FINITE ELEMENT ANALYSIS OF LINGUAL FORCES EFFECT IN ALVEOLAR BONE LOSS CASES

Camelia Szuhanek

Assistant Professor, Department of Orthodontics, University of Medicine and Pharmacy Timisoara, Romania 

office@smile-center.ro

www.lingualnews.com Vol 5 No 1 May 2007

ABSTRACT: The aim of this study was to analyse the stress distribution and values after application of forces in lingual orthodontics, in cases with varying bone height. Based on the normal teeth morphology, 3D models of an upper central incisor with normal bone level, 3 mm bone loss and 6 mm bone loss were constructed. After the construction of the geometrical models, material characteristics were introduced and the resulted numerical models were subjected to orthodontic forces. Tipping forces were applied lingually, with  an intensity of 25g. The application points varied on mesio-distal direction and on different heights from the incisal area. The stress values were concentrated on apical area and on alveolar crest and were higher with the degree of the alveolar bone loss. The statistical analysis showed that  for the same alveolar bone loss degree, the stress are decreasing with the increasing of H and they are less dependent of M-D values. Accurate bracket positioning and keeping the force intensity very low are key elements in achieving clinical success.
KEY WORDS: finite elements analysis, lingual orthodontics, biomechanics, alveolar bone loss

INTRODUCTION
Lingual orthodontics has become the most efficient and esthetic approach to adult treatment, especially in an era of increasing demands for invisible appliances. The biomechanical approach in lingual treatment requires specific principles, as stated in the previous studies 1,2.
Previous studies have shown that treating periodontal patients with lingual appliances requires specific considerations in the biomechanical approach 3, 4. In case of periodontal disease and of alveolar bone loss, the center of resistance will be modified, and the application point of orthodontic forces will vary. Among the advantages in lingual biomechanics is the closer distance between the point of force application and the center of resistance 1,2 .
The finite elements method was extensively used for evaluating the biomechanical effects of labial orthodontic forces 4,5,6,7,8,9,10 etc. There are research studies that compare the biomechanics of labial and lingual orthodontics 1,10,11. Although biomechanics in labial orthodontics has extensive approach, the numerical studies analyzing the lingual biomechanics are very few. A previous study 1 investigated the effect of  vertical forces in labial and lingual orthodontics. The authors demonstrated  that the result of lingual vertical forces cannot be entirely predicted, because it depends both on bracket positioning and the initial  tooth inclination 1.
The variation of force application point in lingual orthodontics can produce unwanted results and stress concentrations, especially in cases with less alveolar support 1,3,10 . 

AIM
The following study evaluated the biomechanical parameters of lingual tipping forces in an upper central incisor with various bone loss levels.

MATERIALS AND METHODS
The following study was conducted with the collaboration of the Department of Department Materials Resistance, Technical University of Timisoara, Romania.  Using the specific morphological data, we constructed three geometrical models of an upper central incisor, with 0mm, 3mm and 6 mm of bone level loss. The geometrical models were imported in a finite elements software(COSMOSM 2.5) and the material characteristics were applied.

Table 1:  Material properties used in the finite element analysis

This resulted in three numerical models with the following structure:
1. Model A (6mm bone loss) 687 nodes and 944 tetrahedral isoparametric 4-noded elements;
2. Model B (3mm bone loss) 1207 nodes and 1615 tetrahedral isoparametric 4-noded elements;
3. Model C (0mm bone loss) 2487 nodes and 3468  tetrahedral isoparametric 4-noded elements.

Table 2: Characteristics of the numerical models and application points used in this study.

The numerical models resulted were loaded with orthodontic forces similar to those used during the orthodontic treatment. The forces were applied lingually, and the application point varied on different heights and on mesio-distal direction. The intensity of tipping forces was 25g.
Statistical interpretation of data was performed using the STATGRAPHICS software 13,14,15. The tests were realized for different alveolar bone loss degree in the experimental domain of H and M-D factors. Tests results allowed doing a representation of responses surfaces:

von Mises stress = f(H, M-D)

Response surfaces were represented for the case of square or linear experimental models by using the least square method. This method allowed explaining experimental models by minimizing the estimated values of von Mises stress deviations, compared to the measured values of the same function, in the explored domain.

RESULTS
Von Mises values were calculated for different orthodontic loads and the results were expressed using a  colour scale.

Table 3: Von Mises values resulted in this study

Fig. 1 abc Graphical representation of stress distribution after the application of the tipping force in the central point of the lingual side. a – no bone loss; b- 3 mm bone loss; c – 6 mm bone loss.

Fig.2 abc Graphical representation of the stress(Von Mises) variation in the three situations:
a -  no alveolar loss; b – 3mm bone loss; c – 6mm bone loss.

Fig.3 Section of the 6 mm bone loss numerical model reaction to a tipping force. Note the high concentrations of stress in the apical, cervical and alveolar bone areas.

Regarding the statistical analysis, for an easy interpretation of the results, the scale of von Mises stress representation was taken the same for all three alveolar bone loss degrees. From the graphical analyses, it can be noticed that for the same conditions, the stress are proportionally higher with the alveolar bone loss degree.
When tipping movement occurs, the highest stress concentrations were noted at the application point, at the cervical and alveolar bone areas. Results show that, for the same orthodontic load, stress values are very low for the case with no bone loss. 
Alveolar bone loss of 3mm caused an increase of maximum stress comparing to the value found in the case with normal bone height.  The values of stress found in the case with 6mm bone loss were extremely high comparing with the other two cases studied.

DISCUSSION
The objectives of our study were the numerical evaluation of tissue  reactions after the application of tipping orthodontic forces on lingual side of an upper central incisor. The variation of bone level and of application point has resulted in a number of 54 situations of orthodontic loading. 
At the variation of the height factor for the force application point, we found that stress values are increasing with the decrease of the distance to incisal margin. The values became lower when force was applied near the cervical area, probably because of the translation component that appears in this case. Results have shown that, the closer the application point was to the incisal area, the  higher were the stress values and concentrations recorded. At the variation of mesio-distal application point, we found stress differences between the central and excentric application  points, but the significancy of mathematical  differences was reduced.
Therefore, for the same alveolar bone loss level, the stress values were reduced with the increasing of height and they were less dependent of mesio-distal variation values. Application of high intensity forces in cases with alveolar bone loss will result in concentrations of stress with high values, that could lead to periodontal damage and hyalinization.
Positioning of the brackets in lingual orthodontics requires specific attention, a small mistake can result in unnecessary stress concentrations and unwanted movements. Precision devices for lingual bracket positioning, such as LBJ(Lingual Bracket Jig) should be used in order to maintain individual tip, torque in-out and vertical control 12. 
Further numerical investigations are necessary in order to investigate the reaction of dento-alveolar structures at complex orthodontic loading from lingual treatment.

CONCLUSIONS
The accuracy of bracket placement is very important in achieving the desired result. The intensity of orthodontic forces should be kept at minimal levels especially in cases with alveolar bone loss, in order to allow bone remodeling and to reduce iatrogenic effects. Using the finite elements method, we can predict the response of the dento-alveolar tissues to orthodontic loads in an unlimited number of situations.

ACKNOWLEDGMENTS
The author would like to thank to Professor Nicolae Faur and Professor Eugen Cicala from the Technical University of Timisoara for providing technical support and advice for  analysis and statistical interpretation. My whole gratitude to Dr.Silvia Geron for her continous encouragements and support in my first steps in lingual orthodontics.

REFERENCES
1. Geron S, Romano R, Brosh T.: Vertical forces in labial and lingual orthodontics applied on maxillary incisors--a theoretical approach. Angle Orthod. 2004 Apr;74(2):195-201.
2. Scuzzo G., Takemoto K.: Invisible orthodontics. Current concepts and solutions in lingual orthodontics. Quintessence Books, Berlin, Chicago, London,  Copenhagen, Paris, Milano, Barcelona, Istanbul, 2003. 

3. Geron S.: Managing the orthodontic treatment of patients with advanced periodontal disease: the lingual appliance. World J Orthod. 2004 Winter;5(4):324-31. 

4. Tanne K, Yoshida S, Kawata T, Sasaki A, Knox J, Jones ML: An evaluation of the biomechanical response of the tooth and periodontium to orthodontic forces in adolescent and adult subjects. Br J Orthod 25:109-115, 1998.

5. Jeon PD, Turley PK, Ting K. Three-dimensional finite element analysis of stress in the periodontal ligament of the maxillary first molar with simulated bone loss. Am J Orthod Dentofacial Orthop. 2001 May;119(5):498-504. 

6. Bourauel C, Freudenreich D, Vollmer D, Kobe D, Drescher D, Jager A. Simulation of orthodontic tooth movements. A comparison of numerical models. J Orofac Orthop. 1999;60(2):136-51.

7. Knox J, Jones ML, Hubsch P, Middleton J, Kralj B. An evaluation of the stresses generated in a bonded orthodontic attachment by three different load cases using the Finite Element Method of stress analysis. J Orthod. 2000 Mar;27(1):39-46. 

8. Carlos Felix, Cobo Juan, Mondragon Pilar, Diaz Belen: La technique vestibulaire par opposition a la technique linguale. Etude et transmission des forces avec la mthode des elements finis. Rev Orthop DEnto Faciale 34 : 279-287, 2000. 

9. Vollmer D, Bourauel C, Maier K, Jager A.:Determination of the centre of resistance in an upper human canine and idealized tooth model. Eur J Orthod 21:633-648, 1999.

10. Szuhanek C.: Periodontal implications in orthodontics. PhD thesis. (Implicatii parodontale in anomaliile dento-maxilare. Teza de doctorat). Timisoara, Romania, 2006.
11. Jost-Brinkmann PG, Tanne K, Sakuda M, Miethke RR. A FEM study for the biomechanical comparison of labial and palatal force application on the upper incisors. Finite element method. Fortschr Kieferorthop. 1993; 54:229. 

12. Geron S.: A new instrument for controlled bracket positioning. J Clin Orthod. 2002 Apr;36(4):206-7.

13. Cicală, E. - Statistical interpretation of experimental data. Metode de prelucare statistică a datelor experimentale, Ed. Politehnica, Timisoara, 1999.

14. Montgomery, D.C., - Design and analysis of experiments, John Wiley & Sons, New York, 1991;

15. *** STATGRAPHICS, Reference Manual, Manugistic, Inc., Cambridge, 1992.

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