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Journal of Medical and Biological Engineering, 29(6): 326-330 326
The Morphometric Analysis of Maxillopalatal and
Mandibular Changes of Skeletal Class III Malocclusion
Treated with Orthopedic Therapy
Pao-Hsin Liu1,* Hong-Po Chang2
1Department of Biomechanical Engineering, I-Shou University, Kaohsiung 840, Taiwan, ROC 2Department of Orthodontics, Kaoshiung Medical University Hospital and College of Dental Medicine, Kaoshiung Medical University,
Kaohsiung 807, Taiwan, ROC
Received 9 Jul 2009; Accepted 3 Nov 2009
Abstract
The purpose of this study was to investigate the treatment effects on the maxillopalatal mandibular configuration
by occipito-mental anchorage (OMA) (maxillary protraction) combined with chin cup appliance (CCA) therapy among
growing children. The assessment of geometric morphometric, using Procrustes analysis, thin plate spline analysis, and
growth-trended vectors, was applied and integrated to evaluate treatment effects on the maxillopalatal mandibular
configuration of 22 children with skeletal Class III malocclusion. Taiwanese children (12 males and 10 females; 22
untreated stage of Class III subjects as pre-treated group; 22 treated stage of Class III subjects as post-treated group)
were traced, and 9 landmarks digitized. Thin-plate spline analysis (TPSA) and growth-trended vectors (GTVs) of
geometric morphometric technique were integrated and utilized to investigate the morphological differences of
dentofacial growth and local effects of orthopedic treatment. Goodall’s analysis of morphometric statistics established
statistical difference (p < 0.01) between the mean configurations of the pre-treated and post-treated groups. Significant
morphological changes on the maxillopalatal mandibular configuration were detected that the skeletal Class III subjects
following orthopedic therapy included the growth of forward extension on the maxillopalatal configuration and the
growth of backward compression on the mandible. In addition, the mandible treated with the CCA therapy appeared to
have a tendency of clockwise rotation. Median and transverse palatine sutures seem to play an important role to
produce the antero-superior elongation on the maxillopalatal configuration when orthopedic force was applied. The
results indicated that the therapy of the OMA+CCA was efficient for correcting developing Class III malocclusion.
Moreover, the morphometric techniques of the TPSA and GTVs are efficient methods to investigate growth change and
treatment effect for craniofacial studies.
Keywords: Class III malocclusion, Thin plate spline analysis (TPSA), Occipito-mental anchorage (OMA), Geometric
morphometry, Growth-trended vectors (GTVs)
1. Introduction
The anteroposterior relationship between the maxilla and
mandible has been evaluated and used in the evaluation of
malocclusion [1]. Mandibular prognathism or skeletal Class III
malocclusion with a prognathic mandible has long been viewed
as one of the most severe maxillofacial deformities [2]. A
skeletal Class III malocclusion can exhibit mandibular
protrusion, maxillary retrusion, or some combination of the
two. According to dental relationship of occlusion, a normal
Class I occlusion is defined by the anteroposterior relationship
* Corresponding author: Pao-Hsin Liu
Tel: +886-7-6577711 ext. 6726; Fax: +886-7-6577711 ext. 6701
E-mail: [email protected]
of the maxillary and mandibular first permanent molars being
correct. Similarly, a Class II malocclusion is defined when the
mandibular first permanent molar is distal to normal in its
relationship with the maxillary first molar. And a Class III
malocclusion is defined as the mandibular first permanent
molar being mesial to normal in its relationship with the
maxillary first molar [3]. Chang reported that the prevalence of
Class III malocclusion in Taiwanese children was 9.9% to
16.8% [4]. On the other hand, many studies demonstrated that
the incidence of Caucasian population afflicted with Class III
malocclusion was below 5% [5,6]. In clinics, various types of
jaw relationship have been found in patients with Class III
malocclusion. Sanborn indicated that 45.2% of the evaluated
Class III subjects showed mandibular protrusion with normal
maxilla; moreover, the maxillary retrusion without mandibular
Technical Note
J. Med. Biol. Eng., Vol. 29. No. 6 2009 327
protrusion was 33%, and the subjects with both maxillary
retrusion and mandibular protrusion were 9.5% [1,7]. Jacobson
et al. reported that the most common of the jaw types in adult
Class III malocclusion was mandibular protrusion with normal
maxilla (49%), and the next was patients who had maxillary
retrusion with a normal mandible (26%) [6]. In addition, Ellis
and McNamara found that 30% of the Class III subjects had
maxillary retrusion and mandibular prognathism, and
furthermore, patients with maxillary retrusion with normal
mandible and mandibular protrusion with normal maxilla were
19.5% and 19.1%, respectively [8]. Clinically using an
occipito-mental anchorage combined with chin cap appliance
(OMA+CCA) was efficient to correct skeletal Class III
malocclusion for growing children [9] because this appliance
can protract the retrognathic maxilla and retard the protrusive
mandible [10].
The conventional cephalometric technique, which mainly
employs angular and linear measurements to represent the
morphologic changes, shows limitation to determine the
localized growth effects of size and shape changes after
orthopedic treatment [11]. Recently, some new geometric
morphometric approaches, e.g. thin-plate spline analysis
(TPSA), have been developed for measuring the size and shape
changes as well as the quantification of morphologic
differences for growth evaluation [12,13]. TPSA can be used to
compare the deformation of craniofacial configuration of
orthopedic treatment between the starting and final stage to
present in terms of the isolated features of skeletal morphology
or the ontogeny of individual skeletal parts [14]. Therefore, the
differences between two configurations can be expressed as a
continuous deformation by visualizing biorthogonal grids [15].
For investigating morphological changes in skeletal Class III
malocclusion, TPSA was utilized to evaluate the morphological
differences in the areas of cranial base, midfacial complex, and
mandible [16-19].
Many treatments have been utilized to correct skeletal
Class III malocclusion using a combination of maxillary
retrognathism and mandibular prognathism during the growth
period. Orthognathic surgery was proposed for treating severe
Class III skeletal disharmony [20,21]. However, such surgery is
still an invasive treatment. Orthopedic appliances such as
OMA+CCA seem to be more desirable for the treatment of
skeletal Class III malocclusion [22-24]. Chang et al. [25] used
TPSA to evaluate the treatment effects of the OMA+CCA. The
study found that the significant results were a forward
advancement of the maxillary complex with negligible rotation
of the palatal plane and a forward direction of growth of the
mandibular condyle associated with a restriction in sagittal
advancement of the chin [25]. Geometric morphometric
integration by TPSA and growth-trended vectors (GTVs) has
not been investigated extensively on the maxilla and/or
mandible when OMA+CCA therapy has been undertaken.
GTVs were developed to present the growth changes of
craniofacial landmarks by two indexes of vectors, magnitude
and direction. Hence, the effects of treatment or growth on the
continuum of landmarks may be visualized as growth behavior.
The purpose of this study was to investigate the morphological
changes of the palatomandibular configuration using
OMA+CCA therapy in subjects with skeletal Class III
malocclusion by geometric morphometric technique. The
technique of geometric morphometric assessments was utilized
for evaluating growth transformation by TPSA and GTVs.
2. Materials and methods
Twenty-two Taiwanese patients (12 males and 10 females)
who received the OMA+CCA therapy were examined. The
mean ages of pre-treatment and post-treatment in the Class III
subjects were 9 years, 8 months and 11 years, 3 months,
respectively. The OMA appliance of maxillary protraction
combined with chin cap is semifixed with bands on the first
molars. The entire maxillary base is pulled forward with
elastics from buccal hooks of the first molars to the horns
extending from the chin cap. Patients treated with the
OMA+CCA were instructed to wear the appliance for 10-12
hours per day. The force for maxillary protraction of 200 to 250
gm was applied on each side. Moreover, total force of 400 to
500 gm between headgear and chin cap was enforced to inhibit
overgrowth of the mandible. The OMA appliance assembly
consisted of three parts, a head cap, a maxillary intraoral
appliance, and a chin cup. In detail, the maxillary intraoral
appliance was composed of a palatal wire frame, a palatal plate,
and bands fixed on the molars (Fig. 1). All subjects had
negative overjet, no vertical skeletal discrepancies as well as no
history of airway problem. No subjects had received
orthodontic and/or orthopedic treatment before the initial
cephalographs were taken. Stopping criteria of the treatment
was that the Class III molar relationships and the anterior
crossbite were corrected.
Figure 1. The lateral view of the occipito-mental anchorage combined
with chin cap appliance therapy (left). Intraoral photograph
of OMA appliance (right).
Lateral cephalograms of the Class III subjects were taken
from beginning (pre-treatment stage) and finishing
(post-treatment stage) of orthopedic treatment for each subject.
The magnification of each cephalogram was standardized to a
10% enlargement factor. Nine points on the palatomandibular
structure of cephalograms were identified and digitized by a
morphometric digitizer that was created using software Matlab
7.1 (Table 1, Fig. 2). All landmarks with x- and y-coordinate
digitizing in this study that demonstrated an inconsistency
of > 2% on duplication were repudiated and redigitized in
accordance with error criteria. To prevent errors of duplication,
digitization and error evaluation were performed by a single
investigator who conducted both digitization and error
Maxillomandibular Changes of Treated Subjects 328
evaluation. The mean configurations of the palatomandibular
landmarks were generated from the subjects of the pre-treated
and post-treated group using the Procrustes superimposition
approach [26]. The pre- and post-treated mean shapes were
taken as the initial and final geometries of TPSA, respectively
[27]. The TPSA was conducted to map points within the
palatomandibular landmarks from the mean shapes of initial
and final geometries. The TPSA was incorporated with the
GTVs to obtain and display shape changes and redirected
growth of the palatomandibular landmarks after orthopedic
treatment.
Figure 2. Nine homologous landmarks of maxillopalatal mandibular
configuration were selected and derived line segments as
bone structures used for TPSA.
Table 1. Landmarks definition of maxillopalatal mandibular
configuration
Designation Interpretation
Co Condylion
Ar Articulare
Go Gonion
Gn Gnathion
B Supramentale
A Subspinale
ANS Anterior nasal spine
MPP Midpalatal point
PNS Posterior nasal spine
Fundamentally, a growing or treated craniofacial bone is
usually considered as a growing continuum that is evaluated by
calculating a displacement of landmark to understand how
morphological configuration changes. In the GTV analysis of
one patient, the original locations of landmarks are associated
with the pre-treatment state, and the displacements of the
landmarks, as a result of treatment, are regarded as associated
with the post-treatment state. The changes are specified by the
length and direction of the growth vectors between the two
states of the landmark. The vertical and horizontal grid
deformations presenting from the TPSA show the contraction
or expansion of the palatomandibular complex due to the
orthopedic treatment. The mean shapes of the palatomandibular
complex of the pre-treatment and the post-treatment groups
were statistically compared using Goodall’s F-test method to
determine whether morphological differences existed between
the two groups [28]. The mean shapes of the pre-treated and
post-treated group were obtained using a Procrustes analysis.
The null hypothesis of this study between the pre- and
post-treated average geometries was not different. Probability
and F value were computed to compare treatment effects by
OMA+CCA appliance. Judging from the above, statistical
significant differences were confirmable for the samples
independently with and without the orthopedic treatment.
Hence, further geometric morphometric analysis using
TPS+GTVs would be approved.
3. Results and Discussion
The skeletal Class III malocclusions treated with the
OMA+CCA were statistically significant (p < 0.01 and
corresponding F value was 1.873), meaning that significant
differences between the morphological configurations of the
pre- and post-treated groups were evidenced. Therefore,
further morphometric analysis was performed by utilizing the
TPSA and GTVs. The undeformed transformation grid was
taken as pre-treatment group to compare with the result of the
post-treatment group. The morphometric results demonstrate
that the OMA caused forward extension of the maxillopalatal
configuration (ANS and A) (Fig. 3). Furthermore, the
transformation grid of the TPSA indicates that a backward
retraction (compression) at the chin region (B and Gn) of the
mandibular portion was caused by the orthopedic forces from
the chin cap appliance to the adjusted elastic string in the
occipital-mental direction (Fig. 3). In addition, the local
differences of transformation grid showed evidence of forward
growth of the mandibular condyle, affecting landmarks at the
articulare (Ar) and the condylion (Co). Antero-inferior
extension of the midpalatal point (MPP) was detected so that
the tendency of forward protraction of the maxillopalatal
configuration appeared to be significant. A slight effect of
forward extension at the landmark of the posterior nasal spine
(PNS) was also detected. The tendency of morphological
change on the gonion landmark (Go) was displaced downward
growth after orthopedic treatment. Correction of mandibular
retraction accompanied with maxillary anterior protraction was
demonstrated obviously by the morphometric representation of
the TPSA and GTVs. The GTVs displays indicated that two
trends of morphological change of the maxillopalatal
landmarks mainly were both antero-inferior and
antero-superior elongation. For orthopedic effects on the Class
III mandible, the GTVs could present compressive tendency,
backward compression at the mandibular chin area (B and Gn).
Combination of the TPSA and GTVs provided further
information regarding morphological change to understand
relationship between the orthopedic treatment and craniofacial
regrowth.
In this study, TPSA is a geometric morphometric
technique that expresses the differences between two
configurat ions as a con tinuous deformat ion. The
morphological display of the GTVs effectively reveals the
changes caused by orthopedic treatment or malocclusion
development. The morphometric analysis of TPSA and GTVs
J. Med. Biol. Eng., Vol. 29. No. 6 2009 329
were utilized and conducted practicable for comparing
morphological differences between the pre- and post-treated
samples. This study apparently demonstrates that treatment
with the OMA+CCA caused the forward movement of the
maxillopalatal configuration. Furthermore, inhibition of
protrusive growth of the mandible was also determined.
Palatine suture plays an important role to produce the forward
displacement of the whole maxilla/palate accompanied by
sutural growth and bone remodeling [29]. Palatine suture,
pressure-related growth sites, is a special tissue structure to
provide the capacity for growth in a field of
biomechanical/orthopedic force. Previous investigations of
craniofacial growth and morphology addressed the transverse
palatine suture to perform the role of growth site for palatal
growth [30].
(a)
(b)
Figure 3. The graphical display of TPSA combined with GTV. (a) The
orthogonal grid was as pre-treatment group (above), and
(b) the deformation of the transformation grid was as
post-treatment group (below). The vectors at the landmarks
showed morphological changes on the maxillopalatal
mandibular configuration between the two groups.
Quantitative expression of morphological differences in
geometric display between different objects at diverse intervals
is important to determine the complex etiology of
morphological dissimilitude, and can help in diagnosis and
treatment planning as well as prognosis for orthodontic
treatment [14]. The method of TPSA combined with GTVs can
be used to derive a graphic representation of morphologic
differences between two forms. The method provided
facilitated information of morphological change by deformed
transformation grid and growth vectors to describe the
treatment effects. The deformed transformation grid was
related to localized differences, including treatment-induced
and growth-induced morphogenetic effects on the
maxillopalatal mandibular morphology [27]. The relationship
between orthopedic force and forward displacement on the
maxillopalatal configuration is confirmed significantly. Further
investigation of orthopedic effect is going to be planned and
undertaken. including increasing sample size for the skeletal
Class III subjects and examination of gender and age.
Comparing treated subjects of Class III malocclusion with
age-matched untreated subjects (a control group to eliminate
native mal-growth effect) will be further investigated to obtain
a force-induced change of orthopedic treatment using strain
tensor analysis.
4. Conclusions
OMA+CCA treatment was used to correct skeletal Class
III malocclusion due to maxillary retardation (undergrowth)
combined with mandibular protrusion (overgrowth). The
results of the orthopedic treatment were evaluated using
morphometric techniques (TPSA and GTVs), which was thus
verified to be efficacious. Forward extension of the
maxillopalatal configuration and backward compression on the
mandible were observed. The displacement and
direction-related regrowth of the maxillopalatal mandibular
landmarks importantly provides more detailed information
than conventional cephalometric study on craniofacial changes
that are caused by orthopedic treatment.
Acknowledgments
The authors would like to thank the National Science
Council of the Republic of China, Taiwan and I-Shou
University, for financially supporting this research under
Contract Nos. NSC 96-2221-E-214-056-MY2 and ISU
97-S-08.
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