morphometric analysis of mandibular growth in skeletal ... · digitization of mandibular landmarks...

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


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.



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


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



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


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



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


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



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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