implants - internationalmagazine of oral implantology

case study _ computer-guided implantology I uationcomesfroma0.1mmmeandeviationand1°de- viation, which implies insufficient inaccuracy. Fancy whatthechanceswouldbeofachievingacceptableac- curacy. Threadtimingandimplantphase Fromamathematicalperspective,itispossibletode- scribe all implant spatial coordinates concentrated on theplatform,wherewecansummariseeverything,and calculate its trajectory to create kind of a spiral path, throughwhichitispossibletostartandstopanimplant platform along all the parameters, thus being able to trulyspeakofimplant-guidedprosthodontics. Theideaisbasedonthefollowing:whenscrewinga coca-cola plug onto the bottle-neck, the final position will always be the same (Figs. 13a & b). Once two final positionshavebeenfound,twothreadswillbeinsidethe plug;oncethreefinalpositionshavebeenfound,three threadswillbepresentontheplug.Thelabelwrittenon the plug can be considered to be a hex (or a trilobe). So thehex,thatistheplatform,caneasilybereproducedin its position because the thread pattern and hex are in- dexed to each other. This means that if we can control thethreadingpattern,wecanconsequentlycontrolthe platformpositiontoo. According to this consideration, all the parameters thatdefinetheplatformpositioncanbecontrolled.The parameters are the position in the arch (B-L and M-D), theaxis,thedepthandtheanti-rotationalfeature(clas- sically,ahex)orientation. The mechanical engineering of a screw is quite dif- ferentfromthatofabullet(smoothsleeve)andwasde- fined by Archimedes (applications of an endless screw are still in use today, like the meat mincer) and by Euler (Swiss mathematician, who died in St Petersburg more thantwocenturiesago).Inparticular,Eulerpointedout that the movement of a circle (in our field, the implant platform) can be described with mathematical formu- las: a point along the circumference (in our field the perimetric projection of a part of the hex) can be pro- jected along a plane orthogonal to the direction of the circle movement itself (in our field, the progression of theplatformwhiletheimplantisbeingscrewedinmul- tiplanarreconstructions).Theprojectionwilldescribea sinewave(inourfield,thesinewaveperiodcanbeiden- tifiedwiththeimplantthreadpitch).Withthisinmind, I developed the device discussed in this article, which controlsthethreadingpattern.Inmechanicalengineer- ing,thisiscalledthreadtiming,andthehexpositioncan bedefinedashextiming.Forbothofthemwecanspeak of phase control (i.e. we can speak of the phase of the implant,bothforthethreadandthehex).Alongthisspi- ral track, the implant can be theoretically and actually screwed and unscrewed as many times as we desire (back and forth), and it will always be possible to know thehexpositionattheendofthespiralpath(finalana- logueandimplantposition;Figs.14a–c).Asaspiralcir- cular motion is transformed into a pure translation, a threaded device will respect also position and axis. The informationneededtocorrectly(positionandaxis,anti- rotational feature and depth) place an implant is in its Fig. 11a_Mathematical proportion to calculate the linear radial apex deviation. Fig. 11b_Calculation of the trigonometric angle deviation. Fig. 11c_Calculation of the trigonometric angle deviation (sine/cosine rule). Fig. 11d_Calculation of the trigonometric angle deviation (tan/cot rule). I 31implants4_2011 Fig. 11d Fig. 11a Fig. 11b Fig. 11c