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A longitudinal cephalometric study of transverse and vertical craniofacial growth
A longitudinal cephalometric study of transverse and vertical craniofacial growth Stephen F. Snodell, DDS, MS," Ram S. Nanda, DDS, MS, PhD, b and G. Fr~ins Currier, DDS, MSD, MEd ° Oklahoma City, Okla. Longitudinal growth changes were studied from posteroanterior cephalometric radiographs of 25 male subjects from 4 to 25 years of age and 25 female subjects from 4 to 20 years of age who had Class I skeletal and dental patterns. Growth for males continued past age18 years for all skeletal. measurements, except for maxillary width. Growth for females was completed by 17 years for all skeletal measurements. At 6 years of age the transverse measurements had a greater percentage of the adult size completed than vertical measurements for both males and females. Gender differences at age 6 years were in the mean widths for the cranium, face, and maxilla. At age 12 years the differences were in cranial width, maxillary width, and maxillary and mandibular intermolar width (6-6). There were gender differences at age 18 years for all the variables, except for nasal width and mandibular intermolar width (6-6). Regression lines provided strong-to-moderate predictive equations to determine the size of most of the measurements at age 18 years, if the value at age 6 years is known. (AMJ ORTHOD DENTOFACORTHOP 1993;104:471-83.)
Avast majority of growth studies have used lateral cephalometric radiographs to analyze changes in the vertical and the sagittal dimensions of the face. Most of the normative data have been based on sagittal aspects of dentofacial structures with the current emphasis on orthodontic diagnosis obtained from information from these films. However, evaluation also is needed in the transverse dimension for a comprehensive dentofacial evaluation. Bilateral facial asymmetries and development of the oronasal area can be better assessed from a transverse analysis of posteroanterior (P-A) cephalometric radiographs. Transverse problems, such as posterior crossbite, are a great concern to the orthodontist and have been mentioned as having great potential for relapse. 1-3Analysis of vertical components, although easily viewed from sagittal cephalometric radiographs, also cannot be fully understood without the assistance of a P-A cephalometric radiograph as bilateral vertical asymmetries can only be evaluated from a frontal view. Review of the literature on ortllodontic diagnosis provides only a sketchy treatment of transverse facial dimensions. Furthermore, facial growth studies that include the transverse component have been even fewer.
From the University of Oklahoma College of Dentistry. aFormer graduate student. bProfessor and Chairman, Department of Orthodontics. CProfessor, Department of Orthodontics. Copyright © 1993 by the American Association of Orthodontists. 0889-5406/93/$1.00 + 0.10 8/1/37218
In relation to diagnosis and treatment, the specialty has been overwhelmingly preoccupied with vertical and sagittal relationships of the dentofacial structures. Those available do not include a detailed analysis of the P-A cephalometric radiographs. This study evaluated longitudinal growth changes in the transverse and vertical dimensions for female subjects from ages 4 to 20 years and for male subjects from ages 4 to 25 years. The objectives of the study were (1) to establish norms of size and annual increments for the nine transverse and five vertical measurements for males and females, (2) to identify relationships between the various components with descriptions of any gender differences, (3) to specify patterns for individual craniofacial growth, and (4) to formulate predictive equations from age 6 to 18 years and from 12 to 18 years for each of the measurements.
MATERIALS AND METHODS This research utilized the longitudinal posteroanterior cephalometric radiographs from the growth study at the Child Research Council, University of Colorado School of Medicine. Twenty-five male and 25 female white subjects were selected on the basis of a balanced skeletal profile and Class I occlusion with the absence of crossbite, presence of only minimal clinical crowding, and no orthodontic treatment during the entire period of the study. There were a minimum of 10 P-A cephalometric radiographs between the ages of 4 and 20 years of age. Eleven of the male subjects had radiographs from the ages of 21 to 25 years that were also included. Each cephalometric radiograph was traced, and the landmarks were computer digitized. A horizontal plane was established to
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1
2 3 4
Fig. 1. Transverse measurements. 1. Cranial width (bieuryon width). 2. Facial width (bizygomatie width). 3. Nasal width (bialare width). 4. Maxillarywidth. 5. Mandibular width (bigonial width). 6,7. Maxillary intermolar width (6-6) and (7-7). 8. Mandibular intermolar width (6-6) and (7-7).
connect the bilateral points that intersected the lesser wing of the sphenoid with the medial rims of the orbits. These points were more 'easily identified than the zygomaticofrontal sutures as used by Ricketts et al. 4 The midsagittal plane used was the line that passes through points crista galli and ANS, also bisecting the medial rims of the orbits. The intersection of the horizontal and midsagittal planes was used to locate nasion. The transverse and vertical measurements used are as shown in Figs. 1 and 2. The following are the nine linear "ransverse measurements: 1. Cranial width (bieuryon width): the width of the cranium from the most lateral points on the cranium parallel to the superior aspect of the orbits. 2. Facial width (bizygomatic width): the width of the zygomatic arch from their most lateral aspect. 3. Nasal width (bialare width): the width of the nasal cavity from the most lateral points on the nasal aperture taken parallel to the horizontal plane. 4. Maxillary width: the width of the maxilla from bilateral points on the jugal process at the intersection of the outline of the tuberosity of the maxilla and the zygomatic buttress. 5. Mandibular width (bigonial width): the width of the mandible from points at the most lateral margin of the angle of the mandible. 6. Intermolar width of maxillary first molars: the width between the most lateral points on the buccal surface of the permanent maxillary first molar crown parallel to the occlusal plane. 7. Intermolar width of maxillary second molars: the width between the most lateral points on the buccal
Fig. 2. Vertical measurements. 1. Total face height. 2. Upper face height. 3, Lower face height. 4. Left ramus height. 5. Night ramus height.
surface of the maxillary permanent second molar crowns parallel to the occlusal plane. 8. Intermolar width of mandibular first molars: the width between the most lateral points on the buccal surface of the mandibular permanent first molar crowns parallel to the occlusal plane. 9. Intermolar width of mandibular second molars: the width between the most lateral points on the buccal surface of the mandibular permanent second molar crowns parallel to the occusal plane. The following are the five linear vertical measurements: 1. Total facial height (TFH): the distance between the intersection of the horizontal and midsagittal planes and the most inferior point on the outline of the mandibular symphysis through the midsagittal plane. 2. Upper face height (UFH): the distance between the intersection of the horizontal and the midsagittal planes and the tip of the anterior nasal spine just below the nasal cavity and above the hard palate. 3. Lower face height (LFH): the distance between the tip of the anterior nasal spine just below the nasal cavity and above the hard palate and the most inferior point on the outline of the mandibular symphysis through the midsagittal plane. 4. Left ramus height (LRH): the distance between the most lateral left margin of the angle of the mandible and the most superior left aspect of the condyle. 5. Right ramus height (RRH): the distance between the most lateral right margin of the angle of the mandible and the most superior right aspect of the condyle.
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::;le Fig. 3, Total increments of size of seven transverse measurements in millimeters for male and female subjects age 6 to 18 years. The number above the line is the male value, and the number below the line is the female value. Error of m e a s u r e m e n t
Fifty P-A cephalometric radiographs were retraced and redigitized 8 weeks after the first set of records were obtained. A combined error of landmark location, tracing, and digitization was determined. The mean measurement error for the transverse measurements was less than 0.50 mm, whereas the mean error for the vertical measurements was less than 0.80 ram.
One of the reasons P-A cephalometric films have not been used as extensively as the lateral cephalometric films in growth studies is the distortion that may be created by the slight movement of the head in the transverse plane, as well as the vertical plane. However, the material available for this study had a standard high quality, because the radiographs were taken in a x;ery rigid cephalostat and the same operator took the films over the length of the study. Analysis of the d a t a
The data were analyzed for growth changes in group means and growth changes at the individual level. To negate the effects of missing data on analysis, a statistical method to find the best fit line of the means, the least squares method5 was used. Least squares means, standard deviations, and minimum and maximum values were recorded for each of the variables at each age group. Least squares means and standard deviations were also calculated for the annual increments for each age group. Two different methods to calculate percent change were also determined for the means of each variable. The first method was calculated using the value at each age expressed as a proportion of the mean value at age 18 years. The second method used the percent change expressed as a proportional increase from the measurement at age 6 years,
22 1 Fig. 4. Total increments of size of five vertical measurements in millimeters for male and female subjects age 6 to 18 years. The number to the above the line is the male value, and the number below the line is the female value.
calculated for each variable at age 12 years and at age 18 years. RESULTS
The total size increments for each measurement in male and female subjects age 6 to 18 years are given in Figs. 3 and 4. The least square mean, standard deviation, and range for transverse and vertical measurements are given in Tables I and II. The percent increase from age 6 to 12 and from 6 to 18 years for each measurement are demonstrated in Fig. 5. The percent completion of adult growth at age 6 years and 90% of the sample who have attained adult size at ages 15 and 18 years are given in Table III. Measurements continuing to grow at age 18 years are also indicated. G e n d e r differences
A t test was performed for each measurement at ages 6, 12, and 18 years to determine gender differences. The p values of 0.05 or less were considered statistically significant, and a summary of p values for each variable at the three age groups is listed in Table IV. At age 6 years, the only three variables different between males and females were cranial width, facial width, and maxillary width. At age 12 years, cranial width, maxillary width, maxillary intermolar width (66), and mandibular intermolar width (6-6) were significantly different. At age 18 years, the following 12 variables were significant: cranial width, facial width, maxillary width, mandibular width, maxillary intermolar width (6-6), maxillary and mandibular intermolar
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Table I. L e a s t s q u a r e s m e a n (LS m e a n ) ,
Table II. L e a s t s q u a r e s m e a n (LS M e a n ) ,
s t a n d a r d d e v i a t i o n ( S D ) , a n d r a n g e for s e v e n t r a n s v e r s e m e a s u r e m e n t s in m i l l i m e t e r s
s t a n d a r d d e v i a t i o n ( S D ) , a n d r a n g e for five v e r t i c a l m e a s u r e m e n t s in m i l l i m e t e r s
Transverse measurement ] Cranial width Males LS mean ± SD range Females LS mean ± SD range Facial width Males LS mean ± SD range Females LS mean ± SD range Nasal width Males LS mean ± SD range Females LS mean ± SD range Maxillary width Males LS mean ± SD range Females LS mean ± SD range Mandibular width Males LS mean ± SD range Females LS mean ± SD range Maxillary intermolar width 6-6 Males LS mean ± SD range Females LS mean ± SD range Mandibular intermolar width 6-6 Males LS mean ± SD range Females LS mean ± SD range
6 years
18 years
142.88 ± 6.55 128.04-158.45 139.23 ± 4.11 131.94-146.68
150.90 ± 7.07 142.08-162.68 144.42 ± 5.02 136.67-152.53
110.82 ± 3.45 104.67-119.96 108.22 ± 3.27 99.33-113.02
134.06 ± 4.80 125.35-140.71 126.03 ± 5.68 121.66-135.71
22.93 ± 1.92 18.21-26.98 22.88 ± 1.66 19.87-26.82
30.48 ± 2.07 29.25-36.55 28.64 ± 2.49 25.56-33.68
56.12 ± 2.34 51.13-60.19 54.44 ± 1.86 51.28-59.00
66.24 ± 3.12 61.08-70.80 61.8 ± 2.97 58.67-66.88
78.43-4.42 72.48 -90.5 76.33 ± 2.77 72.37-81.14
99.36 ± 5.17 89.70-108.92 92.17 ± 3.96 84.89°96.39
53.18 ± 2.66 50.98-58.45 53.67 ± 2.58 49.13-56.79
59.46 ± 2.71 54.26-63.39 55.67 ± 1.51 54.60-59.29
56.00 ± 2.96 49.66-62.38 54.10 ± 2.17 49.45-59.84
56.12 ± 2.17 51.57-58.39 53.72 ± 1.55 52.28-56.98
w i d t h (7-7), U P H , L P H , T F H , a n d R R H a n d L R H . T h e o n l y v a r i a b l e s s h o w i n g n o statistically s i g n i f i c a n t g e n d e r d i f f e r e n c e s at a g e 18 years w e r e n a s a l w i d t h a n d m a n d i b u l a r i n t e r m o l a r w i d t h (6-6).
Individual data correlations To s t u d y t h e c o r r e l a t i o n s b e t w e e n e a c h o f the 14 measurements, Pearson correlation coefficients were c a l c u l a t e d at a g e 14 y e a r s for f e m a l e s a n d at a g e 16 years for m a l e s . T h e s e t w o a g e g r o u p s w e r e s e l e c t e d b e c a u s e t h e y h a d a r e l a t i v e l y large s a m p l e size o f 23 f e m a l e s a n d 21 m a l e s a n d w e r e a g o o d r e p r e s e n t a t i o n o f all the years s t u d i e d . A s u m m a r y o f t h e c o r r e l a t i o n s f o u n d to b e s i g n i f i c a n t at p v a l u e s less t h a n 0 . 0 5 is g i v e n b e l o w a n d are s h o w n in T a b l e s V a n d VI.
Vertical Measurement
Total face height Males LS mean ± SD range Females LS mean ± SD range Upper face height Males LS mean ± SD range Females LS mean ± SD range Lower face height Males LS mean ± SD range Females LS mean ___ SD range Left ramus height Males LS mean __. SD range Females LS mean ___ SD range Right ramus height Males LS mean - SD range Females LS mean ± SD range
6 years
18 years
91.37 ± 6.45 74.65-100.32 90.37-5.36 81.20-98.54
123.35 ± 7.04 106.51-128.90 112.23 ± 7.75 97.45-118.89
40.55 ± 3.43 32.65-46.32 40.19 ± 2.95 34.17-45.33
56.18 ± 3.78 49.57-60.03 49.28 ± 3.66 42.57-55.01
50.92 --- 3.67 42.00-55.92 50.42 ± 3.75 43.35-57.81
67.48 ___ 4.71 56.94-73.14 59.89 ± 5.18 50.39-63.88
45.15 _ 2.48 39.84-48.77 45.56 ± 2.00 41.96-49.16
63.57 _ 5.05 53.18-69.86 57.65 ± 3.50 54.96-63.78
45.13 _ 2.33 40.29-48.41 45.47 ± 2.04 41.58-49.13
63.52 ± 5.17 53.52-70.78 57.71 ± 3.56 54.92-64.24
T h e o n l y m e a s u r e m e n t statistically c o r r e l a t e d w i t h c r a n i a l w i d t h for f e m a l e s w a s f a c i a l w i d t h . Facial w i d t h w a s c o r r e l a t e d w i t h all s k e l e t a l t r a n s v e r s e m e a s u r e m e n t s a l o n g w i t h R R H a n d L R H a n d m a x i l l a r y interm o l a r w i d t h s (6-6 a n d 7-7). N a s a l w i d t h w a s c o r r e l a t e d with maxillary width and maxillary intermolar width (7-7). M a x i l l a r y w i d t h c o r r e l a t e d w i t h m a x i l l a r y interm o l a r w i d t h (6-6) a n d (7-7), L F H , T F H , m a n d i b u l a r i n t e r m o l a r w i d t h (7-7), a n d L R H . M a n d i b u l a r w i d t h Correlated w i t h m a x i l l a r y i n t e r m o l a r w i d t h (7-7). All the d e n t a l w i d t h m e a s u r e m e n t s w e r e h i g h l y c o r r e l a t e d w i t h e a c h other. Total face h e i g h t c o r r e l a t e d w i t h U F H a n d L F H . R i g h t a n d left r a m u s h e i g h t s w e r e h i g h l y correlated. In the male sample, cranial width had correlated o n l y w i t h facial w i d t h for m a l e s . F a c i a l w i d t h c o r r e l a t e d w i t h all t r a n s v e r s e m e a s u r e m e n t s , e x c e p t m a x i l l a r y w i d t h . N a s a l w i d t h w a s also c o r r e l a t e d w i t h m a x i l l a r y w i d t h . M a x i l l a r y w i d t h c o r r e l a t e d w i t h all d e n t a l w i d t h m e a s u r e m e n t s . All d e n t a l w i d t h m e a s u r e m e n t s w e r e h i g h l y c o r r e l a t e d w i t h e a c h other. A l s o m a x i l l a r y int e r m o l a r w i d t h (6-6) was c o r r e l a t e d w i t h R R H a n d L R H . M a x i l l a r y i n t e r m o l a r w i d t h (7-7) was c o r r e l a t e d w i t h T F H a n d L R H . M a n d i b u l a r i n t e r m o l a r w i d t h (6-
American Journal of Orthodontics and Dentofacial Orthopedics Volume 104, No. 5
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45
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35
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64
TRANSVERSE MEASUREMENTS
,ii IIIIIIII! I ',
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Total face
heisht
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helsht
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Lower face
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VERTICAL MEASUREMENTS
Fig. 5. Percent increase in transverse and vertical measurements from age 6 to 12 years (filled and from age 12 to 18 years (unfilled column).
column)
T a b l e III. A t t a i n m e n t o f adult size for 9 0 % o f the sample for the nine transverse and five
vertical m e a s u r e m e n t s % growth completed at 6 years Variable
Male
Cranial width Facial width Nasal width Maxillary width Mandibular width Maxillary intermolar width 6-6 Maxillary intermolar width 7-7 Mandibular intermolar width 6-6 Mandibular intermolar width 7-7 TFH UFH LFH LRH RRH
95 83 75 85 79 89 94 100 102 74 72 75 71 71
I
Female
96 86 80 88 83 96 98 101 103 80 81 84 79 79
6) was correlated with T F H . Total face h e i g h t was correlated with U F H and L F H . Left and right r a m u s heights w e r e highly correlated. The correlation coefficients for cranial and facial widths with T F H w e r e not significant (R = 0 . 2 7 and
Growth ending at or before 15 years
Growth completed past 15 and before 18 years
Growth continuing at 18 years
Male
Male
Male[Female
Female
X
l
female X X X
X X X X
X X X X
X
x x
x
x x x x x
x x x x x
X X
R = 0.21). H o w e v e r , w h e n g r o w t h o f four m a l e subjects w h o w e r e selected on the basis o f two largest and two smallest cranial width (and facial width) measurements at age 18 years were c o m p a r e d with the growth c u r v e s o f T F H , it was found that the large cranial width
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Table IV. T h e t tests for gender difference for
Table VI. Pearson correlation coefficients and p
each variable at age 6, 12, and 18 years
values less than 0.05 for 23 f e m a l e s 14 years o f age b e t w e e n the 14 variables studied; if m u l t i p l e coefficients are presented, the largest p value is on top and the smallest v a l u e on the b o t t o m
Variable
Cranial width Facial width Nasal width Maxillary width Mandibular width Max. intermolar width (6-6) Max. intermolar width (7-7) Mand. intermolar width (6-6) Mand. intermolar width (7-7) UFH LFH TFH RRH LRH
p-value age 6
p-value age 12
p-value age 18
0.039* 0.037* 0.900 0.018" 0.093
0.0025** 0.057 0.428 0.0007** 0.057
0.013" 0.0005** 0.089 0.0003** 0.0006**
0.353
0.0004**
0.0015"*
0.758
0.0004**
0.0069**
0.0527
--
0.196
0.024*
0.747 0.941 0.747 0.093 0.508
0.119 0.099 0.061 0.440 0.436
0.0001"* 0.0001"* 0.0001"* 0.0002** 0.0002**
-0.676
Variable 1
Cranial width Facial width
Nasal width
*Denotes significance at p < 0.05. **Denotes significance at p < 0.01.
Maxillary width
Mandibular width Maxillary 6-6
Table V. Pearson correlation coefficients and p values less than 0.05 for 21 males 16 years o f age b e t w e e n the 14 variables studied; _ multiple coefficients are presented, the largest p value is on top and the smallest value on the bottom Variable 1
Cranial width Facial width
Nasal width Maxillary width
Maxillary 6-6
Maxillary 7-7
Mandibular 6-6 TFH LRH
Variable 2
Facial width Mandibular 6-6 Maxillary 6-6 Nasal width Mandibular 7-7 Mandibular width Maxillary 7-7 Maxillary width Maxillary 7-7 Maxillary 6-6 Mandibular 7-7 Mandibular 6-6 Maxillary 7-7 Mandibular 6-6 Mandibular 7-7 RRH LRH Mandibular 7-7 Mandibular 6-6 TFH RRH Mandibular 7-7 TFH LFH UFH RRH
R
value
0.56 0.61 0.57 0.52 0.51 0.48 0.46 0.56 0.81 0.75 0.55 0.48 0.96 0.85 0.81 0.47 0.45 0.80 0.78 0.52 0.44 0.89 0.46 0.79 0.75 0.99
0.010 0.003 0.006 0.023 0.022 0.032 0.037 0.015 0.0001 0.0002 0.015 0.031 0.0001 0.0001 0.0001 0.036 0.042 0.0001 0.0001 0.015 0.049 0.0001 0.035 0.0001 0.0001 0.0001
Maxillary 7-7 Mandibular 6-6 TFH LRH
Variable 2
Facial width RRH LRH Maxillary 7-7 Maxillary 6-6 Mandibular width Maxillary width Nasal width Maxillary width Maxillary 7-7 Maxillary 7-7 Maxillary 6-6 LFH TFH Mandibular 7-7 LRH Maxillary 7-7 Mandibular 6-6 Maxillary 7-7 Mandibular 7-7 Mandibular 7-7 Mandibular 6-6 Mandibular 7-7 LFH UFH RRH
0.47 0.67 0.63 0.53 0.52 0.51 0.51 0.47 0.54 0.47 0.84 0.60 0.57 0.52 0.48 0.47 0.48 0.89 0.81 0.78 0.81 0.74 0.86 0.87 0.84 0.94
0.027 0.0005 0.001 0.022 0.012 0.027 0.022 0.031 0.021 0.030 0.0001 0.006 0.018 0.036 0.033 0.035 0.041 0.0001 0.0001 0.0001 0.0001 0.0004 0.0001 0.0001 0.0001 0.0001
was associated with small T F H and vice versa (Fig. 6). T h e s a m e was true o f the facial width and T F H as s h o w n in Fig. 7.
Predictive equations T h e predictive equations, R 2 and p values for each m e a s u r e m e n t at age 6 years age g i v e n in Table VII. Predictability for all variables was qualitatively designated as strong w h e n R 2 ->- 0 . 6 0 , m o d e r a t e w h e n R = > 0 . 4 0 and < 0 . 6 0 , and w e a k or nonpredictive at R e --< 0 . 4 0 . The size o f a g i v e n variable at age 18 or 19 years can be predicted f r o m these equations or plots if the v a l u e o f this variable at age 6 or 7 years is known. W h e n using the regression lines for prediction, the size o f the variable at age 6 or 7 years is placed as the X value in the equation, and the Y value will be the predicted value o f the variable at 18 or 19 years. The size o f a g i v e n variable at age 18 o r 19 years can be predicted if the value o f the variable at age 11 or 12 years is k n o w n . The predictive equations, R e and p values for each m e a s u r e m e n t age 12 years are g i v e n in Table VIII.
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American Journal of Orthodontics and Dentofacial Orthopedics Volume 104, No. 5
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175 #109
165 155
. . . . . . . . .
- --#33
1 45 1 35
. . . . . . . . . . . . .
#45
_ _ _ ~ ~ - . . . . . . . .
1 25
#82 ~ # 8 2
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mm.
1 15 1 05
#4 5 #109
95 85
75 65
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I
I
I
I
I
t
d
j
6
7
8
9
10
11
12
13
14
15
16
17
4
18
AGE (years)
....
Cranial
Width
Total Face H e i g h t
Fig. 6. Graphs of two large and two small male subjects for cranial width and their total face height in millimeters from 6 to 18 years. Note that the large subjects for cranial width, #33 and 109, were smaller in total face height, whereas and small subjects for cranial width, #45 and 82, were large for total face height.
DISCUSSION
The findings of this study confirmed previous reports that vertical growth from 6 to 18 years was much greater than transverse growth. 6-7 Facial width was the largest dimension of the face in this study. The percent increase for males from 6 to 18 years demonstrated large increases' in all vertical dimensions within the range of 32% to 40%. For females vertical measurements increased approximately 19% to 26%. Skeletal transverse measurements, excluding cranial width, increased in females 13% to 25% and for males by 18% to 27%. The percentage increase in cranial width was much lower (4% to 6%). The percent change from 6 to 12 years demonstrated little difference between transverse and vertical skeletal measurements, which were in the range of 10% to 20%. The differences were much more marked from ages 12 to 18 years for the males. The females, who matured earlier, did not show large differences in the growth of transverse and vertical measurements after age 12 years (Fig. 5). The highly significant p values from the predictive equations revealed that large persons at age 6 years were also larger than the rest of the sample at age 18 years. The same patterns existed for average and small per-
sons. However, there was variability among the individual growth patterns. This is consistent with the work of Bishara and Jakobsen 8 who found that vertical patterns did not change in 77% of their sample. This investigation revealed that the strength of predictability was related to the percentage change. The variables that had large percent increases were usually weak or moderately predictable, whereas the variables with small percent increases were usually strongly predictable. Cranial width
The limited amount of growth in cranial width demonstrated that it followed the neural growth curve. This is consistent with the work of Scammon. 9 At age 6 years, the cranium had reached 94% to 95% of width at age 18 years for males and females, respectively. This change may seem insignificant, but a 5% change equaled an average 8.0 mm increase in width for the males and a 4% change equaled 5.2 mm for the females. Facial width
Meredith 1° found that males had greater facial widths than females for each age group studied. He reported a difference of 3.4 mm at age 10 years and 6.2 mm at 18 years. This study found the gender dif-
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Fig. 7. Graphs of two large and two small male subjects for facial width and their total face height in millimeters from 6 to 18 years. Note that those who were large for facial width, #33 and 109, were small for total face height and those who were small for facial width, #45 and 82, were large for total face height.
ferences to be similar with 2.7 mm at age 10 years and 7.4 mm at age 18 years. Ricketts et al. 4 found facial width to have a mean value of 115.7 mm at age 9 years with 2.4 mm increases per year. This study found facial width to be 114.7 mm for females with increases of 1.4 to 2.0 mm per year and 117.1 mm increasing 1.2 to 3.1 mm per year for males at age 9 years.
Nasal width The percent increase in nasal width was more than any other transverse measurement in this study. It increased 25% for females and 33% for males between 6 to 18 years. Ricketts et al. 4 found nasal width to have a mean of 25 mm for the 9-year-old subjects, increasing 0.7 mm per year. This study found nasal width to be 24.6 mm for females and 24.7 mm for males with the increases ranging from 0.2 to 1.4 mm per year. Nasal width was correlated with maxillary width for both males and females indicating a relationship between the airway and the width of the maxilla.
Maxillary width The results from this study were consistent with most of the previous studies in the literature. Melsen 11 found the growth of the median suture of the maxilla to fuse at age 16 years in females and 18 years in males. Bj6rk and Skieller 12 from their longitudinal cephalometric study with implants found the growth of the maxilla in the transverse dimension to be complete at 17 years for the majority of the male subjects. Savara and Singh 13 noted maxillary width incremental growth rates to decline from 6 to 13 years for males but with a distinct adolescent peak about 14 to 15 years. This study recorded declining rates of growth for both males and females from 6 to 14 years with an accelerated rate at age 15 years for both males and females. This study found that maxillary width growth increase was most rapid with increases during the period of 7 to 11 years for both males and females. Furthermore, growth was completed for the majority of female subjects at age 15 years, whereas for the majority of males it was completed by age 17 years. Ricketts et al. 4 found that the width of the maxilla
American Journal of Orthodontics and Dentofacial Orthopedics Volume 104, No. 5
Snodell, N a n d a , a n d C u r r i e r
Table VII. P r e d i c t i v e e q u a t i o n s f o r v a r i a b l e s o b t a i n e d b y l i n e a r r e g r e s s i o n a n a l y s i s w i t h X t h e m e a s u r e d v a l u e o f t h e v a r i a b l e a t a g e 6 o r 7 y e a r s a n d Y t h e p r e d i c t e d o r c a l c u l a t e d v a l u e o f t h e v a r i a b l e a t a g e 18 o r 19 y e a r s
Variable name Cranial Width Facial Width Nasal Width Maxillary Width Mandibular Width TFH UFH LFH LRH RRH
Sex
Predictive equation
M F M F M F M F M F M F M F M F M F M F
Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y
= = = = = = = = = = = = = = = = = = = =
15.36 + 0.949X 33.76 + 0.795X - 10.88 + 1.31X 22.06 + 0.952X 12.84 + 0.754X 1.142 + 1.192X 22.26 + 0.781X 32.11 + 0.539X 18.14 + 1.037X 16.50 + 0.979X 54.10 + 0.761X 29.20 + 0.912X 25.47 + 0.747X 14.84 + 1.045X 20.47 + 0.939X 7.32 + 1.045X 16.17 + 1.05X 16.17 + 0.908X 16.37 + 1.04X 15.48 + 0.921X
R2
P value
0.90 0.65 0.77 0.68 0.42 0.52 0.47 0.23 0.90 0.65 0.64 0.55 0.56 0.45 0.60 0.46 0.35 0.60 0.31 0.63
0.0001 0.0014 0.0001 0.0005 0.0113 0.0056 0.0096 0.0960 0.0001 0.0009 0.0004 0.0226 0.0034 0.0176 0.0898 0.0151 0.0201 0.0020 0.0322 0.0012
Table Vlll. P r e d i c t i v e e q u a t i o n s f o r v a r i a b l e s o b t a i n e d b y l i n e a r r e g r e s s i o n a n a l y s i s w i t h X t h e m e a s u r e d v a l u e o f t h e v a r i a b l e a t a g e 11 o r 12 y e a r s a n d Y t h e p r e d i c t e d o r c a l c u l a t e d v a l u e o f t h e v a r i a b l e a t a g e 18 o r 19 y e a r s
Variable name Cranial width Facial Width Nasal Width Maxillary Width Mandibular Width Maxillary Intermolar Width (6-6) Mandibular Intermolar Width (6-6) TFH UFH LFH LRH RRH
Sex M F M F M F M F M F M F M F M F M F M F M F M F
Predictive equation Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y
= = = = = = = = = = = = = = = = = = = = = = = =
2.88 + 1.O05X 12.45 + 0.924X - 18.34 + 1.25X 17.46 + 0.908X 9.32 + 0.779X 0.01 + 1.079X 10.15 + 0.887X 19.27 + 0.704X - 7 . 7 0 + 1.198X 12.30 + 0.919X 8.62 + 0.873X 22.02 + 0.607X 0.805 + 0.985X 21.07 + 0.611X 28.33 + 0.903X - 5 9 . 2 4 + 1.654X - 4 . 9 7 + 1.281X 29.34 + 0.441X 34.07 + 0.592X - 3 5 . 4 4 + 1.717X 10.30 + 1.01X 22.42 + 0.673X 5.804 + 1.09X 24.18 + 0.635X
R2
P value
0.94 0.74 0.94 0.87 0.66 0.79 0.81 0.53 0.96 0.90 0.74 0.81 0.77 0.38 0.52 0.81 0.68 0.32 0.45 0.88 0.47 0.64 0.52 0.67
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0076 0.0001 0.0001 0.0001 0.0001 0.0001 0.0249 0.0024 0.0009 0.0017 0.0668 0.0080 0.0001 0.0064 0.0017 0.0037 0.0010
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was 61.9 mm for the 9-year-old subject and increased 0.6 mm per year. The results of this study revealed a mean of 58.1 mm for females that increased from 0.5 to 1.5 mm per year and 60.0 mm for males that increased from 0.5 to 1.7 mm per year. Mandibular width Mandibular width was similar to other transverse measurements. The male sample showed a growth spurt at age 15 years. There were relatively larger growth rates from 7 to 10 years than from 10 to 18 years. Mandibular width for males at age 6 or 7 years had the highest reliability of prediction among all the variables included in this study (R 2 = 0.90). Thus, considering the amount of growth, mandibular width could be predicted with considerable accuracy on the male subjects in this study. However, the predictability was not as strong for the females (R 2 = 0.65). The predictability of mandibular width at age 11 or 12 years was strong for both females and males. Ricketts et al. 4 found mandibular width, as measured from antegonial notch points, had a norm of 76.1 mm at age 9 years and increased 1.4 mm per year. This study found mandibular width change measured as the bigonial distance to be 82.7 for females and 85.2 for males at age 9 years, increasing from 0.5 to 2.0 mm for females and 1.5 to 3.0 mm for males. The distance between antegonial notches and gonion accounted for the differences between Ricketts et al. and this study. The mean mandibular width demonstrated continued growth in females at age 18 years, later than any other measurement. The continued growth at the gonial angle after the completion of all other facial growth could be induced by the muscle attachments. Mandibular width and mandibular intermolar width (6-6) were rrot correlated in females or males. Mandibular width was a measurement of the outer table of the mandible with effects from muscle attachment, whereas mandibular intermolar width was a measurement more closely associated with the inner table of the mandible with lesser effects of muscle attachments. Intermolar width Woods 14 found maxillary intermolar width increased 2.5 mm for females and 2.6 mm for males from the age of 7 to 15 years. Sillman 15found this measurement to increase from 7 to 13 years by 3.0 mm in a grouped sample of males and females. The mean increase from 7 to 13 years was 1.9 mm for females and 2.9 mm for males. This study also found the mean increase in maxillary intermolar width" from 7 to 16 years to be 2.1 mm for females and 3.6 mm for males. These results
American Journal of Orthodontics and Dentofacial Orthopedics November 1993
were similar to Moyers 16 who determined maxillary intermolar width (6-6) to increase 3.5 mm in females and 4.2 mm in males from 7 to 16 years. Intermolar width increases past age 16 years have not been commonly reported in the literature. This study indicated that there is an average increase in maxillary intermolar width (6-6) of 1.4 mm from 16 to 18 years for males. The pattern of increase in width between the maxillary second molars after they erupt at about 12 to 13 years was comparable to that of the intermolar distance of the maxillary first molars from 6 to 13 years after the eruption of the latter at 6 years. The means for mandibular intermolar width (6-6) demonstrated that from 7 to 18 years there was a decrease of 0.5 mm in females but an increase of 0.4 mm in males. The results from this study confirmed the work of Woods 14who found mandibular intermolar width (66) decreased by 0.7 mm in females and by 0.6 mm in males. However, this is different from the findings of Sillman 15 who found an increase of 1.2 mm in a group of males and females and Moyers ]6 who found an increase of 1.6 mm in females and 2.6 mm in males. All intermolar widths were highly correlated as the sample was chosen on the basis of a Class I occlusion with the absence of crossbite and minimal clinical crowding. Vertical measurements The total percentage increases for the vertical measurements were greater than those of the transverse measurements. From 6 to 18 years TFH increased 35% in males and 24% in females. When the total size of the increment between ages 6 and 12 years was compared between males and females, the differences were very small (16% and 14%, respectively). Hence most of the gender differences developed after the age of 12 years during the pubertal growth period. Nanda reported similar findings from his longitudinal growth studies. 17 Total face height was highly correlated with UFH and LFH for both males and females, as it was the sum of these two measurements. From the ages of 6 to 8 years, LFH was more complete in its growth than UFH. From 8 to 18 years of age, both measurements had similar percent increases. Upper and lower face heights were not correlated for either males or females. Lower face height was a measure of the downward decent of the maxilla and mandible. It was similar to other vertical measurement in this study with large increases from 12 to 18 years for the males. The percent increase from age 6 to 18 years demonstrated large differences between males and females. The percent increase for males was 33%, whereas the percent increase for females was less than 20%.
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As the subjects were selected on the basis of a normal facial profile and occlusion, bilateral asymmetries or differences between RRH and LRH were very small, with less than 1 mm for all subjects. Ramus height was found to increase proportionally greater than any other dimension measured in this study. Nanda 17 demonstrated that the distance sella to gonion, a measure similar to ramus height in this study, had greater proportional growth than any of the other facial dimensions measured. Left and right ramus heights were highly correlated as the sample demonstrated bilateral symmetry. However, ramus heights were not correlated with other vertical measurements. An explanation for the low correlation between ramus height and lower face height was that ramus height measured posterior height and lower face height measured anterior height, and the two were independently variable.
Clinical significance It is important for the clinician to study the bilateral transverse and the bilateral vertical dimension of the face to have a comprehensive evaluation. The rate of growth in width is different from vertical facial measurements taken from lateral cephalometric radiographs. The transverse width of the face grows at a lesser rate than sagittal or vertical growth of the face. However, there are significant changes in facial width that need to be delineated. Timing orthodontic treatment to coincide with growth may be a considerable factor in the stability of the dentition. As many clinicians use maxillary orthopedics, the timing of its use is important. As the growth in width of the maxilla is 95% complete for males and 98% complete for females at age 12 years, one may consider the use of maxillary expansion earlier. The greatest growth" in width of the maxilla occurred from 7 to 11 years in males and from 6 to 11 years in females. There was accelerated growth at age 15 years for males; however, it did not not notably exceed the growth rates from 7 to 11 years. The results from this study indicate that the majority of females had completed maxillary width growth by age 15 years, whereas the majority of males were complete at age 17 years. The midpalatal suture may be fused shortly after these years. Melsen 11 found the suture to fuse at age 16 for females and at age 18 years for males. Therefore the use of orthopedic maxillary expansion should be cautiously applied past the age of 15 years for females and 17 years for males. Furthermore, the increases in maxillary intermolar width at the first and second molars were parallel to increases in the width of the maxilla indicating that
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interdental changes were reflecting the changes in the width of the maxilla. The increments in the maxillary width were large between the ages of 6 to 12 years in females and 7 to 11 years in males, even though a small increase continued through age 16 years. Mandibular intermolar width (6-6) did not increase as did the maxillary intermolar width (6-6). It follows that the mandibular dental arch perimeter is finite after the eruption of permanent first molars as far as the width of the basal bony width is concerned in contrast to the maxillary arch perimeter that may become larger with the continuing growth in width of the maxilla. Nasal width demonstrated the greatest percent increase of any transverse measurement from 6 to 18 years. It was 25% for females (5.8 mm) and 33% (7.6 mm) for males. This growth continued longer than any other transverse measurement in this study. The majority of males and several females had not completed their nasal width growth even at age 20 years. With these large increases, a possibility is offered that some potential may exist for a young patient to "outgrow" a breathing problem. Ramus height demonstrated large increases that would strongly impact facial structure. This was especially true for males who at age 12 years were only 85% complete with respect to their size at age 18 years. Furthermore, growth was not complete until age 20 years for the majority of males. The greatest rates of growth occurred at ages 13 and 14 years for females and at ages 15 through 17 years for males. With continuous growth of the ramus height, the mandibular plane becomes more horizontal, and Frankfort-mandibular plane angle may be reduced as has been demonstrated by Nanda. 18 Much of the vertical ramal growth occurs at the mandibular condyle with large impact on the sagittal growth of the mandible and flattening of the facial profile. Of the 11 males with radiographs past the age of 20 years, 10 demonstrated continued growth in maxillary second intermolar width (0.3 to 1.4 mm), 9 in facial width (0.5 to 1.9 mm), 8 in cranial (0.5 to 1.5 nun) and nasal width (0.4 to 1.4 mm), 7 in maxillary (0.4 to 2.0 mm) and mandibular width (0.3 to 2.1 mm), 6 in mandibular first intermolar width (0.4 to 1.3 mm), 5 in lower face height (0.4 to 2.0 mm) and right and left ramus heights (0.5 to 2.2 mm), 4 in total (0.5 to 2.2 mm) and upper face height (0.5 to 1.3 mm), whereas only 3 subjects had increases in mandibular second intermolar width (0.3 to 0.7 mm) and 2 in maxillary first intermolar width (0.3 to 0.4 mm). This is consistent with the work of Nanda 17 who found continued growth past age 20 years for several male subjects.
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SUMMARY AND CONCLUSIONS Longitudinal records of P-A cephalometric radiographs were used to evaluate growth in the transverse and vertical dimensions for 25 females between the ages of 4 to 20 years and for 25 males between the ages of 4 to 25 years. The subjects were selected on the basis of normal skeletal and dental patterns from the Child Research Council in Denver, Colo. Growth was evaluated from the group means and also on the basis of individual growth patterns. Mean values were calculated for each of the nine transverse and five vertical variables from ages 6 to 18 years, for both the males and females. Individual data correlations and predictive equations were formulated. The following conclusions were established: 1. At 6 years of age, the transverse dimensions had a greater percentage of the adult size completed than the vertical measurements for both males and females. All the transverse measurements were over 80% complete in growth by age 6 years when using age 18 years as 100%, with the exception of nasal width for males, which was only 75% complete. The percent change in growth was similar for females in the transverse and vertical dimensions from age 6 to 18 years. However, males from age 12 to 18 years demonstrated more vertical change than transverse. 2. Numerous significant correlations were found between measurements for both males and females. Cranial width correlated with only facial width. Facial width correlated with all skeletal transverse measurements, except maxillary width for males. Nasal width was correlated with maxillary width. With the exception of mandibular intermolar width (6-6) for males, maxillary width was correlated with all dental measurements, whereas mandibular width correlated only with maxillary intermolar widths for females. All dental measurements were highly correlated with each other. Total face height was highly correlated with upper and lower face heights. However, with the exception of right and left ramus heights, there were no other significant correlations between the vertical measurements. 3. There were multiple statistically different mean values for males and females at 6, 12 and 18 years of age for all 14 variables, except nasal width. At age 6 years, mean differences were found for widths in the cranium, face, and maxilla. At age 12 years, the mean differences were found for cranial width, maxillary width, and maxillary and mandibular intermolar width (6-
American Journal of Orthodontics and Dentofacial Orthopedics November 1993
6). At age 18 years, all the variables were different, except for nasal width and mandibular intermolar width (6-6). . Linear regression analyses revealed several variables that displayed strong (R2 _> 0.060), moderately strong (R = > 0 . 4 0 and <0.60), and nonpredictable or weakly (Re _< 0.40) predictable for age 18 or 19 years if the value at age 6 or 7 years was known. This was also true for age 18 or 19 years if the value at age 11 or 12 years was known. The strength of predictability for each variable in both sexes in the 6- or 7year age group are provided. (a) Strong predictability in both sexes: cranial width, facial width, mandibular width. (b) Strong predictability in males and moderate predictability in females: lower face height, total face height. (c) Strong predictability in females, nonpredictive in males: right and left ramus height. (d) Moderately strong predictive equations in both sexes: nasal width, maxillary width, upper face height. The strength of predictability for each variable in both sexes in the 11 or 12 year age group are provided. (1) Strong predictability in both sexes: cranial width, facial width, nasal width, mandibular width, maxillary intermolar width (6-6). (b) Strong predictability in males, moderately strong predictive in females: maxillary width, upper face height. (c) Strong predictability in females, moderately strong predictability in males: lower face height and total face height. (d) Strong predictability in males, nonpredictive in females: mandibular intermolar width.
REFERENCES 1. Ferris HC. Discussion of Dr. G. V. I. Brown's paper. Dent Cosmos, 1914;56:218. 2. TimmsDJ, MossJP. An histologicalinvestigationintothe effects of rapid maxillary expansion on the teeth and their supporting tissues. Trans Europ Orthod Soc 1971;71:263-71. 3. Herold JS. Maxillary expansion: a retrospective study of three methods of expansion and their long-termsequelae. Br J Orthod 1989;16:195-200. 4. Ricketts RM, Roth RH, Chaconas SJ, SchulofRJ, Engel GA. Orthodontic diagnosisand planning:their roles in preventiveand rehabilitative dentistry. Vol 1. Denver, Colorado:RockyMountain Data Systems, 1982:15-147. 5. Ostle B, Malone LC. Statistics in research: basic conceptsand techniques for research workers. Ames, Iowa: Iowa State University Press, 1988:24-229.
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6. Hellman M. Introduction of growth of the human face from infancy to adulthood. INT J ORTHOD 1932;18:777-98. 7. Goldstein MS. Changes in dimensions and form of the face and head with age. Am J Phy Anthropol 1936;22:37-89. 8. Bishara SE, Jakobsen JR. Longitudinal changes in three normal facial types. AM J ORTHOD 1985;88:466-502. 9. Scammon RE. A summary of the anatomy of the infant and child. Pediatrics, vol. I. Philadelphia: WB Saunders, 1923:89. 10. Meredith HV. Growth in bizygomatic face breadth during childhood. Growth 1954;18:111-34. 11. Melsen B. Palatal growth studied on human autopsy material. A histological microradiographic study. AM J ORTHOD 1975;68:42-54. 12. Bj6rk A, Skieller V. Growth in width of the maxilla studied by the implant method. Scan J Plast Reconstr Surg 1974;8:26-33. 13. Savara BS, Singh IJ. Norms of size and annual increments of seven anatomical measures of maxilla in boys from 3 to 16 years of age. Angle Orthod 1968;38(2):104-20. 14. Woods GA. Changes in width dimensions between certain teeth and facial points during human growth. AM J ORTHOD 1950;36:676-700.
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15. Sillman JH. Dimensional changes of the dental arch: longitudinal study from birth to 25 years. AM J ORTHOD 1964;50:824-42. 16. Moyers RE, v o n d e r Linden FPGM, Riolo ML. Standards of human occlusal development. Monograph 5, Craniofacial Growth Series. Ann Arbor: Center for Human Growth and Development, University of Michigan Press, 1976:176-8. 17. Nanda RS. The rates of growth of several facial components measured from serial cephalometric roentgenogram. AM J ORTnOD 1955;41:658-73. 18. Nanda RS. Growth changes in skeletal-facial profile and their significance in orthodontic diagnosis. AM J ORTHOD 1971;59:501-13. Reprint requests to: Dr. G. Frans Currier University of Oklahoma Health Sciences Center College of Dentistry P.O. Box 26901 1001 Stanton L. Young Blvd. Oklahoma City, OK 73190
Avast majority of growth studies have used lateral cephalometric radiographs to analyze changes in the vertical and the sagittal dimensions of the face. Most of the normative data have been based on sagittal aspects of dentofacial structures with the current emphasis on orthodontic diagnosis obtained from information from these films. However, evaluation also is needed in the transverse dimension for a comprehensive dentofacial evaluation. Bilateral facial asymmetries and development of the oronasal area can be better assessed from a transverse analysis of posteroanterior (P-A) cephalometric radiographs. Transverse problems, such as posterior crossbite, are a great concern to the orthodontist and have been mentioned as having great potential for relapse. 1-3Analysis of vertical components, although easily viewed from sagittal cephalometric radiographs, also cannot be fully understood without the assistance of a P-A cephalometric radiograph as bilateral vertical asymmetries can only be evaluated from a frontal view. Review of the literature on ortllodontic diagnosis provides only a sketchy treatment of transverse facial dimensions. Furthermore, facial growth studies that include the transverse component have been even fewer.
From the University of Oklahoma College of Dentistry. aFormer graduate student. bProfessor and Chairman, Department of Orthodontics. CProfessor, Department of Orthodontics. Copyright © 1993 by the American Association of Orthodontists. 0889-5406/93/$1.00 + 0.10 8/1/37218
In relation to diagnosis and treatment, the specialty has been overwhelmingly preoccupied with vertical and sagittal relationships of the dentofacial structures. Those available do not include a detailed analysis of the P-A cephalometric radiographs. This study evaluated longitudinal growth changes in the transverse and vertical dimensions for female subjects from ages 4 to 20 years and for male subjects from ages 4 to 25 years. The objectives of the study were (1) to establish norms of size and annual increments for the nine transverse and five vertical measurements for males and females, (2) to identify relationships between the various components with descriptions of any gender differences, (3) to specify patterns for individual craniofacial growth, and (4) to formulate predictive equations from age 6 to 18 years and from 12 to 18 years for each of the measurements.
MATERIALS AND METHODS This research utilized the longitudinal posteroanterior cephalometric radiographs from the growth study at the Child Research Council, University of Colorado School of Medicine. Twenty-five male and 25 female white subjects were selected on the basis of a balanced skeletal profile and Class I occlusion with the absence of crossbite, presence of only minimal clinical crowding, and no orthodontic treatment during the entire period of the study. There were a minimum of 10 P-A cephalometric radiographs between the ages of 4 and 20 years of age. Eleven of the male subjects had radiographs from the ages of 21 to 25 years that were also included. Each cephalometric radiograph was traced, and the landmarks were computer digitized. A horizontal plane was established to
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2 3 4
Fig. 1. Transverse measurements. 1. Cranial width (bieuryon width). 2. Facial width (bizygomatie width). 3. Nasal width (bialare width). 4. Maxillarywidth. 5. Mandibular width (bigonial width). 6,7. Maxillary intermolar width (6-6) and (7-7). 8. Mandibular intermolar width (6-6) and (7-7).
connect the bilateral points that intersected the lesser wing of the sphenoid with the medial rims of the orbits. These points were more 'easily identified than the zygomaticofrontal sutures as used by Ricketts et al. 4 The midsagittal plane used was the line that passes through points crista galli and ANS, also bisecting the medial rims of the orbits. The intersection of the horizontal and midsagittal planes was used to locate nasion. The transverse and vertical measurements used are as shown in Figs. 1 and 2. The following are the nine linear "ransverse measurements: 1. Cranial width (bieuryon width): the width of the cranium from the most lateral points on the cranium parallel to the superior aspect of the orbits. 2. Facial width (bizygomatic width): the width of the zygomatic arch from their most lateral aspect. 3. Nasal width (bialare width): the width of the nasal cavity from the most lateral points on the nasal aperture taken parallel to the horizontal plane. 4. Maxillary width: the width of the maxilla from bilateral points on the jugal process at the intersection of the outline of the tuberosity of the maxilla and the zygomatic buttress. 5. Mandibular width (bigonial width): the width of the mandible from points at the most lateral margin of the angle of the mandible. 6. Intermolar width of maxillary first molars: the width between the most lateral points on the buccal surface of the permanent maxillary first molar crown parallel to the occlusal plane. 7. Intermolar width of maxillary second molars: the width between the most lateral points on the buccal
Fig. 2. Vertical measurements. 1. Total face height. 2. Upper face height. 3, Lower face height. 4. Left ramus height. 5. Night ramus height.
surface of the maxillary permanent second molar crowns parallel to the occlusal plane. 8. Intermolar width of mandibular first molars: the width between the most lateral points on the buccal surface of the mandibular permanent first molar crowns parallel to the occlusal plane. 9. Intermolar width of mandibular second molars: the width between the most lateral points on the buccal surface of the mandibular permanent second molar crowns parallel to the occusal plane. The following are the five linear vertical measurements: 1. Total facial height (TFH): the distance between the intersection of the horizontal and midsagittal planes and the most inferior point on the outline of the mandibular symphysis through the midsagittal plane. 2. Upper face height (UFH): the distance between the intersection of the horizontal and the midsagittal planes and the tip of the anterior nasal spine just below the nasal cavity and above the hard palate. 3. Lower face height (LFH): the distance between the tip of the anterior nasal spine just below the nasal cavity and above the hard palate and the most inferior point on the outline of the mandibular symphysis through the midsagittal plane. 4. Left ramus height (LRH): the distance between the most lateral left margin of the angle of the mandible and the most superior left aspect of the condyle. 5. Right ramus height (RRH): the distance between the most lateral right margin of the angle of the mandible and the most superior right aspect of the condyle.
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r<
8.0
>
::;le Fig. 3, Total increments of size of seven transverse measurements in millimeters for male and female subjects age 6 to 18 years. The number above the line is the male value, and the number below the line is the female value. Error of m e a s u r e m e n t
Fifty P-A cephalometric radiographs were retraced and redigitized 8 weeks after the first set of records were obtained. A combined error of landmark location, tracing, and digitization was determined. The mean measurement error for the transverse measurements was less than 0.50 mm, whereas the mean error for the vertical measurements was less than 0.80 ram.
One of the reasons P-A cephalometric films have not been used as extensively as the lateral cephalometric films in growth studies is the distortion that may be created by the slight movement of the head in the transverse plane, as well as the vertical plane. However, the material available for this study had a standard high quality, because the radiographs were taken in a x;ery rigid cephalostat and the same operator took the films over the length of the study. Analysis of the d a t a
The data were analyzed for growth changes in group means and growth changes at the individual level. To negate the effects of missing data on analysis, a statistical method to find the best fit line of the means, the least squares method5 was used. Least squares means, standard deviations, and minimum and maximum values were recorded for each of the variables at each age group. Least squares means and standard deviations were also calculated for the annual increments for each age group. Two different methods to calculate percent change were also determined for the means of each variable. The first method was calculated using the value at each age expressed as a proportion of the mean value at age 18 years. The second method used the percent change expressed as a proportional increase from the measurement at age 6 years,
22 1 Fig. 4. Total increments of size of five vertical measurements in millimeters for male and female subjects age 6 to 18 years. The number to the above the line is the male value, and the number below the line is the female value.
calculated for each variable at age 12 years and at age 18 years. RESULTS
The total size increments for each measurement in male and female subjects age 6 to 18 years are given in Figs. 3 and 4. The least square mean, standard deviation, and range for transverse and vertical measurements are given in Tables I and II. The percent increase from age 6 to 12 and from 6 to 18 years for each measurement are demonstrated in Fig. 5. The percent completion of adult growth at age 6 years and 90% of the sample who have attained adult size at ages 15 and 18 years are given in Table III. Measurements continuing to grow at age 18 years are also indicated. G e n d e r differences
A t test was performed for each measurement at ages 6, 12, and 18 years to determine gender differences. The p values of 0.05 or less were considered statistically significant, and a summary of p values for each variable at the three age groups is listed in Table IV. At age 6 years, the only three variables different between males and females were cranial width, facial width, and maxillary width. At age 12 years, cranial width, maxillary width, maxillary intermolar width (66), and mandibular intermolar width (6-6) were significantly different. At age 18 years, the following 12 variables were significant: cranial width, facial width, maxillary width, mandibular width, maxillary intermolar width (6-6), maxillary and mandibular intermolar
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American Journal of Orthodontics and Dentofacial Orthopedics November 1993
Table I. L e a s t s q u a r e s m e a n (LS m e a n ) ,
Table II. L e a s t s q u a r e s m e a n (LS M e a n ) ,
s t a n d a r d d e v i a t i o n ( S D ) , a n d r a n g e for s e v e n t r a n s v e r s e m e a s u r e m e n t s in m i l l i m e t e r s
s t a n d a r d d e v i a t i o n ( S D ) , a n d r a n g e for five v e r t i c a l m e a s u r e m e n t s in m i l l i m e t e r s
Transverse measurement ] Cranial width Males LS mean ± SD range Females LS mean ± SD range Facial width Males LS mean ± SD range Females LS mean ± SD range Nasal width Males LS mean ± SD range Females LS mean ± SD range Maxillary width Males LS mean ± SD range Females LS mean ± SD range Mandibular width Males LS mean ± SD range Females LS mean ± SD range Maxillary intermolar width 6-6 Males LS mean ± SD range Females LS mean ± SD range Mandibular intermolar width 6-6 Males LS mean ± SD range Females LS mean ± SD range
6 years
18 years
142.88 ± 6.55 128.04-158.45 139.23 ± 4.11 131.94-146.68
150.90 ± 7.07 142.08-162.68 144.42 ± 5.02 136.67-152.53
110.82 ± 3.45 104.67-119.96 108.22 ± 3.27 99.33-113.02
134.06 ± 4.80 125.35-140.71 126.03 ± 5.68 121.66-135.71
22.93 ± 1.92 18.21-26.98 22.88 ± 1.66 19.87-26.82
30.48 ± 2.07 29.25-36.55 28.64 ± 2.49 25.56-33.68
56.12 ± 2.34 51.13-60.19 54.44 ± 1.86 51.28-59.00
66.24 ± 3.12 61.08-70.80 61.8 ± 2.97 58.67-66.88
78.43-4.42 72.48 -90.5 76.33 ± 2.77 72.37-81.14
99.36 ± 5.17 89.70-108.92 92.17 ± 3.96 84.89°96.39
53.18 ± 2.66 50.98-58.45 53.67 ± 2.58 49.13-56.79
59.46 ± 2.71 54.26-63.39 55.67 ± 1.51 54.60-59.29
56.00 ± 2.96 49.66-62.38 54.10 ± 2.17 49.45-59.84
56.12 ± 2.17 51.57-58.39 53.72 ± 1.55 52.28-56.98
w i d t h (7-7), U P H , L P H , T F H , a n d R R H a n d L R H . T h e o n l y v a r i a b l e s s h o w i n g n o statistically s i g n i f i c a n t g e n d e r d i f f e r e n c e s at a g e 18 years w e r e n a s a l w i d t h a n d m a n d i b u l a r i n t e r m o l a r w i d t h (6-6).
Individual data correlations To s t u d y t h e c o r r e l a t i o n s b e t w e e n e a c h o f the 14 measurements, Pearson correlation coefficients were c a l c u l a t e d at a g e 14 y e a r s for f e m a l e s a n d at a g e 16 years for m a l e s . T h e s e t w o a g e g r o u p s w e r e s e l e c t e d b e c a u s e t h e y h a d a r e l a t i v e l y large s a m p l e size o f 23 f e m a l e s a n d 21 m a l e s a n d w e r e a g o o d r e p r e s e n t a t i o n o f all the years s t u d i e d . A s u m m a r y o f t h e c o r r e l a t i o n s f o u n d to b e s i g n i f i c a n t at p v a l u e s less t h a n 0 . 0 5 is g i v e n b e l o w a n d are s h o w n in T a b l e s V a n d VI.
Vertical Measurement
Total face height Males LS mean ± SD range Females LS mean ± SD range Upper face height Males LS mean ± SD range Females LS mean ± SD range Lower face height Males LS mean ± SD range Females LS mean ___ SD range Left ramus height Males LS mean __. SD range Females LS mean ___ SD range Right ramus height Males LS mean - SD range Females LS mean ± SD range
6 years
18 years
91.37 ± 6.45 74.65-100.32 90.37-5.36 81.20-98.54
123.35 ± 7.04 106.51-128.90 112.23 ± 7.75 97.45-118.89
40.55 ± 3.43 32.65-46.32 40.19 ± 2.95 34.17-45.33
56.18 ± 3.78 49.57-60.03 49.28 ± 3.66 42.57-55.01
50.92 --- 3.67 42.00-55.92 50.42 ± 3.75 43.35-57.81
67.48 ___ 4.71 56.94-73.14 59.89 ± 5.18 50.39-63.88
45.15 _ 2.48 39.84-48.77 45.56 ± 2.00 41.96-49.16
63.57 _ 5.05 53.18-69.86 57.65 ± 3.50 54.96-63.78
45.13 _ 2.33 40.29-48.41 45.47 ± 2.04 41.58-49.13
63.52 ± 5.17 53.52-70.78 57.71 ± 3.56 54.92-64.24
T h e o n l y m e a s u r e m e n t statistically c o r r e l a t e d w i t h c r a n i a l w i d t h for f e m a l e s w a s f a c i a l w i d t h . Facial w i d t h w a s c o r r e l a t e d w i t h all s k e l e t a l t r a n s v e r s e m e a s u r e m e n t s a l o n g w i t h R R H a n d L R H a n d m a x i l l a r y interm o l a r w i d t h s (6-6 a n d 7-7). N a s a l w i d t h w a s c o r r e l a t e d with maxillary width and maxillary intermolar width (7-7). M a x i l l a r y w i d t h c o r r e l a t e d w i t h m a x i l l a r y interm o l a r w i d t h (6-6) a n d (7-7), L F H , T F H , m a n d i b u l a r i n t e r m o l a r w i d t h (7-7), a n d L R H . M a n d i b u l a r w i d t h Correlated w i t h m a x i l l a r y i n t e r m o l a r w i d t h (7-7). All the d e n t a l w i d t h m e a s u r e m e n t s w e r e h i g h l y c o r r e l a t e d w i t h e a c h other. Total face h e i g h t c o r r e l a t e d w i t h U F H a n d L F H . R i g h t a n d left r a m u s h e i g h t s w e r e h i g h l y correlated. In the male sample, cranial width had correlated o n l y w i t h facial w i d t h for m a l e s . F a c i a l w i d t h c o r r e l a t e d w i t h all t r a n s v e r s e m e a s u r e m e n t s , e x c e p t m a x i l l a r y w i d t h . N a s a l w i d t h w a s also c o r r e l a t e d w i t h m a x i l l a r y w i d t h . M a x i l l a r y w i d t h c o r r e l a t e d w i t h all d e n t a l w i d t h m e a s u r e m e n t s . All d e n t a l w i d t h m e a s u r e m e n t s w e r e h i g h l y c o r r e l a t e d w i t h e a c h other. A l s o m a x i l l a r y int e r m o l a r w i d t h (6-6) was c o r r e l a t e d w i t h R R H a n d L R H . M a x i l l a r y i n t e r m o l a r w i d t h (7-7) was c o r r e l a t e d w i t h T F H a n d L R H . M a n d i b u l a r i n t e r m o l a r w i d t h (6-
American Journal of Orthodontics and Dentofacial Orthopedics Volume 104, No. 5
475
SnodeU, Nanda, and Currier
45
0"
[ ] 18 YEARS 40 •
0"
0~
12 YEARS
35
I
30
0-"
1 ,c----1 [----1 [---1 [-ui
F,-
25 g~
20
~,
~-?-
15
IIII 1oli,illll .... I lli,iII 0
,
Cranial width
~ , ~ , , ~ . Facial width Nasal width Max. width Mind. width
. . . . . Max. @4
, Mind.
64
TRANSVERSE MEASUREMENTS
,ii IIIIIIII! I ',
I
Total face
heisht
',
I
U p p e r face
helsht
',
',
Lower face
',
',
L ramu.
heisht
heisht
',
[. ramus helsht
VERTICAL MEASUREMENTS
Fig. 5. Percent increase in transverse and vertical measurements from age 6 to 12 years (filled and from age 12 to 18 years (unfilled column).
column)
T a b l e III. A t t a i n m e n t o f adult size for 9 0 % o f the sample for the nine transverse and five
vertical m e a s u r e m e n t s % growth completed at 6 years Variable
Male
Cranial width Facial width Nasal width Maxillary width Mandibular width Maxillary intermolar width 6-6 Maxillary intermolar width 7-7 Mandibular intermolar width 6-6 Mandibular intermolar width 7-7 TFH UFH LFH LRH RRH
95 83 75 85 79 89 94 100 102 74 72 75 71 71
I
Female
96 86 80 88 83 96 98 101 103 80 81 84 79 79
6) was correlated with T F H . Total face h e i g h t was correlated with U F H and L F H . Left and right r a m u s heights w e r e highly correlated. The correlation coefficients for cranial and facial widths with T F H w e r e not significant (R = 0 . 2 7 and
Growth ending at or before 15 years
Growth completed past 15 and before 18 years
Growth continuing at 18 years
Male
Male
Male[Female
Female
X
l
female X X X
X X X X
X X X X
X
x x
x
x x x x x
x x x x x
X X
R = 0.21). H o w e v e r , w h e n g r o w t h o f four m a l e subjects w h o w e r e selected on the basis o f two largest and two smallest cranial width (and facial width) measurements at age 18 years were c o m p a r e d with the growth c u r v e s o f T F H , it was found that the large cranial width
476
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American Journal of Orthodontics and Dentofacial Orthopedics November 1993
Table IV. T h e t tests for gender difference for
Table VI. Pearson correlation coefficients and p
each variable at age 6, 12, and 18 years
values less than 0.05 for 23 f e m a l e s 14 years o f age b e t w e e n the 14 variables studied; if m u l t i p l e coefficients are presented, the largest p value is on top and the smallest v a l u e on the b o t t o m
Variable
Cranial width Facial width Nasal width Maxillary width Mandibular width Max. intermolar width (6-6) Max. intermolar width (7-7) Mand. intermolar width (6-6) Mand. intermolar width (7-7) UFH LFH TFH RRH LRH
p-value age 6
p-value age 12
p-value age 18
0.039* 0.037* 0.900 0.018" 0.093
0.0025** 0.057 0.428 0.0007** 0.057
0.013" 0.0005** 0.089 0.0003** 0.0006**
0.353
0.0004**
0.0015"*
0.758
0.0004**
0.0069**
0.0527
--
0.196
0.024*
0.747 0.941 0.747 0.093 0.508
0.119 0.099 0.061 0.440 0.436
0.0001"* 0.0001"* 0.0001"* 0.0002** 0.0002**
-0.676
Variable 1
Cranial width Facial width
Nasal width
*Denotes significance at p < 0.05. **Denotes significance at p < 0.01.
Maxillary width
Mandibular width Maxillary 6-6
Table V. Pearson correlation coefficients and p values less than 0.05 for 21 males 16 years o f age b e t w e e n the 14 variables studied; _ multiple coefficients are presented, the largest p value is on top and the smallest value on the bottom Variable 1
Cranial width Facial width
Nasal width Maxillary width
Maxillary 6-6
Maxillary 7-7
Mandibular 6-6 TFH LRH
Variable 2
Facial width Mandibular 6-6 Maxillary 6-6 Nasal width Mandibular 7-7 Mandibular width Maxillary 7-7 Maxillary width Maxillary 7-7 Maxillary 6-6 Mandibular 7-7 Mandibular 6-6 Maxillary 7-7 Mandibular 6-6 Mandibular 7-7 RRH LRH Mandibular 7-7 Mandibular 6-6 TFH RRH Mandibular 7-7 TFH LFH UFH RRH
R
value
0.56 0.61 0.57 0.52 0.51 0.48 0.46 0.56 0.81 0.75 0.55 0.48 0.96 0.85 0.81 0.47 0.45 0.80 0.78 0.52 0.44 0.89 0.46 0.79 0.75 0.99
0.010 0.003 0.006 0.023 0.022 0.032 0.037 0.015 0.0001 0.0002 0.015 0.031 0.0001 0.0001 0.0001 0.036 0.042 0.0001 0.0001 0.015 0.049 0.0001 0.035 0.0001 0.0001 0.0001
Maxillary 7-7 Mandibular 6-6 TFH LRH
Variable 2
Facial width RRH LRH Maxillary 7-7 Maxillary 6-6 Mandibular width Maxillary width Nasal width Maxillary width Maxillary 7-7 Maxillary 7-7 Maxillary 6-6 LFH TFH Mandibular 7-7 LRH Maxillary 7-7 Mandibular 6-6 Maxillary 7-7 Mandibular 7-7 Mandibular 7-7 Mandibular 6-6 Mandibular 7-7 LFH UFH RRH
0.47 0.67 0.63 0.53 0.52 0.51 0.51 0.47 0.54 0.47 0.84 0.60 0.57 0.52 0.48 0.47 0.48 0.89 0.81 0.78 0.81 0.74 0.86 0.87 0.84 0.94
0.027 0.0005 0.001 0.022 0.012 0.027 0.022 0.031 0.021 0.030 0.0001 0.006 0.018 0.036 0.033 0.035 0.041 0.0001 0.0001 0.0001 0.0001 0.0004 0.0001 0.0001 0.0001 0.0001
was associated with small T F H and vice versa (Fig. 6). T h e s a m e was true o f the facial width and T F H as s h o w n in Fig. 7.
Predictive equations T h e predictive equations, R 2 and p values for each m e a s u r e m e n t at age 6 years age g i v e n in Table VII. Predictability for all variables was qualitatively designated as strong w h e n R 2 ->- 0 . 6 0 , m o d e r a t e w h e n R = > 0 . 4 0 and < 0 . 6 0 , and w e a k or nonpredictive at R e --< 0 . 4 0 . The size o f a g i v e n variable at age 18 or 19 years can be predicted f r o m these equations or plots if the v a l u e o f this variable at age 6 or 7 years is known. W h e n using the regression lines for prediction, the size o f the variable at age 6 or 7 years is placed as the X value in the equation, and the Y value will be the predicted value o f the variable at 18 or 19 years. The size o f a g i v e n variable at age 18 o r 19 years can be predicted if the value o f the variable at age 11 or 12 years is k n o w n . The predictive equations, R e and p values for each m e a s u r e m e n t age 12 years are g i v e n in Table VIII.
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American Journal of Orthodontics and Dentofacial Orthopedics Volume 104, No. 5
477
175 #109
165 155
. . . . . . . . .
- --#33
1 45 1 35
. . . . . . . . . . . . .
#45
_ _ _ ~ ~ - . . . . . . . .
1 25
#82 ~ # 8 2
~
mm.
1 15 1 05
#4 5 #109
95 85
75 65
I
I
I
I
I
I
I
I
I
t
d
j
6
7
8
9
10
11
12
13
14
15
16
17
4
18
AGE (years)
....
Cranial
Width
Total Face H e i g h t
Fig. 6. Graphs of two large and two small male subjects for cranial width and their total face height in millimeters from 6 to 18 years. Note that the large subjects for cranial width, #33 and 109, were smaller in total face height, whereas and small subjects for cranial width, #45 and 82, were large for total face height.
DISCUSSION
The findings of this study confirmed previous reports that vertical growth from 6 to 18 years was much greater than transverse growth. 6-7 Facial width was the largest dimension of the face in this study. The percent increase for males from 6 to 18 years demonstrated large increases' in all vertical dimensions within the range of 32% to 40%. For females vertical measurements increased approximately 19% to 26%. Skeletal transverse measurements, excluding cranial width, increased in females 13% to 25% and for males by 18% to 27%. The percentage increase in cranial width was much lower (4% to 6%). The percent change from 6 to 12 years demonstrated little difference between transverse and vertical skeletal measurements, which were in the range of 10% to 20%. The differences were much more marked from ages 12 to 18 years for the males. The females, who matured earlier, did not show large differences in the growth of transverse and vertical measurements after age 12 years (Fig. 5). The highly significant p values from the predictive equations revealed that large persons at age 6 years were also larger than the rest of the sample at age 18 years. The same patterns existed for average and small per-
sons. However, there was variability among the individual growth patterns. This is consistent with the work of Bishara and Jakobsen 8 who found that vertical patterns did not change in 77% of their sample. This investigation revealed that the strength of predictability was related to the percentage change. The variables that had large percent increases were usually weak or moderately predictable, whereas the variables with small percent increases were usually strongly predictable. Cranial width
The limited amount of growth in cranial width demonstrated that it followed the neural growth curve. This is consistent with the work of Scammon. 9 At age 6 years, the cranium had reached 94% to 95% of width at age 18 years for males and females, respectively. This change may seem insignificant, but a 5% change equaled an average 8.0 mm increase in width for the males and a 4% change equaled 5.2 mm for the females. Facial width
Meredith 1° found that males had greater facial widths than females for each age group studied. He reported a difference of 3.4 mm at age 10 years and 6.2 mm at 18 years. This study found the gender dif-
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American Journal of Orthodontics and Dentofacial Orthopedics November 1993
140
_#33
130 120 110 mm.
1 1
~-"
#33
100 90 80 70
I
I
I
I
I
t
I
I
I
I
I
E
;
6
7
8
9
10
11
12
13
14
15
16
17
18
AGE (years)
....
Facial
Width
Total Face H e i g h t
Fig. 7. Graphs of two large and two small male subjects for facial width and their total face height in millimeters from 6 to 18 years. Note that those who were large for facial width, #33 and 109, were small for total face height and those who were small for facial width, #45 and 82, were large for total face height.
ferences to be similar with 2.7 mm at age 10 years and 7.4 mm at age 18 years. Ricketts et al. 4 found facial width to have a mean value of 115.7 mm at age 9 years with 2.4 mm increases per year. This study found facial width to be 114.7 mm for females with increases of 1.4 to 2.0 mm per year and 117.1 mm increasing 1.2 to 3.1 mm per year for males at age 9 years.
Nasal width The percent increase in nasal width was more than any other transverse measurement in this study. It increased 25% for females and 33% for males between 6 to 18 years. Ricketts et al. 4 found nasal width to have a mean of 25 mm for the 9-year-old subjects, increasing 0.7 mm per year. This study found nasal width to be 24.6 mm for females and 24.7 mm for males with the increases ranging from 0.2 to 1.4 mm per year. Nasal width was correlated with maxillary width for both males and females indicating a relationship between the airway and the width of the maxilla.
Maxillary width The results from this study were consistent with most of the previous studies in the literature. Melsen 11 found the growth of the median suture of the maxilla to fuse at age 16 years in females and 18 years in males. Bj6rk and Skieller 12 from their longitudinal cephalometric study with implants found the growth of the maxilla in the transverse dimension to be complete at 17 years for the majority of the male subjects. Savara and Singh 13 noted maxillary width incremental growth rates to decline from 6 to 13 years for males but with a distinct adolescent peak about 14 to 15 years. This study recorded declining rates of growth for both males and females from 6 to 14 years with an accelerated rate at age 15 years for both males and females. This study found that maxillary width growth increase was most rapid with increases during the period of 7 to 11 years for both males and females. Furthermore, growth was completed for the majority of female subjects at age 15 years, whereas for the majority of males it was completed by age 17 years. Ricketts et al. 4 found that the width of the maxilla
American Journal of Orthodontics and Dentofacial Orthopedics Volume 104, No. 5
Snodell, N a n d a , a n d C u r r i e r
Table VII. P r e d i c t i v e e q u a t i o n s f o r v a r i a b l e s o b t a i n e d b y l i n e a r r e g r e s s i o n a n a l y s i s w i t h X t h e m e a s u r e d v a l u e o f t h e v a r i a b l e a t a g e 6 o r 7 y e a r s a n d Y t h e p r e d i c t e d o r c a l c u l a t e d v a l u e o f t h e v a r i a b l e a t a g e 18 o r 19 y e a r s
Variable name Cranial Width Facial Width Nasal Width Maxillary Width Mandibular Width TFH UFH LFH LRH RRH
Sex
Predictive equation
M F M F M F M F M F M F M F M F M F M F
Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y
= = = = = = = = = = = = = = = = = = = =
15.36 + 0.949X 33.76 + 0.795X - 10.88 + 1.31X 22.06 + 0.952X 12.84 + 0.754X 1.142 + 1.192X 22.26 + 0.781X 32.11 + 0.539X 18.14 + 1.037X 16.50 + 0.979X 54.10 + 0.761X 29.20 + 0.912X 25.47 + 0.747X 14.84 + 1.045X 20.47 + 0.939X 7.32 + 1.045X 16.17 + 1.05X 16.17 + 0.908X 16.37 + 1.04X 15.48 + 0.921X
R2
P value
0.90 0.65 0.77 0.68 0.42 0.52 0.47 0.23 0.90 0.65 0.64 0.55 0.56 0.45 0.60 0.46 0.35 0.60 0.31 0.63
0.0001 0.0014 0.0001 0.0005 0.0113 0.0056 0.0096 0.0960 0.0001 0.0009 0.0004 0.0226 0.0034 0.0176 0.0898 0.0151 0.0201 0.0020 0.0322 0.0012
Table Vlll. P r e d i c t i v e e q u a t i o n s f o r v a r i a b l e s o b t a i n e d b y l i n e a r r e g r e s s i o n a n a l y s i s w i t h X t h e m e a s u r e d v a l u e o f t h e v a r i a b l e a t a g e 11 o r 12 y e a r s a n d Y t h e p r e d i c t e d o r c a l c u l a t e d v a l u e o f t h e v a r i a b l e a t a g e 18 o r 19 y e a r s
Variable name Cranial width Facial Width Nasal Width Maxillary Width Mandibular Width Maxillary Intermolar Width (6-6) Mandibular Intermolar Width (6-6) TFH UFH LFH LRH RRH
Sex M F M F M F M F M F M F M F M F M F M F M F M F
Predictive equation Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y
= = = = = = = = = = = = = = = = = = = = = = = =
2.88 + 1.O05X 12.45 + 0.924X - 18.34 + 1.25X 17.46 + 0.908X 9.32 + 0.779X 0.01 + 1.079X 10.15 + 0.887X 19.27 + 0.704X - 7 . 7 0 + 1.198X 12.30 + 0.919X 8.62 + 0.873X 22.02 + 0.607X 0.805 + 0.985X 21.07 + 0.611X 28.33 + 0.903X - 5 9 . 2 4 + 1.654X - 4 . 9 7 + 1.281X 29.34 + 0.441X 34.07 + 0.592X - 3 5 . 4 4 + 1.717X 10.30 + 1.01X 22.42 + 0.673X 5.804 + 1.09X 24.18 + 0.635X
R2
P value
0.94 0.74 0.94 0.87 0.66 0.79 0.81 0.53 0.96 0.90 0.74 0.81 0.77 0.38 0.52 0.81 0.68 0.32 0.45 0.88 0.47 0.64 0.52 0.67
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0076 0.0001 0.0001 0.0001 0.0001 0.0001 0.0249 0.0024 0.0009 0.0017 0.0668 0.0080 0.0001 0.0064 0.0017 0.0037 0.0010
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was 61.9 mm for the 9-year-old subject and increased 0.6 mm per year. The results of this study revealed a mean of 58.1 mm for females that increased from 0.5 to 1.5 mm per year and 60.0 mm for males that increased from 0.5 to 1.7 mm per year. Mandibular width Mandibular width was similar to other transverse measurements. The male sample showed a growth spurt at age 15 years. There were relatively larger growth rates from 7 to 10 years than from 10 to 18 years. Mandibular width for males at age 6 or 7 years had the highest reliability of prediction among all the variables included in this study (R 2 = 0.90). Thus, considering the amount of growth, mandibular width could be predicted with considerable accuracy on the male subjects in this study. However, the predictability was not as strong for the females (R 2 = 0.65). The predictability of mandibular width at age 11 or 12 years was strong for both females and males. Ricketts et al. 4 found mandibular width, as measured from antegonial notch points, had a norm of 76.1 mm at age 9 years and increased 1.4 mm per year. This study found mandibular width change measured as the bigonial distance to be 82.7 for females and 85.2 for males at age 9 years, increasing from 0.5 to 2.0 mm for females and 1.5 to 3.0 mm for males. The distance between antegonial notches and gonion accounted for the differences between Ricketts et al. and this study. The mean mandibular width demonstrated continued growth in females at age 18 years, later than any other measurement. The continued growth at the gonial angle after the completion of all other facial growth could be induced by the muscle attachments. Mandibular width and mandibular intermolar width (6-6) were rrot correlated in females or males. Mandibular width was a measurement of the outer table of the mandible with effects from muscle attachment, whereas mandibular intermolar width was a measurement more closely associated with the inner table of the mandible with lesser effects of muscle attachments. Intermolar width Woods 14 found maxillary intermolar width increased 2.5 mm for females and 2.6 mm for males from the age of 7 to 15 years. Sillman 15found this measurement to increase from 7 to 13 years by 3.0 mm in a grouped sample of males and females. The mean increase from 7 to 13 years was 1.9 mm for females and 2.9 mm for males. This study also found the mean increase in maxillary intermolar width" from 7 to 16 years to be 2.1 mm for females and 3.6 mm for males. These results
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were similar to Moyers 16 who determined maxillary intermolar width (6-6) to increase 3.5 mm in females and 4.2 mm in males from 7 to 16 years. Intermolar width increases past age 16 years have not been commonly reported in the literature. This study indicated that there is an average increase in maxillary intermolar width (6-6) of 1.4 mm from 16 to 18 years for males. The pattern of increase in width between the maxillary second molars after they erupt at about 12 to 13 years was comparable to that of the intermolar distance of the maxillary first molars from 6 to 13 years after the eruption of the latter at 6 years. The means for mandibular intermolar width (6-6) demonstrated that from 7 to 18 years there was a decrease of 0.5 mm in females but an increase of 0.4 mm in males. The results from this study confirmed the work of Woods 14who found mandibular intermolar width (66) decreased by 0.7 mm in females and by 0.6 mm in males. However, this is different from the findings of Sillman 15 who found an increase of 1.2 mm in a group of males and females and Moyers ]6 who found an increase of 1.6 mm in females and 2.6 mm in males. All intermolar widths were highly correlated as the sample was chosen on the basis of a Class I occlusion with the absence of crossbite and minimal clinical crowding. Vertical measurements The total percentage increases for the vertical measurements were greater than those of the transverse measurements. From 6 to 18 years TFH increased 35% in males and 24% in females. When the total size of the increment between ages 6 and 12 years was compared between males and females, the differences were very small (16% and 14%, respectively). Hence most of the gender differences developed after the age of 12 years during the pubertal growth period. Nanda reported similar findings from his longitudinal growth studies. 17 Total face height was highly correlated with UFH and LFH for both males and females, as it was the sum of these two measurements. From the ages of 6 to 8 years, LFH was more complete in its growth than UFH. From 8 to 18 years of age, both measurements had similar percent increases. Upper and lower face heights were not correlated for either males or females. Lower face height was a measure of the downward decent of the maxilla and mandible. It was similar to other vertical measurement in this study with large increases from 12 to 18 years for the males. The percent increase from age 6 to 18 years demonstrated large differences between males and females. The percent increase for males was 33%, whereas the percent increase for females was less than 20%.
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As the subjects were selected on the basis of a normal facial profile and occlusion, bilateral asymmetries or differences between RRH and LRH were very small, with less than 1 mm for all subjects. Ramus height was found to increase proportionally greater than any other dimension measured in this study. Nanda 17 demonstrated that the distance sella to gonion, a measure similar to ramus height in this study, had greater proportional growth than any of the other facial dimensions measured. Left and right ramus heights were highly correlated as the sample demonstrated bilateral symmetry. However, ramus heights were not correlated with other vertical measurements. An explanation for the low correlation between ramus height and lower face height was that ramus height measured posterior height and lower face height measured anterior height, and the two were independently variable.
Clinical significance It is important for the clinician to study the bilateral transverse and the bilateral vertical dimension of the face to have a comprehensive evaluation. The rate of growth in width is different from vertical facial measurements taken from lateral cephalometric radiographs. The transverse width of the face grows at a lesser rate than sagittal or vertical growth of the face. However, there are significant changes in facial width that need to be delineated. Timing orthodontic treatment to coincide with growth may be a considerable factor in the stability of the dentition. As many clinicians use maxillary orthopedics, the timing of its use is important. As the growth in width of the maxilla is 95% complete for males and 98% complete for females at age 12 years, one may consider the use of maxillary expansion earlier. The greatest growth" in width of the maxilla occurred from 7 to 11 years in males and from 6 to 11 years in females. There was accelerated growth at age 15 years for males; however, it did not not notably exceed the growth rates from 7 to 11 years. The results from this study indicate that the majority of females had completed maxillary width growth by age 15 years, whereas the majority of males were complete at age 17 years. The midpalatal suture may be fused shortly after these years. Melsen 11 found the suture to fuse at age 16 for females and at age 18 years for males. Therefore the use of orthopedic maxillary expansion should be cautiously applied past the age of 15 years for females and 17 years for males. Furthermore, the increases in maxillary intermolar width at the first and second molars were parallel to increases in the width of the maxilla indicating that
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interdental changes were reflecting the changes in the width of the maxilla. The increments in the maxillary width were large between the ages of 6 to 12 years in females and 7 to 11 years in males, even though a small increase continued through age 16 years. Mandibular intermolar width (6-6) did not increase as did the maxillary intermolar width (6-6). It follows that the mandibular dental arch perimeter is finite after the eruption of permanent first molars as far as the width of the basal bony width is concerned in contrast to the maxillary arch perimeter that may become larger with the continuing growth in width of the maxilla. Nasal width demonstrated the greatest percent increase of any transverse measurement from 6 to 18 years. It was 25% for females (5.8 mm) and 33% (7.6 mm) for males. This growth continued longer than any other transverse measurement in this study. The majority of males and several females had not completed their nasal width growth even at age 20 years. With these large increases, a possibility is offered that some potential may exist for a young patient to "outgrow" a breathing problem. Ramus height demonstrated large increases that would strongly impact facial structure. This was especially true for males who at age 12 years were only 85% complete with respect to their size at age 18 years. Furthermore, growth was not complete until age 20 years for the majority of males. The greatest rates of growth occurred at ages 13 and 14 years for females and at ages 15 through 17 years for males. With continuous growth of the ramus height, the mandibular plane becomes more horizontal, and Frankfort-mandibular plane angle may be reduced as has been demonstrated by Nanda. 18 Much of the vertical ramal growth occurs at the mandibular condyle with large impact on the sagittal growth of the mandible and flattening of the facial profile. Of the 11 males with radiographs past the age of 20 years, 10 demonstrated continued growth in maxillary second intermolar width (0.3 to 1.4 mm), 9 in facial width (0.5 to 1.9 mm), 8 in cranial (0.5 to 1.5 nun) and nasal width (0.4 to 1.4 mm), 7 in maxillary (0.4 to 2.0 mm) and mandibular width (0.3 to 2.1 mm), 6 in mandibular first intermolar width (0.4 to 1.3 mm), 5 in lower face height (0.4 to 2.0 mm) and right and left ramus heights (0.5 to 2.2 mm), 4 in total (0.5 to 2.2 mm) and upper face height (0.5 to 1.3 mm), whereas only 3 subjects had increases in mandibular second intermolar width (0.3 to 0.7 mm) and 2 in maxillary first intermolar width (0.3 to 0.4 mm). This is consistent with the work of Nanda 17 who found continued growth past age 20 years for several male subjects.
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SUMMARY AND CONCLUSIONS Longitudinal records of P-A cephalometric radiographs were used to evaluate growth in the transverse and vertical dimensions for 25 females between the ages of 4 to 20 years and for 25 males between the ages of 4 to 25 years. The subjects were selected on the basis of normal skeletal and dental patterns from the Child Research Council in Denver, Colo. Growth was evaluated from the group means and also on the basis of individual growth patterns. Mean values were calculated for each of the nine transverse and five vertical variables from ages 6 to 18 years, for both the males and females. Individual data correlations and predictive equations were formulated. The following conclusions were established: 1. At 6 years of age, the transverse dimensions had a greater percentage of the adult size completed than the vertical measurements for both males and females. All the transverse measurements were over 80% complete in growth by age 6 years when using age 18 years as 100%, with the exception of nasal width for males, which was only 75% complete. The percent change in growth was similar for females in the transverse and vertical dimensions from age 6 to 18 years. However, males from age 12 to 18 years demonstrated more vertical change than transverse. 2. Numerous significant correlations were found between measurements for both males and females. Cranial width correlated with only facial width. Facial width correlated with all skeletal transverse measurements, except maxillary width for males. Nasal width was correlated with maxillary width. With the exception of mandibular intermolar width (6-6) for males, maxillary width was correlated with all dental measurements, whereas mandibular width correlated only with maxillary intermolar widths for females. All dental measurements were highly correlated with each other. Total face height was highly correlated with upper and lower face heights. However, with the exception of right and left ramus heights, there were no other significant correlations between the vertical measurements. 3. There were multiple statistically different mean values for males and females at 6, 12 and 18 years of age for all 14 variables, except nasal width. At age 6 years, mean differences were found for widths in the cranium, face, and maxilla. At age 12 years, the mean differences were found for cranial width, maxillary width, and maxillary and mandibular intermolar width (6-
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6). At age 18 years, all the variables were different, except for nasal width and mandibular intermolar width (6-6). . Linear regression analyses revealed several variables that displayed strong (R2 _> 0.060), moderately strong (R = > 0 . 4 0 and <0.60), and nonpredictable or weakly (Re _< 0.40) predictable for age 18 or 19 years if the value at age 6 or 7 years was known. This was also true for age 18 or 19 years if the value at age 11 or 12 years was known. The strength of predictability for each variable in both sexes in the 6- or 7year age group are provided. (a) Strong predictability in both sexes: cranial width, facial width, mandibular width. (b) Strong predictability in males and moderate predictability in females: lower face height, total face height. (c) Strong predictability in females, nonpredictive in males: right and left ramus height. (d) Moderately strong predictive equations in both sexes: nasal width, maxillary width, upper face height. The strength of predictability for each variable in both sexes in the 11 or 12 year age group are provided. (1) Strong predictability in both sexes: cranial width, facial width, nasal width, mandibular width, maxillary intermolar width (6-6). (b) Strong predictability in males, moderately strong predictive in females: maxillary width, upper face height. (c) Strong predictability in females, moderately strong predictability in males: lower face height and total face height. (d) Strong predictability in males, nonpredictive in females: mandibular intermolar width.
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6. Hellman M. Introduction of growth of the human face from infancy to adulthood. INT J ORTHOD 1932;18:777-98. 7. Goldstein MS. Changes in dimensions and form of the face and head with age. Am J Phy Anthropol 1936;22:37-89. 8. Bishara SE, Jakobsen JR. Longitudinal changes in three normal facial types. AM J ORTHOD 1985;88:466-502. 9. Scammon RE. A summary of the anatomy of the infant and child. Pediatrics, vol. I. Philadelphia: WB Saunders, 1923:89. 10. Meredith HV. Growth in bizygomatic face breadth during childhood. Growth 1954;18:111-34. 11. Melsen B. Palatal growth studied on human autopsy material. A histological microradiographic study. AM J ORTHOD 1975;68:42-54. 12. Bj6rk A, Skieller V. Growth in width of the maxilla studied by the implant method. Scan J Plast Reconstr Surg 1974;8:26-33. 13. Savara BS, Singh IJ. Norms of size and annual increments of seven anatomical measures of maxilla in boys from 3 to 16 years of age. Angle Orthod 1968;38(2):104-20. 14. Woods GA. Changes in width dimensions between certain teeth and facial points during human growth. AM J ORTHOD 1950;36:676-700.
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15. Sillman JH. Dimensional changes of the dental arch: longitudinal study from birth to 25 years. AM J ORTHOD 1964;50:824-42. 16. Moyers RE, v o n d e r Linden FPGM, Riolo ML. Standards of human occlusal development. Monograph 5, Craniofacial Growth Series. Ann Arbor: Center for Human Growth and Development, University of Michigan Press, 1976:176-8. 17. Nanda RS. The rates of growth of several facial components measured from serial cephalometric roentgenogram. AM J ORTnOD 1955;41:658-73. 18. Nanda RS. Growth changes in skeletal-facial profile and their significance in orthodontic diagnosis. AM J ORTHOD 1971;59:501-13. Reprint requests to: Dr. G. Frans Currier University of Oklahoma Health Sciences Center College of Dentistry P.O. Box 26901 1001 Stanton L. Young Blvd. Oklahoma City, OK 73190