Three-dimensional finite element analysis of …Three-dimensional ﬁnite element analysis of...

ORIGINAL ARTICLE

Three-dimensional finite element analysis ofstrength, stability, and stress distributionin orthodontic anchorage: A conical, self-drillingminiscrew implant system

Shivani Singh,a Subraya Mogra,b V. Surendra Shetty,c Siddarth Shetty,d and Pramod Philipe

Mangalore, India

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Introduction: The aims of this study were to analyze the stress distribution and displacement patterns thatdevelop in an orthodontic miniscrew implant and its surrounding osseous structures for 2 implant materials underhorizontal and torsional loading, with no ossseointegration. Methods: A numeric approach was adopted. Thefinite element method was used to determine the stress and displacement of the various components at a giventime after miniscrew implant application, when, due to viscoelastic relaxation effects, the only remaining stressfield was from the application of the orthodontic load. Results: Stress distribution was not significantly differentbetween the 2 types of implant material. Increased stress values were located at the necks of the implants andthe surrounding cortical bone. Bending of the titaniumminiscrewwas observed in the neck region under horizon-tal traction. Conclusions: The differences between the values of stress and displacement we obtained for the 2types of miniscrew were too small to be clinically significant. Optimization of the miniscrew implant composed ofthe titanium alloy might be achieved by increasing the bulk (quantity) of the material in the neck region. The mini-screw implant can be immediately loaded and used for group movement of teeth. (Am J Orthod DentofacialOrthop 2012;141:327-36)

Recently, orthodontic miniscrew implants havebeen increasingly used in orthodontics becausethey offer additional advantages over the other

types of anchorage mini-implants: their small size,ease of placement and removal, low cost, and the abilityto be loaded immediately. A tapered variety of miniscrewimplant with a sharp pyramidal apex has been developedto eliminate the need for a drill hole because it can be di-rectly threaded into the bone. Most miniscrew implantsare currently made of titanium alloy (Ti6Al4Vn, amixtureof titanium, 6 molecules of aluminum, and 4 molecules

the Department of Orthodontics and Dentofacial Orthopedics, Manipale of Dental Sciences, Mangalore, India.tant professor.ssor.ssor and dean.ssor and head.ciate professor.uthors report no commercial, proprietary, or financial interest in thects of companies described in this article.t requests to: Shivani Singh, Department of Orthodontics and Dentofa-rthopedics, Manipal College of Dental Sciences, Light House Hill Road,alore, India 575001; e-mail, [email protected]; [email protected], January 2011; revised and accepted, July 2011.5406/$36.00ight � 2012 by the American Association of Orthodontists..1016/j.ajodo.2011.07.022

of vanadium; ASTM F 136); however, some continue tobe made of implant-grade stainless steel (ASTM 316L),which is still used in traumatology.1

Despite the many advantages of miniscrew implants,their clinical behavior is still unclear. Various authorshave reported loosening and failure during clinical or-thodontic treatment. Factors that have been reportedto influence their retention are implant type,2 implantdimensions,3 implant surface characteristics,4 insertionangle,5,6 insertion torque,7 force magnitude,8 anatomiclocation,9,10 soft-tissue characteristics,9,10 rootproximity, and primary stability.11 However, since theseimplants are intended to be loaded immediately, theirprimary stability is of the utmost importance. Good pri-mary stability reduces the risk of micromotion and elicitsa positive bone response in the form of increased boneremodeling. The bone remodeling process is correlatedwith the structural response of the surrounding bony tis-sues to the miniscrew implant and to the stress-strainfield developing in the miniscrew implant itself.8

Yano et al2 reported no significant difference whentapered miniscrews were loaded immediately or aftera healing period of 6 weeks, suggesting that taperedminiscrews can be used for orthodontic anchorage im-mediately after their placement. Finite element studies

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328 Singh et al

on load transfer of miniscrew implants have been con-ducted by Dalstra et al12 and Gallas et al,13 who reportedthat areas of maximum stress were concentrated at theneck of the implant in the marginal bone. Graccoet al8 conducted a study to determine the effect of dif-ferent lengths of miniscrew implants and the various os-seointegration levels on their stability. They found thatcritical conditions occur for lengths of 14 mm with anorthodontic load of 2 N, and they preferred partial os-seointegration (50%) over no osseointegration. Kimet al7 compared the stability between cylindrical andconical implant types and concluded that, althoughthe conical mini-implant could induce tight contact tothe adjacent bone tissue and produce good primary sta-bility, the conical shape might need modification of thethread structure and the insertion technique to reducethe excessive insertion torque while maintaining itshigh resistance to removal.

A comprehensive analysis of the mechanical behaviorof a conical self-drilling type of miniscrew implant andthe response of the surrounding osseous structures tominiscrew implants composed of different materialsand for different directions of force application has yetto be carried out. Studies of stress analysis allow optimi-zation of the shape of the screw, the material of its com-position, and its geometric parameters such as length,diameter, taper, and thread pitch. The aim of this re-search was to analyze the stress distribution patternsin a conical self-drilling type of miniscrew implant sys-tem and its surrounding osseous structures, with no oss-seointegration, for 2 implant materials—Ti6Al4Vn alloyand implant-grade stainless steel—under horizontaland torsional loading. A numeric approach was adoptedto investigate how the load transfer at the bone-screwinterface changes for miniscrew implants made of differ-ent materials and for different directions of loading.

MATERIAL AND METHODS

The finite element method is an advanced computertechnique for structural stress analysis. It is used to obtaina solution to a complex mechanical problem by dividingthe problem domain into a collection of a finite numberof much smaller and simpler domains (elements): hencethe term “finite element,” in which the field variablescan be interpolated with the use of a shape function.This method in our study involved the following steps.

The purpose of constructing the geometric modelwas to represent the geometry in terms of points, lines,areas, and volumes. To build the screw model, the di-mensions of an actual conical self-drilling miniscrew im-plant (S.K. Surgicals; Ambegaon, Pune, India) weremeasured by using a toolmaker’s microscope (Mitutoyo,Bangalore, India) with an accuracy of 10 mm. The length

March 2012 � Vol 141 � Issue 3 American

of the screw was 10.62 mm, with a threaded shaft 6.86mm in length, and diameters of 2.48 mm at the head re-gion, 0.95 mm at the upper end of the shaft, and 0.82mm at the lower end of the shaft. The shaft of the mini-screw implant ended in a sharp pyramidal apex 0.54 mmin height. The number of threads was 1 per mm of lengthin the threaded region. The threads were arranged on theshaft in a spiral. The uppermost part of the head con-sisted of a rectangular slot with a width and a depth of1 mm each, and a hole of 1-mm diameter was createdin the center of the head. Measurements of other dimen-sions are given in Figure 1. The length and diameter ofthe head, neck, and shaft were further confirmed bymeasurements made with a profile projector (MetzerBiomedical and Electronics, Wadala, Mumbai, India)with an accuracy of 10 mm. The dimensions obtainedby the 2 methods were the same up to 2 decimal places.The thickness of the cortical bone considered for theanalysis was 2 mm, and the inferior region consisted ofcancellous bone. Dimensions taken from the measure-ments were used to build the 3-dimensional model byusing the solid modeling software Pro/ENGINEER Wild-fire (version 3; PTC, Needham, Mass). The 3-dimensionalmodel was imported to finite element software (version10; ANSYS, Canonsburg, Pa) by using the .iges format.In the geometric model, the osseous structures sur-rounding the miniscrew implant develop as a negativeimpression of the screw. The miniscrew implant modelis placed in contact with the bone. Hence, no stressesappear in the assembly before external loading.

The geometric model was converted to the finite el-ement model. The screw model called the domain wasdivided into smaller subdomains (elements) by a processknown as discretization. It is essential that the elementsdo not overlap but are connected only at key points,termed nodes. The joining of elements at the nodesand the elimination of duplicate nodes is termed mesh-ing. Figure 2 illustrates the cut-open meshed model andthe negative impression of the miniscrew implant in thesurrounding bone. The solid model is discretized by us-ing the mesh generation tool of the software. The SOLID92 element is used for the discretization. This is a qua-dratic element having 10 nodes, and each node has 3 de-grees of freedom. The element also has plasticity, creep,swelling, stress, stiffness, and large deflection and straincapabilities. The numbers of nodes and elements foreach part of the model (ie, the screw and the corticaland cancellous bones) are given in Table I.

To simulate an approximate biologic condition, ma-terial properties were assigned to the relevant areas. Var-ious components of the model are considered to bemade up of isotropic materials that have identical phys-ical properties along all 3 axes. The modulus of elasticity

Journal of Orthodontics and Dentofacial Orthopedics

Fig 1. Detailed dimensions of an actual conicalself-drilling type of miniscrew implant measured witha toolmaker’s microscope.

Singh et al 329

and Poisson’s ratio of the miniscrew implant materials(Ti6Al4Vn alloy [titanium alloy] and implant-gradestainless steel [stainless steel]) and the cortical and can-cellous bones are provided in Table II. The values of thematerial properties used are the averages reported in theliterature.14

The boundaries of the finite element model were re-stricted in all 3 planes. This enabled us to study deforma-tion on application of a load; without boundaryrestrictions, the body would behave like a free-floatingrigid object and would undergo translatory or rotatorymotion or both, without experiencing deformation.

American Journal of Orthodontics and Dentofacial Orthoped

Two load conditions were considered: horizontal andtorsional. The horizontal load was 350 g acting at theedge of the miniscrew implant head, perpendicular toits long axis. A torsional load of 400 g per millimeterwas applied at the periphery of the head of the miniscrewimplant at 2 points diametrically opposite to each otherin a clockwise direction. Both loads were at the level ofthe eye of the screw meant for tying ligatures in a clinicalsituation. The loading and boundary conditions are il-lustrated in Figure 3. The finite element model of thescrew, with all the loading and boundary conditions,was then solved with the ANSYS software for the un-known variables: ie, the displacements and stresses atthe nodes and the elements.

RESULTS

The results of the analysis were viewed in the post-processor of the analysis software. In this analysis, theminiscrew implant was the center of the study, and thematerials (titanium alloy and stainless steel) were con-sidered ductile. The Von Mises criterion was used tostudy the failure and distribution of stress in the mini-screw implants and the surrounding osseous structures.In the color band diagram showing stress distribution,the values are in newtons per square millimeter ormegapascals. The axis of the screw is along the y-axis. The displacement due to torsional loading pre-dominantly occurs in the y-axis direction; hence, thecolor plots are presented for the displacement in thisdirection. For horizontal loading, the displacement ofthe screw was predominantly in the x-axis direction.The dimensions of the model are in millimeters; there-fore, the displacement values in the color band diagramare in millimeters. The stresses and displacements forthe miniscrew implants and the cortical and cancellousbones were studied separately as well as collectively.The results were tabulated according to the areas ofthe model showing prominent and distinguishablestress and displacement patterns. These are shown inTables III and IV.

The patterns of stress distribution and displacementsof the miniscrew implants under horizontal loading wereas follows. The areas of maximum stress concentrationwere located at the neck of the miniscrew implant. Thestainless steel miniscrew implants had greater stress(19.56MPa) compared with the titanium alloy miniscrewimplants (11.35 MPa). Toward the apex, these valuesgradually decreased to 2.17 MPa for the stainless steelminiscrew implants and 1.26 MPa for the titanium alloyminiscrew implants. A general analysis of the stresspatterns in the surrounding bony tissues showed similarstress values irrespective of the material compositionof the miniscrew implant. A maximum stress value of

ics March 2012 � Vol 141 � Issue 3

Table I. Numbers of nodes and elements

Elements NodesCortical bone 33,055 49,028Cancellous bone 113,436 160,255Implant screw 36,334 56,965

Table II. Material properties used in this investigation

Modulus ofelasticity

Poisson’sratio

Titanium alloy 110 GPa 0.33Implant-grade stainless steel 205 GPa 0.29Cortical bone 18 GPa 0.3Cancellous bone 13.7 GPa 0.3

Fig 2. Cut-open meshed finite element model illustrating the miniscrew implant placed in contact withthe bone. Bone is developed as a negative impression of the miniscrew implant surface.

330 Singh et al

approximately 6.5 MPa was concentrated in the upperregion of the cortical bone and decreased graduallytoward its lower end. The amount of stress transferredto the cancellous bone appeared to be minimal(0.1-0.01 MPa).

The color band diagram for displacement values de-picts displacements along the negative x-axis and nega-tive y-axis in blue, and those along the positive x-axisand positive y-axis in red. A general analysis showedthat displacements occur in both the x-axis and the y-axis. The miniscrew implant displacements were muchgreater along the x-axis than the y-axis. However, thebony structures showed less displacement. An importantfinding here was that the titanium alloy miniscrewimplant bends down at its neck region toward the direc-tion of horizontal loading (Fig 4). The amount of dis-placement resulting from this bending could not beobtained along the x-axis, perhaps because of the bend-ing of the screw and a probable deformation at the upperregion. However, due to this bending of the screw at its


neck region, the head appears to be tilted along the y-axis. Both the miniscrew implant and the bone appearto be bent down along the y-axis by 0.162 mm. Anotherappreciable finding is the displacement of the middlepart of the miniscrew implant and the lower parts ofthe cortical and cancellous bones along the negativex-axis (ie, opposite to the direction of force application).This is in contrast with the upper part, which movedalong the positive x-axis, with the direction of force ap-plication (Fig 5).

The patterns of stress distribution and displace-ments of the miniscrew implants under torsional load-ing were as follows. The stress appeared to bedistributed around the head and the neck of the mini-screw implant, and at the cortical bone and the upperthird of the cancellous bone. The areas of maximumstress were concentrated at the point of force applica-tion, and these gradually diminished in a clockwise di-rection. The maximum stress values obtained at the


Fig 3. A, Boundary and loading conditions for a horizontal load of 350 g; B, boundary and loadingconditions for a torsional load of 400 g per millimeter acting in a clockwise direction.

Singh et al 331

neck of the stainless steel and titanium alloy mini-screw implants were 17.2 and 8.7 MPa, respectively,which were slightly lower than those obtained underhorizontal loading. The stress distribution patterns inother parts of the miniscrew implants and the bonytissues showed similar trends to those with horizontalloading. However, the displacement values along they-axis showed almost negligible amounts of displace-ment. A notable finding was increased deflection(0.048 to �0.052 mm) in the region of the eye of


the screw, where the torsional load was concentrated(Fig 6).

DISCUSSION

In this study, a comprehensive analysis of stress dis-tribution and displacement induced in an orthodonticanchorage miniscrew implant and its surrounding osse-ous structures under horizontal and torsional loadingwas conducted for 2 implant materials: stainless steeland titanium alloy. However, this study had some


Table III. Stress (MPa) and displacement (mm) values for the stainless steel and titanium alloy miniscrew implantmodels for a 350-g horizontal load

SSM STM DSM-x DTM-x DSM -y DTM-yScrewUpper third 19.563 11.353 0.916 to 0.385 - 0.154 to

�0.1560.162 to�0.162

Middle third 4.349 3.785 �0.400 - �0.0179 �0.0544Lower third 2.176 1.263 0.385 - 0.0165 0.0176

Cortical boneVicinity of neck 6.323 max

3.513 min6.466 max5.747 min

0.0876 0.0317 0.154 to�0.156

0.162 to�0.162

Vicinity of flute 1.405 1.437 �0.0305 �0.00992 0.0509 0.0536Cancellous boneBoundary of cortical and spongy bones 0.1744 0.175 max

0.136 min�0.0399 �0.0238 0.0527 to

�0.0550.0536 to�0.0184

Upper third 0.1162 0.09741 �0.0115 �0.0377 0.0177 to�0.0174

0.0176

Middle third 0.01938 0.03897 0.00264 0.00397 0.00597 0.0176

SSM, Stress in the stainless steel miniscrew implant model; STM, stress in the titanium alloy miniscrew implant model;DSM-x, displacement in thestainless steel miniscrew implant model along the x-axis; DTM-x, displacement in the titanium alloy miniscrew implant model along the x-axis;DSM-y, displacement in the stainless steel miniscrew implant model along the y-axis;DTM-y, displacement in the titanium alloy miniscrew implantmodel along the y-axis; max, maximum; min, minimum.

Table IV. Stress (MPa) and displacement (mm) values for stainless steel and titanium screw models for a 400-g permillimeter torsional load

SSM STM DSM-y DTM -yScrewUpper third 17.272 8.719 0.00060 to

�0.00100.00081 to�0.00091

Middle third 5.758 2.18 �0.00011 0.00005Lower third 1.92 1.09 0.00024 0.00024

Cortical boneVicinity of neck 8.418 to 0.9353 8.539 to 0.948 0.00181 to

�0.001920.00183 to�0.00194

Cancellous boneUpper third 0.0666 0.0462 0.00153 to

�0.001780.00154 to�0.00175

Lower third 0.0074 0.0051 0.000431 0.000442

SSM, Stress in the stainless steel miniscrew implant model; STM, stress in the titanium alloy miniscrew implant model;DSM-y, displacement in thestainless steel miniscrew implant model along the y-axis; DTM-y, displacement in the titanium alloy miniscrew implant model along the y-axis.

332 Singh et al

limitations, and certain assumptions were made to facil-itate the modeling and solving process. First, we as-sumed that the osseous structures were homogenousand linear, and that they had an elastic material behaviorcharacterized by 2 material constants for Young’s mod-ulus of elasticity and Poisson’s ratio. However, corticaland cancellous bones are nonhomogenous, anisotropiccomposite structures that possess different values for ul-timate stress and the modulus of elasticity when thebone is tested under compression compared with ten-sion. As previously stated, miniscrew implants show a ten-dency toward tipping; however, the total amount oftipping that would occur in a clinical situation cannot be


predicted by this mathematical model, since it gives valuesonly at 1 time point. Hence, the net amounts of displace-ment shown by various authors after prolonged loadingover periods of months are not depicted in our re-sults.15-18 Our findings that can be safely extrapolated tothe clinical scenario are static features such as thedistribution of stress patterns, the displacements thatwould occur for short periods of implant placement, andthe relative comparisons of these values for stainlesssteel and titanium alloy implant materials.

The finite element model neglects the stress pro-duced by the insertion of the screw and considers onlythe stresses produced by horizontal and torsional loads.


Fig 4. Displacement patterns in a titanium miniscrew implant model under horizontal traction in they-axis direction. A, Titanium alloy miniscrew implant bends down at its neck region toward the directionof horizontal loading; B, bending of cortical bone along the y-axis on horizontal loading in the titaniumalloy miniscrew implant model. The color coding shows the areas of bone and miniscrew implant undercompression (blue) and tension (red) and displacement (blue) of the cortical bone (�0.162 mm) alongthe negative y-axis. OMS, Orthodontic miniscrew implant.

Singh et al 333

Gracco et al8 followed the same methodology in their fi-nite element study, supporting the argument by Mano19

that bony tissue behaves as a viscoelastic material, whichresults in relaxation in the stress fields generated by im-plant insertion. In spite of these limitations, the finite el-ement predictions in our investigation are in goodagreement with the results of Dalstra et al,12 Szuhanek


et al,20 and Gallas et al,13 who reported that, when forceis applied perpendicularly to the long axis of the implant,the maximum stresses were located around the neck ofthe implant at the bone-implant interface. The samefinding was observed in this study; maximum stressesoccurred in the cortical bone surrounding the neck ofthe implant at 6 and 8.5 MPa for horizontal and


Fig 5. Displacement patterns in a titanium miniscrew implant model under horizontal traction in thex-axis direction. The color coding (green, yellow, and red) shows the displacement of the upper corticalbone along the positive x-axis (0.0397 mm) and the displacement of middle part of the miniscrew im-plant, the lower cortical bone, and the upper cancellous bone along the negative x-axis (�0.0377mm; dark blue), suggesting the tendency for the miniscrew to tip. Similar displacement patterns wereobtained for the stainless steel miniscrew implant model.

Fig 6. Displacement patterns in theminiscrew implant head region under torsional load. The color cod-ing depicts 0.048 (red) to�0.052 mm (dark blue) displacement along the negative y-axis in the region ofthe eye of the screw where the torsional load is concentrated.

334 Singh et al

torsional loading, respectively; these are far below theyield strength of 122 MPa for this tissue.21 The maxi-mum stress values in cancellous bones were 0.17 and


0.06 MPa for horizontal and torsional loading, respec-tively; these are far below the yield strength of this tis-sue.21 These findings are consistent with those of


Singh et al 335

Gracco et al,8 who reported similar stress values for cor-tical bone that were at least 1 order of magnitude greaterthan those of cancellous bone.

The maximum forces on the miniscrew implantswere concentrated at the neck region, with stress valuesfor the stainless steel model considerably greater thanthose for the titanium alloy model. The increased stressand displacement values obtained at the eye of theminiscrew might be explained by the reduced bulk(quantity) of the material in this region. According toMelsen,1 if an Allen wrench is used for insertion and re-moval, the hole in the center of the screw, whichweakens the neck, might cause the screw to fracture.She suggests the use of a slotted head instead of a hol-low one to prevent the screw from breaking at this re-gion. An important finding of this study was thebending of the titanium miniscrew implant at theneck region under horizontal loading. This might beexplained by the difference in the modulus of elasticitybetween the stainless steel and titanium alloys and thestrengths of these materials. Because titanium alloy isa far weaker material with a smaller modulus of elastic-ity compared with stainless steel, it bends at its thin-nest region to withstand a similar load. Stainless steelcan bear the same amount of load without bending.Consequently, both materials transfer similar residualforces to their surrounding bony tissues. Hence, thestresses and displacements that we observed in thebony tissues were similar for both materials.

We can conclude that, to prevent this bending, theneck region should be as wide as the head region andthe shoulder of the implant. However these resultsshould not lead us to conclude that stainless steel is bet-ter than titanium alloy. It is important to consider thebiocompatibility of titanium and the temporary natureof its use as an anchorage, and that the forces concen-trated at the neck region are far below the yield strengthof titanium. Stahl et al3 also demonstrated a similar ef-fect of modulus of elasticity on stress pattern distribu-tion and displacement. In a finite element study, theyinvestigated the distribution of stress patterns with vary-ing modulus of elasticity values of cancellous bone andfound that the deflection of orthodontic mini-implantsincreases with a reduction in the modulus of elasticityof cancellous bone.

As stated previously, the displacement of the upperpart of the cortical bone was opposite to the displace-ment of its lower part and that of the cancellous bone(x-axis). This was most likely because, upon horizontaltraction, a moment is generated that tends to tip thescrew about a point located approximately at the lowerregion of the cortical bone. Gracco et al8 obtained a sim-ilar finding in a finite element study when they reported


rigid-body rotation of a nonosseointegrated miniscrewabout a point localized at the interface of the corticaland trabecular bones. However, smaller degrees of rota-tion were also reported in the partially and completelyosseointegrated samples.

The maximum stress values obtained for the mini-screw implants during torsional loading were locatedat the neck region. The values obtained for stainless steelwere 19.6 and 17.2 MPa; those for titanium alloy were11.7 and 8.3 MPa under horizontal and torsional forces,respectively. This difference can be explained by differ-ences in the modulus of elasticity of these materials. Im-plant failure, a critical condition, did not occur duringtorsional loading in the clockwise direction. These re-sults are supported by the findings of Cho et al,22 whoreported failure of miniscrews with 2 Ncm of counter-clockwise rotation over a period of 3 weeks; also, thecounterclockwise group showed a significantly lowerbone-implant contact compared with the clockwisegroup. They suggested that counterclockwise momentsmight be a risk factor that can impair a miniscrew’sstability.

In general, these results demonstrate that a conicaltype of miniscrew implant with a length of 10 mm anda diameter of 2.0 mm composed of either stainless steelor titanium alloy can safely resist the high levels of or-thodontic force used for group movements of teeth ormolar uprighting. Previous studies have favored similardimensions for miniscrew implants.8,23,24 Gracco et al8

reported in their finite element study that the criticalcondition of bone failure occurs in screws 14 mm inlength for loads of 2 N, and the optimal screw lengthwas found to be 9 mm. Screws shorter than 9 mmwere also reported to be associated with high stresspeaks.8 Morarend et al23 reported that large-diameter(2.5 mm)monocortical screws provide greater anchorageforce resistance than do monocortical screws witha smaller diameter (1.5 mm), and that smaller-diameterbicortical screws provide anchorage force resistanceequal to that of bicortical screws with a larger diameter(2.5 mm). However, Wang and Liou15 reported extrusionand tipping of miniscrew implants up to 1.5 mm duringen-masse retraction and intrusion of the anterior teeth;this did not correlate with the displacement of a few mi-crometers obtained in our study. This might imply thatminiscrew implant displacement under an orthodonticload could be a progressive process.

CONCLUSIONS

1. The differences between the values of stress and dis-placement for the 2 types of miniscrews were toosmall to be clinically significant.


336 Singh et al

2. A miniscrew implant of the aforementioned dimen-sions can be safely used, under immediate loading,for group mesiodistal movement of teeth and up-righting of a tooth with a winding moment to theminiscrew implant.

3. Implant-grade stainless steel and Ti6Al4Vn alloysare suitable materials for miniscrew implants.

4. The above-mentioned miniscrew implant dimen-sions could be optimized by increasing the bulk(quantity) of material at the neck of the titanium al-loy miniscrew.

5. The head of the miniscrew implant could be madesolid by replacing the eye with a rectangular slot.

We thank Mr. Navin Karanth and Mr. Mahesh B.K. atthe Department of Mechanical Engineering (National In-stitute of Technology, Surathkal, India) for their helpwith the finite element analysis.

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http://dx.doi.org/doi:10.1016/j.msec.2005.01.017

http://dx.doi.org/doi:10.4028/www.scientific.net/KEM.399.199

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