Skeletal factors in anterior open-bite and deep overbite

Skeletal factors in anterior open-bite and deep overbite

Andrew Richardson, M.Sc., B.D.S., D.P.D., D. Orth.* Belfast, Northern Iwland

I t is not surprising that most orthodontists are mainly interest,ed in anteroposterior malrelationships of the teeth, since Edward Angle,l in his traditional classification, laid great emphasis on these common and esthetically displeasing abnormalities. By comparison, little work has been done on the less disfiguring vertical aspects of malocclusion. Sir Norman Bennett’s” classification, t,hough tleficient in other respects, drew attention to the vertical dimension, and clini- cians have come to realize that vertical malrelationships may impose limitations on the treatment of antcropostcrior irregularities.

In general, the vertical malocclusions are more difficult to correct than the anteroposterior ones. In anterior open-bite, the prognosis is either very good 01 very poor. Those eases seen at an early age tend to improve with growth and ccbssation of a habit; those seen later carry a poor prognosis if the condition is associated with a grossly abnormal facial shape or a persistent abnormality of

tongue behavior in swallowing and speech. Mechanical treatment of open-bites is frequently related more to correction of a habit or tongue-thrust than to rear- rangement of the teeth themselves. Attempts to elongate the incisors or depress the posterior teeth face the ever-present difficulties of pulp damage and insta- bility after treatment.

At the opposite extreme, deep overbites tend to improve with the passing 01 time,7j I3 but. most orthodontists make a more positive attempt at treat.ment oT deep overbite than of open-bite. In Britain, the conventional form of mechano- therapy is an anterior bite plane, usually of the Sved type, which brings about overbite reduction by permitting overeruption of posterior teeth or additional development of alveolar bone in this region. Unfortunately, the results tend to bc unstable in about one third of the cases.“’ With fixed appliances, the pros- pects of stable overbite reduction seem to be improved+ Q, l5 but ultimate sta- bility in overbite reduction with any appliance seems to depend upon a good anteroposterior incisor relationship at the end of treatment.

In reviewing the literature I? noted that both dental and skelet,al factors

*Lecturer in Orthodontics, The Queen’s University of Belfast.

114

Volume 56 Number 2 Anterior open-bite and deep overbite 115

may take part in determining the degree of incisal overbite, most authorities seeming to agree that in open-bite the anterior face height, is higher than average.2l 0p 3 I8

In deep overbite, however, Ballard3 and ParkerI concluded that the cause is dental rather than skeletal, the vertical jaw relationship being approximately normal. This is contrary to the weight of evidence advanced by WylieZ3 BjGrk,F Prakash and Margolis,ls Smeets,22 and Atherton2 which argues strongly that the lower face height is smaller than average in deep overbite.

On comparing the two extremes of vertical incisor relationship, the difference in lower face height seems to be the only skeletal factor which has been confirmed and authenticated by repeated investigation. The suggestion by Diamondll that the ramus height is deficient in deep overbite has been denied by Wylie,23 and the relationship between face height and the Frankfort-mandibular plane angle found by Hapak14 and Johnson I6 has been criticized because the Frankfort-mandibular plane angle is not an anatomic entity and the Frank- fort plane is poorly reproducible on cephalometric radiographs.6

It seemed curious that skeletal differences between open-bite and deep overbite should be limited to the lower face, since this is not, usually regarded as a primary growth area. It seems to be generally agreed that the shape of the face is largely determined by genetic influences and the interplay of the mus- cles attached to the mandible, the teeth and alveolar bones simply filling in the intermaxillary gap with which they are presented. One might be excused, therefore, for thinking that variations in lower face height might be secondary to variations in other parts of the craniofacial skeleton. The limited findings for skeletal abnormalities in open-bite and the controversy over the importance of skeletal factors in deep overbite may be attributable to differences in age and sex, the small abnormality of overbite in most of the material which has been investigated, and the possibility that all open-bites or deep overbites are not uniform with respect to etiologic factors. It is also worth remembering that the normal range of dental and skeletal morphology is quite extensive, so that although some of the samples which have been used are large enough to satisfy the arbitrary requirement for a large sample, they may not have been numeri- cally strong enough to raise some differences to the level of statistical significance.

It seemed possible that a comparison of large numbers of patients showing the two extremes of incisor relationship might bring to light further differences in craniofacial morphology which may influence face height and the incisor overbite.

Material

La.teral cephalometric radiographs of 110 open-bite cases were collected. The ages of the subjects ranged from 7 to 27 years. Thirty-three subjects fell within the range of 7 to 10 years, forty-five were between 11 and 14 years of age, and thirty-two were between 15 and 27 years. Radiographs of the same number of deep-overbite cases were collected, so that for every open-bite case there was a deep-overbite case which corresponded with it with respect to sex

116 Kichardso~~ Am. J. Orthodontic Y august 196Y

and age (to within 6 months). All radiographs were taken with the teeth in occlusion. Even in the youngest. subjects, the permanent incisors had erupt.4. Sonc of the subjects had undergone orthodontic trc>atmr>nt.

Analysis of radiographs

A facial polygon defined by the points nasion, sella, articulare, gonion, an<1 mcnton was tl*a(~ed on rach radiogral)h. In addition, face height was divided into uppw ( nasion-ANS) and lowcl ( ASS-menton ) by projecting AKS on the facial plant (E’ig. 1 i. Thus, it n-as possible to make seven linear and fi\,c* angular measurements on each tracing.

The reproducibility of the ccphalometric points used had already bccrr c:hecked in a previous investigation and found to be satisfactory.1° In the prescnl investigation, linear measurements were made on a Perspex scale calibrated to 0.5 mm., and angular values wwc read on a large protractor calibrated to O.-p degrc~c. Each mcasurrment was rcpcntcd only to ascert,ain that the observer had not misread the instrument. For subsequent calculations, the first set of measurements was used.

Analysis of the data

Tn a preliminary analysis, t,hc differences between the means of the linear and angular yalucs in the open-bite and deep-overbite groups were tested for

Fig. 1. The facial polygon used in analyzing the radiographs. N, Nasion; 5, sella; A,

articulare; G, gonion; M, menton; ANS, anterior nasal spine.


Table I. Means and difference between means of linear craniofacial measurements in

open-bite and deep-overbite cases

Measurement (mm.)

Age group (years)

7 to 10 11 to 14 15 to 27 Total

Group iWean 1% Mean IE T.?? Mean IE

Nasion-sella

Sella-art&dare

Articulare-gonion

Gonion-menton

Menton-nasion

Nasion-AN8

ANS-menton

0 65.71

(OFD) “I%

0 30.30

(ODD) “::E

0 40.05

(OTD) “::z

0 62.61

(OYD) “E

0 110.36 D 107.42

(O-D) 2.94

0 45.47

(O?D) “;:;:

0 64.89 (OTD) 59.70

5.19”

69.02 70.22 68.38 70.76 71.88 70.40

0.71 -1.74 0.74 -1.66 0.98 -2.02” 0.51

33.71 33.67 32.68 34.84 34.70 33.88

0.67 -1.13 0.81 -1.03 0.75 -1.20 0.48

45.38 48.11 44.57 43.70 47.42 44.06

0.80 1.68 0.73 0.69 1.07 0.51 0.65

69.51 73.67 68.65 68.24 71.73 67.70

0.94 1.27 1.04 1.94 1.46 0.95 0.84

123.56 130.30 121.41 114.18 116.00 112.53

1.51 9.38” 1.57 14.30* 1.74 8.88* 1.24

51.08 53.47 50.09 51.73 52.84 50.85

0.64 -0.65 0.60 0.63 0.87 -0.76 0.54

72.46 76.83 71.46 62.44 63.16 61.83

1.18 10.02x 1.25 13.67” 1.37 9.63* 1.32

Degrees of freedom 64 88 62 218

0 z Open-bite. D = Deep overbite.

“Denotes significance P < 0.001.

statistical significance, using the 9” test. The results are shown in Tables I and II. (Differences significant at the 0.1 per cent level are marked by asterisks. There is less than one chance in a thousand that these differences could have arisen by chance.) In each case, the mean for the deep-overbite group was sub- tracted from that for the anterior open-bites ; consequently, negative differences indicate that the measurement was greater in deep overbite.

Facial polygons derived from the mean values for the two groups are shown in Fig. 2. Superimposition is on sella-nasion, with the point nasion in register.

Taking the linear differences first, the lower face height ( ANS-menton) proved to be much larger in open-bite cases throughout the age range examined. The increase in total face height in open-bite cases seemed to be largely a re-

118 Richardsort

Table II. Means and differences between means of angular craniofacial measurements in

open-bite and deep-overbite cases -

Age group (yams)

Angle (degrees)

Nasion-sella-articulare 0 125.73 123.57 123.28 124.13 D 124.02 125.18 125.88 125.0::

(0.Dj 1.71 1.23 -1.61 7.06 -2.60 1.30 .-0.90 0.6X

Brlla-:trticulare-gollion 0 139.03 1-1221 144.13 141.81

D 140.24 139.11 13850 139.27 (O-T), --I.21 1.09 3.10 1.97 5.63’ 1.58 3.54" rl.%

Articnlare-gorlion-mellton 0 133.12 134.9” .- 134.72 134.9L n 129.30 128.61 326.43 128.18

(0Dj 5.82" 1.38 6.3 1 i- 1.08 X.30 1.48 6.74% 0.74

(;onion-menton-Ilasion 0 66.39 63.81 61.78 ti3.99 71.48 71.81 71 . 77 I --7.67" 0.88 -10.03” 0.90 -7.7-L’ 0.X

hI~.nton-nasion-sellR 0 72.46 74.47 75.38 7‘4.13

74.51 i6.36 74.71 0.84 ~-0.0-i 0.73 -0.98 1.04 -0.58 l1.5:!

Degrees of freedom 64 YK 62 “IX

0 = Open-bite. TI = Deep overbite.

“Denotes significance P < 0.001.

A&ion of the increase in lower face height, since t,he differences between means for upper face height were very small.

If the current orthodontic theory that the louver face is not a primary growth area is accepted, the difference in lower face height between open-bite ilnd deep-overbite cases must bc secondary to, or at least associated with, variations in the size or the shape of o&r parts of the craniofacial skeleton. The linear results in this investigat,ion gave little indicat,ion of where these maria- tions may lie. The average differences in gonion-menton, articulare-gonion, and

sella-articulare were small and did not rise to t,hc level of statistical significance. As for nasion-sella, the significant differences were negative, indicating that this dimension was smaller, on the average, in the open-bite cases. On geometric grounds, one would expect this smaller measurement to be associated with a reduction, rather than an increase, in the lower face height,.

Turning to the angular measurements, menton-nasion-sella was practically identical, on the average, so that the two groups were comparable with respect, to the protrusion of the lower jaw in relation to the skull base. Consequently, the smaller gonion-menton-nasion angle in open-bite eases was due to a long

Anterior open-bite and deep overbite 119

Fig. 2. Facial polygons derived from mean values for the two groups. Superimposition is on sella-nasion with nasion in register. Continuous line denotes open-bite; broken line, deep overbite.

face rather than a prognathous one, The key angle seemed t,o be articulare- gonion-menton, with some contribution from sella-articulare-gonion in the highest age group. Increases in these angles would certainly have the effect of “open- ing up" the anterior part of the face, thus increasing the lower face height.

This comparison of the two extremes of incisor relationship was based on average figures for the two groups. Not every open-bite case would be expected to show higher jaw or joint angles than every deep-overbite case; indeed, there seemed to be considerable overlapping between the groups in this respect (Figs. 3 and 4). This finding seemed to suggest that the difference in lower face height between anterior open-bite and deep-overbite cases could not be attributed to variation in any one region of the craniofacial skeleton.

In an attempt to glean further information about the interaction of the various lines and angles of the facial polygon, a correlation and multiple regression analysis was carried out with the I.C.T. 1905 computer in the Department of Applied Mathematics, Queen’s University of Belfast (Programme XDS 2). With lower face height the dependent variable, y, the other lines and angles of the facial polygon were labelled x1-l0 (Fig. 1)) x1-s being linear and x6-10 being angular. Total face height was omitted in order to simplify the analysis as far as possible.

In the open-bites, lower face height (y) was correlated significantly with all the other linear facial dimensions. These dimensions, in turn, proved to be significantly correlated with one another, except that the correlation between x2 and x3 was not significant. The only angle which showed a significant correlation with lower face height was x9.

In the deep-overbite cases, the correlations between lower face height and

120 Richardson Am. J. Orthodontics Aqmsf 1969

A I \

I \ I \

/ \ I \

Fig. 3. Frequency distribution of angle articulare-gonion-menton (iaw angle). Continu- ous line denotes open-bite; broken line, deep overbite.

Table III. Multiple correlation coefficients between lower face height and other linear

values

Open-bite Deep overbite

ry.xs 0.640 40 py.xj 0.269 7 R Y.X45 0.707 50 %.W 0.303 9 R Y.X245 0.726 53 R J.X?LT 0.323 10 R Y.1215 0.741 55 R Y.X1215 0.331 11 R Y.X12345 0.742 55 R 1.=12x6 0.331 11

the other linear facial dimensions were not significant, but, as in the open-bite cases, the other linear dimensions showed significant correlations with each other, with the exception of x2 and x3. In this group, also, there was a significant negative correlation between lower face height and x9.

Tables III and IV show the multiple correlation coefficients of the dependent variable (y) on the independent variables (x) , starting with the highest correla-


NUMBER OF CASES

Fig. 4. Frequency distribution of angle sella-articulare-gonion (joint angle). Continuous line denotes open-bite; broken line, deep overbite.

Table IV. Multiple correlation coefficients between lower face height and angular values


Variation in y Variation in y ,accounted for accounted for

(per cent) (per cent)

0.275 8 rY.xs 0.202 4 0.426 18 %a 0.416 17 0.603 36 R Y.Xi80 0.522 27 0.685 47 %.m 0.676 46 0.694 48 RI.%mSIO 0.676 46

tion and incorporating independent variables, one by one, in diminishing order of importance. Alongside is shown the percentage variation of the dependent variable which can be explained in terms of variation in the independent variables. In the open-bite cases, a high percentage of the variation in y could be accounted for by variation in the other linear values; in deep-overbite cases, the correlations were much lower. As regards the angular values, the two groups were rather similar.

122 I-tichardssoa

The multiple regression anal>-sis was used to tc>st which variables matlo :i significant contribution to the estimation of lower fact height. X’ith lower fact, height (y) the dependent variable. the multiple regression equation would hf. of the form

\’ = a + blsl -i- b2s2 i- hFisIl . . l)l,,s,,l where a is a constant and b, to b,” are the partial regression coefficient,s. Tha: values of these coefficients were calculated for the ten independent varia.bles.

It, was found that x1 did not contribute significantly to the regression (‘(lllil- Con in open-bite cases and that x4 and xh did not contribute significant,ly to the: regression equation in the deep-overbite cases. The analyses for the two groups were repeated, omitting x1 in the open-bites and x4 and x8 in the deep overbites, and the difference between the sums of squares due to regression when these vari- a,bles were included and omitted were calculated. The mean squares of the diffcr- cnces were tested against the mean squares of the rosidual variances using the “F” test and were found to he nonsignificant, thus confirming that x1 did not contribute significantly to the linear fit of the regression equation in open-bitt: and t,hat x4 and x8 did not contribute significantly in deep overbite.

The regression equation for open-bite, omitting the nonsignificant v;triabIt>s? was

y = -103.32 4. 0.85x, i- 1.03, :$ Y + 0.70x., - 0.98x, t 0.29X6 4 0.59x7 + 0.57~~ -- 0.36~~ - 0.95x,,

Multiple correlation c~oefficient = 0.995 The regression equation for deep overbit,e, omitting the nonsignificant sari-

ablrs, was y = 13.03 + 0.54x, + 1.00x, -f 0.81x, - 0.94x> / 0.45x, t

0.46~7 - 124x, - 0.57’s,, Multiple correlation coefficient = 0.990

In the two groups, both linear and angular values contributed significantly to the linear fit of the regression equation, but the analyses were repeated, considering the lines and angles separately to find out which lines contributed significantly if only the lines w(lre considered and which angles contributed significantly if only the angles were considered. In t,hc open-bites, x1 did not contribute significantly when only the lines were considered and x8 did not contribute significantly when only the angles were considered. The corresponding findings in the deep overbites were x,xSs4xj for lines and x8 and xl0 for angles.

Discussion

In the preliminary examination of the material in this investigation, lower face height was found to be significantly larger on the average in open-bite cases than in deep-overbite cases. This difference could not be attributed directly to average differences in other linear measurements of the facial polygon but seemed to be related more to the jaw and joint angles-a question of shape rather than size. Although the two groups differed significantly in the meal1 values for these two angles, there proved to be an appreciable overlap in thr individual values. Even the two angles taken together gaT-e an imprecise as- sociation with lower face height, the multiple correlation coefficients being


0.426 in open-bite and 0.416 in deep overbite, thus explaining only 18 percent of the variation in lower face height in open-bite and 17 percent in deep overbite.

Casting about for other features of the facial skeleton which might be associated with variation in lower face height, it was found that lower face height was correlated significantly with all the other facial measurements in open- bite but that the correlation coefficients between lower face height and the other linear measurements were not significant in deep overbite. In both groups, all the other linear measurements were significantly correlated with one another, except that the correlations between the posterior part of the cranial base (x,) and the ramus height (x3) were not significant. With these two exceptions, there is a harmony between the linear facial characteristics in open-bite, but in deep overbite this harmony does not extend to the lower face height.

It, was tempting to suggest that the discrepancy in lower face height in deep-overbite cases was due to angular rather than linear variation, the jaw and joint angles being suspect. This, however, proved unfruitful, for the mul- t.iple correlation between these two angles and lower face height was only 0.416; furthermore, the jaw angle (x8) did not contribute to the linear fit of the regression equation. If attention is narrowed down to the mandible, on geometric grounds, increases in ramus height (x,),, body length (x,), and jaw angle (x, would lead to increases in lower face height. In both groups there was a significant positive correlation between ramus height and body length; that is, as one increased so did the other. In open-bite, the correlations between ramus height and jaw angle and between body length and jaw angle were very low, but in deep overbite the corresponding coefficients were negative and significant. Thus, in deep overbite, increases in ramus height and body length, which would be expected to cause an increase in lower face height, are cancelled out to a certain extent by reduction in the jaw angle; if the first two are large, the jaw angle tends to be small.

In open-bite cases, lower face height is closely associated with the other linear facial dimensions. In this group, 55 per cent of the variation in lower face height can be explained in terms of the other linear dimensions; indeed, it is possible to explain 50 per cent of the variation in lower face height in terms of only mandibular body length (x,) and upper face height (x,). In deep- overbite cases, however, only 11 per cent of the variation in lower face height can be accounted for by variation in the other linear values. Multiple correlation coefficients between lower face height and the angular measurements were approximately equal for the two groups at 0.694 for open-bites and 0.676 for deep overbites, thus explaining some 46 to 48 per cent of the variation in lower face height. These results are endorsed by the quite remarkable finding that, in deep-overbite cases, knowing the size of the posterior part of the cranial base (x,) , the ramus height (x,) , the mandibular body length (x4), and the upper face height (x5) does not contribute significantly toward the estimation of lower face height if only the linear measurements are considered; the length of the anterior part of the cranial base (x,) is the only measurement that matters. This may be contrasted with open-bite cases, where the length of the anterior

124 Richardson

cranial base (x,) is the only linear mcasuremcnt whic.11 doc>s not contribut (A significantly toward the estimation of lower face height. As far as lower fac*e height is concerned, in open-bite the size of the fa~c is more important t.han the: shape, whereas in deep overbite the shape is much more important than the size; however, to achieve an accura.te cstimatcl of lower face height. both lincla1 and angular measurements must bc taken into account. X’hcn this is dontt, the‘ only measurement. which does not contribute significantly to thck regression cqrl;r tion in open-bite is the anterior part of the cranial base (s,), and those whicil do not contribute significantly in deep overMe ill’<‘ the mandibular bodp length (x4) and the jaw angle (x,). Omitting these nonsignificant \-ariablcs, it is pas- siblc to account, for 99 per cclnt of the, \-aviation in Lowe i’a~ height ilr optic- bite and 98 per cent in deep overbite.

One possible clinical application of these findings and the tc~chniqut~ oi’ multiple regression analysis in general is the prediction of facial pattern iit the growing child. The pioneer lvork of Broadbent,’ and BrodiclO suggested that. the shape of the face is constant and immutable, but Bjiirk” has shown that, iu individuals, the facial shape can alter dramatically during the teen-age pcriotl. This makes prediction difficult. Recent investigations in this field have takrll t,he form of family studies to test the hypothesis that children grow to look like their parents. The results have been tlisappointing to date.

Another approach to the problem which has not been fully explored woulrl be the determination of correlations between parts of t,he cranium where growth is eomplcte at 811 early age and the iIlWl of the l’acc RlYJUt~ which one wishes To prognosticate-in this case, lower face height. If? as is commonly bclievcd: the, caraniofacial skeleton grows toward a genticallg prcdetermincd form, with only the details of muscle attachment areas and internal trabeculation being irnprcssed and maintained by- function, it is not, inconceivable that, t,hcrcx is :I relationship between those parts which reach their final form early and those parts in which the final form dots not cmcrg~ until a later stage of clcvelo~~- rne11t.

There are two aspects of prediction in the present contest,. First, it woul(1 be useful to know whether a patient is likely to haye a lower fact height thai is conducive to anterior open-bite or deep overbite in the future. Second, whrlr presented with an open-bite or deep overbite in a child 7 to 10 years of age, it would be a valuable clinical guide if one could predict whether growth changes in the lower face height would be likely to accentuate or minimize the abnormal incisor relationship.

Roth prognostic tests depend upon finciing areas of the craniofacial skclcton which change little during the growth period, thcl most probable region being the endocranial outline of the skull. This is the sort of inforrnation which can be found only in a longitudinal growth study, but, as far as the facial polygon is concerned, some general guidelines may be gleaned from the material in this investigation by comparing measurements in the 7 to 10 age range with those in the 15 to 27 age range for the two groups. These are summarized in Table 1’. The most useful measurements from the standpoint of growth changes would appear to be nasion-sella-articulare and articulare-gonion-menton for


Table V. Differences between means of craniofacial lines and angles in age ranges

7 to 10 and 15 to 27 years years


Mean Standard error Mean Standard error (mm. or (mm. or (mm. or (mm. or degrees) degrees) degrees) degrees)

Nasion-sella 4.51” 0.99 3.40* 0.70 Sella-articulare 3.37” 0.63 2.94* 0.78 Articulare-gonion 8.06” 0.94 6.13” 0.94 Gonion-menton 11.06” 1.38 8.68” 1.11 Nasion-AN8 8.00* 0.73 5.11” 0.79 Naaion-sella-articulare -2.45 1.25 1.86 1.33 Sella-articulare-gonion 5.10* 1.18 -1.74 1.49 Articulare-gonion-menton -0.40 1.41 -2.88 1.40 Gonion-menton-nasion -4.61* 0.88 -0.17 0.93 Menton-nasion-sella 2.92 1.13 2.98” 0.72

*Denotes significance P < 0.001.

both groups, menton-nasion-sella in open bite cases, and sella-articulare-gonion and gonion-menton-nasion in deep-overbite cases only

In order to distinguish the potential open-bite case from the potential deep- overbite case, it would be necessary to have large differences in areas which are relatively immune from growth changes. Using the statistical technique of linear discriminant function described by Fisher,12 this may become a worth- while possibility.

As for the prediction of growth trends within each group, the requirement is for measurements which contribute significantly to the prediction equation and which are relatively unaffected by growth. Within the facial polygon, the possibilities are nasion-sella-articulare, articulare-gonion-menton, and menton- nasion-sella in open-bite and nasion-sella-articulare, sella-articulare-gonion, and gonion-menton-nasion in deep overbite.

In an attempt to determine the relationship between lower face height and these measurements toward the end of the growth period, the multiple regression analysis is being repeated on the 15 to 27 year age group. It remains to be seen whether knowledge of these or endocranial measurements will allow ac- curate prediction of lower face height.

Conclusions

1. The lower anterior face height is significantly greater, on the average, in open-bite cases than in deep-overbite cases.

2. The jaw and joint angles are also significantly larger in open-bite, and the anterior part of the cranial base is significantly larger in deep overbite.

3. On geometric grounds, it was tempting to postulate a cause-and-effect relationship between the size of the jaw and joint angles and the lower face height.

1. Taking the t,wo groups separately, how~~vcr, there is only an imprecise, rfilationship bet\v-ecn 10wcr -face height and the jilw arid joint angles, cGt,hvl singly or in combination.

5. While the sizes of the jaw and ,joint angles may be factors in the ctiolop:\ of open-bitt 01’ deep overbite, they art’ by no moans the only variables whic*h determine lower face height.

6. In open-bite, there is a close relationship between lower face height. anti the length of other lines in the facial polygon. Tn open-bite 55 per cent of tht variation in lowclr face height can be cq~lainrd by variation in thr other lint!;lI* values, and 50 prr cent can be accounted for by variation in only the mandibular body length and upper face height. In deep overbite, however, the lower fan height is not in harmony with the size of other parts of the facial polygon. This reap be the result of an inverse relationship between ramus height and mall-- dibular body length on the one hand and the jaw angle on the other.

7. In the two categories of ovcrbitc relation, both linear and angular meil- surcments of the facial polygon contrihutc significantly to the estimation of lowrr face height. The only nonsignificant variables arc the ant,er’ior part, of thr cArania1 base in open-bite and mandibular body length and the jalv angle in deep orerbite. Omitting these nonsignificant variables, it is possible to account for !W per cent of the variation in lower face height in open-bite and 98 per ccl~t in clccp o\-erbitcL.

8. These findings, and the techniques of multiple regression ancl discriminant, function in general, may prove useful in t,he prediction of facial and dent,al patterns.

The author is happy to acknowledge the time and trouble taken l)g Dr. J. D. Merrett, Department of Medical Statistics, Queen’s University, Belfast, in giving advice on st,ntib- t,ical procedures and in arranging multiple regression analysis of the data by f~lwtrouic~

c:omputer.

REFERENCES

1. Angle, E. 11.: Classification of malocclusion, Dent,al (:osmos 41: 248, 1899. t’. i\therton, J. I).: The influence of the face height upon the incisor occlusion and lip

posture, D. Practitioner 15: 227-231, 1965. G. Ballard, C. F.: The aetiology of malocclusion; an assessment, D. Practitioner 8: 42-51,

1957. 5. Begg, P. It.: Begg orthodontic theory and technique, Philadelphia, 19G5, IV. Ii. Hrtur~-

tiers Company. .j. Bennett, Sir N.: Science and practice of dental surgery, Oxford, 1931, Oxford I-ni-

versity Press. 6. Bjizirk, A.: The face in profile, Lund, 1947, Berlingska Boktryckeriet. 7. BjGrk, A.: Variability and age changes in overjet and overbite, AM. J. ORTHODONTICS

39: 779, 1953.

8. Broadbent, B. H.: The face of the normal child, Angle Orthodontist 7: 183, 1937. 9. Broadway, R. T.: Depression of lower incisors, Tr. Brit. Sot. Orthodont., p. 70, 195i.

10. Brodie, A. G.: Some recent observations on the growth of the face and their implica- t,ions to the orthodontist, AM. J. ORTHODONTICS 26: 741, 1940.

11. Diamond, M.: The development of dental height, AIL J. ORTHODONTICS 30: 589.Gu5, 1944. 12. Fisher, R. A.: The use of multiple measurements in taxonornic problems, Ann. Eugenics

7: 179, 1937.

Volume 56 Number 2 Anterior opewbite ad deep overbite 127

13. Fleming, H. B.: An investigation of the vertical overbite during eruption of the permanent dentition, Angle Orthodontist 31: 53, 1961.

14. Hapak, F. M.: Cephalometric appraisal of the open bite case, Angle Orthodontist 34: 65-72, 1964.

15. Jarabak, J., and Fizzell, J. B.: Technique and treatment with the light wire appli- antes, St. Louis, 1963, The C. V. Mosby Company.

16. Johnson, E. L.: The Frankfort mandibular plane angle and the facial pattern, AM. J. ORTHODONTICS 36: 516-533, 1950.

17. Parker, C. D.: A comparative study of intermaxillary spaces with treated and un- treated occlusions, D. Practitioner 15: (X-82, 1964.

18. Prakash, P., and Margolis, H. I.: Dento-eraniofacial relations in varying degrees of overbite, AM. J. ORTHODONTICS 38: 657-673, 1952.

19. Richardson, A.: An investigation into the reproducibility of some points, planes, and lines used in cephalometric analysis, Ahr. J. ORTHODOXTICS 52: 637-650, 1966.

20. Richardson, A.: A cephalometric investigation of skeletal factors in anterior open bite and deep overbite, Tr. European Orthodont. Sot., pp. 159-171, 1967.

81. Richardson, A., and Adams, C. P.: An investigation into the short and long term effects of the anterior bite plane on the occlusal relati,onship and facial form, Tr. European Orthodont. Sot., pp. 357-383, 1963.

22. Smeets, H. J. L.: A roentgenocephalometric study of the skeletal morphology of Class II, Division 2 malocclusion in adult cases, Tr. European Orthodont. SOC. pp. 247-259, 1962.

23. VVylie, W. L.: The relationship between ramus height, dental height, and ovrbite, All. J. ORTHODONTICS 32: 57-67, 1946.

Documents

Skeletal factors in anterior open-bite and deep overbite