Crecimiento Mandibular

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America,n ournal of ORTHODONTICS

Founded n 1915 Volume86, Number5 November, 1984

CopyrightA 1984by TheC. V. MosbyCompany

ORIGINALARTICLES

Predictionof mandibular growthrotation

aualua,tedrom a,Longitudinal

implant sam,ple

VibekeSkieller,Arne Bj6rk,andTorkildLinde-Hansen

Copenhagen,enma.rk

Theaimof hisstudywas o estimatehepossibilityf predictinghedirectionnd heamount i growthotation

of hemandiblen hebasis f morphologicriteriabservedn a single rofileadiographt pubertalge 'The

difficultyn suchari analysiss due o the act hat heactual rowth otation annotbe evaluatedrom

radiogriphs ymeasurementst outerbonycontoursubiectedo remodeling.hesample onsisted f

twenty.oneersonsn whom heactualmandibularrowth otation asdeterminedrommetallicmplants vera

6-yeai eriod taroundhe imeof puberty. orphologiceaturesrom he irstprofileadiographould herefore

becompared ith he observedroMh hanges ver hestudy eriod nd heirpredictingalues alculated.

totalol iorty-fourmorphologicari'ablesereemployednd he datawereanalyzed y multivariatetatistical

methods. oreaih person,hevariables hich, lon,end n combination,howedhehighest redictivealue

with especto otalmandibularrowthotation respecified.he ourvariables hich,n combination,ave he

bestprognosticstimate86%) f mandibularrowthotationn hissample re 1)mandibularnclination,

representedythreealternatives-(a)ndex (proportionetween osterior nd anterioracialheight, b) ower

goniat ngle GOL),c) nclinationf ower orderNSL-MLI);2) ntermolarngle MOLs-MOL|);3)shape f

lower orderML1-ML2);nd 4) nclinationf symphysisCTL-NSL).hestatisticalnalysis asbased n a

samole f extreme ases. n childrenwitha morenormal rowthpattern,hese eaturesmaybe essdeveloped.

The concordanceetweenhepredictednd he observed rowth hangess illustratedraphicallyor eachperson.

Key words: Prediction,mandibular rowth otation,cephalometrics,etallic mplants

In an early attempt to analyze the possibility of

pre$icting growth of a single facial dimension, Bjcirk

and Pallingl corelated linear and angular measure-'

ments at prepubertal age with the residual gowth of

thesedimensiogsup to adulthood. These correlations,

however, were found to be very low. The variability of

the individual growth changesbetween the two age

levels was remarkably great, between 50Voand 807oof

the variability at prepubertal age. Thesefindings were

confirmed by Meredith,z who also found that a single

morphologic dimension at an early stage will tell us

Dr. Skieller

T T 7

VV itn an increased ealization of the great

individuality in craniofacial growth and development,

the need for a predictive systemhas been imperative in

orthodontic treatment planning. In spite of several at-

tempts n rgcent years, however, there is still doubt as

to the extent to which growth of the face as awhole can

be predicted from a singleprofile radiograph.

From the Institute of Orthodontics, Royal Dental College.

This study was supported by grants from the Danish Medical Research Foun'

dation and the Danish Dental Association (F.U.T.)'



360 Skieller, Bjdrk, and Linde-Hansen ^-,!;r?:i;!;

cently beendevelopedby Bj0rn-Jprgensen.laSincethisprediction further is basedon skeletalage and includesthe actual growth rotations of both mandible andmaxilla, the method seemspromising.

Cephalometricgrowth analysishas generally been

basedon conventionalmeasurementof the facial mor_phology, without taking into account the remodelinsprocessesat the bony surfaces. The dynamics of thJactualgrowth pattern s thereforeoften concealed.Thisapplies especially to the vertical development of theface becauseof the pronouncedgrowth rotationsof themaxillary and mandibular bones nside their more sra-ble soft-tissue matrices, as demonstrated in studieswith metallic implants.

The presentstudy is limited to an estimateof thepossibilitiesof predicting the amount and the directionof the actual growth rotation of the mandible from pre-pubertal age during the subsequentgrowth period. Anecessary ondition was to analyzea sample,followedlongitudinally with metallic implants up to adult age,where the mandibulargrowth rotation could be exactlydetermined.

MATERIALS

Fig.1. Growthotationf hemandibularorpuselativeo heanterior ranialbase NSl) designateds negativewhen heimplant

ineIPU)

rctatedorwardromstage to stageC.

little or nothing about the amount and direction of theresidual growth of this dimension.

Hixons suggested hat the best estimateof an adultfacial dimension for a given child is to use the dimen_sion presentedby the child and add to that the remain_ing average growth for the group. This method wasadoptedby several authors, and Johnstonadevelopedhis grid method on thesepremises.As exemplified byMills,s this estimatewould fit an averagebut not anextremegrowth pattern, where prediction from a clini_

cal point of view is most important.In an earlier approach, Johnston6 applied the

multivariate regressionmethod to growth prediction.Bhatia and associatesT utlined a prediction methodbased on a cluster analysis. Lavergnestried to indi-vidualize the prediction by a subdivision accordins tomorphogenetic types. Ricketts' computerized grJ*ti,forecasts(short range and long range), his treatment_simulation method, and the commercialRocky Moun_tain Data systems,10advocatedby him and his co-workershave gainedconsiderablenterest. n principle,the arcial methodof long-rangegrowth prediction usesgeometricprocedures o extract information about theprevious growth pattern of the mandible and project itto the further development. Statistical tests of thesemethodshavebeenmadeby Greenbergand Johnston,llSchulhof and Bagha,12and Witt and Kciran.ls

A computerized system for short_range facialgrowth prediction and treatment simulation. basedon longitudinal observationsof individual growth rateand growth direction over one or more years, has re_

, A sample of twenty-one subjects were chosen.These ncludednine girls and welve boys whosedenti-tional and facial developmenthasbeenanalyzedby theuse of metallic implants as references.All the subjectswere Danish and n normal physical and mental health.They were selected rom the group of children (250),who wereenrolled n the implant growth study andwhohad not undergoneorthodontictreatrnentbefore or dur-ing the 6year period of observation. Some deciduousand permanent eethweremissing n severalcases.Thesamplewas previously described n I972.tE The readeris referred to that earlier article for a detailed casede-scription. In order to obtain uniformity regardingphys-ical maturity, the analysiswas limited to a periodof 6

yearsencompassinghe time of puberty. The first stageA, 3 yearsbeforepuberty, and the growth changedur-ing the perioduntil 3 yearsafterpubertyhavebeenusedin the presentanalysis.

METHODS

The profile radiographswere superimposedaccord-ing to stablestructures n the anteriorcranial base,atathe nasion-sella ine (NSL) was transferred frorn the

first to the last film, as describedearlier.15-17The observed growth rotation of the mandibular

cor?us from the first to the last stagewas measureds

the change n inclination of the mplant line in theLovterjaw (IPLi) in relarion to NSL (Fig. l). When the fun'

Volm

Numb



Volume 6

NLnlber5

Table .

Index I

GOL

NSL-MLINSL-NL

OLs-ML2

NSL.ML2

ML2-RL

MOLs-MOLi

CTL-NSL

SYMF width

Index II

NSL-OLi

OLi-ML2

Y axis

Index III

MOLi.ML2

Index IV

MLI-ML2

NSL-MOLi

ILi-ML2

0.6191

0.6147

0.6080.6071

0.54690.4924

0.3990

0.38840.3159

0.3'712

0.3606

0.3540

0.34'780.3235

0.3052

0.2967

0.2'768

0-2698

0.2294

0.2291

P < 0.001

P < 0.005

P < 0.010

P < 0.025

P < 0.050

Index I

GOL

NSL-MLI

NSL-NL

OLs-ML2

NSL-ML2

ML2.RL

MOLs-MOLi

CTL.NSL

SYMF width

Index II

NSL.OLi

OLi.ML2

Y axis

Index II I

MOLi-ML2

Index IV

MLI-ML2

NSL-MOLi

ILi.ML2

Prediction of mandibular growth rotation 361

Posterior acial heisht

Anterior facial height

Lower gonial angle (Fig. 3)

NS L to mandibular ine I (Fig. a)

NSL to nasal ine

Upper occlusal in e to ML2

NS L to mandibular in e 2

Jaw angle

Intermolar angle (Fig. 5)

Chin line to NSL (Fig. 7)

Width of symphysis

Ramusheight

Corpus length

NS L to lower occlusal ine

Lower occlusal ine to ML2

NSL to sella prognathion

Clivus Iength

Ramusheight

Lower molar inclination o ML2T' In-^' f"^^ h- i -hr

L"rv- fr* h"tgttt

Angle between he two mandibular ines(Fie. )

NS L to lower molar inclination

Lower incisor nclination o ML 2

,thisudes

: and

been

,For-

ilingI t he

rThis$ ttt,f the

fuu-idies

FI lh'Frlonlipre-p . eIwed

[us.,!ctlyI,,t

iiii

fs.n.bntili

r*"pec$

lFr,h.Frg)'[Ynoilgur-uousiirn'iaderi i ,

tot-

Pvs-fof6Staee

i,o*-r i .iuseoii

li

l)i

Lord'

i andh tne

tbuluboat

;owerLm-

Table l. Correlations t stageA between he six first independent ariables n Table

Index I GOL NSLIMLI NSL-NL OLs-ML2 NSL-ML2

Index I

coLNSL.MLl

NSL-NL

OLs-ML2

NSL-ML2

-0 .86- 0.96

- 0.96- 0 .83- 0.93

- 0 .86

0.93

0.93

0.850.92

- 0 .96

0.93

0.990.83

0.98

- 0.96

0.930.99

0.84

0.98

- 0 .83

0.850.83

0.84

0.84

- 0 .93

0.920.98

0.98

0.84

P < 0 . 0 5 , r = 0 . 4 3 .P < 0 . 0 1 , r = 0 . 5 5 .P<0.001,= 0.67.

plant ine showeda forward rotation of the mandibularco{pus, he rotation was designatedas negativeand aspositivewhen the rotation was directed backward.

The mandibular growth rotation during the 6yearobservationperiod was on an averagedirected -6.0o

forward with a range of 21.7' (Table IV) as describedfor this sample in 1972.15 he observed rotation wasusedas the dependent variable in the following mul-tivariatestatisticalanalysis.

In order to find, on a singleprofile radiograph, themorphologic criteria showing the highest predictive

values and expressing s much as possibleof the ob-servedrotation, forty-four morphologic variablesfromthe first stageA, taken 3yearsprior to maximum puber-

tal growth in bodyheight

(fourlinear, thirty-five angu-lar, and five indices) were registered.These variables

were usedas independentvariables n the multivariate

regressionanalysis.l8 n the regressionanalysis be-tween the dependentand the forty-four independent

variables, the linear combination of the independentvariables that could explain most of the variability ofthe dependent ariablewas determined.To characterize



3OZ Skteuer, BJork, and Ltnde-Iiansen

Fig. 2. Mandibularnclination etermined v Index

Fig. 3. Mandibular nclination etermined y the lowergonialangte.

the regressionanalysis, he squaredmultiple correlationcoefficient, R3, was computed,varying between0 and1. This value indicatedwhat fraction of the total varia_tion could be explained by the independentvariable.The purpose was to selectthose ndependentvariableswhich, aloneor in combination, could explain as muchas possibleof the variability of the dependentvariable.In this procedure herewere two principal puqposes:l)attainment of the greatestpossible R2 values and (2)selection, among morphologic variables with equiva_lent R2 values, of thoseeasiest o apply clinically.

Fig. 4. Mandibularnclination eterminedby the angle NSL.M L1 .

RESULTS

At first a"univariate egressionanalysisfor eachthe forty-four independentmorphologic variableswasperformed. In Table I, twenty of the forty-four inde_pendentvariableswhose evel of significancewas lessthan 5Voare listed consecutively according to the Ffvalues.

The variable showing the highest R3 value of0.6191 was Index I (Fig. 2) . This index is an expres-sion of the proportion between the posterior and the

anterior facial height calculatedas I$$99. Thus,

62Voof the variability of the mandibular-growth

rota-tion in the sample could be explained by Index I, asgraphically illustrated in Fig. 8.

The first six morphologic variables in Table I allshowedhigh R2values.All of them are associatedwiththe inclination of the upper or lower jaw relative to theanterior cranial base and, consequently, are stronglycorrelated(Table tr). As far as the first four variablesareconcerned, herewas no significantdifference n theF values.

For clinical use, however, the first threearemost relevant. Alternatively to Index f, as an expres-sion of mandibular inclination, the lower gonial angle(GOL) (Fig. 3)1eand the angle NSL-MLI could beused (Fig. 4). It may be noted from Table I that theinclination of the mandible showed a considerablylower predicting value when measured as the angleNSL-ML2 (Fig. 3) than when measuredas tle angleNSL-ML1.

As describedabove, nearly ffiVo of the variability

NSL-ML1



Fig. 5. Intermolar ngle.

the observedmandibular growth rotation during the

ation period could be explainedby the mandibu-

inclination at the first stage,expressed y Index I or

equivalent measurements

ln the presentanalysis,Index I was selectedas the

independentvariable in the multivariate analysis.

next step was to find those variables which, in

mbination with Index I, could explain as much as

of the remaining part of thg variability of the

rved rotation.

Owing to the great number of independentvari-

, it waspractically impossible o investigateall the

ible combinations by using a multiple regression

is in order to find the best combination. Instead,

stepwise egressionprocedure was used,l8with a re-

ion evel of p > 0.1.

By the use of the regressionwith two independent

, it was shownthat in combinationwith Index

Ithe intermolar angle (MOLs-MOLi) (Fig. 5) was the

most mportant variable. Together, these wo variables

explain'16%o f the variability of the mandibular

growth rotaiion (Fig. 8). The variable MOLs-MOLi

(Table I) explained 39Voof the variability of the

mandibular growth rotation (Fig. 9). The intermolar

anglehas only a small topographicassociationwith the

ibular inclination repreSented y Index I; the cor-

relations r : 0.47 (Table tr).

The third variable which, in combination with In-

dex I and MOLs-MOLi, could give a still higher F

valueand at the same ime be clinically applicable was

the angle between the two mandibular lines (MLI-

ML2; expressing he shape of the lower border of the


Fig. 6. Shapeof the lowerborderof the mandible.

Fig.7. Inclinationf thesymphysis.

vealedan R2 value of 0.8148, thus explainingSLVo f

the total variability of the mandibular growth rotation

(Fig. 8) by which the R2 value increasedby SVo.The

angleMl-l-Ml-2alone (Table I) explainedonly 27Voof

the variability of the mandibular growth rotation (Fig.

9). The threevariables were only moderatelycorrelated

(Table III).

The next procedure n the stepwiseselectionproce-

dure, the inclination of the symphysls elative to NSL,

determinedby the angleCTL-NSL (Fig. 7), was found

to be the fourth variable which, combined with theFig. O. Combined, these hree variablesre-



364 Skieller, Bjbrk, and Linde-Hansen Am. J.

November

76.8"90.0"s2.5"

180.1 'J . ) -

116.0 '

R'z 0.6191

R2 0.7580

Table lll' Correlationsat stageA between he four independentvariables,which in combination save thebestprognosticestimate

Index I

MOLs-MOLiMLI.ML2

CTL.NSL

P < 0 . 0 5 , r = 0 . 4 3 .P < 0 . 0 1 , r : 0 . 5 5 .P < 0 . 0 0 1 , r : 0 . 6 7 .

Table lV. Dependentvariable

Dependent

variable

NSL.IPLiA4-

6.0' + 5.3 '

Table V. Independentvariables

Independent

variables

0.43

o.2l

0.56

0.85

0. 30.56

0.47

0.2rU . I J

0.470.430.85

A < o

threepreviously mentionedvariables,showed he high-estR2 value of 0. 8612. Thus, 867oof the total variabil-ify of the mandibular $owth rotation in this samplecould be explained (Fig. 8). The fourth variable,CTL-NSL, takenalone(Table I), explained 38Vo f thevariability of the mandibular growrh rotation (Fig. 9).In view of the fact that the inclination of the symphysisrelative to NSL correlatedmore strongly with Index Ithandid both MOLs-MOLi and ML1-ML2 (Table III),this variable enteredas the fourth variable

in the step-wise selection procedure.

It was not possible,by a regressionanalysis, o finda fifth independentvariable which could increasethe R2value to a significantly higher level than that for thefour described variables in combination. No furthervariable was therefore included in this analysis.

The four variableswhich, in combination, gavethebest prognostic estimate(86Vo)of mandibular srowth

< A 1 0

61.0 '

19.0'

159.8"

0.0'

65.0'

29.2 - 0.55 ndex78.2 - 0.32(MOLs-MOLi)

0.46Index71.1 - 0.41 ndex -

rotation in this sample are listed below. Mean valand rangeof variation are given in Table V.

Mandibular inclination, representedby threealternatives:

Index I Fig.Lower gonial angle, GOL Fig.Inclination of lower border, NSL-MLI Fig.Intermolar angle, MOLs-MOLi Fig.

Shapeof lower border, IllfLI-}dL2 Fig.Inclination of symphysis, CTL-NSL Fig.

The ourregressionquationsregivenwith thetion that they relate to a sampleof extremecases:

Index IGOLNSL-MLI

MOLs-MOLi

ML1-ML2

CTL-NSL

63.6"

75.8"35.9'

r73.6") 4 0

87.4"

6.4"

6.7'8.2"

5 .60

l.80

12.2"



INOEX INDEXMOLs-MOLi


Fig. 9. The fraction R'?) f the variabilityn the observedman-

dibulargroMh rotation, xplained y each of the our ndepen-

dent variablesalone.

INDEXIVOLs-l\4OLiML 1ML 2

INDEXMOLs-[rOLiML 1 ML 2CTL -NSL

8. The fraction R'z) f the variabilityn the observedman-

grovvthotation, xplained y (a) ndex alone, b) ndex

in combinationwith one variable, c) two independent ari-

, and (d) three ndependent ariables.

0.28(MOLs-MOLi)

0.64 MLl-ML2)

75.6- 0.59 ndex -

0.32(MOLs-MoLi)

0.98MLI-ML2) +

0.ls (cTL-NsL)

R 2 : 0.8149

R'? 0.8612

A bivariate scatterplot of the dependentvariable

the best ndependentvariable, Index I, is shown

Severalcombinationsof variableshave been com-

puted. Many of the variables could replace each other,

as hey are strongly correlated.A replacementoflndex

I with NSL-ML1 had the following equation:

18.3+ 0.44 NSL-ML1)

0.29(MOLs-MOLi)

0.94(MLI-ML2) +

0.14 CTL-NSL)

R2 : 0.8201

The observedand the predicted values of the man-

dibular rotation are llustratedgraphically in Figs. 1 to

13 for each of the twenty-one cases.

In all forward-rotation cases the direction of the

growth rotation was predicted correctly. Of the two

backward-rotatingcases Cases2and 4), the direction

DEGREES

Y = 2 9 .2 -0 .5 5NDEX:

o

I

o&

5

65

INDEX I

Fig.10.Thebivariatecatterplotf hedependentariableer-

sus hebest ndependentariable,ndex.

of rotation waspredictedcorrectly only when two vari-

ables n Case2 (Fig. 12) and threevariables n Case4

(Fig. 13) were combined.

Prediction of the amount of rotation was generally

improved by addition of variables. By Index I alone(Fig. 11), the difference between he observed and the

predicted values was 3.7o, on an average, for all

twenty-onecases,with a range rom 0.6' to 6.T, not

taking into account whether the predicted value was

higher or lower than the observedvalue. With the use

of all four variables n combination (Fig. 14), the aver-

MOLS- MOLi



366 Skieller, Bjdrk, and Linde-Hansen

NSL-tPLi A_ c

5'

4

3

2

l

o- 1

- 2

- 3

- 7

- 8

- 9

- 1 0

- 1 5

- 1 6

-1 7

Fig. 11. The observedand predicted aluesof the mandibulargrowth otation n each of the twenty-one ases,using ndexalone or prediction.

NSL-tPLi a_ c

Fig.12.Theobservedndpredictedalues f themandibulargrowthotationneach f he wenty-oneases, singndex n

combinationith heangleMOLs-MOLiorprediction.

age difference betweenthe observedand the predictedvaluesdecreasedo 1.3o,with a range rom 0o o 3.6..The prediction was very precise, with a difference ofless han 0.5'in Cases1, 5, 6, 8, 16 , 18, and 19. Agreaterdifference than 2.5owas observed n Cases 3,12, 14, and 17. In more than half of the cases theprediction was progressively improved with the in-

Fig. 13.The observedand predicted aluesof the mandibulargrovvthotationn eachof he wenty-one ases,using ndex ncombinationwith the angles MOLs-MOL|and ML1-ML2 ororediction.

20 cAsEs

- OBSERVEO--. ' - -- tsHEUIUlEU

INDEX +

MOLSMOLI

L4L1ML 2 +

CT L NS L

R2 .8 6

Fig. 14.The observedand predicted aluesof the mandibulargroMh rotationneachof the wenty-one ases,using ndex ncombinationwith he anglesMOLs-MOL|,ML1-ML2, nd CTL-

NSL or orediction.

crease of variables, but it varied inconsistently in

others.

It is of interest to compare the growth tracingsof

the casesdescribed n l972with the graphs n Figs. 11

to 14. In Case 3, for instance,where all signsof an

extreme forward growth rotation were pronounced, he

predictedrotation was overestimated. n Case 12 with

NSL- tPLi a_ c

s'

3

2

1

o- l

- 3

- 5

- 6

- 7

- 9

- 1 0

- 12

- 1 5

- 1 7

Am- J. Orthod.

November 1954

20 CASES

UGgo

4z

tr

6

o

zzIF

Fotr

INDEX +

lilOLs-N.4OLi+

ML l ML 2

Bz= .8 1

3

2

1

0- 1

$ - a6 - sz ^

z

tr

- 1 0

- 1 1

- 1 4

- 1 5

- 1 6

_ 1 7

5"

3

2

1

0

- 1

- 2

@ -

U6 - 4U -

z ^

zo - 7

F - e

H - e- 1 0

- 14

- 1 5

- 17

N S L - t P L i a_ c



Volume865


Fig. 15.Reproductionf Case14 rom he descriptionf the wenty-oneases iven y Bjdrkand

Skieller. ls

an extreme malocclusion, prediction was underesti-

mated, possibly because the predicting signs were

influencedby dysfunction.

The greatest orward rotation of. 14.4'was observed

in Case1a Gig. 15). By Index alone, herotationwas

oredictedto I3.T forward. In combination with the

secondvariable, the prediction improved to 13.6o,and

it improved to 13.9" forward when the third variable

was included. With all four variables combined, the

prediction,however, decreased o 12.8'forward, prob-

ably becauseof the high correlation betweenthe first

and the fourth variables.

The case showing the greatestobserved backward

rotationof 5.3" (Case2) is seen n Fig. 16. Index I

alone gave a prediction of 0.9' forward, indicating a

small forward insteadof backward rotation. However,

the direction of a backward growth rotation was cor-

rectly predicted n the continuedanalysis.With the use

of two variables in combination, the predicted valuewas 2.0o backward; with three variables together, it

was 2.7o; and finally, when all four variables were in-

cluded, t was 3.6obackward.

The other casesmight be studied n the sameway.

DtscussloN

When a sample nvolves many extremevariations,

the biologic relations may be easier o find. However,

it may imply that the conelations found will give an

over- or underestimate of the actual magnitude of the

relations.

In other words, the high level ofprediction reached

in this study by the four variables in combination may

be explainedby the fact thatthis sample ncludedmore

caseswith exfteme growth patternsand severemaloc-

clusions than a random sample. A certain reservation

may therefore be made on the magnitude of the mul-

tivariate regression coefficients. The multivariate sta-

tistical analysis, however, has given an indication of

significant morphologic features to be observed clini-

cally in caseswith extrememandibular growth rotation

and has made it easier to understand the interaction

between different morphologic features. In children

with a more normal growth pattern, these features in

many casesmay be less developed.

By a univariale regression analysis, twenty out of

forty-four morphologic variables from the first stagewere found at a significant level to contribute to the

variability of the mandibular growth rotation taking

place over the pubertal period in a selected sample

(Table I). The prognosticationof these twenty mor-

phologic variables varied bet*een23Vo and62Vo. All

variableswere more or less correlated.By thestepwise

regressionprocedure, a combination of four variables

was found to increase he prognostication o a level of



368 Skieller, Bjdrk, and Linde-Hansen

Fig. 16. Reproduction f Case 2 from the description f the twenty-one ases given by BjcirkandSkieller. ts

Am. J. Orthod.November l9U

o

Fig.17.Molarnclination.hangen nclinationf he owerfirstmolarn orwardotationa) andinbackwardotationb) ot themandible.See ig . .)

86Vo n this sample. This level did not increasesig-nificantly by further increasing he numberof combinedvariables.

The nclination of the mandible,expressed y IndexI or by alternative variables GOL or NSL-MLI,

allgave he samepredictionvalues,nearly fiVoby auni-variate regressionanalysis. Thus, around 4AVoof thevariability of the observed rotation was still unex-plained.This implies that themandibular nclination inrelation to the anterior cranial base at a given devel-opmentalstagemay be consideredas a morphogeneticfeature which only to a moderate degree reflects theactual growth rotation pattern of the mandible. Thisfinding s illustratedby Fig. 19.

Obviously, it wasnecessary o search or variables

Fig.18.Shape f he ower order f hemandibleharacterrz.ing orward a/andbackwardb)growthotation.SeeFig.6.)

which, apart from the mandibular inclination, couldexplain as much as possibleof the residual variabilityof the growth rotation. That the intermolar angleMOLs-MOLi (Fig. 5) was essential for the purpose

of prediction is in accordancewith the observation hatthe intermolar angle tendsto increase n forward rota-tion of the mandible and decreasewhen the rotation isdirected backward (Fig. l7). The change in the inrer-molar angle during growth is even more distinct inbackward-rotatingcaseswhere eruption of the molarsoften is impeded.

For prediction, the importanceof the shapeof thelower border of the mandible, expressedby the angleMLl-ML2 (Fig. 6), is obviouswhenone s looking at a

mandibulargrowth tracing,as n Fig. 15. The apposi



t/olwne86

Nunber5

Prediction of mandibular growth rotatio,n 369

Fig. 20. Lower ace height.Fonvardgrowth otationof themandible ithnormalncisal cclusiona) andwithdeepover-biteand reducedower aceheightb). Backwardrowth ota-tion c) with ncreasbdoweraceheight nd ,doublechin.,,

d

Fig. 9. nclinationf hesymphysis.orward rov,/thotationfthemandiblea andb) characterizedy retroclinationf thesymphysis,rrespectivef small a) or great b) mandibularinclination.ackwardgrowthrotation c) characterizedyproclinationf hesymphysisndgreatnclinationt ne man-dible., Pathologicorm. SeeFigs. and7. )

tion below the anterior part of the m"andiblewas great

becausef the extreme forward rotation, giving rise toaconvex hape f the ower anteriorborder Fig. 18, a).

In contrast,this appositionanteriorly at the lower bor-der does not take place in backward rotation of themandible,as in Fig. 16, resulting in an almost linearshape f the anterior ower border (Fig. 18, b) . Fur-thermore, n backward-rotatingcases he shapeof thelower border of the mandible is characterizedby ap-positionbelow the angularpart, resulting in a convexshape, specially n pathologiccases Fig. 19,d) .

The inclination of the mandibularsymphysis,mea-suredas the angle betweenthe tangent to the anteriorsurfaceof the mandible and the anterior cranial base(Fig. 7), is an important feature in prognosticationofrotationof the mandible in view of the fact that this

surfacenormally is practically free from remodeling,exceptwhen alveolar prognathism is increasedor re-duced.However, the determinationof the nclination ofthesymphysis n extremebackward-rotatingcasesmaybe biasedby apposition at the anterior surface of thechin, occurring especially in associationwith aberrantcondylargrowth.l7 Significant correlationswith the in-clinationof thesymphysiswerenot obtainedwhen mea-suredelative to the occlusalplaneof the owerjaw or tothemandibular border.

Fig, 21. Mean values and ranges orponents.

- 1 4

o

* - ' o

the three rotationcom-

The four selectedvariableswhich, in combination,

gave the highest evel ofprediction confirm the clinicalobservationsdescribedby Bjrirk2o n 1969. Commonfor the variablesnot discussedn Table I was a more orless strongcorrelation with the mandibular inclination:the aw angle, the thicknessof the symphysis,the incli-nation of the Y axis, the inclination of the lower in-cisorsto MI-2, and he ower faceheightrepresented yIndex IV. Whether the Y axis defined by Rickettswould yield correlationsdifferent from the y axis usedin the presentstudy cannotbe inferred from the present



370 Skieller,Bjbrk, and Linde-Hansen

study. Because of its topographic position, a facialdiagonal, it is presumed o give the same nformationabout mandibular growth rotation as the Y axis. Thelower face height is, to someextent, dependenton theincisalocclusion Fig.20,b). An evaluation f sizeand

shape of the condylar head was not included in thisstudy.

The mandibular growth rotation is composed of a

complex system of movements. In a recent report byBjcirk and Skiellerl?the bony mandibularcorpus and ts

soft-tissuecovering, the matrix, have beenconsidered

as independent issue systemscapableof independent

rotation. Both forward and backward rotation was di-vided into three components: otal rotation, referring tothe rotation of the mandibular corpus (implant line orreference ine) relative to the anteriorcranial base..ma-trix rotation, referring to the rotation of the soft-tissue

matrix of the mandible (tangential ine to lower man-

dibular border) relative to tle anteriorcranial base; andintramatrix rotation, referring to the rotation of the

mandibular corpus within its soft-tissuematrix (or thedifference between reference lines), expressing theamount of remodeling at the lower border of the man-

dible. Analyzed from longitudinal samples, the total

rotation, which is the sum of matrix and inftamatrixrotation, generally showeda steady ncreasewith age,

forward or backward, dependenton the case. The ma-

trix rotation, on the contrary, displayed a pendulum

movement, forward or backward, in the sameperson

during development. The inframatrix rotation, like the

total rotation, increased steadily during growth, butwith fluctuations counteracting the pendulum move-

ments of the matrix.

In the presentstudy the observedmandibular rota-tion is a total rotation by definition. In this sample(Fig. 2l) the matrix rotation comprised,on an average,nearly one thfud of the total rotation and the intramatrixrotation around wo thirds, both with rangesabout 507o

of that for the total rotation. The four morphologicfeatures discussedabove in relation to prediction areundoubtedly influenced by both the matrix and theintramatrix rotation components, the shape of thelower border of the mandible apparentlymainly by the

latter.As pointed out before, our statisticalanalysis wasbasedon a sample hat included severalexfreme cases.In a normal sample moderate otation may be difficultto classify according to the discussedeatures or pre-diction of mandibulargrowth. However, if one or moreof these featuresare strongly developed n individualcases, hey indicate that an extreme growth rotation ofthe mandible s going on.

REFERENCES1. Bj<irk A, Palling M: Adolescent age changes in sagittal

relation, alveolar prognathy, and incisal inclination.

Odontol Scand 12: 2nLn2. 1.954.

2. Meredith HV: Selectedanatomic variables analyzed or inter.

relationshipsof the size-size, size-gain, and gain-gain v

In Lipsitt LP, Spiler CC (editon): Advances in childment and behavior, New York, 1965, Academic Press, Inc.vol. 2, pp. 221-256.Hixon EH: hediction of facial growth. Trans Eur Orthod442 127-139. 1968.

4. JohnstonLE: A simplified approach o prediction. Au J67:253-257. 1975.

5. Mills JRE: Principles and practice of orthodontics, Edinbureh

1982, Churchill Livingstone.

6. Johnston LE: A statistical evaluation of cephalometric

tion. Angle Orthod 38: 284-304,1968.

7. Bhatia SN, Wright GW, Irighton BC; A proposedmultimodel for prediction of facial growth. Arrl J ORTHoD25:

28r,1979.8. Lavergne J: Morphogenetic classification of malocclusion as

basis or growth prediction and treafinentplanning. Br J9z 132-145. 1982.

9. Ricketts RM: The value of cephalometrics and

technology. Angle Orthod 42t 1'79-199, 1972.

10. Ricketts RM, Roth RH, ChaconasSJ, Schulhof RI, EnselOrthodontic diagnosis and planning, 1982, Rocky

Data Systems.

11. GreenbergLZ, JohnstonLE: Computerized prediction: The accuracy of a contemporary long-range forecast. ArraJ Onrnoo

243-252. 1975.

12. Schulhof RJ, Bagha L: A statistical evaluation of the Ricketts

and Johnston growth-forecasting methods. Ar'r J Onrnoo 67:

258-276.975.13. Witt E, Kdran I: Unrersuchungur Validitiit der

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l o .

14. Bjom-J6rgensen J: TIOPS: total interceptive orthodontic

ning system. Copenhagen,1983, Odontological Bookshop.

Bjrirk A, Skieller V: Facial development and tooth eruprion: an

implant study at the age of puberty. Au J Onrnon 622 339-383,

r972.Bjtirk A, Skieller V: Postnatal growth and developmentof the

maxillary complex, Monograph No. 6, Craniofacial Growth

Series,Ann Arbor, 1976,Center or Human Growth and Devel-

opment, University of Michigan, pp. 61-99.

Bj6rk A, Skieller V: Normal and abnormal growth of the man'

dible: a synthesisof longitudinal cephalometric implant studies

over a period of 25 yean. Eur J Orthod 5: 1-46, 1983.

Ban A, GoodnightJ, Sall J, Helwig J: A user's guide to SAS 76,

Raleigh, 1976, Sparks Press.

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edgewiseappliances.St. Louis, 1972,T:he C. V. Mosby Con'pany, vol. 1.

20. Bjcirk A: hediction of mandibular growth rotation. Art J

ORTHoD 5: 585-599, 1969.

Reprint requests o:

Dr. Vibeke Skieller

Institute of Orthodontics

Royal Dental College

160 Jagtvej DK-2100

Copenhagen0, Denmark

1 1

18.

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