Effect of Intrusive Forces on Maxillary Central Incisor at Different Inclinations at Normal Bone Height A FEM Study

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1 8 Effect of Intrusive Forces on Maxillary Central Incisor at Different Inclinations at Normal Bone Height A FEM Study Dr. Rahul Kumar Gupta, MDS, Orthodontics and Dentofacial Orthopaedics, Dept of Orthodontics, Babu Banarasi Das College of Dental Sciences (BBDCODS), Lucknow, India Dr. Tripti Tikku, Prof & HOD, MDS Orthodontics and Dentofacial Orthopaedics, Dept of Orthodontics, Babu Banarasi Das College of Dental Sciences (BBDCODS), Lucknow, India Dr. Rohit Khanna, Prof, M.D.S., Orthodontics and Dentofacial Orthopaedics, Dept of Orthodontics, Babu Banarasi Das College of Dental Sciences (BBDCODS), Lucknow, India Dr. Sneh Lata Verma, Reader, M.D.S., Orthodontics and Dentofacial Orthopaedics, Dept of Orthodontics, Babu Banarasi Das College of Dental Sciences (BBDCODS), Lucknow, India Dr. Kamna Srivastava, Reader, M.D.S Orthodontics and Dentofacial Orthopaedics, Dept of Orthodontics, BBDCODS, Lucknow, India ABSTRACT Introduction: For any orthodontic tooth movement, it is essential to apply optimum force level and to evaluate the amount of stress generated on supporting structures. However, it is difficult to estimate amount of stresses generated clinically and this can be done by most advantageous in vitro method like FEM. Aim and Objectives: To calculate the stress and displacement generated at apex of maxillary central incisor for three different magnitudes of intrusive forces (5, 10, 15gm) at three different inclinations { (56º), I (51º), II (61º)} by 3-D finite element method and to calculate the amount of horizontal force require to nullify the moment created by vertical force. Materials and Methods: Three 3D FEM models of the maxillary central incisor tooth were constructed with its supporting structures at three different inclinations. Stress generated at the apex and the amount of displacement were calculated by the ANSYS 10.0 Software. Results: Maximum amount of stress and displacement was observed at apex for 15gm of vertical force (Fv) in all the groups and minimum for 5gm. For every Fv, stresses obtained were maximum for I > I > III. The resultant force (Fr) were directly proportional to Fv. Fr and horizontal force (Fh) were maximum for I > I > III for each Fv. Conclusion: As stresses are concentrated at a smaller area apically, it is always better to use lighter forces for intrusion, thereby making it more comfortable for the patient. Keywords Intrusion, FEM, Biomechanics INTRODUCTION Orthodontics has evolved over the years from an empirical art to a definitive science. In recent years, a greater emphasis has been placed on an understanding of the exact mechanical and biological systems which governs the force needed to produce tooth movement for correction of discrepancies in antero-posterior, vertical and transverse plane. Deep bite is a complex orthodontic problem in a vertical plane that is a common feature of many malocclusions. Correction of deep bite is an important part of orthodontic treatment due to its potential deleterious effects on TMJ, periodontal health and facial esthetics and also because it acts as a limiting factor in anterior teeth retraction. 1 Intrusion of anterior teeth is the preferred treatment option in non growing patient for correction of anterior deepbite. Various factors should be considered before performing intrusion like smile line, incisor display, vertical dimension and inclination of the teeth. 2 Intrusion can be accomplished by numerous ways - Utility arch by Ricketts, Intrusion arches by Burstone, Micro - implants, K-Sir (Simultaneous Intrusion and Retraction arch by Varun Kalra) and the Connecticut Intrusion arch. 3 Before planning for intrusion its biomechanics must be understood clearly as it varies with inclination of teeth and alveolar bone loss. 4-6 During conventional mechanics, when a single intrusive force is applied to the labial surface of the anterior tooth, the tooth will not translate but tend to rotate around CR by generating a moment that results in flaring of normoinclined tooth or excessive flaring of proclined tooth or lingual tipping of retroclined teeth. For any orthodontic tooth movement, it is necessary to know the amount of stresses generated on application of forces. 7 However, it is difficult to estimate amount of stresses generated clinically and this can be done by various in vitro methods like FEM, Photo elastic stress analysis, Mathematical models and Laser holography. 8 FEM has various advantages over the other methods

2 9 methods i.e. it has the ability to include heterogeneity of tooth material and irregularity of the tooth contour in the model design and the relative ease of applying loads at different directions and magnitudes for a more complete analysis. 9 Additionally, it does not require extensive instrumentation, is a non-invasive technique with close resemblance to natural conditions and enables us to perform static and dynamic analysis 10 and was thus used in the present study. Considering this, the effect of intrusive forces of magnitude as low as 5, 10 and 15gms on three different inclinations of maxillary central incisor (normoinclined, proclined, and retroclined) at normal bone height was determined in terms of stresses and displacement generated at the apex by FEM method. It was also decided to calculate the amount of horizontal force required to nullify the moment created by vertical force being applied labially on maxillary central incisor at a point representing the center of bracket slot for different forces and inclinations using simple mathematical calculations. MATERIALS AND METHODS The study was conducted by the Department of Orthodontics, Babu Banarasi Das College Of Dental Sciences in collaboration with Sagar Institute of Technology & Management. Three geometric models of a maxillary central incisor along with its supporting structures were constructed at three different clinical inclinations at normal bone heights according to Ash Dental Anatomy 11 along with PDL and alveolar bone 12 to fit outside the root. (Table 1) The alveolar bone height for each model was constructed from CEJ towards apex i.e. at normal bone height. Figure 1 shows FEM and hypermesh model of maxillary central incisor for different Groups. Assembled finite element model of the tooth were imported into ANSYS software for analysis. The 3D Finite element models were considered to have linear elasticity and isometric properties of the same quality. Young s modulus and poisson s ratio for the Tooth, PDM and alveolar bone were taken as given by Tanne et al(table 2). Geometric models were converted into finite model which approximately consisted of elements and nodes. STEPS INVOLVING CALCULATIONS OF Fr AND Fh USING TRIGONOMETRIC CALCULATION: I. Point of application of force Clinically, a bracket is bonded labially at a distance of 4mm for maxillary central incisor. Hence this point was taken as the point of force application in the present study. II. Magnitude of force To achieve true intrusion, resultant intrusive force should pass through CR of the tooth, that was taken at 2/3 rd the distance from the root apex according to Nanda. On application of an intrusive force on the labial surface of maxillary central incisor, a pure vertical force vector passes labial to the center of resistance, creating counterclockwise moment that results in flaring of teeth. To counteract this moment, either a horizontal force vector can be added in the distal direction or a lingual crown torque can be incorporated in the wire. Assuming the resultant force (Fr) passing through the CR, the value of Fr for different vertical forces (5, 10 and 15gms) selected for the study was calculated using trignometry. A template of maxillary central incisor with accurate dimensions was made on the transparency sheet and was used to trace the maxillary central incisor for different situation assumed in the study to calculate Fr as well as horizontal force needed to counteract the moment induced by vertical force for achieving true intrusion. The procedure is described as follows for one assumption i.e. application of 15 gm of force to normoinclined maxillary central incisor at 56º to occlusal plane at normal bone height(figure 2 ). 1. On graph paper, horizontal line (AB) was drawn considering it to be maxillary occlusal plane and a line BD was drawn at an angle of 56º from point B considering it to be normal inclination of the long axis of the incisor. 2. Template was placed on the line BD with tip of incisal edge coinciding with point B and the tooth was traced. a) CR of the tooth i.e. at 2/3 rd the distance from the root apex was marked at 8.66mm from root apex as point O ( 2/3 13mm = 8.66mm from root apex ). 3. Point of application of force at 4mm from incisal edge on the labial surface was marked as point P. 4. Vertical force (Fv) was drawn from P and horizontal force vector (Fh) was drawn perpendicular to it from point P. 5. Line joining O (i.e. CR) and P represented our desired resultant force passing through CR. 6. Angle between the line OP and Fv was measured as 45º. 7. Using trigonometry, the value of Fr was calculated:- Cos = Base / Hypotenuse; where B (Base) = Fv and H (Hypotenuse) = Fr Cos 45 = 15 / Fr 0.70 = 15 / Fr

3 10 Fr = 15 / 0.70 = gms. Thus 21.42gm is resultant force passing through CR for 15gm of force applied vertically. 8. Using simple mathematical calculation the value of Fh was calculated. As already stated to achieve true intrusion, moment of Fv i.e. Mv should balance moment of Fh i.e. Mh. To calculate moment, a perpendicular distance from CR to Fv was measured as d 1 and was found to be 7.74mm and distance from CR to Fh was measured as d 2 and was measured as 7.67mm. The moments Mv and Mh were considered to be balanced. The values of Fv, d 1 and d 2 were substituted in the equation Mv = Mh to calculate the value of Fh as follows :- Mv = Fv d 1 Mh = Fh d 2 Fv d 1 = Fh d = Fh = Fh 7.67 Fh = This should be the amount of horizontal force acting perpendicular to Fv, which will nullify the moment and help in achieving true intrusion. 9. The value of resultant (Fr) obtained could also be verified by Parallelogram law of forces which states that resultant force for two forces acting at a same point is the diagonal of the completed Parallelogram. (Figure 3). 10. Similarly Fr and Fh was calculated for different inclinations and different intrusive force i.e. 10 and 5gms as well. III. Application of resultant force to Finite Element Model - Respective Fr was applied along CR in their corresponding Finite Element Model. Stresses generated at the apex and amount of displacement was calculated by the software for different assumptions selected in the study OBSERVATION AND RESULTS Table 3 shows the amount of Resultant force (Fr), Vertical force (Fv) and Horizontal force (Fh) at three different tooth inclinations and normal alveolar bone height. Table 4 shows the magnitude of moment Mv at three different inclination and normal alveolar bone height on applying three different vertical forces Fv i.e. 5, 10 and 15gms. Maximum amount of stresses on applying Fr on the respective FEM models of central incisor to achieve true intrusion were noted at the apex in all the conditions. By post processing of results of FEM analysis, stresses in N/mm 2 (Newton per millimetre square) and displacement in mm (millimetres) was calculated by ANSYS software at apex of central incisor model and results were tabulated in Table 5. Figure 4,5 and 6 is a graphical representation obtained by FEM analysis for different subgroups selected for, II and III respectively. Stresses (N/mm 2 ) are depicted by different colours in the figure. Red colour column of spectrum indicated maximum principal stresses and the colours like orange, yellow, green and blue represented reducing level of stress with blue colour representing the lowest level of stress. DISCUSSION Deep bite is a complex orthodontic problem in the vertical plane and its correction requires careful diagnosis and a logically sequenced plan of treatment with adequate mechanics to obtain the desired results. 1 As deep bite correction by extrusion has a limited role in non-growing individuals, 13 where in the best option would be intrusion of maxillary or mandibular teeth depending on various factors like smile line, incisor display, vertical dimension and inclination of the teeth. 2 As recommended intrusive force for single maxillary central incisor varied from 10-20gms by different authors. 4,14,15 Hence, to attain intrusion without inflicting any damage to the periodontium and surrounding bone, it was decided to evaluate the effect of 5,10 and 15gms of intrusive force on the supporting structures of maxillary central incisor. The biomechanics of intrusion can vary with inclination of the teeth, hence it was decided to check the effect of intrusive forces at three different inclinations of incisiors (normoinclined, proclined and retroinclined). The amount of horizontal force required to nullify the moment created on application of intrusive forces at the bracket slot instead of CR was also calculate using simple mathematical calculations. The results of the study indicated that obtained resultant force (Fr) varied for the different forces (Fv) and inclinations at normal bone height. Fr increased as the Fv increased in all the groups with Fr being maximum for I followed by and then II for any particular vertical forces (Fv). Any type of intrusive force produced maximum stress and displacement at the apex. Maximum amount of stress and displacement was observed on applying the calculated Fr for 15gm of Fv in all the three groups and minimum on applying the calculated Fr for 5gm of Fv. For any particular Fv, stresses obtained were maximum for I (51º proclined), followed by (56º normoinclined) and II (61º retroclined). The values of Fh also varied. I

4 11 required maximum Fh followed by and II for any particular Fv. Light intrusive force were also considered in few other studies i.e. 25gm by Rudolph et al, 9 Heravi et al 16 and 32.3gm by Singh et al 5 whereas 10gm by Mathur et al 17. Though vertical forces selected were lower in our study but Fr obtained ranged from 19.58gm to 24.19gm for 15gm of Fv for different groups. Thus the results of the present study on applying obtained Fr for 15gm of force, were comparable to above studies, but the stresses found were more in our study. This can be due to applied resultant force passing through CR for true intrusion and forces were applied on incisors inclined at varying degrees to occlusal plane which was not so in the study by Rudolph et al 9 or Heravi et al 16. Singh et al 5 found stresses of N/mm 2 and displacement of 0.018mm on applying the intrusive force to normoinclined incisor whose inclination was 61º to occlusal plane. They had also calculated values of Fr passing through CR as 46.8gm and Fv as 32.3gm keeping Fh at 33.3gm using trigonometry. As this Fr was much more than our study, the stresses calculated were more in the study by Singh et al. 5 In contrast, the values of displacement were less in their study and the reason could be attributed to difference in inclination of their normoinclined incisor with that of our study. In other studies very high intrusive force were used such as 1N (100gm) by Geramy et al 8, 7N (700gm) and 10N (1000gm) by Brezeanu et al 18 and 1N by Mascarenhas et al 19, so greater amount of stresses were noted at the apex. Thus the heavy intrusive forces are not recommended clinically. Similar to the present study, the role of inclination of the incisor on effective intrusion was also considered by Singh et al 5 but that were on extremes representing proclined (39º) and retroclined incisor (79º). The values of stress and displacement obtained were more than that of their normoinclined group. On the contrary, to have uniformity in selection with respect to the normal values in the present study, inclination of 5º less than normal was considered to be proclined and inclination 5º more than normal was considered to be retroclined. Singh et al 5 had calculated the values of Fr which were much higher than the present study. Extreme inclinations and increased Fr was responsible for increased values of stresses in their study. Singh et al calculated Fv based on Fh whereas we had calculated horizontal force Fh by nullifying the moments obtained for selected Fv of 15, 10 or 5gm to achieve true intrusion which also varied in the present study. Based on the values of stresses and displacement, alteration in biomechanics for different assumption can be made and applied clinically. For Proclined incisors, reduction in vertical force from 15gm to 10gm resulted in reduction of Fr from 24.19gm to 16.12gm, further decreasing to 5gm resulted in Fr of 8.06gm. This reduction in Fr resulted in corresponding decrease in stress values in the present study. In Retroinclined incisors, the intrusive force passes lingual to the center of resistance thereby creating clockwise moment which causes further retroclination of the teeth. Initially for retroclined incisor, vertical force must be reduced so as to decrease the clockwise moment and horizontal force must not be applied at all or mechanics to induce protraction of incisors must be initiated. This will decrease the retroclination of the incisors. As retroclination reduces, vertical forces can be increased with application of adequate horizontal force to nullify the moments of two forces and achieving true intrusion. As different inclination of central incisor (51º, 56º, 61º) taken in the present study were not varied too much from the normal values, thus the point of force application was always labial to CR. For such inclinations 10gm of Fv can be considered appropriate that can provide displacement within the range of thickness of PDL i.e. 0.25mm. The stress generated for this displacement might not be deleterious for the supporting structure and tooth can be intruded without causing any discomfort to the patient. CONCLUSION As stresses are concentrated at a smaller area apically, it is always better to use lighter forces for intrusion, thereby making it more comfortable for the patient. Therefore, obtained Fr for 10g of Fv when applied can result in displacement within limits of PDL thickness hence it can be suggested to use this Fv for incisor intrusion at varying inclinations at normal bone height. REFERENCES [1] Shroff B, Yoon WN, Lindaurer SJ, Burstone CJ. Simultaneous intrusion and retraction using three piece base arch. Angle Orthod 1997;6: [2] Polat Ozsoy O, Arman Ozcırpıcı A, Veziroglu F, Cetinsahin A. Comparison of the intrusive effects of miniscrews and utility arches. Am J Orthod Dentofacial Orthop 2011;139(4): [3] Belludi A, Bhardwaj A, Gupta A, Karandikar A. Orthodontic intrusion: Conventional and mini implant assisted intrusion mechanics. J Asian Pacific Orthod Soc 2011;II(4). [4] Nanda R, Kuhlberg A. Principles of biomechanics. Biomechanics in Clinical Orthodontics. Philadelphia, Penn: WB Saunders Co; 1997:1 22.

5 12 [5] Singh M, Mehrotra P. Biomechanical aspects for true intrusion with lingual mechanics- An FEM study. Lingual Biomechanics: 2009;1(1). [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: [7] McGuinness N, Wilson AN, Jones M. Stresses induced by edgewise appliances in the periodontal ligament-a FEM study. Angle Orthod 1992; 62(1): [8] Jin S, Kim IT, Kook YA. Finite element analysis of the shift in center of resistance of the maxillary dentition in relation to alveolar bone loss. Korea College of Medicine [9] Rudolph DJ, Willes MG, Sameshima GT. A finite element model of apical force distribution from orthodontic tooth movement. Angle Orthod 2001; 71(2): [10] Vikram NR, Hashir YM, Karthikeyan MK. Finite element method in orthodontics. Ind J Multidisciplinary Dent 2010;1(1): [11] Ash M M Dental Anatomy, Physiology and occlusion 6 th ed. W B Saunders, Philadelphia; 1984: [12] Tanne K, Koenig AH, Burstone CJ. Moment to force ratios and the center of rotation. Am J Orthod Dentofacial Orthop 1997;94: [13] Graber TM, Rakosi T, Petrovic AG. Dentofacial orthopedics with functional appliances. 2 nd ed. St Louis: C. V. Mosby;1997: [14] Proffit WR, Fields HW, Ackerman JL, Bailey LJ, Tulloch JFC. Contemporary orthodontics. 3rd ed. St Louis: C. V. Mosby;2000. [15] Steenbergen EV, Burstone CJ, Andersen BP. The influence of force magnitude on intrusion of the maxillary segment. Angle Orthod 2004;75(5): [16] Heravi F, Salari S, Tanbakuchi B, Loh S, Amiri M. Effects of crown-root angle on stress distribution in the maxillary central incisors PDL during application of intrusive and retraction forces: a three-dimensional finite element analysis. Progress in Orthod 2013;14:1-10. [17] Mathur AK, Gupta V, Sarmah A. Apical force distribution due to orthodontic forces: A Finite Element Study. J Contemporary Dent Pract 2011;12(2): [18] Brezeanu L, Bica C, Pacurar M, Sita D. FEM simulation of biomechanical phenomena during Orthodontic tooth displacements. Inter-Ing 2007;15:1-5. [19] Mascarenhas R, Revankar AV, Mathew JM, Chatra L, Husain A, Shenoy S. Effect of intrusive and retraction forces in labial and lingual orthodontics: A finite element study. Asian Pacific Ortho sci 2014;4(2): FIGURES I II Figure 1: FEM and Hypermesh model of maxillary central incisor for different Groups at normal bone height Figure 2: Calculation of Fr for known Fv (15gm) for at normal bone height

6 13 Ia (Fv=15gm) Figure 3: Verification of Fr obtained for at normal bone height using parallelogram law of forces Ib (Fv=10gm) a (Fv=15gm) Ic (Fv=5gm) Figure 5: Stresses and Displacements for Different Subgroups of I b (Fv=10gm) IIa (Fv=15gm) c (Fv=5gm) Figure 4: Stresses and Displacements for Different Subgroups of IIb (Fv=10gm)

7 14 IIa 15gm 51.5º I 51 o IIb 10gm 51.5º IIc 5gm 51.5º IIIa 15gm 40º II 61 o IIIb 10gm 40º IIIc 5gm 40º IIc (Fv=5gm) Figure 6: Stresses and Displacements for Different Subgroups of II TABLES Table 1: Groups made for the study with different inclinations and forces Groups Inclinations Forces (gm) I II III Ia 15gm Normoinclined 56 o Ib 10gm Ic 5gm IIa 15gm Proclined 51 o IIb 10gm IIc 5gm IIIa 15gm Retroclined 61 o IIIb 10gm IIIc 5gm Table 2: Material properties of different supporting structures Material Properties Structure Young s modulus (N/mm²) Poisson ratio Tooth PDL Alveolar Bone Table 3: Amount of (Fr), (Fh), (Fv) for different tooth inclinations and normal bone height Normal bone height Force Groups (Fv) Fr Fh Ia 15gm 45º o Ib 10gm 45º Ic 5gm 45º = Angle between Fr and Fv Cos = Base / Hypotenuse; where B (Base) = Fv and H (Hypotenuse) = Fr Cos = Fv / Fr or Fr = Fv / Cos Table 4: Moments (Mv) for different Fv at different inclinations and normal bone height Distance (d) MOMENT Groups Fv at CR = 8.66 (M = Fv d (Inclination) 1 ) (gm) d 1 d 2 Mv (g mm) Ia o Ib Ic IIa I 51 o IIb IIc IIIa II 61 o IIIb IIIc Mv = Fv d 1, Table 5: Stresses and displacements at apex of central incisor for Groups I, II, III at varying intrusive forces at normal bone height at normal bone height (CR = 8.66mm) Groups Fv Displacem Max. (Inclination) (gm) Fr(gm) ent (mm) Stress (N/mm 2 ) Ia o Ib Ic IIa I 51 o IIb IIc IIIa II 61 o IIIb IIIc