatomicmodels

Material

ElasticmodulusE (GPa)

Poisson’sratio n

Yieldstrength

(MPa)25-27

Trabecular bone12 1.50 0.30 2Cortical bone20 14.7 0.30 133Tooth24 20.7 0.30 –

Miniscrew (Ti6Al4V)27 114 0.34 880PDL (linear model)25 6.89 3 10�5 0.45 –

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and modeled with the ProEngineer Wildfire software(version 4.0, PTC, Needham, Mass). Dimensions andthread design were based on an implant (ACR OAS-T1207, BioMaterials Korea, La Mirada, Calif) witha thread diameter of 1.2 mm and a total length of 8.7mm. This implant is constructed from Ti-6Al-4V tita-nium alloy for biocompatibility and designed for man-dibular placement. The model was exported fromProEngineer in stereolithography format into the Mimicssoftware and placed buccally approximately 1.4 cmdown from the alveolar ridge between the first and sec-ond molars, normally to the cortical surface. Althoughpossibly in unattached mucosa, which increases therisk of inflammation, this location eliminated interfer-ence of adjacent roots, and the objective of this studywas to analyze detailed miniscrew stress behavior inpatient-specific bone.8 This allowed us to cut out thebone block around the implant for separate simulation.The cortical layer at this location was also clearly definedin the CBCT images so that patient-specific geometricaccuracy would be preserved. A subtraction operationwas performed to create a matching drilled hole in themandibular model. The reconstructed mandible, canine,PDL, and miniscrew were exported into the Mimics-

American Journal of Orthodontics and Dentofacial Orthoped

Remesh module as stereolithography models. A volu-metric mesh was then created and optimized by usingtetrahedral elements. The optimized meshes of allmodels including mandible, miniscrew, PDL, and caninewere exported from Mimics as ANSYS (version 11.0,ANSYS, Canonsburg, Pa) input files.

The model input files were read into ANSYS as volu-metric element meshes by using 4-noded 6-degrees offreedom tetrahedral elements. Model coordinates andpositioning of each component into the assembly werealso saved. Four contact pairs (Table I) were created foreach of the 4 interfaces: miniscrew-bone, PDL-tooth,

ics January 2011 � Vol 139 � Issue 1

Table II. Contact pair definitions (m denotes frictioncoefficient)

Interface Contact behaviorMiniscrew-bone m 5 0.3721

PDL-tooth BondedPDL-bone BondedTooth-bone m 5 0.3022

Fig 3. A, Three-dimensional views of final patient-specific FEmodels;B, FEmesh with indicated coordinatesystem (XYz occusal plane, XZ z tangential plane, YZz saggital plane).

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PDL-bone, and tooth-bone. The PDL was glued to thecanine root and the mandibular socket at the innerand outer surfaces, respectively, to prevent slippage orseparation. Contact between the titanium-alloy mini-screw and the mandible was defined with a coefficientof friction equal to 0.37 as the average value reportedby Mischler and Pax,20 whereas a coefficient of frictionequal to 0.30 was assumed for any possible tooth-bone contact upon excessive PDL compression.21

After importing the models into ANSYS, the materialproperties were defined from literature references(Table II).12,19,22-27 All materials used in this studywere defined as homogeneous, isotropic, and linearlyelastic. Our value for the PDL’s elastic modulus wasclose to correctly documented values from originalstudies.23,27,28 The distribution of bone and toothelements was determined in the Mimics software bythe intensity or gray values of the CBCT scans reportedin Hounsfield units (HU). With no loss of generality,the tooth was considered as a homogeneous material.Cortical bone elements were assigned according to anaverage value of 1400 to 2200 HU, and trabecularbone below 600 HU. These ranges fall within reportedHU material limits for CBCT scans.18 Views of the finalFE assembly with individual models and coordinatesare shown in Figure 3.

Figure 4 illustrates the simulated load cases of thisstudy. A 200-cN tangential force was applied perpendic-ular to the miniscrew axis on a central node of the notchin accordance with the reported clinically safe limit forimmediate loading.29 A compressive axial force of 460cN and tightening torque of 200 N$mm were also ap-plied on the miniscrew to simulate maximum placementloading measured experimentally.30 A 100-cN distalhorizontal tipping force was applied in 50 load substepson the buccal crown surface of the canine.31 The point ofapplication of the distal force was varied down the longaxis of the tooth to simulate the changing hook length.Angulation of the force was varied apically from the oc-clusal plane to simulate the changing vertical placementof the miniscrew and the angled line of action for an at-tached spring or elastic band. Nodes at the outer edgesof the bone block were fixed to eliminate rigid body mo-tion. Modeling the bone at a distance greater than 4.2


mm from the site of implant placement yields no signif-icant increase in FE analysis accuracy in the implant re-gion.32 The volumetric meshes of the miniscrew and thesurrounding bone were refined near the interface, andstress profile paths were plotted down the length ofthe miniscrew from neck to tip, down the tooth, andalong the inner PDL surface.

RESULTS

Figure 5 shows the equivalent von Mises stress in theminiscrew implant and surrounding bone under a 200-cN tangential force applied at a center node of the mini-screw notch parallel to the cortical bone surface. Implantstresses were plotted along the surface from the neck tothe tip, and corresponding von Mises stress distribution


Fig 4. FE loading scenarios for A, mandibular left canine subject to distal force F at different verticalhook lengths h and angles a from the occlusal plane corresponding to the changing miniscrew verticallocation, and B, miniscrew in the bone subjected to orthodontic load (tangential force FT) and place-ment loads (tightening torque T and compressive axial force FA).

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contours are shown to the right of each graph. The great-est implant stresses appeared around the neck and at thesmallest diameter cross-sections of the upper threads.The tension side of the miniscrew (Fig 5, A) exhibitedthe highest stress magnitudes, with a maximum vonMises stress of 42 megapascals (MPa) concentrated inthe recession of the first thread and steadily decaying far-ther down the implant. The peri-implant bone experi-enced considerably lower stresses on the tension side.Little stress appeared in the trabecular bone layer. Thecompression side of the miniscrew (Fig 5, B) showedlower stress magnitudes and a broader stress distribu-tion. The maximum von Mises stress of 26.5 MPa onthe compression side appeared in the first thread. Bonestresses on the compression side were greater than onthe tension side, with a distinct peak von Mises stressof 11 MPa above the first bony thread. On the shearside of the miniscrew (Fig 5, C), the local maximumvon Mises stresses in the implant can be clearly seen tocorrespond to the top 6 threads, with the maximumvon Mises stress on this path appearing in the secondthread recession. Bone stress on this path also showedsmoothly decaying behavior.

Relative to the tangential load, the miniscrew experi-enced much higher stresses under a torque of 200 N$mmand compressive axial force of 460 cN to simulate tight-ening loads (Fig 6). Maximum von Mises stress in theminiscrew was about 17.3 GPa and appeared in the


second thread (Fig 6, A). Similar to the tangential load-ing miniscrew stress distribution, maximum von Misesstresses under tightening occurred at the top threadsand decayed farther down the screw. The peri-implantbone carried a much lower portion of the total stress un-der the tightening loads than under the tangential load-ing, although stress magnitudes were significantlyhigher under tightening. Maximum bone stress ap-proached 1.4 GPa (Fig 6, B). The twin-peak behaviorof the local maximum von Mises stresses in the implantshown in Figure 6, A, corresponds to the implantsurfaces oriented at 45�, as shown in the stress profilecontour in Figure 6, C. These surfaces correspond tothe orientation of the principal planes for maximumcompressive or tensile stresses.

In the canine-PDL simulation, a 100-cN distal retrac-tion force was applied at the middle of the buccal crownsurface. The displacement distribution plotted in Figure 7indicated crown-distal tipping and a slight twistingdeflection of the canine. Maximum displacement of thetooth under this load was 82.1 mm at the top of thecrown. The center of rotation can be seen by qualitativeinspection around the top third of the root.

The changes in stress distributions in the PDL withvariable bracket hook lengths are shown in Figure 8.The graph was plotted along the inner PDL surfacefrom the distal side to the mesial side with a distal forceof 100 cN. The compressive and tensile regions can


Fig 5. Miniscrew implant von Mises stress under 200-cN tangential force FT plotted down surface ofminiscrew from the transmucosal neck to the tip and von Mises contour for A, the tension side;B, the compression side; and C, the shear side.

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clearly be seen by the stress curves and correspond tocrown-distal tipping, with compressive stresses showinghigher magnitudes than tensile stresses. These stresseswere much more pronounced than shear stresses. Asthe hook length (or vertical location of the force applica-tion point) was increased from 0 mm at the middlecrown surface to 7 mm down the length of the canine,stress magnitudes in the PDL were significantly reducedalong most regions. Tensile stress in the mesial PDL


region remained relatively unchanged, although thestress magnitude was slightly reduced and spread overa larger area along the path. Maximum compressivestresses along the distal-mesial inner PDL path de-creased from nearly 80 to 22 kPa when the hook lengthvaried from 0 to 7 mm, respectively. Shear stress magni-tudes were largely negligible in comparison.

Figure 9 shows the effects of vertical placement ofthe miniscrew on PDL stresses and deflection of the


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canine for a fixed hook length of 2.3 mm. The angle a in-dicates the angulation of the distal force on the caninefrom the horizontal occlusal plane downward towardthe apex. Maximum compressive and tensile stressesalong a distal-mesial path of the inner PDL decreasedslightly as the distal force was angled apically downward(Fig 9, A). Shear stresses remained largely unchanged.Deflection of the distal surface of the canine is shownin Figure 9, B, for increasing force angulation. As theforce was angled apically downward, canine deflectionabove the center of resistance (CR) decreased slightlybut remained nearly the same below the CR. The locationof the canine’s CR corresponding to the lowest total de-flection also remained steady at nearly two thirds of theroot length from the apex.

DISCUSSION

Miniscrew loading

Under a 200-cN tangential force (Fig 5), the mini-screw experienced local maximum von Mises equivalentstresses in each thread recession at the smallest-diametercross-sections. Similarly, the largest-diameter cross-sec-tions exhibited local minimum stresses. This agrees withprevious numeric studies reporting that maximum im-plant stresses decrease as the endosseus diameter in-creased.12 A clinical trial also reported greater successrates for larger screw diameters.29 Another interestingobservation was that, although the maximum von Misesstresses appeared in the first or second threads on allsides, rapid decay was observed below the second threadthrough approximately 2.5 mm of cortical bone. Thissuggests that the first 2 to 3 mm of this miniscrew im-plant’s endosseus length are the most critical in termsof stress response under tangential loading. In addition,the detailed stress profiles appeared to show little stressin the trabecular bone layer. Previous studies similarlyreported maximum stresses near the implant neck andin the upper cortical layer, with lower stresses in trabec-ular bone.12,15

Yield failure was not predicted in either the miniscrewor the peri-implant bone under the 200-cN tangentialload. Maximum von Mises stress in the cortical boneof 10 MPa on the miniscrew’s compression side at thetop of the first thread was well below the 133-MPa the-oretical yield strength of cortical bone, and maximumtrabecular bone stress was well below the 2-MPa re-ported yield strength (Table I). Similarly, the maximumimplant von Mises stress of 42 MPa in the first threadwas well below the 880-MPa tensile yield limit of thetitanium-alloy miniscrew. These results suggest thatthis miniscrew design should be able to sufficiently with-stand a 200-cN tangential force shortly after loading


through mechanical retention if the patient’s bone ishealthy. It is also suggested that bone fracture as a directresult of such loading is unlikely if there is no previousdamage. Pollei et al14 speculated that failure in sucha case can occur as a result of material fatigue or cyclingloads over time. Mastication or disturbance loads causedby the patient might also play a role in possible mini-screw mobility or failure during such a treatment load.Nevertheless, orthodontic miniscrew clinical trials havereported that 200 cN is a safe limit for immediateminiscrew loading, and our results also demonstratedstability.29 Whereas equivalent stresses appearing inthe implant are of a similar magnitude to those foundin previous FE analysis studies of miniscrews,14,15 bonestresses were slightly reduced from previous reports.15,33

This might be due to slight variations in cortical bonethickness, miniscrew and bone geometry, or FE analysissimulation boundary conditions and material propertydefinitions.

Stress in the miniscrew under tangential loadingwas markedly greater on the tension side of bending(Fig 5, A), whereas bone stress was greater on the com-pression side (Fig 5, B). This can be explained by theimplant’s top thread on the tension side being pulledfrom the bone and thus bending fully. On the com-pression side, however, the bone contact restricts fullbending of the implant, and bending stress is insteadtransferred to the adjacent bone via compression. Onthe shear side of the miniscrew (Fig 5, C), the localgreatest von Mises stresses in the implant clearly corre-sponded to the top 6 threads, and the maximum vonMises stress on this path appeared in the second threadrecession. Bone stress on this path also showeda smoothly decaying behavior and carried a greaterproportion of the total equivalent stress, possibly dueto the increased shear caused by implant-bone fric-tional contact.

When the miniscrew implant was subjected to200 N$mm of tightening torsion and 460 cN of axialcompressive force (Fig 6), it experienced much higherstresses relative to the tangential load. The maximumvon Mises stress in the miniscrew was about 17.3 GPain the second thread, well above the 880-MPa yieldstrength of the titanium-alloy miniscrew. Similar tothe tangential loading miniscrew stress distribution,maximum von Mises stresses occurred at the topthreads and decayed farther down the screw (Fig 6, A).Maximum bone stress was nearly 1.4 GPa (Fig 6, B),again well above the bone’s yield limit, although thebone carried a lower portion of the total stress thanin the tangential loading. The stress distribution ineach thread was also different than in the tangentialloading. The twin-peak behavior of the local


Fig 6. Miniscrew implant von Mises stress under tightening torque T and axial force FA: A, plotteddown the surface of the miniscrew implant from the transmucosal neck to the tip; B, von Mises contourplot of the drilled mandible; and C, 45� orientation of the principal planes for maximum stress on theimplant surface.

Fig 7. Contour distribution of total deflection (mm) of a canine with linear PDL under crown-distal tip-ping from the 100-cN horizontal distal load on the buccal crown surface.

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maximum von Mises stresses in the implant (Fig 6, A)correspond to the implant surfaces oriented at 45�, asshown in the stress profile contour of Figure 6, C.These surfaces correspond to the orientation of theprincipal planes for maximum compressive or tensilestresses.

The applied 200 N$mm of torque used in this studywas the upper limit measured experimentally by Songet al30 using a similar titanium-alloy miniscrew at theend of the placement process. Thus, rather than actualplacement loading, the stress profile under torque andcompression in Figure 6 is analogous to the responsecaused by overtightening the miniscrew shortly afterplacement, after the bone’s viscoelastic relaxation and


dissipation of residual stresses from drilling. In practice,the astronomically high stress magnitudes of Figure 6would never be reached; as brittle materials, the mini-screw and bone would fracture at their respective yieldpoints so that postfailure nonlinear analysis is not nec-essary. Overtightening is a reported clinical risk factorthat might cause tissue trauma, microfractures, andloss of anchorage stability.9 In addition, excessive tor-sion has been clinically reported to cause fracture failureof the implant itself.2,8 Our results confirm that torsion isa more critical process for miniscrew failure and bonetrauma than tangential loading because of the higherstresses generated, as shown quantitatively by thestress profiles. Thus, clinicians should exercise caution


Fig 8. Plots of shear and principal compressive-tensile stress components along the inner PDL fromthe distal force F on the canine applied at the indicated hook lengths h from the center of the crown.

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during miniscrew placement to prevent exceeding thetorque values specified by the implant’s manufacturer.On the other hand, increased miniscrew placementtorques have been linked with increased primarystability.34 Motoyoshi et al13 recommended placementtorque values between 51 and 100 N$mm as an optimalrange to ensure primary stability while minimizing therisks of bone damage and miniscrew fracture. Miniscrewmanufacturers should expect more failures at the top 2threads or 2 to 3 mm of a miniscrew’s endosseouslength, especially under torsion, and design the mini-screw appropriately, possibly by reinforcing the upperthreads or using surface treatments.

Tooth loading

The 100 cN of distal force applied on the simulatedcanine resulted in distal tipping of the crown (Fig 7)and a slight twisting with a maximum displacement atthe crown of 82.1 mm. Modeling the PDL as a nonlinearmaterial resulted in a nearly identical displacement


distribution to that of the linear model in our previousstudy35; however, the magnitude of displacement wassignificantly reduced for similar load magnitudes. Thisdifference was likely due to the increasing stiffness ofthe PDL under increasing loads in experimental tests.36

The relative deflection distribution of Figure 7 is similarto those obtained in previous studies with linear elasticPDLs, although our deflection magnitudes were signifi-cantly higher.18,19 This might be a result of differentmodel geometries, FE simulation boundary conditions,contact definitions, or variations in the elastic modulusof the PDL. The center of rotation can be identifiedqualitatively by inspection near the top third of theroot, in fair agreement with previous studies.19,37

In this study, we found a reduction of stress magni-tudes in the PDL as a result of increasing hook length(Fig 8). This can most likely be attributed to the shortermoment or the power arm from the tooth’s center ofrotation to the point of force application, resulting inlower bending stress. Tensile stress in the mesial PDL


Fig 9. Plots ofA, first principal and XY shear stresses along the inner PDL, andB, total tooth deflectionalong the distal surface from the distal force F on the canine applied at 0� and 30� from the horizontalocclusal plane (hook length h, 2.3 mm from the crown center).

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region remained approximately constant about 20 MPa.Interestingly, compressive stress on the directly oppos-ing distal side decreased. Shear stresses were also notice-ably reduced, but compressive and tensile stresscomponents dominated the overall response. High stressmagnitudes in the PDL have been associated with ische-mia of ligament tissue and abrupt tooth movement37

as well as hyalinization, which might decrease theoverall rate of tooth movement by bone necrosis.16,38

Excessively high loading states of the PDL aregenerally considered undesirable in clinical practice,and light forces have been reported by Cattaneo et al16

as sufficient to cause deformations and mild strains inthe PDL. Thus, our results suggest that applying a distalforce down the vertical axis of the tooth closer to the CRof the canine can cause steadier, more favorable distaltranslation from generation of a more uniform PDLstress distribution. Both numeric39,40 and in vivo41 stud-ies have confirmed bodily translation of a tooth inretraction by attaching a power arm or hook and apply-ing a force closer to the CR, granting the orthodontistgreater control over tooth movement.42

In our simulation, varying the angulation of the distalforce apically downward from the occlusal plane to rep-resent lower buccal placement of the miniscrew resultedin a slight decrease in the first principal stress compo-nent as the angle a was increased from 0� to 30�

(Fig 9, A), but the effect was relatively subtle comparedwith the changing hook length. Cattaneo et al16 reportedsimilar findings using a nonlinear PDL, showing thatPDL stress distribution under a 100-cN tipping loadwas not significantly affected by a vertical masticationforce below 500 cN (corresponding to a resultant force


angulation of a5 79�). The canine displacement profile(Fig 9, B) showed a slight decrease in displacement forincreasing force angulation above the tooth’s CR, butagain the effect was subtle. The approximate locationof the CR at the point of minimum displacement a dis-tance roughly two thirds of the root length from theapex is in fair agreement with previous studies.19,37,41

The insignificant effect of the force angle increasingfrom 0� to 30� on PDL stress and canine deflectionsuggests that orthodontists have some flexibility onthe vertical placement location of a miniscrew in theinterradicular space. Brettin et al43 also reported no sig-nificant difference in the in-vitro stress response be-tween apical and coronal alveolar-process screwpositions. Thus, rather than tooth deflections or stressesin the miniscrew, bone, or PDL, the primary limitingfactor in interproximal miniscrew placement might besoft-tissue irritation from placement in unattached ormovable mucosa.44 Schnelle et al11 suggested flap sur-gery and the use of a rigid attachment or abutmentfrom the miniscrew head to a more occlusal location,and Motoyoshi et al13 reported lower stresses whensuch an attachment was used. However, the invasivenessand complexity of flap surgery could negate much of theadvantage of miniscrew implants in the first place byincreasing the risk of postoperative pain45 and lengthen-ing the treatment time.1 Thus, miniscrew placement inattached or keratinized gingiva is clinically favorable,but our results suggest that clinicians have some verticalleeway in this region.

A previous study determined that PDL tensile stress isgreater than compressive stress under load.16 In con-trast, stress results in our previous nonlinear PDL study


Ammar et al e69

as well as stress profiles in this linear PDL study (Figs 8and 9) show that PDL compressive stresses are notablyhigher than tensile stresses.35 Different FE analysissimulation conditions and contact definitions mightaccount for inconsistencies between numeric studies, in-dicating lack of standardization. Nevertheless, our re-sults can be interpreted in a general sense. The stressdistributions of Figures 8 and 9 largely follow thetraditional behavior of linear tipping in terms of tensileand compressive stress regions. Translation behaviorand reduced PDL stress became more evident withincreasing hook length (Fig 8), whereas increased forceangulation or the effective addition of a minor mastica-tion force had little effect on PDL stress and only slightlydecreased the tooth’s deflection above the CR (Fig 9).These results suggest that hook length or the verticallocation at which a distal force is applied has a greatereffect on PDL stress distribution (and ensuing toothmovement) than slight force angulation.

Our model used miniscrew to retract a single-rootedmandibular canine. In reality, most orthodontic toothmovement involves several teeth that are connectedwith wires, and moments and forces are applied to theteeth. We chose a case with the retraction of a single-rooted canine pitted against a miniscrew only as a start-ing point to demonstrate the efficacy of this newtechnology. This model can be generalized to includemovement of several teeth connected with wires andelastics, by using techniques demonstrated in recentstudies along with our unique patient-specificapproach.39,46 It is expected that 50% of orthodontistswill acquire a CBCT machine in their office in the next5 to 10 years. The use of CBCT technology might soonbe the standard of care for orthodontic treatmentplanning.

Another limitation of this study, and of all ortho-dontic FE analysis simulation routines, is the inabilityto directly predict long-term tooth movement quanti-tatively through simulation. Until the physiologic andbiomechanical processes of orthodontic tooth move-ment are fully understood and represented mathemat-ically in a patient-specific model, this aspect must stillbe left up to the common clinical practice of experi-enced orthodontists. In addition, the wide range ofboundary conditions, contact definitions, and materialproperty definitions used in current FE analyses createsa genuine need for consistency. Future work shouldfocus on developing a strict set of modeling and sim-ulation standards so that investigators can directlycompare their results. Ongoing research is directed to-ward validation of our preoperative protocol by usingin-vivo patient treatment trials in the orthodonticclinic.


CONCLUSIONS

CBCT reconstruction and FE simulation can providereliable information on the stress pattern around theminiscrew implant and the PDL of the loaded tooth.

1. In our model, the critical areas of stress in theloaded miniscrew were at the top 2 threads inthe upper 2.5 mm of cortical bone. Stress responsewas shown to be sensitive to implant diameter,since local stress peaks appeared in the smallest-diameter sections.

2. Tightening loads caused much greater stress in theminiscrew and peri-implant bone than the tangen-tial force, so the clinician should be careful whentightening the implant to prevent fracture andbone damage.

3. Applying a horizontal retraction force closer to a ca-nine’s CR by using a hook reduces stress in the PDLand might account for steadier distal translation ofthe tooth.

4. Increasing the hook length had a greater effect onthe PDL’s stress response than angulating the forceapically downward, suggesting that vertical place-ment of miniscrews in keratinized or nonkeratinizedtissue might not significantly affect tooth move-ment.

By using our fully 3D, patient-specific approach,multi-tooth orthodontic systems can be modeled.Moreover, multiple miniscrew placement points canbe virtually tested preoperatively to determine the op-timal treatment plan. Interference with roots can bepredicted, and patient-specific cortical bone thick-nesses are preserved. This study demonstrates the po-tential of our method as an effective clinical tool foroptimizing miniscrew anchorage stability and minimiz-ing patient risk.

We thank Materialise for its invaluable technical soft-ware assistance and for providing a Mimics project filefrom the internal database upon request.

REFERENCES

1. Prabhu J, Cousley RRJ. Current products and practice: boneanchorage devices in orthodontics. J Orthod 2006;33:288-307.

2. Papadopoulos MA, Tarawneh F. The use of miniscrew implants fortemporary skeletal anchorage in orthodontics: a comprehensive re-view. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2007;103:E6-15.

3. Guay AH, Brown LJ, Wall T. Orthodontic dental patients and ex-penditures—2004. Am J Orthod Dentofacial Orthop 2008;134:337-43.

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


e70 Ammar et al

5. Costa A, Pasta G, Bergamaschi G. Intraoral hard and soft tissuedepths for temporary anchorage devices. Semin Orthod 2005;11:10-5.

6. Mah J, Bergstrand F. Temporary anchorage devices: a statusreport. J Clin Orthod 2005;39:132-6.

7. Poggio PM, Incorvati C, Velo S, Carano A. “Safe zones”: a guide forminiscrew positioning in the maxillary and mandibular arch. AngleOrthod 2006;76:191-7.

8. Kravitz ND, Kusnoto B. Risks and complications of orthodonticminiscrews. Am J Orthod Dentofacial Orthop 2007;131(4 Suppl):S43-51.

9. 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.

10. Vaillancourt H, Pilliar RM, McCammond D. Finite element analysisof crestal bone loss around porous-coated dental implants. J ApplBiomater 1995;6:267-82.

11. Schnelle MA, Beck FM, Jaynes RM, Huja SS. A radiographic evalu-ation of the availability of bone for placement of miniscrews. AngleOrthod 2004;74:832-7.

12. Lim JW, Kim WS, Kim IK, Son CY, Byun HI. Three dimensionalfinite element method for stress distribution on the length anddiameter of orthodontic miniscrew and cortical bone thickness.Korean J Orthod 2003;33:11-20.

13. Motoyoshi M, Yano S, Tsuruoka T, Shimizu N. Biomechanical ef-fect of abutment on stability of orthodontic mini-implant. ClinOral Implants Res 2005;16:480-5.

14. Pollei JK, Rocha EP, Ko CC. Stress comparison between orthodon-tic miniscrews using finite element analysis. Metro Toronto Con-vention Centre Exhibit Hall D-E; 2008.

15. Gracco A, Cirignaco A, Cozzani M, Boccaccio A, Pappalettere C,Vitale G. Numerical/experimental analysis of the stress field aroundminiscrews for orthodontic anchorage. Eur J Orthod 2009;31:12-20.

16. Cattaneo PM, Dalstra M, Melsen B. Strains in periodontal liga-ment and alveolar bone associated with orthodontic tooth move-ment analyzed by finite element. Orthod Craniofac Res 2009;12:120-8.

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

18. Danielyte J, Gaidys R. Numerical simulation of tooth mobility us-ing nonlinear model of the periodontal ligament. Mechanika2008;71:20-6.

19. Field C, Ichim I, Swain MV, Chan E, Darendeliler MA, Li W, et al.Mechanical responses to orthodontic loading: a 3-dimensional fi-nite element multi-tooth model. Am J Orthod Dentofacial Orthop2009;135:174-81.

20. Mischler S, Pax G. Tribological behavior of titanium sliding againstbone. Eur Cells Mater 2002;3:28-9.

21. Janssen D, Mann KA, Verdonschot N. Micro-mechanical modelingof the cement-bone interface: the effect of friction, morphologyand material properties on the micromechanical response. J Bio-mech 2008;41:3158-63.

22. Lei Z, Feng D, Yi Z, Yubo F. Three dimensional finite elementanaysis of the initial tooth displacement in different microimplant-bone interfaces using micro-inplant anchorage system.Proceedings of the IEEE/ICME International Conference onComplex Medical Engineering, 2007;1901-4.

23. Yettram AL, Wright KW, Houston WJ. Centre of rotation of a max-illary central incisor under orthodontic loading. Br J Orthod 1977;4:23-7.


24. Black J, Hastings G. Handbook of biomaterial properties. London,UK; Springer; 1998.

25. Collings EW. Materials properties handbook: titanium alloys. Ma-terials Park, OH: ASM International; 1995.

26. Boccaccio A, Lamberti L, Pappalettere C, Carano A, Cozzani M.Mechanical behavior of an osteotomizedmandible with distractionorthodontic devices. J Biomech 2006;39:2907-18.

27. Rees JS, Jacobsen PH. Elastic modulus of the periodontal ligament.Biomaterials 1997;18:995-9.

28. Ruse ND. Propagation of erroneous data for the modulus of elas-ticity of periodontal ligament and gutta percha in FEM/FEA pa-pers: a story of broken links. Dent Mater 2008;24:1717-9.

29. Crismani AG, Bertl MH, Celar AG, Bantleon HP, Burstone CJ. Min-iscrews in orthodontic treatment: review and analysis of publishedclinical trials. Am J Orthod Dentofacial Orthop 2010;137:108-13.

30. Song Y, Cha J, Hwang C. Mechanical characteristics of variousorthodontic mini-screws in relation to artificial cortical bonethickness. Angle Orthod 2007;77:979-85.

31. Ren Y, Maltha JC, Kuijpers-Jagtman AM. Optimum force magni-tude for orthodontic tooth movement: a systematic literaturereview. Angle Orthod 2003;73:86-92.

32. Teixeira ER, Sato Y, Akagawa Y, Shindoi N. A comparative evalua-tion of mandibular finite element models with different lengthsand elements for implant biomechanics. J Oral Rehabil 1998;25:299-303.

33. 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.

34. Wilmes B, Ottenstreuer S, Su YY, Drescher D. Impact of implant de-sign on primary stability of orthodontic mini-implants. J OrofacOrthop 2008;69:42-50.

35. Ammar H, Ngan P, Crout R, Mukdadi O, Mucino V. Patient-specific3D finite-element analysis of miniscrew implants during ortho-dontic treatment. Proceedings of the ASME International Mechan-ical Engineering Congress and Exposition (IMECE), 2009; LakeBuena Vista, FL.

36. Toms SR, Lemons JE, Bartolucci AA, Eberhardt AW. Nonlinearstress-strain behavior of periodontal ligament under orthodonticloading. Am J Orthod Dentofacial Orthopedics 2002;122:174-9.

37. Toms SR, Eberhardt AW. A nonlinear finite element analysis of theperiodontal ligament under orthodontic tooth loading. Am JOrthod Dentofacial Orthop 2003;123:657-65.

38. von Bohl M, Kuijpers-Jagtman AM. Hyalinization during ortho-dontic tooth movement: a systematic review on tissue reactions.Eur J Orthod 2009;31:30-6.

39. Kim T, Suh J, Kim N, Lee M. Optimum conditions for parallel trans-lation of maxillary anterior teeth under retraction force determinedwith the finite element method. Am J Orthod Dentofacial Orthop2010;137:639-47.

40. Tominaga JY, Tanaka M, Koga Y, Gonzales C, Kobayashi M,Yoshida N. Optimal loading conditions for controlled movement ofanterior teeth in sliding mechanics. Angle Orthod 2009;79:1102-7.

41. Sia S, Koga Y, Yoshida N. Determining the center of resistance ofmaxillary anterior teeth subjected to retraction forces in slidingmechanics. An in vivo study. Angle Orthod 2007;77:999-1003.

42. Jung MH, Kim TW. Biomechanical considerations in treatmentwith miniscrew anchorage. Part 1: the sagittal plane. J Clin Orthod2008;42:79-83.

43. Brettin BT, Grosland NM, Qian F, Southard KA, Stuntz TD,Morgan TA, et al. Bicortical vs monocortical orthodontic skeletalanchorage. Am J Orthod Dentofacial Orthop 2008;134:625-35.


Ammar et al e71

44. Viwattanatipa N, Thanakitcharu S, Uttraravichien A, Pitiphat W.Survival analyses of surgical miniscrews as orthodontic anchorage.Am J Orthod Dentofacial Orthop 2009;136:29-36.

45. Kuroda S, Sugawara Y, Deguchi T, Kyung HM, Takano-Yamamoto T. Clinical use of miniscrew implants as orthodontic


anchorage: success rates and postoperative discomfort. Am JOrthod Dentofacial Orthop 2007;131:9-15.

46. Sung SJ, Jang GW, Chun YS, Moon YS. Effective en-masse retrac-tion design with orthodontic mini-implant anchorage: a finite ele-ment analysis. Am J Orthod Dentofacial Orthop 2010;137:648-57.


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Three-dimensional modeling and finite element …...Three-dimensional modeling and ﬁnite element analysis in treatment planning for orthodontic tooth movement Hussein H. Ammar,a