Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 1 Journal of Computational Methods in Sciences and Engineering -1 (2017) 1 10 1 DOI 10.3233/JCM-170708 IOS Press 1 2 3 Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement: A three dimensional finite element study 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Nishad Prem, Rohan Mascarenhas, Akhter Husain and Ahmed Hashim Department of Orthodontics, Yenepoya University, Deralakatte, Mangalore 575018, India Abstract. This study was conducted using 3-dimensional Finite Element Analysis to evaluate the stress related changes in the periodontal ligament. The objectives of the study were to determine the optimum orthodontic force for both sliding and loop mechanics and to determine efficacy of two loop designs namely T loop and Tear Drop loop. The efficacy of Permachrome and Beta III titanium archwire in loop mechanics were also evaluated. Keywords: Finite element method, periodontal ligament, sliding mechanics, loop mechanics 1. Introduction Canine retraction after first premolar extraction is a very common orthodontic procedure. Many designs have simply evolved and were not analyzed to determine whether they would be able to provide correct force system. The theory of optimum orthodontic force proposed by Storey and Smith [1] stated that the ideal force for bodily canine movement was between 150 200 grams. Sliding mechanics which causes bodily movement along the archwire is a basic method for canine retraction in orthodontic treatment. In 1982, Charles Burstone introduced segmental arch approach to space closure using frictionless attraction springs. Vast studies have been conducted by Burstone [2] on biomechanics. He explained the basic relationships between forces and tooth movement and their potential for clinical relevance. It was found that the center of resistance was at a point one-third of the distance from the alveolar crest to the apex and since most forces are applied at the bracket, it is necessary to compute equivalent force systems at the center of resistance in order to predict tooth movement [3 5]. The 3-dimensional Finite Element Analysis (FEA) which is a better method to model the stress reactions in the supporting tissues was introduced into Orthodontics in 1972 by Yettram, since then a number of studies have been carried by this method. This Finite Element Analysis study attempts to find optimum orthodontic force and to quantify the stresses in the periodontal ligament during the retraction of maxillary canine using different methods. The maxillary canine retraction was carried out with both sliding and loop mechanics. Corresponding author: Rohan Mascarenhas, Department of Orthodontics, Yenepoya University, Deralakatte, Mangalore 575018, India. E-mail: rohanmasc@yahoo.com. 1472-7978/17/$35.00 c 2017 IOS Press and the authors. All rights reserved
Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 2 2 N. Prem et al. / Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 2. Methodology This study was conducted using 3-dimensional finite element analysis to evaluate and compare the stress distribution on and around the maxillary canine during individual canine retraction using sliding and loop mechanics. 2.1. Computer hard ware SYSTEM CONFIGURATION: HP Work station 3030 SOFTWARES USED: GEOMAGIC-CT Scanned images converted to solid model PRO-E WILD FIRE 2-Modeling software HYPERMESH V 7.0-Finite element modelling software ANSYS 10-Analysis software (Structural) ABACUS-Analysis software (Contact) EZIDICOM and AUTOCAD The study was carried out in two parts, 2.2. First part Finite element models of the following were created; 1. Maxillary arch with all the teeth except the 1st premolars and 3rd molars. 2. Two retraction loops (T loop, tear loop) were created with 0.019 0.025 inch wire. The loops are placed in the centre of the extraction space and engaged between canine and the posterior segment. 3. Two continuous archwires, one round (0.018 in) and one rectangular (0.019 0.025 in) and one rectangular (0.019 0.025 in) were also created. 2.3. Second part 1. Placement of all brackets and molar tubes. 2. Engagements of archwires. 3. Load application for stress analysis using sliding mechanics and loop mechanics. 2.4. Finite element modeling Numerical representation of the geometry was created by dividing the geometry into finite number of elements and the elements were connected together with nodes at the junction of the elements. It involves the geometric modelling followed by conversion of the geometric model into the finite element model. 2.5. Geometric modeling of the maxilla and upper dentition In the study CT scan images of the upper dentition and maxilla were taken of a patient in the axial direction at a distance of 1 mm.the scanned images were converted into soft copy and were viewed with the dental software EZIDICOM. Then the images were copied to modeling software AUTOCAD to trace the image. This was done for all images at each slice. The traces taken from the scanned picture were
Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 3 N. Prem et al. / Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement 3 Fig. 1. PRO-E model of maxillary arch. Fig. 2. Continuous round 0.018 inch archwire. 65 66 67 68 69 70 71 assembled in an axial direction to get the complete set of traces into a single unit using modeling software PRO/ENGINEER. The assemblies of traces were brought into finite element analysis software package ANSYS, then areas and volumes were created from the traces. Different volumes were created for all the teeth, bone and periodontal ligament to study the movement of individual teeth in alveolar bone sockets. The brackets considered for the study were the 3M MBT 0.022 0.025 inch slot with molar tubes. The shape of the brackets were multifaceted, hence the 3-D models were created by combining laser scanning and profile projection. The brackets were scanned using a FARO PLATINUM ARM Laser scanner to
Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 4 4 N. Prem et al. / Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 Fig. 3. Continuous 0.019 0.025 inch stainless steel rectangular archwire. achieve the outline. The slot dimensions were then applied using a PROFILE PROJECTOR. A complete scanned 3D image replicating the exact size and shape of the bracket with the tip and torque values incorporated was then processed by transferring the received data into the software PRO/ENGINEER E 2.0 version. A 3D model of the brackets and the buccal tube were then created with the input by engineering designers. The models of the wires were created in PRO/E as specific geometric structures. Contnuous archwires for sliding mechanics 1. 0.018 inch circular stainless steel archwire (Fig. 2). 2. 0.019 0.025 inch rectangular permachrome (3M unitek) stainless steel archwire (Fig. 3). Archwires for loop mechanics 1. T loop 0.019 0.025 inch rectangular archwire (Fig. 4). 2. Tear Drop 0.019 0.025 inch rectangular archwire (Fig. 5). Each loop is made with both permachrome (3M unitek) and Beta III titanium (3M unitek) archwires. Loop dimensions T loop: total length of loop 6 mm, length of vertical legs 4 mm, distance between the horizontal legs 2 mm Tear drop loop: lengths of vertical legs of the loop 6 mm, arch 4 mm. Both the loops were placed in the centre of the extraction space. 2.6. Meshing The process of meshing was carried using a software ALTAIR HYPERMESH 7.0 version. This is a preprocessor used for preprocessing, which includes meshing and applying specific boundary conditions.
Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 5 N. Prem et al. / Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement 5 ct ed pr oo fv er si o n Fig. 4. T loop using 0.019 0.025 inch rectangular archwire. 98 99 100 101 102 103 104 105 106 107 108 109 110 111 The complete model from PRO/E was imported into the HYPERMESH software as an assembly and all the independent parts, tooth, bone, wire, brackets and PDL have been meshed with specific element types based on the geometry. The area of concern is mostly the brackets, wire and the periodontal ligament. So the three parts were modelled with good quality high number of elements to capture the result gradients accurately. The number of elements decides the quality of the results and the system used for solving. The different structures such as alveolar bone, dentition, periodontal ligament and the wire used in the finite element model of human maxilla were assigned their respective material properties. The material characteristics are confirming to data available in the literature. The material data used in this study were taken from finite element studies conducted previously by Tanne et al. (Table 1). The boundary condition in the finite element model basically represents the load imposed on the structures under study and their fixation counter parts. The model was restrained at the superior border of the maxilla in order to avoid any motion against the loads imposed on the dentoalveolar structures. The final model was done in such a way that the dimensions of all the teeth were according to the normal values from Wheelers text book of dental anatomy [7]. Thus the final model was confirmatory from an engineering point of view for this study. co 97 un 96 rre Fig. 5. Tear drop loop using 0.019 0.025 inch rectangular archwire.
Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 6 6 N. Prem et al. / Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement Table 1 Material constant of tooth, alveolar bone, periodontal ligament, stainless steel, permachrome and beta III titanium Material Young s modulus (N/mm 2 ) Poissons ratio Tooth 2 10 4 0.30 Periodontal ligament 6.8 10 1 0.49 Bone 1.4 10 5 0.30 Stainless steel 2 10 5 0.31 Permachrome wire 2.14 10 5 0.30 Beta III titanium wire 1.09 10 5 0.31 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 2.7. Analysis All the analysis were performed using ANSYS version-7 and ABACUS software. The first phase consisted of application of loads between 150 gms 350 gms on the maxillary canine using sliding mechanics. The load at which canine displace bodily was determined. Two analysis were done in the first phase, one with round (0.018 in) and the other with rectangular (0.019 0.025 in) continuous archwires. The second phase was done entirely using ABACUS software. Loads same as the first phase was applied. Four sets of analysis were done using loop mechanics. Analyses of the first two sets were done using two loop desgins (T loop, tear drop). The second two sets were done with permachrome (3M unitek) and beta III titanium (3M unitek) archwires using the same loop designs. 2.8. Post processing phase The stress distribution in the periodontal ligament when the canine displaced bodily were recorded for both sliding and loop mechanics. Interpretations of the various analysis were carried out this stage. Stresses in the periodontal ligament (first principal, second principal, third principal and vonmises) were documented with pictures. 3. Results A distal force is applied on the maxillary canine during the analysis. The resulting stress patterns generated in the periodontal ligament were represented by different colours, from blue to red. Different colors represented different stress levels in the deformed state and is expressed in Newton/mm 2. Positive values with red color indicates maximum tensile stress and negative values with blue color indicates maximum compressive stress. Different distal forces between 150 350 grams were applied on the maxillary canine. When sliding mechanics was used the rectangular permachrome stainless steel archwire showed bodily movement of canine at a force of 210 grams. When round stainless steel archwire was used no bodily movement was achieved. In loop mechanics, both T loop and Tear drop loop gave bodily movement of canine at 200 gms of force. The amount of activation required to deliver 200 gms of force is more for T-loop than for tear drop loop. Beta III titanium archwires required more activation than the permachrome archwire with the same loop design.
Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 7 N. Prem et al. / Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement 7 Table 2 Maximum compressive stress and maximum tensile stress in sliding mechanics and loop mechanics Sliding mechanics RECTANGULAR ARCHWIRE (0.019 0.025) ROUND ARCHWIRE (0.018) Compressive stress N/mm 2 Tensile stress N/mm 2 Compressive stress N/mm 2 Tensile stress N/mm 2 0.084013 0.054239 0.007279 0.006094 Loop mechanics T LOOP TEAR DROP LOOP Compressive stress N/mm 2 Tensile stress N/mm 2 Compressive stress N/mm 2 Tensile stress N/mm 2 0.00150 0.00200 0.00196 0.00373 140 141 142 143 144 145 146 147 148 149 150 151 152 153 Fig. 6. Stress patterns at 210 grams using round archwire. 3.1. Sliding mechanics Round archwire (0.018 in): maximum tensile stress (0.006094 N/mm 2 ) is observed on the cervical area third of the mesial surface and maximum compressive stress ( 0.007279 N/mm 2 ) is observed on the cervical third of the distal surface. The stress patterns indicate tipping of the maxillary canine at 210 gms of force (Fig. 6). Rectangular archwire (0.019 0.025 in): maximum tensile stress (0.054239 N/mm 2 ) is observed on the cervical area third of the mesial surface and maximum compressive stress ( 0.084013 N/mm 2 )is observed on the cervical third of the distal surface. The areas of maximum compressive and tensile stresses are much less than the round wire (Fig. 7). 3.2. Loop mechanics T loop:the caninesmovedbodily at 200 gms of force with both the archwire. The resulting stress patterns were similar. Maximum tensile stress (0.0014 N/mm 2 ) and compressive stress ( 0.0015 N/mm 2 ) on the cervical area of the mesial and distal surfaces of the maxillary canine. The rest of the periodontal ligament showed stresses between (0.00025) and ( 0.00033) (Fig. 8).
Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 8 8 N. Prem et al. / Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement Fig. 7. Stress patterns at 210 grams using rectangular archwire. Fig. 8. Stress patterns at 200 gms using T-loop. 154 155 156 Tear drop loop: analysis similar to T loop was done with this loop design and bodily movements of maxillary canines were achieved. Mesial surface of the maxillary canine showed maximum tensile stress of (0.0023 N/mm 2 ) and distal surface maximum compressive stress of ( 0.0019 N/mm 2 ) (Fig. 9) 157 158 159 160 4. Discussion Canine retraction after first pre molar extraction can be achieved using either sliding or loop mechanics. Too low a force would not move the intended tooth and at the same time heavy forces would result in unwanted movement of the anchor unit. Therefore it becomes important to find the optimum orthodontic
Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 9 N. Prem et al. / Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement 9 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 Fig. 9. Stress patterns at 200 gms using tear drop loop. force for canine retraction. The optimum orthodontic forces in sliding and loop mechanics are different, friction between archwire and bracket being one of the reasons. Over the years researchers have come up with various loop designs for canine retraction. As the canine translates distally, the amount of force delivered by the loop would reduce. The rate of decay of force is called load deflection rate. The different loop designs that are available today were developed to lower the load deflection rate. In this study, distalizing forces between 150 350 gms were applied on the maxillary canine. At 210 gms of force the use of rectangular archwire (0.019 0.025 inch) showed compressive stress of 0.084013 N/mm 2 on the mesial surface and tensile stress of 0.054239 N/mm 2 on the distal surface of the PDL. The use of round archwires showed compressive stresses of 0.007279 N/mm 2 and tensile stress of 0.006094 N/mm 2 at 200 gms of force. The stress patterns showed an equal distribution of compressive and tensile stresses on the PDL of the maxillary canine with the use of rectangular archwire.at the same time the round archwire showed compressive stress patterns extending into the lingual surface and tensile stress patterns into the buccal surface indicating that the canine experienced tipping and rotation. According to Burstone, the T-loop is a better loop design than the simple vertical loop because the load deflection rate is lower and produces adequate moment to force ratio. This according to him is because additional wire is placed apically in the T-loop design. In this study the use of T-loop design showed a compressive stress of 0.00150 N/mm 2 and tensile stress of 0.00200 N/mm 2 in the PDL showed compressive stress of 0.00196 N/mm 2 and tensile stress of 0.00373 N/mm 2. The T-loop design showed a better stress distribution on the PDL than the Tear Drop Loop Design. Based on these findings we can say that the T-loop design is a better loop design for canine retraction. 184 185 186 5. Conclusion The stress patterns clearly indicate that the optimum orthodontic force for canine retraction using sliding mechanics is 210 grams and for loop mechanics is 200 grams. In sliding mechanics, the use of
Galley Proof 8/02/2017; 9:17 File: jcm 1-jcm708.tex; BOKCTP/ljl p. 10 10 N. Prem et al. / Comparison of sliding mechanics and loop mechanics in orthodontic tooth movement 187 188 189 190 191 0.019 0.025 inch rectangular archwire showed bodily movement while the use of round 0.018 inch archwire only showed tipping of canine. In loop mechanics, at 200 grams of force the T loop design was found to be the better loop design than the Tear drop. The permachrome and beta III titanium archwires showed similar stress patterns in each loop design. 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 References [1] E. Storey and R. Smith, Force in orthodontics and its relation to tooth movement, Austal J Dent 56 (1952), 11 13. [2] K. Tanne, M. Sakuda and C.J. Burstone, Three-dimensional finite element analysis for stress in the periodontal tissue by orthodontic forces, Am. J. Orthod. Dentofac. Orthop 92 (1987), 499 505. [3] P.G. Fotos, C.C. Spyrakos and D.O. Bernard, Orthodontic forces generated by a simulated archwire appliance evaluated by the Finite Element Method, The Angle Orthodontis 60(4). [4] M.L. Jones, J. Hickman, J. Middleton, J. Knox and C. Volp, A validated finite element method study of orthodontic tooth movement in the human subject, Journal of Orthodontics 28 (2001), 29 38. [5] D.J. Rudolph, P.M.G. Willes and G.T. Sameshima, A finite element model of apical force distribution from orthodontic tooth movement, Angle Orthod 71 (2001), 127 131. [6] M. Vasquez, E. Calao, F. Becerra, J. Ossa, C. Enriquez and E. Fresneda, Stress differences between sliding and sectional mechanics with an endosseous implant as anchorage: A 3-dimensional finite element analysis, Angle Orthod (2001). [7] M.M Ash, Jr., Textbook of Wheeler s Dental Anatomy, Physiology and Occlusion, Seventh edition, W.B. Saunders Company, 1993, 170 182. [8] W.R. Proffit, Contemporary orthodontics. Third edition, 2000. Mosby, Inc. page number 341 342. [9] M.R Marcotte, Biomechanics in orthodontics, 1990. Publisher, B C Decker Inc.10 12. [10] Ravindra Nanda, Biomechanics in clinical orthodontics published WB Saunders Company page number 2 9. [11] J.C. Bennett and R.P. Mc Laughlin, Controlled space closure with a pre adjusted appliance, J. Clin. Orthod (1990), 251 260. [12] J.C. Bennett and R.P. Mc Laughlin, Trevisi, systemized orthodontic treatment mechanics. [13] P. Ziegler and B. Ingervall, A clinical study of maxillary canine retraction with a retraction spring and with sliding mechanics, Am. J. Orthod. Dentofac. Orthop 95 (1989), 99 106.
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