Craniofacial Growth and the Dentition

Symposium on Oral Health

Craniofacial Growth and the Dentition Robert E. Williams, D.M.D., M.A.,*

and Richard F. Ceen, D.D.S. t

A knowledge of the mechanism and pattern of normal craniofacial growth and development must be coupled with an understanding of how this information can be applied to the individual patient commonly seen in a pediatric practice. Physicians need to be aware that the ability of an orthodontist to successfully treat a skeletal malocclusion is greater in patients who are growing. 31 Since the pediatrician may be the only health-care provider to see a child during the growing years, the early recognition and referral of patients manifesting abnormal growth patterns (for example, retrognathic or prognathic mandibles, open or deep bites, short or long faces) can be a major factor in an orthodontist's ability to achieve a significant modification of the patient's facial growth pattern. The ability to predict the extent and direction of craniofacial growth with the accuracy necessary to achieve clinical significance has been an area of major interest to those involved in treatment of the craniofacial complex. It is the objective of this chapter to discuss the patterns of growth of the craniofacial complex, the effect of this growth on the dentition, and to describe the current research in craniofacial growth prediction.

CRANIOFACIAL GROWTH Studies of craniofacial growth in humans fall into three categories based on the methods used: (1) cross-sectional material has been compared and longitudinal conclusions derived (for example, using dried skulls), 50 • 51 (2) combinations of longitudinal and cross-sectional data (for example, cephalometric radiographic data), 29 ' 30 (3) true longitudinal cephalometric sh1dies using metallic implants.t2-25, 58, 92, 97. 98

Cephalometric Technique Cephalometric roentgenography is an outgrowth of craniometry and the craniostat, a device employed by anthropologists since the nineteenth century *Assistant Professor of Orthodontics, Baltimore College of Dental Surgery, University of Maryland School of Dentistry, Baltimore, Maryland f Associate Professor of Orthodontics, Baltimore College of Dental Surgery, University of Maryland School of Dentistry, Baltimore, Maryland

Pediatric Clinics of North America- Vol. 29, No.3, June 1982

503

504

ROBERT

E.

WILLIAMS AND RICHARD

F.

CEEN

to measure dry skulls. 46 • 71 Since 1922, roentgenographic images have been employed to study facial anthropometry. 107 In 1931, the standardization of cephalometric radiographic procedures as they are employed today was initiated.28· 76 Cephalometric roentgenography differs from other radiographic techniques in that the anode-subject film distances are standardized, and the patient's head is fixed in a reproducible position (Fig. 1). Orientation of the film, either parallel or perpendicular to the sagittal plane of the head, provides a means for measuring the size and relationships of various craniofacial areas. For orthodontic purposes, the disadvantage of measuring three-dimensional facial structures on a two-dimensional image is outweighed by the ability to obtain initial measurements and serially follow changes in an individual's facial dimensions over time. In an attempt to identify skeletal disharmonies and monitor the effects of growth and treatment, orthodontists have developed a multitude of cephalometric analyses that attempt to quantify selected angles, dimensions, or relationships of craniofaciallandmarks. 38 • 44 • 53 • 113 • 127 • 145 • 153 These analyses, in general, are based on mean values from limited populations usually selected for their pleasing facial esthetics and occlusion. Measurements obtained from an individual's cephalogram are usually compared with these means. The validity of some of these analyses may be questioned, however, because of biases in the selection of subjects. For example, few studies pertain to non-white racial groups. 2 • 40 • 4 5, 15 4 All clinically acceptable cephalometric analyses are capable of assessing the following relationships: (1) basal bones to cranium: the relationship of the maxilla and mandible to the cranium, and to each other; (2) teeth to basal bone: the relationship of the teeth to their supporting structures; (3) teeth to teeth: the relationship of the upper and lower teeth to each other; and (4) the contour of the soft tissue profile.

Problems of Analysis of Craniofacial Growth Several problems arise with any attempt to examine or quantify craniofacial growth. 61 First, although the studies of craniofacial growth are basically anatomic research, longitudinal measurements must be derived from radiographic projections that are subject to varying bias. Radiography reduces a dynamic three-dimensional structure to a series of two-dimensional pictures. Second, no absolute reference points exist from which growth can be measured. Depending on the interest and awareness of the observer, any

60"

-14cm

Figure L Anode-subject-film relationships and standardized distances used in cephalometric radiography.

Anode

Subject Film

CRANIOFACIAL CROWTH AND THE DENTITION

505

Figure 2. Mean growth pattern of the cranium and cranial base from age 12 to 20 of 243 male subjects. (From Bjiirk, A.: Cranial base development. Am. J. Orthod., 41(3):198, 1955).

number of landmarks can be used for orientation. However, the way one chooses to superimpose serial cephalograms influences the position of the face in space and may add to, or subtract from, real growth. Third, examination of the pattern of development of the face as a whole obscures the actual growth pattern of individual facial bones. For example, routine cephalometric methods produce a picture suggesting that the pattern of facial growth is downward and forward. The actual growth of the face is much more complex than this oversimplified picture, and thus the growth of individual bones must be examined separately if the pattern of total facial growth is to be meaningful.47, 48

With the above considerations in mind, this discussion of growth of the component parts of the cranial base and face is based on longitudinal cephalometric studies using individuals who have had metallic implants placed in their jaws. 12' 25 • 58 • 92 • 97 • 98 By inserting vitallium implants into the facial bones of subjects, fixed landmarks may be obtained that permit the examination and description of the location, direction, and magnitude of growth changes in the facial area. The findings of these studies have also been supplemented by results of histologic studies on dry skulls. 47 - 53

GROWTH OF THE CRANIAL BASE The evaluation of growth of the face as a whole is usually based on serial cephalograms superimposed on the anterior cranial base, especially the · cribriform plate of the ethmoid. 20 Using this procedure, the general growth pattern of the cranium and cranial base is shown in Figure 2.

506

ROBERT

E.

WILLIAMS AND RICHARD

F.

CEEN

Anterior Cranial Base The anterior cranial base comprises the bones of the anterior cranial fossa, the frontal and ethmoid, and that portion of the sphenoid anterior to sella turcica. The length of the anterior cranial fossa increases by sutural growth until about age ten, when growth of the ethmoid ceases. 16 · 146 From then on, increases in length are due to anterior displacement of the frontal bone as a whole, accompanied by frontal apposition of the glabella and sinus. 16, 52, 146 As a result of the relatively early cessation of growth in the ethmoid area, this region is often used as a reference to evaluate other faster and later growing areas of the face. Any increase in length of the anterior cranial base

will result in a corresponding anterior displacement of the articulating maxilla and midface.

Posterior Cranial Base The posterior cranial base extends posteriorly from sella turcica to the anterior border of the foramen magnum and includes portions of the sphenoid and occipital bones. Growth in this region occurs primarily in the sphenooccipital synchondrosis and continues until late adolescence or early adulthood.16· 52 Dorsal and vertical increases in length of this region result in a distal and inferior displacement of the mandible (averaging 3 to 4 mm). 16

Cranial Base Angle In addition to the anterior, posterior, and vertical displacement of the maxilla and mandible which occur with absolute increases in length of the anterior and posterior cranial base, changes in maxillomandibular relationships may also occur because of changes in the angle between the anterior and posterior cranial base. While the mean anterior-posterior cranial base angle remains stable, individuals may demonstrate a 10-degree widening or flattening of the cranial base angle in response to differential brain growth 16 · 49 · 52 (Fig. 3). The angle of the cranial base will directly influence mandibular position, since change will displace the glenoid fossa anteroposteriorly and directly affect the degree of protrusion of the mandible.

b

Figure 3. Variation in cranial base angle due to growth from age 12 to 20 of two individuals: (a) decreasing angle; (b) increasing angle. (From Bjiirk, A.: Cranial base development. Am. J. Ortbod., 41(3):198, 1955)

507

CRANIOFACIAL CROWTH AND THE DENTITION

5cm

Figure 4. Mean growth pattern of the maxilla and maxillary dentition from age 6 to 14 of 45 male subjects. (From Bjork, A.: Sutural growth of the upper face studied by the implant method, Acta Odont .. Scand., 24:109, 1966)

In addition, changes in the cranial base angle result in a change in head position or balance of the head on the spinal column. A flattening of the cranial base usually will have the effect of tilting the face upward, thereby giving an impression of greater facial prognathism. 16 Rotation of the lateral parts of the cranial base may also be transmitted through the zygomatic processes of the maxilla and have a direct influence on the vertical lowering of the upper facial structures.

GROWTH OF THE MAXILLA The midface of the growing child undergoes a dramatic increase in absolute size, particularly in relation to the cranium, which is more nearly complete at birth. Increases in width, depth, and particularly height continue, primarily in the maxilla, after the seventh year, when there is a cessation of growth in the cranial and orbital cavities, and a reduction in sutural growth. Average sagittal changes in the maxilla and maxillary dentition occurring after age six are presented in Figure 4.

Change in Width Comparison of a newborn's face with that of older children reveals that interorbital width is completed by about three years of age in synchronization with fusion of the midsagittal suture system. 88 Bizygomatic growth lags behind cranial growth in the early years but continues to expand after cranial growth stabilizes; as a result the cheek bones become more prominent with age. 133, 134 Unlike the bones that are more closely related to the cranial base, the maxilla maintains some capacity to expand beyond the time of ossification of the sagittal suture system. Histologic and implant studies have demonstrated that growth in the midpalatal suture continues until puberty, 86 • 99 • 141 with

508

ROBERT E. WILLIAMS AND RICHARD

F.

CEEN

sutural growth accounting for at least two thirds of the increase in maxillary width. 25 Greater increases in width occur posteriorly, resulting in a lateral rotation of the.maxilla, and a larger increase in width of the molar region when compared with the canine region. 25 · 104 Increases in width between the canines are smaller in females than in males, who demonstrate a larger and later increase in width associated with the pubertal growth spurt of the mandible. 103 However, both bimolar and bicanine widths show a gradual decrease during adolescence, so that by age 20 the diameters are approximately the same as those at age 6. 24 · 25 Surgical extirpation of the mid palatal suture has been shown to dramatically decrease lateral growth of the maxilla and increase the incidence of dental crossbites. 55 Conversely, patency of the suture during childhood permits orthopedic expansion of the maxilla and maxillary dental arch, allowing orthodontists to correct many transverse deficiencies. Occlusion of the maxillary and mandibular teeth also appears to influence dental arch expansion, as the increase in width of the maxilla itself exceeds that of the dentition. 25

Change in Depth As the maxilla is displaced anteriorly by growth of the cranial base, limited sutural growth in the body of the maxilla and periosteal apposition at the tuberosity in a posterior direction provide space at the distal end of the maxillary dental arch for eruption of the permanent molars. 16 · 19 · 25 While some contend that the anterior surface of the maxilla and zygomatic process are resorptive, 49· 50 implant studies show these areas to be relatively stable, with resorption associated with more extreme forward rotations of the maxilla.15' 19· 23 · 25 For the zygomatic process there is general agreement that the posterior surface is appositional, 25 · 50 while the infrazygomatic crest appears stable beyond childhood. 25 In addition to changes in depth of the maxilla itself, the dentition as a whole tends to drift forward on the maxilla, resulting in a decrease in incisor space that may increase dental crowding. 25

Change in Height In comparison with changes in width and depth, changes in midface height show the greatest increase from 3 to 16 years of age. 129 Some of this increase is due to apposition on the lower border of the alveolar process, but approximately two thirds is due to growth at the frontal and zygomatic sutures. This sutural change in height is associated with enlargement of the nasal cavity. 16 · 19 · 20 · 25 Lowering of the nasal floor is usually greater anteriorly than posteriorly and is due to resorption on the nasal surface and apposition on the palatal surface. 19 · 20 · 25 Vertical displacement of the maxilla as a whole is often accompanied by a forward or, occasionally, backward rotation in the sagittal plane. This may result from growth of the pterygoid processes or changes in the angle of flexure of the cranial base. 16 · 23 · 25 · 58 Forward rotation of the maxilla will result in an increased alveolar and dental prominence, while a backward rotation is associated with an increase in facial height (Fig. 5).

509

CRANIOFACIAL GROWTH AND THE DENTITION

v

v

20yr--

f2 yr -·-20yr--

a

b

132& 12 yr----

177&

Figure 5. Variation in dento-alveolar prominence due to growth from age 12 to 20 of two individuals: (a) increased vertical height associated wit!:> a decreasing cranial base angle and dorsal rotation of the maxilla; (b) increased prognathism associated with an increasing cranial base angle and ventral rotation of the maxilla. (From Bjork, A.: Cranial base development. Am. J. Orthod., 41(3):198, 1955)

Correlations with Somatic Growth The pubertal growth spurt at the facial sutures, which increases the height and width of the maxilla, may occur before, concurrently, or after the spurt in body height or the onset of epiphyseal-diaphyseal fusion. 19 • 105 • 106 The spurt in width of the maxilla coincides with that of stature, but terminates earlier. 24 Vertical growth of the maxilla exhibits an earlier and larger increase than does depth or width; width shows the smallest increment of change. 129 • 138 The adolescent spurt in maxillary growth occurs one to three years earlier in females than in males. 129 Significant disagreement exists among investigators regarding the relationship between pubertal facial growth and dental development. 22

GROWTH OF THE MANDIBLE The esthetics of an individual's lower face depends on the relative position of the mandible in relation to the superior facial structures. Since individuals maintain virtually the same vertical distance between the upper and lower teeth (mandibular rest position) throughout life, mandibular growth must constantly compensate for the vertical eruption of the teeth, growth of the alveolar process, descent of the midface, and changes in the angle of flexure of the cranial base. It must also attain differentially greater growth in depth than the midface to produce the characteristic mandibular prominence and flattening of the profile that occurs in childhood and adolescence. The resulting mean growth pattern of the mandible and mandibular dentition is shown in Figure 6.

Condylar Growth Growth in length of the mandible occurs chiefly at the condyles. 15 • 18 • 20 Total protrusion of the mandible depends on both the amount and direction of

510

ROBERT E. WILLIAMS AND RICHARD

F.

CEEN

Scm Figure 6. Mean growth pattern of the mandible and mandibular dentition from age 6 to 11 of 45 male subjects. (From Bjork, A.: Variations in the growth pattern of the human mandible. J. Dent. Res., Supplement to No. 1, 42:400, 1963)

growth of the condyles, 16 and bodily displacement due to growth of the cranial baseY· 13 The direction of growth of the condyles influences the general shape of the mandible. Growth at the condyles is not usually aligned with the posterior border of the ramus, but is slightly forward, with individual variations up to 45°. 18 • 21 Growth in an upward direction will increase vertical height, while growth in a backward direction will increase sagittallength 16 (Fig. 7).

.

'

'

I,) . (--,_ '

.. a

/

Scm

b

Figure 7. Variation in mandibular growth and path of dental eruption of two subjects: (a) extreme vertical growth from 11 years, 7 months to 17 years, 7 months; (b) extreme sagittal growth from 10 years, 6 months to 15 years, 6 months. (From Bjork, A.: Variation in growth pattern of the human mandible. J. Dent. Res. Supplement to No. 1, 42:400, 1963)

CRANIOFACIAL GROWTH AND THE DENTITION

511

Both the amount and direction of condylar growth influence the shape of the gonial (corpus-ramus) angle. Vertical growth of the condyle decreases the gonial angle, and usually results in increased resorption beneath the angle and apposition under the symphysis. In contrast, sagittal growth of the condyle is usually associated with less resorption, or even apposition beneath the angle, and reduced apposition beneath the symphysis 18 (Fig. 7). Condylar growth in males averages approximately 3 mm annually, with a well-defined prepubertal minimum at 11 years 9 months. A pubertal maximum of 5 mm occurs at a mean age of 14lfz years, with cessation of growth varying from 12% to over 20 years of age. 18 Growth of the condyles and cranial base is more closely related to growth in body height than the growth spurt in other facial measurements. Clinically, orthopedic correction of maxillomandibular malrelations may be treated more successfully during an active growth spurt. That is, a retrognathic mandible will tend to become less severe with average mandibular growth, while a prognathic mandible will tend to worsen. In regard to the direction of growth, the average resultant of growth of the face is downward and forward in approximately equal amounts. In an individual with marked horizontal (forward) growth, there is a tendency toward a skeletal deep bite, while with marked vertical (downward) growth, there is a tendency for a skeletal open bite to develop. Every individual may have periods when marked horizontal or vertical growth predominates, but the overall pattern for most individuals is still downward and forward.

Symphyseal Growth There is no appreciable growth on the anterior aspect of the chin except in rare cases of pathology, in which either resorption or apposition may occur. 18 • 20 · 21 The area between the chin and alveolar process is primarily resorptive in nature. 88 • 138 Thickening of the symphysis is a result of apposition on its posterior and inferior surface, the latter contributing somewhat to an increase in height of the symphysis and a lengthening of the mandible.20· 2 1. 97 • 98 While Bjork' 8 originally found the inner cortex of the symphysis, the mandibular canal, and the floor of the unerupted tooth germs to be relatively stable areas, Matthews and Ware 98 demonstrated that only the symphysis does not change substantially.

Mandibular Rotation Rotational growth of the mandible often occurs about a point that may be located anywhere between the symphysis and the condyles. Forward rotation around the center of the temporomandibular joint is most common, with a resulting reduction in anterior facial height, and an increase in vertical overlap of the upper and lower incisors. 2 1. 58 • 92 • 93 Forward rotation around a point near the incisors, accompanied by normal vertical anterior growth, results in an increase in posterior facial height and movement of the posterior part of the mandible away from the maxilla. Backward rotation of the mandible occurs less often and is usually associated with an increase in anterior facial height, development of the skeletal open bite, lingually inclined mandibular incisors, a reduction in alveolar prognathism, and lip incompetence.21

512

ROBERT

E. WILLIAMS AND RICHARD F. CEEN

Rotational movements may also act as compensators for discrepancies in growth of the maxilla and mandible themselves. 82 • 93 When mandibular growth greatly exceeds that of the maxilla, the excess is dissipated through a high degree of anterior rotation. Conversely, when growth of the mandible is insufficient, there appears to be significantly less forward rotation. 92 A study of the effect of orthodontic treatment indicates that orthodontics may be capable of changing mandibular rotations into vertical translations, thereby influencing chin prominence. 82

Influence of Mandibular Growth on the Dentition In general, the path of eruption of the lower dentition is primarily vertical (Fig. 6). In cases of pronounced vertical growth of the mandibular condyle, eruption appears to be directed more anteriorly, while posterior drift and a reduction in arch length appear to be associated with sagittal condylar growth 18 (Fig. 7). The path of eruption also seems to be strongly influenced by the direction of mandibular rotation. Forward rotation of the mandible tends to increase alveolar prognathism, dental crowding, and overbite; while a backward rotation tends to decrease alveolar prognathism, increase the incidence of dental open bites, and results in a lingual inclination of the incisors. Arch length is increased not by the addition of bone to the mandibular corpus, but through resorption of the anterior border of the ramus, with a corresponding apposition on the posterior surface. Insufficient resorption of the anterior border may result in impaction of the mandibular third molars.

ASSOCIATED CHANGES IN THE DENTAL ARCH Having reviewed the effects of craniofacial growth on the size and position of the alveolar processes, let us now examine the changes that occur in various dental arch dimensions. In association with the greater increase in width and lateral rotation of the maxilla from age 3 to 18, intercuspid width shows a mean increase of 5 mm in the upper arch and 3 mm in the lower. lntermolar mean width increases 4 mm for the upper arch, and 2 mm for the lower, with an individual variation ± 3 mm. 102 • 104 • 136 Bimolar diameter shows a more or less steady increase, while bicanine diameter increases rapidly until the primary canines are shed, and then decreases about 1 mm. 33 • 85 While the absolute length of the dental arches increases due to apposition on the maxillary tuberosity and resorption of the anterior border of the ramus, anterior arch length, as measured from the labial surface of the incisors to the midpoint of a line connecting either the distal surface of the second primary molars or the mesial of the first permanent molars, remains relatively constant from 3 to 9 years of age, then decreases slightly in both the upper and lower arches from age 9 to 16. 60 • 85 • 102 • 104 Similarly, arch circumference, measured from either the distal surface of the second primary molar or the mesial surface of the first permanent molar on one side, around the arch to the similar surface on the opposite side, increases about 1 mm in the upper arch and decreases about 4 mm in the lower from age 5 to 18. 104 These decreases in

CRANIOFACIAL GROWTH AND THE DENTITION

513

anterior arch length and circumference are due to a forward drift of the posterior teeth during the transition from large primary molars to the smaller permanent bicuspids that replace them. The continuation of mandibular growth after the cessation of growth in the maxilla results in a relative reduction in the protrusion of the upper incisors in relation to the lower from age 12 to 20. 7 Vertical overlap of the incisors averages about 40 per cent at age 6 and changes very little until age 16, when it decreases slightly. 14 · 104

FACIAL-SOMATIC GROWTH CORRELATIONS One of the long-sought goals in the treatment of children with growth or skeletal discrepancies is to identify those periods of growth when treatment intervention will produce maximal results with minimal time and effort. Since variations in both the magnitude and velocity of growth of various craniofacial components have been identified, all that remains is to determine when and to what extent these variations will occur in any given patient. Unfortunately, children demonstrate considerable variation in the time required to reach similar stages of development. For this reason, chronologie age has not proved to be a reliable guide in the assessment of physical maturity.6, 10, 62, 8o, 91, 125, 126, 130, 142, 149, 15o, 151 As a result, various measures of developmental status, particularly skeletal maturation as indicated by standing height or hand-wrist radiographs, have been used to aid in growth evaluation. Unfortunately, studies are divided between those that have shown a high correlation between facial growth and standing height6 • 35 · 80 · 95 · 105 · 139 and others that have shown a low correlation. 74 · 79 · 101 · 124 · 125 · 128 Other studies have shown high correlations between facial growth and skeletal age (as measured by hand-wrist films or height) for males but not females."· 80 · 108 · 139· 140 · 142 · 150 In spite of these diverse findings, the following trends may be of some assistance in gauging an individual's maturation. Maturation of the ulnar-sesamoid as shown on hand-wrist films occurs approximately 12 months prior to the pubertal spurt in standing heighe 2· 135 · 137 (about 11 to 12 years of age in females, and 13 to 14 years of age in males.)."· 22 · 135 · 150 The spurt in height, in turn, occurs approximately 12 months prior to menarche in females (Fig. 8). 22 · 54 · 66 Girls with an early spurt in height tend to mature earlier, to have an earlier menarche, and to exhibit less growth than girls who mature later and have a later menarche. 43 · 150 The spurt in maxillary growth also follows the spurt in standing height, and approximates the spurt in mandibular growth (Fig. 9). 4· 105 · 135 Longitudinal data presented in the growth atlases prepared by Riolo et al. 123 and Broadbent et al.3° present gradual increases in mandibular length and position without the dramatic circumpubertal spurt found in most studies. Beginning as early as 1922158 numerous investigators'· 5· 8· 17 · 22 · 27 · 36 · 42 · 57 · 59, 62, 64, 66, 78, 89, 91, 94, loo, 144, 147, 15B have examined the relationship between tooth formation (or eruption) and skeletal maturation (or growth in stature). Most of these studies report widely varying correlations between dental development and skeletal maturation, ranging from near zero to a high of r = 0.97. 66 In virtually all cases, however, dental age is more closely correlated with skeletal age than chronologie age. 22 · 37 · 62 · 66

514

ROBERT

E. WILLIAMS AND RICHARD F. CEEN

MATURATION STAGES AT PUBERTY

.....

I

(.!)

CM/YEAR

H

jjj I

> 0

0 CD

z w ..... <( 0::

I

..... 3: 0

0:: (.!)

,---.L----'---.L - -

10

11

__J______ __ _j__--.-.JL______l___L___

12

13

14

15

16

__j__

17

___[__

__..

18

AGE IN YEARS Figure 8. Mean stages of maturation. and growth curves at puberty for both sexes. H, maximum pubertal growth in body height; S, ossification of the sesamoid; M, menarche. (From Bjork, A., and Helm, S.: Prediction of the age of maximum pubertal growth in body height. Angle Orthod., 37:134, 1967)

CM I MM PER YEAR

GROWTH TIMING

10

BOYS

T I I

I I

I----A-_,

5

o-----"""'_...tL-_-+/ CONDYLES

',

SUTURE&-.. "l··r.;- -

0

/

T / 1

II ' ,' J.

',

T

'

_,/, ..........•.•,,L., ..... ·-·• "!!!-.+'-r·· · J.. •••• ••

',

'

---~=2·=·~~::·~~·- ........ ::.-.:~.>~~-.::~~ l ..

8

10

12

14

16

18

. . . . .::::-20

---=--=---::::L..-

22 AGE IN YEARS

24

Figure 9. Relationship between peak growth in standing height, growth of the condyles and facial sutures. (From Bjork, A.: Sutural growth of the upper face. Acta Odont. Scand., 24:109, 1966)

CRANIOFACIAL GROWTH AND THE DENTITION

515

Simply knowing that craniofacial growth will occur is not sufficient. Attempts to predict growth with the accuracy necessary to achieve clinical significance have produced points of major controversy to those interested in the treatment of the craniofacial complex. The final section of this article will attempt to describe the current research and the state of the art in craniofacial growth prediction.

CRANIOFACIAL GROWTH PREDICTION The Need for Growth Prediction When orthodontic treatment is indicated for a child, the clinician is interested in developing a treatment plan that will allow for maximizing the interaction of the patients' growth potential with their treatment needs. Numerous cephalometric studies have confirmed that significant positional changes of the teeth, and alterations in the spacial relationships of the maxilla and mandible, occur during orthodontic treatment. The effects of these movements are manifested by changes in the patient's facial profile in addition to the changes that occur in the patient's dentition. It is important to understand the extent that orthodontic therapy and normal growth contribute to these changes. 34 Growth, whether or not it is altered by treatment, is always a major factor in the end product of facial development. Once orthodontists realized the impact of growth and treatment on the craniofacial skeleton, changes occurred in the philosophy of orthodontic treatment that required a consideration of growth prediction. These changes included the initiation of treatment prior to adolescence, thereby allowing therapy to proceed during major growth periods; the improvement of orthodontic treatment techniques, which allow for modification of the skeletal pattern through the use of orthopedic forces; and the recognition of the combined effect of orthodontic therapy and growth on the facial soft tissue profile. 65 In the growing individual, an orthodontic treatment plan is designed to develop ideal dental relationships that will harmonize with the child's anticipated adult facial characteristics. The ability to predict changes in the expected growth pattern of the patient enhances the orthodontist's ability to develop treatment plans that attempt to achieve the desired esthetic and functional results. Surgical treatment alternatives may be considered when the skeletal dysharmony is too severe to be corrected with orthodontic or orthopedic treatment alone. Additionally, prediction of an individual's growth provides the clinician with a "visual goal against which treatment progress can be measured and monitored." 65 Examination of serial cephalometric head films taken during treatment allows the clinician to monitor the effects of growth and treatment and to adjust for deviations from the predicted response.

Considerations in Growth Prediction Several variables of craniofacial growth have been considered in the attempt to develop useful predictive techniques. For example, the future size

516

ROBERT

E. WILLIAMS AND RICHARD F. CEEN

and relationship of the bones of the craniofacial skeleton, the vectors and velocity of growth, the timing of growth events, and the effect of orthodontic treatment on these parameters, have all been considered important as possible predictors of craniofacial growth. 73 The current status of research in this area may be summarized as follows: The ability to predict the future size and relationship of facial bones with accuracy on an individual basis would represent an important advance in the diagnosis and treatment of patients with a skeletal imbalance. Unfortunately, studies attempting to predict these parameters have not achieved the accuracy necessary for individual patients. 3· 34 · 70 · 73 • 83 · 109 The assumption that a bone will grow along a single established vector has been one of the more popular methods of assessing facial growth. 109 Since it has been established that these vectors vary in many individuals,3· 83 this method of prediction may be useful when considering population norms, but it is not useful on an individual basis. The focus of research in this area is now centered on predicting the change in these growth vectors, but the consistency of accurate prediction is stilllimited. 131 The timing of growth and the velocity of growth are separate but related elements in growth prediction. As with other segments of the body, there is a significant variation in both of these parameters. 81 While the time of onset, duration, and rate of growth during a spurt are all important,73 the results of research on these variables are too general to be clinically useful.2 2· 56 Prediction of the onset of peak growth velocity has significant treatment implications for two reasons. First, when growth increments are at their maximum, the amount of actual tooth movement required is decreased if the patient is growing favorably. Second, there is a possibility that hormonal changes associated with the circumpubertal growth spurt may enhance tooth movement. 34 The accurate prediction of variations in velocity may be significantly more complicated than other methods discussed thus far. 73 Clinical evidence suggests that orthodontic therapy itself has a considerable influence on many of the preceding variables. 53 · 114 · m Since orthodontic treatment may result in a permanent alteration in facial growth, treatment itself may be an important predictive factor. 3 Thus, of all the variables considered, orthodontic treatment designed to achieve certain predicted goals may enhance the success rate of the original growth prediction.

Prediction Methods and Controversy Developmental studies of postnatal facial shape and proportion have demonstrated significant individual variability. 12 · 15 · 18 · 38 · 105 Over the past 30 years, considerable research has attempted to accurately predict individual skeletal and soft tissue changes using data generated from cephalometric studies of orthodontically normal and abnormal populations.3· 9, 34, 41, 65, 10, 73, 77, 83. go, 96, 110-120, 122, 156, 157 However, considerable disagreement exists regarding the accuracy of the methods currently available for predicting individual growth. 63 · 75 · 84 · 131 Commentary on the subject of growth prediction ranges from strong advocacy of the accuracy of computerized cephalometric prediction techniques 121 to the critical assertion that cephalometric studies fail to show any improvement in the prediction of individual growth over mean population changes. 75 Interest in the prediction of craniofacial growth is also found in the fields

CRANIOFACIAL GROWTH AND THE DENTITION

517

of human genetics and mathematics. Investigators have sought information regarding the effect of heritability on craniofacial growth and its contribution to occlusal variation. 39 • 67 • 69 Noting that population norms used in cephalometric prediction are not an effective means of predicting individual growth in a heterogeneous society, Harris 69 has proposed the use of familial information to develop a system of prediction based on the presumption that heredity plays a direct role in most malocclusions. 68 Others argue that environmental effects are more important than heredity. 39 • 67 The phenomenon of family resemblance may make the question of genetics vs. environment a moot point. 143 Family resemblance may be cautiously used as an additional clinical tool for prediction, regardless of why it occurs. Various mathematical models have been proposed for growth prediction.73 Models based on the transformed coordinate method 148 and the use of equations to produce curves descriptive of growth processes have been found to be too general to describe any single growth pattern. They are inadequate, therefore, for routine use by orthodontists trying to predict growth in individual patients. Other mathematical methods used in industry and science have also been evaluated for use. Four of these methods that initially appeared to have promise may be categorized as (1) theoretical, (2) regressional, (3) experiential, and (4) time series. Theoretical and regressional methods were found to be either imprecise or inadequate for use in the prediction of individual growth. 73 The experiential method is currently the most popular 110' 116 and enjoys considerable use in the orthodontic profession today. It is based on the experience of the clinician using a data base of cephalometric means of a large sample of treated patients. The information is stored in a computer and is continually augmented to increase the data base. Criticism of this method arises from the assumption that an individual will grow identically to the mean of the sample population, irrespective of his similarities to that population group. This method also assumes that the skeletal morphology of the mandible or other facial bones can be used to determine future facial growth. Independent studies have not confirmed the morphology hypothesis, and they find that the efficiency of this prediction method is clinically negligible. 3 • 77 The time series method has recently demonstrated the greatest promise for use in prediction of craniofacial growth. This method has been tested in other scientific fields and found to be versatile, capable of modification, and effective when applied to individual patientsY Adaptation of this method to the needs of the orthodontist is now being studied. 72 • 73 The application of mathematics to craniofacial growth prediction has been increasing steadily, and a new model for predicting craniofacial growth using a transformational approach was recently published. 152 Although disagreement exists among mathematicians regarding the appropriate methodology,26 there is a considerable amount of ongoing research at this time. What, then, is the current status of craniofacial growth prediction? Many orthodontists currently use computerized cephalometric growth predictions or other techniques to assist them in the development of treatment plans. Unfortunately, it is not yet known when these methods are misleading, and no technique for orthodontic growth prediction has achieved universal acceptance as a valid clinical tool. From the previous discussion it is obvious that much research needs yet

518

ROBERT

E. WILLIAMS AND RICHARD F. CEEN

to be done. The infinite complexity and diversity of human craniofacial growth does not lend itself to one unique method of growth prediction. It would seem that an answer may lie in the "synthesis of biology and mathematical analysis." 155 The future holds significant promise in this regard. The ability to completely understand and accurately predict human craniofacial growth may still elude the clinician. However, the importance of this understanding to successful orthodontic treatment has been well substantiated. Patients treated for skeletal malocclusions during an active growth period have a significantly better prognosis, and the early recognition and referral qf these children by the pediatrician can be a major factor in the success of their orthodontic treatment.

REFERENCES 1. Abernathy, E. M.: Correlations in physical and mental growth. J. Educ. Psycho!., 16:458, 539, 1925. 2. Alexander, T. L., and Hitchcock, P.: Cephalometric standards for American Negro children. Am.]. Orthod., 74:298, 1978. 3. Balback, D. R.: The cephalometric relationship between the morphology of the mandible and its future occlusal position. Angle Orthod., 39:29, 1969. 4. Bambha, J. K.: Longitudinal cephalometric radiographic study of face and cranium in relation to body height. J. Am. Dent. Assoc., 63:776-799, 1961. 5. Bambha, J. K., and Van Natta, P.: A longitudinal study of occlusion and tooth eruption in relation to skeletal maturation. Am. J. Orthod., 45:847-855, 1959. 6. Bambha, J. K., and Van Natta, P.: Longitudinal study of facial growth in relation to skeletal maturation during adolescence. Am. J. Orthod., 49:481-493, 1963. 7. Bauerle, J. R.: A longitudinal study of incisor overbite from the deciduous dentition to age 15. University of Iowa, M.S. thesis, 1949. 8. Becks, H.: Orthodontic prognosis evaluation of routine dentofacial examination to determine "good or poor risks." Am.]. Orthod., 25:610, 1939. 9. Bench, R. W.: The visual treatment objective: Orthodontic's (sic) most effective treatment planning tool. Foundation Orthod. Res. Proc., 4:165, 1971. 10. Bergersen, E. 0.: The male adolescent facial growth spurt: Its prediction and relation to skeletal maturation. Am. J. Orthod., 42:319, 1972. 11. Bishara, S. E., Jamison, J. E., Pederson, L. C., eta!.: Longitudinal changes in standing height and mandibular parameters between the ages of 8 and 17 years. Am. J. Orthod., 80:115, 1981. 12. Bjork, A.: The face in profile. Sven. Tandlak. Tidskr., 40(Suppl 5B), Lund., 1947. 13. Bjork, A.: The significance of growth changes in facial pattern and their relationship to changes in occlusion. Dent. Record 71:197, 1951. 14. Bjork, A.: Variability and age changes in overbite and overjet. Am.]. Orthod., 39:779, 1953. 15. Bjork, A.: Facial growth in man, studied with the aid of metallic implants. Acta. Odontol. Scand., 13:9, 1955. 16. Bjork, A.: Cranial base development: A follow-up x-ray study of the individual variation in growth occurring between the ages of 12 and 20 years and its relation to brain case and face development. Am.]. Orthod., 41:198, 1955. 17. Bjork, A.: Bite development and body build. Dent. Rec., 75:8-19, 1955. 18. Bjork, A.: Variations in the growth pattern of the human mandible: Longitudinal radiographic study by the implant method. J. Dent. Res., 42:400, 1963. 19. Bjork, A.: Sutural growth of the upper face studied by the implant method. Acta Odont. Scand., 24:109, 1966. 20. Bjork, A.: Use of metallic implants and the shtdy of facial growth in children: Method and application. Am. J. Phys. Anthropol., 29:243, 1968. 21. Bjork, A.: Prediction of mandibular growth rotation. Am.]. Orthod., 55:585, 1969. 22. Bjork, A., and Helm, S.: Prediction of age at maximum pubertal growth in body height. Angle Orthod., 37:134, 1967. 23. Bjork, A., and Skieller, V.: Facial development and tooth eruption: an implant study at the age of puberty. Am. J. Orthod., 62:339, 1972. 24. Bjork, A., and Skieller, V.: Growth in width of the maxilla studied by the implant method. Scand. J. Plast. Reconstr. Surg., 8:26, 1974.

CRANIOFACIAL CROWTH AND THE DENTITION

519

25. Bjork, A., and Skieller, V.: Growth of the maxilla in three dimensions as revealed radiographically by the implant method. Br. J. Orthod., 4:53, 1975. 26. Bookstein, F. L.: Comment on Issues related to the prediction of craniofacial growth. Am. J. Orthod., 79:442, 1981. 27. Brauer, J. C., and Bahador, M.A.: Variations in calcification and eruption of the deciduous and the permanent teeth. J. Am. Dent. Assoc., 29:1373, 1942. 28. Broadbent, B. H.: A new x-ray technique and its application to orthodontia. Angle Orthod., 1 :45, 1931. 29. Broadbent, B. H.: The face of the normal child. Angle Orthod., 7:183, 1977. 30. Broadbent, B. H., Sr., Broadbent, B. H., Jr., and Golden, W. Y.: Bolton Standards ofDentofacial Developmental Growth. St. Louis, C. V. Mosby Co., 1975. 31. Brodie, A. G., Downs, W. B., Goldstein, A., and Myer, E.: Cephalometric appraisal of orthodontic results: A preliminary report. Angle Orthod., 8:261, 1938. 32. Buehl, C., and Pyle, I.: The use of age at first appearance of three ossification centers in determinging the skeletal status of children. J. Pediatr., 21:335-342, 1942. 33. Burson, C. E.: A study of individual variation in mandibular bicanine dimension during growth. Am. J. Orthod., 78:848, 1952. 34. Burstone, C. J.: Process of maturation and growth prediction. Am. J. Orthod., 49:907, 1963. 35. Bushra, E.: Correlations between certain craniofacial measurements, trunk length, and stature. Hum. Bioi., 21:246-256, 1949. 36. Cattell, P.: The Dentition as a Measure of Maturity. Cambridge, Harvard University Press, 1928. 37. Cheraskin, E., and Ringsdorf, W. M.: Biology of orthodontic patient. III. Relationship of the chronological age and dental age in terms of vitamin C state. Angle Orthod., 42:56-59, 1972. 38. Cohen, S. E.: The integration of facial skeletal variants. Am. J. Orthod., 41:407, 1955. 39. Cormccini, R. S., and Potter, R. H.: Genetic analysis of occlusal variation in twins. Am. J. Orthod., 78:140, 1980. 40. Cotton, W. N., Tanaka, W. S., and Wong, W. W.: The Downs analysis applied to three other ethnic groups. Angle Orthod., 21:213, 1951. 41. Curtner, R. M.: Predetermination of the adult face. Am. J. Orthod., 39:201, 1953. 42. Demisch, A., and Waterman, P.: Calcification of mandibular third molar and its relation to skeletal and chronological age in children. Child Dev., 27:459-473, 1956. 43. Dermaut, L. R., and O'Reilly, M. I.: Changes in anterior facial height in girls at puberty. Am. J. Orthod., 48:163, 1978. 44. Downs, W. B.: Variations in facial relationships. Am. J. Orthod., 34:812, 1948. 45. Drummond, R. A.: A determination of cephalometric norms for the negro race. Am. J. Orthod., 54:670, 1968. 46. Duckworth, W. L. H.: Morphology and Anthropology. New York, Cambridge University Press, 1904, p. 238. 47. Enlow, D. H.: Morphogenic analysis offacial growth. Am. J. Orthod., 52:283, 1966. 48. Enlow, D. H.: Morphogenic interpretation of cephalometric data. J. Dent. Res., 46:1209, 1967. 49. Enlow, D. H.: The human face. New York, Hoebar Medical Division, Harper & Row, 1968. 50. Enlow, D. H., and Bang, S.: Growth and remodeling of the human maxilla. Am. J. Orthod., 51 :446, 1965. 51. Enlow, D. H., and Harris, D. B.: A study of the postnatal growth of the human mandible. Am. J. Orthod., 50:25, 1964. 52. Enlow, D. H., Kuroda, T., and Lewis, A. B.: The morphological and morphogenic basis for craniofacial form and pattern. Am. J. Orthod., 41:161, 1971. 53. Enlow, D. H., Moyers, R. E., Hunter, W. S., and McNamara, J. A.: A procedure for the analysis of intrinsic facial form and growth. Am. J. Orthod., 54:6, 1969. 54. Flory, C. S.: Osseous development in the band as an index of skeletal development. Monogr. Soc. Res. Child Dev., 1:1-141, 1936. 55. Freng, A.: Growth in width of the dental arches after partial extirpation of the midpalatal suture in man. Scand. J. Plast. Reconstr. Surg., 12:267, 1978. 56. Frisancho, A. R., Garn, S. M., and Rohmann, C. G.: Age at menarche: A new method of prediction and retrospective assessment based on hand x-rays. Hum. Bioi., 41:42, 1969. 57. Garn, S.M., Lewis, A. B., and Kerewsky, R. S.: Genetic nutritional and maturational correlates of dental development. J. Dent. Res., 44:228-243, Suppl. to No. 1, 1963. 58. Casson, N., and Lavergne, J.: Maxillary rotation during human growth: Annual variation and correlations with mandibular rotation. Acta Odont. Scand., 35:13, 1977. 59. Gleiser, I., and Hunt, E. E.: Tbe permanent mandibular first molar: Its calcification, eruption, and decay. Am. J. Phys. Anthropol., 13:253, 1955. 60. Goldstein, M.S., and Stanton, F. L.: Changes in dimensions and form of the dental arches with age. Int. J. Orthod., 21:357, 1935. 61. Grainger, R. M.: Complexity of facial growth analysis, problems in analysis and dentofacial abnormalities. J. Dent. Res., 46:1210, 1967.

520

ROBERT

E. WILLIAMS AND RICHARD F. CEEN

62. Green, L. J.: The interrelationships among height, weight and chronological, dental, and skeletal ages. Angle Orthod., 31:189-193, 1961. 63. Greenberg, L. A., and Johnston, L. E.: Computerized prediction: The accuracy of a contemporary long range forecast. Am. J. Orthod., 67:243, 1975. 64. Gq;n, A. M.: Prediction of tooth emergence. J. Dent. Res., 41:573-585,..962. 65. Gugino, C. F.: An Orthodontic Philosophy, 5th ed. Denver, EDCO Associates, 1971, p. 69. 66. Gupta, D. S.: The relationship between skeletal maturation, malocclusion, and dentition. Aust. Dent. J.,21:217, 1976. 67. Harris, E. F., and Smith, R. J.: A study of occlusion and arch widths in families. Am. J. Orthod., 78:155, 1980. 68. Harris, J. E.: Genetic factors in growth of the head: Inheritance of the craniofacial complex and malocclusion. Dent. Clin. North Am., 19:151, 1975. 69. Harris, J. E., and Kowalski, C. J.: All in the family: Use offamilial information in orthodontic diagnosis. Case assessment and treatment planning. Am. J. Orthod., 69:493, 1976. 70. Harvold, E.: Some biologic aspects of orthodontic treatment in the transitional dentition. Am. J. Orthod.,49:1, 1963. 71. Hellman, M.: Changes in the human face. Trans. First Int. Orthodont. Cong., pp. 80-120, 1926. 72. Hirschfeld, W.: Times series and exponential smoothing methods applied to the analysis and prediction of growth. Growth, 34:129, 1970. 73. Hirschfield, W. J., and Moyers, R. E.: Prediction of craniofacial growth: The state of the art. Am. J. Orthod., 60:435, 197l. 74. Hixon, E. H.: Prediction offacial growth. Europ. Orthod. Soc. Trans., 44:127-139, 1968. 75. Hixon; E. H.: Cephalometries: A perspective. Angle Orthod., 42:200, 1972. 76. Hofrath, H.: Bedeutung der Roentgenfern- und Abstandsoufnahme fur die Diagnostik der Kieferanomolies. Fortschr. Der Ordhod., 1:232, 1931. After Brodie, A. G.: Growth of the human head from 3 months to 8 years. Am. J. Anat., 68:209, 1931. 77. Horowitz, S. L., and Hixon, E. H.: The Nature of Orthodontic Diagnosis. St. Louis, C. V. Mosby Co., 1966, p. 303. 78. Hotz, R., Boulanger, G., and Weisshaupt, H.: Calcification time of permanent teeth in relation to chronological and skeletal age in children. Helv. Odont. Acta, 3:4-9, 1959. 79. Howells, W. W.: A factorial study of constitutional type. Am. J. Phys. Anthropol., 10:91-118, 1952. 80. Hunter, C. J.: The correlation of facial growth with body height and skeletal maturation at adolescence. Angle Orthod., 36:44-53, 1966. 81. Hunter, W. S., and Miller, R. L.: Individual incremental growth graphs from lateral cephalograms. International Association for Dental Research, Abst. No. 39, 1968. 82. Isaacson, R. J., Zapfel, R. J., Worms, F. W., eta!.: Some effects of_mandibular growth on the dental occlusion and profile. Angle Orthod., 47:97, 1977. 83. Johnston, L. E.: A statistical evaluation of cephalometric prediction. Angle Orthod., 38:284, 1968. 84. Johnston, L. E.: A simplified approach to prediction. Am. J. Orthod., 61:253, 1975. 85. Knott, V. B.: Size and form of the dental arches in children with good occlusion studied longitudinally from age 9 years to late adolescence. Am. J. Phys. Anthropol., 19:263, 1961. 86. Krebs, A.: Midpalatal suture expansion studied by the implant method over a 7 year period. Trans. Eur. Orthod. Soc., 131, 1964. 87. Krogman, W. M.: Maturation age of the growing child in relation to the timing of stature and facial growth at puberty. Trans. Stud. Coli. 1!hysicians Phila., 5th series, 1:33, 1979. 88. Kurihara, S., Enlow, D. H., and Rangel, R. D.: Remodeling reversals in anterior parts of the human mandible and maxilla. Angle Orthod., 50:98, 1980. 89. Lamons, F. F., and Gray, S. W.: A study of relationship between tooth eruption age, skeletal development age, and chronological age in sixty-one Atlanta children. Am. J. Orthod., 44:687-691, 1958. 90. Lande, M. J.: Growth behavior of the human bony facial profile as revealed by serial cephalometric roentgenology. Angle Orthod., 22:78, 1952. 91. Lauterstein, A. M.: A cross sectional study of dental development and skeletal age. J. Am. Dent. Assoc., 62:161, 1965. 92. Lavergne, J., and Casson, N.: A metal implant study of mandibular rotation. Angle Orthod., 46:144, 1976. 93. Lavergne, J., and Casson, N.: Direction and intensity of mandibular rotation in the sagittal adjustment during growth of the jaws. Scand. J. Dent. Res., 85:193, 1977. 94. Lewis, A. B., and Gam, S.M.: The relationship between tooth formation and other maturational factors. Angle Orthod., 30:70-77, 1960. 95. Lindegard, B.: Variations in human body build. Acta Psychiatr. Neurolog. 86(Suppl.):1-163, 1953. 96. Maj, G., and Luzi, C.: Longitudinal study of mandibular growth between nine and thirteen years as a basis for an attempt of its prediction. Angle Orthod., 34:220, 1964.

CRANIOFACIAL GROWTH AND THE DENTITION

521

97. Mathews, J. R., and Payne, G. S.: Quantitative computerized analysis of! ower incisor changes: a longitudinal implant study in man. Angle Orthod., 50:218, 1980. 98. Mathews, J. R., and Ware, W. H.: Ldngitudinal mandibular growth in children with tantalum implants. Am. J. Orthod., 74:633, 1978. 99. Melsen, B.: Palatal growth studied on human autopsy material: A histologic microradiographic study. Am. J. Orthod., 68:42, 1975. 100. Meredith, H. V.: Relation between the eruption of selected mandibular permanent teeth and the circumpuberal acceleration in stature. J. Dent. Child., 26:75-78, 1959. 101. Meredith, H. V.: Childhood interrelations of anatomic growth rates. Growth, 26:23-39, 1962. 102. Moorrees, C. F. A.: The dentition of the growing child. Cambridge, Harvard University Press, 1959. 103. Moorrees, C. F. A., Fanning, E. A., and Gri
522

ROBERT

E. WILLIAMS AND RICHARD F. CEEN

132. Schudy, F. F.: The rotation of the mandible resulting from growth: its implications in orthodontic treatment. Angle Orthod., 35:36, 1965. 133. Scott, J. H.: The growth of the human face. Proc. R. Soc. Med., 47:5, 1954. 134. Scott, J. H.: The growth in width of the facial skeleton. Am. J. Orthod., 43:366, 1957. 135. Shuttleworth, F. K.: Sexual maturation and the physical growth of girls age 6 to 19. Monograph, Society for Research in Child Development. Vol. 2, No.5, Washington, D.C., 1937. 136. Sillman, J. H.: Dimensional changes in the dental arches: longitudinal study from birth to 25 years. Am. J. Orthod., 50:824, 1964. 137. Simmons, K., and Gruelich, W. W.: Menarchial age and the height, weight and skeletal age of girls, 7-17 years. J. Pediatr., 22:518-548, 1943. 138. Singh, I. J., and Savara, B. S.: Norms of size and annual increments of seven anatomical measures of maxillae in girls hom 3 to 16 years of age. Angle Orthod., 36:312, 1966. 139. Singh, I. J., Savara, B.S., and Miller, P. A.: Interrelations of skeletal measurements of the face and body in preadolescent and adolescent girls. Growth, 31:119-131, 1967. 140. Singh, I. J., Savara, B: S., and Newman, M. T.: Growth in the skeletal and non-skeletal components of head width from 9 to 14 years of age. Hum. Bioi., 39:182-191, 1967. 141. Skieller, V.: Expansion of the midpalatal suture by removeable plates, analyzed by the implant method. Trans. Eur. Orthod. Soc., 40:143, 1964. 142. Smith, R. J.: Misuse of hand wrist radiographs. Am. J. Ortbod., 77:75, 1980. 143. Smith, R. J., and Bailit, H. L.: Problems and methods in research on the genetics of dental occlusion. Angle Orthod., 47:65, 1977. 144. Stein, K. F., Kelley, T. J., and Wood, E.: Influence of heredity in the etiology of malocclusion. Am. J. Orthod.,42:125-141, 1956. 145. Steiner, C. C.: Cephalometries for you and me. Am. J. Orthod., 39:729, 1953. 146. Stramud, L.: External and internal cranial base: A cross-sectional study of growth and association in form. Acta Odont. Scand., 17:239, 1959. 147. Sutow, W., Terasaki, T., and Ohwada, K.: Comparison of skeletal maturation with dental status in Japanese children. Pediatrics, 14:327-333, 1954. 148. Thompson, D'A.: On Growth and Form. New York, Cambridge University Press, 1917. 149. Thompson, G. W., and Popovich, F.: Relationship of craniofacial changes and skeletal age increments in females. Hum. Bioi., 45:595--603, 1973. 150. Thompson, G. W., and Popovich, F.: Relationship of mandibular measurements to stature and weight in humans. Growth, 38:187, 1974. 151. Thompson, G. W., Popovich, F., and Anderson, D. L.: Maximum growth changes in mandibular length, stature and weight. Hum. Bioi., 48:285--293, 1976. 152. Todd, J. T., and Mark, L. S.: Issues related to the prediction of craniofacial growth. Am. J. Orthod., 79:63, 1981. 153. Tweed, C. H.: The Frankfort mandibular plane angle in orthodontic diagnosis, classification, treatment planning, and prognosis. Am. J. Orthod., 32:175, 1946. 154. Useato, G., Zennosuke, K., Kawamoto, T., eta!.: Steiner cephalometric norms for Japanese and Japanese Americans. Am. J. Orthod., 73:321, 1978. 155. Vig, P. S.: Comments on the new geometric approach to cephalometries. Am. J. Orthod., 79:218, 1981. 156. Walker, G. F.: A new approach to the analysis of craniofacial morphology and growth. Am. J. Orthod., 61:221, 1972. 157. Wasson, J. L.: Evaluation of a method of predicting craniofacial growth that compares cephalometric roentgenograms of children and parents (abstract). Am. J. Orthod., 49:864, 1963. 158. Woodrow, H., and Lowell, F.: Anatomic age and its relation to intelligence. Pedagogical Seminary, 29:1, 1922. University of Maryland School of Dentistry 666 W. Baltimore Street Baltimore, Maryland 21201