more time is required for extraction 
 cases , such as for adult patients , which is a great concern and poses high risk of 
 caries , external root 
 resorption .
thus , accelerating 
 orthodontic tooth movement and the resulting shortening of the treatment duration would 
 be beneficial .
many researchers have utilized different biochemical methods involving 
 medications to improve the speed and quality of orthodontic treatment , but the systemic 
 influence on the body 's metabolism makes this difficult to apply in orthodontics . 

recently , investigators have begun studying local techniques for stimulating better 
 orthodontic tooth movement . surgically aided rapid tooth movement has become one of the 
 novel techniques for accelerating canine retraction . for premolar extraction cases ,
biologic tooth movement can 
 be achievedwith conventional 
 orthodontic treatment techniques , but the canine retraction phase usually lasts for 6 to 
 8 months .
extraoral or intraoral anchorage mechanics are required to maintain the space 
 obtained during canine distalization , particularly when maximum anchorage is required . 

to date , several novel surgical modalities and techniques for rapid canine retraction 
 have been reported to accelerate canine distalization .
these attempts fall mainly into 
 two categories : the first , dentoalveolar distraction osteogenesis , evolved from 
 distraction osteogenesis .
osteotomies surrounding the canines are created to achieve rapid 
 movement of the canines in the dentoalveolar segment , in compliance with the principles 
 of distraction osteogenesis .
the second technique is periodontal distraction aided by 
 surgical undermining of the interseptal bone .
nevertheless , the 
 question remains regarding which of the above techniques is more effective for rapid 
 canine retraction .
until now , these research modalities and techniques for accelerating canine retraction 
 have been applied in animal experiments and clinical case reports .
after 
 the application of an inappropriate external force to the oral environment , the 
 development of a stress field in the supporting tissues typically leads to an 
 unsuccessful outcome .
finite element analysis has become a powerful tool for dental 
 biomechanical research due to its increased availability , capacity , and ease of use of 
 computer software in biologic modeling .
what is the status of stress in the maxillary teeth , the periodontal ligament ( pdl ) , and 
 alveolar bone during rapid canine retraction ? how does the biomechanics differ between 
 dentoalveolar distraction osteogenesis and periodontal distraction aided by surgical 
 undermining of the interseptal bone ?
will it produce side - effects in addition to tooth 
 movement ? to address these questions via the finite element ( fe ) method , in this study 
 we constructed a three - dimensional ( 3d ) finite element model of the maxillary teeth , the 
 periodontal ligament ( pdl ) , and alveolar bone after extracting the first premolars .
for better simulation of the movement of canine retraction during orthodontic 
 treatment with different auxiliary surgical methods , a patient with bimaxillary 
 protrusion was selected from the orthodontic department of first affiliated hospital 
 of xinjiang medical university .
after the maxillary teeth were aligned and leveled by means of an invisible aligner , 
 images of the patient 's teeth and alveolar bone were obtained in a dicom ( digital 
 imaging and communication in medicine ) data format via 64-slice ( a slice thickness of 
 0.5 mm ) spiral computed tomography ( ct ) .
the geometric shapes of the maxillary teeth 
 and alveolar bone ( cancellous and cortical bone ) were reconstructed by mimics 
 ( version 15.0 ; materialise , leuven , belgium ) , then exported to geomagic studio ( 2013 , 
 raindrop inc . , rock hill , south carolina , u.s.a . ) , and modified by unigraphics nx 
 ( version 8.5 , siemens , mnich , germany ) . the initial 3d finite element model of the 
 maxilla and the maxillary teeth was established with 416,931 nodes and 227,784 solid 
 elements ( figure 1 ) , and analyzed by ansys 
 workbench ( version 13.0 ; ansys inc . ,
canonsburg , pennsylvania , u.s.a . ) . the initial 3d finite element model of the maxilla and the maxillary teeth although periodontal ligament thicknesses differ according to age , position , and 
 individual variations , the thickness of the periodontal ligament was considered to be 
 consistently 0.25 mm .
the 3d finite element models of the 
 alveolar bone were fabricated to fit the teeth and the periodontal ligament , and the 
 thickness of cortical bone was considered to be 2 mm . in this study , we defined the non - surgically - aided canine retraction model as model 
 1 .
the numbers of nodes and elements of the initial model are shown in figure 2 . according to the two types of 
 auxiliary surgical methods for accelerating canine retraction , we simulated the same 
 surgical process in the initial 3d finite element model , and two 3d fems were 
 generated based on the two different surgeries for comparison with the initial model 
 ( model 1 ) .
pdl = periodontal 
 ligament we defined the fem of periodontal distraction aided by surgical undermining of the 
 interseptal bone as model 2 ( pd ) .
after the first premolar was removed , the 
 interseptal bone mesial to the extraction socket was undermined .
the bone in the 
 premolar socket was eliminated vertically along the buccal and lingual sides , 
 extending obliquely toward the base of the interseptal bone to weaken resistance .
the 
 interseptal bone was not cut through mesio - distally toward the canine ( figure 3 ) .
the depth of the undermining grooves 
 was dependent on the thickness of the interseptal bone .
note depths and positions of 
 undermining grooves the final model ( model 3 ) was the fem model of dentoalveolar distraction osteogenesis 
 ( ddo ) .
the first premolar was extracted , and the buccal cortical bone of the 
 extraction socket was removed .
an osteotomy line was determined between the buccal 
 root apex of the first premolar and canine apex ( figure 4).the root of the upper canine tooth was outlined mesially and 
 distally , with the dentoalveolar segment to be used as a transport disc at the apical 
 region .
the cortical bone , especially at the level of the apical region , was also 
 eliminated for maximal bodily movement during distraction .
surgical techniques for dentoalveolar distraction osteogenesis the mechanical properties of the teeth , pdl , and cortical and cancellous bone were 
 defined as isotropic , homogenous , and linearly elastic .
young 's modulus and poisson 's 
 ratio for all materials were calculated according to previously described methods 
 ( figure 5 ) .
pdl = periodontal ligament the coordinate system and directions of forces and loads are shown in figure 6 . a simulated retraction force of 1.5 n 
 ( approximately 150 g )
was loaded bilaterally to the center of the crown between the 
 first molar and the canine , and stress distribution and its magnitude were analyzed 
 by ansys workbench , a 3d finite element analysis program .
an assessment of the stress 
 on the bone elements was performed by von mises equivalent stress and maximum shear 
 stress , and we used the total deformation value to assess the initial displacement of 
 the teeth and the pdl .
a mesiodistal simulated retraction force of 1.5 n was 
 loaded bilaterally to the center of the crown between the first molar and the 
 canine
for better simulation of the movement of canine retraction during orthodontic 
 treatment with different auxiliary surgical methods , a patient with bimaxillary 
 protrusion was selected from the orthodontic department of first affiliated hospital 
 of xinjiang medical university .
after the maxillary teeth were aligned and leveled by means of an invisible aligner , 
 images of the patient 's teeth and alveolar bone were obtained in a dicom ( digital 
 imaging and communication in medicine ) data format via 64-slice ( a slice thickness of 
 0.5 mm ) spiral computed tomography ( ct ) .
the geometric shapes of the maxillary teeth 
 and alveolar bone ( cancellous and cortical bone ) were reconstructed by mimics 
 ( version 15.0 ; materialise , leuven , belgium ) , then exported to geomagic studio ( 2013 , 
 raindrop inc . , rock hill , south carolina , u.s.a . ) , and modified by unigraphics nx 
 ( version 8.5 , siemens , mnich , germany ) . the initial 3d finite element model of the 
 maxilla and the maxillary teeth was established with 416,931 nodes and 227,784 solid 
 elements ( figure 1 ) , and analyzed by ansys 
 workbench ( version 13.0 ; ansys inc . ,
canonsburg , pennsylvania , u.s.a . ) . the initial 3d finite element model of the maxilla and the maxillary teeth although periodontal ligament thicknesses differ according to age , position , and 
 individual variations , the thickness of the periodontal ligament was considered to be 
 consistently 0.25 mm .
the 3d finite element models of the 
 alveolar bone were fabricated to fit the teeth and the periodontal ligament , and the 
 thickness of cortical bone was considered to be 2 mm . in this study , we defined the non - surgically - aided canine retraction model as model 
 1 .
the numbers of nodes and elements of the initial model are shown in figure 2 . according to the two types of 
 auxiliary surgical methods for accelerating canine retraction , we simulated the same 
 surgical process in the initial 3d finite element model , and two 3d fems were 
 generated based on the two different surgeries for comparison with the initial model 
 ( model 1 ) .
pdl = periodontal 
 ligament we defined the fem of periodontal distraction aided by surgical undermining of the 
 interseptal bone as model 2 ( pd ) .
after the first premolar was removed , the 
 interseptal bone mesial to the extraction socket was undermined .
the bone in the 
 premolar socket was eliminated vertically along the buccal and lingual sides , 
 extending obliquely toward the base of the interseptal bone to weaken resistance .
the 
 interseptal bone was not cut through mesio - distally toward the canine ( figure 3 ) .
the depth of the undermining grooves 
 was dependent on the thickness of the interseptal bone .
note depths and positions of 
 undermining grooves the final model ( model 3 ) was the fem model of dentoalveolar distraction osteogenesis 
 ( ddo ) .
the first premolar was extracted , and the buccal cortical bone of the 
 extraction socket was removed .
an osteotomy line was determined between the buccal 
 root apex of the first premolar and canine apex ( figure 4).the root of the upper canine tooth was outlined mesially and 
 distally , with the dentoalveolar segment to be used as a transport disc at the apical 
 region .
the cortical bone , especially at the level of the apical region , was also 
 eliminated for maximal bodily movement during distraction .
the mechanical properties of the teeth , pdl , and cortical and cancellous bone were 
 defined as isotropic , homogenous , and linearly elastic .
young 's modulus and poisson 's 
 ratio for all materials were calculated according to previously described methods 
 ( figure 5 ) .
a simulated retraction force of 1.5 n 
 ( approximately 150 g ) was loaded bilaterally to the center of the crown between the 
 first molar and the canine , and stress distribution and its magnitude were analyzed 
 by ansys workbench , a 3d finite element analysis program .
an assessment of the stress 
 on the bone elements was performed by von mises equivalent stress and maximum shear 
 stress , and we used the total deformation value to assess the initial displacement of 
 the teeth and the pdl . the coordinate system .
a mesiodistal simulated retraction force of 1.5 n was 
 loaded bilaterally to the center of the crown between the first molar and the 
 canine
immediately after loading of the retraction forces of 1.5 n ( approximately 150 g ) 
 bilaterally between the crown of the first molar and the canine , the initial 
 displacement of the canine was highly concentrated in the distal area of the crown in 
 all three models .
compared with the total deformation of the canine in model 1 
 ( non - surgical ) and model 3 ( ddo ) , the canine in model 2 had the maximum value of 
 total deformation of 1.9812 mm ( table 1 , 
 figure 7 ) .
total deformation values induced in three models pd = periodontal distraction ; pdl= periodontal ligament ddo = dentoalveolar distraction osteogenesis total deformation values induced in different parts of three models .
pdl= 
 periodontal ligament compared with the maximum value of equivalent ( von mises ) stress on the canine in 
 models 1 and 3 ( ddo ) , the canine in model 2 ( pd ) had the lowest equivalent ( von 
 mises ) stress value of 0.35494 mpa ( table 2 , 
 figure 8) .
likewise , compared with model 1 
 ( non - surgical ) and model 3 ( ddo ) , the value of maximum shear stress of the canine in 
 model 2 ( pd ) was the lowest ( table 3 ) .
equivalent ( von mises ) stress values induced in three models pd = periodontal distraction ; pdl= periodontal ligament ddo = dentoalveolar distraction osteogenesis equivalent ( von mises ) stress values induced in different parts of three 
 models .
pdl= periodontal ligament maximum shear stress values induced in three models pd = periodontal distraction ; pdl= periodontal ligament ddo = dentoalveolar distraction osteogenesis as the anchor tooth , the value of total deformation on the first molar in model 2 was 
 0.12674 mm , which is the lowest in comparison with that of the molar in model 1 
 ( non - surgical ) and model 3 ( ddo ) ( table 
 1 ) .
distribution of maximum equivalent ( von mises ) stress on the root and in the pdl of 
 the first molar in all three models was concentrated in the root furcation of the 
 molar , and the value of maximum equivalent ( von mises ) stress of the first molar in 
 model 2 ( pd ) was the lowest ( table 2 ) .
the 
 value and distribution of maximum shear stress on the root and in the pdl of the 
 first molar in all three models showed the same tendency as the maximum equivalent 
 ( von mises ) stress , although the values differed . compared with cancellous bone ,
the buccal side of cortical bone around the canine 
 root was the most stressed area .
the value of maximum equivalent ( von mises ) stress 
 on the cortical bone around the canine root in model 2 ( pd ) and model 3 ( ddo ) was 
 lower than that in model 1 ( non - surgical ) ( table 
 2 ) .
the value of maximum shear stress on the buccal side of cortical bone 
 around the canine root in model 2 ( pd ) was the lowest ( table 3 ) .
immediately after loading of the retraction forces of 1.5 n ( approximately 150 g ) 
 bilaterally between the crown of the first molar and the canine , the initial 
 displacement of the canine was highly concentrated in the distal area of the crown in 
 all three models .
compared with the total deformation of the canine in model 1 
 ( non - surgical ) and model 3 ( ddo ) , the canine in model 2 had the maximum value of 
 total deformation of 1.9812 mm ( table 1 , 
 figure 7 ) .
total deformation values induced in three models pd = periodontal distraction ; pdl= periodontal ligament ddo = dentoalveolar distraction osteogenesis total deformation values induced in different parts of three models .
pdl= 
 periodontal ligament compared with the maximum value of equivalent ( von mises ) stress on the canine in 
 models 1 and 3 ( ddo ) , the canine in model 2 ( pd ) had the lowest equivalent ( von 
 mises ) stress value of 0.35494 mpa ( table 2 , 
 figure 8) .
likewise , compared with model 1 
 ( non - surgical ) and model 3 ( ddo ) , the value of maximum shear stress of the canine in 
 model 2 ( pd ) was the lowest ( table 3 ) .
equivalent ( von mises ) stress values induced in three models pd = periodontal distraction ; pdl= periodontal ligament ddo = dentoalveolar distraction osteogenesis equivalent ( von mises ) stress values induced in different parts of three 
 models .
pdl= periodontal ligament maximum shear stress values induced in three models pd = periodontal distraction ; pdl= periodontal ligament ddo = dentoalveolar distraction osteogenesis
as the anchor tooth , the value of total deformation on the first molar in model 2 was 
 0.12674 mm , which is the lowest in comparison with that of the molar in model 1 
 ( non - surgical ) and model 3 ( ddo ) ( table 
 1 ) .
distribution of maximum equivalent ( von mises ) stress on the root and in the pdl of 
 the first molar in all three models was concentrated in the root furcation of the 
 molar , and the value of maximum equivalent ( von mises ) stress of the first molar in 
 model 2 ( pd ) was the lowest ( table 2 ) .
the 
 value and distribution of maximum shear stress on the root and in the pdl of the 
 first molar in all three models showed the same tendency as the maximum equivalent 
 ( von mises ) stress , although the values differed .
compared with cancellous bone , the buccal side of cortical bone around the canine 
 root was the most stressed area .
the value of maximum equivalent ( von mises ) stress 
 on the cortical bone around the canine root in model 2 ( pd ) and model 3 ( ddo ) was 
 lower than that in model 1 ( non - surgical ) ( table 
 2 ) .
the value of maximum shear stress on the buccal side of cortical bone 
 around the canine root in model 2 ( pd ) was the lowest ( table 3 ) .
in this study , orthodontic force was applied to three fems which simulated two different 
 surgical interventions and conventional treatment for canine retraction .
stress 
 distribution and deformation on the root , pdl , and cortical bone were evaluated .
the 
 stress patterns in the pdl , root , and bone were displayed in separate illustrations , so 
 that the complex responses of these tissues to different types of surgical interventions 
 could be readily compared .
the forces were applied to the surfaces of the teeth , 
 mesio - distally , as in normal clinical practice .
the results of this study , which showed 
 stress distribution along the root , pdl , and alveolar bone , provided insight into 
 clinical observations .
orthodontic tooth movement is a biological process characterized by sequential reactions 
 of periodontal tissue against a biomechanical force system .
it is also a process in which the application of a 
 mechanical force induces alveolar bone resorption on the pressure side and alveolar bone 
 deposition on the tension side .
the 
 orthodontic force system is a complicated three - dimensional system which is difficult to 
 evaluate in clinical conditions and orthodontic force plays an important role in the 
 entire biomechanical process during tooth movement . in our study
, it was found that the 
 effects of force application would be changed when the force - loading environment was 
 changed
. for accelerating canine retraction speed , periodontal tissue , especially hard 
 tissue such as alveolar bone around the canine , is the most important source of 
 resistance .
compared with the conventional method of canine retraction , we found that ddo 
 ( dentoalveolar distraction osteogenesis ) and pd ( periodontal distraction aided by 
 surgical undermining of the interseptal bone ) could reduce resistance during canine 
 retraction in this finite element analysis .
this finding was consistent with those of 
 previous clinical reportsand animal experimentswith rapid orthodontic tooth movement . compared with ddo , it was 
 noteworthy , from the mechanical analysis in this study , that pd had more advantages in 
 reducing resistance and accelerating canine movement .
it also showed that the stress 
 along the distal side of the canine root was reduced more significantly in model 2 ( pd ) 
 ( figures 8 , 9 ) , with more obvious canine displacement than in model 3 ( ddo ) ( figure 7 ) .
the main pathway of canine movement was 
 via the cancellous bone and the interseptal bone , since the main portion of cancellous 
 bone in the pathway of canine distalization was removed by pd .
as a result , it is more 
 effective to accelerate canine retraction through periodontal distraction aided by 
 surgical undermining of the interseptal bone .
pdl= 
 periodontal ligament on the basis of previous studies , resistance to tooth movement is increased when the 
 roots are torqued lingually or buccally .
this principle was used by rickets ( 1979 ) and is called cortical anchorage . 
 generally , cortical bone offers more resistance to resorption
. the cortical bone could 
 also block tooth movement in most cases in orthodontic treatment . in this study
, we 
 observed the distribution of stress on the buccal side of cortical bone around the 
 canine root , which implied that the cortical bone on the buccal side of the canine was 
 also the source of resistance to canine movement . that explained the principle of 
 surgical procedures for ddo , which was designed with the dentoalveolus as a bone 
 transport segment for posterior movement .
however , based on our results , pd was more effective in canine 
 retraction . furthermore , in clinical applications , the interseptal bone distal to the 
 canine was undermined to weaken its resistance immediately after dental extraction , and 
 a tooth - borne appliance was used for rapid tooth retraction .
in addition to proper orthodontic force , the center of resistance ( cr ) of a tooth is 
 also a critical factor in predicting and planning the esthetic movement of anterior 
 teeth .
ideally , force should 
 be applied as closely as possible to the cr of a tooth , to achieve movement of the tooth 
 in orthodontic treatment .
although we can not apply the force on the cr , we could change 
 the conditions around the cr .
the concentration point of stress on the pressure side of 
 the canine root tended to move closely to the crown after surgical undermining of the 
 interseptal bone in the pd model . in that case , the canine cr became closer to the crown 
 through resistance - reducing surgery , especially in the pd model , and this would lead to 
 possible canine body movement .
otherwise , the lowest maximum equivalent ( von mises ) 
 stress value on the distal side of the root surface in model 2 ( pd ) implied that 
 reducing the resistance around the canine cr in that model would reduce the stress 
 value .
the lower and more uniform stress on the root indicated that translational tooth 
 movement may be achieved , which made it more effective in accelerating canine retraction 
 speed .
however , it should be pointed out that the concentrated point of force loading at the 
 distal side of the canine cervix for the pdl and alveolar bone shifted to the lingual 
 side in the pd model , and , conversely , in the ddo model , this point shifted to the 
 buccal side .
this indicated to us that the canine had a tendency to rotate lingually in 
 the pd model and buccally in the ddo model after resistance was reduced .
the reason for 
 this might be that after the different positions of resistance source were reduced by 
 surgery , the canine would move to the position with the lowest resistance .
therefore , we 
 should avoid this side - effect when using pd or ddo during orthodontic treatment .
an 
 obvious strategy for anchorage control would be to concentrate the force needed to 
 produce tooth movement where it was desired , and then to dissipate the retraction force 
 in the pdl of anchor teeth as much as possible . in this study ,
the value of maximum 
 equivalent ( von mises ) stress in the pdl of the first molar in two models was surgical 
 reduction of resistance to a level lower than in the canine .
further , the value of total 
 deformation of the first molar in the ddo and pd models was far below that of the canine 
 at the initial stage of force loading .
this indicated that reducing resistance by ddo or 
 pd to accelerate canine retraction was a safe way to protect anchorage and would not 
 reduce anchorage during canine retraction .
furthermore , the pattern of force 
 distribution in the pdl and root of the first molar showed that high stress 
 concentration is observed on the root surface at the furcation level , which is in 
 contrast to the canine , which displayed a greater apical concentration .
this may explain 
 the high incidence of apical root resorptionthat appears to occur in the maxillary molar on the root surface 
 at the furcation level , which is difficult to see radiographically in orthodontic 
 treatment .
this study and others have demonstrated that fem provides a solid , workable foundation 
 for modeling a system of orthodontic tooth movement .
the chief advantage of fem is that it can be magnified nearly 
 infinitely , in terms of both the actual volumetric construction itself and the 
 mathematical variability of its material parameters .
however , as with any theoretical 
 model of a biological system , there are limitations .
the mechanical behavior of the 
 materials was assumed to be linear elastic ( homogeneous and isotropic ) , and the value of 
 each material was inferred from previous reports .
cortical bone thickness and cancellous 
 bone quality were not incorporated into the analysis , to prevent bone stress from being 
 dominated by bone quality and potentially confounding the outcomes related to other 
 relevant factors .
in addition , the stress analysis of soft tissues was not considered in 
 this study .
the soft tissues , such as gingival and facial muscles , are also sources of 
 resistance for blocking rapid tooth movement .
regardless of these limitations , we 
 integrated a finite element approach with variable analysis to investigate the 
 comparative influences of resistance source , the pathway of canine movement , and 
 different types of surgeries for rapid canine retraction by reducing resistance .
in this study , compared with dento - alveolar distraction osteogenesis , periodontal 
 distraction aided by surgical undermining of the interseptal bone would reduce the 
 resistance in the pathway of canine movement more effectively to accelerate canine 
 retraction speed in rapid canine movement during orthodontic treatment .
the results indicated that rapid canine retraction aided by the surgical reduction of 
 resistance might create side effect : 1 ) it might lead to canine rotation during 
 distalization , 2 ) the geometry of the root of maxillary first molar makes it less prone 
 to apical stress concentration , therefore , resorption on the root surface at the 
 furcation level of the molars is more easily caused .
 objectivethe aims of this study were to compare different surgical approaches to rapid 
 canine retraction by designing and selecting the most effective method of reducing 
 resistance by a three - dimensional finite element analysis . 
 material and methodsthree - dimensional finite element models of different approaches to rapid canine 
 retraction by reducing resistance and distraction were established , including 
 maxillary teeth , periodontal ligament , and alveolar . 
 the models were designed to 
 dissect the periodontal ligament , root , and alveolar separately . 
 a 1.5 n force 
 vector was loaded bilaterally to the center of the crown between first molar and 
 canine , to retract the canine distally . 
 the value of total deformation was used to 
 assess the initial displacement of the canine and molar at the beginning of force 
 loading . 
 stress intensity and force distribution were analyzed and evaluated by 
 ansys 13.0 through comparison of equivalent ( von mises ) stress and maximum shear 
 stress . 
 resultsthe maximum value of total deformation with the three kinds of models occurred in 
 the distal part of the canine crown and gradually reduced from the crown to the 
 apex of the canine ; compared with the canines in model 3 and model 1 , the canine 
 in model 2 had the maximum value of displacement , up to 1.9812 mm . 
 the lowest 
 equivalent ( von mises ) stress and the lowest maximum shear stress were 
 concentrated mainly on the distal side of the canine root in model 2 . 
 the 
 distribution of equivalent ( von mises ) stress and maximum shear stress on the pdl 
 of the canine in the three models was highly concentrated on the distal edge of 
 the canine cervix.conclusionsremoval of the bone in the pathway of canine retraction results in low stress 
 intensity for canine movement . 
 periodontal distraction aided by surgical 
 undermining of the interseptal bone would reduce resistance and effectively 
 accelerate the speed of canine retraction . 
INTRODUCTION
MATERIAL AND METHODS
3D FE model generation
Material properties
Experimental conditions
RESULTS
Canine
Molar
Alveolar
DISCUSSION
CONCLUSIONS