Optimized Orthodontic Palatal Miniscrew Implant Insertion Angulation: A Finite Element Analysis Arash Poorsattar Bejeh Mir, DDS1/Mehdi Ravadgar, DDS, MS2/ Morvarid Poorsattar Bejeh Mir, DDS, CES, DipOrtho3 Purpose: There is a controversial body of evidence regarding optimal insertion angulation of an orthodontic miniscrew as a mean of skeletal anchorage. Materials and Methods: A bracket head–type 8-mm–long miniscrew (60-degree symmetrical trapezoid thread, 0.1-mm thread fillet, 0.2-mm thread height, with 0.5-mm thread pitch) was designed and monocortically inserted at 30, 45, 55, 70, 90, 110, 125, 135, and 150 degrees of inclination to the surface of bone. A bilayer cortical (1.6 mm) and cancellous (8.5 mm) bone model was constructed, adopted from a 22-year-old male patient’s cone beam computed tomography (CBCT) image of his anterior hard palate area. A horizontal force of 2 N was applied parallel to the bone surface. Bone material was simulated as normal and osteoporotic bone. The maximum equivalent von Mises stress and microstrain values were separately calculated for the miniscrew, cortical bone, and cancellous bone. Deflections of the whole bone and miniscrew were also reported. Results: A significant lower stress was found in the cancellous bone compared to the cortical bone. Osteoporotic bone displayed higher strain values. Overall, 30-degree models exhibited the lowest von Mises stress and strain values for the cortical layer and miniscrew in both normal and osteoporotic models. Meanwhile, 90-degree models displayed the lowest strain values in the osteoporotic and normal cancellous bones. Minimum bone and miniscrew deflection values were related to the model of 30-degree insertion angulation. Conclusion: These results showed that, within the limitations of the study, the 30-degree angulation of miniscrew insertion toward the direction of applied force could lower the cortical bone stress and strain. Int J Oral Maxillofac Implants 2015;30:e1–e9. doi: 10.11607/jomi.3636 Key words: angulation, finite element analysis, miniscrew, stability, stress
S
ince 1997 when Kanomi reported the first use of miniscrew implants (MSI) in orthodontics, they have gained increasing popularity as a reliable temporary anchorage device (TAD) providing absolute anchorage for tooth movements applying various biomechanical forces.1 Their small size, low cost, decreased need for patient compliance, shorter overall chairside time, enhanced anchorage with lower anchorage loss, ability for immediate loading after insertion, insertion via minor surgery, and ability to provide an opportunity for the very special cases that were only surgically treatable at one time make them a promising choice in orthodontics.2
1Researcher,
Dental Materials Research Center, Dentistry School, Babol University of Medical Science, Babol, Iran. 2 Assistant Professor, Department of Orthodontics, Dentistry School, Babol University of Medical Science, Babol, Iran. 3 Private Practice of Orthodontics, Montreal, Quebec, Canada. Correspondence to: Dr Arash Poorsattar Bejeh Mir, Dental Materials Research Center, Dentistry School, Babol University of Medical Science, Ganj Afrooz Square, Babol, Iran. Fax: +98-151-3216383. Email: [email protected] ©2015 by Quintessence Publishing Co Inc.
Orthodontic mini-implants have exhibited a lower success rate when compared to prosthodontic implants, likely due to their smaller size and contact surface. Moreover, compared to palatal implants with success rates of 74% to 93%, miniscrews have a higher failure rate (as high as 40%), although it should be noted that this higher failure rate should be weighed against the increased probability of interfering with growth of the midpalatal suture, a longer healing period, and more invasive surgical procedure for inserting and removing palatal implants.3,4 Anchorage enforcement and maintenance are more important in the maxilla, especially in patients with Class II, division 1 malocclusion for retraction of the maxillary incisors because of the greater root surface of maxillary anterior teeth, need for their bodily movement, and less dense cancellous bone in the maxilla.5 More specifically, the anterior palatal region should be regarded as an exceptional part of the maxilla, considering the absence of tooth and root proximity and lack of large nerves and arteries; moreover, one should note the presence of the midpalatal suture and its growth, lower density and cortical thickness, and greater mucosal thickness when comparing the anterior paramedian maxillary palate with interradicular maxillary sites.6 The International Journal of Oral & Maxillofacial Implants e1
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assumed the miniscrew as a material fully bonded to the bone. The intent of this numeric analytic study was to determine whether the insertion angle of an orthodontic miniscrew in relation to the bone surface (ie, miniscrews that are not osseointegrated) and bone quality contribute to the periminiscrew bone stress when the miniscrew is loaded immediately after insertion.
MATERIALS AND METHODS Three-Dimensional Model Design Fig 1 Three-dimensional (3D) meshes of the miniscrew and bone block models.
Table 1 Miniscrew Design and Dimensions Specification
Dimension
Miniscrew threaded length
8 mm
Bracket-head length
0.8 mm
Bracket slot
0.022 × 0.025 in
Transgingival length
2.2 mm
Thread design
Trapezoidal
Thread pitch
0.5 mm
Thread width
0.1 mm
Thread height
0.2 mm
External diameter
1.6 mm
The main problem with miniscrews as TADs is the failure rate. Higher internal stress could increase bone damage and resorption at the bone-implant surface, threatening miniscrew stability, which consequently may lead to miniscrew loosening and failure.7,8 Inclined insertion of miniscrews has been proposed mainly to avoid adjacent root damage and to provide greater retention by means of the longer traversed length through the cortical layer, which should be weighed against the effects of an increased lever arm and the risk of slippage over the cortical layer during insertion.7,8 To date, there are some numerical analyses of stress around angulated miniscrews with conflicting data. There exist some claims that “tent pegging” of a miniscrew by inclining the miniscrew away from the direction of applied force may have some geometric and biomechanical advantages. Some authors have advocated angulated miniscrews, and some have suggested the use of vertically placed miniscrews in terms of lowering von Mises stresses.9–12 However, results by some authors showed that angulation does not significantly contribute to the success rate.7,10,13,14 The main point is that all previous finite element analyses (FEAs)
A segment of human maxillary palate was modeled, which was constructed of a 1.6-mm–thick upper cortical layer and lower attached cancellous bone covered with 2.2-mm–thick mucosa. Data were obtained from the cone beam computed tomography (CBCT) scan of a healthy Iranian male patient aged 22 years; the CBCT image was located 8 mm posterior to the incisive canal and 3 mm left of the midpalatal suture. The miniscrew was first modeled in AutoCAD software (Autodesk) and was inserted in the bone through a prespecified hole with various insertion angulations of 30, 45, 55, 70, and 90 degrees, and their respective reciprocal angles of 110, 125, 135, and 150 degrees with regard to the bone surface (Fig 1). The final mesh for each model was dissolved using finite element analysis software (ANSYS version 14) for comparative evaluations. Specifications of the miniscrew are displayed and presented in Table 1.
Elements and Nodes
The miniscrew and its 2-mm circular surrounding bone from the surface of the miniscrew (defined as the region of interest [ROI]) were meshed with a 10-node tetrahedron element (ie, three degrees of freedom) as permitted by the geometry of the miniscrew-bone interdigitation. The remaining bone was meshed using 20-node hexahedron element. A convergence test with mesh refinement was performed to reassure the accuracy of the model. Elements of the ROI were reduced so that the maximum obtained von Mises stresses for cortical and cancellous bone of two consecutive sets were changed by less than 7% (tolerance rate). The final size of the element was approximately 150 μm. The total number of nodes and elements ranged from 149,684 to 189,182 and 98,095 to 125,387, respectively, based on insertion angulation (Table 2).
Interface Condition and Loads
The miniscrew-bone interface was modeled using a frictional contact element (CONTA174 and TARGE170) with a frictional coefficient of 0.3.15 All remaining nodes including the cortical and cancellous contact surface were constrained in all directions with no
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Poorsattar Bejeh Mir et al
assumed movement. A force of 2 N was applied on the most peripheral node of the bracket head of the miniscrew parallel to the bone surface directed from the left side to the right side of the bone block.
Table 2 Number of Nodes and Elements Used for Each Model of Insertion Angulation Angle (degrees)
Elements
Nodes
125,387
189,182
45
99,157
151,352
55
98,453
150,242
30
Material Properties
All materials used were considered as linearly elastic, homogenous, and isotropic. Material properties were entered into the software based on the existing literature (Table 3). To simulate osteoporotic bone, Young’s moduli of cortical and cancellous layers were reduced 33% and 66%, respectively.9,15,16
Output Variables
Peak von Mises stresses were reported for cortical and cancellous layers and the miniscrew separately to compare the maximum induced values for each model. Maximum elastic strain (εmax), which is indicative of collective normal and shear strain at a given point, was calculated and reported mainly to compare the inevitable produced strains under normal and osteoporotic conditions.17 Maximum deflection (displacement) was also calculated and reported for both the bone and the miniscrew. Nodes on the peripheral cortical bone edge were selected in a 30-degree circumferential-section manner starting from the point of force application to the 180-degree point, and corresponding maximum von Mises stresses were reported (ie, seven nodes were selected for each model). The remaining half of the circumferential section was eliminated due to its similarity. Outputs displayed in color-scale figures ranged from blue to red. Red indicated higher stress, and blue indicated lower stress. The engineering safety factor was calculated by dividing the reported strength of the cancellous bone, cortical bone, and miniscrew with 2,133, and 880 values, respectively, by the maximum reported von Mises stress of each model to compare the safety magnitude of produced stress levels in the bone and miniscrew.15
RESULTS Peak equivalent von Mises stress, maximum elastic strain, and deflection values are presented in Tables 4 and 5. Stress and strain values were remarkably lower in cancellous bone compared to the cortical bone. Higher von Mises stresses and deflection occurred on the miniscrew in comparison to the bone. Most stress and strain occurred at the compression side in the cortical bone (Fig 2). The least displacement occurred in the bone adjacent to the miniscrew apex, while the bracket head of the miniscrew sustained the highest deflection, and the miniscrew apex displayed the lowest deflection.
70
98,095
149,684
90
105,444
154,366
110
98,095
149,684
125
98,453
150,242
135
99,157
151,352
150
125,387
189,182
Table 3 Properties of Materials Used in Finite Element Model Material Miniscrew (Ti-6Al-4V) Cortical bone (normal) Cortical bone (osteoporotic) Cancellous bone (normal) Cancellous bone (osteoporotic)
Young’s modulus (MPa)
Poisson’s ratio
114,000
0.34
13,700
0.30
917
0.30
1,600
0.20
540
0.20
Insertion Angulations
Models with angulations toward the force direction exhibited lower stress than their reciprocals, which were angulated away from the direction of the force (see Tables 4 and 5). Overall, 30-degree models exhibited the lowest von Mises stress and strain values related to the cortical bone layer and miniscrews of both normal and osteoporotic models. Meanwhile, 90-degree models displayed the lowest strain values in the osteoporotic and normal cancellous bone. Minimum bone deflection and minimum miniscrew von Mises stress and deflection values were related to the model of 30-degree insertion angulation in both normal and osteoporotic models. In all models, the compression side of the cortical bone exhibited the highest magnitude of von Mises stress concentrated at the corresponding bone adjacent to the thread fillet of the three uppermost threads. Cancellous bone in 30- to 70-degree models revealed even distribution of stress and strain in the compression and tension sides, while in 90- to 150-degree models, von Mises stresses appeared higher in magnitude over a larger area on the tension side (Fig 3). The latter models also displayed more concentrated cancellous bone stresses near the fillet of lower engaged threads. The International Journal of Oral & Maxillofacial Implants e3
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Table 4 Maximum Stress, Strain, and Deflection Values Induced at Various Insertion Angles for Normal Bone Insertion angle (degrees)
Cortical bone
Cancellous bone
σvm (MPa)
εmax (μm/μm)
σvm (MPa)
30
4.40
321
0.30
193
45
5.21
380
0.39
55
5.99
437
0.38
Whole bone
εmax (μm/μm) Deflection (μm)
Miniscrew σvm (MPa)
Deflection (μm)
0.034
8.62
0.76
248
0.057
12.06
0.96
241
0.068
14.33
1.89 1.53
70
10.28
750
0.41
257
0.086
19.28
90
11.07
701
0.31
182
0.088
23.55
1.79
110
13.58
991
0.34
216
0.077
22.36
2.36 2.44
125
8.67
633
0.29
185
0.070
23.68
135
11.61
848
0.50
313
0.120
21.55
2.67
150
9.55
697
0.29
185
0.061
17.61
3.19
σvm = equivalent von Mises stress; εmax = maximum elastic strain (data should be read at E−006 [× 10 −6]).
Table 5 Maximum Stress, Strain, and Deflection Values Induced at Various Insertion Angles for Osteoporotic Bone Insertion angle (degrees)
Cortical bone
Cancellous bone
Whole bone
εmax (μm/μm) Deflection (μm)
Miniscrew
σvm (MPa)
εmax (μm/μm)
σvm (MPa)
30
3.99
435
0.19
360
0.061
σvm (MPa) 9.25
0.88
45
4.71
513
0.24
457
0.109
12.97
1.11
Deflection (μm)
55
5.99
613
0.38
397
0.122
14.33
1.41
70
10.60
1,155
0.28
528
0.150
20.28
1.89
90
9.60
946
0.19
338
0.142
24.05
2.20
110
10.60
1,115
0.21
395
0.194
23.01
2.85
125
7.20
758
0.22
413
0.163
26.76
2.89
135
9.30
1,013
0.29
397
0.105
22.63
3.10
150
7.65
833
0.20
378
0.103
18.46
3.75
σvm = equivalent von Mises stress; εmax = maximum elastic strain (data should be read at E−006 [×
Fig 2 Strain in the cortical bone model of the (top) 30-, (middle) 90-, and (bottom) 150-degree models for respective upper, middle, and lower sets.
10 −6]).
Fig 3 Stress distribution pattern in cancellous bone for the (top row: left to right) 30-, 70-, (bottom row: left to right) 90-, 110-, and 150-degree models.
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Fig 4 Stress distribution patterns for miniscrews presented for (top row: left to right) 30-, 70-, 90-, (bottom row: left to right) 110- and 150-degree models.
1
18
2
3
4
16 Bone Miniscrew
14 12
1: Bracket head 2: Transmucosal shaft 3: Cortical part 4: Cancellous part
10 8 6 4 2
30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0
Maximum von Mises stress (Mpa)
Maximum von Mises stress (Mpa)
20
0 0 a
1
2 3 4 5 6 7 8 9 10 11 12 Distance along longitudinal axis (mm)
1
2
3
4 Bone Miniscrew 1: Bracket head 2: Transmucosal shaft 3: Cortical part 4: Cancellous part
0 b
1
2 3 4 5 6 7 8 9 10 11 12 Distance along longitudinal axis (mm)
Fig 5 Miniscrew and bone von Mises stress along the longitudinal axis on (a) compression side and (b) tension side.
Normal vs Osteoporotic Bone
Overall, higher stress, strain, and deflection occurred in osteoporotic bone when compared to the normal bone. Precisely, average peak von Mises stress and
10 9 8 7 6 5 4 3 2 1 0
Maximum von Mises stress (Mpa)
The tension side of the miniscrew sustained higher von Mises stresses over the recession of the first thread in 30- to 90-degree inclined models, while the stress was distributed more broadly on the compression side of the miniscrew, down to the second to third thread (Figs 4 and 5). As circumferential nodes’ data showed, a lower, steadier, and almost flat pattern of stress distribution in cortical bone was monitored for angulated miniscrews toward the force direction, and a comparably higher and peaked stress pattern in cortical bone was obvious for surrounding bone of miniscrews angulated away from the direction of force (Fig 6). The engineering safety factor equation revealed that 30-degree angulated insertion provided 30, 6, and 102 times less stress than the yield-strength limits of cortical bone, cancellous bone, and miniscrew, respectively (Table 6).
30 45 55 70 90 110 125 135 150
0
30
60
90
120
150
180
Circumferential 30-degree sections Fig 6 Stress distribution pattern of peripheral cortical bone shown for all models displayed for circumferential bone.
strain increased by 55% and 130.73% in the cortical bone and by 22% and 81% in the cancellous bone, respectively. Moreover, bone deflection increased by 69% when an osteoporotic condition was assumed. The International Journal of Oral & Maxillofacial Implants e5
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Table 6 Safety Factor Values for Various Insertion Angles* Insertion angle (degrees)
Cortical bone†
Cancellous bone‡
30
30.22
6.66
102.03
45
25.51
5.26
72.96
Miniscrew§
55
22.20
5.17
61.40
70
12.93
4.87
45.64
90
12.01
6.45
37.36
110
9.79
5.88
39.35
125
15.34
6.89
37.16
135
11.45
4.00
40.83
150
13.92
6.89
49.97
*Data are presented for normal bone. †σ /133 (σ ‡ § vm vm = equivalent von Mises stress). σvm/2. σvm/880.
DISCUSSION Angulation
The main purpose of the present study was to compare the effect of different insertion angulations of miniscrews in a simulated maxillary palate on periminiscrew bone stress by means of finite element analysis. Quantified data showed that the cortical layer absorbs almost all the transmitted stresses when the miniscrew is loaded horizontally, which is similar to the findings of previous researchers.7,12,18 The 30-degree angulation is the safest angulation in terms of safety engineering factor. It should be mentioned that the calculated engineering safety factors for the other angulations were also much greater than a safety factor of 1, ranging between 11.45 to 25.51 and 37.14 to 72.96 for the cortical bone and miniscrew, respectively. The lowest bone-equivalent von Mises stresses, strain, and deflection values in the cortical layer were observed for the 30-degree inclined miniscrew in both normal- and osteoporotic-imitated bone models; however, normal bone and osteoporotic bone did not show similar results in cancellous bone. Higher stresses would increase the probability of periminiscrew inflammation and release of inflammatory cytokines, which in turn might deteriorate the primary stability of the miniscrew.8 As shown in Fig 2, the 30-degree inclined model demonstrated a more uniform distribution of strain at the cortical edge when loaded as compared to 90and 150-degree inclined models. Moreover, an even pattern of equivalent von Mises stress in peripheral entangled bone in the cortical layer was observed in inclined models toward the applied force (see Fig 6).
It has been proved that more uniform distribution of strain prevents localized concentration of strain and mechanical stresses. This lowers the chance of loosening and failure of the miniscrew.19,20 Numerical analysis revealed similar data for the miniscrew in terms of von Mises stress and deflection for the aforementioned inclination. Overall, greater stress was located in the miniscrew’s transcortical part, which is in agreement with previous reports.9,15,16,21 The compression side of the bone sustained the highest von Mises stress in all models near the thread top. Meanwhile, von Mises stress was greater on the tension side of the miniscrew in inclined models toward the force in the first thread recession. This pattern was translocated to the compression side of the miniscrew and to the lower threads in inclined models opposing the direction of applied force. Described patterns are assumed to be related to the model of transmission of force to the miniscrew and its surrounding bone under horizontal force.15 Existing literature with assumptions of combined orthodontic horizontal force, assessment of diverse insertion angulations including their reciprocals, and immediate loading circumstances without osseointegration is inconsistent. Osseointegration would change the strain and stress values.22 The present results showed that inclined miniscrews toward the applied orthodontic force transfer would lower the stress and strain to the adjacent bone in comparison to their reciprocals, in opposition to the proposed “tent pegging” hypothesis. This finding is in agreement with Lin et al, who investigated von Mises stress with FEA comparing 60- and 120-degree inclined MSIs.12 In the present study models, 30-degree inclined-position MSIs induced less stress than 90-degree vertically positioned MSIs. Similarly, Suzuki et al reported lower stress in a 30-degree model (1.3 × 9.1-mm implant; F = 2 N horizontal; FEA, bonded surface of implant and bone).11 On the contrary, Woodall et al (1.5 × 11-mm implants with 6-mm intrabony length; F = 40 N horizontal; FEA, bonded surface of implant and bone) and Jasmine et al (1.3 × 8-mm implants; F = 2 N horizontal; FEA, bonded surface of implant and bone) concluded that MSIs should best be positioned vertically.9,10 Conflicting data also exist from various studies in which maximum insertion torque (MIT), pull-out test, and bone strain were evaluated during insertion and removal as indicators of stability comparing vertically inserted MSIs with angulated MSIs.8,23–25 Some sources of these diverse and contradictory results may be related to the following factors: (1) A bonded defined miniscrew-bone contact would result in lower stress than when a friction coefficient is entered in the model, which is due to the higher contact
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surface in osseointegrated models.26 (2) Patterns of anisotropy differ in various parts of craniofacial skeleton. This neglected predictor is simply overlooked when the result of different parts of the maxilla and mandible are compared. For instance, the anterior maxillary palate is among the least anisotropic parts of the maxillofacial skeleton (E2/E3 = 0.85), while the mandible is more anisotropic; hence, the response may be different when force is applied in either direction of maximum stiffness, minimum stiffness, or perpendicular axes.27 (3) Orthodontic forces for posterior retraction of maxillary incisors are mainly parallel to the cortical plate of the palate. Hence, many results of vertical pullout tests, which were interpreted as primary stability, should not be generalized and interpreted for horizontally tracked miniscrew stability.
Entries of Model and FEA
Wide variations on the anterior palate cortical bone thickness (CBT) have been observed in adult patients referred to a private oromaxillofacial radiology center located in northern Iran, ranging from 0.5 to 2.7 mm (Haghanifar S, Poorsattar Bejeh Mir A, unpublished data, 2014). Cortical thickness has been reviewed as a crucial factor for MSI primary stability, and 1 mm is the minimum required thickness. The present study assumed that the CBT of the bone block was 1.6 mm according to the patient data, which met the minimum requirement.28 The extrabony part of the designed miniscrew consisted of a 0.8-mm bracket head and a 2.2 mm–long transmucosal part, which was obtained from the CBCT data. The authors observed a diverse range of anterior palatal mucosal thickness in the referral patients (0.5 to 6.34 mm). Hence, an approximate estimation of mucosal thickness at the desired area (eg, bone sounding, CBCT data) would be helpful in choosing a proper miniscrew and insertion site. It is important to keep in mind that the area with a thick cortex may accompany thick mucosa as well (Haghanifar S, Poorsattar Bejeh Mir A, unpublished data, 2014). Choosing a miniscrew with a short transmucosal part may accelerate surrounding soft tissue inflammation, which may threaten miniscrew stability. On the other hand, an excessive lever arm, as long as 6 mm, would confer damaging moment forces with increased stresses and consequent reduced stability.12,23 The best balanced parts in terms of mucosal thickness and cortical height were selected from the test patient to ensure adequate cortical thickness, satisfactory overlying mucosa, and an adequate distance from both the incisive canal and midpalatal suture to prevent unintentional damage. In addition, it has been advocated that diet may influence bone quality as related to the transmitted masticatory forces.29 For instance, in northern Iran, rice and
bread are main constituents of the daily diet regimen. Hence, the optimal palatal insertion site should be decided individually. Accordingly, a CBCT evaluation is recommended prior to insertion of an MSI, which may provide valuable data regarding cortical bone thickness, mucosal thickness, and bone density.30–32 The miniscrew was tracked from the head with a 2-N horizontal force. Applied orthodontic forces range from 30 to 500 gf for various purposes, although Crismani et al suggested that 2 N is the maximum safe limit for immediate loading of a miniscrew from its biologic aspect.33
Cancellous Bone Measurements
The lowest observed strain values in cancellous bone were related to 90-degree models in both the osteoporotic and normal bone models. More concentrated stress was observed in the lower thread plateau of reciprocal models deep in the cancellous bone. This was probably due to greater displacement of the miniscrew and bone in the reciprocal models. Typically, the cortical layer is the main focus of measurements in FEA studies. In the current research, all measurements were calculated for cancellous bone as well. Previously, Suzuki et al concluded that cancellous bone is not a significant determinant in bone stresses; nevertheless, histologic findings by Woods et al showed that the most reliable and predictable osseointegration would occur in the cancellous apical area.11,34 Hence, the neglected role of cancellous bone in long-term stability should be taken into account along with the crucial role of the cortical bone in maintaining primary stability of miniscrews.
Osteoporotic vs Normal Bone
Lower bone density and cortical thickness is frequently observed in adolescents (maturing group) and elderly patients (osteoporotic group).34,16 A lower success rate and lower primary stability have been reported for low-density bone in comparison to normal bone.16 Interestingly, the anterior maxillary palate is among the least dense locations of the maxillofacial skeleton, with an approximate density of 1.65 g/cm3.27 An inclined miniscrew traverses a greater distance through this layer; hence, as suggested by Wilmes et al, angulated insertion of miniscrews may be of benefit, especially when bone quality is low in terms of density and cortical thickness.8 Previous studies extensively investigated the role of cortical thickness in bone stress, though the effect of low bone quality on immediately loaded angulated miniscrew strain has not been clearly investigated.35,36 Hence, the authors opted to use the same cortical thickness in all bone models, with the main focus on bone density as the model resembling younger and The International Journal of Oral & Maxillofacial Implants e7
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older ages rather than adulthood with thick, mature, and higher-quality bone. In the osteoporotic model, maximum bone deflection was higher than in the normal model. This outcome is in concordance with Xiao et al, who conducted an FEA and reported better stress distribution and lower bone displacement of normal bone than osteoporotic bone.16 Values of normal bone indicated lower strains, similar to Kurniawarn et al, who speculated that strain value has a reverse relation with bone density.22 Considering yield strain of bone, Kurniawan et al recommended that a higher degree of osseointegration is needed for lower quality bone to be considered safe.22
Limitations
In the present study, the bone was assumed to be a linearly elastic, homogenous, and isotropic material. Stress levels were far below the yield strength of the bone; therefore, assuming the bone as a ductile material in this study material is justified. Moreover, the anterior palate has the least anisotropy in the maxilla with negligible anisotropy; hence, it was assumed as an isotropic material.29 The micro-CT–based threedimensional finite element analysis study by Limbert et al revealed that even if trabeculation is modeled in detail, the homeostatic pattern of strain levels would be maintained.37 Thereby, the main assumptions of response behavior of bone as a linearly elastic, homogenous, and isotropic material, although not realistic, still are acceptable in the finite element analyses and modeling of the present study.38 Moreover, the authors designed the miniscrew with given specifications according to the patient’s anatomical data, which is not commercially available. In addition, insertion torque was not assessed and was not included in the final interpretation of the proper angulation of the miniscrew. Moreover, the palate was considered as a flat bone block, although it has a curvature beginning from the posterior incisive canal wall to the posterior nasal spine.32
Suggestions for Future Investigation
In vitro maximum insertion and removal torque assessment of various inclined miniscrews including reciprocals, preferably in fresh human maxillary cadavers, and comparison of partially osseointegrated inclined miniscrews with their reciprocals in terms of miniscrew peripheral bone stress and strain are suggested for future investigations.
CONCLUSIONS Within the limitations of the study, the following outcomes can be concluded: 1. Regardless of insertion inclination angle, maximum observed von Mises stresses were less than the yield strength limits of cancellous bone, cortical bone, and titanium alloy miniscrews. These findings indicate that a titanium miniscrew and palatal bone could safely resist a horizontal orthodontic force as an anchorage unit. 2. Numerical analyses showed that the cortical layer absorbs most of the stresses during traction force loading, and little is transmitted to the cancellous layer. 3. The comparison of von Mises stress and strain in the cortical layer showed that insertion angulation of 30 degrees offers the lowest transmitted stress and strain in both osteoporotic and normal bone. 4. The comparison of microstrain in the cancellous layer showed that an insertion angulation of 30 degrees offers the lowest transmitted strain in both osteoporotic and normal bone. 5. The comparison of deflection values showed that normal bone exhibits lower displacement than the osteoporotic bone.
ACKNOWLEDGMENTS The authors thank Jaber Mahdinejad Gorji, MSc in mechanical engineering, and Prof Stig Hansson, PhD in biomechanics, for their valuable work with numerical analysis and help during the progress of the project. The authors also appreciate the scientific comments by Dr Shiva Khatami, Department of Orthodontics, College of Dental Medicine, Nova Southeastern University. The authors reported no conflicts of interest related to this study.
REFERENCES 1. Kanomi R. Mini-implant for orthodontic anchorage. J Clin Orthod 1997;31:763–767. 2. Heymann GC, Tulloch JF. Implantable devices as orthodontic anchorage: A review of current treatment modalities. J Esthet Restor Dent 2006;18:68–79. 3. Herman R, Cope JB. Miniscrew implants: IMTEC mini Ortho Implants. Semin Orthod 2005;11:32–39. 4. Tsui WK, Chua HD, Cheung LK. Bone anchor systems for orthodontic applications: A systematic review. Int J Oral Maxillofac Surg 2012;41:1421–1438. 5. Nanda R, Kuhlberg A, Uribe F. Biomechanic basis of extraction space closure. In: Nanda R (ed). Biomechanics and Esthetic Strategies in Clinical Orthodontics, ed 1. St Louis: Elsevier Saunders, 2005:194–210.
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6. Lombardo L, Gracco A, Zampini F, Stefanoni F, Mollica F. Optimal palatal configuration for miniscrew applications. Angle Orthod 2010;80:145–152. 7. Watanabe H, Deguchi T, Hasegawa M, Ito M, Kim S, Takano-Yamamoto T. Orthodontic miniscrew failure rate and root proximity, insertion angle, bone contact length, and bone density. Orthod Craniofac Res 2013;16:44–55. 8. Wilmes B, Su YY, Drescher D. Insertion angle impact on primary stability of orthodontic mini-implants. Angle Orthod 2008;78:1065–1070. 9. Jasmine MI, Yezdani AA, Tajir F, Venu RM. Analysis of stress in bone and microimplants during en-masse retraction of maxillary and mandibular anterior teeth with different insertion angulations: A 3-dimensional finite element analysis study. Am J Orthod Dentofacial Orthop 2012;141:71–80. 10. Woodall N, Tadepalli SC, Qian F, Grosland NM, Marshall SD, Southard TE. Effect of miniscrew angulation on anchorage resistance. Am J Orthod Dentofacial Orthop 2011;139:e147–e152. 11. Suzuki A, Masuda T, Takahashi I, Deguchi T, Suzuki O, Takano-Yamamoto T. Changes in stress distribution of orthodontic miniscrews and surrounding bone evaluated by 3-dimensional finite element analysis. Am J Orthod Dentofacial Orthop 2011;140:e273–e280. 12. Lin TS, Tsai FD, Chen CH, Lin LW. Factorial analysis of variables affecting bone stress adjacent to the orthodontic anchorage mini-implant with finite element analysis. Am J Orthod Dentofacial Orthop 2013;143:182–189. 13. Miyawaki S, Koyama I, Inoue M, Mishima K, Sugahara T, TakanoYamamoto T. Factors associated with the stability of titanium screws placed in the posterior region for orthodontic anchorage. Am J Orthod Dentofacial Orthop 2003;124:373–378. 14. El-Beialy AR, Abou-El-Ezz AM, Attia KH, El-Bialy AM, Mostafa YA. Loss of anchorage of miniscrews: A 3-dimensional assessment. Am J Orthod Dentofacial Orthop 2009;136:700–707. 15. Ammar HH, Ngan P, Crout RJ, Mucino VH, Mukdadi OM. Threedimensional modeling and finite element analysis in treatment planning for orthodontic tooth movement. Am J Orthod Dentofacial Orthop 2011;139:e59–e71. 16. Xiao JR, Li YF, Guan SM, Song L, Xu LX, Kong L. The biomechanical analysis of simulating implants in function under osteoporotic jawbone by comparing cylindrical, apical tapered, neck tapered, and expandable type implants: A 3-dimensional finite element analysis. J Oral Maxillofac Surg 2011;69:e273–e281. 17. Chou HY, Müftü S, Bozkaya D. Combined effects of implant insertion depth and alveolar bone quality on periimplant bone strain induced by a wide-diameter, short implant and a narrow-diameter, long implant. J Prosthet Dent 2010;104:293–300. 18. Miyamoto I, Tsuboi Y, Wada E, Suwa H, Iizuka T. Influence of cortical bone thickness and implant length on implant stability at the time of surgery—Clinical, prospective, biomechanical, and imaging study. Bone 2005;37:776–780. 19. Watanabe F, Hata Y, Komatsu S, Ramos TC, Fukuda H. Finite element analysis of the influence of implant inclination, loading position, and load direction on stress distribution. Odontology 2003;91:31–36. 20. Chen YJ, Chang HH, Lin HY, Lai EH, Hung HC, Yao CC. Stability of miniplates and miniscrews used for orthodontic anchorage: Experience with 492 temporary anchorage devices. Clin Oral Implants Res 2008;19:1188–1196. 21. Hansson S, Werke M. The implant thread as a retention element in cortical bone: The effect of thread size and thread profile: A finite element study. J Biomech 2003;36:1247–1258.
22. Kurniawan D, Nor FM, Lee HY, Lim JY. Finite element analysis of bone-implant biomechanics: Refinement through featuring various osseointegration conditions. Int J Oral Maxillofac Surg 2012;41:1090–1096. 23. Petrey JS, Saunders MM, Kluemper G, Cunningham LL, Beeman CS. Temporary anchorage device insertion variables: Effects on retention. Angle Orthod 2010;80:634–641. 24. Patel PS, Shepherd DE, Hukins DW. The effect of screw insertion angle and thread type on the pullout strength of bone screws in normal and osteoporotic cancellous bone models. Med Eng Phys 2010;32:822–828. 25. Noble J, Karaiskos NE, Hassard TH, Hechter FJ, Wiltshire WA. Stress on bone from placement and removal of orthodontic miniscrews at different angulations. J Clin Orthod 2009;43:332–334. 26. Huang HL, Hsu JT, Fuh LJ, Tu MG, Ko CC, Shen YW. Bone stress and interfacial sliding analysis of implant designs on an immediately loaded maxillary implant: A non-linear finite element study. J Dent 2008;36:409–417. 27. Peterson J, Wang Q, Dechow PC. Material properties of the dentate maxilla. Anat Rec A Discov Mol Cell Evol Biol 2006;288:962–972. 28. Motoyoshi M, Yoshida T, Ono A, Shimizu N. Effect of cortical bone thickness and implant placement torque on stability of orthodontic mini-implants. Int J Oral Maxillofac Implants 2007;22:779–784. 29. Shimizu Y, Ishida T, Hosomichi J, Kaneko S, Hatano K, Ono T. Soft diet causes greater alveolar osteopenia in mandible than in the maxilla. Arch Oral Biol 2013;58:907–911. 30. Ryu JH, Park JH, Thu TVT, Bayome M, Kim Y, Kook Y. Palatal bone thickness compared with cone-beam computed tomography in adolescents and adults for mini-implant placement. Am J Orthod Dentofacial Orthop 2012;142:207–212. 31. Park HS, Lee YJ, Jeong SH, Kwon TG. Density of the alveolar and basal bones of the maxilla and mandible. Am J Orthod Dentofacial Orthop 2008;133:30–37. 32. Farnsworth D, Rossouw PE, Ceen RF, Buschang PH. Cortical bone thickness at common miniscrew implant placement sites. Am J Orthod Dentofacial Orthop 2011;139:495–503. 33. Crismani AG, Bertl MH, Celar AG, Bantleon HP, Burstone CJ. Miniscrews in orthodontic treatment: Review and analysis of published clinical trials. Am J Orthod Dentofacial Orthop 2010;137:108–113. 34. Woods PW, Buschang PH, Owens SE, Rossouw PE, Opperman LA. The effect of force, timing, and location on bone-to-implant contact of miniscrew implants. Eur J Orthod 2009;31:232–240. 35. Motoyoshi M, Inaba M, Ono A, Ueno S, Shimizu N. The effect of cortical bone thickness on the stability of orthodontic mini-implants and on the stress distribution in surrounding bone. Int J Oral Maxillofac Surg 2009;38:13–18. 36. Okumura N, Stegaroiu R, Kitamura E, Kurokawa K, Nomura SH. Influence of maxillary cortical bone thickness, implant design and implant diameter on stress around implants: A three-dimensional finite element analysis. J Prosthodontic Res 2010;54:133–142. 37. Limbert G, van Lierde C, Muraru OL, et al. Trabecular bone strains around a dental implant and associated micromotions—A microCT-based three-dimensional finite element study. J Biomech 2010:43:1251–1261. 38. Schwartz-Dabney CL, Dechow PC. Variations in cortical material properties throughout the human dentate mandible. Am J Phys Anthropol 2003;120:252–277.
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S
ince 1997 when Kanomi reported the first use of miniscrew implants (MSI) in orthodontics, they have gained increasing popularity as a reliable temporary anchorage device (TAD) providing absolute anchorage for tooth movements applying various biomechanical forces.1 Their small size, low cost, decreased need for patient compliance, shorter overall chairside time, enhanced anchorage with lower anchorage loss, ability for immediate loading after insertion, insertion via minor surgery, and ability to provide an opportunity for the very special cases that were only surgically treatable at one time make them a promising choice in orthodontics.2
1Researcher,
Dental Materials Research Center, Dentistry School, Babol University of Medical Science, Babol, Iran. 2 Assistant Professor, Department of Orthodontics, Dentistry School, Babol University of Medical Science, Babol, Iran. 3 Private Practice of Orthodontics, Montreal, Quebec, Canada. Correspondence to: Dr Arash Poorsattar Bejeh Mir, Dental Materials Research Center, Dentistry School, Babol University of Medical Science, Ganj Afrooz Square, Babol, Iran. Fax: +98-151-3216383. Email: [email protected] ©2015 by Quintessence Publishing Co Inc.
Orthodontic mini-implants have exhibited a lower success rate when compared to prosthodontic implants, likely due to their smaller size and contact surface. Moreover, compared to palatal implants with success rates of 74% to 93%, miniscrews have a higher failure rate (as high as 40%), although it should be noted that this higher failure rate should be weighed against the increased probability of interfering with growth of the midpalatal suture, a longer healing period, and more invasive surgical procedure for inserting and removing palatal implants.3,4 Anchorage enforcement and maintenance are more important in the maxilla, especially in patients with Class II, division 1 malocclusion for retraction of the maxillary incisors because of the greater root surface of maxillary anterior teeth, need for their bodily movement, and less dense cancellous bone in the maxilla.5 More specifically, the anterior palatal region should be regarded as an exceptional part of the maxilla, considering the absence of tooth and root proximity and lack of large nerves and arteries; moreover, one should note the presence of the midpalatal suture and its growth, lower density and cortical thickness, and greater mucosal thickness when comparing the anterior paramedian maxillary palate with interradicular maxillary sites.6 The International Journal of Oral & Maxillofacial Implants e1
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assumed the miniscrew as a material fully bonded to the bone. The intent of this numeric analytic study was to determine whether the insertion angle of an orthodontic miniscrew in relation to the bone surface (ie, miniscrews that are not osseointegrated) and bone quality contribute to the periminiscrew bone stress when the miniscrew is loaded immediately after insertion.
MATERIALS AND METHODS Three-Dimensional Model Design Fig 1 Three-dimensional (3D) meshes of the miniscrew and bone block models.
Table 1 Miniscrew Design and Dimensions Specification
Dimension
Miniscrew threaded length
8 mm
Bracket-head length
0.8 mm
Bracket slot
0.022 × 0.025 in
Transgingival length
2.2 mm
Thread design
Trapezoidal
Thread pitch
0.5 mm
Thread width
0.1 mm
Thread height
0.2 mm
External diameter
1.6 mm
The main problem with miniscrews as TADs is the failure rate. Higher internal stress could increase bone damage and resorption at the bone-implant surface, threatening miniscrew stability, which consequently may lead to miniscrew loosening and failure.7,8 Inclined insertion of miniscrews has been proposed mainly to avoid adjacent root damage and to provide greater retention by means of the longer traversed length through the cortical layer, which should be weighed against the effects of an increased lever arm and the risk of slippage over the cortical layer during insertion.7,8 To date, there are some numerical analyses of stress around angulated miniscrews with conflicting data. There exist some claims that “tent pegging” of a miniscrew by inclining the miniscrew away from the direction of applied force may have some geometric and biomechanical advantages. Some authors have advocated angulated miniscrews, and some have suggested the use of vertically placed miniscrews in terms of lowering von Mises stresses.9–12 However, results by some authors showed that angulation does not significantly contribute to the success rate.7,10,13,14 The main point is that all previous finite element analyses (FEAs)
A segment of human maxillary palate was modeled, which was constructed of a 1.6-mm–thick upper cortical layer and lower attached cancellous bone covered with 2.2-mm–thick mucosa. Data were obtained from the cone beam computed tomography (CBCT) scan of a healthy Iranian male patient aged 22 years; the CBCT image was located 8 mm posterior to the incisive canal and 3 mm left of the midpalatal suture. The miniscrew was first modeled in AutoCAD software (Autodesk) and was inserted in the bone through a prespecified hole with various insertion angulations of 30, 45, 55, 70, and 90 degrees, and their respective reciprocal angles of 110, 125, 135, and 150 degrees with regard to the bone surface (Fig 1). The final mesh for each model was dissolved using finite element analysis software (ANSYS version 14) for comparative evaluations. Specifications of the miniscrew are displayed and presented in Table 1.
Elements and Nodes
The miniscrew and its 2-mm circular surrounding bone from the surface of the miniscrew (defined as the region of interest [ROI]) were meshed with a 10-node tetrahedron element (ie, three degrees of freedom) as permitted by the geometry of the miniscrew-bone interdigitation. The remaining bone was meshed using 20-node hexahedron element. A convergence test with mesh refinement was performed to reassure the accuracy of the model. Elements of the ROI were reduced so that the maximum obtained von Mises stresses for cortical and cancellous bone of two consecutive sets were changed by less than 7% (tolerance rate). The final size of the element was approximately 150 μm. The total number of nodes and elements ranged from 149,684 to 189,182 and 98,095 to 125,387, respectively, based on insertion angulation (Table 2).
Interface Condition and Loads
The miniscrew-bone interface was modeled using a frictional contact element (CONTA174 and TARGE170) with a frictional coefficient of 0.3.15 All remaining nodes including the cortical and cancellous contact surface were constrained in all directions with no
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Poorsattar Bejeh Mir et al
assumed movement. A force of 2 N was applied on the most peripheral node of the bracket head of the miniscrew parallel to the bone surface directed from the left side to the right side of the bone block.
Table 2 Number of Nodes and Elements Used for Each Model of Insertion Angulation Angle (degrees)
Elements
Nodes
125,387
189,182
45
99,157
151,352
55
98,453
150,242
30
Material Properties
All materials used were considered as linearly elastic, homogenous, and isotropic. Material properties were entered into the software based on the existing literature (Table 3). To simulate osteoporotic bone, Young’s moduli of cortical and cancellous layers were reduced 33% and 66%, respectively.9,15,16
Output Variables
Peak von Mises stresses were reported for cortical and cancellous layers and the miniscrew separately to compare the maximum induced values for each model. Maximum elastic strain (εmax), which is indicative of collective normal and shear strain at a given point, was calculated and reported mainly to compare the inevitable produced strains under normal and osteoporotic conditions.17 Maximum deflection (displacement) was also calculated and reported for both the bone and the miniscrew. Nodes on the peripheral cortical bone edge were selected in a 30-degree circumferential-section manner starting from the point of force application to the 180-degree point, and corresponding maximum von Mises stresses were reported (ie, seven nodes were selected for each model). The remaining half of the circumferential section was eliminated due to its similarity. Outputs displayed in color-scale figures ranged from blue to red. Red indicated higher stress, and blue indicated lower stress. The engineering safety factor was calculated by dividing the reported strength of the cancellous bone, cortical bone, and miniscrew with 2,133, and 880 values, respectively, by the maximum reported von Mises stress of each model to compare the safety magnitude of produced stress levels in the bone and miniscrew.15
RESULTS Peak equivalent von Mises stress, maximum elastic strain, and deflection values are presented in Tables 4 and 5. Stress and strain values were remarkably lower in cancellous bone compared to the cortical bone. Higher von Mises stresses and deflection occurred on the miniscrew in comparison to the bone. Most stress and strain occurred at the compression side in the cortical bone (Fig 2). The least displacement occurred in the bone adjacent to the miniscrew apex, while the bracket head of the miniscrew sustained the highest deflection, and the miniscrew apex displayed the lowest deflection.
70
98,095
149,684
90
105,444
154,366
110
98,095
149,684
125
98,453
150,242
135
99,157
151,352
150
125,387
189,182
Table 3 Properties of Materials Used in Finite Element Model Material Miniscrew (Ti-6Al-4V) Cortical bone (normal) Cortical bone (osteoporotic) Cancellous bone (normal) Cancellous bone (osteoporotic)
Young’s modulus (MPa)
Poisson’s ratio
114,000
0.34
13,700
0.30
917
0.30
1,600
0.20
540
0.20
Insertion Angulations
Models with angulations toward the force direction exhibited lower stress than their reciprocals, which were angulated away from the direction of the force (see Tables 4 and 5). Overall, 30-degree models exhibited the lowest von Mises stress and strain values related to the cortical bone layer and miniscrews of both normal and osteoporotic models. Meanwhile, 90-degree models displayed the lowest strain values in the osteoporotic and normal cancellous bone. Minimum bone deflection and minimum miniscrew von Mises stress and deflection values were related to the model of 30-degree insertion angulation in both normal and osteoporotic models. In all models, the compression side of the cortical bone exhibited the highest magnitude of von Mises stress concentrated at the corresponding bone adjacent to the thread fillet of the three uppermost threads. Cancellous bone in 30- to 70-degree models revealed even distribution of stress and strain in the compression and tension sides, while in 90- to 150-degree models, von Mises stresses appeared higher in magnitude over a larger area on the tension side (Fig 3). The latter models also displayed more concentrated cancellous bone stresses near the fillet of lower engaged threads. The International Journal of Oral & Maxillofacial Implants e3
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Poorsattar Bejeh Mir et al
Table 4 Maximum Stress, Strain, and Deflection Values Induced at Various Insertion Angles for Normal Bone Insertion angle (degrees)
Cortical bone
Cancellous bone
σvm (MPa)
εmax (μm/μm)
σvm (MPa)
30
4.40
321
0.30
193
45
5.21
380
0.39
55
5.99
437
0.38
Whole bone
εmax (μm/μm) Deflection (μm)
Miniscrew σvm (MPa)
Deflection (μm)
0.034
8.62
0.76
248
0.057
12.06
0.96
241
0.068
14.33
1.89 1.53
70
10.28
750
0.41
257
0.086
19.28
90
11.07
701
0.31
182
0.088
23.55
1.79
110
13.58
991
0.34
216
0.077
22.36
2.36 2.44
125
8.67
633
0.29
185
0.070
23.68
135
11.61
848
0.50
313
0.120
21.55
2.67
150
9.55
697
0.29
185
0.061
17.61
3.19
σvm = equivalent von Mises stress; εmax = maximum elastic strain (data should be read at E−006 [× 10 −6]).
Table 5 Maximum Stress, Strain, and Deflection Values Induced at Various Insertion Angles for Osteoporotic Bone Insertion angle (degrees)
Cortical bone
Cancellous bone
Whole bone
εmax (μm/μm) Deflection (μm)
Miniscrew
σvm (MPa)
εmax (μm/μm)
σvm (MPa)
30
3.99
435
0.19
360
0.061
σvm (MPa) 9.25
0.88
45
4.71
513
0.24
457
0.109
12.97
1.11
Deflection (μm)
55
5.99
613
0.38
397
0.122
14.33
1.41
70
10.60
1,155
0.28
528
0.150
20.28
1.89
90
9.60
946
0.19
338
0.142
24.05
2.20
110
10.60
1,115
0.21
395
0.194
23.01
2.85
125
7.20
758
0.22
413
0.163
26.76
2.89
135
9.30
1,013
0.29
397
0.105
22.63
3.10
150
7.65
833
0.20
378
0.103
18.46
3.75
σvm = equivalent von Mises stress; εmax = maximum elastic strain (data should be read at E−006 [×
Fig 2 Strain in the cortical bone model of the (top) 30-, (middle) 90-, and (bottom) 150-degree models for respective upper, middle, and lower sets.
10 −6]).
Fig 3 Stress distribution pattern in cancellous bone for the (top row: left to right) 30-, 70-, (bottom row: left to right) 90-, 110-, and 150-degree models.
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Fig 4 Stress distribution patterns for miniscrews presented for (top row: left to right) 30-, 70-, 90-, (bottom row: left to right) 110- and 150-degree models.
1
18
2
3
4
16 Bone Miniscrew
14 12
1: Bracket head 2: Transmucosal shaft 3: Cortical part 4: Cancellous part
10 8 6 4 2
30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0
Maximum von Mises stress (Mpa)
Maximum von Mises stress (Mpa)
20
0 0 a
1
2 3 4 5 6 7 8 9 10 11 12 Distance along longitudinal axis (mm)
1
2
3
4 Bone Miniscrew 1: Bracket head 2: Transmucosal shaft 3: Cortical part 4: Cancellous part
0 b
1
2 3 4 5 6 7 8 9 10 11 12 Distance along longitudinal axis (mm)
Fig 5 Miniscrew and bone von Mises stress along the longitudinal axis on (a) compression side and (b) tension side.
Normal vs Osteoporotic Bone
Overall, higher stress, strain, and deflection occurred in osteoporotic bone when compared to the normal bone. Precisely, average peak von Mises stress and
10 9 8 7 6 5 4 3 2 1 0
Maximum von Mises stress (Mpa)
The tension side of the miniscrew sustained higher von Mises stresses over the recession of the first thread in 30- to 90-degree inclined models, while the stress was distributed more broadly on the compression side of the miniscrew, down to the second to third thread (Figs 4 and 5). As circumferential nodes’ data showed, a lower, steadier, and almost flat pattern of stress distribution in cortical bone was monitored for angulated miniscrews toward the force direction, and a comparably higher and peaked stress pattern in cortical bone was obvious for surrounding bone of miniscrews angulated away from the direction of force (Fig 6). The engineering safety factor equation revealed that 30-degree angulated insertion provided 30, 6, and 102 times less stress than the yield-strength limits of cortical bone, cancellous bone, and miniscrew, respectively (Table 6).
30 45 55 70 90 110 125 135 150
0
30
60
90
120
150
180
Circumferential 30-degree sections Fig 6 Stress distribution pattern of peripheral cortical bone shown for all models displayed for circumferential bone.
strain increased by 55% and 130.73% in the cortical bone and by 22% and 81% in the cancellous bone, respectively. Moreover, bone deflection increased by 69% when an osteoporotic condition was assumed. The International Journal of Oral & Maxillofacial Implants e5
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Table 6 Safety Factor Values for Various Insertion Angles* Insertion angle (degrees)
Cortical bone†
Cancellous bone‡
30
30.22
6.66
102.03
45
25.51
5.26
72.96
Miniscrew§
55
22.20
5.17
61.40
70
12.93
4.87
45.64
90
12.01
6.45
37.36
110
9.79
5.88
39.35
125
15.34
6.89
37.16
135
11.45
4.00
40.83
150
13.92
6.89
49.97
*Data are presented for normal bone. †σ /133 (σ ‡ § vm vm = equivalent von Mises stress). σvm/2. σvm/880.
DISCUSSION Angulation
The main purpose of the present study was to compare the effect of different insertion angulations of miniscrews in a simulated maxillary palate on periminiscrew bone stress by means of finite element analysis. Quantified data showed that the cortical layer absorbs almost all the transmitted stresses when the miniscrew is loaded horizontally, which is similar to the findings of previous researchers.7,12,18 The 30-degree angulation is the safest angulation in terms of safety engineering factor. It should be mentioned that the calculated engineering safety factors for the other angulations were also much greater than a safety factor of 1, ranging between 11.45 to 25.51 and 37.14 to 72.96 for the cortical bone and miniscrew, respectively. The lowest bone-equivalent von Mises stresses, strain, and deflection values in the cortical layer were observed for the 30-degree inclined miniscrew in both normal- and osteoporotic-imitated bone models; however, normal bone and osteoporotic bone did not show similar results in cancellous bone. Higher stresses would increase the probability of periminiscrew inflammation and release of inflammatory cytokines, which in turn might deteriorate the primary stability of the miniscrew.8 As shown in Fig 2, the 30-degree inclined model demonstrated a more uniform distribution of strain at the cortical edge when loaded as compared to 90and 150-degree inclined models. Moreover, an even pattern of equivalent von Mises stress in peripheral entangled bone in the cortical layer was observed in inclined models toward the applied force (see Fig 6).
It has been proved that more uniform distribution of strain prevents localized concentration of strain and mechanical stresses. This lowers the chance of loosening and failure of the miniscrew.19,20 Numerical analysis revealed similar data for the miniscrew in terms of von Mises stress and deflection for the aforementioned inclination. Overall, greater stress was located in the miniscrew’s transcortical part, which is in agreement with previous reports.9,15,16,21 The compression side of the bone sustained the highest von Mises stress in all models near the thread top. Meanwhile, von Mises stress was greater on the tension side of the miniscrew in inclined models toward the force in the first thread recession. This pattern was translocated to the compression side of the miniscrew and to the lower threads in inclined models opposing the direction of applied force. Described patterns are assumed to be related to the model of transmission of force to the miniscrew and its surrounding bone under horizontal force.15 Existing literature with assumptions of combined orthodontic horizontal force, assessment of diverse insertion angulations including their reciprocals, and immediate loading circumstances without osseointegration is inconsistent. Osseointegration would change the strain and stress values.22 The present results showed that inclined miniscrews toward the applied orthodontic force transfer would lower the stress and strain to the adjacent bone in comparison to their reciprocals, in opposition to the proposed “tent pegging” hypothesis. This finding is in agreement with Lin et al, who investigated von Mises stress with FEA comparing 60- and 120-degree inclined MSIs.12 In the present study models, 30-degree inclined-position MSIs induced less stress than 90-degree vertically positioned MSIs. Similarly, Suzuki et al reported lower stress in a 30-degree model (1.3 × 9.1-mm implant; F = 2 N horizontal; FEA, bonded surface of implant and bone).11 On the contrary, Woodall et al (1.5 × 11-mm implants with 6-mm intrabony length; F = 40 N horizontal; FEA, bonded surface of implant and bone) and Jasmine et al (1.3 × 8-mm implants; F = 2 N horizontal; FEA, bonded surface of implant and bone) concluded that MSIs should best be positioned vertically.9,10 Conflicting data also exist from various studies in which maximum insertion torque (MIT), pull-out test, and bone strain were evaluated during insertion and removal as indicators of stability comparing vertically inserted MSIs with angulated MSIs.8,23–25 Some sources of these diverse and contradictory results may be related to the following factors: (1) A bonded defined miniscrew-bone contact would result in lower stress than when a friction coefficient is entered in the model, which is due to the higher contact
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Poorsattar Bejeh Mir et al
surface in osseointegrated models.26 (2) Patterns of anisotropy differ in various parts of craniofacial skeleton. This neglected predictor is simply overlooked when the result of different parts of the maxilla and mandible are compared. For instance, the anterior maxillary palate is among the least anisotropic parts of the maxillofacial skeleton (E2/E3 = 0.85), while the mandible is more anisotropic; hence, the response may be different when force is applied in either direction of maximum stiffness, minimum stiffness, or perpendicular axes.27 (3) Orthodontic forces for posterior retraction of maxillary incisors are mainly parallel to the cortical plate of the palate. Hence, many results of vertical pullout tests, which were interpreted as primary stability, should not be generalized and interpreted for horizontally tracked miniscrew stability.
Entries of Model and FEA
Wide variations on the anterior palate cortical bone thickness (CBT) have been observed in adult patients referred to a private oromaxillofacial radiology center located in northern Iran, ranging from 0.5 to 2.7 mm (Haghanifar S, Poorsattar Bejeh Mir A, unpublished data, 2014). Cortical thickness has been reviewed as a crucial factor for MSI primary stability, and 1 mm is the minimum required thickness. The present study assumed that the CBT of the bone block was 1.6 mm according to the patient data, which met the minimum requirement.28 The extrabony part of the designed miniscrew consisted of a 0.8-mm bracket head and a 2.2 mm–long transmucosal part, which was obtained from the CBCT data. The authors observed a diverse range of anterior palatal mucosal thickness in the referral patients (0.5 to 6.34 mm). Hence, an approximate estimation of mucosal thickness at the desired area (eg, bone sounding, CBCT data) would be helpful in choosing a proper miniscrew and insertion site. It is important to keep in mind that the area with a thick cortex may accompany thick mucosa as well (Haghanifar S, Poorsattar Bejeh Mir A, unpublished data, 2014). Choosing a miniscrew with a short transmucosal part may accelerate surrounding soft tissue inflammation, which may threaten miniscrew stability. On the other hand, an excessive lever arm, as long as 6 mm, would confer damaging moment forces with increased stresses and consequent reduced stability.12,23 The best balanced parts in terms of mucosal thickness and cortical height were selected from the test patient to ensure adequate cortical thickness, satisfactory overlying mucosa, and an adequate distance from both the incisive canal and midpalatal suture to prevent unintentional damage. In addition, it has been advocated that diet may influence bone quality as related to the transmitted masticatory forces.29 For instance, in northern Iran, rice and
bread are main constituents of the daily diet regimen. Hence, the optimal palatal insertion site should be decided individually. Accordingly, a CBCT evaluation is recommended prior to insertion of an MSI, which may provide valuable data regarding cortical bone thickness, mucosal thickness, and bone density.30–32 The miniscrew was tracked from the head with a 2-N horizontal force. Applied orthodontic forces range from 30 to 500 gf for various purposes, although Crismani et al suggested that 2 N is the maximum safe limit for immediate loading of a miniscrew from its biologic aspect.33
Cancellous Bone Measurements
The lowest observed strain values in cancellous bone were related to 90-degree models in both the osteoporotic and normal bone models. More concentrated stress was observed in the lower thread plateau of reciprocal models deep in the cancellous bone. This was probably due to greater displacement of the miniscrew and bone in the reciprocal models. Typically, the cortical layer is the main focus of measurements in FEA studies. In the current research, all measurements were calculated for cancellous bone as well. Previously, Suzuki et al concluded that cancellous bone is not a significant determinant in bone stresses; nevertheless, histologic findings by Woods et al showed that the most reliable and predictable osseointegration would occur in the cancellous apical area.11,34 Hence, the neglected role of cancellous bone in long-term stability should be taken into account along with the crucial role of the cortical bone in maintaining primary stability of miniscrews.
Osteoporotic vs Normal Bone
Lower bone density and cortical thickness is frequently observed in adolescents (maturing group) and elderly patients (osteoporotic group).34,16 A lower success rate and lower primary stability have been reported for low-density bone in comparison to normal bone.16 Interestingly, the anterior maxillary palate is among the least dense locations of the maxillofacial skeleton, with an approximate density of 1.65 g/cm3.27 An inclined miniscrew traverses a greater distance through this layer; hence, as suggested by Wilmes et al, angulated insertion of miniscrews may be of benefit, especially when bone quality is low in terms of density and cortical thickness.8 Previous studies extensively investigated the role of cortical thickness in bone stress, though the effect of low bone quality on immediately loaded angulated miniscrew strain has not been clearly investigated.35,36 Hence, the authors opted to use the same cortical thickness in all bone models, with the main focus on bone density as the model resembling younger and The International Journal of Oral & Maxillofacial Implants e7
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Poorsattar Bejeh Mir et al
older ages rather than adulthood with thick, mature, and higher-quality bone. In the osteoporotic model, maximum bone deflection was higher than in the normal model. This outcome is in concordance with Xiao et al, who conducted an FEA and reported better stress distribution and lower bone displacement of normal bone than osteoporotic bone.16 Values of normal bone indicated lower strains, similar to Kurniawarn et al, who speculated that strain value has a reverse relation with bone density.22 Considering yield strain of bone, Kurniawan et al recommended that a higher degree of osseointegration is needed for lower quality bone to be considered safe.22
Limitations
In the present study, the bone was assumed to be a linearly elastic, homogenous, and isotropic material. Stress levels were far below the yield strength of the bone; therefore, assuming the bone as a ductile material in this study material is justified. Moreover, the anterior palate has the least anisotropy in the maxilla with negligible anisotropy; hence, it was assumed as an isotropic material.29 The micro-CT–based threedimensional finite element analysis study by Limbert et al revealed that even if trabeculation is modeled in detail, the homeostatic pattern of strain levels would be maintained.37 Thereby, the main assumptions of response behavior of bone as a linearly elastic, homogenous, and isotropic material, although not realistic, still are acceptable in the finite element analyses and modeling of the present study.38 Moreover, the authors designed the miniscrew with given specifications according to the patient’s anatomical data, which is not commercially available. In addition, insertion torque was not assessed and was not included in the final interpretation of the proper angulation of the miniscrew. Moreover, the palate was considered as a flat bone block, although it has a curvature beginning from the posterior incisive canal wall to the posterior nasal spine.32
Suggestions for Future Investigation
In vitro maximum insertion and removal torque assessment of various inclined miniscrews including reciprocals, preferably in fresh human maxillary cadavers, and comparison of partially osseointegrated inclined miniscrews with their reciprocals in terms of miniscrew peripheral bone stress and strain are suggested for future investigations.
CONCLUSIONS Within the limitations of the study, the following outcomes can be concluded: 1. Regardless of insertion inclination angle, maximum observed von Mises stresses were less than the yield strength limits of cancellous bone, cortical bone, and titanium alloy miniscrews. These findings indicate that a titanium miniscrew and palatal bone could safely resist a horizontal orthodontic force as an anchorage unit. 2. Numerical analyses showed that the cortical layer absorbs most of the stresses during traction force loading, and little is transmitted to the cancellous layer. 3. The comparison of von Mises stress and strain in the cortical layer showed that insertion angulation of 30 degrees offers the lowest transmitted stress and strain in both osteoporotic and normal bone. 4. The comparison of microstrain in the cancellous layer showed that an insertion angulation of 30 degrees offers the lowest transmitted strain in both osteoporotic and normal bone. 5. The comparison of deflection values showed that normal bone exhibits lower displacement than the osteoporotic bone.
ACKNOWLEDGMENTS The authors thank Jaber Mahdinejad Gorji, MSc in mechanical engineering, and Prof Stig Hansson, PhD in biomechanics, for their valuable work with numerical analysis and help during the progress of the project. The authors also appreciate the scientific comments by Dr Shiva Khatami, Department of Orthodontics, College of Dental Medicine, Nova Southeastern University. The authors reported no conflicts of interest related to this study.
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