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Transcript of 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.)'
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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
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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
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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
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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
Prediction of mandibular growth rotation 363
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-
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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"
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INOEX INDEXMOLs-MOLi
Prediction of mandibular growth rotation 365
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
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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
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Volume865
Prediction of mandibular growth rotation 367
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
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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
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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
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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.
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Reprint requests o:
Dr. Vibeke Skieller
Institute of Orthodontics
Royal Dental College
160 Jagtvej DK-2100
Copenhagen0, Denmark
1 1
18.