the arrival of osteoclasts is the required first step in orthodontic tooth movement ( otm ) 
 , and any interference with the function of these cells results in decreased efficiency and effectiveness of orthodontic treatment 
 . experimental studies that aim to understand the influence of distinct mechanisms involved in the regulation of otm require , therefore , a meticulous evaluation of the osteoclastic activity . most of these studies make this assessment by counting osteoclasts in histological sections 


  or by histomorphometry , calculating the osteoclast surface per bone surface 


 . it is well known that the biomechanical and cellular cascades initiated by orthodontic forces reshape the bony contour of the alveolus 
 . after osteoclasts gain access to the mineralized bone , matrix dissolution occurs and the resorption lacuna is formed . the frontal resorption of bone may thus cause structural changes at the bone surface , resulting in its increased irregularity . thus , few investigations have studied the periodontal ligament ( pdl)-bone interface because its complexity does not allow for numerical assessment by euclidean geometrical principles 
 . studies have evaluated the irregularity of the junctions between the tissues in order to discriminate normal tissue or benign from malignant tumors 




 . with the use of fractal analysis , a method for characterizing the complexity , and thus capable of quantifying morphologies that are generally considered irregular 
 , larger fractal dimensions the fractal dimension of an object characterizes its self - similarity and describes its space - filling properties 
 ; the more space the object occupies , the higher the fractal dimension . due to the bone surface recontouring promoted by osteoclasts , we hypothesized that the quantification of surface irregularity can be measured by fractal analysis and that this value may reflect the level of osteoclastic activity . thus , the purpose of this study was ( 1 ) to estimate the degree of bone resorption by osteoclast counts , ( 2 ) to analyze the fractal dimension of the pdl - bone interface , and ( 3 ) to verify whether there is a relationship between osteoclastic activity and fractal dimension . to consider the possible influence of other factors related to orthodontic tooth movement that could interfere with the fractal dimension , we proposed the administration of alendronate , a compound that promotes suppression of osteoclasts 
 , allowing the assessment of the actual influence of osteoclastic activity in the fractal dimension of the pdl - bone interface . this in vivo experimental study sample consisted of 14 male new zealand white rabbits , 16-week - old , with a mean weight of 2.60.3 kg . the animals were randomly divided into two groups , the control group and the alendronate - treated experimental group . they were acclimatized for 1 week , individually housed in cages inside a room with a 12-hour light - dark cycle and fed with water and powdered commercial pellets ( to avoid damage to the orthodontic appliance ) ad libitum . the study protocol was reviewed and approved by the ethics committee on animal use in scientic research at the heath center of the federal university of rio de janeiro ( protocol number labce01 ) , and was carried out in accordance with the directive 2010/63/eu of the european parliament and of the council of the european union on the protection of animals used for scientific purposes . alendronate sodium trihydrate ( alendronate sodium trihydrate a4978 , sigma - aldrich , saint louis , mo , usa ) in crystalline form was dissolved in distilled water and vortexed for 60 seconds to obtain a solution containing 3 mg per milliliter of alendronate . the solution was prepared immediately before each administration in order to prevent interference in its stability caused by environmental and storage conditions . the experimental group received weekly subcutaneous injections of alendronate at a dosage of 3 mg / kg for 6 weeks ( 3 doses before and 3 after appliance activation ) , whereas saline solution was injected in the control group under the same protocol . the mandibular right first molars of all animals were mesially tipped with a constant force of 85 cn for 3 weeks . the orthodontic appliance was composed of a nickel titanium closed coil spring ( mola ortodntica fechada niti para miniparafuso  12 mm , morelli , sorocaba , sp , brazil ) stretched from the cervical area of the molar to a staple adapted to the mandibular incisors , until the desired strength was achieved , as measured by a dynamometer accurately calibrated ( dynamometer 040 - 711 , dentaurum , ispringen , baden - wrttemberg , germany ) . all procedures were carried out under general anesthesia using intramuscular injection of a mixed solution of ketamine ( 35 mg / kg ) , acepromazine ( 1 mg / kg ) and xylazine ( 5 mg / kg ) , an adequate dose to produce anesthesia during the entire procedure . every week , a veterinarian examined the animals to evaluate their physical conditions , and the researcher performed oral hygiene , evaluated the integrity of tissues and appliances , and the amount of tooth movement . after 21 days of load application , the rabbits were euthanatized by intracardiac injection of a lethal dosage of thiopental with prior sedation . tissue sections of the left and right quadrants of the mandible were fixed in 10% neutral buffered formalin for 48 hours , decalcified in 14% ethylenediaminetetraacetic acid ( edta ) for 60 days and embedded in paraffin . longitudinal 6-m thick sections in a mesiodistal direction were obtained from the buccal surface of the mandibles . the first section that included the entire height of the alveolar bone , from the alveolar crest to the mandibular basal bone on the mesial side of the first molar , was selected and stained with hematoxylin and eosin . the number of osteoclasts was counted on the pressure side of the pdl by a single and blinded examiner ( asa ) . a square grid with a side length of 1.23 mm was placed over the sections , parallel to the long axis of the first molar , with the top side of a square coinciding with the bone crest . the osteoclasts on the alveolar bone surface within this square , corresponding to the cervical third of the molar , were counted manually under light microscopy ( 400x magnification ) . light micrographs of the interface between bone and periodontal ligament of the same area of osteoclast counting were captured with a 10x objective lens . the lateral edge of the images coincided with the top of the mesial bone crest of the first molar , and the top edge was positioned parallel to the cementum of this tooth ( figure 1a ) . the pdl - bone interface within this image was drawn using the photoshop software ( photoshop cs6 , adobe systems , san jose , ca , usa ) as 1 pixel thick line ( figure 1b ) . the corresponding pdl - bone interface outlines were saved in tiff format , 300 dpi and 945x945 pixel dimension ( figure 1c ) . a : micrographs captured with a 10x objective lens of the pdl - bone interface of the mesial of the lower first molar ; b : pdl - bone interface outlined ; c : image used to calculate the fractal dimension 
  the image j software ( version 1.46r , national institutes of health , bethesda , md , usa ) was used to measure the fractal dimension ( fd ) of the pdl - bone interface by the automated box counting method , using square grids with side lengths of 4 , 8 , 16 , 32 , 64 , 128 and 356 pixels . to obtain the fractal dimension , we first selected the file > open option to locate and open the image file . next , the image was converted to binary image ( process > binary > make binary ) , and then the fractal dimension was calculated ( analyze > tools > fractal box counter ) . the values of box sizes described above were determined and the d value , which represents the fractal dimension , was acquired ( figure 2 ) . the entire process was performed by a single and blinded examiner ( asa ) . figure 2imagej software used to obtain the fractal dimension , represented by the value d 
  all measurements were repeated with a two weeks interval , and the intraclass correlation coefficients for  single measures  were found to be 0.976 for osteoclast counts and the mean between the 2 measurements was used for further statistical analysis , performed at a 5% level of significance . intergroup and intragroup comparisons were analyzed with unpaired and paired student s t - test , respectively . correlation analysis , using the pearson correlation coefficient , was performed to evaluate relationships between fd of the pdl - bone interface and number of osteoclasts in order to estimate the influence of osteoclastic activity on this variable . this in vivo experimental study sample consisted of 14 male new zealand white rabbits , 16-week - old , with a mean weight of 2.60.3 kg . the animals were randomly divided into two groups , the control group and the alendronate - treated experimental group . they were acclimatized for 1 week , individually housed in cages inside a room with a 12-hour light - dark cycle and fed with water and powdered commercial pellets ( to avoid damage to the orthodontic appliance ) ad libitum . the study protocol was reviewed and approved by the ethics committee on animal use in scientic research at the heath center of the federal university of rio de janeiro ( protocol number labce01 ) , and was carried out in accordance with the directive 2010/63/eu of the european parliament and of the council of the european union on the protection of animals used for scientific purposes . alendronate sodium trihydrate ( alendronate sodium trihydrate a4978 , sigma - aldrich , saint louis , mo , usa ) in crystalline form was dissolved in distilled water and vortexed for 60 seconds to obtain a solution containing 3 mg per milliliter of alendronate . the solution was prepared immediately before each administration in order to prevent interference in its stability caused by environmental and storage conditions . the experimental group received weekly subcutaneous injections of alendronate at a dosage of 3 mg / kg for 6 weeks ( 3 doses before and 3 after appliance activation ) , whereas saline solution was injected in the control group under the same protocol . the mandibular right first molars of all animals were mesially tipped with a constant force of 85 cn for 3 weeks . the orthodontic appliance was composed of a nickel titanium closed coil spring ( mola ortodntica fechada niti para miniparafuso  12 mm , morelli , sorocaba , sp , brazil ) stretched from the cervical area of the molar to a staple adapted to the mandibular incisors , until the desired strength was achieved , as measured by a dynamometer accurately calibrated ( dynamometer 040 - 711 , dentaurum , ispringen , baden - wrttemberg , germany ) . all procedures were carried out under general anesthesia using intramuscular injection of a mixed solution of ketamine ( 35 mg / kg ) , acepromazine ( 1 mg / kg ) and xylazine ( 5 mg / kg ) , an adequate dose to produce anesthesia during the entire procedure . every week , a veterinarian examined the animals to evaluate their physical conditions , and the researcher performed oral hygiene , evaluated the integrity of tissues and appliances , and the amount of tooth movement . after 21 days of load application , the rabbits were euthanatized by intracardiac injection of a lethal dosage of thiopental with prior sedation . tissue sections of the left and right quadrants of the mandible were fixed in 10% neutral buffered formalin for 48 hours , decalcified in 14% ethylenediaminetetraacetic acid ( edta ) for 60 days and embedded in paraffin . longitudinal 6-m thick sections in a mesiodistal direction were obtained from the buccal surface of the mandibles . the first section that included the entire height of the alveolar bone , from the alveolar crest to the mandibular basal bone on the mesial side of the first molar , was selected and stained with hematoxylin and eosin . the number of osteoclasts was counted on the pressure side of the pdl by a single and blinded examiner ( asa ) . a square grid with a side length of 1.23 mm was placed over the sections , parallel to the long axis of the first molar , with the top side of a square coinciding with the bone crest . the osteoclasts on the alveolar bone surface within this square , corresponding to the cervical third of the molar , were counted manually under light microscopy ( 400x magnification ) . light micrographs of the interface between bone and periodontal ligament of the same area of osteoclast counting were captured with a 10x objective lens . the lateral edge of the images coincided with the top of the mesial bone crest of the first molar , and the top edge was positioned parallel to the cementum of this tooth ( figure 1a ) . the pdl - bone interface within this image was drawn using the photoshop software ( photoshop cs6 , adobe systems , san jose , ca , usa ) as 1 pixel thick line ( figure 1b ) . the corresponding pdl - bone interface outlines were saved in tiff format , 300 dpi and 945x945 pixel dimension ( figure 1c ) . a : micrographs captured with a 10x objective lens of the pdl - bone interface of the mesial of the lower first molar ; b : pdl - bone interface outlined ; c : image used to calculate the fractal dimension 
  the image j software ( version 1.46r , national institutes of health , bethesda , md , usa ) was used to measure the fractal dimension ( fd ) of the pdl - bone interface by the automated box counting method , using square grids with side lengths of 4 , 8 , 16 , 32 , 64 , 128 and 356 pixels . to obtain the fractal dimension , we first selected the file > open option to locate and open the image file . next , the image was converted to binary image ( process > binary > make binary ) , and then the fractal dimension was calculated ( analyze > tools > fractal box counter ) . the values of box sizes described above were determined and the d value , which represents the fractal dimension , was acquired ( figure 2 ) . the entire process was performed by a single and blinded examiner ( asa ) . figure 2imagej software used to obtain the fractal dimension , represented by the value d all measurements were repeated with a two weeks interval , and the intraclass correlation coefficients for  single measures  were found to be 0.976 for osteoclast counts and the mean between the 2 measurements was used for further statistical analysis , performed at a 5% level of significance . intergroup and intragroup comparisons were analyzed with unpaired and paired student s t - test , respectively . correlation analysis , using the pearson correlation coefficient , was performed to evaluate relationships between fd of the pdl - bone interface and number of osteoclasts in order to estimate the influence of osteoclastic activity on this variable . after induction of tooth movement , the number of osteoclasts increased only in the control group ( p=0.008 ) ( table 1 ) . however , on the side with otm there was a significant reduction in osteoclasts in the experimental group ( p=0.041 ) , showing the inhibitory effect of alendronate on these cells . the lower first molarorthodontic tooth movementcontrol animalsexperimental animalsgroup differences 
 mean 

 sd 

 mean 

 sd 

 p 
 no11.254.0413.368.350.559yes27.43 * 13.5514.142.750.041*significant ( p=0.008 ) change in the number of osteoclasts after orthodontic tooth movement . * significant ( p=0.008 ) change in the number of osteoclasts after orthodontic tooth movement . similarly , as with the number of osteoclasts , tooth movement increased the fd of the pdl - bone interface in the control group , but did not cause changes in the experimental group ( figure 3 ) . the osteoclast activity was responsible for the increase in fd , due to an increment in boundary irregularity caused by the presence of more active resorption sites . in the pearson correlation , the number of osteoclasts was strongly related to fd ( r=0.808 , p<0.01 ) , and accounted for 65.3% ( r 
 = 0.653 ) of the variability in the fd value ( figure 4 ) . . a : left and b : right side of a control animal ; c : left and d : right side of an experimental animal . note the increase in bone surface irregularity in the control group and almost no change in the experimental group after 21 days of induced tooth movement ; e : values represent the mean sd ( standard deviation ) of fd . strong correlation was found for both control ( r=0.86 , p<0.01 ) and alendronate groups ( r=0.813 , p<0.01 ) , as well as the entire sample ( r=0.808 , p<0.01 ) . note that with the increase in the number of osteoclasts , there was an increase in fractal dimension in the present study , the complexity of the pdl - bone interface was measured and proposed as a new method for evaluating osteoclastic activity induced by mechanical loading . after otm , there was an increase in the bone surface irregularity due to the frontal resorption promoted by osteoclasts , and this irregularity could be measured by fractal analysis . few studies 


  have used fractal analysis to assess the periodontal region after orthodontic tooth movement , and only one 
  evaluated fractal dimension change of the pdl - bone interface after mechanical stresses produced by an orthodontic appliance . that paper showed an increase in the fractal dimension caused by the mechanical loading and directly proportional to the magnitude of force applied . however , unlike the present study , the authors stated that the increase occurred apart from mechanisms of bone cell directed remodeling . actually , cellular interference could not be analyzed since the force was applied for only 6 hours , insufficient time for the manifestation of significant osteoclastic activity . at 6 hours , many osteoclasts and pre - osteoclastic cells are still observed in vascular canals 
 . the number of osteoclasts in the periodontal ligament and adjacent alveolar bones increases only on day 1 
 , with a peak level about 50 hours after orthodontic force application . in this study , the mechanical loading was applied until day 21 , when frontal bone resorption had already significantly occurred and osteoclastic activity could be evaluated . to eliminate the possibility of misinterpretation and ensure that the change in fractal dimension was due to the activity of osteoclasts , apart from other factors involved in the orthodontic tooth movement such as the mechanical loading , the administration of alendronate was performed in the experimental group . alendronate is a nitrogen - containing bisphosphonate , orally administered , and commonly prescribed for the prophylaxis and treatment of osteoporosis 
 . after administration , it is redistributed to the bone , particularly to areas of increased bone turnover , and subsequently incorporated into osteoclasts involved in bone resorption 
 . within these cells , the compound interferes with specific intracellular pathways , resulting in disruption of cytoskeletal function and intracellular signaling 


 . the consequences of these events include the suppression of osteoclastic activity , loss of osteoclast cytoskeletal integrity and ruffled border , and ultimately cell apoptosis 
 . as expected , the number of osteoclasts on the mesial bone surface of the right first molar was significantly higher in the control group ( figure 5a ) than in the experimental group ( figure 5b ) . this result corroborates the finding of other studies 


  that also revealed a decline in the number of osteoclasts on the pressure side along the bone surface . moreover , osteoclasts with chromatin condensation were occasionally observed in the alendronate - treated group , suggesting the presence of cells in apoptosis ( figures 5c , 5d ) . figure 5micrograph of the compression side of a right first molar from a : control and b : experimental group . the number of osteoclasts ( black arrows ) was significantly lower in the alendronate - treated rabbits . c , d : osteoclasts with nuclear condensation , a sign of apoptosis , were found ( yellow arrows);(hematoxylin and eosin staining , 400x ) 
  ( hematoxylin and eosin staining , 400x ) the inhibitory effect of bisphosphonates on osteoclasts results is the initiation of fewer active remodeling sites on bone surfaces 


 , the most prominent effect of these compounds seen in histological analysis 
 . moreover , in addition to reducing the number of active resorption units , bisphosphonates decrease the size of these sites 
 . due to the initiation of resorption cavities in smaller quantity and size , administration of alendronate resulted in lower bone surface complexity than that in the control group during tooth movement , because the osteoclastic activity was inhibited by the bisphosphonate . therefore , the current research does not corroborate the finding of wagle , et al . ( 2005 ) , who attributed the change of the fractal dimension of the pdl - bone interface merely to mechanical loading . the action of osteoclasts was necessary to increase the fractal dimension , otherwise an increase in this variable would also have occurred in the experimental group in which orthodontic force was applied , but the mechanical loading was not sufficient to increase the fractal dimension . thus , it is suggested that the larger number of resorption sites produced as a consequence of the increased frequency of osteoclasts activation led to a significant increment in fractal dimension . this makes fractal analysis by the box counting method a potential tool for the assessment of osteoclastic activity on bone surfaces in microscopic examination . the merit of this study was to present a new methodology for evaluating osteoclastic activity induced by orthodontic force . the method is practical , simple , reproducible , inexpensive , and easier than osteoclast counting , a method that requires more time for its execution , greater attention to the correct recognition of the cells or the use of specific staining techniques ( tartrate resistant acid phosphatase ) to facilitate identification . although fractal analysis has been used , in this study , as an evaluation of osteoclastic activity after application of mechanical loading and alendronate administration , we believed that it might be used for the assessment of osteoclastic activity on bone surface in other situations . through this study on the fractal analysis as a method for evaluating osteoclastic activity , we can reach the following conclusions : the action of osteoclasts enhanced the fractal dimension of the pdl - bone interface as a consequence of increasing irregularity of the bone surface . this study provides bases for the use of fractal analysis by the box counting method as a tool for the evaluation of osteoclastic activity .
orthodontic tooth movement ( otm ) is a dynamic process of bone modeling involving osteoclast - driven resorption on the compression side . 
 consequently , to estimate the influence of various situations on tooth movement , experimental studies need to analyze this cell . 
 objectives the aim of this study was to test and validate a new method for evaluating osteoclastic activity stimulated by mechanical loading based on the fractal analysis of the periodontal ligament ( pdl)-bone interface.material and methods the mandibular right first molars of 14 rabbits were tipped mesially by a coil spring exerting a constant force of 85 cn . to evaluate the actual influence of osteoclasts on fractal dimension of bone surface , alendronate ( 3 mg / kg ) 
 was injected weekly in seven of those rabbits . 
 after 21 days , the animals were killed and their jaws were processed for histological evaluation . 
 osteoclast counts and fractal analysis ( by the box counting method ) of the pdl - bone interface were performed in histological sections of the right and left sides of the mandible.results an increase in the number of osteoclasts and in fractal dimension after otm only happened when alendronate was not administered . 
 strong correlation was found between the number of osteoclasts and fractal dimension.conclusions our results suggest that osteoclastic activity leads to an increase in bone surface irregularity , which can be quantified by its fractal dimension . 
 this makes fractal analysis by the box counting method a potential tool for the assessment of osteoclastic activity on bone surfaces in microscopic examination .