CAD/CAM - international magazine of digital dentistry

I special _ guided implantology 12 I CAD/CAM 1_2012 beenused)andbonedensitygradient,oranisotropy for the subsequent axis. Accepting inaccuracy, manufacturers and re- searchers have created depth-control systems in the hope of offering certainty about this parameter at least, but the gap will be responsible for not only position and axis deviations, but also depth errors. In fact, the implant mount endo-stop will match up with the sleeve at an angle. The first contact will be beyond the desired depth, and keeping on screwing the implant will create a great torque with surgical guide deformation and tension on the bone. The complete contact will correspond to a deeper im- plant position than desired. The correct depth may be halfway (maybe operator dependent and deter- mined using the naked eye). Depth error, axis devia- tion and translation in crestal position in the axial deviation direction will be the results (Figs. 12a–e). Thelikelihoodofideallypositioningtwoimplants is one out of seven billion and 500 million possibili- ties(justafewmillionless,ifitisanycomforttous). Andthisevaluationcomesfroma0.1mmmeande- viation and 1° deviation, which implies insufficient inaccuracy. Fancy what the chances would be of achieving acceptable accuracy. Threadtimingandimplantphase Fromamathematicalperspective,itispossibleto describe all implant spatial coordinates concen- trated on the platform, where we can summarise everything, and calculate its trajectory to create kind of a spiral path, through which it is possible to start and stop an implant platform along all the parameters, thus being able to truly speak of im- plant-guided prosthodontics. The idea is based on the following: when screw- ing a coca-cola plug onto the bottle-neck, the final positionwillalwaysbethesame(Figs.13a&b).Once two final positions have been found, two threads will be inside the plug; once three final positions have been found, three threads will be present on the plug. The label written on the plug can be con- sidered to be a hex (or a trilobe). So the hex, that is theplatform,caneasilybereproducedinitsposition because the thread pattern and hex are indexed to each other. This means that if we can control the threadingpattern,wecanconsequentlycontrolthe platform position too. According to this consideration, all the parame- ters that define the platform position can be con- trolled. The parameters are the position in the arch (B-L and M-D), the axis, the depth and the anti- rotational feature (classically, a hex) orientation. The mechanical engineering of a screw is quite different from that of a bullet (smooth sleeve) and was defined by Archimedes (applications of an endless screw are still in use today, like the meat mincer) and by Euler (Swiss mathematician, who diedinStPetersburgmorethantwocenturiesago). In particular, Euler pointed out that the movement ofacircle(inourfield,theimplantplatform)canbe described with mathematical formulas: a point alongthecircumference(inourfieldtheperimetric projection of a part of the hex) can be projected along a plane orthogonal to the direction of the circle movement itself (in our field, the progression of the platform while the implant is being screwed in multiplanar reconstructions). The projection will Figs. 12a–d_Missed implant position parameters in the depth-control systems owing to congruent triangle considerations (implant axis deviation and endo-stop angle). Figs. 13a & b_Coca-cola screw plug analogy. Fig. 14a_Euler’s formula. Fig. 14a Fig. 12c Fig. 12d Fig. 13a Fig. 13b Fig. 12a Fig. 12b