1986 Dermaut Et Al. Experimental Determination of the Center of Resistance of the Upper First

8/13/2019 1986 Dermaut Et Al. Experimental Determination of the Center of Resistance of the Upper First

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E x p er i m en t a l d et er m i n a t i o n o f th e cen t er o fr esi st a n c e o f th e u p p er i r st m o l a r i n am a cer a ted d r y h u m a n sk u l l su b m i t t ed to

h o r i zo n t a l h e ad g ea r t r a c ti o n

L. R . De rm au t , D .D .S . , Ph .D . , J . P. J . K leu tghe n , D .D .S . , M.D . , and H . J . J . De C le r ck , D .D .S .Gent Belgium

Laser speckle interferometry, recent ly developed for noninvas ive meas urem ent of smal l d isp lacements(microns), wa s used to study the m ovem ent of maxil lary molars subm itted to extraoral traction.Using an antenna-headgear at different horizontal levels, Ioadings of 700 gm were appliedperpendicular to the long axes of these tee th . Bodi ly movement was observed when the t rac t ion l inepass ed s ightly occlusal to the tr ifurcation of the roots. Therefore, the cente r of resistance o f theupp er molar was expe rime ntally localized at this level . Laser speckle interferom etry prov ed to be apromising technique for dental research.

AMJ ORTHOD DENTOFAC ORTHOP 90: 29-36, 1986.)

K ey wo rds : Center of resistance force orthodontic tooth movement laser speckle interferometry headgear

W h e n a p p l y i n g d i f fe r e n t f o r c es o n t e et hac tua l con t ro l o f the m ove me n t i s neces sa ry t o a s su ree ff i c i ency i n c l i n ica l o r thodon t i c s . The re fo re t he g row -ing i n t e r e s t i n b iomechan ic s a s an expe r imen ta l andc l in ica l d i s c ip l i ne can b e ea s i l y obse rv ed i n t he o r tho -don t i c l i t e r a tu r e a s s imp le emp i r i c obse rva t i ons have

been exp la ined o r ove r ru l ed b y b iophys i ca l t heo r ie s andinves t i ga ti ons . I n t he man ipu l a t i on o f app l i ances mos to r thodon t i s t s cons ide r t he r e l a t i onsh ip o f the fo r ce vec -to r t o t he cen t e r o f r e s i s t ance o f a t oo th o r a g roup o ft ee th . I ndeed whe the r an ob j ec t w i ll d i sp lay a t i pp ingo r a bod i ly move me n t when submi t t ed t o a s i ng l e fo r cei s ma in ly de t e rmined by t he l oca t i on o f t he cen t e r o fr e s i s tance o f t hi s ob j ec t and t he d i s t ance be tween theforce vec tor an d th is cente r o f res is tance . 1.14

In m os t ca se s t he pos i t i on o f t he cen t e r o f r e s i st ancewi th in a t oo th can ne i t he r be i n f luenced by app l i ancedes ign no r by i ts a c ti va t i on . The re fo re ac tua l t oo th

d i sp l acemen t i s pa r t i a l l y de t e rmined by v a ry ing t he pa -r ame te r s o f fo r ce app l i ca t ion . These pa rame te r s a r e t hed i r ec ti on t he du ra t i on and the magn i tude o f t he app l i edfo rce . Moreov e r t he se f ac to r s a re in f luenced by t hepo in t o f app l i ca t i on o f t he fo r ce sys t em on the ob j ec tunde r cons ide ra t i on .

Neve r the l e s s accu ra t e fo r ce app l i ca t i on a l so r e -

Chairman, D epartm ent of Orthodontics, State University of Gent.Assistant Professor, Depa rtmen t of Orthodontics.

qu i r e s some kno wledg e o f t he l oca ti on o f t he cen te r o fr e s i s t ance o f t he ob j ec t t o be moved . The cen t e r o fres is tance 14 has b een def ined as the po in t o f the grea tes tr e s i s t ance t o t he movemen t o f a t oo th . I t i s f u r the rdef ined as the poin t tha t a l lows the tooth to d isp lay apur e t ran s la t ion 9 wi tho ut exhib i t ing e i ther a ro ta t iona l

t endency o r a mo me n t when the fo r ce vec to r r ega rd l e s sof i t s d i rec t ion passes throug h i t.

The cen t e r o f r e s i s t ance shou ld no t be r ega rded a sa f ixed po in t w i th in a t oo th bu t r a the r a s the comp os i t epo in t o f a l l f a c to r s 3 o ff e r ing d i f f e r en t com ponen t s o fr e s i s t ance t o a ce r t a in fo r ce app l i ca t i on . A na lys i s o f t here s i s t ance t o den ta l m ove me n t shou ld t he re fo re t ake thefo l l owing pa rame te r s i n to cons ide ra t i on :1 . The t oo th ana tom y and mass d i s t ri bu t ion w i th in t he

tooth2 . The s t ruc tu re o f t he pe r iodon ta l a t t a chmen t s3 . The deg ree o f bon y su r round ings

4 . The ad j acen t t ee thHaa ck and W eins t ein 7 s t ud ied fo rce d i s t r i bu tion i n

the pe r iodon ta l l i gam en t s on a two -d imens iona l mo de lo f an i nc i so r w i th a pa rabo l i c - shaped roo t . Pu re t r ans -l a t ion was ob t a ined wh en a s i ng l e fo r ce pas sed t h roughthe cen t e r o f r e si s t ance o r whe n a s i ng l e fo r ce ap -p l i ed a t t he b r acke t was com bined w i th a we l l -de f inedm o m e n t .

Exam ina t ion o f t he de sc r ibed expe r imen t s le ads t othe obse rv a t i on t ha t t he cen t e r o f r e s is t ance fo r a s i ng l e -

9


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30 De rm au t Kle utg he n an d De Cle rck Am. J. Orthod. Dentofac. Orthop.July 986

Fig. 1. A small ribbon like metal plate g lued parallel to the vestibular surface of the left molar just belo wthe hea dgear tube.

rooted tooth might be found a t approximate ly ha l f thedistance of the apex to the alveolar crest. L ater, Worms,Isaacson, and Speidel ~6 studied the mov emen ts of theuppe r f irst mola r submitted to cervical headg ear tractionin 15 patients. To register the type of displacement ofthe molars, they used cephalometric laminographsthrough the buccal quadrant taken at regular intervalsduring the extraoral treatment. In the mea ntime, routine

lateral head plates with the face-bo ws in activationserved to elucidate the actual force vector o f the head-gear t rac t ion . Bodi ly movement of molars was foundin three patients in whom the traction l ine passedthrou gh the trifurcat ion area. The authors ~6 concl udedthat the center of resistance of the upper f irst molarshould be located at this level .

Studying the displacements of incisors on humansubjects in three dimensions (f irst with dial microm etersand later with double exposure holograms). Burstoneand co-workers4' l l calculated the location of the theo-retic center of resistance. In the two-dimensional rep-

resentation of a model of the upper incisor, the centerof resistance was located at 40% of the distance of theroot length apical to the alveolar crest . The same com-putation was corrected to a value of 33% of the rootlength when the model was assumed to possess a tr i-d imensional geom etry,

Experimental determination of the center of resis-tance was then performe d on a 10:1 model of an incisoralso with the aid of the holographic measuring tech-niqu e . Com pared to the theoretic location of the centerof resistance, i t was foun d to be sl ightly more o cclusal .For a two-dimensional geometry, the theoretic center

of resistance was 11.0 mm from the bracket; for a

tr idimensional representation, a distance 10.2 mm wascalculated. The experimental center of resistance waslocalized at 9.9 mm from the bracket. For multi-rooted teeth (mandibular molars) , Burstone andPryputniew icz 2 tested a fresh, human -skull specimenreplacing the periodontal l ig ament w ith si l icone rubber.The center of res is tance was be tween 30% and 40% ofthe distance from the alveolar crest to the root apices,

being 1-2 m m apical of the furcation. ~4 Reviewing thisdata, one must con clude that the center of resistance isalways very close to the geometric center (centroid) ofthe supported tooth m ass betwe en the alveolar crest andapices. Theoretically, i t should be possible to determineby clinical investigation the center of resistance of theupper molar. But in reali ty too many parameters inter-fere, such as the f lexibil i ty of the wires, the inconsis-tency i n loading as well as in duration, and the am ountand direction of the force. As previously mentioned,Worm s, Isaacson , and Speidel ~6 clinically determinedthe location of the center of resistance of the maxil lary

molars in the area of the root tr ifurcation. These findingsconfirm the hypothetical location of the center of re-sistance for the upper f irst molars according to differentauthors, t.~0.t~ Des pite this o bse rva tion , ex peri men tal de-termination is st i l l advantageous because i t providesbetter control of the parameters involved. Precise mea-surement of in i t ia l tooth movem ents should enablean exact determination of tooth posit ion before and afterloading while direction and amount of force are keptPerfectly constant . Therefore, possible errors are re-duced compared wi th a method in which super impo-sit ion of tracings might be the cause of some in-

accuracy. ~


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Volume90 etermination of center o f resistance of upper first mo lar 31u m b e r l

Fig 2. Antenna headgear.

MATERIAL AND METHODSMaterials

To approach biologic reali ty as much as possible,the use of mechanical simulators as experimental mod-els was disregarded mainly because reproduction of thetooth surroundings is practically impossible. Instead ofreplicas, a macerated, dry human skull was chosen asthe test object . Although some differences of biome-chanical behavior between this kind of model and thepatient may be expected, a sufficient degree of simi-lari ty exists to use i t as a rel iable simulation model. Askull was selected that met specific cri teria. Checking

the denti t ion of this skull , a symmetric posit ion (notmesial to the left and right upper f irst molars) wasobserved. Simultaneously, the alveolar crest was alsofound to be within normal l imits for both teeth on thevestibular and the palatal sides. Because the skull ap-parently was derived from an adult , fully erupted sec-ond maxil lary molars were in contact with the experi-mental teeth. Dental con tact zones with the second pre-molars were also judge d to be normal. In preparationfor the experiment, al l teeth were carefully removed.During this procedure any damage to the alveolar bonewas avoided. The per odontal l igam ent had to be re-

placed by an art if icial one. For this purpo se, a thin laye rof Araldit 208 was injected into the empty sockets:Afterwards the teeth were cautiously reposit ioned. Thisspecial glue, Araldit 208, when mixed with the harder956 in a rat io of 10 to 1, displays nearly the same elast icpropert ies as the human periodontium according toD i j k m a n ?

To evalua te the degree o f t ipping and bodi ly move -ment more accurately, a small r ibbon-like metal plate(0.5 cm 2 cm) was glued parallel to the vestibularsurface of the le f t m olar jus t be low the headgear tube(Fig. 1). This plate, serving as an extension, enabled

measu remen ts to be taken no only in the center of the

crown along the tooth axis, but also on the mesial anddistal coronal extremities. In that way three scanningspots were def ined for measurements- -one on the me-sial side, one in the middle, and one on the distal side.At the start a comm erciall y available headg ear had beenadapted to create a traction l ine through the tr ifurcationarea. When applying a total load of 700 gin, this ap-pliance show ed a significant amoun t of bending. Thiseffect not only lowered the traction l ine, requiring re-adaptation of the inclination between outer and innerbows to a much larger extent , but also caused an un-wanted extrusive effect on the molars. This parasit ic

force-effect could have interfered with the displaceme ntto be tes ted . Therefore , a spec ia l "antenna-headgear"was developed (Fig. 2). Instead of an outer bow todetermine the l ines of traction, an antenna was solderedto an inner bow that was entirely reinforced except forthe segments to be introduced into the molar tubes. Atdifferent levels of the antenna, hooks were at tached tosupport a nylon wire running along a neck simulator.Because the lat ter could also be changed for differentvertical levels, traction lines parallel to a certain ref-erence l ine could be realized. The loading was appliedby means of a calibrated spring attached to the nylon

wire (Fig. 3) . The l ine, contacting the incisal edge ofthe canines and the mes ioves tibular cusp of the f irstmolar, was chosen as the reference l ine. This l ine wasfairly Perpendicular to the apico-occlusal axis of thefirst molars. I t was represented by a nylon wire t ied tothe f ixation supports of the skull .

Method

In this study initial displacemen t of molars was me a-sured by means of speckle interferometry, an opticalnondestructive measuring technique. Laser speckle me-trology is an optically precise measurement technique

designed for registrat ion of small displacements mi-


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32 De rm au t Kle utg he n an d De Cle rck Am. J. Orthod. Dentofac. Orthop.July 986

BC

DE

F

Fig. 3. Indication of level of traction lines. A Throu gh apices. B Mola r root trifurcation. C 10 mmabove the occlusal level. D 5 mm abo ve the occlusal level. E Occlusal level. F 10 mm below theocclus al level. G 20 mm be low the occiusal level.

Fig. 4. Fixation of the skull b y mean s of three intermed iate resinshields attached to a solid metal framework using five metalsupp orts--tw o for the occipital area the third on the dorsal sideof the parietal bones and two on the forehead.

crons). T herefore, any source of vibration and all par-asit ic movemen ts should b e strictly banished from theexperimental room. Although the standards of vibra-tion-isolation for speckle metrology are generally con-sidered to be less strict than those for holography, theysurely may not be underestimated. Thus, the skull wasrigidly affixed to a solid metal framew ork by m eans offive metal su ppo rts-- two for the occipital area, the thirdon the dorsal side of the parietal bones, and two on theforehead (Fig. 4). With massive bolts and nuts, theskull was carefully stabilized between the metal sup-ports avoiding any ef fect of force by clamping in order

to prevent unwanted strain in the skull. The support

zones were further consolidated with three intermediateresin shields. This fram ework was then firmly clampedto an optical bench, together with all elements of theregistration unit. Preceding the experiments, the valid-ity of this stabilization was controlled by real-timeholography; afterwards mechanical microcomparatorsconfirmed its reliability.

In the experimental situation, a simulator replacedthe patient s neck. I t consisted of three frictionless pul-

leys mounted on a flat metal bar. T he distance betweenthe pulleys--imitating the transverse dimension of thepatient s neck--could be adjusted by means of screws.A specially designed fixation Suppo~ attached to thesolid base of the fram ework enabled us to use d ifferentlevels of traction by raising or lowering the neck sim-ulator.

The following seven traction levels parallel to theocclusal plane (check ed on cephalograms) were chosenduring loading (Fig. 3):A. Throug h the apices of the rootsB. Area of root tr ifurcation

C. 10 mm above the occlusal level (apical third of theroot length)

D. 5 mm above the occlusal level, sl ightly below thecementoenamel junct ion

E. Occlusal level (a plane, conn ecting the mesioves-tibular cusps o f the first molars and the incisal edgesof the canines)

F. 10 mm be low the occlusal levelG. 20 mm below the occlusal level

All traction l ines w ere rigorously checked for par-allelism with the reference line during the applicationof forces.

Among the noninvasive optical biometric tech-


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olume 9 etermination o f center of resistance o f upper f irs t molar3 3N u m b e r

N LY S I S U N I T

~ L S E R

S P E C K L E S C N N E R

o o oM O N I TO R

Fig. 5 Ana lysis uni t .

A

L S E R

B

I q

I l l ' I

l

Fig. 6. A , Schematic representation of the creation of Young s fringes w hen lase r beam is passingthrough two h oles in a screen. B , Schematic drawing of the displacementd ) of a speckle pa ttern ona double-exposedhologra phic plate due to force application. A laser beam passing through the speckle-gram creates a fringe pattern (Young s phenom enon), C, Th e amo unt of displacement is invers elyproportionate with the distance b etwe en two fringesd); the direction of displacement is perpendicularto the orientation of the fringes.

niques laser speck le m etro l ogy ~2-~3 was cho sen as theexpe r imen ta l p rocedu re fo r two r ea sons . I n t he f i r s tp l ace t he amo un t o f d i sp l acem en t i nduced by ex t r ao ra lfo r ce s co r r e sponds w i th t he measu remen t r ange o f t h i sop t i ca l t e chn ique . I n t he s econd p l ace no t on ly t he

amo un t o f t he mo vem en t s bu t a l so the i r d i r ec t ion can

be r eco rded immed ia t e ly when r e s t r i c t ed t o a two-d i -me nsi on al f ield. ~3

P r o c e d u r e s o f s p e c k le i n t e rf e r o m e t r y

When an expanded l a se r beam i l l umina t e s a d i f fu se

re f l ec ti ng ob j ec t a r andom d i s t r i bu t ion o f b r igh t and


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4 De rm au t, Kle utg hen , an d D e Cle rck Am. J. Orthod. Dentofac. Orthop.July1986

a b l e I Stat is t ica l evaluat ion of data (ca lcula ted to check re l iabi l i ty of exper imenta l procedure)

Angu lar m easurements (o) Linear measurem ents (ram)Scanning spots

( N = I 3 ) M e a n [ S D [ o f e r r o r M e a n [ S D [ o f e r r o r

Mesial 16.8 1.85 11% 41.65 5.05 12%Median 28.15 1.70 6% 40.76 1.30 3 %

Distal 39.6 3.41 8% 39.65 3.41 4%MEAN PERCENTAGE 8% 6%

OF ERROR

Loading = 700 gm during 1.5 minutes with intervals of 3 minutes relaxation. Procedure was perfo rmed 13 times for each scanning spot.

a b l e I I. Direct ion and amo unt of d isplacem ent of the three scanning p oints on the m eta l p la te

Distal Median MesialTraction Degree of

level ~j dl ~2 d2 fl~ d3 tip ping a

A -3 7 12 ixm -2 6 11 txm -1 7 11 Izm -1 6 B -2 5 17 ~m -2 2 17 I~m -2 1 17 ~m -4

C - 25 20 p~m - 28 22 ixm - 29 22 ~m + 3

D - 12 29 ~m - 19 32 ixm -2 4 34 ~m +3 2

E -7 43 p~m - 16 46 p,m -2 3 50 I~m +5 9

F - 5 49 I~m - 17.5 52 p,m - 28 54 i~m + 86

G + 1 50 p~m - 17 51 p~m -3 2 55 Ixm + 123

The direction (13) of the three displacem ent vectors is measure d in degrees ( - = extrusion; + = intrusion). The amo unt of displac ement (d)

is calculated in microns. In the last column the degree of tipping is shown by means of the angle et multipled by 103 (see Fig. 7). A negativesign stands for a distal root tipping; a positive sign indicates a distal crown tipping.

dark spo t s supe r imposed on the ob jec t su r face can be

obse rved . These spe ck les a re a s soc ia t ed wi th theobject surface so that when the o bject i s d isplaced, thespeckle pat tern moves in an ident ica l manner. Regis-t ra t ion of two spec kle pat terns , on e before and one af terobject d isplacemen t , i s rea l ized on the sam e photo . F orour expe r imen t , two work ing un i t s were con s t rnc ted - -a regis t ra tion uni t and an analys is uni t . T he regis t ra t ionun i t cons i s t ed o f t he me ta l f r amework suppor t ing theskul l wi th the headgear, neck s imulator, and weightcarder. Th e surface of the meta l p la te , g lued to the lef tmolar, i s i l luminated by a d iverged laser beam. Theref lec ted speckle pat tern is regis t ra ted twice (once be-

fore and on ce af ter force appl ica t ion) on a photographicpla te in a camera placed perpendicular to the opt ica laxis . Af ter process ing, the photographic p la te , ca l ledspeck le -g ram, i s a ff ixed in the spec k le scanne r o fthe analys is uni t (Fig . 5) . By m anipula t ing two s l id ingscrew shaf ts , one hor izonta l and one ver t ica l , the

spe ck le -g ra m can be d isp laced in a p l ane o r thogo-na l ly to the l a se r beam. Keep ing the l a se r beam s t eadyand moving the f r ame in X-Y d i r ec t ion to the beam,any chosen po in t on the speck le -g ram can be se l ec t edfor measurem ent . A t a cer ta in d is tance behind the spec-kle scanner, a pr imary screen is f ixed to the opt ica l

bench . A we l l - focused la se r beam pass ing th rough the

selected point on the photograph in terferes wi th thecorre la ted speckle-pat terns of the emu ls ion, creat ing animage d iv ided by f r inges (F ig . 6 ) . The appea rance o fthese in ter ferenc e f r inges i s based on the o pt ica l phe-nom enon advoca ted by Young .~7 The f r inges a re p ro -j ec t ed on the sc reen and th is image i s t hen cap tu red bya v ideo camera connec ted to a mon i to r. The d i s t ancebe tween two f r inges i s i nve r se ly p ropor t iona te to theamoun t o f d i sp lacemen t to be measured . S imple ma th -emat ic ca lcula t ion gives the exact values in microme-ters . A rota t ing t ransparent d isc wi th ca l ibra ted angu-l a tion r eadou t i s a t t ached ov e r the mo n i to r s c reen . T he

d i rec tion o f the ob jec t d i sp lacemen t i s pe rpend icu la r t othe f r inge inc lina tion . M easuremen t o f t he ang le o f t hef r inges on the mo n i to r no t on ly a l lows the de te rmina t ionof the d i rec t ion of object d isplacem ent , bu t a lso createsthe poss ib i li t y o f r e so lu t ion o f vec to r com ponen t s (F ig .6 , C) . This procedure is very important for the s t ressanalys is of ext raora l or thodont ic forces because i t in-dicates la tera l and dorsal force com ponen ts . In th is wayi t is poss ible to determ ine the displacem ent vectors andthe i r componen t s fo r t he th ree po in t s on the me ta lp l a t e , wh ich i s g lued to the mov ing upper f i r s tmolar.


7/8

olume 9 D e t e r m i n a t i o n o f c e n t e r o f r e s is t a n c e o f u p p e r f i r s t m o l a r3 5N u m b e r

I ES - , ST [ ,,~/ v. . / IA f ~ ) ; I A

. . . .

. . . . , ~ B

F i g .7 . Sch em at i c r ep resen ta t ion o f t he deg ree o f ti pp ing .

R e l i a b i l i t y o f t h e m e t h o d

Rel i ab i l i t y and r ep roduc ib i l i t y o f t he p rocedu re

were checked by succes s ive ly app ly ing t he s ame load -ing amoun t (700 gm) 13 t imes . The app l i ca t i ons we remade du r ing 13 t ime pe r iods o f 1 .5 minu te s du ra t i onwi th i n t e rva l s o f 3 m inu te s fo r r e l axa t i on . P rev ious ly,t w o " d r y r u n s " h a d b e e n p e r f o r m e d o n th e s a m e t i m eschedu le . Fo r t he se l oad ings , t r ac t i on - leve l A was m a in -ta ined .

L i s t ed i n Tab le I a r e t he means and s t anda rd dev i a -t i ons o f t he mea su rem en t s u sed t o check t he r e l i ab il i ty.The t h r ee s cann ing spo t s - -one on t he mes i a l a spec t ,one i n t he midd le o f t he mo la r ax i s , and on e on t hed i s t a l a spec t - -we re eva lua t ed fo r t he d i r ec t i on o f t he

d i sp l acem en t ( r ep re sen t ed by t he angu la t i on o f t hef r i nges ) and fo r t he magn i tude o f t he movemen t a smeasu red i n mi l l ime te r s ( f r i nge i n t e rd i s t ance ) .

C o m p a r i s o n o f t h e a c c u r a c y b e t w e e n a n g u l a r a n dl inea r measu remen t s con f i rmed the no rma l expec t a t i ontha t e r ro r s a r e mor e r educed fo r l inea r t han fo r angu la rr eg i s t r a t i ons ( a s t he mean pe rcen t ages o f e r ro r i nd i -c a t e d - 8 % f o r an g u la r a nd 6 % f o r li n ea r m ea s u re -men t s ) . Th e accu rac y d i f f e r ences fo r bo th k inds o f mea -su remen t s be tween the mes i a l ve r sus t he med ian andd i s t a l s cann ing spo t s cou ld even tua l l y be exp l a ined bya sma l l d ive rgen ce o f t he r ec t angu la r me ta l spec imen

to t he op t i ca l ax i s o f t he r eg i s t r a ti ng cam era . I n f ac t ,t h is me ta l su r f ace shou ld be pe r f ec t l y o r i en t ed pe rpen -d i cu l a r t o t he ax i s o f t he camera .

F I N D I N G S

To loca t e t he cen t e r o f r e s i st ance fo r t he upp e r f i r stmo la r s o f t h i s sku l l, t he m ode l w as sub j ec t ed t o a l oad -ing o f 700 gm a t the s even t r ac t i on l eve ls (F ig . 3 ) . Fo re a c h l e v e l , t w o d r y r u n s w e r e p e r f o r m e d f o l l o w e d b yth ree fo r ce app l i ca t i ons fo r ac tua l measu remen t u s ingthe same t ime schedule as tha t for the re l iab i l i ty tes t .The ave rages o f t he se t e st s a r e r ep re sen t ed i n Tab le I I .

- 1= - l 's - -

F i g . 8 . Avera ge de g ree o f t i pp ing pe r l eve l o f t r ac tion l i ne . Or-d ina t e = Leve l o f t r ac t ion l i nes . Absc i s sa = Deg ree o f t i pp inga ) . Nu mb ers t o t he l e f t o f t he o rd ina t e r ep resen t d i s t a l c rown

t ipp ing ; numbers t o t he r igh t i nd ica t e d i s t a l roo t t i pp ing . Po in to f i n t e r sec tion r ep resen t s bod i ly mo vem en t w i thou t ro t a t ion .

For each o f t he d i sp l acemen t vec to r s o f t he t h r eescann ing po in t s , t he ang l e o f d i sp l acemen t~ 1 , ~ 2 , [ 3 3 )and the amo un t o f d i sp l acemen t (d l , d2,d 3 w e r e enu -mera t ed (F ig . 7 ) . Com par ing t he amoun t o f d i sp l ace -men t i n t he t r ac t i on l eve l s , i t became appa ren t t ha td i sp l acemen t i nc rea sed when the l evel o f t r ac t ion waslower. F rom l eve l D to G , t he t r ac ti on l i ne pa s sedth rough the mo la r c rown and the amoun t o f d i sp l ace -men t i nc rea sed r emarkab ly. The d i f f e r ence be tweenleve l D and E w as mo s t s t r ik ing ; howeve r, t h i s g r ad i en t

was no t con t inued a t t he s ame r a t e fo r F and G (Tab leI I ) . A l l r eg i s tr a t i ons d i sp l ayed an ex t ru s ive vec to r com -pon ent (neg at ive s ign o f angle 13) exce pt for the d is ta lspo t a t l evel G . The d eg ree o f t ipp ing , i den ti f ied i nTable I I as cx was c a lcula ted s ta r t ing f rom the va lueso f amoun t and d i r ec t i on o f t he t h r ee vec to r s o f d i s -p l acemen t . Tw o l ine s connec t ing t he t h r ee po in t s be fo reand a f t e r f o r ce app l i ca t i on were subs t it u t ed (F ig . 7 ) .The ang l e a be t w een bo th l i nes was de f ined a s t he" d e g r e e o f t i p p i n g . " N e g a t i v e s ig n s w e r e o b t a in e d f o rt rac t ion levels A and B, and po s i t ive s igns for a l l o thert r ac t i on l eve l s w i th i nc rea s ing amoun t f rom l eve l C to

G (Tab le I I ) . The r eg i s t e r ed deg ree o f t i pp ing has beent r ans f e r r ed t o t he d i ag ram in F ig . 8 . On the o rd ina t eare the levels of t rac t ion . T he va lues of t i lt ing are rep-r e sen t ed on t he absc i s sa . Nega t ive va lues i nd i ca t e adis ta l root t i l t ing; pos i t ive s igns s tand for d is ta l c rownt ipp ing . Bod i ly mov em en t w i thou t ro t a t i on wou ld berea l i zed when the l i ne connec t ing t he da t a fo r t i pp ingin tersec ts the ord ina te .

C O N C L U S I O N S

Rev iew ing the da t a o f Tab le I I , the i nc remen t s i nt h e a m o u n t o f d i s p l a c e m e n t o f t he u p p e r m o l a r c o u l d ,


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36 Derm au t K leu tghen an d De C le rck Am. J . Orthod . Dentofac .OrthopJuly 1986

b y l o w e r i n g t h e t r a c t i o n l e v e l , b e a t t r i b u t e d t o t h e r e -s i s t a n c e c a u s e d b y t h e b o n y s u r r o u n d i n g s o f t h e r o o t s .B y l o w e r i n g t h e l e v e l o f t r a c t i o n , t h e r e s i s t a n c e t o t h ea p p l i e d f o r c e s d e c r e a s e d w i t h a g r e a t e r t i l t i n g o n t h em o l a r c r o w n . F o r t r a c ti o n l e v e l G , t h e d i s t a l c r o w n

t i p p in g w a s s o p r o n o u n c e d t h a t e v e n a s m a l l i n t ru s i o no f t h e d is t a l s c a n n i n g p o i n t o c c u r r e d . E x a m i n a t i o n o fF i g . 8 l e a d s t o t h e c o n c l u s i o n t h a t t h e c e n t e r o f r e s is -t a n c e o f t h e u p p e r f i rs t m o l a r, w h e n s u b m i t t e d t o a ne x t r a o r a l t r a c t i o n o f 7 0 0 g r n d i r e c t e d p e r p e n d i c u l a r t oi ts l o n g a x i s , s h o u l d b e e s t i m a t e d to l ie s o m e w h a t b e l o wt h e tr i fu r c a t io n a r e a . B o d i l y m o v e m e n t o f t h e m o l a rw a s r e a l i z e d w h e n a f o r c e w a s a p p l i e d b e t w e e n l e v e l sB a n d C b e c a u s e t h e l i n e c o n n e c t i n g t h e t i l t i n g v a l u e sfor leve l s B and C in F ig . 8 in te r sec t s the o rd ina te . T h iso b s e r v a t i o n c o n f i rm s t h e s t a te m e n t o f W o r m s , I s a a c s o n ,a n d S p e i d e l , ~6 w h o n o t e d t h a t t h e c e n t e r o f r e s i s t a n c e

d e s c e n d s i n a n a p i c o - o c c l u s a l d i r e c t i o n i f a f u l l y e r u p t e ds e c o n d m o l a r c o n t a c t s th e e x p e r i m e n t a l t o o t h .

F u r t h e r m o r e , t h i s e x p e r i m e n t p r o v e s t h a t s p e c k l ei n t e r f e r o m e t r y c a n b e e s t i m a t e d a s a w o r t h w h i l e , r e l i -a b l e , a n d a c c u r a t e p r o c e d u r e f o r t h e e x p e r i m e n t a l a n a l -y s i s o f i n i t ia l o r t h o d o n t i c e x t r a o r a l fo r c e s . T h i s o p t i c a lt e c h n i q u e o f f e r s m o r e p o s s i b i l i t ie s f o r p r e c i s i o n m e a -s u r e m e n t s i n d e n t a l r e s e a r c h ) th a n p a s t p r o c e d u r e s .A l o n g w i t h h o l o g r a p h y, i t a l s o d e s e r v e s i n t h i s c o n t e x ta f u ll y r e c o g n i z e d p l a ce a m o n g t h e n o n i n v a s i v e m e a -s u r e m e n t t o o l s .

T h e a u t h o r s w i s h t o th a n k P r o f e s s o r D r. 1 . P. B o o n e a n d

M r , M . D e C a l u w e f r o m t h e D e p a r t m e n t o f R e s i s t a n c e o fM a t e r i a l s f o r t h e i r a s s i s t a n c e a n d h e l p d u r i n g t h e e x p e r i -m e n t s . T h e y a l s o w a n t t o t h a n k M r s . B . J o u r et f o r t y p i n g t h em a n u s c r i p t a n d M r, G , D e r m o u t f o r m a k i n g t h e t r ac i n g s a n d

p h o t o g r a p h s .

R E F E R E N C E S1 . B u r s t o n e C J : B i o m e c h a n i c s o f to o t h m o v e m e n t .In Kraus BS,

Riedel RA (edi tors) : Vis tas in or thodont ics , Phi lade lphia , 1962,Lea Febig er, pp 197-213.

2 . Burs tone CJ , P ryputn iewicz RJ , Week s R: Center of res i s tanceof the hum an mand ibular molars . J Dent Res 60: 515 , 1981.

3 . Burs tone CJ , Prypu tn iewicz RJ : Holographic de terminat ion ofcenters of ro ta t ion pro duced b y or thodont ic forces . AM J ORTHOD77: 396-409, 1980.

4 . Chr is t iaensen RL, Burs tone C J : Centers of ro ta t ion wi th intheperiod ontal sp ace. AM J ORTHOD 55: 353-36 9, 1969.

5 . Di jkman JFP: Krachtenverde l ing b i j o r thodon t i sche behandel ing .

Doctora l thes is , Univers i ty of Ni jmegen, The N ether lands , 1969.6 . Haack D, Weins te in S : The mechanics of cent r ic and eccent r iccervic al traction. AM J ORTHOD 44: 346-3 57, 1958.

7 . H a a c k C D , W e i n s te i n S : G e o m e t r y an d m e c h a n i c sas relatedtotooth m o v e m e n t s t u d ie d b y m e a n s o f a t w o - d i m e n s i o n a l m o d e l .J Am Den t Assoc 66: 157-164, 1963.

8 . K l e u t g h e n J , D e r m a u t L R , B o o n e P M , D e C a l u w e M : T h eanal-y s i sof ex t raora l or thodont ic forces on a macera ted skul l by meansof speckle in te r ferometry : A pre l iminary repor t . Pro ceedings ofthe Socie ty of Photo-Opt ica l Ins t rumenta t ion Engineers , Edin-burgh, 1982.

9 . M u l l ig a n T F : C o m m o n s e n s e m e c h a n i c s . 2 . F o r c es a n d m o -ments . J Cl in Or thod 13: 676-683, 1979.

I0 . Oos thuizen L, Di jkman JFP, Evans WG: A mechanica lappraisalo f t h e K l o e h nextraoral assembly.A n g l e O r t h o d 4 3 : 2 2 1 - 2 3 2 ,1973.

11 . Pryputn iewicz RJ , Burs tone C J : The effec t of t ime and forcemagni tude on or thodo nt ic tooth mov emen t . J Dent Res 58: 1754-1764, 1979.

12 . Pryputn iewicz RJ : Laser speckle method for b ios te reometr ics .( In terna t iona l Symposium on Prec is ion and Speed in CloseRange Photogram metry, York , England , 1982. ) In t . Archives ofPhotogram metry 24: 387-397, 1982.

13 . Pryputn iew icz RJ , B urs tone CJ : A new technique for s tudies oftooth and bone mot ion . J Dent Res 61: A926, 1982.

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17 . Young TH: Phi los Trans R Soc 12: 38 7 , 1802.

Reprint requeststo:L. DermautKl in iek voor Tand- , Mond- en KaakziektenD e p a r t m e n t o f O r t h o d o n t i csA k a d e m i s c h Z i e k e n h u i sDe Pin te laan 185B - 9 0 0 0 G e n tB e l g i u m

1986 Dermaut Et Al. Experimental Determination of the Center of Resistance of the Upper First

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Transcript of 1986 Dermaut Et Al. Experimental Determination of the Center of Resistance of the Upper First