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318 J Formos Med Assoc | 2006 • Vol 105 • No 4
J.Z.C. Chang, et al
Background: The craniofacial growth patterns of untreated individuals with skeletal Class III malocclusionhave rarely been systemically investigated. This study used morphometric techniques to investigate the growthcharacteristics of the mandible in individuals with skeletal Class III malocclusion.Methods: Lateral cephalometric head films of 294 individuals with untreated skeletal Class III malocclusion(134 males, 160 females) were selected and divided into five triennial age groups (T1–T5) and by gender toidentify the morphologic characteristics and sexual dimorphism in changes of mandibular growth. Procrustes,thin-plate spline, and finite element analyses were performed for localization of differences in shape and sizechanges. Maximum and minimum principal axes were drawn to express the directions of shape changes.Results: From T1 (age 6–8 years) to T4 (age 15–17 years), the distribution of localized size and shape changesof the mandible was very similar between the two genders. From T1 to T2 (age 9–11 years), significantlengthening of the condylar region was noted (23.4–39.7%). From T2 to T3 (age 12–14 years), the greatestsize and shape change occurred at the condylar head (27.4–34.9%). From T3 to T4, the greatest size andshape changes occurred in the symphyseal region (23.6–42.1%). From T4 to T5 (age 18 years), significantsexual dimorphism was found in the distribution and amount of localized size and shape changes. Femalesdisplayed little growth increments during T4. Despite differences in the remodeling process, the wholemandibular configurations of both genders exhibited similarly significant upward and forward deformationfrom T4 to T5.Conclusion: We conclude that thin-plate spline analysis and the finite element morphometric method areefficient for the localization and quantification of size and shape changes that occur during mandibulargrowth. Plots of maximum and minimum principal directions can provide useful information about thetrends of growth changes. [J Formos Med Assoc 2006;105(4):318–328]
Key Words: Class III malocclusion, finite element analysis, growth
School of Dentistry, College of Medicine, National Taiwan University, Taipei, and 1Institute of Biomedical Engineering, National Cheng-Kung University,Tainan, Taiwan.
Received: May 12, 2005Revised: June 21, 2005Accepted: September 13, 2005
Skeletal Class III malocclusion is one of the most
difficult facial deformities to manage because
of the great diversity in the anatomic craniofacial
structures and the unpredictable growth in pa-
tients with this skeletal pattern.1–6 Early ortho-
pedic treatment during growth has been pro-
posed for patients with skeletal Class III maloc-
clusions, but the treatment responses vary great-
ly.7–11 In order to achieve accurate diagnosis and
*Correspondence to: Dr. Wan-Hong Lan, School of Dentistry, College of Medicine, National Taiwan University,1, Chang-Te Street, Taipei 100, Taiwan.E-mail: [email protected]
obtain appropriate early orthopedic treatment
plans for patients with skeletal Class III maloc-
clusion, knowledge of the craniofacial growth pat-
tern of these patients is important.
Few studies on the normal growth and devel-
opment of untreated individuals with skeletal
Class III malocclusion have been reported. The
main reasons for this lack of information are the
relatively low prevalence of Class III malocclu-
ORIGINAL ARTICLE
Morphometric Analysis of MandibularGrowth in Skeletal Class III MalocclusionJenny Zwei-Chieng Chang, Yi-Jane Chen, Frank Hsin-Fu Chang, Jane Chung-Chen Yao, Pao-Hsin Liu,1
Chih-Han Chang,1 Wan-Hong Lan*
©2006 Elsevier & Formosan Medical Association
319J Formos Med Assoc | 2006 • Vol 105 • No 4
Mandibular growth in Class III malocclusion
the paucity of longitudinal data and ethical con-
cerns, a cross-sectional study design was used to
identify mandibular morphologic differences
between different age groups from childhood to
adulthood.
Methods
SubjectsLateral cephalometric head films of 294 children
and young adults (134 males, 160 females) were
selected from the files of the Orthodontics Depart-
ment of National Taiwan University Hospital.
These films were obtained during the patients’ ini-
tial visit to our department. The inclusion criteria
for the study were as follows: Chinese ethnicity;
lateral cephalograms of adequate quality; diag-
nosis of skeletal Class III malocclusion; no cleft
lip or cleft palate or any other craniofacial de-
formities; no history of active orthodontic treat-
ment; normal morphology and number of teeth;
mandibular plane (MP) angle (sella nasion [SN]–
MP angle) between 28° and 38° ; and absence of
marked midline deviation. Subjects were grouped
according to age into five triennial ranges and
also by gender. The sample distribution in the re-
sulting 10 groups of patients with skeletal Class III
malocclusion is shown in Table 1.
Digitization of mandibular landmarksThe lateral cephalograms were traced with a
0.3-mm lead pencil on frosted acetate tracing films
in random order and checked by one investigator.
Twelve homologous mandibular landmarks were
identified and digitized (Figure 1, Table 2). These
sion and the performance of early intervention in
many patients with anterior crossbite.12 Previous
studies that were conducted using longitudinal
data featured few patients and short observation
periods, and some of these subjects underwent
minor orthodontic therapy to correct anterior cross-
bite.13–18 Few cross-sectional studies have been re-
ported with adequate numbers of subjects to clearly
identify patterns of change.6,12 Consequently, little
definitive information is available on the cranio-
facial growth of untreated individuals with skel-
etal Class III abnormalities.
Most previous studies of skeletal Class III
growth were performed using the roentgeno-
graphic cephalometric method.6,12–18 This approach
depends upon reference planes and points. If the
registration points or planes vary greatly, use of
this technique may lead to misdiagnosis or mis-
interpretation.19,20 As the linear and angular meas-
urements made by traditional methods are insuf-
ficient for the analysis of size and shape changes
of complex craniofacial forms, newer geometric
morphometric methods for shape comparisons
have been developed to measure the biological
size and shape changes induced by growth and
treatment. These approaches include thin-plate
spline analysis, Euclidean distance matrix analy-
sis, finite element scaling analysis, tensor analy-
sis, Fourier analysis, and shape-coordinate analy-
sis.21–24 These methods are all preferable to con-
ventional cephalometry in that they provide ex-
planatory visualization of shape changes and
highlight regions of localized dissimilarity.
The purpose of the present study was to in-
vestigate the growth characteristics of the man-
dible in untreated Class III malocclusion. Due to
Table 1. Sample distribution in 10 age and gender groups of individuals with skeletal Class IIImalocclusion
Stage T1 T2 T3 T4 T5Age range, yr 6–8 9–11 12–14 15–17 18Gender M F M F M F M F M FGroup M1 F1 M2 F2 M3 F3 M4 F4 M5 F5Subjects, n 17 22 36 39 12 18 20 17 49 64Total number of subjects 39 75 30 37 113
320 J Formos Med Assoc | 2006 • Vol 105 • No 4
J.Z.C. Chang, et al
landmarks were selected with preference given
to those that encompassed developmental sites,
were easily distinguishable, and were located in
the midsagittal plane where possible. All cephalo-
grams were retraced after a 1-week interval, and
the landmarks were redigitized by the same per-
son. None of the landmarks showed a discrepancy
of greater than 1% for each x,y coordinate on du-
plicate digitization. Thus, errors of identification
were neglected.
Procrustes superimposition and statisticalestimationThe scaled mean mandibular configurations of
each age group for both sexes (Groups M1, M2,
M3, M4, M5, F1, F2, F3, F4, F5) were generated
by Procrustes analysis. This analytical method,
using the least squares principle, was also used to
translate, rotate, and iteratively scale the coordi-
nates of every subject in each group until all sub-
jects’ configurations in this group could no longer
be improved by the least-squares fit.25 The mean
configurations at each stage for both sexes were
tested for significance using Goodall’s F test.26
Interpolation using the thin-plate splinefunctionPrior to the application of finite element meth-
odology, the thin-plate spline function was used
to interpolate points within the mandibular mean
geometry. The interpolation function mapped
points of the mean configuration of one group on-
to corresponding points of the mean configuration
of the other group.21
Finite element scaling analysisFinite element scaling analysis using the strain
tensor principles was incorporated with the spline
interpolation function to create a triangular mesh
within the mean mandibular configurations. A
total of 8100 linear triangular elements were ob-
tained for each configuration. Nodal coordinates
of each triangular element in the mean mandibu-
lar configuration for each stage (age group) were
compared with the corresponding coordinates of
the next stage. The differences in these coordinates
were used to calculate the growth strains of the
triangular elements and were further computed and
transferred into descriptions of maximum and
minimum principal axes of growth tensors. Size
changes were computed as the product of the prin-
cipal axes, and shape changes as the ratio of the
greater principal axis divided by the lesser princi-
pal axis.27 The measures of these size and shape
changes were color-mapped into each initial geo-
metric form and provided graphical displays of
the change in configurations. The maximum and
minimum axes were also graphically displayed
to express the directions and magnitudes of the
localization of the extension and contraction vec-
tors within the mandibular form.28
Table 2. Definition of 12 mandibularhomologous landmarks
1. Cd Condylion2. Ab Anterior border of ramus3. LIB Lower incisor lingual bony contact4. Id Infradentale5. B B point or supramentale6. Pm Protuberance menti or suprapogonion7. Pog Pogonion8. Gn Gnathion9. Me Menton10. Go Gonion11. Pb Posterior border of ramus12. Ar Articulare
Figure 1. The12 mandibular
homologouslandmarks.
321J Formos Med Assoc | 2006 • Vol 105 • No 4
Mandibular growth in Class III malocclusion
Results
Goodall’s F testResiduals from the Procrustes analysis were
tabulated and compared by means of an F dis-
tribution (Table 3). The level of a significant dif-
ference between the mean mandibular configu-
rations was set at p < 0.05 or p < 0.01 for all com-
parisons. Further graphical analyses were per-
formed when significant differences between all
stages were identified.
Mandibular growth changes from T1 to T2The localized size changes in the mandibular
configuration of males and females from T1 (age
6–8 years) to T2 (age 9–11 years) are shown in
Figures 2A and 2E, respectively. The localized
shape changes of males and females are shown in
Figures 2B and 2F, respectively. The plots of maxi-
mum and minimum principal directions of tensor
vectors in the mandibular configuration of males
are shown in Figures 2C and 2D, and those of
females are shown in Figures 2G and 2H.
Increase in size was revealed in the whole man-
dibular configuration in both genders except at the
lower posterior border of the ramus between points
Pb (posterior border of ramus) and Go (gonion),
where a negative allometry (0.1–6.7% decrease in
local size) was seen only in males, while females
had a small positive allometry in this region (5.5–
9.1%). The greatest increase in size occurred at the
upper posterior portion of the ramus and the con-
dylar region (26.4–39.7% in males; 23.4–30.6%
in females). The mandibular corpus and the den-
toalveolar region showed moderate increase in
local size (13.2–19.8% in males; 16.2–19.8% in
females). Males exhibited a 26.4–39.7% increase
in local size at the anterior border of the chin, while
females showed only a 5.5–9.1% increase in this
region.
The mandibular corpus was highly isotropic
with little or no change in shape (0.0–3.6% in
males; 0.1–2.2% in females). The area above
the gonial angle exhibited anisotropy of 21.5–
25.1% in males and 8.8% in females. The area
below the condylar neck showed 17.9–21.5%
Table 3. Residuals, F values and probability of statisticsequivalence between mean mandibular configurationsfor different age groups as determined by Procrustesanalysis
Mandible
Males Females
F value Probability F value Probability
T1 vs. T2 3.0721 < 0.001 2.6317 < 0.001T2 vs. T3 2.6582 < 0.001 1.9436 < 0.005T3 vs. T4 1.7746 < 0.025 1.5582 < 0.050T4 vs. T5 1.5336 < 0.050 1.5473 < 0.050
Figure 2. From T1 (age 6–8 years) to T2 (age 9–11 years): localized (A) size changes(scale unit = 100%) and (B) shape changes in the mandibular configuration of malesubjects; plot of the (C) maximum principal directions and (D) minimum principaldirections in the mandibular configuration of male subjects (extension vectorsplotted in blue and compression vectors in red); localized (E) size changes and(F) shape changes in the mandibular configuration of female subjects; plot of the(G) maximum principal directions and (H) minimum principal directions in themandibular configuration of female subjects.
AA B
CC D
EE F
GG H
322 J Formos Med Assoc | 2006 • Vol 105 • No 4
J.Z.C. Chang, et al
change in shape in males and 8.8–13.1% in
females. Regions of the mandibular symphysis
and anterior dentoalveolus showed minimal shape
change of 3.6–10.8% in males and greater shape
change of 13.1–15.3% in females. The area between
points Pm (suprapogonion) and Pog (pogonion)
had moderate anisotropy of 14.4–17.9% in males
and 8.8% in females.
The extension vectors are plotted in blue and
the compression vectors in red in the plots of max-
imum and minimum principal directions of ten-
sor vectors (Figures 2C, 2D, 2G and 2H). The up-
per portion of the ramus and the condylar region
had greater extension vectors parallel to the Ar
(articulare)–Pb line, with a lesser extent perpen-
dicular to the Ar–Pb line. The lower border of the
mandibular corpus had greater vectors extending
horizontally along the Go–Me (menton) axis and
smaller vectors extending perpendicular to the
Go–Me axis. The extension vectors for the gonial
angle region were directed forward anteriorly along
the Go–Ab (anterior border of ramus) axis, while
the compression vectors were directed vertically
along the Pb–Go line. Downward and forward vec-
tors were seen at the mandibular symphyseal area.
Smaller horizontal extension vectors and larger
vertical extension vectors were found at the anteri-
or alveolar area in males. However, females had
horizontal compression vectors instead of exten-
sion vectors at the anterior dentoalveolar region.
Mandibular growth changes from T2 to T3The localized size changes in the mandibular
configuration of male and female subjects from T2
to T3 (age 12–14 years) are shown in Figures 3A
and 3E, respectively. The localized shape changes
of males and females are shown in Figures 3B and
3F, respectively. The plots of maximum and mini-
mum principal directions of tensor vectors in the
mandibular configuration of males are shown in
Figures 3C and 3D, and those of female subjects
are shown in Figures 3G and 3H.
Both males and females showed an increase
in size in the whole mandibular configuration
except at the anterior alveolar region in males,
which showed a 0.0–5.4% decrease in local size.
The greatest increase in size occurred at the con-
dylar region (27.4–32.8% in males; 30.3–34.9%
in females). The region at the anterior border of
the chin had a positive allometry of 11.0% for
males and 25.7% for females. The rest of the man-
dibular area showed an increase of 16.4–21.9%
in local size in males and 2.9–7.4% in females.
The overall mandibular configuration was
highly isotropic with little or no change in shape
(0.0–2.8% in males; 0.1–2.5% in females) except
Figure 3. From T2 (age 9–11 years) to T3 (age 12–14 years): localized (A) sizechanges (scale unit = 100%) and (B) shape changes in the mandibular configuration
of male subjects; plot of the (C) maximum principal directions and (D) minimumprincipal directions in the mandibular configuration of male subjects (extension
vectors plotted in blue and compression vectors in red); localized (E) size changesand (F) shape changes in the mandibular configuration of female subjects; plot of
the (G) maximum principal directions and (H) minimum principal directions in themandibular configuration of female subjects.
A B
C D
E F
G H
323J Formos Med Assoc | 2006 • Vol 105 • No 4
Mandibular growth in Class III malocclusion
in the condylar region, the incisive alveolar re-
gion, and the area between points B (position of
deepest concavity on anterior profile of the man-
dibular symphysis) and Pm. The condylar region
exhibited greatest anisotropy of 16.5–19.2% in
males and 14.5–16.9% in females. The area be-
tween points B and Pm showed moderate aniso-
tropy (about 13.8% in males and 7.3–9.3% in
females). The incisive alveolus had shape change
of only 8.3% in males and 7.3–9.3% in females.
The condylar region had greater extension
vectors parallel to the Cd (condylion)–Ar axis, and
smaller extension vectors perpendicular to the
Cd–Ar axis. The area between points B and Pm
had greater extension vectors parallel to the B–Pm
line, and minimal extension vectors perpendicu-
lar to the B–Pm line. The mandibular incisive al-
veolar region exhibited horizontal compression
vectors and very small extension vectors.
Mandibular growth changes from T3 toT4 in malesThe localized size changes in the mandibular
configuration of males from T3 to T4 (age 15–17
years) are shown in Figure 4A, and the localized
shape changes are shown in Figure 4B. The plots
of maximum and minimum principal directions
of tensor vectors are shown in Figures 4C and 4D,
respectively.
The greatest positive allometry occurred at the
anterior border of the chin (30.2–42.1%). The up-
per portion of the mandibular ramus showed a
24.2% increase in size. The mandibular corpus in-
creased by about 18.3%. The condylar area, gonial
angle region, anterior dentoalveolar portion, and
the anterior inferior border of the chin had the least
positive allometry (0.4–6.3%).
Shape changes only occurred at the upper pos-
terior border of the mandibular ramus and at
the mandibular symphysis. The region between
points Ar and Pb showed evidence of anisotropy
of about 17.1–22.8%. The mandibular symphy-
sis exhibited 17.1–39.8% anisotropy, whereas the
area between Pm and Pog showed the greatest
change in shape (34.1–39.8%). The rest of the
mandibular body was highly isotropic with little
or no change in shape (ranging from 0.0% to
5.8%).
The extension vectors for the upper portion
of the ramus paralleled the Ar–Pb line. The man-
dibular symphysis had compression vectors paral-
leling the Me–Gn (gnathion) axis and extension
vectors directed downward and forward perpen-
dicular to the Me–Gn axis.
Figure 4. From T3 (age 12–14 years) to T4 (age 15–17 years): localized (A) sizechanges (scale unit = 100%) and (B) shape changes in the mandibular configurationof male subjects; plot of the (C) maximum principal directions and (D) minimumprincipal directions in the mandibular configuration of male subjects (extensionvectors plotted in blue and compression vectors in red); localized (E) size changesand (F) shape changes in the mandibular configuration of female subjects; plot ofthe (G) maximum principal directions and (H) minimum principal directions inthe mandibular configuration of female subjects.
A B
C D
E F
G H
324 J Formos Med Assoc | 2006 • Vol 105 • No 4
J.Z.C. Chang, et al
Mandibular growth changes from T3 toT4 in femalesThe localized size changes in the mandibular
configuration of females from T3 to T4 are shown
in Figure 4E, and the localized shape changes are
shown in Figure 4F. The plots of maximum and
minimum principal directions of tensor vectors are
shown in Figures 4G and 4H, respectively.
The greatest positive allometry occurred at the
anterior border of the chin (17.1–30.1%). The up-
per posterior border of the mandibular ramus
showed a 10.7–17.1% increase in size. The man-
dibular corpus increased by about 4.2%. How-
ever, the gonial angle region, the anterior dentoal-
veolar portion, the condylar region and the anteri-
or inferior border of the chin showed signs of
negative allometry.
The mandibular symphyseal region showed
evidence of anisotropy of about 13.5–31.5%,
whereas an area of marked anisotropy (27.0–
31.5%) was found localized between points Pm
and Pog. Change in shape of 13.5–18.5% oc-
curred at the upper posterior border of the man-
dibular ramus. The condylar head and the inci-
sive alveolar region exhibited anisotropy of about
13.5%. The mandibular corpus showed about
9.1% change in shape.
The extension vectors for the upper posterior
portion of the ramus were in a direction parallel
to the Ar–Pb line, and the compression vectors
were perpendicular to the Ar–Pb line. The man-
dibular symphysis had compression vectors paral-
lel to the Me–Gn axis and extension vectors
directed downward and forward perpendicular
to the Me–Gn axis. The mandibular corpus had
extension vectors parallel to the Ab–Me axis and
compression vectors perpendicular to the Ab–
Me axis.
Mandibular growth changes from T4 toT5 in malesThe localized size changes in the mandibular
configuration of males from T4 to T5 (age 18
years) are shown in Figure 5A, and the localized
shape changes are shown in Figure 5B. The plots
of maximum and minimum principal directions
of tensor vectors are shown in Figures 5C and 5D,
respectively.
The greatest increase in size occurred at the
mandibular symphysis region (10.4–16.3%). The
region at the posterior border of the upper ramus
had about 7.5–10.4% increase in size. The rest of
the mandibular regions showed slight positive
allometry of about 1.7–4.6%.
The anterior border of the mandible showed
the greatest anisotropy of 10.3–13.8%. The poste-
rior border of the upper portion of the ramus
showed 6.9–10.3% change in shape. The condylar
head and the posterior half of the mandibular
corpus showed 6.9% change in shape. The rest of
the mandibular regions showed minimal changes
of 1.7–5.2%.
The extension vectors at the anterior border of
the mandible were parallel to the Gn–Me axis,
while the compression vectors were perpendicular
to the Gn–Me axis. The most anterior and inferior
border of the chin had greater extension vectors
parallel to the Gn–Me axis and smaller extension
vectors perpendicular to the Gn–Me axis. Exten-
sion vectors at the posterior border of the upper
ramus were parallel to the Ar–Pb line. The posteri-
or part of the mandibular corpus had small verti-
cal extension vectors and horizontal compression
vectors.
Mandibular growth changes from T4 toT5 in femalesThe localized size changes in the mandibular
configuration of females from T4 to T5 are shown
in Figure 5E, and the localized shape changes
are shown in Figure 5F. The plots of maximum and
minimum principal directions of tensor vectors are
shown in Figures 5G and 5H, respectively.
Very little increase in size was detected at the
condylar region, the upper portion of the man-
dibular ramus, the mandibular corpus, and the
symphyseal area (0.0–4.0%). In contrast, the go-
nial angle region exhibited localized negative
allometry (about 2–10% decrease in size).
The area above the gonial angle exhibited
greatest anisotropy (10.0–11.4%). The posterior
dentoalveolar region and the most anteroinferior
325J Formos Med Assoc | 2006 • Vol 105 • No 4
Mandibular growth in Class III malocclusion
border of the chin showed 8.5% change in shape.
The condylar head, the upper posterior portion of
the ramus, and the anterior region of the mandi-
ble showed the least amount of anisotropy (1.4–
2.8%).
The gonial angle region had significant com-
pression vectors parallel to the Pb–Go axis. The
extension vectors at the most anteroinferior bor-
der of the mandible were parallel to the Gn–Me
axis, while the compression vectors were perpen-
dicular to the Gn–Me axis. The posterior alveolar
region had compression vectors parallel to the
Ab–Me axis and extension vectors perpendicular
to the Ab–Me axis.
Discussion
Geometric morphometric analysis is superior to
conventional cephalometry in that: no convention-
al reference lines are required; an explanatory vi-
sualization of morphologic differences is provided;
and it can localize the actual sites where the size
and shape changes occur.19,20,29 Several morpho-
metric approaches have been proposed in the last
two decades. Each technique has relative merits
and is able to provide certain types of information.
Fourier analysis uses mathematical techniques to
quantify shape changes, but it does not provide
graphical outputs.23 Thin-plate spline analysis dis-
plays the differences between two configurations
by means of transformation grids, but the presen-
tations of findings as eigenvalues, partial warps,
and bending energies might not be appropriate for
use by clinicians.24,30,31 The finite element analysis
generates color-coded configurations that allow
visualization of the distribution of size and shape
changes within the configurations.32 However, the
poverty of accepted landmarks used in this meth-
od leads to the generation of too few triangular
elements, and the large element size employed
fails to reflect detailed local differences.33–35 Re-
cently, finite element morphometry has been pro-
posed by Singh et al to integrate the finite element
modeling and the thin-plate spline interpolating
function.36–38 The drawbacks caused by interpret-
ing changes from limited numbers of triangular
elements could be overcome through the mapping
function of thin-plate spline analysis. However,
color-coded displays of size and shape differences
cannot express the directions of change. There-
fore, in addition to graphical displays of size and
shape changes (following the method introduced
Figure 5. From T4 (age 15–17 years) to T5 (age 18 years): localized (A) sizechanges (scale unit = 100%) and (B) shape changes in the mandibular configurationof male subjects; plot of the (C) maximum principal directions and (D) minimumprincipal directions in the mandibular configuration of male subjects (extensionvectors plotted in blue and compression vectors in red); localized (E) size changesand (F) shape changes in the mandibular configuration of female subjects; plot ofthe (G) maximum principal directions and (H) minimum principal directions inthe mandibular configuration of female subjects.
A B
C D
E F
G H
326 J Formos Med Assoc | 2006 • Vol 105 • No 4
J.Z.C. Chang, et al
by Singh et al), we used maximum and minimum
principal directions in this study to describe the
magnitudes and directions of morphologic chang-
es within the mandibular configuration. The di-
rections and amount of principal strain tensors can
express the trend in growth change within the man-
dibular configuration.
Our results revealed that significant modifica-
tions in mandibular morphology occurred at all
maturation stages for both genders. During the
growth interval from T1 to T2, the greatest posi-
tive allometry occurred at the condylar region and
the upper posterior portion of the ramus in both
males and females. Significant modifications in
shape were also noticed in this area, which dis-
played significant lengthening along the Cd–Ar
axis (an upward and slight forward direction of
condylar growth). The gonial angle region exhi-
bited significant reshaping in both groups, espe-
cially in males, where the gonial angle tended to
become more acute. The incisive alveolus grew
vertically to corroborate with the vertical condylar
growth. The symphysis exhibited a downward and
forward growth. The distribution of localized size
changes of the mandibular configurations was
similar between the sexes during this period. The
closure of the gonial angle and the upward–
forward growth of the condyle implied the exist-
ence of a tendency for anterior morphogenic ro-
tation of the mandible.
During the growth interval from T2 to T3,
the greatest increase in local size and change in
shape occurred at the condylar head, which had
an upward and forward growth. The rest of the
mandibular configuration did not show much
shape change, while the localized size continued
to increase during this period. The amount and
distribution of localized size and shape changes
were comparable between the genders.
During the growth interval from T3 to T4, the
greatest size and shape changes took place at the
symphyseal region between points B and Pog,
which exhibited substantial growth directed an-
teroinferiorly. The upper posterior border of the
ramus had a moderate amount of vertical growth.
The mandibular corpus showed very little signs
of anteroinferior growth. The distribution of
localized size and shape changes were similar
between the two genders. However, the overall
growth increments decreased in female subjects
(except at the area between points B and Pog),
while male subjects maintained a considerable
increase in size.
During the growth interval from T4 to T5, sig-
nificant sexual dimorphism was noted in the dis-
tribution and amount of localized size and shape
changes. Females showed very little growth incre-
ments in the whole mandibular configuration,
while considerable localized shape modifications
were noticed. The gonial angle in females became
more acute. A forward and upward rotation of the
mandibular corpus and posterior alveolus was
evident. The most anteroinferior border of the
symphysis (region of Pog–Gn–Me) also revealed a
forward and upward deformation resulting in a
stronger appearance of the mental protuberance.
Meanwhile, growth increments continued in males.
The upper posterior border of the ramus exhibited
a vertical lengthening of up to 10.4%. The antero-
inferior border of the symphysis (Pog–Gn–Me)
demonstrated an additional 16.3% increment in
size. The anterior border of the mandible revealed
an upward and forward deformation. The region
near the antegonial notch displayed a downward
deformation. Thus, the whole mandibular config-
uration in males also exhibited an upward and for-
ward rotation. This result is in accordance with the
metallic implant studies of Björk, which showed
that the mandible rotated during growth.39,40 This
remodeling in shape was an attempt to dissipate
excessive mandibular growth increments in rela-
tion to the maxilla and to maintain a proportional
relationship in the craniofacial structures.41,42
Due to the nature of the cross-sectional ap-
proach, we could not highlight individual vari-
ations. We failed to detect a definitive pubertal
growth spurt in males or females as the subjects
were grouped triennially according to their chron-
ologic ages. Thus, individual skeletal matura-
tion was not evaluated. However, we found that
males showed considerable growth even beyond
17 years of age, while females displayed small
327J Formos Med Assoc | 2006 • Vol 105 • No 4
Mandibular growth in Class III malocclusion
growth increments at the age of 15–17 years. It
was interesting that, during the stages in which
growth increments occurred, the distribution of
localized size and shape changes was very similar
between the two genders. Further investigations
that group samples according to their individual
skeletal maturity are needed. Either appraisal of
the skeletal maturation stage from cervical verte-
brae43 or hand radiographs44 should be performed
prior to grouping of the subjects.
Although based on cross-sectional data, this
study demonstrated general trends in localized
size and shape changes in mandibular configura-
tion from childhood to adulthood in subjects
from Taiwan with skeletal Class III malocclusion.
Those who exhibited opposite extremes of vertical
growth pattern (with SN–MP angle < 28° or > 38° )
were excluded from the study to minimize the
confounding effects that different vertical facial
patterns might cause. The morphometric analyses
used in this study appeared to be efficient for the
description and quantification of the size and
shape changes that occurred during mandibular
growth. The plots of maximum and minimum
principal directions provided clearer visualization
of the trends in growth changes within the man-
dibular configuration.
We conclude that thin-plate spline analysis
and finite element morphometry are efficient
methods for the localization and quantification
of the size and shape changes that occur during
mandibular growth. The plots of maximum and
minimum principal directions allow better visual-
ization of the trends in growth changes.
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