Abstract:
A quasi-hyperbolic endodontic instrument having a cylindrical, elongated shaft with a radius that varies as a smooth, continuous curve along the length of the shaft and is larger near the distal portion of the file than near the proximal end of the file. The distal radius may be 10% or more larger than the proximal radius. This design provides a flexible file that minimizes the possibility of breaking, and ensures that if breakage does occur, it will occur near the handle, allowing the broken bit to be easily removed from the tooth canal. The instrument may further, or instead, have a metal cable connecting the cutting head to the handle to help reduce metal fatigue.

Description:
CROSS REFERENCE TO APPLICATIONS 
     This application is related to, and claims priority from, U.S. Provisional Patent Application No. 61/231,474 filed on Aug. 5, 2009 by E. Rzhanov et al. titled “High Safety Files for Root Canal Treatment”, the contents of which are hereby incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to endodontic instruments and their method of manufacture, and more particularly, to rotatable endodontic instruments having radius profiles and structures that produce a favorable distribution of torsion angle per unit length along the length of the instrument and/or reduce metal fatigue associated with repeated use of the instrument. 
     BACKGROUND ART 
     Endodontic therapy is a dental procedure, colloquially know as a “root canal”, undertaken to repair and save a tooth by removing and replacing infected dental pulp. 
       FIG. 1   a  show a cross-section of an exemplary healthy tooth  10 . The main body  12  of the tooth is composed of dentin, a matrix of mineralized connective tissue, that supports an overlay of hard, brittle tooth enamel  14 . The main body  12  of the tooth is supported by the gums  16  that cover the jaw bone  18 , and also contains dental pulp  20 , a soft connective tissue. Nerves in the dental pulp  20  connect with the rest of the body via one or more canals  22  located in the roots of the tooth  24 . 
     When dental pulp  20  becomes irritated, it swells up. Since the dental pulp  20  is encased in a rigid matrix of dentin, there is little or no room for expansion and the nerves in the dental pulp  20  are squeezed or pinched, causing a great deal of pain. A “root canal” is an endodontic procedure designed to alleviate this pain and save the tooth by removing the dental pulp  20  and replacing it with a bio-inert material such as gutta-percha. 
       FIG. 1   b  shows the first step in a typical root canal procedure. A portion of the tooth enamel  14  has been removed, along with a portion of the main body  12  of the tooth and the bulk of the dental pulp  20 . This removal is typically effected using a tungsten carbide, or diamond, tipped dental bur  26 , a.k.a. a dental drill bit. 
       FIG. 1   c  shows a further step in a typical root canal procedure. At this stage, the dental pulp  20  has been removed from the right hand canal  22 , and the dental pulp  20  is in the process of being removed from the left hand canal  22  by means of an endodontic instrument  28 . 
       FIG. 1   d  shows a completed root canal treatment. The dental pulp  20  has been completely removed and replaced by a bio-inert material  34 . 
       FIG. 2   a  shows an exemplary, prior art, endodontic instrument  28  used to remove dental pulp  20  from the canals  22  in a root canal procedure. The endodontic instrument  28  has a shank  42 , a quick change, cam drill holder  44 , a cylindrical shaft  46  and a flexible cutting bit  48 . The cam drill holder  44  may be one of the standard handles for connecting the endodontic instrument  28  to an endomotor. 
     Prior art endodontic instruments  28  are typically made from a Nickel-Titanium (NiTi) alloy. NiTi alloys are more flexible than more conventional stainless steels, but are subject to metal fatigue and may break after repeated use, or after a number of flexures in a single use. Prior art endodontic instruments  28  also typically have screw shaped flexible cutting bits  48  that may result in the bit becoming “screwed in” to the canals  22 , creating a situation where the flexible cutting bit  48  may be torsionally overloaded. Prior art endodontic instruments  28  typically have a tapered, or conical, flexible cutting bit  48  that narrows down from the proximate end of the bit to the distal end. 
       FIG. 2   b  shows a close-up view of the distal end of a prior art endodontic instrument  28 .  FIG. 2   b  clearly showing the screw shaped cutting edge  50 . 
       FIG. 2   c  shows a close-up view of a cross-section of the flexible cutting bit  48  of a prior art endodontic instrument  28  showing the cutting edges  50 . 
       FIG. 2   d  shows a close up view of the flexible cutting bit  48  of a traditional rotary NiTi endodontic instrument  28 .  FIG. 2   d  clearly shows the tapered, or conical, flexible cutting bit  48  that narrows down from the proximate end of the bit to the distal end. 
     In use, the endodontic instrument  28  may be attached by the cam drill holder  44  to a rotary drill or rotary endomotor. The endomotor, which may be an electrically powered drill, applies a torque to the endodontic instrument  28  that is transmitted via the handle the shank  42  to the flexible cutting bit  48 . The applied torque results in a slight twisting of the flexible cutting bit  48  as the cutting edges  50  engage the dental pulp  20  in the canals  22  and the surrounding dentin in the main body  12 . 
       FIG. 3   a  shows a plot of c(z), the torsional rigidity of a NiTi flexible cutting bit  48 , measured in dyne·cm 2 , as a function of distance along the axis  52  of the flexible cutting bit  48 , measured in cm. 
     The plot  56  is calculated for a NiTi flexible cutting bit  48  having a diameter D 0  at the distal end  54  of 0.25 mm. The distal end  54  is also where z, the distance along the axis  52 , is taken to be zero. The length L of the flexible cutting bit is 16 mm and the cone shape of the flexible cutting bit  48  is 2%, i.e., the radius of cross-section increases by 0.02 mm along each mm from the tip of instrument. 
     From plot  56 , it is evident that the torsional rigidity of the flexible cutting bit  48  is at its least at the distal end  54 , where the radius of the flexible cutting bit  48  is smallest. 
       FIG. 3   b  shows τ(z), the torsion angle per unit length, of the same NiTi flexible cutting bit  48 , plotted as a function of distance z, measured in cm, along the axis  52  of the flexible cutting bit  48 . τ(z), the torsion angle per unit length, is shown for two different values of applied torque when the tip of the endodontic instrument  28  is held stationary. 
     Plot  58  shows the torsion angle per unit length τ(z) of the typical, conical endodontic instrument  28  when a torque of 100 dyne·cm is applied to the shank  42  while the distal end  54  is held stationary. 
     Plot  60  shows the torsion angle per unit length τ(z) of the typical, conical endodontic instrument  28  when a torque of 150 dyne·cm is applied to the shank  42  while the distal end  54  is held stationary. These plots are based on mathematical analysis shown in detail in, for instance, U.S. Provisional Patent Application No. 61/231,474 filed on Aug. 5, 2009 by E. Rzhanov et al. titled “High Safety Files for Root Canal Treatment”, the contents of which are hereby incorporated by reference. 
     From these plots, it is evident that the torsion angle per unit length τ(z) will most probably first exceed some upper critical value in the vicinity of the distal end  54  of the endodontic instrument  28 . This is where the flexible cutting bit  48  is located. The flexible cutting bit  48 , particularly the distal end of the flexible cutting bit  48 , is, therefore, where any excessive torque applied to the endodontic instrument  28  will most likely begin to deform the endodontic instrument  28 , and it is also the region where any breakage is most likely to occur. 
     When a flexible cutting bit  48  breaks deep in a canal  22 , it is often impossible to retrieve the broken portion. The broken, distal portion of the flexible cutting bit  48 , therefore, often has to be left in place where it broke in the canal  22 . This is not a very satisfactory outcome for the patient as it sometimes means that the tooth then has to be removed, which is what the root canal procedure was intended to avoid. 
     An endodontic instrument  28  with a cutting bit that is flexible, robust and not inclined to break is, therefore, highly desired. It is further highly desired that the endodontic instrument  28  is manufactured so that, if breakage does occur, the distal portion of the broken instrument may be easily removed from the patient&#39;s tooth. 
     SUMMARY OF INVENTION 
     Technical Problem 
     The technical problem addressed by the present invention includes, but is not limited to, providing a flexible cutting bit suitable for endodontic therapy, that is shaped, or constructed, so as to minimize the possibility of the bit breaking. Significant causes of bit breakage include excessive torsional force and metal fatigue from repeated flexing. Moreover, the flexible cutting bit is preferably shaped, or constructed, so that, if breakage does occur, it will most likely occur in a portion of the endodontic instrument that allows the distal portion of the broken bit to be easily removed from the tooth, even when the distal end of the tip is trapped deep in a dental pulp canal. 
     Solution to Problem 
     The present invention solves the technical problem by providing a quasi-hyperbolic endodontic instrument having a cylindrical, elongated shaft with a radius that is a smooth, continuous curve. Moreover, the radius of the elongated shaft is larger near the working, or distal, portion of the file than near the handle, or proximate end, of the instrument. The distal radius may, for instance, be 10% or more, larger than the proximal radius. This design provides a flexible instrument that reduces the possibility of the instrument breaking, and helps ensure that if breakage does occur, it will occur near the handle, allowing the broken bit to be easily removed from the tooth canal. 
     In a preferred version, the working portion of the instrument, i.e., the portion located near the shaft&#39;s distal end, extends less than one-third of the way along the shaft and is shaped to have at least one cutting surface. The instrument may also have a capture node, located near the handle, or proximal end, of the shaft. The capture node may have an effective radius that is 10% or more larger than the radius of the shaft at the place where the shaft joins the capture node. The endodontic instrument of this invention may also have a region of weakest torsional rigidity located between the capture node and the proximal end of the shaft, ensuring that if the file does break, the capture node will remain attached to the broken off end that is lodged in the tooth canal. The capture node may have one or more flat or grippable facets on its outer surface, so that tweezers, flat pliers, or a specially designed capture tool, may easily grip and remove the broken end from the tooth canal. 
     In a further embodiment of the invention, the technical problem may be solved by providing a flexible endodontic instrument having a metal cable. A cutting head may be attached to the distal end of the cable, while the proximal end of the cable may be attached to a handle. 
     In a further preferred embodiment of the invention, the cable may have at least seven strands of metal wire of equal lengths, with six of the strands being helically wound around the seventh strand, to form the cable. 
     The handle may be made of a tube surrounding, and attached to, the cable. The tube forming the handle may extend for a third or more of the length of the cable. The tube may ensure the endodontic instrument is of the required length, while the length of the free cable from the handle to the cutting blade is of sufficient length to provide the required stiffness and flexibility. 
     The cable connection between the handle and the blade provides flexibility. It also tends to increase the safety of the file, as the fibers in a cable tend to be tension loaded. The torsion loading on the cable is, therefore, significantly less than it would be on a solid rod made of the same material. This allows each of the cable fibers to work within the elastic range of the metal it is made from, thereby avoiding any accumulating damage and significantly reducing the probability of deformation or breakage of the instrument. 
     In further embodiments, the invention may combine or incorporate elements from each of the embodiments described above. 
     Advantageous Effects of Invention 
     Advantages effects of the invention include, but are not limited to, providing endodontic instruments that have the required flexibility and cutting ability but are less susceptible to breakage than existing endodontic instruments. 
     These and other features of the invention will be more fully understood by references to the following drawings. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1   a  shows a schematic cross-section of an exemplary healthy tooth. 
         FIG. 1   b  shows a schematic view of a first step in a root canal procedure. 
         FIG. 1   c  shows a schematic view of an endodontic instrument being used to remove dental pulp from a tooth canal. 
         FIG. 1   d  shows a schematic view of a final stage of a root canal in which the dental pulp has been replaced by a bio-inert material. 
         FIG. 2   a  shows a schematic side view of an exemplary, prior art, endodontic instrument. 
         FIG. 2   b  shows a schematic close-up view of the distal end of a prior art flexible cutting bit. 
         FIG. 2   c  shows a schematic close-up view of a cross-section of a prior art flexible cutting bit. 
         FIG. 2   d  shows a schematic close up view of a prior art flexible cutting bit. 
         FIG. 3   a  shows a plot of c(z), the torsional rigidity, of a prior art NiTi flexible cutting bit as a function of distance along the axis. 
         FIG. 3   b  shows plots of τ (z) ,and τ 1(z) as a function of distance (z) along the axis. 
         FIG. 4   a  shows a schematic, 3D, view of an exemplary quasi-hyperbolic endodontic instrument of the present invention. 
         FIG. 4   b  show a plot of radius as a function of distance for an exemplary quasi-hyperbolic endodontic instrument. 
         FIG. 4   c  shows a plot of torsional rigidity as a function of position along the central axis an NiTi flexible shaft having the radius profile shown in  FIG. 4   b.    
         FIG. 4   d  show plots of τ(z), the torsion angle per unit length as a function of position along the central axis an NiTi flexible shaft having the radius profile shown in  FIG. 4   b.    
         FIG. 5   a  shows a schematic, side view of an exemplary quasi-hyperbolic endodontic instrument of the present invention. 
         FIG. 5   b  shows a schematic side view of an exemplary quasi-hyperbolic endodontic file 
         FIG. 5   c  shows a schematic, close-up view of the working portion of the quasi-hyperbolic endodontic file. 
         FIG. 5   d  shows a close-up schematic view of the proximal end of the quasi-hyperbolic endodontic file. 
         FIG. 5   e  shows a cross-sectional view drawn on “AA”. 
         FIG. 5   f  shows a cross-sectional view drawn on “BB”. 
         FIG. 6   a  shows a schematic, sectional side view of a cable endodontic instrument of the present invention. 
         FIG. 6   b  shows a view of an exemplary cable endodontic file of the present invention. 
         FIG. 6   c  shows the cable  106  attached to the working portion  66  of the cable endodontic file. 
         FIG. 6   d  shows a cross section on “CC”. 
         FIG. 6   e  shows a cross-section on “DD”. 
         FIG. 6   f  shows a cross-section view of a cable have seven strands of metal wire. 
         FIG. 6   g  shows a cross-section view of a cable  106  have nineteen strands of metal wire  112 . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present invention will now be described in detail by reference to the accompanying drawings in which, as far as possible, like elements are designated by like numbers. 
       FIG. 4   a  shows a schematic, 3D, view of an exemplary quasi-hyperbolic endodontic instrument  62  of the present invention. The quasi-hyperbolic endodontic instrument  62  includes a working portion  66 , a flexible shaft  70 , a handle  72  and a drill attachment mechanism  74 . The quasi-hyperbolic endodontic instrument  62  may also include a capture node  64  and a region of weakest torsional rigidity  68 . The capture node  64  may be located near the proximal end  78  of the flexible shaft  70 . The working portion  66  of the reverse curved endodontic instrument  62  may be located near the distal end  76  of the flexible shaft  70 . The working portion  66  may have one or more cutting edges, and typically extends for as little as 5% of the flexible shaft  70 , though it may be as much as 20% or even 33% of the length of the flexible shaft  70 . The flexible shaft  70  is preferably made from a suitable metal or metal alloy such as, but not limited to, a NiTi alloy, a stainless steel alloy, silver, gold, titanium or a super-elastic Nickel, Titanium and Niobium alloy or some combination thereof. The flexible shaft  70  may be rotationally symmetric about a central axis  82 . The radius of the flexible shaft  70  at its distal end  76  may be about 10% or more larger than the radius of the flexible shaft  70  near its junction with the capture node  64 . The capture node  64  may have one or more flat or grippable surfaces. In a preferred embodiment the cross-section of the capture node  64  may be a polygon, and preferably a regular polygon, such as, but not limited to, a triangle, a square, a pentagon, a hexagon, or an octagon. The handle  72  of the reverse curved endodontic instrument  62  may also include a depth indicator  80 . 
       FIG. 4   b  show a plot  84  of r(z), the radius r as a function of z, the position along the central axis  82  of the flexible shaft  70 , of an exemplary quasi-hyperbolic endodontic instrument  62 . 
     In a preferred embodiment, the flexible shaft  70  has a circular cross-section. The radius profile of the flexible shaft  70  is a smooth curve that is larger at the distal end (z=0) than at the proximal end (z=20). In the example shown, the distal radius is approximately 25% larger than the proximal radius. In various embodiments of the present invention, the distal radius may be only 10% larger the proximal radius, or it may be larger by a factor greater than 10% depending on factors such as, but not limited to, the material the flexible shaft  70  is made from, its length, the required flexibility or some combination thereof. 
       FIG. 4   c  shows a plot  86  of c(z), the torsional rigidity as a function of position along the central axis  82  for a NiTi flexible shaft  70  having the radius profile in  FIG. 4   b . The torsional rigidity is greatest at the distal end of the flexible shaft  70  and a minimum at the proximal end of the flexible shaft  70 . 
       FIG. 4   d  show plots of τ(z), the torsion angle per unit length as a function of z, the position along the central axis  82 . 
     Plot  90  of τ(z) corresponds to a NiTi flexible shaft  70  having a radius profile corresponding to the hyperbolic function  91 : 
     
       
         
           
             
               r 
               ⁡ 
               
                 ( 
                 z 
                 ) 
               
             
             = 
             
               k 
               
                 
                   z 
                   + 
                   a 
                 
                 4 
               
             
           
         
       
     
     and a torque load of 1000 dyne·mm. _k and a are engineering parameters that determine the radius of the flexible shaft  70  at the distal end  76  and the region adjacent to the capture node  64  respectively. 
     In plot  90 , torsion angle per unit length τ increases substantially linearly with z. Torque loading on the flexible shaft  70  is, therefore, greatest near the handle and decreases toward the distal end of the flexible shaft  70 . If the quasi-hyperbolic endodontic instrument  62  is subject to excess torque, breakage will, most likely, occur at the proximal end of the flexible shaft  70 . As the proximal end tends to usually be clear of the tooth canal  22 , there should usually be an exposed portion of the broken flexible shaft  70  that may be used to extract it from the tooth. 
     The hyperbolic function  91  corresponds to the optimum radius profile for the flexible shaft  70  based on equations derived in, for instance, U.S. Provisional Patent Application No. 61/231,474 filed on Aug. 5, 2009 by E. Rzhanov et al. titled “High Safety Files for Root Canal Treatment”, the contents of which are hereby incorporated by reference. 
     Such equations include, for instance, a fundamental relation relating torsional rigidity c(z) and the torsion angle per unit length τ(z) to the applied torque M:
 
 C ( z )·τ( z )= M  
 
     Other related or similar radius profiles may be used so long as they provide a uniform distribution of torsion rigidity, having no extremes, or discontinuities, along the flexible shaft  70 . Moreover, the distribution of torsion angle per unit length on the flexible shaft  70  should be a slightly increasing function of z such as, but not limited to, a linear function with a small inclination. The slight increase of torsion angle per unit length τ(z) with z compensates for practical uncertainties such as, but not limited to, inhomogeneity of the material used to manufacture the flexible shaft  70 , defects introduced during manufacture, damage as a result of storage, transportation, packaging or prior use, or some combination thereof. The slight increase of torsion angle per unit length τ(z) helps ensure that any breakage is most likely to occur at the proximal end of the flexible shaft  70 , close to the handle, allowing for easy retrieval of the broken bit. 
     In order to minimize the effect of uncertainties associated with manufacture, the flexible shaft  70  is preferably made by grinding and polishing a substrate to the correct shape and surface smoothness. Good surface smoothness helps ensure that the correct torque is applied to the working portion  66  during an endodontic procedure. The instruments should also be carefully examined using instrumentation designed for nondestructive testing and detection of flaws in metal objects such as, but not limited to, the well known supersonic reflectoscope and the well known phased-array, ultrasonic test instruments, or some combination thereof. 
     Plot  88  of τ(z) corresponds to a NiTi flexible shaft  70  having a radius profile corresponding to the hyperbolic function and a torque load of 1500 dyne·mm. 
       FIG. 5   a  shows a schematic, side view of an exemplary quasi-hyperbolic endodontic instrument  62  of the present invention. The quasi-hyperbolic endodontic instrument  62  includes a working portion  66 , a flexible shaft  70 , a handle  72  and a drill attachment mechanism  74 . The quasi-hyperbolic endodontic instrument  62  may also include a capture node  64  and a region of weakest torsional rigidity  68 . 
       FIG. 5   b  shows a schematic side view of an exemplary quasi-hyperbolic endodontic instrument  92 . 
     In one embodiment of the present invention, there is a pilot tip  100 . The pilot tip  100  may be shaped as a portion of a sphere, such as, but not limited to, a hemisphere. The pilot tip  100  preferably has a diameter that is about 50% of the largest diameter of the flexible shaft  70 , though it may vary from 20% to 80% of that diameter. The pilot tip  100  is intended to help guide the reverse-curved endodontic instrument  62  down the canals  22  during removal of the dental pulp  20 , and avoid, for instance, the instrument being misdirected down a side canal. 
     In one embodiment of the present invention, there is a capture node  64  that is hexagonal in cross-section. The capture node  64  may serve as a clamping point during calibration of the quasi-hyperbolic endodontic instrument  92  to determine permissible torque loads. As the region of weakest torsional rigidity  68  is located between the capture node  64  and the handle  72 , if breakage does occur, the capture node  64  will most likely stay attached to the portion of the quasi-hyperbolic endodontic instrument  92  that has lodged in the tooth canal. The broken quasi-hyperbolic endodontic instrument  92  may, therefore, be easily removed using a tool such as, but not limited to, a pair of tweezers, a pair of flat nosed pliers or a specially designed tool such as, but not limited to, the special removal tool described in, for instance, U.S. Provisional Patent Application No. 61/231,474 filed on Aug. 5, 2009 by E. Rzhanov et al. titled “High Safety Files for Root Canal Treatment”, the contents of which are hereby incorporated by reference, or some combination thereof. 
     The capture node  64  may be joined to the flexible shaft  70  by means of a smooth curve  96  that avoids any discontinuities in the torsion angle per unit length τ(z). Similarly, on the proximal side of the capture node  64 , it may be joined to the region of weakest torsional rigidity  68  by a suitable smooth curve  96 . 
     The cutting edges  94  may vary in detailed shape to allow files that cut smoothly, or aggressively or have more of a rasping action. Such cutting edge variations are well known in the art. Each type of cutting edges  94  may be useful at various stages of removing the dental pulp  20  from the canals  22 . 
     The shaft to handle transition  98  should also be by means of a smooth curve  96  that avoids any discontinuities in the torsion angle per unit length τ(z) as such discontinuities may result in concentration of torque forces and lead to deformation or breakage. 
       FIG. 5   c  shows a close-up schematic view of the working portion  66  of the quasi-hyperbolic endodontic instrument  92 , showing the cutting edges  94  and the pilot tip  100 . 
       FIG. 5   d  shows a close-up schematic view of the proximal end of the quasi-hyperbolic endodontic instrument  92 . The view shows the smooth curve  96  that connects the capture node  64  to the flexible shaft  70 , as well as the smooth curve  96  that connects the capture node  64  to the region of weakest torsional rigidity  68 . The view also shows the shaft to handle transition  98  that is a smooth curve connecting the region of weakest torsional rigidity  68  to the handle  72 . 
       FIG. 5   e  shows a cross-sectional view drawn on “AA” showing the cutting edges  94  formed by four grooves ground into the working portion  66  of the flexible shaft  70 . 
       FIG. 5   f  shows a cross-sectional view drawn on “BB” showing flat facets  102  and an hexagonal cross section. The flat facets  102  that may facilitate both clamping during calibration of the quasi-hyperbolic endodontic instrument  92 , and the removal of the broken quasi-hyperbolic endodontic instrument  92 . 
       FIG. 6   a  shows a schematic, sectional side view of a cable endodontic instrument  104  of the present invention. In a preferred embodiment, the cable endodontic instrument  104  may have a cable  106 . The proximal end  78  of the cable  106  may be enclosed by a cylindrical tube  108 . The cylindrical tube  108  in turn may fit into a handle  72  that is attached to a drill attachment mechanism  74 . The handle  72  may have a slideably attached depth indicator  80 . At the distal end  76  of the cable  106  a working portion  66  may be attached to the cable  106 . 
       FIG. 6   b  shows a view of an exemplary flexible endodontic file  110  of the present invention. 
     The cable  106  may be made from a number of strands of metal wire  112 . The strands of metal wire  112  may be made from suitable metal or metal alloys such as, but not limited to, stainless steel, TiNi alloy or a super-elastic Nickel, Titanium and Niobium alloy or some combination thereof. The strands of metal wire  112  may be substantially equal in length and may be helically wound around a central strand. The cable  106  is substantially uniform in cross-section and therefore has a substantially uniform torsion angle per unit length τ(z). 
     The proximal end  78  of the cable  106  may be encased in a cylindrical metal tube made from a suitable metal or metal alloys such as, but not limited to, stainless steel, TiNi alloy, silver, gold, titanium or a super-elastic Nickel, Titanium and Niobium alloy or some combination thereof. The cable  106  may be fixed to the cylindrical tube  108  by, for instance, welding. The cylindrical tube  108  allows the flexible endodontic file  110  to have the required stiffness for cutting and the necessary overall length. 
     The distal end  76  of the cable  106  may be attached to the cutting head  67  of the flexible endodontic file  110 . The cutting head  67  may include one or more cutting blades  114  and a pilot tip  100 . The pilot tip  100  may be shaped as a portion of a sphere, such as, but not limited to, a hemisphere. The pilot tip  100  preferably has a diameter that is about 50% of the diameter of the cable  106 , though it may vary from 20% to 80% of the diameter. The cutting blades  114  may be made from a suitable metal or metal alloys such as, but not limited to, stainless steel, TiNi alloy, silver, gold, titanium or a super-elastic Nickel, Titanium and Niobium alloy or some combination thereof, and may be attached to the cable  106  by, for instance, welding or brazing. Stainless steels typically contain elements selected from a group such as, but not limited to, Chrome, Nickel, Molybdenum and Titanium or a combination thereof. The amount of such elements may vary from as little as 1% to as much as 20%. Chrome may, for instance, be incorporated in a steel alloy at a percentage of weight ranging from 10% to 15%. 
     The cutting head  67  with the cutting blades  114  may, for instance, be turned from a stainless steal tube that may be soldered on to the distal end of the cable  106 . In an alternate embodiment, the cutting head  67  may be made form the cable  106  by, for instance welding and grinding. 
       FIG. 6   c  shows the cable  106  attached to the working portion  66  of the flexible endodontic file  110  showing the strands of metal wire  112  of the cable, the cutting blades  114  and the pilot tip  100 . 
       FIG. 6   d  shows a cross section on “CC”, showing the cutting blades  114 . 
       FIG. 6   e  shows a cross-section on “DD”, showing the cylindrical tube  108  and the strands of metal wire  112 . 
       FIG. 6   f  shows a cross-section view of a cable  106  have seven strands of metal wire  112 . The six outer strands of metal wire  112  are helically wound around the central strand of metal wire  112 . 
       FIG. 6   g  shows a cross-section view of a cable  106  have nineteen strands of metal wire  112 . 
     The cable endodontic instruments  104  are preferably made to satisfy ISO standards and be manufactured having cutting diameters such as, but not limited to, diameters of 0.08 mm, 0.1 mm, 0.15 mm, 0.2 mm and 0.25 mm. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Thickness 
                 Thickness 
                   
                 Strain in 
                   
               
               
                 No 
                 of wire 
                 of cable 
                 Kind of tubing 
                 fiber 
                 Comments 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 16 μm 
                   1×19 = 80 μm 
                 32 REG, ACCU-TUBE 
                 0.4% 
                 R = 2 
                 mm 
               
               
                 2 
                 20 μm 
                   1×19 = 100 μm 
                 17-7, ACCU-TUBE 
                 0.5% 
                 R = 2 
                 mm 
               
               
                 3 
                 30 μm 
                   1×19 = 150 μm 
                 29 REG, ACCU-TUBE 
                 0.75% 
                 R = 2 
                 mm 
               
               
                 4 
                 38 μm 
                   1×19 = 190 μm 
                 27 REG, ACCU-TUBE 
                 0.95% 
                 R = 2 
                 mm, 
               
               
                   
                   
                   
                   
                   
                   head = 200 
                 μm 
               
               
                 5 
                 46 μm 
                   1×19 = 230 μm 
                 26 REG, ACCU-TUBE 
                 1.15% 
                 R = 2 
                 mm, 
               
               
                   
                   
                   
                   
                   
                   head = 250 
                 μm 
               
               
                 6 
                 66 μm 
                   1×19 = 330 μm 
                 24 TW, ACCU-TUBE 
                 0.85% 
                 R = 4 
                 mm, 
               
               
                   
                   
                   
                   
                   
                   head = 350 
                 μm 
               
               
                   
               
             
          
         
       
     
     Table 1 shows the calculated strain in cable fibers for cables corresponding to the ISO standard sizes detailed above. The calculations are shown in detail in, for instance, U.S. Provisional Patent Application No. 61/231,474 filed on Aug. 5, 2009 by E. Rzhanov et al. titled “High Safety Files for Root Canal Treatment”, the contents of which are hereby incorporated by reference, or some combination thereof. The depend on the derived relationship: 
     
       
         
           
             
               σ 
               
                 zz 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 max 
               
             
             = 
             
               E 
               · 
               
                 r 
                 R 
               
             
           
         
       
     
     in which r represents the radius of the strands of metal wire  112 , R represents the radius curvature of the canals  22  that the instrument is working on E represents Young&#39;s modulus of elasticity for the material that the strands of metal wire  112  are made of, and σ zz max  represents the maximum stress in the strands of metal wire  112 . In Table 1, R is either 2 mm or 4 mm. 
     Permissible stress for stainless steel has experimentally been found to be 1.5 to 2.0%. This is the strain at which stainless steel will begin to deform non-elastically. 
     As can be seen from Table 1, for a seventeen strand cable, the maximum strain in each strand for all the ISO radius instruments, is well below the maximum permissible strain for the practical flexibility needed in performing endodontic procedures on teeth. 
     Although the invention has been described in language specific to structural features and/or methodological acts, it is to be understood that the invention defined in the appended claims is not necessarily limited to the specific features or acts described. Rather, the specific features and acts are disclosed as exemplary forms of implementing the claimed invention. Modifications may readily be devised by those ordinarily skilled in the art without departing from the spirit or scope of the present invention.