Growth Patterns in Subjects With Long and Short Faces

8/2/2019 Growth Patterns in Subjects With Long and Short Faces

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Growth pa t te rns in subjects w i th long and shor t facesSurender K . Nanda , DMD, MSAnn Arbor, MichiganThe pu rpose o f t h i s s tudy w as t o asses s ske le ta l fac to r s a ssoc ia ted w i t h t he d eve lopm en t o f ve r t ica lf ac ia l d i sp ropo r t ions . A ngu la r mea su reme n ts based on l ong i t ud ina l la te ra l cepha lome t r i c r ad iog raphso f 16 m a le and 16 f ema le sub jec ts , fr om the age s o f 4 t h rough 18 yea rs , w e re used . S ub jec t s w e rese lec ted on t he bas i s o f low e r f ace he igh t (A N S -Me) as a pe rcen tage o f m o rpho log i c face he igh t(N -Me) . A s i ng le x - ray pho tog raph a t age 15 f o r t he boys and 13 .5 f o r t he g i r l s w as u sed to c l ass i fyeach sub jec t 's o cc lus ion as e i t he r open -b i t e o r deep -b it e . S e l l a -nas ion /pa la ta l p lane ,se l i a -nas ion /m and ibu la r p l ane , se l l a -nas ion /ana tom ic occ lusa l p l ane , pa la ta l p l ane /m and ibu la rp lane, and c ra n ia l base an g le were a na lyze d s ta t is t ica l ly and grap h ica l ly . I t wa s foun d tha t (1 ) w i ththe exce p t i on o f se l la -nas ion /pa la ta l p l ane and c ran ia l base ang les , a l l angu la r measu rem en tsdem ons t ra ted a p rog ress i ve reduc t i on t h rougho u t deve lopm en t i n bo th open b i t es and deep b i tes ; ( 2 )t he pa la tom and ibu la r ang le d i sc rim ina ted be tw een op en b i t es and deep b i t es t h rougho u t t hedeve lopm en ta l phase ; ( 3 ) w i t h i n each sex , t ypo log i c d if f e rences w e re ev iden t i n a l l angu la rmea su remen ts , w i t h t he excep t i on o f c ran ia l base and occ lusa l p lane ; and (4 ) t he c ran ia l base ang ledem ons t ra ted c l ea r sexua l d imo rph i sm, a nd i t s mag n i t ude w as no t assoc ia ted w i t h ve r ti ca l dysp las ia .The p rog ress i ve reduc t ion o f ang les i n ske le ta l open b it e r educed o r m a in ta i ned t he magn i t ude o ft he imba lances , w h i l e t he reduc t i on o f ang les accen tua ted t he ske le ta l deep b i t e w i th age . T heinc l ina t i on o f t he pa la ta l p l ane and i t s cons tancy sugges ted t ha t dow nw ard a nd backw a rd ro ta ti on o ft he m and ib le i n open b i t e sub jec ts i s p recom mi t t ed i n r esponse to den toa l veo la r compensa to r ychang es w i t h t he cen te r o f r o ta ti on a t the mo la r s . The m agn i t ude o f t he m and ibu la r p l ane ang le i sno t adequa te f o r a ssessm en t o f d i agnos t i c o r p rognos t ic p red i c ti ve va lue i n de te rmin ing t he pa t t e rno f g row th . (AMJ ORTHOD DENTOFACORTHOP 1990;98:247-58.)

T h e t w o m o s t c o m m o n t y p es o f v e r ti c al f a-c i a l dysp l a s i a a re gene ra l l y de f ined a s hype rd ive rgen tand hyp od ive rgen t , '2 SchendeP desc r ibed t he fo rmera s " long face syndrome"; Opdebeeck 4 named the l a t t e r"shor t f a ce syndrom e ." As t he names sugges t , t he hy-pe rd ive rgen t " l ong face" i s cha rac t e ri z ed by a t endencytoward a r e l a t i ve ly l a rge l ower f ace , com pared wi th t hehypod ive rgen t "shor t f a ce . "An ea r l ie r s t udy ,5 e s t ab l ished t ha t t he comp onen t so f an t e r io r f a c i a l he igh t have d ive rgen t pa t te rns o f ske l -e t a l deve lopment i n open b i t e ( l ong- face ) and deep b i t e(short - face) , whi le those of poster ior fac ia l he ight dono t . The d i f f e rences be tween the se two ex t remes o ffac ia l he ight ra ise the possibi l i ty tha t there a lso ma y berecogn izab le r e l a t ionsh ips be tw een the pos i t ions o f t hefour basic hor izonta l c raniofac ia l p lanes (crania l base ,pa la ta l p lane , occ lusa l p lane , and mandibular plane) inopen-bi te and deep-bi te faces.As noted by severa l invest iga tors , the hor izonta lfac ia l p lanes tend to be steeper and more divergent inpersons wi th la rge lower face he ight (open bi te ) thanF rom the Depar tment of On!hodonti c s and P edia t r i c Dent i s t ry , Unive rs i ty ofMichigan S chool of Dent i s t ry8 l 1 15265

i n deep-b it e sub j ec t s wi th sm a l l l ower f ace he igh t whosefacial plane s are m ore p arallel .6-,0 Several inve stigatio nshave conf i rmed tha t t he i nc rea sed ang l e o f t he man d ib -u l a r p lane com mo nly found in pe r sons wi th l ong face sis associa ted wi th a backward rota t ional growth pa t te rntha t can affec t the ver t ica l proport ions of the anter iorcom pon ent of the face . 3 .4 .n '2z Indee d, i t has been as-sumed by ma ny inves t i ga to r s tha t ex tr eme va lue s o f t hemandibular plane angle are prognost ic c r i te r ia for pre-d i c t i ng t he d imens ions , p ropor t i ons , and d i r ec t i on o ffac ia l growthJ H owe ver , Baum rind e t a l . 2~ and Skie l le rand Bj r rk 24 sugges t ed t ha t a h igh mand ibu l a r p l aneang le i s no t a good p red i c to r o f f a c i a l g rowth and t ha tpe r sons wi th h igh mand ibu l a r p l ane ang l e s c an havebo th backward and fo rward mand ibu l a r g rowth pa t -te rns.

Num erous i nves t i ga to r s have a l so i nd i ca ted t ha t anobtuse gon ia l angle i s associa ted wi th ske le ta l open bi te ,whi le a re la t ive ly smal l angle i s associa ted wi th deepbite. 3`4"8.n '16.tg"2: 'z5"29 How eve r , B j r rk 6 d id no t f i nd t hegonia l angle to be a discr iminat ing fac tor be tw een thetwo ve r t i c a l ex t remes o f f a c i a l type . En low 3'3~ ar ri ve da t a d i f f e ren t conc lus ion conce rn ing t he r e l a ti onsh ip o fgonia l angle to upper face and crania l base ; he con-tended tha t the gonia l angle und ergoes a counterrota t ion

2 47


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2 4 8 N an da Am. J. Orthod. Dentofac. Orthop.September 1990T a b l e IA . C ompar i s on o f lower fa ce he igh t a s a pe rcen tage o f to t a l an te r io r f a ce he igh t fo r open-b i t e andde ep-b i t e s ub jec t s (mea n age : f e ma le s , 13 yea rs 6 mon ths ; ma le s , 15 yea rs )

Facial lTpe Mean (%) I Range(% ) Me an(% ) I Range(% )Open bite 60.65 59.48-63.24 59.67 57.62-62.03Deep bite 53.61 52.34-54.92 53.27 48.27-55.45

LFHITAFH*(Males)I S D (% 1

1.21.3

LFHITAFH(Females)I S D (% )

2.41.2

*LPH, Lower facial height; TAFH, total anterior facial height.

Tab l e lB . C ompar i s on o f mea n va lue s fo r lower fa ce he igh t a s a pe rcen tage o f to t a l an te r io r f a ce he igh t ins tud ie s by o the r re s ea rche rs

I Fields and associates Subte/ny and Sakuda [Facial type (%) (%) [ Hapak (%)Open bite 58.0 58.5 58.0Normal 56.0 55.1 --Deep bite 54.0 - - --

d u r i n g f a c i a l g r o w t h t o c o m p e n s a t e f o r t h e b a c k w a r dro ta t ion o f the ma nd ib le , r e s u l t ing in a re duc t ion o f theg o n i a l a n g le w i t h a g e . O n t h e o t h e r h a n d , B j f r k a n dSk ie l l e r32 repor t ed tha t r a ma l inc l ina t ion does no tc ha nge bu t ma in ta ins a cons tan t r e l a t ions h ip w i th them a n d i b u l a r c o r p u s d u r i n g g r o w t h .

Wi th rega rd to the pa la t a l p l ane , s eve ra l i nves t i -ga to rs have no ted tha t t he pos te r io r ha l f o f the pa la t et e n d s t o b e t i p p e d d o w n w a r d i n p e r s o n s w i t h o p e nbi te , 3 .4.7 ,9 .t9 carr ying the mo lars dow nw ard. W ith pos-t e r io r t e e th ac t ing a s a fu l c rum, the re i s a ba ckwardro ta t ion o f the mand ib le and , cons eque n t ly , t he loweran te r io r f a ce he igh t and the pa la tomand ibu la r ang le in -c re a s e . How e ve r , Sub te lny and Sa kud a , t~ E l li s andM c Nam ara , 29 and C a ng ia los F fou nd tha t t he pa la t a lp la ne a ng le i s c ompa rab le in open-b i t e and de ep -b i t efac e s . La rge pa la toma nd ibu la r a ng le s a re o f t en a s s o -c ia t ed w i th open b i t e and wi th exce s s ive lowe r an te r io rfa ce he ig ht . 9'~'~6"22"33"34 In an ea rli er stu dy , ho w ev er ,Nah oum ~5 repor t ed no rm a l pa la tom a nd ibu la r ang le s ins ub je c t s w i th open-b i t e .

Wi th re s pec t to the oc c lus a l p l ane , F i s h e t a l . , ~sSchend e l e t a l . , 3 and El l i s a nd M c Nam ara , 29 repor t eds te e pe r oc c lus a l p l a ne s in ind iv idua l s w i th ope n b i t e ,w h i l e n o d e m o n s t r a b l e d i f f e r e n c e s in t h e m a x i l l a ry o c -c l u sa l p l a n e w e r e o b s e r v e d b y N a h o u m a n d H o r o w i t z , 28E l l is a n d M c N a m a r a , 29 a n d C a n g i a l o s i f

Seve ra l i nves t iga to r s have s ugges ted tha t l a rge r c ra -n ia l ba s e ang le s and the co r re s pond ing pos i t iona l de -v ia t ions o f the mand ib le 6,8,9.3 are asso ciate d wi th op enb i t e . Thes e s tud ie s con te nd ed tha t the c ra n ia l ba s e a ng le

i s a key fac to r in in f luenc ing fac ia l t ype . Howeve r ,Sub te ln y and Saku da ~4 repor t ed no s ign i f i c an t d i f fe r -ence in the c ran ia l ba s e ang le be tween the no rma l ando p e n - b i t e g r o u p .

I t i s ev iden t f rom the p rev ious s tud ie s tha t s ome o ft h e m o r p h o l o g i c c h a r a c t er i s ti c s o f t h e f a c e m a y b e d e -penden t on the inc l ina t ion o f the fou r ho r i zon ta l p l anes .A l l o f the p re v ious ly repor t ed s tud ie s a re cross-sect ionaland dea l w i th preado lescen t o r postadolescent agegroups . T he re a re s t il l i n s u f f i c ien t da ta conce rn ing theb a s ic d i f f e r e n c e s b e t w e e n " o p e n - b i t e " a n d " d e e p - b i t e "p a t te r n s o f d e v e l o p m e n t .

T h e p u r p o s e o f t h i s s t u d y i s t o e x a m i n e t h e d i s -p lacemen t o f the max i l l a and the mand ib le re l a t ive tothe c ran ia l ba s e du r ing g ro wth o f pa t i en t s w i th ex t remeve r t i c a l f a c i a l p ropor t ion s . B y loo k ing a t fou r ho r i zon ta lp lanes in a c epha lome t r i c s tudy o f two ca re fu l ly s e -l e c t ed s ample s o f bo th long face and s ho r t f a ce s yn -d r o m e , w e w e r e a b l e t o i d e n t i fy m e a s u r a b le d i f f e r e n c e sb e t w e e n t h e t w o e x t r e m e v e r t i ca l f ac i a l ty p e s . W e b e -l i eve the ana lys i s o f chang ing fo rm and p ropor t ionscou ld have c l in i ca l imp l i ca t ions fo r o r thodon t i c d i ag -nos i s , t r e a tmen t p l ann ing , p rognos i s , and the s t ab i l i t yo f t r e a tmen t re s u l t s w i th re s pec t to changes in ve r t i c a lfac ia l fo rm.M A T E R I A L A N D M E T H O D S

L o n g i t u d i n a l c e p h a l o g r a m s o f g r o w i n g c h i l d r e nw e r e g a t h e r e d u n d e r t h e a u s p i c e s o f t h e C h i l d R e s e a r c hC oun c i l i n D enve r , C o lo ra do . 8 A l l s ub jec t s we re w h i t ea n d h a d r e c e i v e d n o o r t h o d o n t i c t re a t m e n t . F r o m a s a m -


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Volume 98Number 3 G r o w t h p a t t e r n s h i s u b j e c t s w i t h l o n g a n d s h o r t f a c e s 2 4 9

~ a l a ta l P l a n e

lomical, ,so l P lane

C e p h a l o m e t r i cMeasure Six ,a r P l a n e

Fig. 1. Cephalometr ic landm arks and planes used to const ruct six angular measurem ents a nalyzedin study.

p l e o f 2 5 0 y o u n g p e r s o n s , o n l y 3 2 s u b j e c t s w e r es e l e c t e d - - s i x t e e n m a l e a n d s i x t e e n f e m a l e . T h e d a t aus ed in th i s s tudy cove red a pe r iod f rom age 3 th rough20 yea rs . M os t o f the s e s ub jec t s had to be e l imina tedbeca us e o f mis s ing annua l l a t e ra l r ad iog raphs o r r e c -o rds cove r ing a n age ra nge o f l e s s than 4 to 18y e a r s .

The re s u l t ing s ubs ample was , i n tu rn , pa r t i t i onedi n to f o u r g r o u p s a c c o r d i n g t o g e n d e r a n d o p e n - b i t e a n ddeep-b i t e f a c i a l fo rms . The s e l ec t ion o f the s e s ub jec t swas ba s ed on s ke le t a l r e l a t ions h ips , w i thou t r e fe renceto c l in i ca l e va lua t ion o f the i r occ lus ions . D i f fe ren t i a t ionbe tween open b i t e and dee p b i t e was ba s ed on re l a t ivel o w e r f a c e h e i g h t ( A N S - M e ) a s a p e r c e n t a g e o f m o r -p h o l o g i c f a c e h e i g h t ( N a - M e ) . T h e l o w e r f a c e h e i g h tp r o p o r t i o n s o f t h e s u b j e c ts w e r e d e t e r m i n e d a t a p p r o x -ima te ly 15 yea rs o f age fo r boy s and 13 ye a rs 6 mon thso f a g e f o r g ir l s. T h e u s e o f t h e s e a g e s f o r s a m p l e s e -l e c ti o n w a s b a s e d o n t h e r e c o g n i z e d se x u a l d i m o r p h i s min the t iming o f de ve lop men t . 3537

T h e p u r p o s e o f t h i s s e l e ct i o n p r o ce s s w a s t o m a x -imiz e the s e l ec t ion o f s ub jec t s f rom the ends o f thecon t inuum o f fa c ia l he igh t s to be t t e r con t ra s t and in -s pec t d i f fe re nc es and s imi la r i t i e s be tween face s w i ths ke le t a l open b i t e a nd deep b i t e .

T h e p e r c e n t a g e o f l o w e r f a c e h e i g h t v a l u e s f o r t h es ub je c t s in th i s s tudy exc e eds the va lue s de te rmin ed bys eve ra l i nves t iga to r s fo r cha rac te r i z ing s ub jec t s w i ths ke le t a l open b i t e and deep b i t e (Tab le s IA and

I B ). 13"14'21 S e r i a l c e p h a l o m e t r i c r o e n t g e n o g r a m s f r o mthe s e l ec ted ind iv idua l s we re t r a ced , and l andm arks andp lanes we re then ob ta ined acco rd ing to the de s c r ip t ionb y K r o g m a n a n d S a s s o u n i ) s

Fro m an ana lys i s o f the l i t e ratu re , i t was a s ce r t a inedtha t s ix s pec i f i c c epha lome t r i c angu la r meas u remen t swere the be s t c r i t e r i a fo r iden t i fy ing s ub jec t s w i th ve r -t i c a l dys p la s i a . S ix angu la r meas u rem en t s (F ig . 1 ) we r ereco rded :

1 . Se l l a -na s ion to pa la t a l p l ane ang le (S-N toA N S - P N S )

2 . Se l l a -na s ion to man d ibu la r p l ane ang le (S-N tom a n d i b u l a r p l a n e )

3 . G o n i a l an g l e ( a r ti c u l a r e - g o n i o n - m e n t o n ) ( T h ep o s i ti o n o f g o n i o n w a s d e t e r m i n e d t h r o u g h b i -s ec t ion o f the ang le fo rmed by the t angen t s tot h e l o w e r b o r d e r o f t h e m a n d i b l e o r m a n d i b u l a rp l a n e a n d t h e p o s t e r i o r b o r d e r o f t h e r a m u s o rr a m a l p l a n e . )

4 . P a l a t o m a n d i b u l a r a n g l e ( A N S - P N S t o m a n d i b -u la r p l ane )

5 . Se l l a -na s ion to ana tomic occ lus a l p l ane ang le(S-N to a l i ne b i s ec t ing the ove rb i t e o f the in -c i s o rs and the in t e rcus pa t ion o f mo la r s )

6 . C ran ia l ba s e ang le (N-S-B a )Data ana lys is

Graph ic and s t a t i s t i c a l me thods we re us ed to cha r -a c t e ri z e e a c h s a m p l e . A b s o l u t e c u r v e s o f g r o w t h w e r e


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2 5 0 N a n d a Am. J. Orthod. Dentofac. Ortbop.September 1990

I0de g ~ o~Deep8 ~ Deep

n . 6.z " - . / " " - ,. ~ ,~ - ~ ._ < ~ - ~ / ~ . . . . ~ Opent , . O , , . . . . . ~ - - = ~4 ~ " " - - - ~ / ~ " - - ~ - ' - o ~O p e

/2 .I I I I I I I

4 6 8 I0 12 14 16 18a g e i n y e a r s

Fig. 2. Comparison of mean absolute curves of growth for pal -atal p lane incl inat ion for four groups, seg regated b y facial type.

3 8deg.3 63 43 23 0 i

28

- ~ ~ ' - ' - - ~ ~ . . . . 9 Open~ ' ~ - ~ " ' 0 " 0 p en

~ O ' O e e pI I I I I I I~ D e e p4 6 8 I0 12 I4 16 18a g e i n ye o r s

F i g . 3 . C o m p a r i s o n o f m e a n a b s o l u te c u r v e s o f g ro w t h f o r m a n -d i b u l a r p l a n e a n g l e f o r s e x a n d f a c i a l t y p e s . T h e m a n d i b u l a rp l a n e a n g l e d e c r e a s e d s t e a d i l y w i t h a g e i n a l l t h e f o u r g r o u p s .G r a p h i c a l l y , t h e r e i s a s u g g e s t i o n o f d i f f e r e n c e i n f a c i a l f o r mb e t w e e n o p e n - b i te a n d d e e p - b i t e g ro u p s , w i t h t h e a n g l e o f t h em a n d i b u l a r p l a n e s m a l l e r i n d e e p - b i t e g r o u p s .

d e r i v e d f o r e a c h o f t h e s ix a n g u l a r m e a s u r e m e n t s f o reach o f t h e fo u r g ro u p s . F o r t h o se su b j ec t s o n wh o md ata a t a p a r t i cu l a r ag e was mi ss in g , a p o ly n o mia lr e g r e s s i o n w a s c a l c u l a t e d f o r e a c h o f t he s i x m e a s u r e -men t s t o o b t a in i n t e rp o l a t ed an n u a l i n c remen t s .

Year ly ab so lu t e v a lu es fo r each o f t h e s i x an g u l a rm e a s u r e m e n t s w e r e c a l c u l a t e d f o r e a c h g r o u p a t e a c ha g e b e t w e e n 4 a n d 1 7 y e a r s . A n a l y s e s o f v a r i a n c e w e r ep er fo rme d t o t e s t f o r t h e o v era l l e f f ec t s o f ag e , v e r t i ca lp ro p o r t i o n s (o p en b i t e o r d eep b i t e ) , s ex , an d t h e i n -t e r ac t i o n o f t h ese f ac to r s . S t a t i s ti ca l co mp ar i so n s w erem a d e b e t w e e n o p e n - b i t e a n d d e e p - b i te g r o u p s f o r s a m -p l e s f r o m b o t h m a l e a n d f e m a l e p a t i e nt s . T h e o r t ho g -o n a l co n t r as t s b e tween o p en b i t e s an d d eep b i t e s i nm a l e s a n d f e m a l e s w e r e d e t e r m i n e d . T h e l e v e l o f s i g -n i f i c a n c e f o r e a c h c o m p a r i s o n w a s d e t e r m i n e d a t a na lp h a l ev e l o f 0 .0 5 . T h e F t e s t , w i th t h e Bo n fe r ro n ip r o c e d u r e f o r p a i rw i s e c o m p a r i s o n o f e a c h s a m p l e a t

o

130 -d e g . |

\ \ \I z c - " ~ . ~ , .~ . ~ ~ . -, % .. .. ._

1 1 5 - ~ D e e p"N \6-0=I10 I I I ] I I I I4 6 8 I0 12 14 16 18age in years

Fig. 4. Comparison of mean absolute curves for gonial angleby sex and fac ia l type . The gon ia l ang le p rogress ive ly de-creased in al l four groups. The four curves are segregated bysex until the a doles cen t spurt eliminates sexually related dif-ferences.

d e g l - ~3 2 [ . - ~ . ~ .

F ~ - - ~ ' ~ " ~ " - - - ~ ~ ,---- 0 ' O pe n

~ 2420 _

/ I I I I t I I I4 6 8 I0 12 14 16 18a g e i n y e o r sFig. 5. The mean absolute curves of growth of the palatoman-dibular p lane angle for open bi te and deep bi te are cle ar ly seg-regated by facial type, e l iminat ing sexual d imorphism.

each ag e (4 t o 1 7 y ea r s ) , was ap p l i ed t o d e t e rmin e t h es i g n if i c a nc e o f d i f f e r e n c e b e t w e e n t h e m e a n v a l u e s .R E S U L T S

A b s o l u t e m e a n g r o w t h c u r v e s f o r e a c h a n g u l a r m e a -su rem en t w ere p lo t t ed fo r th e ag es o f 4 t o 1 8 y ea r s toev a lu a t e t h e as so c i a t i o n b e tween ag e an d p a t t e rn s o ff ac i a l g ro wth i n su b j ec t s wi th o p en b i t e an d t h o se wi thd eep b i t e (F ig s . 2 t o 7 ) . Th i s ap p ro ach r ev ea l ed su b -s t an t ia l v a r i a t i o n amo n g t h e fo u r g ro u p s , d e mo n s t r a t i n gth a t ce r t a i n an g l es were co n s i s t en t l y l a rg e r o r smal l e r ,b ased o n sex an d f ac i a l t y p e .S e l l a - n a s i o n t o p a l a t a l p l a n e a n g l e ( T a b l e I I , Fig . 2 )

D i f f e r e n c e s i n m e a n p a l a t a l p la n e a n g l e w e r e c l e a r l yev id en t b e tween t h e two f ac i a l t y p es , i r r e sp ec t i v e o f


5/12

Volume 98Number 3134deg.13 2

o 13CcO12 812 6

- - _ ~ . . . . . . . ~ D e e p

~Deepf--~"' ~Open

- l/1 I I I I I I I4 6 8 I0 12 14 16 18a g e i n y e a r s

F i g . 6 . C o m p a r i s o n o f m e a n a b s o l u t e c u r v e s o f g r o w t h f o r o p e nb i t e a n d d e e p b i t e b y s e x a n d f a c i a l t y p e . T h e f o u r c u r v e s a r ec l u s t e r e d , a n d t h e c o n c o r d a n c e i n d i c a te s t h a t t h e i n c l i n a ti o n o fo c c l u s a l p l a n e i s s i m i l a r a n d n o n d i s c r i m i n a t o r y .

G r o w t h p a t t e r n s in s u b j e c t s w i t h l o n g a t zd s h o r t f a c e s 2 5 1

22deg2Oo 1 812.IZ)Z 16

1412

~ - . . ~ Open~ ~ D e ~I I I I t I I I4 6 8 IO 12 14 16 18a g e i n y e a r s

F i g . 7. C o m p a r i s o n o f m e a n a b s o l u t e c u r v e s o f c r a n i a l b a s ea n g l e b y s e x a n d f a c i a l t y p e . T h e c u r v e s a r e s e g r e g a t e d b ys e x . i t i s i n te r e s t i n g t o n o t e t h a t t h e f e m a l e g r o u p s h a v e h i g h e rv a l u e s t h a n m a l e s , a n d s u g g e s t i n g t h a t th e r e a r e n o d i f f e r e n c e si n f a c i a l f o r m w i t h i n e a c h s e x .

T a b l e I I. D e s c r i p t i v e s t a t i s ti c s o n t h e a b s o l u t e v a l u e s ( i n d e g r e e s ) o f p a l a t a l p l a n e i n c l i n a t i o n i n s u b j e c t sf r o m 4 t o 1 7 y e a r s o f a g e f o r f o u r g r o u p s - - B o n f e r r o n i t e s t o f d i f f e r e n c e s in s i g n i f i c an c e ( p v a l u e s )b e t w e e n o p e n - b i t e a n d d e e p - b i t e g r o u p s

Male F e maleOpe n b i t e De e p b i t e Ope n b i t e De e p b i t e

O 'r ) Me an SD Me an SD p v a lue s Me an SD Me an SD4 2.62 2.81 8.15 2.67 0.002* 5.34 4.8 5.71 3.745 3.65 2.61 9.08 4.11 0 .005* 5.53 3.97 6.22 3.356 4.18 3.74 8.47 2.19 0.01 4' 5.27 3.81 6.59 3.167 4.16 3.64 8.97 2.76 0.009* 4.78 4.10 7.31 3.228 3.91 3.73 8.47 1.28 0.008* 5.50 4.37 8.16 2.559 3,89 4.0 9.06 2.02 0.005* 4.87 4.58 7.98 2.5510 4.98 4.33 8.73 1.16 0.038* 4.72 4.76 8.63 2.2311 4.66 3.94 8.92 1.23 0.018* 4.71 4.86 8.51 2.2812 4.45 3.99 8.87 ! .43 0.011" 5.11 4.43 8.87 2.1713 4.66 4.07 8.57 1.40 0.026* 4.94 4.65 8.68 2.0114 4.59 4.60 8.90 1.55 0.017" 4.80 4.38 8.93 2.0215 4.14 4.58 9.04 2.30 0.009* 5.10 4.45 8.73 1.8916 3.93 4.97 9.50 2.13 0 .005" 4.90 4.55 8.70 2.0017 3.88 4.73 9.06 2 .06 0.006* 5.00 4 .15 8.70 2.32

p r a lue s0.8290.7000.4270.1550.1090.0820.031"0.033*0.028*0.032*0.022*0.049*0,048*0.044*

*p < 0.05.

s e x . D e e p - b i t e s u b j e c t s o f b o t h s e x e s h a d l a r g e r a n g l e sa t ea c h c h r o n o l o g i c a g e , w i t h t h e v a l u e s f o r t h e f e m a l eo p e n - b i t e s u b j e c ts a c t u a l l y e x c e e d i n g t h o s e f o r t h e m a l eo p e n - b i t e s u b j e c t s a t 4 y e a r s o f a g e . B y 1 0 y e a r s o fa g e , t h e m a l e o p e n - b i t e c u r v e a p p r o x i m a t e d t h e f e m a l eo p e n - b i t e c u r v e .

A l t h o u g h t h e s e l l a -n a s i o n t o p a l a ta l p l an e a n g l e s o ft h e tw o f e m a l e g r o u p s w e r e a p p r o x i m a t e l y e q u a l a t a g e4 , t h e d e e p - b i t e g r o u p s h o w e d a s i g n i f i ca n t in c r e a s e( p < 0 . 0 3 ) i n th i s a n g l e a t a g e 7 . T h e p a l a t a l p l a n e

a n g l e i n c r e a s e d s i g n i f i c a n t l y ( p < 0 . 0 2 ) i n th e m a l ed e e p - b i t e g r o u p i n c o m p a r i s o n w i t h th a t o f t h e m a l eo p e n - b i t e s u b j e c t s a t 1 0 y e a r s o f a g e . T h e p a l a t a l p l a n ea n g l e d i d n o t s h o w a n y f u r t h e r s i g n if i c a n t d i f f e r e n c e sa c r o s s a g e b e t w e e n o p e n - b i t e a n d d e e p - b i t e g r o u p sa c r o s s th e a g e r a n g e o r b e t w e e n s e x e s a f t er 1 0 y e a r s o fa g e . T h i s l a c k o f d i f f e r e n c e s u g g e s t s t h a t t h e re w e r em i n i m a l c h a n g e s i n t h e i n c l i n a t i o n o f t h e p a l a ta l p l a n e .T h e B o n f e r r o n i t e s t fu r t h e r s u p p o r t e d t h e i n t e r p r e t a t io n so f t h e g r a p h i c d a t a t h a t d i f f e r e n c e s b e t w e e n f a c i a l t y p e s


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2 5 2 Nanda Am. J. Orthod. Dentofac. Orthop.September1990Table I l l. Des c r ip t ive s t a t i s ti c s on the ab s o lu te v a lue s ( in deg ree s ) o f the m and ibu la r p l ane in s ub jec t s f r om4 to 17 yea rs o f age fo r fou r g roups . B onfe r ron i t e s t o f d i f fe rences in s ign i f i c ance (p va lue s ) be tweeno p e n - b i t e a n d d e e p - b i t e g r o u p s

Male FemaleOpen bite Deep biteeep bite Open bite

SD I Mean ] SD2.31 36.28 3.92

AgeO'r) Mean SD p vahtesD Mean p vahtes Mean4 35.56 3.79 34.59 0.634 31.05 5.52 0.015"5 35.92 4.21 33.37 2.38 0.236 35.77 4.03 31.00 5.59 0.0315"6 35.75 4.42 33.35 2.65 0.262 35.76 3.61 30.98 5.52 0.030*7 34.93 4.84 32.17 2.91 0.232 35.41 3.93 30.72 5.86 0.047*8 35.04 4.62 31.97 2.93 0.179 35.23 3.86 30.81 5.86 0.056*9 34.52 4.50 31.50 2.76 0.174 34.87 3.60 31.02 5.86 0.087

10 34.77 4.11 30.78 3.00 0.075 34.70 3.84 30.83 5.80 0.08311 34.70 4.56 30.98 3.23 0.104 34.25 3.99 31.10 5.60 0.16512 34.09 4.23 30.59 2.83 0.115 34.01 4.25 30.63 5.47 0.12713 34.41 4.93 30.60 2.74 O. 1 0 34.00 4. i 2 30.87 6.03 0.18614 34.29 5.91 29.70 3.13 0.059 34.02 4.28 30.03 5.49 0.09915 33.51 4.93 29.77 3.32 0.112 33.69 4.19 29.62 5.54 0.08516 32.75 5.29 29.37 3.32 0.162 33.51 4.50 29.35 5.41 0.08717 33.04 5.22 28.75 3.62 0.074 33.34 4.13 28.84 5.32 0.060

*p < 0.05.

w i th in ea c h s ex (ma le s ke le t a l open-b i t e ve r s us ma les ke le t a l deep -b i t e , f ema le s ke le t a l open-b i t e ve r s us fe -ma le s ke le t a l dee p -b i t e ) we re s ign i f i c an t f rom 4 to 17y e a r s o f a g e f o r t h e m a l e g r o u p s a n d f r o m 1 0 t o 1 7yea rs fo r the fema le s ub jec t s .S e l l a -n a s i o n t o m a n d i b u l a r p l a n e a n g l e (Table Ill,F i g . 3 )

T h e r e l a t i v e p o s i t i o n s o f t h e f o u r c u r v e s f o r t h emea n man d ibu la r p l ane ang le re p re s e n t a d i rec t r e ve rs a lf rom the o rde r fo r the mea n pa la t a l p l ane ang le . Thecurve s a re c l e a r ly s e g rega ted a cc o rd ing to fa c ia l t ypef r o m 4 t o 1 8 y e a r s o f a g e , w i t h t h e m a g n i t u d e o f t h emand ibu la r p l ane ang le be ing l a rge r in bo th open-b i t eg r o u p s i n c o m p a r i s o n w i t h t h at o f t h e d e e p - b i t e g r o u p s .H o w e v e r , t h e c h a n g e i n t h e m a n d i b u l a r p l a n e a n g l e d i dno t s how a ny s ign i f i c an t d i f fe re nc e in e i the r the ma leo r t h e f e m a l e s a m p l e s e x c e p t t h a t t h e f e m a l e d e e p - b i t eg roup was s ign i f i c a n t ly d i f fe ren t f rom the open-b i t eg roup a t 4 to 8 ye a rs o f age (Ta b le I I I ) .

T h e m a n d i b u l a r p l a n e a n g l e d e c r e a s e d p r o g r e s s iv e l yt h r o u g h o u t t h e p e r i o d o f s t u d y ; h o w e v e r , t h e m a l e d e e p -b i t e g r o u p e x h i b i t e d a n a c c e l e r a t e d r a t e o f d e c r e a s ef rom 4 to 10 ye a rs . The rea f t e r , t he dec rea s e wa s c om-pa ra b le w i th tha t fo r the fema le dee p -b i t e s ub je c t s . Th ere duc t ion in the mand ibu la r p l ane ang le was s ign i f i -c an t ly d i f fe re n t fo r the ma le d eep -b i t e s ub je c t s a t 5 yea rs

(p < 0 . 01 ) , 10 yea rs (p < 0 . 02 ) , and 15 yea rs o f age( p < 0 . 0 4 ) .G o n i a l a n g l e ( T a b l e IV , F i g . 4 )

B o t h o p e n a n d d e e p - b i t e g r o u p s d e m o n s t r a te d a t e n -d e n c y t o w a r d p r o g r e s s i v e d e c r ea s e i n m e a n g o n i a l a n g l ef rom 4 to 18 yea rs o f age , w i th a re s u l t an t up r igh t ingo f t h e r e m u s . T h e d i f f e r e n c e i n t h e d e c r e a s e in t h eg o n i a l a n g l e b e t w e e n d e e p - b i t e an d o p e n - b i t e m a l e s u b -j ec t s was s ign i f i can t at 5 yea rs (p < 0 . 02 ) and 7 yea rso f a g e ( p < 0 . 0 4 ) .P a l a t o m a n d i b u l a r a n g l e (T a b l e V , F ig . 5 )

T h e m e a n c u r v e s f o r t h e p a l a t o m a n d i b u l a r a n g l erevea led c l ea r -cu t and h igh ly s ign i f i c an t d i f fe ren ces be -tween fac ia l t ypes in bo th ma le and fema le s ample sth roughou t the en t i re s tudy pe r iod . Thes e d i f fe rencesw e r e s o p r o n o u n c e d t h a t t h e f e m a l e o p e n - b i t e v a l u e se x c e e d e d t h e c o r r e s p o n d i n g v a l u e s f o r m a l e d e e p - b i t es ub jec t s and revea led a s exua l d imorph i s m in the pa l -a t o m a n d i b u l a r a n g l e. T h e m a g n i t u d e o f d e c r e a s e i n t h ep a l a t o m a n d i b u l ar a n g l e w a s r e m a r k a b l y c o n s i s t e n t b e -t w e e n s k e l e t a l o p e n - b i t e a n d d e e p - b i t e c u r v e s f r o m 4to 18 yea rs . Th e changes in the pa la toma nd ibu la r ang lewere s ign i f i c an t fo r bo th fac ia l t ypes w i th in eachs ex (ma le p < 0 . 0 2 , f ema le p < 0 . 01 ) a t 14 yea rso f a g e .


7/12

Volume 98Number 3 G r o w t h p a t t e r n s i n su b j e c t s w i t h l o n g a n d s h o r t f a c e s 2 5 3

Tab l e I V. D e s c r i p t i v e s t a t is t i c s o n th e a b s o l u t e v a l u e s ( i n d e g r e e s ) o f t h e g e n i a l a n g l e i n s u b j e c t s f r o m 4 t o1 7 y e a r s o f a g e f o r f o u r g r o u p s : B o n f e r r o n i t e s t o f d i f f e r e n c e s i n s i g n i f i c a n c e ( p v a l u e s ) b e t w e e n o p e n - b i t ea n d d e e p - b i t e g r o u p s

Age(yr)

Open biteMale

Open biteeep bi te

4 .734 .093 .984 ,734 . 1 64 . 4 75 . 3 44 . 7 33 .835 .165 .135 .135 .365 .35

Female

IMean I SD Mean p values M ean SD Mean4 123.88 4.61 122.02 0.513 125.32 4.39 123.075 125.40 5.71 121.61 0.176 124.56 4125 122.096 124.13 5.79 120.75 0.213 124.41 3.92 120.617 124.63 6.54 119.34 0.075 122.89 3.99 119.818 122.37 6.59 118.44 0.201 121.88 5.19 118.289 121.67 7.02 116.44 0.085 122.06 4.19 117.41

10 120.55 7.38 116.55 0.221 121.80 4.53 116.9011 119.62 7.25 115.79 0.223 121.05 3.86 115.8112 119.71 7.37 116.11 0.253 119.80 3.62 114.7913 120.09 2.83 116.30 0.273 119.41 4.10 114.5014 118.45 7.88 114.92 0.291 118.83 3.68 114.4415 117.07 7.71 114.04 0.357 118.04 4.13 114.8416 116.44 7.04 113.69 0.415 117.77 4.12 114.6617 114.76 8.60 111.44 0.365 117.37 4.36 114.96

Deep bi te

I , o7 .937.216 .887 ,087 ,497 .097 .727 .798 .367 .878.318.089 ,059 .35

p vahtes0 . 4 2 90 . 3 7 50 . 1 6 30 . 2 9 00 . 2 4 00 .1230 . 1 3 60 . 0 9 00 .1150 , 1 5 80 . 1 9 00 .3330 . 3 5 70 . 5 1 0

Tab l e V . D e s c r i p t i v e s t a t i s t ic s o n t h e a b s o l u t e v a l u e s ( i n d e g r e e s ) o f t h e p a l a t o - m a n d i b u ! a r p l a n e a n g l e i ns u b j e c t s f r o m 4 t o 1 7 y e a r s o f a g e f o r f o u r g r o u p s : B o n f e r r o n i t e s t o f d i f f e r e n c e s i n s i g n i f i c a n c e ( p v a l u e s )b e t w e e n o p e n - b i t e a n d d e e p - b i t e g r o u p s

Male FemaleOpen bite Dee p bite Open bite Deep bi te

Iyr) Mean SD I IMean SD ] p values Mean SD Mean ] SD p values4 32 .93 2 .06 26 .19 1 .48 0 .0000" 30 .98 2 .46 25 .33 3 .54 0 .0001 " "5 32 .27 2 .55 24 .10 4 ,23 0 .0001" 20 .21 2 .83 24 .79 4 ,15 0 .0040*6 31 .56 3 .00 24 .60 2 .61 0 .0003 * 30 .38 3 .19 24 .37 4 .33 0 .00 13"7 30 .77 3 .13 23 .20 3 ,10 0 .0005* 30 .59 3 .53 23 .40 5 .25 0 .0009*8 31 .12 2 .54 23 .30 3 .16 0 .0002* 29 .85 3 .66 22 .64 5 .00 0 .0006*9 30 .62 2 .88 22 .56 3 .43 0 .0004* 30 .00 3 .92 23 .03 5 .43 0 .0018"

10 29 .78 3 .63 21 .99 3 .84 0 .0007* 29 .97 3 .57 22 .07 5 .07 0 .0006*11 30 .03 3 ,71 21 .86 3 .88 0 .0004* 29 .53 3 .60 22 .58 4 .86 0 .00 19"12 29 .63 3 .64 21 .71 3 .95 0 .0007* 28 .85 3 .59 21 .51 5 .15 0 .0014 "13 29 .75 3 .83 22 .02 3 .53 0 .0009* 29 .02 3 .87 22 .18 5 .22 0 .0028*14 29 .70 4 .13 20 .85 4 .39 0 .0003* 29 .15 4 .02 21 .09 4 .81 0 .0009*15 29 .22 4 .24 20 .74 5 ,24 0 .0010 " 28 .62 3 .88 20 .88 4 .96 0 .0023*16 28 .56 3 ,94 19 .79 5 ,03 0 .0006* 28 .69 3 .94 20 .63 5 .05 0 .001 3"17 29 .15 3 .66 19 .68 4 .79 0 .0001" 29 .39 3 .62 20 .14 4 .74 0 .0006*

*p < 0 .05 .

S e l l a - n a s i o n t o o c c l u s a l p l a n e a n g l e ( T a b l e V I ,F ig . 6 )

I n c o n t r a s t t o t h e g r o w t h c u r v e s f o r t h e palatal planea n g l e , t h e m a n d i b u l a r p l a n e a n g l e , a n d t h e g e n i a l a n g l e ,

t h e g r o w t h c u r v e s f o r t h e o c c l u sa l p l a n e a n g l e w e r ec o n f l u e n t a n d c o u l d n o t b e d i s c r i m i n a t e d e i t h e r b y s e xo r f a ci a l ty p e . F o r b o t h s e x e s , t h e o c c l u s a l p l a n e a n g l es h o w e d n o s i g n i f i ca n t d i f fe r e n c e s ( T a b l e V I ) t h r o u g h o u t


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2 5 4 N an da Am. J. Orthod. Dentofac. Orthop.September1990T a b l e Vl. Descr ipt ive sta t i s t ics on the absolute va lues ( in degrees) of the occ lusa l p lane in subjec ts f rom4 to I7 y ea r s o f age fo r fou r g roups : Bon fe r ron i te s t o f d i f f e rences i n s i gn i fi c ance (p va lue s ) be tweenopen-b i t e and deep-b i t e g roups

Open biteAgeO'r) Mean

Male FemaleDeep bite Open bite Deep bite

] SD Mean I SD p va lues Mean SD Mean I SD4 18.56 3.62 19.68 3.03 0.702 19.75 3.73 17.96 9.90 0.5435 18.04 3.04 18.79 2.13 0,755 19.60 4.69 17.43 7.40 0.3696 18.25 3.52 18.70 2.47 0.820 19.46 4.09 17.22 5.35 0.2727 18.17 4.01 18.63 2.44 0.822 19.34 3.97 17.58 5.32 0,3938 18.88 4.20 20.78 5.42 0.406 19.48 4.46 19.19 3.81 0.8999 17.96 3.60 19.25 2.46 0.471 18.93 3.84 19.35 4.01 0.813

10 19.48 3.23 17.03 1.54 0.167 19.12 3.67 19.78 4.14 0.70411 19.46 3.33 17.97 2,67 0.380 18.78 3.52 18.95 3.72 0.91712 19.24 4.61 17.68 2.40 0.410 18.19 4.08 18.79 3.54 0.75413 17,73 4.35 17.68 2,07 0.977 18.17 3.28 18.00 3.77 0.91814 17.45 4.8 0 16.74 2.41 0.703 17.26 3.56 17.68 3.73 0.82415 16.37 4.52 16.90 3.08 0.774 17.19 3.11 16.63 3.72 0.76116 15.37 4.53 15.51 3.31 0.937 16.31 3.40 16.22 3.16 0.96017 13.89 4.79 15.50 3.55 0.417 16.24 2.97 15.77 4.04 0.810

p values

t he pe r iod o f s t udy . By the age o f approx ima te ly 10yea r s t he dece l e ra t i on r a t e s fo r t he four cu rves we recomparab l e . The changes i n t he occ lusa l p l ane ang l ewere s i gn i fi c an t fo r t he ma le open-b i t e and deep-b i t egroups a t 10 years (p < 0 .002 ) , a t 13 years (p < 0 .04)and a t 15 yea r s (p < 0 .05) , bu t a t 15 yea r s o f age t hecurves w e re t i gh t l y c lus t e red , and t hey t ended t o l eve lo f f a t 18 yea r s o f age .C r a n i a l b a s e a n g l e ( T a b l e V I I, F ig . 7 )

The c ran i a l ba se ang l e show ed no s ign i f ic an t d i f -f e rence be tween open-b i t e and deep-b i t e g roups fo r e i -t he r sex ; howeve r , t he cu rves fo r ma le and fema legroups we re s i gn i f ic an t ly d i f f e ren t a t eve ry age i n t e rva l(Tab le VI I I ) . The va lue s fo r t he f ema le g roup exceededthe co r re spond ing va lue s fo r ma le sub j ec t s th rough ou tthe study per iod. A s igni f icant chang e in the crania lba se ang l e was obse rved a t 5 yea r s (p < 0 .003) , a swas a r educ t ion i n t he ang l e a t 17 yea r s o f age(p < 0 .05) fo r the ma le open-b it e g roup .D I S C U S S I O N

The pa ra ll e l na tu re s o f l ong i tud ina l g rowth cu rvesfor the pa la ta l p lane inc l ina t ion in the open-bi te anddeep-bi te faces c lear ly demonst ra te tha t anteroposter iorinc l ina t ion of the pa la ta l p lane i s s table , despi te s ig-ni f icant ver t ica l d isplaceme nt , and tha t i t i s establ i shedat an ear ly age . This f inding i s consistent wi th previ -ous ly r epor t ed st ud ies . 31,32,39

Thi s s t udy a l so sugg es t s t ha t t he i nc l ina t i on o f t he

pa l a ta l p l ane i s s i gn i f i c an t ly d i f f e ren t be tween open-b i t e and deep-b i t e f a ce s t h roughou t comparab l e phase so f deve lopment , r ega rd l e ss o f sex . Pa l a tomand ibu l a rinc l ina t ion in the ske le ta l open-bi te and deep-bi teg roups w as a l so s i gn i f i can t ly d i f f e ren t be tween the twofac i a l t ypes t h roughou t deve lopment and ma y have evenmasked any e f fec t s o f sexua l d imorph i sm.

On the o the r hand , t he magn i tude o f t he gon ia l ang leand the i nc l i na t i ons o f t he occ lusa l and mand ibu l a rp l anes w e re n o t s i gn i f i c an t ly d i f f e ren t be tween the twoex t reme ve r t i c a l dysp l a s i a s i n e i t he r sex . Dur ing t hecomparab l e phase s o f deve lopment howeve r , the man-d ibu l a r p l ane , t he occ lusa l p l ane , and t he gon ia l ang l es t ead i ly dec rea sed i n bo th ske l e ta l open-b i t e and deep-b i t e sub jec t s f rom 4 t o 18 yea r s o f age . The dec rea sewas l e a s t in t he m and ibu l a r p l ane ang l e and g rea t e s t i nthe gon ia l ang l e , w i th t he occ lusal p l ane occupy ing anin t e rmed ia t e pos i t i on .The re su l ts o f t h i s s t udy i nd i ca t e tha t t he ex t en t o fin f luence o f pa l a t a l p l ane i nc l ina t i on on l ow er an t e r io rface he igh t i s de t e rmined by i ts geom e t r i c r el a t ionsh ipswi th ex i s t i ng bones . For examp le , i n open-b i t e sub j ec ts ,t he pa l a t a l p l ane i s t i pped down pos t e r iody , r e su l t i ngin t he max i l l a ry mola r s be ing l oca t ed i n a more i n fe r io rpos i t i on . Wi th t h i s pos i t i on , t he mola r s may ac t a s afu l c rum wi th t he mand ibu l a r t e e th , r e su l t i ng i n t he po-s i t iona l ro t a t i on d i scussed by Lave rgne and Gasso n , 4the ma t r i x ro t a t ion s tud i ed by B j r rk and Sk ie l l e r ,4t andthe dis placem ent rota t ion descr ibed by Enlow . 3~ Thiscond i t i on may a l so con t r i bu t e cons ide rab ly t o l ower


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Volume98Number 3 G r o w t h p a t t e r n s i n s u b j e c t s w i t h l o n g a n d s h o r t f a c e s 2 5 5

Tab le VI I. Descr ip t ive s ta t i s t ics on the a bso lu te va lues ( in deg rees ) o f the c r an ia l base ang le o f sub jec tsf rom 4 to 17 year s o f age in fou r g roups : B on fer ron i tes t o f d i f f e r ences in s ign i f icance (17 va lues ) be twee nopen -b i te and deep -b i te g roups

Male

A ge(yr) Mean

FemaleOpen bi te Deep bi te Open bi te Deep bi te

I SD Mean l SD p values Mean l SD M e a n l S D p values4 126.25 5.64 129,21 6.02 0.224 133.64 3.50 132.29 3.26 0.5765 127.68 5.13 129.19 5.56 0.504 133.60 3,44 132.32 3.32 0.5706 128.44 4.09 129.66 4.78 0.549 133.23 3.79 132.60 3.34 0.7577 128.49 4.08 129.49 6.14 0.672 133.28 3.47 133.24 3.79 0.9868 128.28 4.48 128.75 5,05 0.822 133.04 3.55 133.07 3.23 0.9869 128.45 5.11 129.38 6.26 0.702 132.63 3.37 133.23 3.96 0.802

10 129.62 7.02 129.37 6.10 0.926 133.03 3.88 133.27 3.72 0.92811 129.06 5.43 129.42 4.95 0.873 132.82 3.70 133.70 3.62 0.69912 129.27 5.38 129.43 5.05 0.947 133.48 3.97 133.36 3.66 0.95513 129.20 5.17 129.58 5,21 0.870 133.18 4.09 133.50 3.42 0.80714 129.60 5.61 129.42 5.63 0.943 132.88 4.38 133.14 4.09 0.91615 129.16 4.71 129.89 5.62 0.760 133.17 4.50 133.28 3.95 0.96216 129.19 5.01 129.93 5.34 0.759 132.90 4,73 133.23 4.08 0.89417 128.56 4.94 130.19 6.18 0.526 132.67 4.61 133.03 4,32 0.889

an te r io r f ace he igh t and he lp increase the mand ibu la rp lane ang le . S ince the observed inc l ina t ion o f the pa l-a ta l p lane and i t s p ropo r t ion r emain cons tan t w i th age ,d o w n w a r d a n d b a c k w a r d r o t a t i o n o f t h e m a n d i b l e i nopen -b i te sub jec ts m ay be p recomm it ted in r esponse tod e n t o a lv e o l a r c o m p e n s a t o r y c h a n g e s .B h a t i a ,42 in h i s e xp lana t ion o f the r educ t ion o f ma n-d ibu la r p lane and pa la tomand ibu la r p lane ang les in along i tud ina l s tudy , a r r ives a t a qu i te d i f f e r en t conc lu -s ion concern ing the r e la t ionsh ip o f the ang le be tweenthe pa la ta l and mand ibu la r p lanes . H e s ta tes tha t thepa la ta l p lane tip s down ward an te r io r ly , wh i le the m an-d ibu la r p lane t ip s downw ard a t the back . ( I t shou ld beno ted tha t the pa la ta l p lane ang le was no t spec i f ica l lymeasu red wi th r espec t to a r e f e r ence p lane . )Even equ a l den toa lve o la r g rowth in bo th open -b i teand deep -b i te f aces can ha ve d i f f e r en t imp l ica t ions fo rthe f ina l ou tcom e o f f ac ia l g rowth . T he p r ima ry de te r -mina n t o f lower an te r io r f ace he igh t i s the spa t ia l con -f igu ra t ion o f the pa la ta l p lane w i th i ts ad jacen t bone s ,wh i le mand ibu la r ro ta t ion i s secondary to the ex is t inginc l ina t ion o f the max i l la . I t mus t be r ecogn ized tha tt h e m a x i l l a r y c o m p l e x i s w e d g e d b e t w e e n t h e c r a n ia lb a s e a n d t h e m a n d i b l e . I n t e rp o s e d b e t w e e n t h e b o n e so f t h e u p p e r a n d l o w e r j a w s a r e t h e a l v e o la r b o n e a n dtee th . The m o lar s a r e the f i rs t t ee th to come in con tac twi th each o ther and , as a r esu l t , the r emain ing an te r io rtee th e rup t ver t ica l ly to main ta in con tac t w i th the op -pos ing tee th , thus con t r ibu t ing to the change in theinc l ina t ion o f the occ lu sa l p lane . Any decrease in the

Tab le VI II . Or thogona l con t r as t s be tw een thesexes w i th r espec t to c r an ia l base ang le

Age O'r) I p alues4 0.004*5 0.007*6 0.011"7 0.015'8 0.004*9 0.025*

10 0.064II 0.017"12 0.017'13 0.020*14 0.050*15 0.035*16 0.049*17 0.062

*p < 0.05.

gon ia l ang le o r increase in r amal he igh t i s p robab lycomp ensa t ion fo r d en toa lveo la r g rowth , a~

An a l te rna t ive hypo thes i s o f f e r ed here to exp la inthe ro ta t ion o f the man d ib le i s tha t ver t ica l ly d ivergen tf ac ia l fo rms a r e the r esu l t o f d i sp ropo r tiona te d i sp lace-men t o f the pa la ta l p lane in the ver t ica l d ime ns ion andt h e r e s u lt i n g r o ta t i o n o f t h e m a n d i b le . T h e m e c h a n i s mof ad ju s tme n t in response to the ro ta t ion o f the mand ib lei s change in the gon ia l a ng le , d i f f e r en t ia l den toa lve o la rgrow th , a~ and posit ion al ro tat ion . 4


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2 5 6 Nanda Am. J. Orthod. Dentofac. Orthop.September 1990

T h e m a g n i t u d e o f t h e m a n d i b u l a r p l a n e a n g l e i so f t en a s s ume d to be a de te rminan t in the ro ta t ion pa t t e rn( f o r w a r d v e r s u s b a c k w a r d ) o b s e r v e d d u r i n g f a c i a lg rowth . Howeve r , t he d ia gnos t i c and p rognos t i c va lue so f ma nd ibu la r p l ane inc l ina t ion a re no t adequa te fo ra s s e s s me n t o f the pa t t e rn o f g row th . Th es e f ind ings a rec ons i s t en t w i th thos e re por t e d b y Sk ie l l e r a nd B j r rk 24and b y B aum r ind e t a l . 23 Th e l a rge r va lue s o f the m an-d ibu la r p l a ne a ng le in open b i t e , a s r epo r t ed in th i ss tudy , a re p roba b ly s econ da ry to the s pa t ia l o r i e n ta t ionof the pa la t a l p l ane . Th e ma nd ibu la r p l a ne i s cons ta n t lyr e m o d e l i n g , r e s u l t in g i n a p p o s i ti o n o f b o n e o n t h epos te r io r - in fe r io r pa r t o f the co rpus , w i th o r w i thou tr e m o d e l i n g a t t h e l o w e r b o r d e r o f t h e s y m p h y s i s . A f t e rs ome t ime , the gon ia l ang le i s dec rea s ing , compe ns a t -ing fo r the ve r t i c a l i nc rea s e o f the ramus and fo r thed i r e c ti o n o f c o n d y l a r g r o w t h . 4~

Th e in terpr e ta t ion by Enlo w, 3 .3t Bj /Srk an dSkie l le r , 32 and M oss 43 is tha t the gon ia l a ngle is gr ea te rin pos te r io r - in fe r io r tha n s upe r io r -pos te r io r ro t a t ions o fthe ma nd ib le . Fu r the r , i t ha s be e n repor t e d by I s aa c s o nand c ow orke rs , 2 J ens e n and Pa l l ing , 27 Sas s oun i andNand a , s Su b te lny and Sa kud a , 14 En low , 3~ and Trou tene t a l ) 9 tha t i n the ca s e o f ope n-b i t e , t he gon ia l an g leinc rea s e s . In t e re s t ing ly , t h i s s tudy re vea l s tha t t he gon -i a l a ng le doe s no t d i f fe r be twee n fa c ia l type s ; i t c on -t inues to dec rea s e p ropor t iona l ly f rom 4 to 18 ye a rs ,i r r e s pe c t ive o f the fa c ia l fo rm . Ho we ve r , the c on t inuedreduc t ion o f the gon ia l ang le and inc l ina t ion o f them a n d i b u l a r p l a n e a r e u n e q u a l , a n d t h e m a g n i t u d e o fgon ia l ang le re duc t ion i s rough ly tw ice tha t o f the man -d i b u l a r p l a n e , a s o b s e r v e d b y t h e s l op e s o f t h e i r c u r v e s .Th e inc l ina t ion o f the occ lus a l p l a ne i s ma in ta ine d un t i lt he age o f 10 yea rs in bo th open-b i t e and dee p -b i t eg roups . Af te r the a ge o f 10 yea rs the re i s a s ha rp de -c rea s e in oc c lus a l p l ane ang le .

T h e p r o b l e m , t h e n , i s to e x p l a i n t h e m e c h a n i s m o fdow nw ard inc l ina t ion o f the oc c lus a l p l ane pos te r io r ly .In the p re s en t con tex t , i t mus t be a s s umed tha t t hed i f fe ren t i a l a ppos i t ion o f bon e a t t he a ng le o f the man -d i b l e a n d t h e l o w e r b o r d e r o f t h e s y m p h y s i s , a s s h o w nby B j r rk and Sk ie l l e r , 32 re s u l t s i n a red uc t ion o f s t e ep -ne s s o f the mand ibu la r p l ane and the gon ia l ang le , w h i l et h e c o n d y l a r v e r t i c a l g r o w t h a c c o m m o d a t e s e x t e n s i v er e m o d e l i n g a t t h e a n g l e o f t h e m a n d i b l e . A l o n g w i t ht h e a b o v e - m e n t i o n e d c h a n g e s , d e n t o a l v e o l a r g r o w t ha l s o re s ponds to d i f fe ren t i a l i nc re a s e s in the a n te r io rand pos te r io r s e gmen t s o f the den ta l a rches a s a nec -e s s a r y m e c h a n i s m o f a d a p t a t i o n r e g a r d l e s s o f f a c i a lconf igu ra t ion .

The g rowth pa t t e rn o f the c ran ia l ba s e a ng le in ou rs ub jec t s demons t ra t ed no s ign i f i c an t change w i th re -s p e c t t o e i t h e r se x o r t y p o l o g y b e tw e e n t h e a g e s o f

4 a n d 1 8 y e a r s . A n u m b e r o f c o m p a r a b l e f i nd i n g srega rd ing the s t ab i l i t y o f the pa t t e rn have been re -port ed. 4449 O f part icular s ignif icanc e is the fac t th a t thec ran ia l ba s e ang le in the two fac ia l t ypes c l e a r ly dem-ons t ra t e s s exua l d imorph i s m. Th i s i s i n con t ra s t t o thef ind ings o f Kno t t ,49 wh o found no s t a t is t i c a lly s ign i f i -c an t d i f fe rence in c ran ia l ba s e ang le be tween s exes . Ina n o t h e r s t u d y S c h u l t e r : u s i n g d r y s k u l ls , o b s e r v e dpopu la t ion and s ex d i f fe rence s in the c ran ia l ba s e ang le .

B j r r k 47 demons t ra t ed the in f luence o f the c ran ia lba s e ang le and i t s a s s oc ia t ed e f fec t i n bo th s ag i t t al andve r t i c a l dys p la s i a s . I t ha s been a s s umed tha t t h i s ang lere f l e c t s the pos i t ion o f the g leno id fos s a and the t em-p o r o m a n d i b u l a r j o i n t s . T h u s , w h e n t h e a n g l e i s a c u te ,the mand ib le i s a s s umed to be in a fo rwa rd pos i t ion ;conve rs e ly , when the ang le i s ob tus e , i t i s a s s umed tha tthe mand ib le i s i n a re t ruded pos i t ion . S imi la r in t e r -p r e t at i o n s w e r e a d v a n c e d b y D e C o s t e rH an d S a s s o u n i )s ugges t ing an a s s oc ia t ion be tween a l a rge c ran ia l ba s ea n g l e a n d o p e n b i t e a n d , c o n v e r s e l y , b e t w e e n s m a l l e rc ran ia l bone an g le s and deep b i t e . Ye t , t he compa rab lep a t te r n s o f g r o w t h i n b o t h o p e n - b i t e a n d d e e p - b i t e f a c e so f bo th s exes in the p re s en t s tudy ind ica te tha t the re i sn o i n t e r a c t io n o f m a g n i t u d e o f t h e c r a n ia l b a s e a n g l ein s ub jec t s w i th ve r t i c a l dys p la s i a . Even the s ign i f i -c an t ly l a rge r magn i tude o f the ang le in fema le s ub jec t sf a i le d t o s h o w a n y e f f e c t o f t h e c r a ni a l b a s e a n g l e o nve r t i c a l dys p la s i a .

T h e s e o b s e r v a t i o n s a r e c o m p a r a b l e t o t h o s e o fKno wles , ~ wh o repor t ed tha t s ub jec t s w i th exce s s iveo r de f i c i en t mid fac ia l r eg ions had no s ign i f i c an t d i f fe r -ences in c ran ia l ba s e ang le s . B j r rk ' s 47 ra t iona le o f ro -t a t ion i s ba s ed on the s phenoocc ip i t a l s ynchondros i sand i t s e f fec t on the backward ro ta t ion o f the g leno idfos s a ; fo r example , he ma in ta ins tha t t he po in t ba s ions h i f t s pos te r io r ly , becaus e o f add i t ion o f bone a t t hes phenoocc ip i t a l s ynchondros i s . H i s a s s e r t ion i s ba s edon the a s s umpt ion tha t t he an te r io r l imb o f the c ran ia lba s e i s e s s en t i a l ly comple te a t an ea r l i e r age . In con-t ras t , Sco t t , 52 Ba er and Na nda , 53 and Co ben ~4'55 imp liedtha t ba s ion i s a s t ab le re fe ren ce po in t tha t a f fec t s fo r -w a r d a n d u p w a r d g r o w t h o f t h e a n t e r i o r c r a n ia l b a s e .C o b e n54'55 con clud ed tha t the dis tance fro m ba s ion toa r t i cu la re i s s t ab le du r ing the deve lopmen ta l p roce s s .Subs equ en t ly , C oben ss reg i s t e red on ba s ion , u s ing thean te r io r c ran ia l ba s e ( s e l l a -na s ion ) fo r s upe rpos i t ion ingto demons t ra t e d i f fe ren t c ran io fac ia l pa t te rns o f g row thd u r i n g s u c c e s si v e g r o w t h c h a n g e s .

E a c h o f t h e a b o v e c o n c e p t i o n s o f t h e r e l a t i o n sh i po f the c ran ia l ba s e to the conf igu ra t ion o f the fa ce i svu lne rab le to c r i t i c i s m, howeve r , e i the r on theo re t i c a lg rounds o r in t e rms o f con f l i c t ing da ta . In oppos i t ionto B j r rk ' s 47 con ten t ion , Nand a s6 hypo the s ized the e f fec t


11/12

Volume 9 8Number 3

Gro ,wh pa t t e rns in sub jec t s wi th long and shor t fac es 2 5 7

o f t h e c r an i a l b ase an g l e o n t h e r e l a t i v e p ro t ru s io n o rr e t ru s i o n o f t h e m a n d i b l e . T h e t e m p o r a l b o n e s a r e b i -l a t e r a l s t ru c tu res an d t h e i n f l u en ce o f t h e mid l i n e s t ru c -t u r e s m e a s u r e d i n t h e c r a ni a l b a s e a n g l e , N a n d a m a i n -t a i n e d , m a y b e d i s s i p a t e d b e f o r e t h e y i m p i n g e o n t h eg l en o id fo ssa . F u r th e r , i t i s p o ss ib l e t h a t co mp en sa to ryc h a n g e s m a y t a k e p l a c e i n t h e f o r m a n d p o s i t i o n s o ft h e t emp o ra l b o n e t h a t n eg a t e t h e i n f lu en ce o f t h e c r an i a lb a s e a n g l e . T h u s , t h e a n t e r o p o s te r i o r g r o w t h t h a t p o -s h i o n s t h e l a t e r a l e l e m e n t s o f t h e c r a n i u m m a y n o to p era t e i n t o t a l sy n ch ro n y wi th t h e mid l i n e . Ev enEn lo w 3~ co n t en d e d t h a t t h e co n v en t i o n a l c r an i a l b asean g l e i s n o t a t r u e r e f l ec t i o n o f t h e p ro t ru s iv e o r r e t ru s iv ep o s i ti o n o f t h e m a n d i b l e .

In su mmary , i t i s ev id en t t h a t n o c lo se co r r esp o n -d en ce ex i s t s b e tween t h e c r an i a l b ase an g l e an d v e r t i ca ld y sp l as i as o f th e f ace ; r a t h e r , t h e re i s a sex u a l l y r e l a t edd i f f e r en ce i n t h e mag n i tu d e o f t h e c r an i a l b ase an g l e .Th e ev id en ce su g g es t s t h a t t h e re a r e s i g n i f i can t d i f -f e r e n c e s i n t he i n c l i n a ti o n o f t h e p a l a ta l p l a n e - -p a l a t o m a n d i b u l a r a n g l e t h r o u g h o u t t h e g r o w i n g p e r i o din o p en -b i t e an d d eep -b i t e f aces . I t f u r t h e r su g g es t s t h a tt h e i n t r i ca te ch a n g in g sp a t i a l r e l a t i o n sh ip s o f t h e b o n e sin t h e d en to fac i a l s t ru c tu res a r e a fu n c t i o n o f d i f f e r en tr a t es o f g ro wth an d t h a t t h ey i n f l u en ce t h e u l t ima t ef a c i a l f o r m .

T h e d i f f e r e n c e s a m o n g c o n c e p t u a l e x p l a n a t i o n sa n d c o n c l u s i o n s r e g a r d i n g t h e m e c h a n i s m o f r o -tatio n ~m,4,41'43'576 m ay be trac ed to the sel ec tion ofd i f f e r en t su p erp o s i t i o n in g p o in t s an d c ro ss - sec t i o n a ls a m p l e s b y t h e v a r i o u s r e s e a r c h e r s . A n o t h e r p r o b l e mf req u en t l y en co u n t e red i n t h e l i t e r a tu re i s t h e l ack o fd i s t i n c t i o n b e t w e e n d i f f e r e n t f a c i a l f o r m s , w h i c h m a ym a s k t h e b a s i c p a t t e rn o f r o t a t io n o f t h e m a n d i b l e . T h ee f f e c t o f r ot a t io n p a t t e r n s o f t h e c o m p o n e n t s o f t h e f a c es h o u l d b e e x a m i n e d i n h o m o l o g o u s g r o u p s o f s i m i l a rf ace co n f ig u ra t i o n s . Th ere fo re , a d i s t i n c t i o n b e tweenp a t i en t s wi th o p en b i t e an d t h o se wi th d eep b i t e sh o u ldb e mad e wi th r esp ec t t o t h e sp a t i a l r e l a t i o n sh ip s o f t h ed i f f e r en t v e r t i ca l s eg men t s o f t h e f ace ( i . e . , l o wer an -t e r i o r f ace h e ig h t s ) .C l i n i c a l i m p l i c a t i o n s

Th e o b se rv a t i o n s r ep o r t ed i n t h i s s t u d y o n v e r t i ca lf a c i a l e x t r e m e s h a v e d i s c l o s e d f u n d a m e n t a l p o s i t i on a lr e l a t i o n sh ip s b e tween d en to fac i a l s t ru c tu res . Th e c l i n -i ca l imp l i ca t i o n s o f t h e s t u d y su g g es t t h a t , d esp i t e t h ed i sp a ra t e i n i t i a l mo rp h o lo g i e ch a rac t e r i s t i c s , ad j acen tb o n es i n t h e an a to mic s t ru c tu re u n d erg o p ro g ress iv ep o s i t i o n a l ch an g es t h ro u g h o u t d i f f e r en t p h ases o f d e -v e l o p m e n t , r e g a r d l e s s o f s e x o r f a c i a l c o n f i g u r a t i o n .Th e ev id en ce f ro m th i s s t u d y , wh ich c l as s i f i ed i n d iv id -u a l s o n t h e b a s i s o f e x t r e m e p r o p o r t io n a l v a l u e s o f l o w e r

face h e ig h t t o t o t a l f ace h e ig h t , p o in t s t o t h e f ac t t h a tt h e re a r e l a rg e i n d iv id u a l v a r i a t i o n s i n t h e p o s i t i o n a lr e l a t i o n sh ip s o f t h e h o r i zo n t a l p l an es o f t he f ace d u r in gd e v e l o p m e n t , r e g a r d le s s o f t h e n a t u r e o f v e r t ic a l d y s -p l a s i a . T h e d e c r e a s e i n m a n d i b u l a r p l a n e , p a l a t o m a n -d ib u l a r p l an e , o cc lu sa l p l an e , an d g o n i a l an g l es wi l lh av e sp ec i f i c c l i n i ca l e f f ec t s o n f ac i a l co n f ig u ra t i o n o fp a t i en t s wh o h av e sev ere v e r t i ca l d y sp l as i a . F o r ex -a m p l e , i n o p e n - b i te s u b j e c t s , t h e m a g n i t u d e o f d y s p l a s i awi l l a t t en u a t e ; o n t h e o th e r h an d , i n d eep -b i t e su b j ec t si t w i l l b e i n t en s i f i ed wi th t h e se r i e s o f v e r t i ca l ch an g e s .A s t a t i c cep h a lo m et r i c an a ly s i s o f an o r t h o d o n t ic p a t i en twi th an ad o p t ed s t an d ard b ased o n p read o l escen t o rad o l escen t ag e g ro u p s i s n o t ad eq u a t e . F u r th e r , i t i sf a l l ac io u s t o a s ses s an o r t h o d o n t i c p a t i en t ' s d en to fac i a ls t ru c tu re b y r e f e r r i n g t o p a r t i cu l a r n o rm s o f a s t ru c tu re .Ra th e r , t h ese p a r t s sh o u ld b e ev a lu a t ed b y t h e man n erin wh ich each a f f ec t s t h e mo rp h o lo g i c u n i t tO wh ich i tb e l o n g s . C o m p e n s a t o r y a d j u s t m e n t s i n o t h e r r e l a t e dp a r ts o f t he d e n t o f a c i a l c o m p l e x m a y r e d u c e , m a i n t a i n ,o r e x a g g e r a t e t h e m a g n i t u d e o f d y s p l a s i a .

Hen ce , i n c l i n i ca l s t u d i es a imed a t e s t ab l i sh in g t h ee f f i c a cy o f d e n t o f a c i a l o r t h o p e d ic m e t h o d s , t h e b a s i sf o r c o m p a r i s o n o f t r e a t m e n t e f f e c t s s h o u l d a l s o i n c l u d ea c o n s id e r a t io n o f e x p e c t e d g r o w t h c h a n g e s , b a s e d o nth e mo rp h o lo g i c t y p o lo g y o f b o th t r ea t ed an d u n t r ea t edco n t ro l s (ma t ch ed fo r t y p o lo g y , ag e , an d g en d er ) . S e -l ec t i o n o f su ccess fu l l y t rea t ed cases fo r p o s th o c an a ly s i so f t r e a t m e n t e f f e c t s i s m e t h o d o l o g i c a l l y u n s o u n d a n dl i ab l e t o b i as .REFERENCES1. Sassouni V. The fa ce in five dimensions. 2nd ed. Morgantown,West Virginia: University Press, 1962.2. Schu dy FF. V ertical grow th versus anteroposterior grow th asrelated to function and treatm ent. Angle O rthod 1964;34:75-93.3. Schendel SA, Eisenfeld J, Bell WH, E pker B. T he long facesyndrome: v erticalmaxillaryexc ess . AM J ORTHOD1976;70:398-

408.4. OpdebeeckH, Bell WH. The sho rt face syndrome. Ar, J OarnOD1978;73:499-511.5. NandaSK. Patterns of vertical growth in the fac e. A~l J OR'rHoDDE~rrOFAORTHOP1988;93:103-16.6. Bjrrk A. The face in profile: an anthropological x-ray investi-gation on Sw edish children and conscripts. SvenskTandl Tidskr1947:40. No. 5B, Suppl.7. Muller G. Gro~th and development of the middle face. J DentRes 1963;42:385-99.8. Sassouni V, N anda SK. Ana lysis of dentofacial vertical propor-tions. AM J OR~IOD 1964;50:801-23.9. SassouniV. A classificationof skeletal acial ypes. Ar~i O R'moP1969;55:109-23.10. Isaacson RJ, Zappel RJ, Worms FW, Bevis RR, Speidel TM.Effects of rotational jaw grow th on the occlusion and profile.A.,,i J OR ~OD 1977;72:276-86.1 . DeCosterL. Ope n bite. IN r J OR~O D ORALStrRG 193 6;22:912-38.


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Reprint Requests to"Dr . S ure nde r K . N a ndaT he U nive r s i ty o f M ic h iga n S c hoo l o f De n t i s t ryDe pa r tm e n t o f Or thodon t ic s a nd P e d ia t r i c De n t i s t ryA n n A r b o r , M I 4 8 1 0 9 - 1 07 8

Growth Patterns in Subjects With Long and Short Faces

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