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The determination of the tooth rotation center
THE DETERMINATION
OF THE TOOTH
ROTATION
CENTER
HEN discussing the protdem of tooth anchorage and its relationship to forces applied to the crow11, it, is ~mmon practice to calculate tur.Gnx moments by assuming a fixed center of rotation at, the a.pictal thirtl of the root.’ 111such studies it is assumed further that the inherent resistance of the toothsupporting structures against tipping is the same at dl the intro-al~eola r root levels. The results of torque calculations obtained under various theorrtid conditions are used to explain clinical cantilever effects. The assumption of a rotation center localized at the apical third of the root is based on histologic studies by Klein,’ who described what could 1~ ccalletl a “biologic rotation venter.” The particular hourglass shal)e oP the periodontal membrane used for the location of the rotation center is N>ltut*e’s morphologic answer to a multitude oi’ mechanical forces Mferent in magnitutlt~. direction, and duration. It is highly questionable that the tipping of ;I tooth always occurs around the biologic rotation center when a single force loatls the crown. It, has been shown” thilt the instantaneous rotat,ion center ol’ teeth (‘all vary in position a.ccoding 10 the size ~1x1 i~ngdation oi’ forces applied to the (‘I’OM’IIS. Since torque ltlomellts ilre tlepenclent on the localization of the ~~of~~Con center, it seems ~~r~eferahle to bane torque calculations and clinic;11 vanelusions on previously estal)lishrd tletr~~nlinationu)tls of the rotation venter. In II previous rel)ort’S almni tooth mol)ilit,y measurements iitltl toot.h rot;Ition centers, a paradoxical finding was nlacle t,hat CYNIM not IW er~tlait~rtl at that time. The evaluntiotl CI~’some tucasurements seemed to show that nntler certain condit~ions the rotation center \\rils located not apically to the cer\-ical region. hut coi~mall~-. Further eslv2riments gave e\-iclence that these tintlilig.; errors that c~ultl be, at1c1 xvere, eliminate(1. were due to methodological ‘l’hc Ihresent report tlesvvil)es a nlethotl that dlo~x :I IL exact tletc~~~tninatiot~ OF the inst.antaneous rotation c+elitel. of single-rooteti teeth. The illstiltlt.i\rl~~o~~s rotat.ion venter is tletet3ninetl lp means OF t.ootli mobility fHeBslII’(Jllt(‘ttts usilig ;I rtiici3bdial indicator.“~ i lial~ioliilgual or lit~guol~biill c’twwti excursions (p. b’ig. 1) produced by a. know11 force ((;m, Fig. 1 ) are measuretl Rt three clifl’erent l)oints of t.he crown. These points (I, (‘, and F. b’ig. 1) ;II’~’ ilr the tnitlsa.gittal plane of the tooth and shoulcl h tliwrtt~ly nicketl with it cli;t~ttot,tl stone. The contact needle OF the tlial intlic:ltctr is :~l,l)lietl >lt >I right ;~ngle to the c~*own surface very ne;lta, Imt not on. t,hese markings, which :I rg usetl fell. orientation later. After the measurements at I, (‘, and % (giviug thr 1;llri;rI
W
F~I~I
the
lrnivcrsity
of Minnesota.
Division 392
of l’erio
School
of
Dentistry
DETERMINATIOS
OF TOOTH
ROTATIOK
:j!)::
('KXTER
excursion of i’, c’, nlztr! r, for example), an imljression is taken of the C~IY~~II die is nlade. This with elastic compound and copper band, ant1 an antalgan~ amalgam model is cut lahiolingually in two halves. the cut going through I, (‘, it~ltl F. Either section of the crown is l)hotogral)hetl and a print. c~largetl twenty times, is made. l~‘rorn the enlarged l)rillt, the mown is cut out, I\-it11 scissors. This paper crow11 model is usctl for the constrnc4ion of’ the rotation wntrr as seen in b’ig. 1. b’irst. the sh:rl)e of the (~~OWIL with the points 1, f’. antI
P’ig.
I.--1,inguolabial
moment calculated
(b) from
groducecl by perpen~liculars
known through
force f”,
( GWI ). I”, mtl
Rotation c”.
writer’
( Kf’l
F is traced on drawing paper. The values of the CIYIWII excursion, i’, c’, and f’, mnlt~iplied by the enlargement factor of the print. are transferred perpentlioularly to the points I, C, and F, yielding I’, C”, and P’. The paper crown motlrl then is oriented within I’, C’, and P’. Only one position is possible, and the paper crown is traced again in this new position which c~orresponds to the position the clinical crown had when the linguolal~ial Force was applied. Points 1, f’, and I” arc united with points I”, C”‘, and F”. The middle perpendicu!ars 011 these lirlcs (z“I, “~8,f”) intersect, at the instantaneous rotation (aenter KC’. A7 is the distance fwn KC to the labial cervicoenamcl junction (E’) and can be used to exljress that distance numerically.
394
HANS
R. iUtillLICXIANX
AND
RZARJIION
I\‘.
HOUGLUJI
References Inl-estigations of thy brriodontal Width, Ztschr. f, Stonratol. 26: A.: ‘Systematic 417, 1928. untl ~~athologische Zahrlbe~~,egliehk~,it,. Schr< ri/. 3. Miihlemann, H. R.: Die ph.vsiologisclre Monatschr. f. Zahnh. 61: I> 1951. (&\I. 4. Miihlemann, H. It.: Periodontonlrt ry. A Method for 1le;Lsurir~g Tooth Mol)ility, 2. Klein,
SURG., ORAL MED.,
AND OR.AL PATH.
4: .1220, 196 1.
OF THE TOOTH
ROTATION
CENTER
HEN discussing the protdem of tooth anchorage and its relationship to forces applied to the crow11, it, is ~mmon practice to calculate tur.Gnx moments by assuming a fixed center of rotation at, the a.pictal thirtl of the root.’ 111such studies it is assumed further that the inherent resistance of the toothsupporting structures against tipping is the same at dl the intro-al~eola r root levels. The results of torque calculations obtained under various theorrtid conditions are used to explain clinical cantilever effects. The assumption of a rotation center localized at the apical third of the root is based on histologic studies by Klein,’ who described what could 1~ ccalletl a “biologic rotation venter.” The particular hourglass shal)e oP the periodontal membrane used for the location of the rotation center is N>ltut*e’s morphologic answer to a multitude oi’ mechanical forces Mferent in magnitutlt~. direction, and duration. It is highly questionable that the tipping of ;I tooth always occurs around the biologic rotation center when a single force loatls the crown. It, has been shown” thilt the instantaneous rotat,ion center ol’ teeth (‘all vary in position a.ccoding 10 the size ~1x1 i~ngdation oi’ forces applied to the (‘I’OM’IIS. Since torque ltlomellts ilre tlepenclent on the localization of the ~~of~~Con center, it seems ~~r~eferahle to bane torque calculations and clinic;11 vanelusions on previously estal)lishrd tletr~~nlinationu)tls of the rotation venter. In II previous rel)ort’S almni tooth mol)ilit,y measurements iitltl toot.h rot;Ition centers, a paradoxical finding was nlacle t,hat CYNIM not IW er~tlait~rtl at that time. The evaluntiotl CI~’some tucasurements seemed to show that nntler certain condit~ions the rotation center \\rils located not apically to the cer\-ical region. hut coi~mall~-. Further eslv2riments gave e\-iclence that these tintlilig.; errors that c~ultl be, at1c1 xvere, eliminate(1. were due to methodological ‘l’hc Ihresent report tlesvvil)es a nlethotl that dlo~x :I IL exact tletc~~~tninatiot~ OF the inst.antaneous rotation c+elitel. of single-rooteti teeth. The illstiltlt.i\rl~~o~~s rotat.ion venter is tletet3ninetl lp means OF t.ootli mobility fHeBslII’(Jllt(‘ttts usilig ;I rtiici3bdial indicator.“~ i lial~ioliilgual or lit~guol~biill c’twwti excursions (p. b’ig. 1) produced by a. know11 force ((;m, Fig. 1 ) are measuretl Rt three clifl’erent l)oints of t.he crown. These points (I, (‘, and F. b’ig. 1) ;II’~’ ilr the tnitlsa.gittal plane of the tooth and shoulcl h tliwrtt~ly nicketl with it cli;t~ttot,tl stone. The contact needle OF the tlial intlic:ltctr is :~l,l)lietl >lt >I right ;~ngle to the c~*own surface very ne;lta, Imt not on. t,hese markings, which :I rg usetl fell. orientation later. After the measurements at I, (‘, and % (giviug thr 1;llri;rI
W
F~I~I
the
lrnivcrsity
of Minnesota.
Division 392
of l’erio
School
of
Dentistry
DETERMINATIOS
OF TOOTH
ROTATIOK
:j!)::
('KXTER
excursion of i’, c’, nlztr! r, for example), an imljression is taken of the C~IY~~II die is nlade. This with elastic compound and copper band, ant1 an antalgan~ amalgam model is cut lahiolingually in two halves. the cut going through I, (‘, it~ltl F. Either section of the crown is l)hotogral)hetl and a print. c~largetl twenty times, is made. l~‘rorn the enlarged l)rillt, the mown is cut out, I\-it11 scissors. This paper crow11 model is usctl for the constrnc4ion of’ the rotation wntrr as seen in b’ig. 1. b’irst. the sh:rl)e of the (~~OWIL with the points 1, f’. antI
P’ig.
I.--1,inguolabial
moment calculated
(b) from
groducecl by perpen~liculars
known through
force f”,
( GWI ). I”, mtl
Rotation c”.
writer’
( Kf’l
F is traced on drawing paper. The values of the CIYIWII excursion, i’, c’, and f’, mnlt~iplied by the enlargement factor of the print. are transferred perpentlioularly to the points I, C, and F, yielding I’, C”, and P’. The paper crown motlrl then is oriented within I’, C’, and P’. Only one position is possible, and the paper crown is traced again in this new position which c~orresponds to the position the clinical crown had when the linguolal~ial Force was applied. Points 1, f’, and I” arc united with points I”, C”‘, and F”. The middle perpendicu!ars 011 these lirlcs (z“I, “~8,f”) intersect, at the instantaneous rotation (aenter KC’. A7 is the distance fwn KC to the labial cervicoenamcl junction (E’) and can be used to exljress that distance numerically.
394
HANS
R. iUtillLICXIANX
AND
RZARJIION
I\‘.
HOUGLUJI
References Inl-estigations of thy brriodontal Width, Ztschr. f, Stonratol. 26: A.: ‘Systematic 417, 1928. untl ~~athologische Zahrlbe~~,egliehk~,it,. Schr< ri/. 3. Miihlemann, H. R.: Die ph.vsiologisclre Monatschr. f. Zahnh. 61: I> 1951. (&\I. 4. Miihlemann, H. It.: Periodontonlrt ry. A Method for 1le;Lsurir~g Tooth Mol)ility, 2. Klein,
SURG., ORAL MED.,
AND OR.AL PATH.
4: .1220, 196 1.