Biomechanical aspects for true intrusion with lingual mechanics- An FEM study

www.lingualnews.com Vol 1 No 1 June 2011

ABSTRACT

Introduction: Certain clinical conditions often demand selective intrusion of anterior teeth like Class II div.1 or the Class II div.2 cases where only the incisors or anteriors are extruded especially in adult patients in which esthetics hold a major issue leading to the increased demand of lingual orthodontic appliance. Therefore, the present study aimed to evaluate the amount of intrusive force ratio as compared to the retractive force required for true intrusion of maxillary central incisor with lingual bracket system and, to compare these biomechanical responses with that of labial bracket system.
Material and Method: A FE Model of maxillary central incisor was prepared using Solid Edge and HYPERMESH and analysis was carried out with ANSYS software. Three inclinations to occlusal plane were created i.e. normal inclination (61 deg), retroclination (79 deg) and proclination (39 deg). Various force magnitudes were applied to determine a distinctive ratio of intrusive and counterbalancing retractive forces such that pure intrusion could occur in all the three clinical scenarios.
Results: It was found that true intrusion can be achieved with lingual mechanics similar to that of labial mechanics when an accurate biomechanical principle is applied.
Conclusion: Significantly different force ratios were obtained for labial and lingual brackets so that pure intrusion could occur in all three clinical scenarios.
Keywords: Lingual mechanics, Labial mechanics, Intrusion, FEM, biomechanics.

INTRODUCTION

Application of basic biomechanical principles in treatment improves the efficacy of the appliance system and simplifies the treatment, thereby, improvising the force delivery which ultimately helps in achieving a more predictable tooth movement with minimal side effects1,2. No matter how vigorously esthetic labial brackets have been promoted over the years, many adults do not seek orthodontic treatment due to the perceived embarrassment of wearing braces because of its certain limitations3. Patients with high aesthetic demands seem more interested in the newly introduced lingual orthodontic approach because the brackets are not visible at all during the treatment4,5.
Scuzzo and Takemoto6 have explained that the biomechanics of lingual orthodontics differ considerably from those of labial systems and this difference is due to the entirely different aspect of point of force application which is on the lingual aspect of the tooth. Geron and co-workers1 have found a difference between the reactions7,8 of teeth when the vertical forces are applied from the labial and lingual aspect through a geometric model of a maxillary central incisor.
Hence, this study investigated the biomechanical responses of teeth to orthodontic intrusive forces applied at the labial bracket positions and to compare these responses to that with the lingual bracket positions with finite element modeling technique which has improved the accuracy of the results. Definite intrusive and retractive force ratios were also established which would cause true intrusion of the maxillary central incisor in the three clinical situations9 with labial as well as lingual system.


 

METHODOLOGY

Three geometric models of a maxillary central incisor (Table 1)10,11 along with supporting structures were constructed at three different clinical inclinations 9 i.e. 61 deg (normal inclination), 39 deg (proclination) and 79 deg (retroclination) to the occlusal plane12 (OP) (Figure 1). The labial and the lingual brackets of maxillary central incisor tooth i.e. Kurz – ORMCO  7th generation (lingual) and 3 M unitek MBT prescription (labial) and its modeling was done using SOLID EDGE software by reverse engineering technique. The cervico-incisal positioning of the labial bracket was 5.2mm (middle of the clinical crown)13 and for lingual bracket 6.8 mm from the occlusal plane such that the base of bracket adapts well on lingual surface14,15. The details of the bracket slots were not taken into consideration as the brackets were used just to mimic the point of force application. The geometric models were then imported into HYPERMESH software for meshing. Assembled finite element model of the tooth and bracket was then imported into ANSYS 10.1 software for analysis. Isotropic material properties16-18 were applied for enamel, dentin, PDL, alveolar bone and brackets in the model as summarized in table (Table 2). For all the cases the bottom portion of the cortical bone was fixed. This study was thus chosen to be a finite element study to determine more accurate results and findings25,26. It also helped us reveal effects on the periodontium i.e. the stresses generated during application of force on the tooth with labial and lingual system which was not observed in the studies performed on geometric model1.
For true intrusion, the resultant force vector should pass through the Centre of resistance (Cres) of the tooth. So, to calculate the force ratios, firstly, the resultant force was made to pass through the Cres of the maxillary central incisor and then the horizontal force (Fh) and the vertical force (Fv) vectors were calculated with trigonometric calculations by constructing a parallelogram where Fv and Fh were perpendicular to each other and the angle θ was calculated (between Fr and Fh) (Fig. 2)
Since, Cos θ = Adjacent / Hypotenuse
• Cos θ = Fh/Fr

Total length	23.5mm
Crown length	10.5mm
Root length	13mm

Figure 1: Three geometric models of a maxillary central incisor along with supporting structures were constructed at three different clinical inclinations:  i.e. 61 deg (normal inclination), 39 deg (proclination) and 79 deg (retroclination) to the occlusal plane12 (OP)

Figure 2: Finite Element Model of the Maxillary Central Incisor with 61 deg inclination with labial mechanics. It is showing the force vectors (Fv and Fh) and the Fr passing through Cres.

A number of force combination i.e. intrusive force as well as retractive force were applied. Average intrusive force value is 25 gm per tooth20,21 ranging from 15 to 40 gm. The higher and lower range of the intrusive force value was kept according to Burstone20,21 and Ricketts22 while the average retractive force was 37.5 gm/tooth ranging between 25 to 50 gm per tooth according to Burstone et al20, Ricketts22 , Proffit23 and Mclaughlin et al13

RESULTS

For true intrusion, the moment generated by the intrusive force vector should be nullified by another reactionary moment such that the resultant force would pass through the Cres Since, in this study the resultant was itself made to pass through the Cres of the tooth in all the three situations with both the mechanics, and then the ratio of intrusive force and retractive force was calculated which could be applied clinically to cause true intrusion, hence, it was supposed that the moment generated is nullified.

For normal inclination with labial mechanics i.e. 61 degree inclination to OP the angle formed by the resultant force and the horizontal force vector was calculated as 44.730 (Figure 3). Fh was chosen to be 33.3 gms which was towards the higher limit of normal range to calculate Fv and Fr:
• Cos θ = Adj/Hyp
• Cos θ = Fh/Fr
• Cos (44.3)deg = 33.3 / Fr
• Fr= 46.87 gms.
To calculate Fv:
• Tan θ = Fv/Fh
• Tan(44.3) = Fv/33.3
• Fv= tan (44.3) × 33.3 = 0.97 × 33.3 = 32.3 gm = 0.296 Nmm
Force ratio = Fv : Fh = 0.96:1
Similarly other force ratios for other inclinations were obtained with labial as well as lingual mechanics (Figures 2, 4, 6, 8, 10, 12; Table 3 & Graph 1). The biomechanical aspects of force application on both the labial and lingual systems are also demonstrated in the form of stress pattern generated and the amount of displacement that has occurred are summarized in table (Figures 3, 5, 7, 9, 11, 13; Graph 2 & 3; Table 4&6).
A comparison of the force ratios and stress (N/mm2) was made as given in (Graph 2 &3).

Figure 3: Longitudinal section of root of Maxillary central incisor at 61 deg with labial mechanics showing maximum stress with red and minimum stress with blue after force application.

 

Figure 4: Finite Element Model of the Maxillary Central Incisor with 39 deg inclination with labial mechanics. It is showing the force vectors (Fv and Fh) and the resultant force passing through Cres.

Figure 5: : Longitudinal section of the root of Maxillary central incisor at 39 deg with labial mechanics showing maximum stress with red and minimum stress with blue after force application.

Figure 6: Finite Element Model of the Maxillary Central Incisor with 79 deg inclination with labial mechanics. It is showing the force vectors (Fv and Fh) and the resultant force passing through Cres.

Figure 7: Longitudinal section of root of Maxillary central incisor at 79 deg with labial mechanics showing maximum stress with red and minimum stress with blue after force application.

Figure 8: Finite Element Model of the Maxillary Central Incisor with 61 degree inclination with lingual mechanics. It is showing the force vectors (Fv and Fh) and the resultant force passing through Cres.

Figure 9: Longitudinal section of root of Maxillary central incisor at 61 degree with lingual mechanics showing maximum stress with red and minimum stress with blue after force application.

Figure 10: Finite Element Model of the Maxillary Central Incisor with 39 degree inclination with lingual mechanics. It is showing the force vectors (Fv and Fh) and the resultant force passing through Cres.

Figure 11: Longitudinal section of root of Maxillary central incisor at 39 degree lingual mechanics showing maximum stress with red and minimum stress with blue after force application

Figure 12: Finite Element Model of the Maxillary Central Incisor with 79 degree inclination with lingual mechanics. It is showing the force vectors (Fv and Fh) and the resultant force passing through Cres

TABLE 3:
Inclination Fv (Gm) Fv (N) Fh (Gm) Fh
(N) Fr
(Gm) Fr(N) Displacement of Tooth (mm) Ratio (Fv/Fh)
61 deg 32.3 0.296 33.3 0.305 46.8 0.429 0.018 0.96:1
39 deg 13.8 0.126 33.3 0.305 30.7 0.281 0.05 0.41:1
79 deg 40.32 0.370 21 0.192 45.65 0.419 0.037 1.96:1

Inclination	Fv (Gm)	Fv (N)	Fh (Gm)	Fh (N)	Fr (Gm)	Fr(N)	Displacement of Tooth (mm)	Ratio (Fv/Fh)
61 deg	32.3	0.296	33.3	0.305	46.8	0.429	0.018	0.96:1
39 deg	13.8	0.126	33.3	0.305	30.7	0.281	0.05	0.41:1
79 deg	40.32	0.370	21	0.192	45.65	0.419	0.037	1.96:1

Figure 13: Longitudinal section of root of Maxillary central incisor at 79 degree lingual mechanics showing maximum stress with red and minimum stress with blue after force application.

Inclination	Fv (Gm)	Fv (N)	Fh (Gm)	Fh(N)	Fr(Gm)	Fr(N)	Displacement of Tooth (mm)	Ratio (Fv/Fh)
61 deg	25	0.229	4.8	0.044	25.4	0.24	0.015	5.45:1
39 deg	25	0.229	15.5	0.142	29.5	0.271	0.047	1.6:1
79 deg	25	0.229	4.6	0.042	25.4	0.24	0.032	5.4:1

DISCUSSION

The previous analysis demonstrates that control of root position during movement requires both a force to move the tooth in desired direction, and a couple to produce a necessary counterbalancing moment for control of root position. The moment of the intrusive force, when applied to the incisors, tips the crown facially which can be counterbalanced in two ways either by applying a force to retract the incisors, which would create a moment in opposite direction or to place a twist in the wire of anterior segment, to torque the incisors lingually15. The torque given in the wire while performing intrusion, generates a high magnitude of reactive force which may cause root resorption, also the magnitude of the reactive force is not known with certainty because of the indefinite force system formed with which makes it impossible to accurately adjust the archwire24. Thus, the present study aimed to find the ratio between the intrusive and retractive force such that the moment generated is nullified and true intrusion occurs in all the three clinically applicable ratios.
There are certain clinical conditions that often demand selective intrusion of anterior teeth like Class II div.1 patients or the Class II div.2 cases where only the incisors are extruded. Hence, the three inclinations of maxillary central incisor were chosen for this study9 normal inclination, proclination and retroclination of anterior teeth.
The difference in the bracket positioning and so the point of force application in the lingual mechanics as compared to labial mechanics has an important impact on the biomechanical aspects related to tooth movement since the distance (D) between the Cres and point of force application is smaller in Lingual Orthodontics than in Labial Orthodontics as summarized and supported by Scuzzo and Takemoto6,15.
After interpretation of the results, on the labial aspect, it was observed that for true intrusion, when load was applied on the 61̊ inclined tooth, the Fh and Fv were nearly equal to each other, for inclination of 39 ̊ the Fv was nearly half of Fh whereas for the 79 ̊ inclination, Fv was nearly twice higher than Fh.
Force ratios, on the lingual aspect, were totally different. It was observed that in all the cases the intrusive force magnitude (Fv) was more as compared to Fh. For 61 deg and 79 deg inclinations for true intrusion, Fv was nearly five and a half times greater than (Fh), and in 39 deg the magnitude of intrusive force was 1.6 times more than retractive force.
It was also observed that among all the inclinations with labial as well as lingual mechanics the maximum stress as produced in all the three inclinations are different but are concentrated maximum at the root apex as summarized in (Table 4 & 6; Graph 3). Since the maximum Von Mises stress at root apex was least in the normal inclination case with both the mechanics it is more reasonable to perform intrusion when the tooth is at its normal inclination to the occlusal plane also lesser stress was generated with lingual mechanics than labial as supported by Brinkman J et al25.
The present study was a linear study which was undertaken by simplifying the load conditions. Toms et al26 in contrary to this stated the nonlinear stress behavior of the periodontal ligament which is age-dependent, location dependent, and load-direction dependent.
The force ratios for performing pure intrusion using a lingual bracket in the present study is applicable with the abovementioned incisor inclinations only when the horizontal distance of bracket slot to tooth surface is at the determined transitional point (4 mm in this study) otherwise change in bracket position on the lingual side can create an unpredictable and extensive change in the torque and vertical distance of the point of force application to the Cres.

CONCLUSION
For true intrusion of maxillary incisors with lingual mechanics there should be an entirely different force ratio between the vertical and horizontal force component as compared to labial mechanics. Application of forces to teeth in a proper ratio can give the desired tooth movement with any mechanics. Lingual system can be more beneficial for selective true intrusion of the maxillary incisor as compared to the labial system.



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www.lingualnews.com
Adult and Lingual Orthodontics
EDITORS:
Dr. Silvia Geron D.M.D., M.Sc
Dr. Rafi Romano D.M.D., M.Sc
Dr. Pablo Echarri D.M.D., M.Sc