before discussing the methodology , a detailed understanding of finite element method and its significance is essential . the basic idea in finite element method is to find the solution for a complicated problem by replacing it by a simpler one . in finite element method , the actual continuum or body of the matter
these elements are considered to be interconnected at specified points , which are called nodes or nodal points .
a variety of element types and shapes are available to provide users with the required flexibility to meet the compatibility and completeness requirements .
it is useful in solving complex structural problems by dividing the complex structures into many simpler and smaller segments .
the technical improvement in computers and finite element software , has improved accuracy and speed of this analysis . in the general field of medicine
microsoft windows 98 se ( operating system)computer aided designing ( cad ) or modeling software  proe-2001msc 
microsoft windows 98 se ( operating system ) computer aided designing ( cad ) or modeling software  proe-2001 msc 
the creation of geometric model , mesh generation , and boundary conditions were applied . in the case of postprocessing simulating ,
creation of geometric model before developing a finite element model of any system , a geometric model should be generated using cad software .
the three - dimensional model to create is a maxillary four incisors and its surrounding structures such as alveolar bone and its periodontal ligament .
the morphological dimensions of the teeth used were as given by wheeler 's dental anatomy 
( 6 edition ) . from the standard dimensions , the bounding points of the cross - section ( in space x , y , and z coordinates ) were determined and plotted in the cad graphics screen . with the bounding points called the key points ,
smooth lines were drawn connecting all the key points simulating the profile of the natural tooth . with the sketch model , volume for the section of the body
is created ( solid modeling ) [ figures 1 and 2 ] . in a similar manner , the periodontal ligament surrounding the tooth and alveolar bone
as it was difficult to obtain the hourglass shape of the periodontal ligament in our study , it was assumed to be 0.25 mm thickness around the radicular portion , although the thickness varies from the alveolar crest to the apex .
the alveolar bone was modeled as a rectangular block of structure with labial thickness of 3 mm apically and 5 mm distally to the existing tooth [ figure 4 ] .
sectioned natural tooth sectioned natural tooth periodontal ligament surrounding alveolar bone and tooth are modeled alveolar bone modeled in rectangular block finite element model generation ( mesh generation ) this forms the backbone of the finite element analysis . in this stage , the geometric model is converted into the finite element model .
the cad model was meshed or divided into several three - dimensional tetrahedral shaped finite elements [ table 1 ] .
tetrahedral elements are used in order to precisely mesh the curved and irregular regions present in the tooth [ figure 5 ] .
the mechanical properties of each material such as bone , periodontal ligament and the tooth are taken from the previously published values [ table 2 ] .
number of elements and nodes in the model mechanical properties for tooth , periodontal ligament and alveolar bone superior surface of bone model the boundary conditions with the areas where the model was restrained from any further movements were assigned as follows , at the superior surface of the bone model ( area representing the palatal surface ) , the area was constrained at their bases to avoid overall rigid body motion 3 [ figure 5 ] .
the three - dimensional model was oriented in such a way that the mesiodistal plane was represented by x axis , the vertical plane by the y axis and the labiolingual plane by the z axis . to evaluate the center of resistance
the force was applied at a distance of 5.2 mm from the incisal edge of the modeled tooth in the labiolingual direction ( along the z axis ) .
the magnitude of force given was 15 g of intrusive force and 120 g of retractive force for each tooth .
determination of center of resistance center of resistance of a tooth is a point through which a pure force if acts will produce linear movement without rotation .
since , it is a geometric property the finite element analysis itself can easily locate it .

 microsoft windows 98 se ( operating system)computer aided designing ( cad ) or modeling software  proe-2001msc 
microsoft windows 98 se ( operating system ) computer aided designing ( cad ) or modeling software  proe-2001 msc 
the creation of geometric model , mesh generation , and boundary conditions were applied . in the case of postprocessing simulating , the tooth movement and determination of center of resistance were done .
creation of geometric model before developing a finite element model of any system , a geometric model should be generated using cad software .
the three - dimensional model to create is a maxillary four incisors and its surrounding structures such as alveolar bone and its periodontal ligament .
the morphological dimensions of the teeth used were as given by wheeler 's dental anatomy 
( 6 edition ) . from the standard dimensions , the bounding points of the cross - section ( in space x , y , and z coordinates ) were determined and plotted in the cad graphics screen . with the bounding points called the key points ,
smooth lines were drawn connecting all the key points simulating the profile of the natural tooth . with the sketch model , volume for the section of the body
is created ( solid modeling ) [ figures 1 and 2 ] . in a similar manner , the periodontal ligament surrounding the tooth and alveolar bone
as it was difficult to obtain the hourglass shape of the periodontal ligament in our study , it was assumed to be 0.25 mm thickness around the radicular portion , although the thickness varies from the alveolar crest to the apex .
the alveolar bone was modeled as a rectangular block of structure with labial thickness of 3 mm apically and 5 mm distally to the existing tooth [ figure 4 ] .
sectioned natural tooth sectioned natural tooth periodontal ligament surrounding alveolar bone and tooth are modeled alveolar bone modeled in rectangular block finite element model generation ( mesh generation ) this forms the backbone of the finite element analysis . in this stage , the geometric model is converted into the finite element model .
the cad model was meshed or divided into several three - dimensional tetrahedral shaped finite elements [ table 1 ] .
tetrahedral elements are used in order to precisely mesh the curved and irregular regions present in the tooth [ figure 5 ] .
the mechanical properties of each material such as bone , periodontal ligament and the tooth are taken from the previously published values [ table 2 ] .
number of elements and nodes in the model mechanical properties for tooth , periodontal ligament and alveolar bone superior surface of bone model the boundary conditions with the areas where the model was restrained from any further movements were assigned as follows , at the superior surface of the bone model ( area representing the palatal surface ) , the area was constrained at their bases to avoid overall rigid body motion 3 [ figure 5 ] .
the three - dimensional model was oriented in such a way that the mesiodistal plane was represented by x axis , the vertical plane by the y axis and the labiolingual plane by the z axis . to evaluate the center of resistance the force
was applied at a distance of 5.2 mm from the incisal edge of the modeled tooth in the labiolingual direction ( along the z axis ) .
the magnitude of force given was 15 g of intrusive force and 120 g of retractive force for each tooth .
determination of center of resistance center of resistance of a tooth is a point through which a pure force if acts will produce linear movement without rotation .
since , it is a geometric property the finite element analysis itself can easily locate it .
creation of geometric model before developing a finite element model of any system , a geometric model should be generated using cad software .
the three - dimensional model to create is a maxillary four incisors and its surrounding structures such as alveolar bone and its periodontal ligament .
the morphological dimensions of the teeth used were as given by wheeler 's dental anatomy 
( 6 edition ) . from the standard dimensions , the bounding points of the cross - section ( in space x , y , and z coordinates ) were determined and plotted in the cad graphics screen . with the bounding points called the key points ,
smooth lines were drawn connecting all the key points simulating the profile of the natural tooth . with the sketch model , volume for the section of the body
is created ( solid modeling ) [ figures 1 and 2 ] . in a similar manner ,
the periodontal ligament surrounding the tooth and alveolar bone were also modeled [ figure 3 ] .
as it was difficult to obtain the hourglass shape of the periodontal ligament in our study , it was assumed to be 0.25 mm thickness around the radicular portion , although the thickness varies from the alveolar crest to the apex .
the alveolar bone was modeled as a rectangular block of structure with labial thickness of 3 mm apically and 5 mm distally to the existing tooth [ figure 4 ] .
sectioned natural tooth sectioned natural tooth periodontal ligament surrounding alveolar bone and tooth are modeled alveolar bone modeled in rectangular block finite element model generation ( mesh generation ) this forms the backbone of the finite element analysis . in this stage , the geometric model is converted into the finite element model .
the cad model was meshed or divided into several three - dimensional tetrahedral shaped finite elements [ table 1 ] .
tetrahedral elements are used in order to precisely mesh the curved and irregular regions present in the tooth [ figure 5 ] .
the mechanical properties of each material such as bone , periodontal ligament and the tooth are taken from the previously published values [ table 2 ] .
number of elements and nodes in the model mechanical properties for tooth , periodontal ligament and alveolar bone superior surface of bone model the boundary conditions with the areas where the model was restrained from any further movements were assigned as follows , at the superior surface of the bone model ( area representing the palatal surface ) , the area was constrained at their bases to avoid overall rigid body motion 3 [ figure 5 ] .
the three - dimensional model was oriented in such a way that the mesiodistal plane was represented by x axis , the vertical plane by the y axis and the labiolingual plane by the z axis . to evaluate the center of resistance
the force was applied at a distance of 5.2 mm from the incisal edge of the modeled tooth in the labiolingual direction ( along the z axis ) .
the magnitude of force given was 15 g of intrusive force and 120 g of retractive force for each tooth .
determination of center of resistance center of resistance of a tooth is a point through which a pure force if acts will produce linear movement without rotation .
since , it is a geometric property the finite element analysis itself can easily locate it .
the location of center of resistance has been studied over the years with numerous model systems , these studies include , analytical models , direct measurement in vivo , photo elastic technique , strain gauge technique , laser reflection technique , and holographic method , etc .
although these model systems have provided some insight into the displacement characteristics of the tooth to the applied forces , these studies have obvious limitations such as direct measurement in vivo have a distinct disadvantage of being invasive .
furthermore , it is difficult to apply controlled force variables on human subjects because of anatomic constraints .
the major limitation in studies that used physical models was that synthetic substances were used to simulate the periodontal ligament .
many of those materials did not have physical properties exactly duplicating that of the periodontal ligament . in the analytical techniques
, the root morphology has been approximated to parabolid , conical or wedge shape leading to different results . to overcome
the essence of this method is that a predetermined force is idealized into an assemblage of separated finite regions or elements .
these are then considered to be interconnected at specific points called nodes on their common boundaries.[5 .
the results obtained in this study is in accordance with the study of matsui et al .
 aim : the aim of this study is to evaluate the center of resistance of maxillary incisors during simultaneous intrusion and retraction.subjects and methods : in this study , the following steps were employed namely , ( 1 ) preprocessing - the creation of geometric model , mesh generation and boundary conditions . 
 ( 2 ) postprocessing - the tooth movement and determination of center of resistance.results:the center of the mid - sagittal plane approximately 6 mm apical and 4 mm posterior to a line perpendicular to the occlusal plane from the labial alveolar crest of the central incisor resistance for the maxillary four incisors was located within the.conclusion:finite element is a sound mechanical method of analysis as it was sufficient enough to provide insight into interactions between orthodontic forces , and dental tissues and reliability of this study . 
 further by using this study clinically , the center of resistance can be precisely located in single rooted tooth during orthodontic treatment . 
Subjects and Methods
Software used in the study
Preprocessing
Postprocessing (simulating the movements and its analysis)
Discussion