x - ray micro computed tomography ( mxct ) has many applications in various fields including 
 medicine , geology , materials science , dentistry , art and archaeology , among 
 others .
the methodology combines a non - destructive and 
 noninvasive analysis with the ability to quantify the geometrical characteristics of 
 irregular specimens such as bones , archaeological remains , teeth , etc .
the technique is 
 constantly being improved through hardware and software developments and the subsequent increase in 
 resolution provides researchers with new information and approaches for the 
 investigation of the material properties . in the dental field , mxct has been extensively used to quantify the geometrical changes 
 in the root canal anatomy during endodontic therapy , comparing pre and post 
 instrumentation analyses .
root canals receive a chemo - mechanical treatment with 
 successively larger endodontic files ( figure 1 ) in 
 order to prepare the anatomy and surface of the root canal to support the dental posts . 

this is a very demanding task as endodontic files must cut the dentin and remove the 
 dental debris , preserving the curvature of the root canals without fracture .
root 
 fracture is the biggest complication during instrumentation , jeopardizing the outcome of 
 endodontic therapy . despite the evolution of endodontic files over the last 
 four decades and
the large number of available endodontic systems , no system is free of 
 problems and drawbacks .  
b : depth marking 
 facilitates determination of the exact position of the file on x - ray .
c : silicon 
 rubber for working length marking . color coding indicated according to iso 
 requirements ( yellow : n 20 , red : n 25 , blue : n 30 . ) .
e : 
 the number of engraved rings on the shaft determines the taper of the instrument . 

one ring represents taper .02 , 2 rings for .04 and 3 rings for taper .06 .
f : 
 specially designed shaft to be fitted in the handle of the low torque motor . the 
 scale on the left is in mm endodontic files are made from different grades of austenitic stainless steel or ni - ti alloys characterized by a variety of geometrical 
 features such as taper , cross - section , helix and rake angle , and the distance between 
 the successive cutting blades .
these 
 features are critical factors in the mechanical resistance of endodontic files to load 
 forces ( i.e. , bending and torsion ) , their cutting capacity , and the clearance of dental 
 chips .
the introduction of the ni - ti alloy in file 
 manufacturing was followed by the development of a variety of new cross - sectional 
 designs with an increased taper compared to the 0.02 employed in k- and h - type files 
 made of stainless steel as dictated by the international standard organization ( iso ) 
 specification 3630 .
nevertheless , the determination of other important 
 geometrical features such as the surface area and volume of the endodontic files remain 
 unknown , limiting the assessment of other parameters derived from these basic features . 

precise estimation of the basic geometrical features might provide an additional 
 approach to explain the differences in the clinical performance among various file 
 designs and establish a valuable tool for development of new and more efficient 
 geometrical designs .   apart from the k - files , where the surface area and volume can be calculated based on the 
 untwisted tapered blank values employing mathematical formulas , the calculation of these 
 features was impossible before the introduction of mxct .
this technique has been 
 extensively used to determine the geometrical features , such as shape , surface area and 
 the volume of the root canals before and after treatment with endodontic 
 instruments but has never been utilized to determine the geometrical features of 
 endodontic files .  
the aim of this study was to determine , for the first time , the surface area , volume and 
 specific surface area of successive file sizes of a commercially available ni - ti system . 
 additionally , we tested the hypothesis that mxct is capable of discriminating the 
 quantitative differences in the aforementioned geometrical properties between the 
 successive sizes of endodontic files .
these differences exist by definition due to the 
 progressively increased size of the successive files used in root canal therapy .
the 
 hypothesis tested was that there are significant differences in the surface area , volume 
 and specific surface area among the different sizes of endodontic files .
three sets of flex - master ni - ti files ( vdw ; munich , germany ) , 6 files each ( iso sizes 
 n 20/lot 0411310306 , n 25/lot 0410310302 and n 30/lot 
 0406310290 ) all of 0.04 taper , were utilized in this study . to avoid any inclination 
 from the vertical axis ,
the files were placed on the stage , employing a custom made 
 attachment and then scanned by a mxct scanner ( skyscan model 1072 ; aartselaar , belgium ) 
 operated under the following conditions : wo ka source ( 100 kv , 98 a ) , 2.36 
 m pixel size , 180 rotation , 0.9 rotation step , 1.9 sec exposure time 
 averaging by two frames , and 1 mm al filter .
the surface area and volume of all files 
 were determined from the tip up to the 16 mm level , taking 6,782 horizontal slices .
the 
 files were successively scanned using the automated routine of oversize mode , for 16 h 
 each .
a fixed threshold was applied to discriminate the crosssection from the air , 
 providing high contrast images of the horizontal cross - sections .
the surface area ( sa ) and 
 volume ( v ) of each file were determined by the embedded software ( ctan , skyscan , 
 aartselaar , belgium ) employing the following formulas :   with n = number of slices , s = slice thickness , pi = measured periphery in slice i 
 and ai = measure area in slice i the specific surface area ( the surface to volume ratio ) was also calculated .
the 
 percentage differences between the successive file sizes for the aforementioned 
 properties were calculated based on the formula : horizontal slices of all scanned files were also inspected for the presence of internal 
 defects such as cracks or pores .
all data were statistically analyzed using oneway anova and snk multiple comparison 
 tests at a 95% significance level , employing the file size as the discriminating 
 variable .
linearity of the surface area and volume data versus iso size was analyzed 
 employing linear regression analysis .
all data were statistically analyzed using oneway anova and snk multiple comparison 
 tests at a 95% significance level , employing the file size as the discriminating 
 variable .
linearity of the surface area and volume data versus iso size was analyzed 
 employing linear regression analysis .
figure 2 demonstrates two representative 
 horizontal sections ( perpendicular to the longitudinal file axis ) from the mxct . the 
 left image has been taken from a region near the handle and the right from a region near 
 the cutting tip of a ni - ti file , demonstrating the difference in the cross - sectional 
 surface area .
the cross - section was found to be free of internal defects such as pores 
 or cracks . left and right images show two horizontal cross sections of the same file .
the right image has a smaller cross- 
 sectional surface , as it is closer to the cutting tip the quantitative results for the surface area , volume and specific surface area of 
 successive file sizes are presented in table 1 . 

the surface area of the n 30 files showed the highest value followed by 
 n 25 and n 20 .
the increase in total surface area was 8.9% between 
 n 20/n 25 and 16.6% between n 25/n 30 files , 
 demonstrating close to a 100% increase for the latter .
similar results were found for 
 the volume of the ni - ti files tested . however , the increase in volume declined towards 
 the larger file sizes .
the percentage increase was estimated as 21.1% between n 
 20/n 25 and 17.2% between n 25/n 30 ) .
the file n 20 
 showed a significantly higher specific surface area followed by n 25 and 
 n 30 .
the specific surface area showed a 10.1% decrease between n 20/n 25 , but 
 only 0.4% between n 25/n 30 .
regression analysis revealed a strong 
 linearity between the surface area ( figure 3a ) and 
 volume ( figure 3b ) versus file sizes .
the raw 
 data , the fitted line , the 95% confidence intervals , the yielded analytical formula , and 
 the regression coefficient ( r ) are all presented in figures 3a and 3b for the 
 surface area and volume , respectively .  
mean values and standard deviations for the surface area ( sa ) , volume ( v ) , and 
 specific surface area ( ssa ) of flexmaster ni - ti files .
the percentage differences 
 ( dif ) between successive file sizes are also presented   the same superscripts indicate mean values without statistical significant 
 differences ( p>0.05 ) raw data , fitted line with the 95% confidence intervals , mathematical equations 
 and liner regression coefficients ( r ) , for the surface area ( a ) and 
 volume ( b ) of the flexmaster ni - ti system
the results of the current study showed significant differences for the surface area and 
 volume between the files tested , thus the original hypothesis is accepted .
it is 
 noteworthy that this analysis provided significant differences for the endodontic files 
 with different iso sizes , demonstrating the ability of this analysis to discriminate the 
 quantitative differences of the geometrical characteristics among the different 
 endodontic file sizes .
this discrimination has also been facilitated due to the 
 increased resolution of 2.36 m obtained in this study .
the transition to scanner 
 technology has a beneficial effect on the resolution of mxct from 1000 m for 
 conventional tomography , which was insufficient for endodontic applications , to roughly 30 m , providing the ability 
 for more extensive research , especially in the root canal anatomy after chemo - mechanical 
 treatments .
however , beyond the technological advancement , the 
 resolution of a specific analysis with a given mxct scanner is limited by the size of 
 the object , as it is magnification dependent .
this is a disadvantage in addition to the 
 restriction that all horizontal projections produced during rotation must be fitted to 
 the maximum horizontal width of the ccd camera .
the mxct device used in 
 this study has a maximum isotropic resolution of 1.8 m but the maximum 
 achievable isotropic resolution for endodontic file scanning remained at 2.36 m , 
 due to dimensional constraints .
the scanning of an alloy with a homogeneous elemental 
 atomic ratio and a uniform x - ray 
 absorption through its bulk facilitates image contrast and thus the selection of the 
 proper threshold level to discriminate the edges of the cross - sections .
all tested files 
 were found free of internal defects such as pores or cracks , a finding which is in 
 agreement with previous cross - sectional and mxct analyses .  
despite the increased isotropic resolution available through technological advancements , 
 the accuracy of the quantitative analysis remains unknown , at least for endodontic 
 applications dealing with the quantification of the geometrical features of the root 
 canals and endodontic files .
it is logical to assume that this accuracy is dependent on 
 the isotropic resolution and might increase towards smaller isotropic resolutions . 

however , such an approach requires the development of specific standards made of the 
 same material as the unknown sample , in order to preserve the same contrast .
this could 
 be a milestone for the application of mxct in the quantification of the geometrical 
 features and could be an interesting subject for future research .  
the surface area and volume of the endodontic files , as presented for the first time by 
 the present study , was found to increase towards higher file sizes with significant 
 differences between the successive file sizes ( table 
 1 ) .
linear regression analysis showed a linear correlation of both the surface 
 area and volume with the nominal file sizes .
the surface area and volume are not 
 physically dependent on the nominal iso sizes and the equations presented in figure 3 are simply an engineering relationship 
 between two different physical magnitudes .
finally , the aforementioned equations are not 
 universal and should be used exclusively for the tested ni - ti endodontic system . for the 
 other ni - ti files , linear models with different coefficient values are anticipated .  
although the geometrical configuration and design of the ni - ti files are important 
 factors in controlling the clinical performance of these micro - instruments , the 
 assessment of their clinical performance with experimental testing remains 
 questionable .
some studies provide results with great differences , 
 not only among the different brands but also within one brand and type .
the main 
 weakness of the currently available experimental protocols is that the clinical 
 performance of the endodontic files has been biased as to the influence of various 
 factors and has been determined separately . on the other hand , the 
 results of the current study do not have any immediate clinical implications , as they 
 must be combined with further experimental results of the clinical properties ( such as 
 cutting efficiency , loading of dental chips , etc . ) in order to determine any possible 
 correlation .
for instance , it is logical to assume that a file with a greater surface 
 area has the increased ability of loading dental chips but this requires experimental 
 documentation .  
the surface area and volume between the successive files showed significant differences 
 and thus there is no overlap between the successive file numbers , as occurs with the 
 first diameter ( d1 ) below the tip . as expected , both the surface area and 
 volume show an increase towards the higher file sizes .
the percentage difference between 
 n 25/n 30 ( 16.6% ) is almost double the value of n 20/n 
 25 ( 8.9% ) files sizes , whereas the percentage increase in volume was similar ( 21.1% and 
 17.2% for n 20/n 25 and n 25/n 30 , respectively ) showing 
 a completely different increasing pattern .
it should be mentioned that the percentage 
 differences in the surface area show an abrupt increase towards the larger file sizes , 
 while volumetric changes exhibit a declining trend .
this implies that the surface area 
 and volume progress towards larger files with a completely different pattern , a finding 
 reflected by the values of the specific surface area ( figure 3 ) .
the latter is a property that defines the total surface area 
 per unit of bulk volume and has significant importance in cases 
 where the surface area has a significant effect on the system studied .
the n 20 
 files have the highest specific surface area , indicating that more surface area is 
 exposed per volume unit than in n 25 and n 30 sizes . 

this value is characteristic of the geometrical design and it is expected to vary 
 significantly among different file designs .
files with a non - standard taper ( i.e. , 
 protaper ) are anticipated to demonstrate increased specific surface area due to the 
 significant reduction in file volume .  
it is noteworthy that beyond the estimation of the surface area and volume of the 
 scanned files , the 2d and 3d analysis of the scanned files provides tremendous 
 opportunities .
firstly , all the geometrical features ( i.e. , cutting angle , depth of 
 flutes , crosssectional diameter ) measured in longitudinal and cross - section analyses , 
 with optical and electron microscopy can be readily measured with mxct methodology .
this 
 analysis is advantageous over traditional techniques , as it is non - destructive and thus 
 there is no need for specimen preparation ( embedding , cutting , metallographic polishing , 
 conductive coating ) .
computational analysis of 3d models can be used to quantify any 
 selected geometrical feature for any region of interest .
for instance , the real surface 
 area of a file working in a root canal can be easily estimated , selecting the relative 
 region of interest .
secondly , 3d modeling of scanned files can provide more accurate 
 models for subsequent finite 
 element analyses . on the other hand , 

the drawbacks of mxct methodology are the inferior resolution compared to optical and 
 electron microscopy and prolonged scanning times for the model reconstruction in high 
 isotropic resolution .
another limitation is that the image quality might be affected by the beam 
 hardening phenomena .
normally , an x - ray beam contains photons with a vast range of 
 energies . in physical metallurgy
, the beam hardening phenomenon refers to the absorption 
 of lower energy photons during the passing of a beam through a metal object and once 
 this happens , " beam hardening " occurs as the mean energy of a beam increases . in this 
 study , to minimize the beam hardening effect an al filter was utilized and a beam 
 hardening correction routine was applied .
the former was used to pre - harden the beam by 
 cutting the lower energy photons , while the latter is a correction algorithm which was 
 applied during the reconstruction process .
the estimation of the surface area and volume 
 of endodontic files might provide a new approach for the characterization of 
 clinically - related properties such as cutting efficiency , loading of dentin debris etc . 

this study demonstrates that mxct is a powerful tool with interesting applications for 
 endodontic research .
continuing technological advancements allowing development of more 
 powerful mxct scanners should accelerate the applications of this methodology in the 
 near future .
the surface area and volume demonstrated an almost linear increase , while the specific 
 surface area demonstrated an abrupt decrease towards the higher file sizes .
for the 
 first time , we have shown that mxct is capable of discriminating the quantitative 
 differences in the geometrical properties of the successive sizes of endodontic files . 

this type of analysis should be used to investigate the unexplored correlations of the 
 various clinical properties of the geometrical characteristics of the endodontic files , 
 opening new avenues for research in the field of endodontics .
the authors would like to thank the research group program for funding this research 
 project .
this study has been funded by a research grant ( # rgp - vpp-206 ) from the 
 research group program , deanship of scientific research , king saud university , 
 riyadh , saudi arabia .
 objectivethe aim of this study was to quantify the surface area , volume and specific 
 surface area of endodontic files employing quantitative x - ray micro computed 
 tomography ( mxct ) . 
 material and methodsthree sets ( six files each ) of the flex - master ni - ti system ( n 20 , 25 and 
 30 , taper .04 ) were utilized in this study . 
 the files were scanned by mxct . 
 the 
 surface area and volume of all files were determined from the cutting tip up to 16 
 mm . 
 the data from the surface area , volume and specific area were statistically 
 evaluated using the one - way anova and snk multiple comparison tests at 
 =0.05 , employing the file size as a discriminating variable . 
 the 
 correlation between the surface area and volume with nominal iso sizes were tested 
 employing linear regression analysis . 
 resultsthe surface area and volume of n 30 files showed the highest value 
 followed by n 25 and n 20 and the differences were statistically 
 significant . 
 the n 20 files showed a significantly higher specific surface 
 area compared to n 25 and n 30 . 
 the increase in surface and volume 
 towards higher file sizes follows a linear relationship with the nominal iso sizes 
 ( r2=0.930 for surface area and r2=0.974 for volume 
 respectively ) . 
 results indicated that the surface area and volume demonstrated an 
 almost linear increase while the specific surface area exhibited an abrupt 
 decrease towards higher sizes . 
 conclusionsthis study demonstrates that mxct can be effectively applied to discriminate very 
 small differences in the geometrical features of endodontic micro - instruments , 
 while providing quantitative information for their geometrical properties . 
INTRODUCTION
MATERIAL AND METHODS
Statistical analysis
RESULTS
DISCUSSION
CONCLUSIONS
ACKNOWLEDGMENT