THE KOREAN JOURNAL of ORTHODONTICS
Original Article pISSN 2234-7518 • eISSN 2005-372X http://dx.doi.org/10.4041/kjod.2016.46.3.155
Effect of labiolingual inclination of a maxillary central incisor and surrounding alveolar bone loss on periodontal stress: A finite element analysis Sung-Hwan Choi Young-Hoon Kim Kee-Joon Lee Chung-Ju Hwang
Department of Orthodontics, The Institute of Craniofacial Deformity, College of Dentistry, Yonsei University, Seoul, Korea
Objective: The aim of this study was to investigate whether labial tooth inclination and alveolar bone loss affect the moment per unit of force (M t/ F) in controlled tipping and consequent stresses on the periodontal ligament (PDL). Methods: Three-dimensional models (n = 20) of maxillary central incisors were created with different labial inclinations (5 o, 10o, 15o, and 20o) and different amounts of alveolar bone loss (0, 2, 4, and 6 mm). The Mt/F necessary for controlled tipping (Mt/Fcont) and the principal stresses on the PDL were calculated for each model separately in a finite element analysis. Results: As labial inclination increased, Mt/Fcont and the length of the moment arm decreased. In contrast, increased alveolar bone loss caused increases in Mt/Fcont and the length of the moment arm. When Mt/F was near Mt/Fcont, increases in Mt/F caused compressive stresses to move from a predominantly labial apical region to a palatal apical position, and tensile stresses in the labial area moved from a cervical position to a mid-root position. Although controlled tipping was applied to the incisors, increases in alveolar bone loss and labial tooth inclination caused increases in maximum compressive and tensile stresses at the root apices. Conclusions: Increases in alveolar bone loss and labial tooth inclination caused increases in stresses that might cause root resorption at the root apex, despite the application of controlled tipping to the incisors. [Korean J Orthod 2016;46(3):155-162] Key words: Labial tooth inclination, Alveolar bone loss, Controlled tipping, Periodontal stress
Received May 27, 2015; Revised October 12, 2015; Accepted October 21, 2015. Corresponding author: Chung–Ju Hwang. Professor, Department of Orthodontics, The Institute of Craniofacial Deformity, College of Dentistry, Yonsei University, 50-1 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea. Tel +82-2-2228-3106 e-mail [email protected] The authors report no commercial, proprietary, or financial interest in the products or companies described in this article.
© 2016 The Korean Association of Orthodontists. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
a large force or high stress on the PDL led to external apical root resorption.13-15 The aim of this study was to investigate how tooth inclination and bone loss affected the amount of moment per unit of force (Mt/F) needed for controlled tipping and consequent stresses on the PDL. Our null hypothesis was that the stress on the PDL imposed by controlled tipping applied to the incisor would not change with different tooth inclinations or with different amounts of alveolar bone loss.
With increasing numbers of adult patients seeking orthodontic care, it is becoming more common to treat patients with periodontal disease. Common charac teristics of dentition with periodontal disease include labial flaring of the maxillary anterior teeth, diastema, irregular interdental spacing, rotation, extrusion, tipping, and drifting.1 A recent study showed that labial flaring due to pathologic migration of the maxillary anterior teeth was a common complication of moderate-tosevere periodontitis and often motivated patients to seek periodontal and orthodontic therapy.2 Several studies have investigated teeth in the upright position to evaluate stress distributions and movement patterns in teeth with different amounts of alveolar bone loss.3-6 However, the maxillary incisors are typically labially inclined by about 60o toward the occlusal plane rather than positioned upright.7 Moreover, the incisors are often more labially inclined when pathologic tooth migration is present in patients with alveolar bone loss2,8; therefore, the force vector is rarely perpendicular to the long axis of the incisor. Often, to correct a flared incisor in a patient with hori zontal bone loss, the minimum moment per unit force (controlled tipping) is delivered with the expectation that the lowest stress is applied to the root apex.9 However, when orthodontic force is applied to a tooth with alveolar bone loss, the strain-stress distribution changes in the periodontal ligament (PDL).10 This is important, because the magnitude and direction of an orthodontic load determines whether the tissue reacts with bone formation, bone resorption, or iatrogenic external apical root resorption. 11,12 Recent studies that used threedimensional (3D) imaging technology suggested that
A
MATERIALS AND METHODS Construction of finite element models Stress on the PDL and tooth movements were inves tigated with a finite element analysis program (ANSYS ver. 12.1; Swanson Analysis System, Canonsburg, PA, USA). We created 3D models (n = 20) of maxillary central incisors with different labial inclinations and different amounts of alveolar bone loss (Figure 1). Tooth morphology was based on 3D scans of dental models produced from a sample survey of adults with normal occlusion in Japan (Model-i21D-400G; Nissin Dental Products, Kyoto, Japan). An orthodontic bracket was modeled based on the Micro-arch® (Tomy Co., Tokyo, Japan) structure. The PDL was 0.25 mm thick, and formed an even layer over the entire root surface.16,17 The alveolar bone was modeled 1 mm above the cementoenamel junction (CEJ), and followed the curvature of the CEJ in cases with normal bone levels. The axis of the normal incisor was inclined 60o from the occlusal plane.7 The long axes of the abnormal incisor models were inclined facially at 0o, 5o, 10o, 15o, and 20o relative to the axis of the normal incisor model (Figure 2). Alveolar
B
C B
13.2 mm M 24.2 mm
1 mm
D
CEJ Z
4.5 mm
60
Y Occlusal plane
Z Y P
Figure 1. The basic model of an incisor. A, Tooth length, 24.2 mm; tooth root, 13.2 mm; bracket position midpoint, 4.5 mm. The alveolar bone (dark blue) is situated 1 mm above the cementoenamel junction (CEJ). B, Normal inclination of an incisor 60° from the occlusal plane. C, A tetrahedral mesh covers the tooth surface and bracket. M, Mesial; D, distal; B, buccal; P, palatal. 156
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Choi et al • Controlled tipping, bone loss, and periodontal stress
A
Z 60
55
Y
Normal = 0
50
5
45
10
15
20
40 Occlusal plane
B
Z
Y Bone loss 0 mm
2 mm
4 mm
6 mm
Figure 2. Models of incisors with different inclinations and different amounts of alveolar bone loss. A total of 20 models were created (5 different inclinations and 4 levels of bone loss). A, Experimental incisor models with labial inclinations of 5o, 10o, 15o, and 20o. B, Models demonstrating 0, 2, 4, and 6 mm of alveolar bone loss. Table 1. Mechanical properties of each material Young’s modulus (MPa) Periodontal ligament Alveolar bone Teeth Stainless steel
0.05
Poisson ratio 0.49
2,000
0.30
20,000
0.30
200,000
0.30
bone loss (0, 2, 4, and 6 mm) was assumed to be equivalent in the buccolingual and mesiodistal direc tions. As a result, in a model with 2 mm of bone loss, alveolar bone extended to 3 mm above the CEJ, and so on. Each of the 20 models consisted of an incisor, a PDL, and alveolar bone. All structures were subdivided into elements and nodes with a 3D brick tetrahedral mesh. Mechanical properties of the materials All materials were assumed to be homogeneous, iso tropic, and linear-elastic. The properties of each material are listed in Table 1.18,19 Loading conditions and boundary conditions Each of the 20 models was subjected to 3 loads www.e-kjo.org
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applied to the crown as follows. 1. A retraction force (F) of 100 gf that caused the crown to move lingually. 2. A counter-tipping moment of force (Mt) that caused the crown to move in the labial direction. The Mt was created by applying coupled forces. The length of the moment arm was 1.5 mm. The Mt/F ratio varied from 0 to 10 (Figure 3A). 3. A counter-rotation moment (M r) resulted in a distolingual rotation designed to counteract the confounding moment generated by the asymmetric morphology of the incisor (Figure 3B).20 The Mr was created by applying a coupled force, and calculated such that the mesial and distal ends of the incisal edge moved equal distances in the same direction. The length of the moment arm was 3.6 mm. Because the retraction force and length of the moment arm were the same regardless of the experimental conditions, Mr was set to be constant to prevent undesirable tooth rotation under all conditions. For the boundary condition, all nodes at the base of the model (bone) were fixed in all directions to constrain free-body motion. Calculation for controlled tipping (Mt/Fcont) Controlled tipping (Mt/Fcont) was defined as the force that caused minimum movement of the root apex. The 157
Choi et al • Controlled tipping, bone loss, and periodontal stress
A
B 5
z
C
1
y
4 x
2 1 3 Z Y
Occlusal plane
Y X
=
2
2
( x) + ( y) + ( z)
2
Figure 3. Forces associated with the 3 different loads applied to the tooth models. A, The first load (1) was a retraction force (100 gf) applied parallel to the occlusal plane at the midpoint of the bracket. The second load was a coupled force (2, 3) that created a counter-tipping moment (Mt). B, The third load was a coupled force (4, 5) that created a rotation tipping (M )tipping was defined asdisplacement the force that caused minimum movement of the rootthe movement cont Controlled Controlled tipping Controlled (M was tipping defined )(M was defined the ) was force as defined the that force caused as the thatforce minimum caused thatminimum caused movement minimum movement of root of the root of the root t/Fcont)(M t/Fcont t/Fas cont moment (Mr).Controlled C, Calculation of thet/Fthree-dimensional (Δ) of the apex. apex. The totalThe displacement of The the apical root was sum of root the indisplacements 3 of dimensions, apex. apex. total The displacement apex. total displacement total of the displacement apical ofnode the root apical node ofthe the root was apical node the sum wasdisplacements node of thethe sum was displacements of thethe sum the in 3displacements dimensions, in 3 dimensions, in 3 dimensions,
total displacement of the apical root node was the Table 2. Mt/F ratios for controlled tipping (Mt/Fcont) of 20 20 20 20 , the center of rotation should as shown Figure 3C. According to theAccording definition given by Burstone , theloss center , the of center rotation ,and the of should center rotation of should rotation should asin shown as inshown Figure asin3C. shown Figure According in3C. to the 3C. definition According to the incisor definition given to theby definition given Burstone given Burstone by Burstone sum of the displacements in 3 dimensions, asFigure shown the for eachbybone amount each labial in Figure 3C. According to the definition given by inclination be at thebeapex when tipping iswhen simulated. A simple, two-dimensional conceptualization of at the be apex atcontrolled the when be apex controlled at the when apex controlled tipping controlled istipping simulated. istipping simulated. A simple, is simulated. Atwo-dimensional simple,Atwo-dimensional simple, conceptualization two-dimensional conceptualization conceptualization of of of Burstone,9 the center of rotation should be at the apex Labial inclination of the incisor Bone loss when controlled tipping simulated. AisΔy simple, twothat definition isisthat that the Δy displacement) the0°apex would 0apex with that definition definition is that that(anterior-posterior the definition that(anterior-posterior theisΔy that(anterior-posterior the Δy (anterior-posterior displacement) at the displacement) apex at be the would atbethe would 0controlled with apex becontrolled would 0 withbe controlled 0 with controlled (mm) atdisplacement) +5° +10° +15° +20° dimensional conceptualization of that definition is that 0with 8.5 8.0a counter-rotational 7.0 5.0 the tipping. tipping. In this study, though rotation was controlled acontrolled counter-rotational moment (Mr),6.0 the Δy (anterior-posterior displacement) at the apex In tipping. thiseven study, In tipping. this even study, In though this even study, rotation though even was rotation though controlled was rotation with was a counter-rotational controlled with with a counter-rotational moment (M moment moment r), the (M r), the (Mr), the 2 9.0 8.5 7.5 6.5 5.5 would be 0 with controlled tipping. In this study, even direction of the force caused an intrusion effect on the teeth due to the inclination. As ainclination. result, direction of the force direction the caused force ofanthe caused intrusion forceancaused intrusion effect an onintrusion effect the teeth on effect the due60° teeth toon the the due 60° teeth toinclination. thedue 60°to the As60° a the result, inclination. As the a result, As the a result, the though rotation wasdirection controlled with aofcounter-rotational 4 9.5 9.0 8.0 7.0 6.0 moment (M r), the direction of the force caused an 6 three-dimensionally. 11.0 9.0We defined 6.5the apex moved two-dimensionally (anterior-posterior) and We defined the8.0 3D apex both moved apex both moved two-dimensionally apexboth moved two-dimensionally both two-dimensionally (anterior-posterior) (anterior-posterior) (anterior-posterior) and three-dimensionally. and10.0 three-dimensionally. and three-dimensionally. Wethe defined 3DWe defined 3D the 3D intrusion effect on the teeth due to the 60o inclination. As a result, movement the apex moved both two-dimensionally (Δ) asmovement follows: movement (Δ) as follows: movement (Δ) as follows: (Δ) as follows: (anterior-posterior) and three-dimensionally. We defined maximum tensile stress) and the minimum value of the the 3D movement (Δ) as follows: third principal stress (S3, maximum compressive stress) were � ).recorded for each model and each M/F ratio. �(Δz) +(Δx) (Δy) (Δz) Δ = (�(Δx) (Δy) (Δy)� ).+ (Δz) Δ = �(� Δ =� �(+�+(Δy) (Δx) Δ =� �(+). (Δx)��).+ (Δz)
Thus, controlled tipping was defined as the smallest RESULTS possible Δ for a given bone level and tooth inclination. Thus, controlled Thus, controlled tipping Thus,defined controlled was tipping defined was tipping as defined the was smallest as defined the smallest possible as the asmallest possible Δgiven for a bone given possible Δ forlevel bone a given Δ and for level bone a given andlevel tooth bone andlevel toothand tooth Thus, controlled tipping was as the smallest possible Δ for tooth Because of the intrusive movement of the apex, the For each amount of labial inclination and alveolar bone smallest Δ was always > 0inclination. (Figure 3). The amount ofofofthe loss ofthe the we investigated /F for inclination. Because of Because the intrusive of Because the intrusive movement movement of the apex, movement of incisors, the theapex, smallest the thealways apex, Δ smallest wasthe always was>M always 0tΔ (Figure was always 03). (Figure > 03). (Figure 3). inclination. Because of theinclination. intrusive movement theintrusive apex, smallest Δofwas >Δ 0smallest (Figure 3). cont>ratios moment per unit of force (M t/F ratio) necessary for controlled tipping. We found that as labial inclination /Funit ratio) /F necessary ratio) necessary for ratio) controlled necessary for controlled tipping for controlled (M )(M was tipping was The amount The of amount moment Theunit of amount per moment unit of of per moment force (M of pertforce (M of tforce /F ratio) necessary fort(M tipping (Mcontrast, )tipping was The amount ofcont moment per of force (M t/F t/Fcont t/Fcont) t/Fcont) was controlled tipping (M t/F ) was calculated for each increased, M /Fcontrolled decreased. In increases in(M tunit t/Fcont cont model separately. alveolar bone loss caused increases in Mt/Fcont (Table 2). calculated calculated for eachcalculated model for each separately. model for each separately. model separately. calculated for each model separately. For the incisor with 6 mm of bone loss combined with Analysis of the stress distribution on the periodontal an inclination of 20o, the Mt/Fcont was 6.5, which was ligament lower than that of the normal tooth (Mt/Fcont, 8.5). Stress on the PDL was calculated in terms of principal Additionally, Figure 4 shows that as labial inclination stresses. The principal stresses were identified by increased, the length of the moment arm (the perpen Analysis Analysis of thedistribution stress Analysis of the distribution stress of the distribution stress on distribution periodontal on the periodontal onligament the periodontal ligamentthe ligament determining Analysis the planes at which the traction vector wasthe dicular distance between line of action of the force of the stress on the periodontal ligament purely normal with no shear component. In a 3D stress and the center of resistance) decreased. In contrast, an field, there are 3 principal stress components ranked in increase in alveolar bone loss caused increases in the onStress the PDL onStress was the PDL calculated oninwas the PDL calculated in terms was calculated of in principal terms of in principal terms stresses. of principal The stresses. principal The stresses. principal stresses Theidentified were principal stresses identified were stresses identified were identified Stress Among onStress the PDL was calculated terms principal stresses. Themoment principal stresses descending order. these principal stresses onofthe length of the arm. Thewere position of the center of PDL, the maximum by value ofby thedetermining first principal stress (S1, resistance associated with alveolar bone loss determining theby planes determining the at planes which the at the planes which traction at the which vector traction the was vector traction purely was vector normal purely was with normal purely no shear with normal component. no shear with conditions component. no In shear component. In In by determining the planes at which the traction vector was purely normal with no shear component. In
a 3Dfield, stress a there 3D field, stress athere 3D stress are there 3 principal field, are there 3 components principal stress are 3components principal stress components stress ranked components inranked descending inranked descending order. in descending Among order. these Among order. these Among these a 3D stress are 3field, principal stress ranked in descending order. Among these
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www.e-kjo.org stresses on principal stresses thethe PDL, on stresses the thePDL, maximum onvalue the the PDL, maximum ofmaximum the value first of principal the value first of(S1, principal the stress first (S1, principal stress maximum (S1, stress maximum tensile (S1, maximum tensile tensile http://dx.doi.org/10.4041/kjod.2016.46.3.155 principalprincipal stressesprincipal on the PDL, maximum ofvalue thethefirst principal stress maximum tensile stress) stress) the minimum and stress) the of minimum and value ofminimum value theprincipal third of value the principal third of (S3, the principal stress third (S3, principal stress maximum (S3, stress maximum compressive (S3,stress) maximum compressive stress) were stress) were stress) were stress) and the and minimum value thethe third stress maximum compressive werecompressive
Choi et al • Controlled tipping, bone loss, and periodontal stress
increased, a given M t/F imparted greater maximum tensile and compressive stresses on the PDL. Moreover, in teeth with greater alveolar bone loss, the stress changed more abruptly with changes in the Mt/F ratio. When the labial inclination of the incisor was increased without changing the amount of alveolar bone loss, the Mt/F ratio decreased for the lowest principal stress.
14 12 10
1.70E + 01
Maximum tensile stress
2
Principal stress (g/mm )
The length of the moment arm (mm)
was defined in reference to a previous study.5 For each inclination and simulated bone loss amount, we plotted the relationship between the Mt/F ratio and principal stresses on the PDL (Figure 5). As bone loss
8 6 Alveolar bone loss 0 mm 2 mm 4 mm 6 mm
4 2 0 0
5
10
15
7.00E + 00 2.00E + 00 .00E + 00
0 1 2 3 4 5 6 7 8 9 10
Mt/F ratio
.00E + 00
20 1.30E + 01
Labial inclination of a maxillary central incisor ( )
1.80E + 01
Figure 4. Changes in the length of the moment arm (the perpendicular distance between the line of action of the force and the center of resistance) according to changes in maxillary central incisor inclination and surrounding alveolar bone loss. A
1.20E + 01
Alveolar bone loss 0 mm 2 mm 4 mm 6 mm
Maximum compressive stress
Figure 5. Relationship between the M t /F ratio and principal stresses in tooth models with 20o of labial incli nation. The minimum principal stress levels are indicated by triangles.
B Labial
Palatal
Palatal
Labial
Palatal
Palatal
Maximum tensile stress
Mt/F = 4.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 6.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 5.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 7.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 6.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 8.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 7.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 9.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 8.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 10.0 Maximum compressive stress
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Figure 6. Incisor root stress distribution patterns under conditions with M t /F near M t/F cont (red area, maximum tensile stress; blue area, maximum compressive stress). A, A tooth model with no alveolar bone loss and an incisal inclination of 15 o ; controlled tipping occurs at M t/F = 6. B, A tooth model with 6 mm of alveolar bone loss and an incisal inclination of 15 o ; controlled tipping occurs at Mt/F = 8. 159
Choi et al • Controlled tipping, bone loss, and periodontal stress
The patterns of stress distributed over the root were examined under conditions with an M t/F value near that of Mt/Fcont (Figure 6). With increases in the Mt/F ratio near Mt/Fcont, compressive stresses dominant in the labial apical region moved to the palatal apical area (Mt/ F above Mt/Fcont). In contrast, tensile stresses dominant in the labial area (Mt/F below Mt/Fcont) moved from the cervical to the mid-root regions (Mt/F above Mt/Fcont). These patterns were similar under all experimental conditions.
DISCUSSION Previous studies analyzed upright incisors and forces applied perpendicular to the occlusal plane. 3,4,21,22 Moreover, many studies that investigated alveolar bone loss and stress distributions did not consider the facial inclination of teeth.3-5,23 The present study evaluated how tooth inclination and bone loss affected the M/ F ratio in controlled tipping and the resulting PDL stresses. We chose the maxillary central incisor because it typically undergoes the most detailed tooth movement, and carries a higher risk of external apical root resorption than all other teeth, except for the maxillary lateral incisor.24 Often, correction of a flared incisor with alveolar bone loss involves a combination of retraction and intrusion. A mere retraction of flared teeth would lead to deepening of the bite.25 In the present study, force was applied parallel to the occlusal plane without an intrusive vector. Adding an intrusive force would incline the direction of the net force; this result would be comparable to applying a horizontal force to a tooth with a greater inclination. Therefore, we did not apply an intrusive force in this study (Figure 3). Geramy 5 reported that alveolar bone loss caused the center of resistance to move toward the apex; however, its relative distance to the alveolar crest decreased at the same time. Figure 4 also shows that alveolar bone loss caused increases in the length of the moment arm. Siatkowski 26 reported that an increase of 38% was needed to obtain bodily movement when 5 mm of alveolar bone loss had occurred. Therefore, the applied force and moment magnitudes must be reduced proportionally to maintain physiologically tolerable movement, because reduced support of the PDL and alveolar bone causes changes in the center of resistance.5,27,28 The incisor was modeled at inclinations over an average range (0o to 20o), both with and without different levels of alveolar bone loss (0 to 6 mm). When controlled tipping was applied to the incisor, the maximum compressive stress migrated along the y-axis to the root apex, and the maximum tensile stress migrated
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from the cervical area to the middle of the root. This distribution of stress was consistent with the findings of Kanjanaouthai et al.20 They found that incisors with a high degree of inclination experienced more compressive stress concentrated at the apices than incisors that were more upright. Labial inclination resulted in an increased intrusive force component directed parallel to the long axis; that force enhanced compressive stress at the apex and tension in the PDL in the longitudinal direction (Figure 6). As a result, facial inclination of the incisor caused a concentration of compressive stress at the apex; thus, controlled tipping of an incisor with a corrective force may lead to increased root resorption. 24 This interpretation is consistent with findings reported in the literature, which suggested that increases in the angle between the central incisor and palatal plane were strongly correlated with increases in external apical root resorption.29 Furthermore, it was shown that the risk of external apical root resorption was enhanced by the movements of teeth with mature roots, extensive movement of the root, and intrusive mechanics.30 Previous studies showed that teeth with alveolar bone resorption experienced increased maximum tensile and compressive stresses relative to those found in teeth with normal bone heights.6 In the present study, increasing the bone loss in teeth without changing the incisal inclination caused increased root apex displacements and greater maximum compressive and tensile stresses. However, for each level of alveolar bone loss, these stresses could be reduced with controlled tipping versus uncontrolled tipping or root movements. This suggested that in patients with alveolar bone loss, an inadequate force system might cause radical root apex displacement and stress. External root resorption occurs when forces at the apex exceed the resistance and reparative ability of periapical tissues29; thus, applied force and moment magnitudes must be reduced proportionately to main tain physiologically tolerable movements without causing further damage to supporting structures.5 The present study had some limitations. First, we used principal stresses to evaluate stress distributions in the PDL. For the PDL, the 3 principal stresses are very approximate because of the low values of Young’s modulus, and because Poisson’s ratio approached 0.5, which represents that of water. Thus, at a certain node in the PDL, the 3 principal stresses were either compressive or tensile, with values approximating those found in nature. Second, the PDL was not constructed with a thickness that varied from the cervix to apex. In addition, alveolar bone loss was assumed to occur only in the horizontal direction, and the amounts were equivalent in the buccolingual and mesiodistal directions.
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Choi et al • Controlled tipping, bone loss, and periodontal stress
CONCLUSION When controlled tipping was applied to incisors, alveolar bone loss and labial tooth inclination caused increases in the maximum compressive and tensile stresses at the root apices. This finding suggested that an inadequate force system applied to facially inclined incisors might cause greater stress at the root apices and induce external apical root resorption in teeth with alveolar bone loss compared with teeth without bone loss.
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25. Melsen B. Adult orthodontics. Chichester, West Sussex: Blackwell Publishing; 2012. p. 212. 26. Siatkowski RE. Optimal orthodontic space closure in adult patients. Dent Clin North Am 1996;40:83773. 27. Tanne K, Nagataki T, Inoue Y, Sakuda M, Burstone CJ. Patterns of initial tooth displacements associated with various root lengths and alveolar bone heights. Am J Orthod Dentofacial Orthop 1991;100:66-71. 28. Sung SJ, Kim IT, Kook YA, Chun YS, Kim SH, Mo SS. Finite-element analysis of the shift in center of
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resistance of the maxillary dentition in relation to alveolar bone loss. Korean J Orthod 2009;39:27888. 29. Parker RJ, Harris EF. Directions of orthodontic tooth movements associated with external apical root resorption of the maxillary central incisor. Am J Orthod Dentofacial Orthop 1998;114:677-83. 30. Dermaut LR, De Munck A. Apical root resorption of upper incisors caused by intrusive tooth movement: a radiographic study. Am J Orthod Dentofacial Orthop 1986;90:321-6.
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Original Article pISSN 2234-7518 • eISSN 2005-372X http://dx.doi.org/10.4041/kjod.2016.46.3.155
Effect of labiolingual inclination of a maxillary central incisor and surrounding alveolar bone loss on periodontal stress: A finite element analysis Sung-Hwan Choi Young-Hoon Kim Kee-Joon Lee Chung-Ju Hwang
Department of Orthodontics, The Institute of Craniofacial Deformity, College of Dentistry, Yonsei University, Seoul, Korea
Objective: The aim of this study was to investigate whether labial tooth inclination and alveolar bone loss affect the moment per unit of force (M t/ F) in controlled tipping and consequent stresses on the periodontal ligament (PDL). Methods: Three-dimensional models (n = 20) of maxillary central incisors were created with different labial inclinations (5 o, 10o, 15o, and 20o) and different amounts of alveolar bone loss (0, 2, 4, and 6 mm). The Mt/F necessary for controlled tipping (Mt/Fcont) and the principal stresses on the PDL were calculated for each model separately in a finite element analysis. Results: As labial inclination increased, Mt/Fcont and the length of the moment arm decreased. In contrast, increased alveolar bone loss caused increases in Mt/Fcont and the length of the moment arm. When Mt/F was near Mt/Fcont, increases in Mt/F caused compressive stresses to move from a predominantly labial apical region to a palatal apical position, and tensile stresses in the labial area moved from a cervical position to a mid-root position. Although controlled tipping was applied to the incisors, increases in alveolar bone loss and labial tooth inclination caused increases in maximum compressive and tensile stresses at the root apices. Conclusions: Increases in alveolar bone loss and labial tooth inclination caused increases in stresses that might cause root resorption at the root apex, despite the application of controlled tipping to the incisors. [Korean J Orthod 2016;46(3):155-162] Key words: Labial tooth inclination, Alveolar bone loss, Controlled tipping, Periodontal stress
Received May 27, 2015; Revised October 12, 2015; Accepted October 21, 2015. Corresponding author: Chung–Ju Hwang. Professor, Department of Orthodontics, The Institute of Craniofacial Deformity, College of Dentistry, Yonsei University, 50-1 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea. Tel +82-2-2228-3106 e-mail [email protected] The authors report no commercial, proprietary, or financial interest in the products or companies described in this article.
© 2016 The Korean Association of Orthodontists. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
a large force or high stress on the PDL led to external apical root resorption.13-15 The aim of this study was to investigate how tooth inclination and bone loss affected the amount of moment per unit of force (Mt/F) needed for controlled tipping and consequent stresses on the PDL. Our null hypothesis was that the stress on the PDL imposed by controlled tipping applied to the incisor would not change with different tooth inclinations or with different amounts of alveolar bone loss.
With increasing numbers of adult patients seeking orthodontic care, it is becoming more common to treat patients with periodontal disease. Common charac teristics of dentition with periodontal disease include labial flaring of the maxillary anterior teeth, diastema, irregular interdental spacing, rotation, extrusion, tipping, and drifting.1 A recent study showed that labial flaring due to pathologic migration of the maxillary anterior teeth was a common complication of moderate-tosevere periodontitis and often motivated patients to seek periodontal and orthodontic therapy.2 Several studies have investigated teeth in the upright position to evaluate stress distributions and movement patterns in teeth with different amounts of alveolar bone loss.3-6 However, the maxillary incisors are typically labially inclined by about 60o toward the occlusal plane rather than positioned upright.7 Moreover, the incisors are often more labially inclined when pathologic tooth migration is present in patients with alveolar bone loss2,8; therefore, the force vector is rarely perpendicular to the long axis of the incisor. Often, to correct a flared incisor in a patient with hori zontal bone loss, the minimum moment per unit force (controlled tipping) is delivered with the expectation that the lowest stress is applied to the root apex.9 However, when orthodontic force is applied to a tooth with alveolar bone loss, the strain-stress distribution changes in the periodontal ligament (PDL).10 This is important, because the magnitude and direction of an orthodontic load determines whether the tissue reacts with bone formation, bone resorption, or iatrogenic external apical root resorption. 11,12 Recent studies that used threedimensional (3D) imaging technology suggested that
A
MATERIALS AND METHODS Construction of finite element models Stress on the PDL and tooth movements were inves tigated with a finite element analysis program (ANSYS ver. 12.1; Swanson Analysis System, Canonsburg, PA, USA). We created 3D models (n = 20) of maxillary central incisors with different labial inclinations and different amounts of alveolar bone loss (Figure 1). Tooth morphology was based on 3D scans of dental models produced from a sample survey of adults with normal occlusion in Japan (Model-i21D-400G; Nissin Dental Products, Kyoto, Japan). An orthodontic bracket was modeled based on the Micro-arch® (Tomy Co., Tokyo, Japan) structure. The PDL was 0.25 mm thick, and formed an even layer over the entire root surface.16,17 The alveolar bone was modeled 1 mm above the cementoenamel junction (CEJ), and followed the curvature of the CEJ in cases with normal bone levels. The axis of the normal incisor was inclined 60o from the occlusal plane.7 The long axes of the abnormal incisor models were inclined facially at 0o, 5o, 10o, 15o, and 20o relative to the axis of the normal incisor model (Figure 2). Alveolar
B
C B
13.2 mm M 24.2 mm
1 mm
D
CEJ Z
4.5 mm
60
Y Occlusal plane
Z Y P
Figure 1. The basic model of an incisor. A, Tooth length, 24.2 mm; tooth root, 13.2 mm; bracket position midpoint, 4.5 mm. The alveolar bone (dark blue) is situated 1 mm above the cementoenamel junction (CEJ). B, Normal inclination of an incisor 60° from the occlusal plane. C, A tetrahedral mesh covers the tooth surface and bracket. M, Mesial; D, distal; B, buccal; P, palatal. 156
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Choi et al • Controlled tipping, bone loss, and periodontal stress
A
Z 60
55
Y
Normal = 0
50
5
45
10
15
20
40 Occlusal plane
B
Z
Y Bone loss 0 mm
2 mm
4 mm
6 mm
Figure 2. Models of incisors with different inclinations and different amounts of alveolar bone loss. A total of 20 models were created (5 different inclinations and 4 levels of bone loss). A, Experimental incisor models with labial inclinations of 5o, 10o, 15o, and 20o. B, Models demonstrating 0, 2, 4, and 6 mm of alveolar bone loss. Table 1. Mechanical properties of each material Young’s modulus (MPa) Periodontal ligament Alveolar bone Teeth Stainless steel
0.05
Poisson ratio 0.49
2,000
0.30
20,000
0.30
200,000
0.30
bone loss (0, 2, 4, and 6 mm) was assumed to be equivalent in the buccolingual and mesiodistal direc tions. As a result, in a model with 2 mm of bone loss, alveolar bone extended to 3 mm above the CEJ, and so on. Each of the 20 models consisted of an incisor, a PDL, and alveolar bone. All structures were subdivided into elements and nodes with a 3D brick tetrahedral mesh. Mechanical properties of the materials All materials were assumed to be homogeneous, iso tropic, and linear-elastic. The properties of each material are listed in Table 1.18,19 Loading conditions and boundary conditions Each of the 20 models was subjected to 3 loads www.e-kjo.org
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applied to the crown as follows. 1. A retraction force (F) of 100 gf that caused the crown to move lingually. 2. A counter-tipping moment of force (Mt) that caused the crown to move in the labial direction. The Mt was created by applying coupled forces. The length of the moment arm was 1.5 mm. The Mt/F ratio varied from 0 to 10 (Figure 3A). 3. A counter-rotation moment (M r) resulted in a distolingual rotation designed to counteract the confounding moment generated by the asymmetric morphology of the incisor (Figure 3B).20 The Mr was created by applying a coupled force, and calculated such that the mesial and distal ends of the incisal edge moved equal distances in the same direction. The length of the moment arm was 3.6 mm. Because the retraction force and length of the moment arm were the same regardless of the experimental conditions, Mr was set to be constant to prevent undesirable tooth rotation under all conditions. For the boundary condition, all nodes at the base of the model (bone) were fixed in all directions to constrain free-body motion. Calculation for controlled tipping (Mt/Fcont) Controlled tipping (Mt/Fcont) was defined as the force that caused minimum movement of the root apex. The 157
Choi et al • Controlled tipping, bone loss, and periodontal stress
A
B 5
z
C
1
y
4 x
2 1 3 Z Y
Occlusal plane
Y X
=
2
2
( x) + ( y) + ( z)
2
Figure 3. Forces associated with the 3 different loads applied to the tooth models. A, The first load (1) was a retraction force (100 gf) applied parallel to the occlusal plane at the midpoint of the bracket. The second load was a coupled force (2, 3) that created a counter-tipping moment (Mt). B, The third load was a coupled force (4, 5) that created a rotation tipping (M )tipping was defined asdisplacement the force that caused minimum movement of the rootthe movement cont Controlled Controlled tipping Controlled (M was tipping defined )(M was defined the ) was force as defined the that force caused as the thatforce minimum caused thatminimum caused movement minimum movement of root of the root of the root t/Fcont)(M t/Fcont t/Fas cont moment (Mr).Controlled C, Calculation of thet/Fthree-dimensional (Δ) of the apex. apex. The totalThe displacement of The the apical root was sum of root the indisplacements 3 of dimensions, apex. apex. total The displacement apex. total displacement total of the displacement apical ofnode the root apical node ofthe the root was apical node the sum wasdisplacements node of thethe sum was displacements of thethe sum the in 3displacements dimensions, in 3 dimensions, in 3 dimensions,
total displacement of the apical root node was the Table 2. Mt/F ratios for controlled tipping (Mt/Fcont) of 20 20 20 20 , the center of rotation should as shown Figure 3C. According to theAccording definition given by Burstone , theloss center , the of center rotation ,and the of should center rotation of should rotation should asin shown as inshown Figure asin3C. shown Figure According in3C. to the 3C. definition According to the incisor definition given to theby definition given Burstone given Burstone by Burstone sum of the displacements in 3 dimensions, asFigure shown the for eachbybone amount each labial in Figure 3C. According to the definition given by inclination be at thebeapex when tipping iswhen simulated. A simple, two-dimensional conceptualization of at the be apex atcontrolled the when be apex controlled at the when apex controlled tipping controlled istipping simulated. istipping simulated. A simple, is simulated. Atwo-dimensional simple,Atwo-dimensional simple, conceptualization two-dimensional conceptualization conceptualization of of of Burstone,9 the center of rotation should be at the apex Labial inclination of the incisor Bone loss when controlled tipping simulated. AisΔy simple, twothat definition isisthat that the Δy displacement) the0°apex would 0apex with that definition definition is that that(anterior-posterior the definition that(anterior-posterior theisΔy that(anterior-posterior the Δy (anterior-posterior displacement) at the displacement) apex at be the would atbethe would 0controlled with apex becontrolled would 0 withbe controlled 0 with controlled (mm) atdisplacement) +5° +10° +15° +20° dimensional conceptualization of that definition is that 0with 8.5 8.0a counter-rotational 7.0 5.0 the tipping. tipping. In this study, though rotation was controlled acontrolled counter-rotational moment (Mr),6.0 the Δy (anterior-posterior displacement) at the apex In tipping. thiseven study, In tipping. this even study, In though this even study, rotation though even was rotation though controlled was rotation with was a counter-rotational controlled with with a counter-rotational moment (M moment moment r), the (M r), the (Mr), the 2 9.0 8.5 7.5 6.5 5.5 would be 0 with controlled tipping. In this study, even direction of the force caused an intrusion effect on the teeth due to the inclination. As ainclination. result, direction of the force direction the caused force ofanthe caused intrusion forceancaused intrusion effect an onintrusion effect the teeth on effect the due60° teeth toon the the due 60° teeth toinclination. thedue 60°to the As60° a the result, inclination. As the a result, As the a result, the though rotation wasdirection controlled with aofcounter-rotational 4 9.5 9.0 8.0 7.0 6.0 moment (M r), the direction of the force caused an 6 three-dimensionally. 11.0 9.0We defined 6.5the apex moved two-dimensionally (anterior-posterior) and We defined the8.0 3D apex both moved apex both moved two-dimensionally apexboth moved two-dimensionally both two-dimensionally (anterior-posterior) (anterior-posterior) (anterior-posterior) and three-dimensionally. and10.0 three-dimensionally. and three-dimensionally. Wethe defined 3DWe defined 3D the 3D intrusion effect on the teeth due to the 60o inclination. As a result, movement the apex moved both two-dimensionally (Δ) asmovement follows: movement (Δ) as follows: movement (Δ) as follows: (Δ) as follows: (anterior-posterior) and three-dimensionally. We defined maximum tensile stress) and the minimum value of the the 3D movement (Δ) as follows: third principal stress (S3, maximum compressive stress) were � ).recorded for each model and each M/F ratio. �(Δz) +(Δx) (Δy) (Δz) Δ = (�(Δx) (Δy) (Δy)� ).+ (Δz) Δ = �(� Δ =� �(+�+(Δy) (Δx) Δ =� �(+). (Δx)��).+ (Δz)
Thus, controlled tipping was defined as the smallest RESULTS possible Δ for a given bone level and tooth inclination. Thus, controlled Thus, controlled tipping Thus,defined controlled was tipping defined was tipping as defined the was smallest as defined the smallest possible as the asmallest possible Δgiven for a bone given possible Δ forlevel bone a given Δ and for level bone a given andlevel tooth bone andlevel toothand tooth Thus, controlled tipping was as the smallest possible Δ for tooth Because of the intrusive movement of the apex, the For each amount of labial inclination and alveolar bone smallest Δ was always > 0inclination. (Figure 3). The amount ofofofthe loss ofthe the we investigated /F for inclination. Because of Because the intrusive of Because the intrusive movement movement of the apex, movement of incisors, the theapex, smallest the thealways apex, Δ smallest wasthe always was>M always 0tΔ (Figure was always 03). (Figure > 03). (Figure 3). inclination. Because of theinclination. intrusive movement theintrusive apex, smallest Δofwas >Δ 0smallest (Figure 3). cont>ratios moment per unit of force (M t/F ratio) necessary for controlled tipping. We found that as labial inclination /Funit ratio) /F necessary ratio) necessary for ratio) controlled necessary for controlled tipping for controlled (M )(M was tipping was The amount The of amount moment Theunit of amount per moment unit of of per moment force (M of pertforce (M of tforce /F ratio) necessary fort(M tipping (Mcontrast, )tipping was The amount ofcont moment per of force (M t/F t/Fcont t/Fcont) t/Fcont) was controlled tipping (M t/F ) was calculated for each increased, M /Fcontrolled decreased. In increases in(M tunit t/Fcont cont model separately. alveolar bone loss caused increases in Mt/Fcont (Table 2). calculated calculated for eachcalculated model for each separately. model for each separately. model separately. calculated for each model separately. For the incisor with 6 mm of bone loss combined with Analysis of the stress distribution on the periodontal an inclination of 20o, the Mt/Fcont was 6.5, which was ligament lower than that of the normal tooth (Mt/Fcont, 8.5). Stress on the PDL was calculated in terms of principal Additionally, Figure 4 shows that as labial inclination stresses. The principal stresses were identified by increased, the length of the moment arm (the perpen Analysis Analysis of thedistribution stress Analysis of the distribution stress of the distribution stress on distribution periodontal on the periodontal onligament the periodontal ligamentthe ligament determining Analysis the planes at which the traction vector wasthe dicular distance between line of action of the force of the stress on the periodontal ligament purely normal with no shear component. In a 3D stress and the center of resistance) decreased. In contrast, an field, there are 3 principal stress components ranked in increase in alveolar bone loss caused increases in the onStress the PDL onStress was the PDL calculated oninwas the PDL calculated in terms was calculated of in principal terms of in principal terms stresses. of principal The stresses. principal The stresses. principal stresses Theidentified were principal stresses identified were stresses identified were identified Stress Among onStress the PDL was calculated terms principal stresses. Themoment principal stresses descending order. these principal stresses onofthe length of the arm. Thewere position of the center of PDL, the maximum by value ofby thedetermining first principal stress (S1, resistance associated with alveolar bone loss determining theby planes determining the at planes which the at the planes which traction at the which vector traction the was vector traction purely was vector normal purely was with normal purely no shear with normal component. no shear with conditions component. no In shear component. In In by determining the planes at which the traction vector was purely normal with no shear component. In
a 3Dfield, stress a there 3D field, stress athere 3D stress are there 3 principal field, are there 3 components principal stress are 3components principal stress components stress ranked components inranked descending inranked descending order. in descending Among order. these Among order. these Among these a 3D stress are 3field, principal stress ranked in descending order. Among these
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www.e-kjo.org stresses on principal stresses thethe PDL, on stresses the thePDL, maximum onvalue the the PDL, maximum ofmaximum the value first of principal the value first of(S1, principal the stress first (S1, principal stress maximum (S1, stress maximum tensile (S1, maximum tensile tensile http://dx.doi.org/10.4041/kjod.2016.46.3.155 principalprincipal stressesprincipal on the PDL, maximum ofvalue thethefirst principal stress maximum tensile stress) stress) the minimum and stress) the of minimum and value ofminimum value theprincipal third of value the principal third of (S3, the principal stress third (S3, principal stress maximum (S3, stress maximum compressive (S3,stress) maximum compressive stress) were stress) were stress) were stress) and the and minimum value thethe third stress maximum compressive werecompressive
Choi et al • Controlled tipping, bone loss, and periodontal stress
increased, a given M t/F imparted greater maximum tensile and compressive stresses on the PDL. Moreover, in teeth with greater alveolar bone loss, the stress changed more abruptly with changes in the Mt/F ratio. When the labial inclination of the incisor was increased without changing the amount of alveolar bone loss, the Mt/F ratio decreased for the lowest principal stress.
14 12 10
1.70E + 01
Maximum tensile stress
2
Principal stress (g/mm )
The length of the moment arm (mm)
was defined in reference to a previous study.5 For each inclination and simulated bone loss amount, we plotted the relationship between the Mt/F ratio and principal stresses on the PDL (Figure 5). As bone loss
8 6 Alveolar bone loss 0 mm 2 mm 4 mm 6 mm
4 2 0 0
5
10
15
7.00E + 00 2.00E + 00 .00E + 00
0 1 2 3 4 5 6 7 8 9 10
Mt/F ratio
.00E + 00
20 1.30E + 01
Labial inclination of a maxillary central incisor ( )
1.80E + 01
Figure 4. Changes in the length of the moment arm (the perpendicular distance between the line of action of the force and the center of resistance) according to changes in maxillary central incisor inclination and surrounding alveolar bone loss. A
1.20E + 01
Alveolar bone loss 0 mm 2 mm 4 mm 6 mm
Maximum compressive stress
Figure 5. Relationship between the M t /F ratio and principal stresses in tooth models with 20o of labial incli nation. The minimum principal stress levels are indicated by triangles.
B Labial
Palatal
Palatal
Labial
Palatal
Palatal
Maximum tensile stress
Mt/F = 4.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 6.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 5.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 7.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 6.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 8.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 7.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 9.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 8.0
Maximum compressive stress
Maximum tensile stress
Mt/F = 10.0 Maximum compressive stress
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Figure 6. Incisor root stress distribution patterns under conditions with M t /F near M t/F cont (red area, maximum tensile stress; blue area, maximum compressive stress). A, A tooth model with no alveolar bone loss and an incisal inclination of 15 o ; controlled tipping occurs at M t/F = 6. B, A tooth model with 6 mm of alveolar bone loss and an incisal inclination of 15 o ; controlled tipping occurs at Mt/F = 8. 159
Choi et al • Controlled tipping, bone loss, and periodontal stress
The patterns of stress distributed over the root were examined under conditions with an M t/F value near that of Mt/Fcont (Figure 6). With increases in the Mt/F ratio near Mt/Fcont, compressive stresses dominant in the labial apical region moved to the palatal apical area (Mt/ F above Mt/Fcont). In contrast, tensile stresses dominant in the labial area (Mt/F below Mt/Fcont) moved from the cervical to the mid-root regions (Mt/F above Mt/Fcont). These patterns were similar under all experimental conditions.
DISCUSSION Previous studies analyzed upright incisors and forces applied perpendicular to the occlusal plane. 3,4,21,22 Moreover, many studies that investigated alveolar bone loss and stress distributions did not consider the facial inclination of teeth.3-5,23 The present study evaluated how tooth inclination and bone loss affected the M/ F ratio in controlled tipping and the resulting PDL stresses. We chose the maxillary central incisor because it typically undergoes the most detailed tooth movement, and carries a higher risk of external apical root resorption than all other teeth, except for the maxillary lateral incisor.24 Often, correction of a flared incisor with alveolar bone loss involves a combination of retraction and intrusion. A mere retraction of flared teeth would lead to deepening of the bite.25 In the present study, force was applied parallel to the occlusal plane without an intrusive vector. Adding an intrusive force would incline the direction of the net force; this result would be comparable to applying a horizontal force to a tooth with a greater inclination. Therefore, we did not apply an intrusive force in this study (Figure 3). Geramy 5 reported that alveolar bone loss caused the center of resistance to move toward the apex; however, its relative distance to the alveolar crest decreased at the same time. Figure 4 also shows that alveolar bone loss caused increases in the length of the moment arm. Siatkowski 26 reported that an increase of 38% was needed to obtain bodily movement when 5 mm of alveolar bone loss had occurred. Therefore, the applied force and moment magnitudes must be reduced proportionally to maintain physiologically tolerable movement, because reduced support of the PDL and alveolar bone causes changes in the center of resistance.5,27,28 The incisor was modeled at inclinations over an average range (0o to 20o), both with and without different levels of alveolar bone loss (0 to 6 mm). When controlled tipping was applied to the incisor, the maximum compressive stress migrated along the y-axis to the root apex, and the maximum tensile stress migrated
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from the cervical area to the middle of the root. This distribution of stress was consistent with the findings of Kanjanaouthai et al.20 They found that incisors with a high degree of inclination experienced more compressive stress concentrated at the apices than incisors that were more upright. Labial inclination resulted in an increased intrusive force component directed parallel to the long axis; that force enhanced compressive stress at the apex and tension in the PDL in the longitudinal direction (Figure 6). As a result, facial inclination of the incisor caused a concentration of compressive stress at the apex; thus, controlled tipping of an incisor with a corrective force may lead to increased root resorption. 24 This interpretation is consistent with findings reported in the literature, which suggested that increases in the angle between the central incisor and palatal plane were strongly correlated with increases in external apical root resorption.29 Furthermore, it was shown that the risk of external apical root resorption was enhanced by the movements of teeth with mature roots, extensive movement of the root, and intrusive mechanics.30 Previous studies showed that teeth with alveolar bone resorption experienced increased maximum tensile and compressive stresses relative to those found in teeth with normal bone heights.6 In the present study, increasing the bone loss in teeth without changing the incisal inclination caused increased root apex displacements and greater maximum compressive and tensile stresses. However, for each level of alveolar bone loss, these stresses could be reduced with controlled tipping versus uncontrolled tipping or root movements. This suggested that in patients with alveolar bone loss, an inadequate force system might cause radical root apex displacement and stress. External root resorption occurs when forces at the apex exceed the resistance and reparative ability of periapical tissues29; thus, applied force and moment magnitudes must be reduced proportionately to main tain physiologically tolerable movements without causing further damage to supporting structures.5 The present study had some limitations. First, we used principal stresses to evaluate stress distributions in the PDL. For the PDL, the 3 principal stresses are very approximate because of the low values of Young’s modulus, and because Poisson’s ratio approached 0.5, which represents that of water. Thus, at a certain node in the PDL, the 3 principal stresses were either compressive or tensile, with values approximating those found in nature. Second, the PDL was not constructed with a thickness that varied from the cervix to apex. In addition, alveolar bone loss was assumed to occur only in the horizontal direction, and the amounts were equivalent in the buccolingual and mesiodistal directions.
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Choi et al • Controlled tipping, bone loss, and periodontal stress
CONCLUSION When controlled tipping was applied to incisors, alveolar bone loss and labial tooth inclination caused increases in the maximum compressive and tensile stresses at the root apices. This finding suggested that an inadequate force system applied to facially inclined incisors might cause greater stress at the root apices and induce external apical root resorption in teeth with alveolar bone loss compared with teeth without bone loss.
REFERENCES 1. Gkantidis N, Christou P, Topouzelis N. The ortho dontic-periodontic interrelationship in integrated treatment challenges: a systematic review. J Oral Rehabil 2010;37:377-90. 2. Towfighi PP, Brunsvold MA, Storey AT, Arnold RM, Willman DE, McMahan CA. Pathologic migration of anterior teeth in patients with moderate to severe periodontitis. J Periodontol 1997;68:967-72. 3. Cobo J, Argüelles J, Puente M, Vijande M. Dento alveolar stress from bodily tooth movement at different levels of bone loss. Am J Orthod Dento facial Orthop 1996;110:256-62. 4. Cobo J, Sicilia A, Argüelles J, Suárez D, Vijande M. Initial stress induced in periodontal tissue with diverse degrees of bone loss by an orthodontic force: tridimensional analysis by means of the finite element method. Am J Orthod Dentofacial Orthop 1993;104:448-54. 5. Geramy A. Alveolar bone resorption and the center of resistance modification (3-D analysis by means of the finite element method). Am J Orthod Dentofacial Orthop 2000;117:399-405. 6. Geramy A. Initial stress produced in the periodontal membrane by orthodontic loads in the presence of varying loss of alveolar bone: a three-dimensional finite element analysis. Eur J Orthod 2002;24:2133. 7. McLaughlin RP, Bennett JC, Trevisi HJ. Systemized orthodontic treatment mechanics. Edinburgh: Mosby; 2001. 8. Tian YL, Liu F, Sun HJ, Lv P, Cao YM, Yu M, et al. Alveolar bone thickness around maxillary central incisors of different inclination assessed with conebeam computed tomography. Korean J Orthod 2015;45:245-52. 9. Burstone CJ. The mechanics of the segmented arch techniques. Angle Orthod 1966;36:99-120. 10. Cattaneo PM, Dalstra M, Melsen B. Moment-to-force ratio, center of rotation, and force level: a finite element study predicting their interdependency
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