Abstract:
An endodontic file includes a uniform tapered working length made of shape memory material with at least two helical shaped flutes and narrow spiraled lands in between, having a width no greater than 0.075 mm as measured in a plane perpendicular the central axis of rotation of instrument. The land width is preferably constant along the working length but may vary provided the width of the lands in a waist portion of the file are no greater than those above or below the waist portion. The instrument resists mid-root transportation and exhibits superior fatigue performance and cutting efficiency compared to prior art instruments.

Description:
CROSS REFERENCE TO CO-PENDING APPLICATIONS 
       [0001]    This application is a continuation-in-part of, and claims priority to, U.S. patent application Ser. 13/945,696 filed Jul. 18, 2013. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    Field of the Invention. 
         [0003]    This invention relates generally to the field of dentistry and more particularly to endodontic files or reamers used in the cleaning of material present in the root canal of human teeth and for enlarging and shaping the root canal so that it is prepared for receiving filling material. 
         [0004]    Description of the Related Art. 
         [0005]    Instruments that enable an endodontist to clear and clean the root canal of a tooth are well-known in the art. Because of the geometry of a root canal, these instruments—typically referred to as endodontic files—experience significant flexing and twisting while in use, making them susceptible to breakage. Because of the breakage problem and the danger that it poses to a patient, nickel-titanium alloy (NiTi or Nitinol™) generally is viewed as a better material for use in manufacturing these instruments than is stainless steel. Relative to stainless steel, NiTi is able to withstand a far greater amount of twisting or bending without experiencing permanent deformation or breaking. 
         [0006]    The design challenge is multi-dimensional: to provide a NiTi instrument that is flexible, resists torsional breakage and cyclic fatigue, cuts efficiently, and does not transport the root canal during cutting. Unfortunately, these design objectives run counter to one another. Therefore, prior art instrument designs represent the various tradeoffs made among these objectives. To date, all the prior art instrument designs teach away from providing narrow radial land widths along the entire working length of a straight or uniform taper instrument. 
         [0007]    The prior art has assumed that radial lands in the range of at least 0.004 to 0.006 inches (about 0.102 to 0.152 mm) are required to get optimum cutting and guide use when a standard K-file or reamer is employed in a curved root canal. See e.g., U.S. Pat. Nos. 4,934,934 to Arpaio, Jr. et al.; Re. 34,439 (reissue of 4,871,312) and 5,762,497 to Heath; and 5,941,760 to Heath et al. To achieve this performance, the land width selected in this range should be held constant along the working length of the instrument. However, land widths must be increased to prevent transportation of the canal path. See e.g., U.S. Pat. App. Pub. No. 2007/0026360 to Buchanan. 
         [0008]    Where lands having a width below 0.004 inches (about 0.102 mm) are disclosed, the instrument shape is altered from a uniform or straight taper shape and the narrow lands are only located at the tip and shank portions of the instrument. For example, U.S. Pat. App. Pub. No. 2007/0026360 to Buchanan discloses a land width below that of Arpaio, Jr. and Heath, in the range of 0 to 0.004 inches, except for lands located along an under-contoured (narrower) intermediate or middle waist portion of the working length. The lands in the waist portion are relatively wide—for example, in the range of 0.004 to 0.006 inches—compared to those in the tip and shank portions. Buchanan claims that the combination of multiple contours or heights and multiple land width variations along the working length reduces taper lock, increases cutting efficiency, and minimizes or eliminates transportation. See Buchanan at para. 0030 (noting “the wider land in the mid-region of the instrument prevents or minimizes straightening of curved canals at their mid-points.”) Similar to Arpaio, Jr. and Heath, Buchanan also discloses that a wide land width prevents transportation of the root canal path but increases the likelihood of breakage due to cyclic fatigue because of reduced cutting efficiency (therefore requiring more revolutions to accomplish a certain shaping objective). On the other hand, a narrow land width reduces the likelihood of breakage because of increased cutting efficiency but increases the chances of mid-root transportation. 
         [0009]    Buchanan also found that a straight taper instrument having narrow land widths toward the shank end of the instrument and relatively wider land widths toward the tip end increases mid-root transportation to unacceptable levels. See Buchanan at para. 0006. This transportation is most likely the result of stiffness created by the increasing land widths in the waist portion of the instrument. Additionally, as the width of the radial land increases, torque strength increases but so does drag. 
         [0010]    Subsequent testing by the Applicant has discovered that a straight taper instrument having narrow land widths in the shank and tip portions but wider lands in the waist portion does lead to stiffness, which is evidenced by stress concentrations in the waist portion as the instrument traverses a curved portion of a root canal. The Applicant also has conducted experimentation with instruments having a wider waist portion relative to the shank and tip end portions and narrow lands along the length of the instrument. These instruments also experienced unacceptable mid-root transportation. The Applicant then decided to manufacture a straight taper K-file having narrow radial lands along its entire length. Unexpectedly and surprisingly, the instrument exhibited no mid-root transportation in addition to superior cutting performance and resistance to cyclic fatigue. Preferred embodiments of this file are disclosed herein. 
       SUMMARY OF THE INVENTION 
       [0011]    An improved endodontic file made according to this invention eliminates mid-root transportation but not at the expense of flexibility, cyclic fatigue, and cutting performance. The file has a uniform tapered working length made out of shape memory material and includes spiraled right hand twist flutes with radial lands in between having a land width no greater than 0.101 mm (0.0039 inches) as measured in a plane perpendicular the central axis of rotation of the instrument. 
         [0012]    Because the file is operated in a clockwise direction during use, the right-hand twist or orientation allows the file to transport debris toward the shank end of the file rather than compact it further into a root canal. The land width may vary along the working length provided that it does not exceed 1 or 2 degrees of arc and is preferably no greater 0.101 mm at any diameter location D n  along the working length, n being in a range of 1 to the total working length of the file. The taper is preferably in the range of 0.02 to 0.08 mm per mm, with the instrument size being in the range of 8 to 70. Preferably, the land width is in a range of 0.025 mm (0.001 in.) to 0.051 mm (0.002 in.) or, even more preferably, in a range of 0.025 mm to 0.034 mm (0.0013 in.), with an 0.04 to 0.06 taper and the instrument size in a range of 20 to 70. 
         [0013]    The uniform tapered working length portion of the file—that is, the portion that includes the spiraled flutes and narrow radial lands—is made of bendable, shape memory material such as nickel titanium or its equivalent. The uniform tapered working length portion has a total length N between a shank end and a tip end of the working length, with diameters D n , where n is an integer distance in a range of 1 to N in mm as measured from the tip end, N being no greater than 16 as measured in mm. A mid- or waist portion of the file is located in a range of D4 to D H . The waist portion has the same uniform taper as the portion of the file below D 4  and above D H . 
         [0014]    An object of this invention is to provide an improved endodontic instrument that provides superior cutting performance and resistance to cyclic fatigue. Another object of this invention is to provide an endodontic instrument that does not transport the root canal as the instrument navigates and shapes a curved portion of the canal. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]      FIG. 1  is a view of a preferred embodiment of an endodontic file according to this invention. The file has a uniform taper, at least two helical flutes, and narrow radial lands located between the helical flutes along the entire working length of the file. 
           [0016]      FIG. 2  is a view taken along section line  2 - 2  of  FIG. 1  illustrating a preferred embodiment of the endodontic file. The file has four substantially straight helical flute surfaces with narrow radial lands located between each adjacent pair of flutes. The cutting edges provide a neutral rake angle (−15° or less).  FIG. 3  is a view taken along section line  3 - 3  of  FIG. 1  illustrating another preferred embodiment of the endodontic file. The file has four concave-shaped helical flutes with narrow radial lands located between each adjacent pair of flutes. The cutting edges provide a neutral rake angle. 
           [0017]      FIG. 4  is a view taken along section line  4 - 4  of  FIG. 1  illustrating yet another preferred embodiment of the endodontic file. The file has three substantially straight helical flute surfaces with narrow radial lands located between each adjacent pair of flutes. The cutting edges provide a neutral rake angle. 
           [0018]      FIG. 5  is a view taken along section line  5 - 5  of  FIG. 1  illustrating yet another preferred embodiment of the endodontic file having three concave-shaped helical flutes defined by a radius of curvature and forming narrow radial lands between each adjacent flute. The cutting edges provide a neutral rake angle. 
           [0019]      FIG. 6  is a view taken along section line  6 - 6  of  FIG. 1  illustrating another preferred embodiment of the endodontic file. The file has three convex-shaped helical flutes with narrow radial lands located between each adjacent pair of flutes. The cutting edges provide a neutral rake angle. 
           [0020]      FIG. 7  is a graphical depiction of a prior art endodontic file having wide lands in the mid-portion of the working length—or alternatively narrow lands in a wider mid-portion of the working length—as the working length of the file would appear when traversing a curved root canal. 
           [0021]      FIG. 8  is a graphical depiction of the endodontic file of  FIG. 1  as its working length would appear when traversing a curved root canal. 
           [0022]      FIG. 9  is an enlarged view of the curved and stressed mid-portion of the working length of the prior art endodontic file of  FIG. 7 . Because of the wide lands (or the wider waist portion) the mid-portion experiences severe and moderate stress concentrations which make it prone to cyclic fatigue and breakage. 
           [0023]      FIG. 10  is a view an enlarged view of the mid-portion of endodontic file of  FIG. 8 . The narrow lands in the mid-portion eliminate the areas of stress concentration which are experienced by the wider landed or wider waist file of  FIG. 9 . 
           [0024]      FIG. 11  is a view of the prior art endodontic file of  FIG. 7  as it traverses a curved root canal and experiences mid-root transportation. 
           [0025]      FIG. 12  is a view of the file of  FIG. 1  as it traverses a curved root canal. The file experiences no mid-root transportation. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0026]    Preferred embodiments of an endodontic file made according to this invention will now be described in reference to the drawings and the following element numbering: 
         [0000]    
       
         
               
               
             
           
               
                   
               
             
             
               
                 10 
                 Endodontic file 
               
               
                 11 
                 Flute surfaces 
               
               
                 13 
                 Shank or proximal end 
               
               
                 14 
                 Waist or mid-portion 
               
               
                 15 
                 Tip or distal end 
               
               
                 17 
                 Radial land 
               
               
                 19 
                 Central axis of rotation 
               
               
                 20 
                 Plane perpendicular to 19 
               
               
                 21 
                 Handle portion 
               
               
                 23 
                 Depth calibration grooves 
               
               
                 24 
                 Working length 
               
               
                 25 
                 Transportation 
               
               
                 27 
                 Area of moderate stress concentration 
               
               
                 29 
                 Area of severe stress concentration 
               
               
                   
               
             
          
         
       
     
         [0027]    For the purpose of this disclosure, an endodontic file is a tapered and pointed metal file with a right-hand flute orientation and cutting edges used to enlarge the root canal by clockwise rotation or filing action. Unlike pluggers, compactors, or spreaders—which are left-hand oriented, flat-ended, and designed for use in obturation techniques to compact material vertically downward within a prepared root canal and cannot be used to prepare a canal, see e.g., McSpadden (U.S. Pat. No. 4,457,710) and Heath et al. (U.S. Pat. No. 5,302,129)—an endodontic file is designed to prepare (clean, cut and shape) a root canal and extract canal material out of the canal so that a plugger, compactor, or spreader may be used. 
         [0028]    Referring first to  FIG. 1 , an endodontic file  10  includes two or more continuously spiraled flute surfaces  11  extending between the shank end  13  and tip end  15  of the file  10 . Adjacent flute surfaces  11  form a radial land  17  that provides an edge for cutting or scraping the wall of a root canal in order to shape the canal as the file  10  is manually or mechanically manipulated about its central axis of rotation  19 . Preferably, the edge has a neutral rake angle of −15° or less. Therefore, the radial lands  17  are located along the active portion or working length  24  that lies between the shank and tip ends  13 ,  15 . Working length  24  is preferably about 16 mm to  25  mm in length and follows a predetermined straight or uniform taper so that the diameter at its tip end  15  is less than the diameter at its the shank end  13 . Although not forming a part of this invention, the handle portion  21  of file  10  may be configured for manual or mechanical manipulation and includes depth calibration grooves  23 . 
         [0029]    Referring now to  FIGS. 2 to 6 , the flute surfaces  11  may be straight, convex or concave surfaces that form radial lands  17 . The cross-sectional shape of the working length  24  is preferably constant. That is to say, the desired number and shape of flute surfaces  11  do not change from one cross-section to the next along working length  24 . At any diameter along the working length  24 , the cross-section or core of the file  10  is greater than half the area represented by a circle drawn about the cross-section, the lands  17  lying on, and forming points of, the circle (see e.g.  FIG. 2 ). 
         [0030]    Central to this invention is that the radial lands  17  are narrow lands, meaning that their width as measured in a plane  20  lying perpendicular to the central axis of rotation  19  is no greater than 0.0039 inches (0.101 mm) and preferably less than 0.101 mm. In one preferred embodiment, the radial lands  17  were so narrow as to appear to form a sharp point, much less than 0.1 mm. 
         [0031]    Measured in terms of degrees of arc a, the maximum degrees of arc a at each diameter Dn for various sizes of files having a 0.02 mm per mm taper does not exceed those as listed in Table 1, where n is the distance in millimeters from tip end  15 . For example, a size 8 file having a 0.02 taper has a D1 diameter of 0.08 mm and a D2 of 0.10. A size 8 file having a 0.08 taper has a D1 and D2 diameter of 0.08 and 0.16 mm, respectively. To calculate the maximum degrees of arc “a” at any given cross-section “n” so as to not exceed a predetermined maximum land width “w” at that cross-section “n” for any given size file “s” and taper “t”, the following formula may be used: 
         [0000]    
       
         
           
             
               Max 
                
               
                   
               
                
               
                 α 
                 n 
               
             
             = 
             
               
                 360 
                  
                 
                     
                 
                  
                 
                   w 
                   n 
                 
               
               
                 π 
                  
                 
                   [ 
                   
                     
                       
                         ( 
                         
                           n 
                           - 
                           1 
                         
                         ) 
                       
                        
                       t 
                     
                     + 
                     s 
                   
                   ] 
                 
               
             
           
         
       
     
         [0032]    where “n” is measured from the tip end of the file and “s” is the file size in hundredths (e.g., size 8 equates to an “s” of 0.08 mm). The land width, w, can be calculated using this same formula by solving for w (see Tables 2 and 3). Preferably, the land width does not exceed 1 or 2 degrees of arc, α, and a maximum width of no greater than 0.101 mm can be set along the entire working length. More preferably, the land width is in a range of 0.025 mm (0.001 in.) to 0.051 mm (0.002 in.) or 0.075 mm (0.003 in.) or, even more preferably, in a range of 0.025 mm to 0.034 mm (0.0013 in.),It has always been assumed by the designers of endodontic files that wider radial lands are needed in the waist portion  14  of the file to keep the file from transporting the root canal. The waist portion  14  generally begins about 9 to 11 mm from proximal end  13  and ends about 2½to 3 mm from the tip end  15 , respectively (or about 9 to 11 mm from the distal end. However, referring now to  FIGS. 7, 9 &amp; 11 , digital photography revels that a prior art endodontic file having narrower radial lands at the shank and tip portions  13 ,  15  and wider radial lands at the waist portion  14  still experiences unacceptable levels of mid-root transportation  25  as the file navigates about a 45° curvature of a simulated root canal R in a resin block B. 
         [0033]    Thermal spectroscopy also reveals areas of moderate  27  and severe  29  stress concentration in the waist portion  14  as the prior art file traverses the curvature of canal R. These areas of stress concentration  27 ,  29  negatively affect the cyclic fatigue performance of the file. These findings are in line with those of Buchanan, as was discussed in the Background section. However, Buchanan, in keeping with conventional wisdom, tried to solve the problem by keeping the wider lands in the waist portion  14  but altering the contour of the file. 
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Maximum degrees of arc to achieve an arc length no greater than 0.101 mm at the D 1   
               
               
                 to D 16  diameters for various file sizes having a 0.02 taper. 
               
             
          
           
               
                 File 
                 Working length diameter D n   
               
             
          
           
               
                 Size 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
               
               
                   
               
             
          
           
               
                 8 
                 145 
                 116 
                 96 
                 83 
                 72 
                 64 
                 58 
                 53 
                 48 
                 45 
                 41 
                 39 
                 36 
                 34 
                 32 
                 30 
               
               
                 10 
                 116 
                 96 
                 83 
                 72 
                 64 
                 58 
                 53 
                 48 
                 45 
                 41 
                 39 
                 36 
                 34 
                 32 
                 30 
                 29 
               
               
                 15 
                 77 
                 68 
                 61 
                 55 
                 50 
                 46 
                 43 
                 40 
                 37 
                 35 
                 33 
                 31 
                 30 
                 28 
                 27 
                 26 
               
               
                 20 
                 58 
                 53 
                 48 
                 45 
                 41 
                 39 
                 36 
                 34 
                 32 
                 30 
                 29 
                 28 
                 26 
                 25 
                 24 
                 23 
               
               
                 25 
                 46 
                 43 
                 40 
                 37 
                 35 
                 33 
                 31 
                 30 
                 28 
                 27 
                 26 
                 25 
                 24 
                 23 
                 22 
                 21 
               
               
                 30 
                 39 
                 36 
                 34 
                 32 
                 30 
                 29 
                 28 
                 26 
                 25 
                 24 
                 23 
                 22 
                 21 
                 21 
                 20 
                 19 
               
               
                 35 
                 33 
                 31 
                 30 
                 28 
                 27 
                 26 
                 25 
                 24 
                 23 
                 22 
                 21 
                 20 
                 20 
                 19 
                 18 
                 18 
               
               
                 40 
                 29 
                 28 
                 26 
                 25 
                 24 
                 23 
                 22 
                 21 
                 21 
                 20 
                 19 
                 19 
                 18 
                 18 
                 17 
                 17 
               
               
                 45 
                 26 
                 25 
                 24 
                 23 
                 22 
                 21 
                 20 
                 20 
                 19 
                 18 
                 18 
                 17 
                 17 
                 16 
                 16 
                 15 
               
               
                 50 
                 23 
                 22 
                 21 
                 21 
                 20 
                 19 
                 19 
                 18 
                 18 
                 17 
                 17 
                 16 
                 16 
                 15 
                 15 
                 14 
               
               
                 55 
                 21 
                 20 
                 20 
                 19 
                 18 
                 18 
                 17 
                 17 
                 16 
                 16 
                 15 
                 15 
                 15 
                 14 
                 14 
                 14 
               
               
                 60 
                 19 
                 19 
                 18 
                 18 
                 17 
                 17 
                 16 
                 16 
                 15 
                 15 
                 14 
                 14 
                 14 
                 13 
                 13 
                 13 
               
               
                 70 
                 17 
                 16 
                 16 
                 15 
                 15 
                 14 
                 14 
                 14 
                 13 
                 13 
                 13 
                 13 
                 12 
                 12 
                 12 
                 12 
               
               
                 80 
                 14 
                 14 
                 14 
                 13 
                 13 
                 13 
                 13 
                 12 
                 12 
                 12 
                 12 
                 11 
                 11 
                 11 
                 11 
                 11 
               
               
                 90 
                 13 
                 13 
                 12 
                 12 
                 12 
                 12 
                 11 
                 11 
                 11 
                 11 
                 11 
                 10 
                 10 
                 10 
                 10 
                 10 
               
               
                 100 
                 12 
                 11 
                 11 
                 11 
                 11 
                 11 
                 10 
                 10 
                 10 
                 10 
                 10 
                 9 
                 9 
                 9 
                 9 
                 9 
               
               
                 110 
                 11 
                 10 
                 10 
                 10 
                 10 
                 10 
                 9 
                 9 
                 9 
                 9 
                 9 
                 9 
                 9 
                 9 
                 8 
                 8 
               
               
                 120 
                 10 
                 9 
                 9 
                 9 
                 9 
                 9 
                 9 
                 9 
                 9 
                 8 
                 8 
                 8 
                 8 
                 8 
                 8 
                 8 
               
               
                 130 
                 9 
                 9 
                 9 
                 9 
                 8 
                 8 
                 8 
                 8 
                 8 
                 8 
                 8 
                 8 
                 8 
                 7 
                 7 
                 7 
               
               
                 140 
                 8 
                 8 
                 8 
                 8 
                 8 
                 8 
                 8 
                 8 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
               
               
                 150 
                 8 
                 8 
                 8 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
                 7 
                 6 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Land width (in ten thousandths mm) for 2 degrees of arc at D1 to D16 diameters 
               
               
                 for various file sizes having a 0.02 taper. 
               
             
          
           
               
                   
                 Working length diameter Dn 
               
             
          
           
               
                 Size 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
               
               
                   
               
             
          
           
               
                 8 
                 14 
                 17 
                 21 
                 24 
                 28 
                 31 
                 35 
                 38 
                 42 
                 45 
                 49 
                 52 
                 56 
                 59 
                 63 
                 66 
               
               
                 10 
                 17 
                 21 
                 24 
                 28 
                 31 
                 35 
                 38 
                 42 
                 45 
                 49 
                 52 
                 56 
                 59 
                 63 
                 66 
                 70 
               
               
                 15 
                 26 
                 30 
                 33 
                 37 
                 40 
                 44 
                 47 
                 51 
                 54 
                 58 
                 61 
                 65 
                 68 
                 72 
                 75 
                 79 
               
               
                 20 
                 35 
                 38 
                 42 
                 45 
                 49 
                 52 
                 56 
                 59 
                 63 
                 66 
                 70 
                 73 
                 77 
                 80 
                 84 
                 87 
               
               
                 25 
                 44 
                 47 
                 51 
                 54 
                 58 
                 61 
                 65 
                 68 
                 72 
                 75 
                 79 
                 82 
                 86 
                 89 
                 93 
                 96 
               
               
                 30 
                 52 
                 56 
                 59 
                 63 
                 66 
                 70 
                 73 
                 77 
                 80 
                 84 
                 87 
                 91 
                 94 
                 98 
                 101 
                 105 
               
               
                 35 
                 61 
                 65 
                 68 
                 72 
                 75 
                 79 
                 82 
                 86 
                 89 
                 93 
                 96 
                 99 
                 103 
                 106 
                 110 
                 113 
               
               
                 40 
                 70 
                 73 
                 77 
                 80 
                 84 
                 87 
                 91 
                 94 
                 98 
                 101 
                 105 
                 108 
                 112 
                 115 
                 119 
                 122 
               
               
                 45 
                 79 
                 82 
                 86 
                 89 
                 93 
                 96 
                 99 
                 103 
                 106 
                 110 
                 113 
                 117 
                 120 
                 124 
                 127 
                 131 
               
               
                 50 
                 87 
                 91 
                 94 
                 98 
                 101 
                 105 
                 108 
                 112 
                 115 
                 119 
                 122 
                 126 
                 129 
                 133 
                 136 
                 140 
               
               
                 55 
                 96 
                 99 
                 103 
                 106 
                 110 
                 113 
                 117 
                 120 
                 124 
                 127 
                 131 
                 134 
                 138 
                 141 
                 145 
                 148 
               
               
                 60 
                 105 
                 108 
                 112 
                 115 
                 119 
                 122 
                 126 
                 129 
                 133 
                 136 
                 140 
                 143 
                 147 
                 150 
                 154 
                 157 
               
               
                 70 
                 122 
                 126 
                 129 
                 133 
                 136 
                 140 
                 143 
                 147 
                 150 
                 154 
                 157 
                 161 
                 164 
                 168 
                 171 
                 175 
               
               
                 80 
                 140 
                 143 
                 147 
                 150 
                 154 
                 157 
                 161 
                 164 
                 168 
                 171 
                 175 
                 178 
                 182 
                 185 
                 188 
                 192 
               
               
                 90 
                 157 
                 161 
                 164 
                 168 
                 171 
                 175 
                 178 
                 182 
                 185 
                 188 
                 192 
                 195 
                 199 
                 202 
                 206 
                 209 
               
               
                 100 
                 175 
                 178 
                 182 
                 185 
                 188 
                 192 
                 195 
                 199 
                 202 
                 206 
                 209 
                 213 
                 216 
                 220 
                 223 
                 227 
               
               
                 110 
                 192 
                 195 
                 199 
                 202 
                 206 
                 209 
                 213 
                 216 
                 220 
                 223 
                 227 
                 230 
                 234 
                 237 
                 241 
                 244 
               
               
                 120 
                 209 
                 213 
                 216 
                 220 
                 223 
                 227 
                 230 
                 234 
                 237 
                 241 
                 244 
                 248 
                 251 
                 255 
                 258 
                 262 
               
               
                 130 
                 227 
                 230 
                 234 
                 237 
                 241 
                 244 
                 248 
                 251 
                 255 
                 258 
                 262 
                 265 
                 269 
                 272 
                 276 
                 279 
               
               
                 140 
                 244 
                 248 
                 251 
                 255 
                 258 
                 262 
                 265 
                 269 
                 272 
                 276 
                 279 
                 283 
                 286 
                 290 
                 293 
                 297 
               
               
                 150 
                 262 
                 265 
                 269 
                 272 
                 276 
                 279 
                 283 
                 286 
                 290 
                 293 
                 297 
                 300 
                 304 
                 307 
                 311 
                 314 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Land width (in ten thousandths mm) for 2 degrees of arc at D1 to D16 diameters 
               
               
                 for various file sizes having a 0.08 taper. 
               
             
          
           
               
                   
                 Working length diameter Dn 
               
             
          
           
               
                 Size 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
               
               
                   
               
             
          
           
               
                 8 
                 14 
                 28 
                 42 
                 56 
                 70 
                 84 
                 98 
                 112 
                 126 
                 140 
                 154 
                 168 
                 182 
                 195 
                 209 
                 223 
               
               
                 10 
                 17 
                 31 
                 45 
                 59 
                 73 
                 87 
                 101 
                 115 
                 129 
                 143 
                 157 
                 171 
                 185 
                 199 
                 213 
                 227 
               
               
                 15 
                 26 
                 40 
                 54 
                 68 
                 82 
                 96 
                 110 
                 124 
                 138 
                 152 
                 166 
                 180 
                 194 
                 208 
                 222 
                 236 
               
               
                 20 
                 35 
                 49 
                 63 
                 77 
                 91 
                 105 
                 119 
                 133 
                 147 
                 161 
                 175 
                 188 
                 202 
                 216 
                 230 
                 244 
               
               
                 25 
                 44 
                 58 
                 72 
                 86 
                 99 
                 113 
                 127 
                 141 
                 155 
                 169 
                 183 
                 197 
                 211 
                 225 
                 239 
                 253 
               
               
                 30 
                 52 
                 66 
                 80 
                 94 
                 108 
                 122 
                 136 
                 150 
                 164 
                 178 
                 192 
                 206 
                 220 
                 234 
                 248 
                 262 
               
               
                 35 
                 61 
                 75 
                 89 
                 103 
                 117 
                 131 
                 145 
                 159 
                 173 
                 187 
                 201 
                 215 
                 229 
                 243 
                 257 
                 271 
               
               
                 40 
                 70 
                 84 
                 98 
                 112 
                 126 
                 140 
                 154 
                 168 
                 182 
                 195 
                 209 
                 223 
                 237 
                 251 
                 265 
                 279 
               
               
                 45 
                 79 
                 93 
                 106 
                 120 
                 134 
                 148 
                 162 
                 176 
                 190 
                 204 
                 218 
                 232 
                 246 
                 260 
                 274 
                 288 
               
               
                 50 
                 87 
                 101 
                 115 
                 129 
                 143 
                 157 
                 171 
                 185 
                 199 
                 213 
                 227 
                 241 
                 255 
                 269 
                 283 
                 297 
               
               
                 55 
                 96 
                 110 
                 124 
                 138 
                 152 
                 166 
                 180 
                 194 
                 208 
                 222 
                 236 
                 250 
                 264 
                 278 
                 291 
                 305 
               
               
                 60 
                 105 
                 119 
                 133 
                 147 
                 161 
                 175 
                 188 
                 202 
                 216 
                 230 
                 244 
                 258 
                 272 
                 286 
                 300 
                 314 
               
               
                 70 
                 122 
                 136 
                 150 
                 164 
                 178 
                 192 
                 206 
                 220 
                 234 
                 248 
                 262 
                 276 
                 290 
                 304 
                 318 
                 332 
               
               
                 80 
                 140 
                 154 
                 168 
                 182 
                 195 
                 209 
                 223 
                 237 
                 251 
                 265 
                 279 
                 293 
                 307 
                 321 
                 335 
                 349 
               
               
                 90 
                 157 
                 171 
                 185 
                 199 
                 213 
                 227 
                 241 
                 255 
                 269 
                 283 
                 297 
                 311 
                 325 
                 339 
                 353 
                 367 
               
               
                 100 
                 175 
                 188 
                 202 
                 216 
                 230 
                 244 
                 258 
                 272 
                 286 
                 300 
                 314 
                 328 
                 342 
                 356 
                 370 
                 384 
               
               
                 110 
                 192 
                 206 
                 220 
                 234 
                 248 
                 262 
                 276 
                 290 
                 304 
                 318 
                 332 
                 346 
                 360 
                 374 
                 387 
                 401 
               
               
                 120 
                 209 
                 223 
                 237 
                 251 
                 265 
                 279 
                 293 
                 307 
                 321 
                 335 
                 349 
                 363 
                 377 
                 391 
                 405 
                 419 
               
               
                 130 
                 227 
                 241 
                 255 
                 269 
                 283 
                 297 
                 311 
                 325 
                 339 
                 353 
                 367 
                 380 
                 394 
                 408 
                 422 
                 436 
               
               
                 140 
                 244 
                 258 
                 272 
                 286 
                 300 
                 314 
                 328 
                 342 
                 356 
                 370 
                 384 
                 398 
                 412 
                 426 
                 440 
                 454 
               
               
                 150 
                 262 
                 276 
                 290 
                 304 
                 318 
                 332 
                 346 
                 360 
                 374 
                 387 
                 401 
                 415 
                 429 
                 443 
                 457 
                 471 
               
               
                   
               
             
          
         
       
     
         [0034]    Although Buchanan saw the need for narrow radial lands at the tip and shank end of the file, he avoided narrow radial lands in the waist portion  14  because conventional wisdom held that to provide narrow lands in this portion of the file would require that the waist portion  14  be widened. However, widening the waist portion  14  leads to similar transportation  25  and stress concentration  27 ,  29  because a wider waist causes stiffness. Therefore, Buchanan elected to narrow the waist portion but widen the lands relative to the tip and shank portions. 
         [0035]    The prior art also teaches that a file having a straight or uniform taper but narrow radial lands  17  along its entire working length  14  would experience unacceptable levels of transportation  25  due to, for example, flexing of the waist portion as either the shank or tip ends  13 ,  15  thread into the root canal R or their cutting or scraping edges drag across the walls of canal R. Buchanan is indicative of the lengths that endodontic designers will go to in order to avoid narrow lands in the waist portion  14  of the file. Compared to the current invention, Buchanan&#39;s design is complex and more costly to manufacture. 
         [0036]    Referring now to  FIGS. 8, 10 &amp; 12  a preferred embodiment of an endodontic file made according to this invention was tested in a simulated root canal R in a resin block B. Unexpectedly and surprisingly, the file  10  exhibited no mid-root transportation in its waist portion  14  as the file traversed a 45° curvature. Furthermore, thermal spectroscopy indicated no areas of severe or moderate stress concentrations in the waist portion  14  or along the working length  24 . 
         [0037]    The fact that improved endodontic file  10  experiences no mid-root transportation and has no areas of stress concentration was demonstrated in subsequent testing. Two PROFILE® files (DENTSPLY Tulsa Dental Specialties, Tulsa, Okla.) were made according to this invention and compared under the same set of test conditions to other prior art, sharp-cutting non-landed files (see Table 4). One of the PROFILE® files was made out of M-WIRE™ NiTi wire (DENTSPLY Tulsa Dental Specialties, Tulsa, Okla.) and the other was made out of NiTi wire. The advantage of the M-WIRE is in enhanced resistance to cyclic fatigue. The straight taper of file  10  in combination with the narrow radial lands  17  along its working length  24  improved cutting efficiency by a factor of about 1.4. 
         [0000]                                                                                                                    TABLE 4                   Cyclic fatigue and cutting efficiency of various endodontic       files having a 0.04 taper and a 25 mm working length.                M-WIRE ™ NiTi Wire   NiTi Wire                Non-Landed   Landed   Non-Landed   Landed                    FLEX-   PROFILE ®   Twisted       PROFILE ®           K-File   MASTER ®   (land width &lt;   File   K-File   (land width ≈           (sharp Δ)   (sharp convex Δ)   &lt;0.101 mm)   (sharp Δ)   (sharp Δ)   0.102 mm)                        Cyclic Fatigue   16.16   3.45   4.73   2.88   2.00   2.31       (min)       Efficiency   2.24   1.41   1.47   1.43   1.43   1.08       (mm/sec)                    
Unexpected and surprisingly, a reduction of about 50% in land width (about 0.05 mm as opposed to 0.102 mm), translated into doubling the cyclic fatigue, increasing cutting efficiency by about 50% while at the same time eliminating mid-root transportation with no areas of severe or moderate stress concentrations along the working length.
 
         [0038]    While an endodontic file having narrow radial lands along its entire working length has been described with a certain degree of particularity, many changes may be made in the details of construction and the arrangement of components without departing from the spirit and scope of this disclosure. An endodontic file according to this disclosure, therefore, is limited only by the scope of the attached claims, including the full range of equivalency to which each element thereof is entitled.