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Dental arch depth and width studied longitudinally from 12 years of age to adulthood
Dental arch depth and width studied longitudinally from 12 years of age to adulthood William
H.
DeKock,
r~a0). h'npias,
B.A.,
D.D.S.,
M.S.*
IOU!~
T
his investigation deals with changes in dental arch depth and width for persons of each sex with good odontic occlusion. The period of ontogeny covered is from the age of 12 years to early adulthood, wit.11 emphasis on the period after orthodontic treatment is usually completed. Specifically, changes in arch depth and width are presented and discussed for intervals from 12 to 15, 12 to 26, 15 60 26, and 17 to 26 years of age. Several longitudinal studiesl-S have been reported dealing with dental arch depth and width changes prior to 15 years of age, but reports dealing with material on into the third decade of ontogeny are scanty. This type of material is of particular value to the clinical orthodontist, who needs information on “normative material” for evaluation of some of the postretention changes occurring in orthodontically treated cases. Purpose
l’hc primary aims of the study are to investigate, on a strictly longitudinal sample of sixteen malt and ten female subjects with acceptable occlusion: 1. Nean size and variability in size of dental arch depth and width at annual intervals from age 12 to age 17 and at age 26 years. L’. Variability of increments for each variable in the age periods 12 to 15 years, 12 to 26 years, 15 to 26 years, and 17 to 26 years. 3. Associations between changes in dental arch depth and width in the early teens and later changes in these variables. 4. Individual differences in patterns of change for t,he age intervals from 15 to 26 years of age and from 17 to 26 years of age. 5. Varieties of change in dental arch clepth among persons studied from the ages of 12 to 26 years. *Clinical
56
Assistant
Professor,
Ilepartment
of
Orthotlontics,
University
of
Iowa.
Devitul Earlier
studies-Arch
arch
depth
aad
width
57
depth
Speck1 studied arch depth utilizing enlarged photographs of dental casts and, in a series of forty-nine persons, concluded that total arch depth occupied by the deciduous dent,ition was greater in forty-one of the instances. Brown and Daugaard-Jensen? analyzed twenty-four subjects longitudinally during adolescence and early adulthood. Over intervals varying from 3 years to 12 years, twenty-four (100 per cent) of the maxillary casts decreased in arch depth, and twenty-three (95.8 per cent) of the mandibular casts decreased in arch depth. The average decrease in the maxillary arch was 1.6 mm., and in the mandibular arch it was 1.7 mm. In a longitudinal study of sixteen boys and thirteen girls, Knott? found that in the 3-year period from t,he ages of 12 to 15 years all twenty-nine subjects registered a decrease in arch depth. The amount of decrease varied from “near zero to over 3.0 mm. averaging approximately 1.5 mm. for each arch of each sex.” Generalizing, she concluded that when depth is determined by the methods and for children similar to those used in her study, one would rarely expect any increase in depth around the time of eruption of the permanent premolars. Changes in arch depth have also been studied by Bjiirk4 with respect to observations on a longitudinal sample studied by the implant method. In a discussion of “mandibular rotation,” Bjiirk reported that the lower incisor teeth are functionally related to the upper incisors, and since the interincisor angle usually changes less than “rotation” of the mandible and “rotation” displaces the paths of eruption of all the teeth in a mesial direction, this results in “crowding” or “packing” of the anterior segment and a subsequent decrease in arch depth. Earlier
studie+Arch
width
Woods5 measured dental arch width from frontal and lateral roentgenograms. He showed increases in eight of twenty-four subjects from 9 years to 15 years of age, with the remainder showing a decrease or no change. Brown and Daugaard-Jensen,” in a study previously discussed, found variability in the direction of change for this measurement. For the twenty-four mandibular casts, five showed no change, twelve showed a decrease, and seven increased. Knott3 found mean increases in width of both dental arches in boys between the ages of 11 and 15 years. The mean values were 1.2 mm. and 0.9 mm. for the maxillary and mandibular arches, respectively. Between the ages of 9 and 15 years, twenty-eight of the twenty-nine subjects showed some increase in both lower and upper dental arch width. Material
The subjects for the present study were enrolled in a longitudinal growth study conducted at the University of Iowa between 1946 and 1960. The subjects were healthy persons from families of above average socioeconomic status, Caucasoid, and primarily of northwest European ancestry. Beginning in 1968, these subjects were contacted and asked to participate
58
DeKock
z
yEq* Fig.
1. Measurements
= ARCH WIDTH
= CD 8 ARCH DEPTH used
to obtain
arch
depth
and
arch
width.
in an additional examination. The only criterion for participation in the additional examination was previous participation in the study and a minimum age of 23 years. Alginate impressions were secured at each examination, and white plaster dental casts made from these impressions were utilized for all measurements. The sample used in this investigation consists of sixteen male and ten female subjects. The average age of these persons at the time of the additional examination was 26.3 years. The range was from 23.2 years to 30.1 years. All subjects in this investigation underwent orthodontic evaluation at all prior examinations, and the occlusion was judged suficiently acceptable that at no time was orthodontic treatment recommended. Measurements
Arch depth and arch width were determined by marking three points on each dental cast, measuring three distances, am1 deriving arch depth by formula. The landmarks are depicted in Fig. 1. To locate the posterior landmarks, the maximum transverse diameter at the permanent first molars was determined on each dental cast at the age of 12 years, and the point on each molar that gave this maximum was carefully marked with a hard pencil. Since comparable landmarks at all ages were necessary, the points marked on the cast at the age of 12 years were used as an odontic reference to mark all casts of the same arch for a given subject, marking one side at a time. The mark for the anterior landmark was placed at the most lingual point on the labial surface of the reproduction of the gingival tissue midway between the permanent central incisors. Again the mark on the cast at the age of 12 years was used as a guide to mark all other casts of the same subject in order to reduce the possibility of slight change in placing the point at different ages. Arch depth was computed from the three measurements by the formula for the median of any triangle with known sides (Fig. 1).
Dental Table
I.
maxilla
and
Means
and
mandible
standard
deviations
of each
sex studied
I
for
dental
arch
width
and
depth
59 in the
longitudinally*
Maxilla
Dental
12 13 14 15 16 17 26
5R.l 58.5 58.9 59.3 59.3 59.6 59.6
2.03 2.09 2.16 2.15
12
35.7 35.0 34.7 34.3 34.0 33.7 32.8
1.55 1.53 1.58 1.64
13 14 15 16 17 26
(mm.)
arch depth ami width
2.28
2.01
“N = sixteen males, ten females method described in text.
55 . 0 54.9 54.9 54.9 54.8 54.9 54.9 Dental 34.8 34.0 33.4 33.0 33.0 33.0 31.8
arch
width
2.02 2.05 2.03 2.05 1.99 arch depth 1.16 1.18 1.25 1.14 1.02
55.0 55.2 55.5 55.6 55.7 55.8 55.9
1.43 1.58 1.67 1.65
31.0 30.2 29.6 29.1 28.8 28.6 27.8
1.83 1.74 1.83 1.76
1.77
2.00
51.4 51.4 51.6 51.6 51.6 51.5 51.7
1.88 1.93 1.86 1.97
29.8 29.2 28.7 28.4 28.2 2i.9 27.2
1.64 1.57 1.49 1.39
1.97
1.36
except at ages 16 and 17, where means were derived
t)y
Measurements were made by means of sliding calipers with sharpened tips. Two investigators, working independently, measured each distance to the nearest 0.1 mm. If the initial measurements differed by more than 0.2 mm., two additional measurements were obtained and either the average of the four or, in instances of an obvious misreading of the scale, the average of the homogeneous three was used. Reliability estimates using this procedure have been reported previously by Knott” ,and by Meredith and Cox. 6 The reliability coefficient in the latter study between two independent determinations of maximum buccal diameter of the permanent first molars at the age of 9 years was 0.99. Group
findings
for
size
Table I presents means and standard deviations for dental arch depth and width in each sex. Both statistics at annual ages from 12 years to 15 years and at age 26 years were obtained from measurements on the dental cast of all twentysix subjects. Since casts were not available at ages 16 and 17 years for all twentysix subjects, and since the mean change from age 15 years to age 26 years for the nineteen subjects (eleven males and eight females) on whom casts were available at ages 16 and 17 years was no different from that for the twenty-six subjects, estimated means at these ages were derived from mean annual changes for nineteen subjects (eleven males and eight females). Trends drawn to the means in Table I are depicted in Fig. 2. Considering the tabular and graphic findings jointly, selected findings are as follows :
60
DeKock
!+-p.i~
.:-:;::I::.:-----.~~~~~-: 27 -
MANDIBULAR
DENTAL
ARCH
----------• ARCH: FEMALES
DEPTH
26 f
~/,/
MAXILLARY
ARCH:MALES
.
F 57 MANDIBULAR
56 --.---e--L--.--a
55
ARCH: MALES
MAXILLARY ----------------
.
ARCH: FEMALES --------+
54 53 52
MANDIBULAR ARCH: _____ *--------
L---C/&------.--
FEMALES ---v-----d
51
50
DENTAL
ARCH
WIDTH
F
4911
I2
’
I3
’
I4
’
15
’
16
’
I7
AGE
Fig. 2. Trends to age 26.
drawn
to means
for
twenty-six
’
18
IN
’
Is
’
20
’
21
’
22
’
23
’
24
’
25
I 5
L
2(
YEARS
subjects
studied
longitudinally
from
age
1. There is a decrease with age throughout the period studied in mandibular and maxillary arch depth. The means for both male and female subjects between the ages of 12 and 26 years yield declining trends. Although the rate of change is slight after the age of 15, means for both arches in each sex continue to decrease to the age of 26 years. 2. The standard deviations do not indicate a difference in variability in either sex for arch depth or arch width at any time during the period of ontogeny studied. 3. Means for arch width differ from those for arch depth. Trends drawn to female means for arch width reveal no significant change in either arch at any time during the 14-year age period from 12 to 26 years. For males there is a slight, statistically significant, increase in each arch from the age of 12 years to the age of 15 years.
12
Table first
II.
Mean
permanent Age
changes molars
for
(mm.)
in width
males
and
and
depth
Ma1 es
12 1% 15 17
15 26 26 26
1.16 1.i:i (0.27) (0.10)
15 26 26 26
0.5x 0.89 (0.31) (0.07)
Changes
h)-potheGs mean change
in
arch
arches
of
no
mean enclosed
depth
and
not
measured
at
the
Depth Malts
change map in parentheses.
Fema,lcs
nwk
(-0.12) (-0.06) ( 0.06 ) ( 0.06) Nnndihulnr
*The each
dental
Females JlnxiZTn~y
12 to 12 to 15 to 17 to
the
Width,
intervnl ( yea.rs)
to to to to
of
females*
- 1 .‘Li -2.x; - I .4-J-0.9);
-1.76 -3.0 1
- 1.9:3 -3.20
- 1.35 -2.60 -1.25 -0.i’)
-1.25
-0.9X
trrch ( ( ( (
0.19 ) 0.31 ) 0.12) 0.05)
be rejected
-1.27
-O.iB at
the
0.01
level
of
confidence
for
width
Table II presents mean changes for selected intervals between the ages of 1% and 26 years. Selected findings are as follows: 1. In the mandibular arch there are approximately 10 per cent and !I per cent decreases in arch depth for males and females, respectively, over the period between the ages of 12 and 26 years. For males the decrease between the ages of 12 and 15 years is 6 per cent, with the remaining 4 per cent decline occurring between the ages of 15 and 26 years. For females, the decrease between the ages of 12 and 15 years is 4.5 per cent and the decrease from age 15 to age 26 is 4.2 per cent. 2. In each sex, mean decrease in arch depth between the ages of 17 and 26 years is near 3 per cent of arch depth at the age of 17 for the maxillary arch and in excess of 2.5 per cent for the mandibular arch. 3. For males only, small statistically significant increases in arch width are found in both arches for the intervals from the ages of 12 to 15 years and from 12 to 26 years. Since a statistically significant increase in arch width was not found for the interval between the ages of 15 and 26 years, it is apparent that the increase in width between the ages of 12 and 26 years is due primarily to an increase between the ages of 12 and 15 years. 4. Considering all age intervals, at no time was there a sufficiently large sex difference in mean changes in arch depth to allow rejection of the null hypothesis at the 0.05 level of confidence. Not tabled are bivariate associations of the change-change variety which were investigated by means of the Pearson product-moment correlation coefficient, r. With one exception, the computed r’s were not large enough to allow rejection of the hypothesis that the population r is zero. The relationship between (1) dental arch depth decrease from the ages of 12 to 1-I years and (2) dental arch depth decrease from the ages of 14 to 26, for males, was found to
62
DeKock
26t 35 35 --
--
-
-
-
% 34 -
‘l. ‘\
33 33 32 32
--
‘\
l.
‘\ L-4, ‘i
=t
F49 ---_
---_
31 31 -
---_
----__
---.
I
30-
2g e--*---•-
--., ~-..------- FB
-.----
28’
12
” 13
14
” 15
” 17
16
I8
AGE Fig. 3. greatest
Individual and least
curves change
in arch from age
bc r = -0.55. This nrgatire fidence. Difference
in
change
among
-------------
20
” 21
22
” 23
24
‘-I 25
26
IN YEARS
depth for 12 to early
correlation
” 19
two male adulthood.
and
two
female
subiects,
with
was dependable at the 0.05 level of con-
individuals
Table III presents the distribution of individual changes in dental arch depth and width for the age periods from 15 to 26 years and from 17 to 26 years. Since there was no sex difference in changes in these dimensions for these intrrvals, both sexes were combined and the distributions shown in Table III arc compiled from the individual changes of all twenty-six subjects used in the investigation. Selected findings are as follows : 1. In width of the mandibular arch, twenty-two of the twenty-six subjects are clustered between an increase of 0.75 mm. and a, decrease of 0.25 mm. Similarly, for the maxillary arch, nineteen of the twentysix subjects are clustered in the same 1.0 mm interval. 2. All twenty-six subjects show decreases in arch depth between the ages of 15 and 26 years for both arches. Similarly, each of the seventeen persons for whom casts were available at 17 years of age showed a decrease for the g-year period from 17 to 26 years of age in both arches. Generalizing, arch depth, when measured by methods utilized in this study and for persons similar to those studied in this investigation, invariably decreases after the age of 15 years and continues to decrease after the age of 17 years.
Dental Table the
III. first
Distributions
permanent
of
molar
individual
(males
and
Moxillavy
Jlidpoin t of intcrral
Width
changes
arch
width
and
depth
dfnntikbulas
flrch Depth
Width
at
Depth
to 26 years
1
11
-0.5
3
3
1
1
-1.0 -1.5
1
7 7
1
12 7
1 1 11
-2.0
7
-2.5
1 17 yews 7 7 3
to
1
4 1 26 years 6 7 3 1
5 7 5
1
7 8 1
age 15 to 26 years,
individual
63
nrch
1 2 8 11
0.5 0 -0.5 -1.0 -1.5 -2.0 *For
in dental
width
females)*
15 years 1.5 1.0 0.5 0
(mm.)
arch. depth ad
patterns
of
N =
26; for
age l’i to 26 years,
N =
Ii.
change
This section deals with individual change in arch depth. As an aid in the discussion, Fig. 3 depicts the change in arch depth for two female and two male subjects. The persons selected were subjects in each sex who had the least and greatest amount of decrease in arch depth over the period from age 12 years to early adulthood. Over a 12-year span from the ages of 12 to 24 years, M68 decreased a total of 4.5 mm. in arch depth. For males, the minimum decrease during the same span was a 2.0 mm. decline by M61. It can also be noted from Fig. 3 that, at the age of 12 years, the arch depth of M68 was 0.5 mm. greater than the arch depth of M61. By early adulthood, however, this ranking was reversed and the arch depth of M61 was 2.0 mm. greater than that of M68. For females, the maximum decrease in arch depth was 3.8 mm. by F49. During a similar age span from age 12 years to early adulthood, the minimum decline in arch depth was 1.1 mm. by F8. Clinical
implications
Any implications from the findings in this study cannot be properly drawn, or applied clinically, without a full realization of the limitations and scope of the project. All of the subjects were judged to have satisfactory dental occlusion. They were healthy Caucasoid persons, primarily from families of northwest European ancestry and of above average socioeconomic status.
64
DeKock
Given such a sample, information about the changes in l-he dentit,ion ma!- I‘(‘late to changes seen in the postrctenlion orthoclont~ic I)aticnt. For example, ever> ort’hodontist has expcrienccd t,he frustratjon OH more than one occasion of having a patient WtlWJl to his office a few yeat’s out of’ retent,ion v,-it,h some degree ot crowding of the mandibular incisors. Ma~rv times t,his ha ppons even in c~stractiolt cases where the mandibular incisors ilrt’ meticulously uprightetl to a li~Jgn;il position hopefully sufficient to obtain stability as well as maximum esthetics. It may be possible that t,ht: tendency toward a return of crowding in the mandibular incisor area is at least partially related to decrease in arch depth after the age of 15 years, ant1 even after the age of 17 years. Assuming that the orthodontist has treated the patient properly antI established a “normal occtl~~sion” with upright, well-aligned mandibular incisors, closed all spaces, arl(1 achieved good intcrdigitation at the age of II or 15 years, it conld be that the patient follows a path similar to that of the subject,s in this study. This would mean a decrease in arch depth after the age of 15 years and a subsequent illcrease in crowding of the mandibular incisors. The method used for measuring a,rch depth in t,his study is not t,he same as the commonly used clinical methods of measuring “arch length.” It is obvious, however, that a given measure of decrease in arch depth, as defined in this study, will result in decreases in arch length that are even greater than the measured decrease in arch depth. If one relates the mean decrease in arch depth from 12 to 15 years of age to tlecrease in arch length observed clinically during this same period, it may make the measured decrease in arch depth found in this study more meaningful from a clinical stand-point. During the early part of this 3-year period, loss of deciduous teeth and eruption of permanent successors are often still occurring, along with a change in relationship brtween the permanent first molars whereby the mandibular first molar assumes a more mesial position relative to the maxillary first molar. For females, arch depth decrease from 15 to 26 years of age is nearly equal to arch depth decrease from 12 to 15 years (the latter period often including the time during eruption of prcmolars and canines). For males, the decrease from age 15 to 26 years is only :! per cent less than the arch depth decrease from 12 to 15 years. Every person in the present study showed n decrease irt arch depth from 15 to ,% years of age. The 4 per cent mean decrease in arch depth for males from age 15 to 26 years could have considerable bearing on the course of many treated cases. Although there is a slightly greater rate of decrease from age 15 to li years than from age 17 years to 26 years, the decline was still present in every subject during the span from 17 to 26 years of age. If one is willing to a.ccept that his treated patients could be represented by the sample in the present study, he could conclude that invariably ‘larch length” will continue to decrease at a declining rate from the ages of 15 to 26 years. The moderate negative association (r = -0.55) found between arch depth decrease from 12 to 14 years of age with arch depth decrease from 14 to 26 years of age is of some interest clinically. Generalizing, there is a slight tendency
Detbtal arch depth ayld width
65
for those persons whose arches decrease a large amount between the ages of 12 ant1 14 years to have less decrease in arch depth from 14 to 26 years. Nothing has been mentioned with respect to causative factors involved in I he reported arrh tlcpth dccarease. These fac+ors arc l~q-on~l the scope of the ~‘r1w~llt~stw1y. Summary
This investigation was designed to study dental arch depth and arch width in male and female subjects from the age of 12 years to adulthood. Arch depth ant1 width measurements were taken from dental casts of twenty-six subjects at annual intervals from 12 to 17 years of age and at an additional examination of these subjects after they had reached the age of 23 years. The age range of the subjects at the time of the additional examination was 23.2 years to 30.1 years. The mean age was 26.3 years. All subjects were North American Caucasians with acceptable occlusion. Summarily, selected findings are as follows : 1. Means for both maxillary and mandibular arch depth decrease with age throughout the period studied in each sex, with the rate of change being less after the age of 15 years. The mean decrease in mandibular arch depth from 12 to 26 years of age was 3.2 mm. for male subjects, or approximately a 10 per cent decrease. For female subjects, mean decrease in arch depth was 2.6 mm., or approximately a 9 per cent decline. 2. For female subjects, means for arch width in each arch revealed no significant change during the 14-year span from 12 to 26 years of age. In males there was a small statistically significant increase in arch width from 12 to 15 years of age. 3. Every person in the study showed a decrease in arch depth after the age of 15 years. The range of decrease in the mandibular arch for the period from 15 to 26 years of age was 0.1 mm. to 2.3 mm. For the same age group, 92 per cent of the decreases were in excess of 0.75 mm. and 46 per cent of the decreases were in excess of 1.25 mm. 4. No evidence was found to reject the null hypothesis of no sex difference in mean change in arch depth for any of the age intervals studied. 5. A moderate negative association (r = -0.55) was found between (a) arch depth decrease from 12 to 14 years of age and (b) arch depth decrease from 14 to 26 years of age. 6. Individual comparisons of four subjects were presented, demonstrating the constancy of direction but variability in amount of arch depth decrease from age 12 to early adulthood. The Howard
author is V. Meredith
grateful to for critical
Dr. Virginia B. Knott reading of the manuscript.
for
statistical
assistance
and
human
lower
to
Dr.
REFERENCES
1. Speck, arches,
P*‘. T.: A longitudinal study of Angle O&hod. 20: 215228, 1950.
developmental
changes
in
dental
66
DeKock
2. Brown, V. P., and Daugaasd-Jensen, I.: Changes ill Ilre d(*nlii ion from the ca~ly t~nl; to the early twenties, Acta Odontol. Scand. 9: 177-192, I!)fil. ::. .Knott, V. H.: Size and form of the dental arches in (‘hil(l~t~n with good occ,lusiou stutlie~l longitudinally .frt)m age 9 ?-ears to Iatc ;ttlole~ircll~c~, a\tti. .I. I’h>,s. Ar~thropol. 19: t’Ki384, 1961. 4. RjGrk, A.: Prediction of rnandilmla~ growth rotat,ion, AM. .I. ~)Kl'liOl). 55: 5%~
H.
DeKock,
r~a0). h'npias,
B.A.,
D.D.S.,
M.S.*
IOU!~
T
his investigation deals with changes in dental arch depth and width for persons of each sex with good odontic occlusion. The period of ontogeny covered is from the age of 12 years to early adulthood, wit.11 emphasis on the period after orthodontic treatment is usually completed. Specifically, changes in arch depth and width are presented and discussed for intervals from 12 to 15, 12 to 26, 15 60 26, and 17 to 26 years of age. Several longitudinal studiesl-S have been reported dealing with dental arch depth and width changes prior to 15 years of age, but reports dealing with material on into the third decade of ontogeny are scanty. This type of material is of particular value to the clinical orthodontist, who needs information on “normative material” for evaluation of some of the postretention changes occurring in orthodontically treated cases. Purpose
l’hc primary aims of the study are to investigate, on a strictly longitudinal sample of sixteen malt and ten female subjects with acceptable occlusion: 1. Nean size and variability in size of dental arch depth and width at annual intervals from age 12 to age 17 and at age 26 years. L’. Variability of increments for each variable in the age periods 12 to 15 years, 12 to 26 years, 15 to 26 years, and 17 to 26 years. 3. Associations between changes in dental arch depth and width in the early teens and later changes in these variables. 4. Individual differences in patterns of change for t,he age intervals from 15 to 26 years of age and from 17 to 26 years of age. 5. Varieties of change in dental arch clepth among persons studied from the ages of 12 to 26 years. *Clinical
56
Assistant
Professor,
Ilepartment
of
Orthotlontics,
University
of
Iowa.
Devitul Earlier
studies-Arch
arch
depth
aad
width
57
depth
Speck1 studied arch depth utilizing enlarged photographs of dental casts and, in a series of forty-nine persons, concluded that total arch depth occupied by the deciduous dent,ition was greater in forty-one of the instances. Brown and Daugaard-Jensen? analyzed twenty-four subjects longitudinally during adolescence and early adulthood. Over intervals varying from 3 years to 12 years, twenty-four (100 per cent) of the maxillary casts decreased in arch depth, and twenty-three (95.8 per cent) of the mandibular casts decreased in arch depth. The average decrease in the maxillary arch was 1.6 mm., and in the mandibular arch it was 1.7 mm. In a longitudinal study of sixteen boys and thirteen girls, Knott? found that in the 3-year period from t,he ages of 12 to 15 years all twenty-nine subjects registered a decrease in arch depth. The amount of decrease varied from “near zero to over 3.0 mm. averaging approximately 1.5 mm. for each arch of each sex.” Generalizing, she concluded that when depth is determined by the methods and for children similar to those used in her study, one would rarely expect any increase in depth around the time of eruption of the permanent premolars. Changes in arch depth have also been studied by Bjiirk4 with respect to observations on a longitudinal sample studied by the implant method. In a discussion of “mandibular rotation,” Bjiirk reported that the lower incisor teeth are functionally related to the upper incisors, and since the interincisor angle usually changes less than “rotation” of the mandible and “rotation” displaces the paths of eruption of all the teeth in a mesial direction, this results in “crowding” or “packing” of the anterior segment and a subsequent decrease in arch depth. Earlier
studie+Arch
width
Woods5 measured dental arch width from frontal and lateral roentgenograms. He showed increases in eight of twenty-four subjects from 9 years to 15 years of age, with the remainder showing a decrease or no change. Brown and Daugaard-Jensen,” in a study previously discussed, found variability in the direction of change for this measurement. For the twenty-four mandibular casts, five showed no change, twelve showed a decrease, and seven increased. Knott3 found mean increases in width of both dental arches in boys between the ages of 11 and 15 years. The mean values were 1.2 mm. and 0.9 mm. for the maxillary and mandibular arches, respectively. Between the ages of 9 and 15 years, twenty-eight of the twenty-nine subjects showed some increase in both lower and upper dental arch width. Material
The subjects for the present study were enrolled in a longitudinal growth study conducted at the University of Iowa between 1946 and 1960. The subjects were healthy persons from families of above average socioeconomic status, Caucasoid, and primarily of northwest European ancestry. Beginning in 1968, these subjects were contacted and asked to participate
58
DeKock
z
yEq* Fig.
1. Measurements
= ARCH WIDTH
= CD 8 ARCH DEPTH used
to obtain
arch
depth
and
arch
width.
in an additional examination. The only criterion for participation in the additional examination was previous participation in the study and a minimum age of 23 years. Alginate impressions were secured at each examination, and white plaster dental casts made from these impressions were utilized for all measurements. The sample used in this investigation consists of sixteen male and ten female subjects. The average age of these persons at the time of the additional examination was 26.3 years. The range was from 23.2 years to 30.1 years. All subjects in this investigation underwent orthodontic evaluation at all prior examinations, and the occlusion was judged suficiently acceptable that at no time was orthodontic treatment recommended. Measurements
Arch depth and arch width were determined by marking three points on each dental cast, measuring three distances, am1 deriving arch depth by formula. The landmarks are depicted in Fig. 1. To locate the posterior landmarks, the maximum transverse diameter at the permanent first molars was determined on each dental cast at the age of 12 years, and the point on each molar that gave this maximum was carefully marked with a hard pencil. Since comparable landmarks at all ages were necessary, the points marked on the cast at the age of 12 years were used as an odontic reference to mark all casts of the same arch for a given subject, marking one side at a time. The mark for the anterior landmark was placed at the most lingual point on the labial surface of the reproduction of the gingival tissue midway between the permanent central incisors. Again the mark on the cast at the age of 12 years was used as a guide to mark all other casts of the same subject in order to reduce the possibility of slight change in placing the point at different ages. Arch depth was computed from the three measurements by the formula for the median of any triangle with known sides (Fig. 1).
Dental Table
I.
maxilla
and
Means
and
mandible
standard
deviations
of each
sex studied
I
for
dental
arch
width
and
depth
59 in the
longitudinally*
Maxilla
Dental
12 13 14 15 16 17 26
5R.l 58.5 58.9 59.3 59.3 59.6 59.6
2.03 2.09 2.16 2.15
12
35.7 35.0 34.7 34.3 34.0 33.7 32.8
1.55 1.53 1.58 1.64
13 14 15 16 17 26
(mm.)
arch depth ami width
2.28
2.01
“N = sixteen males, ten females method described in text.
55 . 0 54.9 54.9 54.9 54.8 54.9 54.9 Dental 34.8 34.0 33.4 33.0 33.0 33.0 31.8
arch
width
2.02 2.05 2.03 2.05 1.99 arch depth 1.16 1.18 1.25 1.14 1.02
55.0 55.2 55.5 55.6 55.7 55.8 55.9
1.43 1.58 1.67 1.65
31.0 30.2 29.6 29.1 28.8 28.6 27.8
1.83 1.74 1.83 1.76
1.77
2.00
51.4 51.4 51.6 51.6 51.6 51.5 51.7
1.88 1.93 1.86 1.97
29.8 29.2 28.7 28.4 28.2 2i.9 27.2
1.64 1.57 1.49 1.39
1.97
1.36
except at ages 16 and 17, where means were derived
t)y
Measurements were made by means of sliding calipers with sharpened tips. Two investigators, working independently, measured each distance to the nearest 0.1 mm. If the initial measurements differed by more than 0.2 mm., two additional measurements were obtained and either the average of the four or, in instances of an obvious misreading of the scale, the average of the homogeneous three was used. Reliability estimates using this procedure have been reported previously by Knott” ,and by Meredith and Cox. 6 The reliability coefficient in the latter study between two independent determinations of maximum buccal diameter of the permanent first molars at the age of 9 years was 0.99. Group
findings
for
size
Table I presents means and standard deviations for dental arch depth and width in each sex. Both statistics at annual ages from 12 years to 15 years and at age 26 years were obtained from measurements on the dental cast of all twentysix subjects. Since casts were not available at ages 16 and 17 years for all twentysix subjects, and since the mean change from age 15 years to age 26 years for the nineteen subjects (eleven males and eight females) on whom casts were available at ages 16 and 17 years was no different from that for the twenty-six subjects, estimated means at these ages were derived from mean annual changes for nineteen subjects (eleven males and eight females). Trends drawn to the means in Table I are depicted in Fig. 2. Considering the tabular and graphic findings jointly, selected findings are as follows :
60
DeKock
!+-p.i~
.:-:;::I::.:-----.~~~~~-: 27 -
MANDIBULAR
DENTAL
ARCH
----------• ARCH: FEMALES
DEPTH
26 f
~/,/
MAXILLARY
ARCH:MALES
.
F 57 MANDIBULAR
56 --.---e--L--.--a
55
ARCH: MALES
MAXILLARY ----------------
.
ARCH: FEMALES --------+
54 53 52
MANDIBULAR ARCH: _____ *--------
L---C/&------.--
FEMALES ---v-----d
51
50
DENTAL
ARCH
WIDTH
F
4911
I2
’
I3
’
I4
’
15
’
16
’
I7
AGE
Fig. 2. Trends to age 26.
drawn
to means
for
twenty-six
’
18
IN
’
Is
’
20
’
21
’
22
’
23
’
24
’
25
I 5
L
2(
YEARS
subjects
studied
longitudinally
from
age
1. There is a decrease with age throughout the period studied in mandibular and maxillary arch depth. The means for both male and female subjects between the ages of 12 and 26 years yield declining trends. Although the rate of change is slight after the age of 15, means for both arches in each sex continue to decrease to the age of 26 years. 2. The standard deviations do not indicate a difference in variability in either sex for arch depth or arch width at any time during the period of ontogeny studied. 3. Means for arch width differ from those for arch depth. Trends drawn to female means for arch width reveal no significant change in either arch at any time during the 14-year age period from 12 to 26 years. For males there is a slight, statistically significant, increase in each arch from the age of 12 years to the age of 15 years.
12
Table first
II.
Mean
permanent Age
changes molars
for
(mm.)
in width
males
and
and
depth
Ma1 es
12 1% 15 17
15 26 26 26
1.16 1.i:i (0.27) (0.10)
15 26 26 26
0.5x 0.89 (0.31) (0.07)
Changes
h)-potheGs mean change
in
arch
arches
of
no
mean enclosed
depth
and
not
measured
at
the
Depth Malts
change map in parentheses.
Fema,lcs
nwk
(-0.12) (-0.06) ( 0.06 ) ( 0.06) Nnndihulnr
*The each
dental
Females JlnxiZTn~y
12 to 12 to 15 to 17 to
the
Width,
intervnl ( yea.rs)
to to to to
of
females*
- 1 .‘Li -2.x; - I .4-J-0.9);
-1.76 -3.0 1
- 1.9:3 -3.20
- 1.35 -2.60 -1.25 -0.i’)
-1.25
-0.9X
trrch ( ( ( (
0.19 ) 0.31 ) 0.12) 0.05)
be rejected
-1.27
-O.iB at
the
0.01
level
of
confidence
for
width
Table II presents mean changes for selected intervals between the ages of 1% and 26 years. Selected findings are as follows: 1. In the mandibular arch there are approximately 10 per cent and !I per cent decreases in arch depth for males and females, respectively, over the period between the ages of 12 and 26 years. For males the decrease between the ages of 12 and 15 years is 6 per cent, with the remaining 4 per cent decline occurring between the ages of 15 and 26 years. For females, the decrease between the ages of 12 and 15 years is 4.5 per cent and the decrease from age 15 to age 26 is 4.2 per cent. 2. In each sex, mean decrease in arch depth between the ages of 17 and 26 years is near 3 per cent of arch depth at the age of 17 for the maxillary arch and in excess of 2.5 per cent for the mandibular arch. 3. For males only, small statistically significant increases in arch width are found in both arches for the intervals from the ages of 12 to 15 years and from 12 to 26 years. Since a statistically significant increase in arch width was not found for the interval between the ages of 15 and 26 years, it is apparent that the increase in width between the ages of 12 and 26 years is due primarily to an increase between the ages of 12 and 15 years. 4. Considering all age intervals, at no time was there a sufficiently large sex difference in mean changes in arch depth to allow rejection of the null hypothesis at the 0.05 level of confidence. Not tabled are bivariate associations of the change-change variety which were investigated by means of the Pearson product-moment correlation coefficient, r. With one exception, the computed r’s were not large enough to allow rejection of the hypothesis that the population r is zero. The relationship between (1) dental arch depth decrease from the ages of 12 to 1-I years and (2) dental arch depth decrease from the ages of 14 to 26, for males, was found to
62
DeKock
26t 35 35 --
--
-
-
-
% 34 -
‘l. ‘\
33 33 32 32
--
‘\
l.
‘\ L-4, ‘i
=t
F49 ---_
---_
31 31 -
---_
----__
---.
I
30-
2g e--*---•-
--., ~-..------- FB
-.----
28’
12
” 13
14
” 15
” 17
16
I8
AGE Fig. 3. greatest
Individual and least
curves change
in arch from age
bc r = -0.55. This nrgatire fidence. Difference
in
change
among
-------------
20
” 21
22
” 23
24
‘-I 25
26
IN YEARS
depth for 12 to early
correlation
” 19
two male adulthood.
and
two
female
subiects,
with
was dependable at the 0.05 level of con-
individuals
Table III presents the distribution of individual changes in dental arch depth and width for the age periods from 15 to 26 years and from 17 to 26 years. Since there was no sex difference in changes in these dimensions for these intrrvals, both sexes were combined and the distributions shown in Table III arc compiled from the individual changes of all twenty-six subjects used in the investigation. Selected findings are as follows : 1. In width of the mandibular arch, twenty-two of the twenty-six subjects are clustered between an increase of 0.75 mm. and a, decrease of 0.25 mm. Similarly, for the maxillary arch, nineteen of the twentysix subjects are clustered in the same 1.0 mm interval. 2. All twenty-six subjects show decreases in arch depth between the ages of 15 and 26 years for both arches. Similarly, each of the seventeen persons for whom casts were available at 17 years of age showed a decrease for the g-year period from 17 to 26 years of age in both arches. Generalizing, arch depth, when measured by methods utilized in this study and for persons similar to those studied in this investigation, invariably decreases after the age of 15 years and continues to decrease after the age of 17 years.
Dental Table the
III. first
Distributions
permanent
of
molar
individual
(males
and
Moxillavy
Jlidpoin t of intcrral
Width
changes
arch
width
and
depth
dfnntikbulas
flrch Depth
Width
at
Depth
to 26 years
1
11
-0.5
3
3
1
1
-1.0 -1.5
1
7 7
1
12 7
1 1 11
-2.0
7
-2.5
1 17 yews 7 7 3
to
1
4 1 26 years 6 7 3 1
5 7 5
1
7 8 1
age 15 to 26 years,
individual
63
nrch
1 2 8 11
0.5 0 -0.5 -1.0 -1.5 -2.0 *For
in dental
width
females)*
15 years 1.5 1.0 0.5 0
(mm.)
arch. depth ad
patterns
of
N =
26; for
age l’i to 26 years,
N =
Ii.
change
This section deals with individual change in arch depth. As an aid in the discussion, Fig. 3 depicts the change in arch depth for two female and two male subjects. The persons selected were subjects in each sex who had the least and greatest amount of decrease in arch depth over the period from age 12 years to early adulthood. Over a 12-year span from the ages of 12 to 24 years, M68 decreased a total of 4.5 mm. in arch depth. For males, the minimum decrease during the same span was a 2.0 mm. decline by M61. It can also be noted from Fig. 3 that, at the age of 12 years, the arch depth of M68 was 0.5 mm. greater than the arch depth of M61. By early adulthood, however, this ranking was reversed and the arch depth of M61 was 2.0 mm. greater than that of M68. For females, the maximum decrease in arch depth was 3.8 mm. by F49. During a similar age span from age 12 years to early adulthood, the minimum decline in arch depth was 1.1 mm. by F8. Clinical
implications
Any implications from the findings in this study cannot be properly drawn, or applied clinically, without a full realization of the limitations and scope of the project. All of the subjects were judged to have satisfactory dental occlusion. They were healthy Caucasoid persons, primarily from families of northwest European ancestry and of above average socioeconomic status.
64
DeKock
Given such a sample, information about the changes in l-he dentit,ion ma!- I‘(‘late to changes seen in the postrctenlion orthoclont~ic I)aticnt. For example, ever> ort’hodontist has expcrienccd t,he frustratjon OH more than one occasion of having a patient WtlWJl to his office a few yeat’s out of’ retent,ion v,-it,h some degree ot crowding of the mandibular incisors. Ma~rv times t,his ha ppons even in c~stractiolt cases where the mandibular incisors ilrt’ meticulously uprightetl to a li~Jgn;il position hopefully sufficient to obtain stability as well as maximum esthetics. It may be possible that t,ht: tendency toward a return of crowding in the mandibular incisor area is at least partially related to decrease in arch depth after the age of 15 years, ant1 even after the age of 17 years. Assuming that the orthodontist has treated the patient properly antI established a “normal occtl~~sion” with upright, well-aligned mandibular incisors, closed all spaces, arl(1 achieved good intcrdigitation at the age of II or 15 years, it conld be that the patient follows a path similar to that of the subject,s in this study. This would mean a decrease in arch depth after the age of 15 years and a subsequent illcrease in crowding of the mandibular incisors. The method used for measuring a,rch depth in t,his study is not t,he same as the commonly used clinical methods of measuring “arch length.” It is obvious, however, that a given measure of decrease in arch depth, as defined in this study, will result in decreases in arch length that are even greater than the measured decrease in arch depth. If one relates the mean decrease in arch depth from 12 to 15 years of age to tlecrease in arch length observed clinically during this same period, it may make the measured decrease in arch depth found in this study more meaningful from a clinical stand-point. During the early part of this 3-year period, loss of deciduous teeth and eruption of permanent successors are often still occurring, along with a change in relationship brtween the permanent first molars whereby the mandibular first molar assumes a more mesial position relative to the maxillary first molar. For females, arch depth decrease from 15 to 26 years of age is nearly equal to arch depth decrease from 12 to 15 years (the latter period often including the time during eruption of prcmolars and canines). For males, the decrease from age 15 to 26 years is only :! per cent less than the arch depth decrease from 12 to 15 years. Every person in the present study showed n decrease irt arch depth from 15 to ,% years of age. The 4 per cent mean decrease in arch depth for males from age 15 to 26 years could have considerable bearing on the course of many treated cases. Although there is a slightly greater rate of decrease from age 15 to li years than from age 17 years to 26 years, the decline was still present in every subject during the span from 17 to 26 years of age. If one is willing to a.ccept that his treated patients could be represented by the sample in the present study, he could conclude that invariably ‘larch length” will continue to decrease at a declining rate from the ages of 15 to 26 years. The moderate negative association (r = -0.55) found between arch depth decrease from 12 to 14 years of age with arch depth decrease from 14 to 26 years of age is of some interest clinically. Generalizing, there is a slight tendency
Detbtal arch depth ayld width
65
for those persons whose arches decrease a large amount between the ages of 12 ant1 14 years to have less decrease in arch depth from 14 to 26 years. Nothing has been mentioned with respect to causative factors involved in I he reported arrh tlcpth dccarease. These fac+ors arc l~q-on~l the scope of the ~‘r1w~llt~stw1y. Summary
This investigation was designed to study dental arch depth and arch width in male and female subjects from the age of 12 years to adulthood. Arch depth ant1 width measurements were taken from dental casts of twenty-six subjects at annual intervals from 12 to 17 years of age and at an additional examination of these subjects after they had reached the age of 23 years. The age range of the subjects at the time of the additional examination was 23.2 years to 30.1 years. The mean age was 26.3 years. All subjects were North American Caucasians with acceptable occlusion. Summarily, selected findings are as follows : 1. Means for both maxillary and mandibular arch depth decrease with age throughout the period studied in each sex, with the rate of change being less after the age of 15 years. The mean decrease in mandibular arch depth from 12 to 26 years of age was 3.2 mm. for male subjects, or approximately a 10 per cent decrease. For female subjects, mean decrease in arch depth was 2.6 mm., or approximately a 9 per cent decline. 2. For female subjects, means for arch width in each arch revealed no significant change during the 14-year span from 12 to 26 years of age. In males there was a small statistically significant increase in arch width from 12 to 15 years of age. 3. Every person in the study showed a decrease in arch depth after the age of 15 years. The range of decrease in the mandibular arch for the period from 15 to 26 years of age was 0.1 mm. to 2.3 mm. For the same age group, 92 per cent of the decreases were in excess of 0.75 mm. and 46 per cent of the decreases were in excess of 1.25 mm. 4. No evidence was found to reject the null hypothesis of no sex difference in mean change in arch depth for any of the age intervals studied. 5. A moderate negative association (r = -0.55) was found between (a) arch depth decrease from 12 to 14 years of age and (b) arch depth decrease from 14 to 26 years of age. 6. Individual comparisons of four subjects were presented, demonstrating the constancy of direction but variability in amount of arch depth decrease from age 12 to early adulthood. The Howard
author is V. Meredith
grateful to for critical
Dr. Virginia B. Knott reading of the manuscript.
for
statistical
assistance
and
human
lower
to
Dr.
REFERENCES
1. Speck, arches,
P*‘. T.: A longitudinal study of Angle O&hod. 20: 215228, 1950.
developmental
changes
in
dental
66
DeKock
2. Brown, V. P., and Daugaasd-Jensen, I.: Changes ill Ilre d(*nlii ion from the ca~ly t~nl; to the early twenties, Acta Odontol. Scand. 9: 177-192, I!)fil. ::. .Knott, V. H.: Size and form of the dental arches in (‘hil(l~t~n with good occ,lusiou stutlie~l longitudinally .frt)m age 9 ?-ears to Iatc ;ttlole~ircll~c~, a\tti. .I. I’h>,s. Ar~thropol. 19: t’Ki384, 1961. 4. RjGrk, A.: Prediction of rnandilmla~ growth rotat,ion, AM. .I. ~)Kl'liOl). 55: 5%~