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Heretofore, all endodontic instruments have a center of rotation and a center of mass that are identical, which dictates a linear trajectory and path of motion. Intuitively, a file design with an axis of rotation, which is coincident with the center of mass, maximizes the restoring force of the file and minimizes flexibility. And files manufactured from nickel-titanium maximizes the restoring force further. The work of Peters, et al., 2001, indicates that this restoring force prevents these instruments from contacting the entire anatomy of the root canal preparation, leaving as much as 35% of the internal anatomy of the canal untouched, and the preparation poorly centered and unclean. In evaluating these problems, it became clear that a review of Herbert Schilder’s requirements for an ideal endodontic cavity preparation would be necessary to design a new file. Ideally a design that would mimic Schilder’s envelope of motion would mitigate these problems. Again referring to Figure 1A, it becomes apparent that Schilder’s envelope of motion was created using a unique method of manipulating the root canal file, whereby each pre-curved instrument that revolved within the canal walls could only cut in the greatest portion of the curve. Thus, as each instrument was inserted into deepest portion of the canal, although the rotation was around a central axis, the cutting itself was occurring around a precessional axis. As an example, Figure 1B demonstrates how a series of seven successively larger instruments could be used to expand the cutting envelope, but again notice that cutting is done intermittently and along a precessional axis or via mechanical waves. Our objective, then, was the development of Volume 9 Number 2

Figure 2: A schematic demonstrating the orientation of the cutting flutes of Protaper Next. Note the offset rectilinear cross section, which permits intermittent cutting along a precessional axis, much like Schilder’s envelope of motion

new method of canal enlargement that would mimic this concept. Although this idea was conceptual (Figure 2), the machine tool capabilities of Maillefer Dental Products or Dentsply International (Ballaigues, Switzerland) made this concept a reality. More than a dozen prototypes were engineered and tested over an 8-year period, which led to the development of what was originally called “swaggering files,” now called X-files and embodied in the ProTaper NEXT™ design. In referring to Figure 2, it can seen that the cutting edges of the file are oriented such that they cut in the perimeter of the cutting envelope or precessionally, enabling intermittent cutting. It can also be seen how a design like this might mitigate binding and the predisposition for breakage, while improving hauling or debris removal.

Performance ProTaper NEXT was designed to mimic Schilder’s envelope of motion by offsetting a rectilinear cross section, which revolves (6-7 revolutions) around the central axis. These revolutions are also called pitch. In Figure 3, the central or rotational axis of the X-file is shown by Axis 1. Axis 2 follows the center of mass or geometric center of the X-file. The

Figure 3: A schematic of the profile and dual axis of Protaper Next. Axis 1 is the central or rotational axis and axis 2 is the cutting or precessional axis. The distance X between the two axes decrease continuously from shank to tip, where the axes meet, leaving the tip completely centered. The offset center of mass, inherent in this design, enables the X-file to cut precessionally. Precession describes a motion whereby a body is spinning; however, the body of the object is spinning about another axis Endodontic practice 27


Figure 1B: A schematic demonstrating the enlargement root canal utilizing pre-curved instruments and employing Schilder’s strategy for creating the envelope of motion. Note that the first instruments are directed to toward the apical segment, while the last instruments are directed toward the orifice of the canal. The confluence of the prepared segments produces the continuously tapering shape characteristic of this technique

amount of offset between the center of rotation and the center of mass is defined by the distance between these two axes and varies along the length of the file or distance X. When observed during operation, precession of the X-file gives the appearance of a traveling wave (Scianamblo, 2005, 2006, 2011, and 2015). What is essential to the design of the X-file is that the undulating nodes and precessional axis of the X-file circumscribes an envelope of motion similar to Schilder’s pre-curved file (Figure 1A). What is also essential to the design of the X-file is that the offset cross section mitigates the restoring force, similar to Roane’s balanced force technique, which should improve centering. This is dictated by Newton’s laws for the mass moment of inertia and the parallel-axis theorem. Simply stated, the resistance to bending and distortion of a given lamina or cross section can be increased or decreased exponentially, as the distance of the centroid (center of mass) from the central axis is varied. The testing of the X-files has demonstrated that offsetting the center of mass produces not only efficient cutting instruments, but also instruments that remained exceptionally well centered, minimizing transportation (Pasqualini, et al., 2015; Burklein, et al., 2015; Saber, et al., 2015; Zhao, et al., 2104; and Elnaghy, et al., 2014) and corroborated clinically (Figures 4, 5, 8, and 9). For further analysis, we will define each arc as a wave of amplitude X as shown in Figure 6. The total distance traveled by any point on the arc can then equal 2X, which defines the cut diameter. Thus, the cutting envelope associated with any node along the instrument’s profile is potentially twice as wide as the instrument at that cross section. As mentioned, this file design (Figures 2 and 7) features an offset rectilinear cross section. As can be seen from this figure, only two cutting angles engage the walls of the root canal at any one time. This offset rectilinear cross section not only contributes to the innate flexibility of the file, but also

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Endodontic Practice - Summer 2016 Vol 9 No 2  

Endodontic Practice - Summer 2016 Vol 9 No 2  

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