oiginal articles annals and essences of dentistry...oiginal articles annals and essences of...

Oiginal articles Annals and Essences of Dentistry

Vol. - III Issue 2 Apr – jun 2011 33

doi:10.5368/aedj.2011.3.2.1.7

A 3-D ANALYSIS TO STUDY THE CENTER OF RESISTANCE MODIFICATION WITHALVEOLAR BONE RESORPTION- A FINITE ELEMENT METHOD

1Chandrashekhar B.S1 Associate professor, Department of orthodontics and Dentofacial Orthopaedics.

2 Chandralekha B 2Professor and Head, Department of orthodontics and Dentofacial Orthopaedics.3Vinay.P 3 Professor, Department of orthodontics and Dentofacial Orthopaedics .

1,3, Krishnadevaraya college of Dental sciences, Bangalore, Karnataka, India.2 Vydehi Dental college and Hospital, Bangalore

ABSTRACT

The aims of this investigation were to define the modified location of CRES and CROT in a maxillary centralincisor with different alveolar bone heights. A three dimensional finite element model of the upper central incisor with itssupporting structures was created using ANSYS software on a PIII computer. Five three dimensional models of an uppercentral incisor with 1 to 6.5 mm of alveolar bone loss were formulated and used by the author. Center of resistance andcenter of rotation were located for the various stages of alveolar bone loss. The results revealed that the moment/forceratio (at the bracket level) required to produce bodily movement increases in association with alveolar bone loss. Boneloss causes center of resistance movement towards the apex, but its relative distance to the alveolar crest decreases atthe same time. Greater amounts of displacements of incisal edge and apex were observed with increased alveolar boneloss for a constant applied force. Center of rotation of the tipping movement also shifted towards the cervical line. Amongthe many differences between orthodontic treatment of an adolescent and an adult patient is the presence of alveolarbone loss in the adult cases. Alveolar bone loss causes change in center of resistance as a result of alteration in bonesupport. This necessitates modifications in the applied force system to produce the same movement as in a tooth with ahealthy supporting structure.

KEY WORDS:. FEM, Alveolar bone loss,modification of CRES and CROT.

INTRODUCTION

Orthodontic treatment strategies have traditionally beenoriented towards an adolescent and preadolescent agegroup, in which a developing or newly formedmalocclusion is present. Over the last few years, adultmalocclusion, aesthetic and functional benefits oforthodontic treatment are some of the factors responsiblefor increased popularity of adult orthodontics. Recentimprovements in orthodontic materials as well asaesthetically pleasing and biomechanically soundappliances have also played a positive role.

The percentage of adult patients who seekorthodontic treatment has increased significantly in recentdecades1,2. These patients often require multidisciplinarytreatment, especially when they are periodontallycompromised. A major challenge with advancedperiodontal bone loss is performing controlled toothmovement without causing complications because of anincreased crown to root ratio.

Although bone resorption among orthodonticpatients is not usual, in most patients, it can cause manyproblems that should be considered in force systemapplications. Some important points are as follows:

The reduced root surface to reactive alveolarbone ratio requires an adaptation of forcemagnitude.

The apical shifting of the center of resistanceentails a different force system (moment to forceratio) to determine the type of tooth movement.

Periodontally affected teeth imply a decreasedanchorage quality so that undesirable sideeffects are more difficult to control.

Investigators have studied the behavior of toothmovement from different points of view; histologically,physiologically and biomechanically. In vivomeasurement of stress is difficult at best; thus,development of an effective model for this system is aworthy goal.

The Finite Element Method(FEM) is a highlyprecise technique used to analyze structural stress. It isexpected that the FEM may be capable of analyzingsystematically and quantitatively the biomechanical



tissue response. In orthodontics, FEM has been usedsuccessfully to model the application of forces to singletooth systems. Alveolar bone loss was shown to lowerthe center of resistance of the tooth and alter the stresspatterns on the root1,3. Similar changes were observed inaltering root length4. It has been shown by FEM that thebiomechanical properties of the periodontal ligament aredifferent between adults and adolescents4.

This study is designed to evaluate the influenceof the height of bone support on the location of center ofresistance and center of rotation in a maxillary centralincisor. Thus, it is of clinical significance to understandoptimal force consideration for adults with altered crown-root ratios, particularly during initial application of load.The maxillary central incisor was chosen because itundergoes the most detailed tooth movement and is athigh risk for root resorption than all other teeth except themaxillary lateral incisor5.

Materials and Methods

Five three dimensional finite element models of

an upper central incisor were designed. Each model

comprised a maxillary central incisor, the periodontal

ligament and alveolar bone consisting of 19,400 to

16,948 nodes and 15,500 to 14,045 tetrahedron 10 node

solid elements (Table 1). The elements were of mesh

mapped pattern.

Average anatomic data of the upper central incisor was

based on dimensions given by Tanne K6. The height of

the tooth (distance from the apex of the root to the incisal

edge) was 23.5mm and the mesio-distal and labio-palatal

widths of the crown were 8.5mm and 7mm respectively.

The alveolar bone was the sole difference of these five

models and was considered to have 13 (normal

situation), 12, 10.5, 8 and 6.5mm height respectively.

The periodontal ligament was simulated as 0.2 mm thick

layer around the root (Fig.1, Fig.2 Fig.3 Fig.4 and

Fig.5)

Table 1. Characteristics of the models used in thisstudy

Model Nodes Elements AlveolarBoneHeight(mm)

Boneloss

(mm)

1 19400 15500 13 02 19100 15200 12 13 18600 14900 10.5 2.54 17392 14314 8 55 16948 14045 6.5 6.5

Fig.1 Schematic representation of the three-dimensional FEM model for the Upper central

Incisor.

The computer program used for the analysis was theANSYS program (ELAN Computer Group, America).

In the present study, all materials were assumed tobe isotropic and elastic. The mechanical properties(Poisson's Ratio, Young's Modulus) of the periodontalligament, tooth and alveolar bone were obtained fromprevious studies7. The material constants are as shown inthe Table 2.

Table 2. Mechanical properties for the structuralelements

Material Young’s Modules(kg/mm2)

Poisson’s Ratio

Tooth 2 x 103 0.30PDL 6.8 x 10-2 0.49

Alveolar 1.4 x 103 0.30

The boundary conditions were defined tosimulate how the model was constrained and to prevent itfrom free body motion.

Loading conditions

For all the five above mentioned models, a forceof 100 gm was applied to the labial surface of the toothcrown at each phase of the study at 5.5mm apical inrespect to the incisal edge (this was presumed to be thelocation of the bracket). The point of force application wascentered mesiodistally. Congruence of the line of action ofthe force with the long axis of the tooth avoids any rotationtendency at the models, due to the lack of any momentarm with respect to the long axis arm.

There are two reliable criteria to study thebehavior of tooth movement, center of resistance andcenter of rotation; consequently, finding the center ofrotation of a simple tipping movement and center ofresistance of each model are two main goals of eachphase of this study. Application of a point force of 100gmis suitable to find the center of rotation of the model.Evaluation of the displacement of nodes at the root



Fig.2. An Isometric view of 3-dimensional modelwith no bone loss

Fig.3. An Isometric view of 3-dimensional modelwith 2.5mm of bone loss

Fig.4. An Isometric view of 3-dimensional modelwith 5mm of bone loss

Fig.5. An Isometric view of 3-dimensional modelwith 6.5mm of bone loss

surface reveals that there are always two adjacent nodesat two different levels that show opposite directions ofdisplacement. The center of rotation was determined bythe method used by Smith and Burstone for each model7

(with different alveolar bone heights).

As the second phase of the study, differentMoment/Force (M/F) ratios were applied. The nearestsituation to the bodily movement (being specified by thealmost equal amounts of node displacements at differentroot levels) showed the distance apically from the bracketposition to center of resistance.

Results

As the center of resistance moved apically with thealveolar bone loss, its distance to the alveolar crestdiminished. Without bone loss, center of resistance wasapproximately 3.9mm apical to alveolar crest, decreasingto 1.7mm for 6.5mm of alveolar bone loss (Table 3).Alveolar bone loss caused a decrease of distancebetween center of resistance and center of rotation.

Table. 3. Exact location CRES with various bone heights

Bone loss(mm)

Alveolar boneheight (mm)

CRES Apicallyfrom alveolarcrest (mm)

0 13 3.91 12 3.1

2.5 10.5 2.75 8 2

6.5 6.5 1.7

This study suggests that the center of rotation liesapical to the center of resistance by a small amount in atooth with healthy bone support. As more bone loss occurs,



Graph 1. CRES and CROT: Alterations due to alveolar bone loss

Graph 2. Modification of the M/F Ratio needed

Graph 3. Incisal Edge, Cervical & Apical area displacements v/s influence of the alveolar bone loss



the center of rotation of a simple tipping movement movemore apically. The center of rotation was located at 7.5,6.5, 5.0 and 3.9mm from the apex with alveolar bone lossof 1, 2.5, 5 and 6.5mm respectively (Table 4, Graph 1).

Table 4. The location of CRES and CROT with variousbone heights

Bone loss(mm)

Alveolar boneheight(mm)

CROT Incisallyfrom apex

(mm)

CRES incisallyfrom apex

(mm)0 13 8.0 9.1-1 12 7.5 8.9

-2.5 10.5 6.5 7.8-5 8 5.0 6.0

-6.5 6.5 3.9 4.8

The findings from this study revealed that the M/F rationeeded to produce bodily movement without alveolar boneloss was -8.9 mm (point of force application was 5.5mmapical to the incisal edge). The M/F ratio increased from9.1, 10.2,12 and 13.2 for 1, 2.2, 5 and 6.5mm alveolar boneloss (Table 5 and Table 6, Graph 2).

Table No 5. M/F ratio to maintain bodily movement withdifferent alveolar bone heights.

AlveolarBone Loss

(mm)-1 -2.5 -5 -6.5

M/F Ratio9.1 10.2 12 13.2

Table. 6. M/F Ratio increments to maintain bodilymovement with different alveolar bone heights for bodily

movement (different amounts of alveolar bone loss)

Alveolar bone loss(mm)

-1 -2.5 -5 -6.5

M/F Ratio 3% 17.29% 37.21%48.30%

Table No 7. Change of the movements in different partsof an upper central incisor caused by alveolar bone

loss

Bone Loss(mm)

Incisal edgeMovement

(mm)

Cervical Partmovement

(mm)

Apical PartMovement

(mm)0 1 1 1-1 1.41 1.5 1.39

-2.5 2.33 2.66 2.0-5 6.98 9.02 4.62

-6.5 14 20 9.01

The stress patterns after the application of the same forceafter a reduction in the bone support of 1, 1.2, 2.5 and6.5mm generates an increasing stress in different parts ofthese models. The results of our study shows that a 6.5 mmbone loss causes up to 14 times the incisal edgemovements compared with a normal condition (Table 7,Graph 3).

Discussion

As the number of adults seeking orthodontictreatment has increased over the years, concern for thepotential of adult iatrogenic problems must also increase.Clinical studies report a slight loss of periodontalattachment in adults or adolescents during treatment withfixed orthodontic appliances. This results in an increasedcrown to root ratio1.

The flexibility of the FEM in modifying geometryallowed the simulation of various amounts of bone loss.The results of this study show the significant increase inpressure and the stress concentration in the periodontalligament because of an increased crown to root ratio.Because of the reduced bony support and periodontalligament area, the same magnitude of load on the crowncaused more pressure in the periodontal ligament thanwithout the bone loss. This is in agreement with otherstudies 2,3,8,9.

In this study initial tooth displacements increasedin response to reduced alveolar bone heights. Thedisplacement of the tooth at the incisal edge increased from1.41 and 2.33 to 6.98 and then to 14 times withapproximately 8%, 19%, 38%, and 50% alveolar bone losswhen compared with a tooth with no alveolar bone loss4.

A similar result was obtained by Tanne et al4 in astudy conducted on maxillary central incisor with variouslevels of alveolar bone loss. The displacement of the toothat the incisal edge increased from 2.3 to 6.9 and then to16.5 times with approximately 19%,38% and 50% alveolarbone loss when compared with a tooth with no alveolarbone loss.

In a similar study conducted by Geramy A2 onmaxillary central incisor with various alveolar bone heights,the displacement of the tooth at the incisal edge increasedfrom 1.46 to 44.2 times with approximately 8% to 61%alveolar bone loss.

Since an increase of tooth displacement generallyleads to an increase in tooth mobility, force levels should belowered in patients with short roots and/or substantialalveolar bone loss because mobility may become severe.

Using an FEM model, the present study quantifiesthe effects of alveolar bone loss on center of rotation of asimple tipping movement and center of resistance of thetooth. Center of rotation of the tooth with healthy bone



support was 8.0mm from the apex. As more bone lossoccurs the center of rotation of a simple tipping movementmoved more apically. The center of rotation was located at7.5, 6.5, 5.0, and 3.9 mm from the apex with alveolar boneloss of 1, 2.5, 5, and6.5mm respectively (Table 4). A similarstudy4 showed apicogingival levels of center of rotationfrom a single force ranging from 5.4 to 2.3 mm apical toalveolar crest, in the cases of the alveolar bone heightbeing varied from 13.0 to 6.5mm respectively.

Similarly the center of resistance moved apicallywith alveolar bone loss. Without bone loss, center ofresistance was approximately 3.9mm apical to alveolarcrest, decreasing to 1.7mm for 6.5mm of alveolar boneloss. Alveolar bone loss caused a decrease in distancebetween center of resistance and center of rotation.

The moment to force ratio needed to producebodily movement without bone loss was -8.9 (point offorce application was 5.5mm apical to incisal edge).Alveolar bone loss of 6.5mm increases the M/F rationeeded to produce bodily movement to -13.2. The resultsare almost similar to a study designed by Geramy A2. TheM/F ratio increased from -8.44 (no bone loss) to -12.46(8mm of bone loss).

Tanne et al4 studied the effect of alveolar boneloss on the M/F ratio for bodily movement of a maxillarycentral incisor with 13.0mm root length, with the use of a3-D finite element model. According to their results, theM/F ratio increased from 10.7 (no bone loss) to 12.3, 13.9,and 15 for 2.5, 5.0, and 6.5mm alveolar bone loss. A linearrelationship was observed between the level of bone lossand the amount of force reduction. In clinical practice, thelinear graph can be useful to approximate the reduction inforce magnitude that corresponds with the level of boneloss.

Geramy A2 reported that a 2.5mm of alveolarbone loss causes 14.46% of M/F ratio increment and 5mm of bone loss causes 37.1% M/F ratio increment.Siatkowski10 reports an increase of 38% needed toproduce bodily movement when 5mm of marginal boneloss occurs.

Cobo et al5 stated that with alveolar bone loss,center of resistance can be located above the alveolarcrest. This study shows a decrease of center of resistancedistance to alveolar crest, but the center of resistance wasnever found beyond the alveolar bone crest which is inaccordance with a previous study done by Geramy A2.

Clinical implications

In recent years, the number of studies designedto establish specific principles for orthodontic diagnosisand treatment in adults has increased considerably, due inpart to the greater number of adult patients having alveolarbone loss induced by periodontal diseases3. Excessive

orthodontic force with advanced periodontal bone lossmay traumatize the periodontium, and increased apicalpressure because of reduced bony support may contributeto apical root resorption. Thus in these patients, increaseddemands are placed on clinician for careful application ofthe force systems used in tooth movement.

The reduced supporting periodontal ligamentarea and volume resulted in higher amounts ofdisplacements in supporting structures of affected teeth fora given level of force and moment magnitude. Appliedforce and moment magnitudes must be reduced inproportion in order to maintain physiologically tolerablemovements without further damage to these supportingstructures.

CONCLUSION

The 3-D finite element analysis of stress in theperiodontal ligament of the maxillary central incisor withbone loss clearly demonstrated a significant increase inpressure and stress concentration in the periodontalligament because of orthodontic force. To maintain thelevel of stress close to what was obtained without boneloss, a combination of force reduction and increased M/Fratio was required to achieve evenly distributed stress inthe periodontal ligament of a central incisor with bone loss.These results were obtained from a simulated model, fromwhich biologic variables may occur. In the tooth and itssupporting structures, anatomic variation amongindividuals can affect the actual value of M/F ratio;therefore these variables should be integrated with thefuture modeling system. The resultant values can be usedonly as a reference to aid clinical judgment.

References

1. Boyd RL, Leggott PJ, Quinn RS, Eakle WS, Chambers D.Periodontal implication of orthodontic treatment in adults withreduced or normal periodontal tissue versus those ofadolescents. Am J Orthod Dentofacial Orthop. 1989Sep;96(3):191-8.doi:10.1016/0889-5406(89)90455-1

2. Geramy A. Alveolar bone resorption and the center ofresistance modification (3-D analysis by means of the finiteelement method). Am J Orthod Dentofacial Orthop. 2000Apr;117(4):399-405.doi:10.1016/S0889-5406(00)70159-4

3. Cobo J, Argüelles J, Puente M, Vijande M. Dentoalveolarstress from bodily tooth movement at different levels of bone loss.Am J Orthod Dentofacial Orthop. 1996 Sep;110(3):256-62.doi:10.1016/S0889-5406(96)80008-4

4. Tanne K, Nagataki T, Inoue Y, Sakuda M, Burstone CJ.Patterns of initial tooth displacements associated with variousroot lengths and alveolar bone heights. Am J Orthod DentofacOrthop 1991;100:66-71.doi:10.1016/0889-5406(91)70051-W

http://dx.doi.org/10.1016/0889-5406(89)90455-1http://dx.doi.org/10.1016/S0889-5406(00)70159-4http://dx.doi.org/10.1016/S0889-5406(96)80008-4http://dx.doi.org/10.1016/0889-5406(91)70051-W



5. Rudolph DJ, Willes MG, Sameshima GT. A Finite elementmodel of apical force distribution from orthodontic toothmovement. The Angle Orthodontist 2001; 71(2):127-131.PMid:11302589

6. Tanne K, Koenig HA, Burstone CJ. Moment to force ratio andthe center of rotation. Am J Orthod Dentofacial Orthop. 1988Nov;94(5):426-31.doi:10.1016/0889-5406(88)90133-3

7. Smith RJ, Burstone CJ. Mechanics of tooth movement. Am JOrthod. 1984 Apr;85(4):294-307doi:10.1016/0002-9416(84)90187-8

8. Cobo J, Sicilia A, Argüelles J, Suárez D, Vijande M. Initialstress induced in periodontal tissue with diverse degrees of boneloss by an orthodontic force: tridimensional analysis by means ofthe finite element method. Am J Orthod Dentofacial Orthop. 1993Nov;104(5):448-54.doi:10.1016/0889-5406(93)70071-U

9. Jeon PD, Turley PK, Ting K. Three-Dimensional finite elementanalysis of stress in the periodontal ligament of the maxillary firstmolar with simulated bone loss. Am J Orthod Dentofacial Orthop.2001 May;119(5):498-504.doi:10.1067/mod.2001.112999PMid:11343021

10. Siatkowski RE. Optimal orthodontic space closure in adultpatients. Dent Clin North Am. 1996 Oct;40(4):837-842PMid:8886542

Corresponding Author

Chandra Sekhar BSDepartment of orthodontics and Dentofacial

orthopaedics,Krishnadevaraya college of dental sciences,

Bangalore.Ph. +91-9880722525

email: [email protected]
http://dx.doi.org/10.1016/0889-5406(88)90133-3http://dx.doi.org/10.1016/0002-9416(84)90187-8http://dx.doi.org/10.1016/0889-5406(93)70071-Uhttp://dx.doi.org/10.1067/mod.2001.112999mailto:[email protected]

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