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: phliu@isu.edu.tw

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.

References

[1] R. T. Sanborn, “Differences between the facial skeletal patterns of Class III malocclusion and normal occlusion,” Angle Orthod.,

25: 208-222, 1955. [2] R. Susami, Y. Asai, K. Hirose, T. Hosoi and I. Hayashi, “The

prevalence of malocclusion in Japanese school children,” J. Jpn.

Orthod. Soc., 31: 319-324, 1972. [in Japanese] [3] U. C. Dietrich, “Morphological variability of skeletal Class 3

relationships as revealed by cephalometric analysis,” Rep. Congr. Eur. Orthod. Soc., 47: 131-143, 1970.

[4] H. P. Chang, “Components of Class III malocclusion in

Taiwanese,” Kaohsiung J. Med. Sci., 1: 144-155, 1985. [5] L. W. Graber, “Chin cup therapy for mandibular prognathism,”

Am. J. Orthod., 72: 23-41, 1977. [6] A. Jacobson, W. G. Evans, C. B. Preston and P. L. Sadowsky,

“Mandibular prognathism,” Am. J. Orthod., 66: 140-71, 1974.

[7] N. Kitai, K. Takada, Y. Yasada, S. Adachi and M. Sakuda, “School health database and its application,” J. Jpn. Orthod.

Soc., 24: 33-38, 1989. [in Japanese] [8] E. E. Ellis and J. A. McNamara, “Components of adult Class III

malocclusion,” Int. J. Oral Maxillofac. Surg., 42: 295-305, 1984.

[9] H. C. Lin, H. P. Chang and H. F. Chang, “Treatment effects of occipitomental anchorage appliance of maxillary protraction

combined with chincup traction in children with Class III

Maxillomandibular Changes of Treated Subjects 330

malocclusion,” J. Formos. Med. Assoc., 106: 380-391, 2007. [10] J. L. Ackerman and W. R. Profitt, “Diagnosis and planning

treatment in orthodontics,” in: T. M. Graber and B. F. Swain

(Eds.), Current Orthodontic Concepts and Techniques, Philadelphia: WB Saunders Co., 1-110, 1975.

[11] K. Kajiyama, T. Murakami and A. Suzuki, “Evaluation of the modified maxillary protractor applied to Class III malocclusion

with retruded maxilla in early mixed dentition,” Am. J. Orthod.

Dentofac. Orthop., 118: 549-559. 2000. [12] G. R. J. Swennen and F. Schutyser, “Three-dimensional

cephalometry: spiral multi-slice vs cone-beam computed tomography,” Am. J. Orthod. Dentofac. Orthop., 130: 410-416,

2006.

[13] L. Franchi, T. Baccetti and J. A. McNamara, “Thin-plate spline analysis of mandibular growth,” Angle Orthod., 71: 83-89, 2001.

[14] M. L. Zelditch, F. L. Bookstein and B. L. Lundrigan, “Ontogeny of integrated skull growth in the cotton rat sigmodon

fulviventer,” Evolution, 46: 1164-1180, 1992.

[15] F. L. Bookstein, “Principal warps: thin-plate splines and the decomposition of deformations,” IEEE Trans. Pattern Anal.

Mach. Intell., 11: 567-585, 1989. [16] H. P. Chang, P. H. Liu, H. F. Chang and C. H. Chang,

“Thin-plate spline (TPS) graphical analysis of the mandible on

cephalometric radiograph,” Dentomaxillofac. Radiol., 31: 137-141, 2002.

[17] P. H. Liu, C. H. Chang, H. P. Chang and H. F. Chang, “Evaluation of chin cup treatment effects on mandible for Class

III malocclusion: strain tensor analysis,” Quintessence Int., 35:

621-629, 2004. [18] H. P. Chang, P. H. Liu, Y. H. Yang, H. C. Lin and C. H. Chang,

“Craniofacial morphometric analysis of mandibular prognathism,” J. Oral Rehabil., 33: 183-193, 2006.

[19] Z. C. Chang, P. H. Liu, Y. J. Chen, C. C. Yao, H. P. Chang, C. H.

Chang and H. F. Chang, “Thin-plate spline analysis of the effects of face mask treatment in children with maxillary

retrognathism,” J. Formos. Med. Assoc., 105: 147-154, 2006. [20] D. H. Enlow (Ed.), Role of the TMJ in Facial Growth and

Development, Conference on Examination, Diagnosis, and

Management of Temporomandibular Disorders, Chicago: American Dental Association, 1983.

[21] T. Deguchi and J. A. McNamara, “Craniofacial adaptations

induced by chincup therapy in Class III patients,” Am. J. Orthod. Dentofac. Orthop., 115: 175-182, 1999.

[22] T. Deguchi, T. Kuroda, Y. Minoshima and T. M. Graber, “Craniofacial features of patients with Class III abnormalities:

growth-related changes and effects of short-term and long-term

chincup therapy,” Am. J. Orthod. Dentofac. Orthop., 121: 84-92, 2002.

[23] Z. Kinoshita, J. Yamamoto, K. Shimozuma, S. Kubo, M. Kagawa, S. Murao and H. Yamawaki, “Treatment effects of

occipito-mental anchorage appliance and orthopedic mask,” J.

Kinki-Tokai Orthod. Soci., 12: 71-81, 1977. [24] I. Yoshida, H. Ishii, N. Yamaguchi and I. Mizoguchi, “Maxillary

protraction and chincup appliance treatment effects and longterm changes in skeletal Class III patients,” Angle Orthod.,

69: 543-552, 1999.

[25] H. P. Chang, H. C. Lin, P. H. Liu and C. H. Chang, “Geometric morphometric assessment of treatment effects of maxillary

protraction combined with chin cup appliance on the maxillofacial complex,” J. Oral Rehabil., 32: 720-728, 2005.

[26] C. R. Goodall, “Procrustes methods in the statistical analysis of

shape,” J. R. Stat. Soc. Ser. B-Stat. Methodol., 53: 285-339, 1991.

[27] P. H. Liu, C. H. Chang and H. P. Chang, “Investigation of maxillo-mandibular morphologics: Strain Tensor Analysis,” J.

Chin. Inst. Eng., 26: 771-780, 2003.

[28] G. D. Singh, J. A. McNamara, Jr and S. Lozanoff, “Morphometry of the cranial base in subjects with Class III

malocclusion,” J. Dent. Res., 76: 694-703, 1997. [29] A. H. King and E. D. Schneiderman, “Differential growth

among components of the palate in rhesus monkeys (Macaca

mulatta),” Cleft Palate-Craniofac. J., 30: 302-307, 1993. [30] K. Tanne and S. Matsubara, “Association between the direction

of orthopedic headgear force and sutural responses in the nasomaxillary complex,” Angle Orthod., 66: 125-130, 1996.

J. Med. Biol. Eng., Vol. 29. No. 6 2009 331