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(J Formos Med Assoc2002;101:790–4)

Key words:mandibular prognathismClass III malocclusionchin cupchin capthin-plate spline (TPS) analysis

Department of Orthodontics, School of Dentistry, National Taiwan University, Taipei; 1Department of Orthodontics, Schoolof Dentistry, Kaohsiung Medical University, Kaohsiung; 2Institute of Biomechanical Engineering, National Cheng KungUniversity, Tainan.Received: 3 May 2002. Revised: 3 June 2002. Accepted: 9 July 2002.Reprint requests and correspondence to: Dr. Hong-Po Chang, Department of Orthodontics, School of Dentistry, KaohsiungMedical University, 100 Shih-Chuan 1st Road, Kaohsiung 80708, Taiwan.

THIN-PLATE SPLINE GRAPHICAL ANALYSIS OF THE

MANDIBLE IN MANDIBULAR PROGNATHISM

Hsin-Fu Chang, Hong-Po Chang,1 Pao-Hsin Liu,2 and Chih-Han Chang2

Conventional roentgenographic cephalometrics, basedon angular, linear and ratio measurements, have shownan increasing number of limitations [1, 2]. The actualsites of putative mandibular skeletal change are insuf-ficiently visible in traditional cephalometric analysis[1], and conventional cephalometrics cannot analyzesize and shape changes of complex anatomical formssuch as the mandible [1]. Bookstein introduced a newmorphometric method for shape comparisons calledthin-plate spline (TPS) analysis [3, 4]. TPS analysisfacilitates the construction and display of transforma-tion grids that capture the shape change betweenforms. This conceptually simple maneuver quickly showsthe location and extent of deformation.

A relatively high prevalence of Class III malocclu-sion has been observed in Asian populations [5–8].Class III malocclusion is a common clinical problem inorthodontic patients. Studies suggest that skeletal Class

Abstract: The chin cup has been used to treat skeletal mandibular prognathism ingrowing patients for 200 years. The pull on the orthopedic-force chin cup is orientedalong a line from the mandibular symphysis to the mandibular condyle. Variouslevels of success have been reported with this restraining device. The vertical chincup produces strong vertical compression stress on the maxillary molar regions whenthe direction of traction is 20° more vertical than the chin-condyle line. This treatmentstrategy may prevent relapse due to counter-clockwise rotation of the mandible. Inthis report, we describe a new strategy for using chin-cup therapy involving thin-plate spline (TPS) analysis of lateral cephalometric roentgenograms to visualizetransformation of the mandible. The actual sites of mandibular skeletal change arenot detectable with conventional cephalometric analysis. A case of mandibularprognathism treated with a chin cup and a case of dental Class III malocclusionwithout orthodontic treatment are described. The case analysis illustrates that specificpatterns of mandibular transformation are associated with Class III malocclusionwith or without orthopedic therapy, and that visualization of these deformationsis feasible using TPS graphical analysis.

III malocclusion presents in 63 to 72% of patients withClass III malocclusion [5, 6]. Mandibular prognathismor Class III malocclusion with a prognathic mandiblehas long been viewed as one of the most severe facialdeformities [9]. A number of treatment protocols havebeen used to address skeletal Class III malocclusion.The chin cup is recommended in growing patients whohave a moderately protrusive mandible and a relativelynormal anteroposterior position and maxilla size [10].However, treatment of skeletal Class III malocclusionin growing children is one of the most challengingproblems confronting the practicing orthodontist.Relapse after treatment is occasionally an embarrass-ing situation for the orthodontist, the patient, and theparents.

The aim of this study was to apply TPS to mandibu-lar configurations on lateral cephalographs andto determine the local form differences between initial

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and final cephalographs in subjects with Class IIImalocclusion, with or without orthodontic treatment.

Case Reports

Case 1Two patients were selected for study. The first patient was aboy, aged 7 years, who was referred to us with Class IIImalocclusion in early mixed dentition. Dental Class III witha Class III deciduous molar and Class III deciduous caninerelationships were noted. He had a Class I permanent molaron the left side and a Class III permanent molar on the otherside. He also had an anterior crossbite (Fig. 1A). He receivedno treatment and was followed up regularly. The anteriorcross-bite corrected itself and the molar occlusion became aClass I relationship at the age of 9 years 7 months (Fig. 1B).

Case 2The second patient was a girl, aged 8 years and 8 months, whocame to the orthodontic clinic with Class III malocclusion inearly mixed dentition. Skeletal Class III malocclusion withClass III deciduous canine and Class III molar relationshipsand an incisal edge-to-edge bite were noted (Fig. 2A). Chincup treatment was given for 2 years, which corrected theincisal edge-to-edge bite to a normal overbite. However, thebite was not deep enough to provide sufficient anteriorguidance and there was still a Class III molar relationship (Fig.2B). Severe skeletal Class III malocclusion with super Class IIImolar and Class III canine relationships, anterior cross-bite,and anterior open-bite developed at the age of 16 years 1month (Fig. 2C). Orthognathic surgical treatment combinedwith orthodontic therapy was performed to correct the prob-lem after completion of growth when she moved to the USA.The posttreatment result was stable.

TPS analysisFor TPS analysis in these two patients, 12 homologous land-marks were determined for the mandible on the lateralcephalograph: condylion, anterior border of ramus, lowerincisor lingual bony contact, infradentale, supramentale,protuberance menti, pogonion, gnathion, menton, gonion,posterior border of ramus, and articulare. The anterior borderof ramus is the intersection of the functional occlusal planewith the anterior border of the ramus, and the posterior borderof ramus is the intersection of the functional occlusal planewith the posterior border of the ramus (Figs. 1C and 2D;Table). TPS graphical analysis showed the shape differenceor deformation, which appeared as vertical compression/extension and/or horizontal compression/extension of thegrids on the graphical displays when the pre- and post-treatment lateral cephalographs were superimposed and thelandmark configurations compared. TPS software was usedas previously described [11]. A more detailed review of thetheoretical basis and calculation procedures of TPSmorphometrics can be found in Bookstein [3, 4] and Drydenand Mardia [12].

Results

TPS analysis of the lateral cephalographs in Case 1without orthodontic treatment showed a slight clock-wise rotation of the mandibular condyle and ascendingramus, a compression in the region of the antero-inferior portion of the mandibular symphysis, and aslight counter-clockwise rotation of the mandibularbody (Fig. 1D).

After chin cup therapy, TPS analysis of the lateralcephalographs in Case 2 revealed a slight forwardcompression of the mandibular condyle, an extensionin the region of the anterior portion of the mandibularsymphysis, and a counter-clockwise rotation of theinferior portion of the mandibular symphysis (Fig. 2E).TPS analysis of the follow-up cephalograph showeda posterior extension of the mandibular condyle andascending ramus and an extension in the region ofthe anterior portion of the mandibular symphysis(Fig. 2F).

Discussion

This study used TPS analysis to visualize transforma-tions and to provide insight into the localization ofactual anatomic deformations of the mandible in twopatients with Class III malocclusion. The TPS functionfits the differences in the positions of the landmarksin one form relative to their positions in another [3,4, 12]. This method models shape differences as adeformation between landmarks. The interpolationfunction used in spline analysis can be described bya physical metaphor in which the landmarks of oneform located on an infinitely thin metal plate aredeformed, so that the height over each landmark isequal to the coordinates of the corresponding point inthe other form [3, 4]. While TPS analysis is also suitablefor three-dimensional studies, in this study we onlyused two-dimensional data derived from lateralcephalographs.

The use of the chin cup in the treatment of man-dibular prognathism was first reported in the early1800s [13]. Cellier in France and Fox, Kinsley andFarrar in the USA designed appliances that resembletoday’s chin cup. While chin-cup therapy for mandi-bular prognathism has been used for a long time,varying levels of success have been reported. Differ-ences in these findings may be causally related to theduration of treatment, level of force utilized in theappliance, and/or the age of the patient being treated.This orthopedic appliance is effective for mandibular

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Fig. 1. Case 1. Class III maloc-clusion in a boy without orth-odontic treatment. A) Initialcephalometric roentgenogram.B) Final cephalometric roent-genogram. C) Graphical dis-play of initial mandibularconfiguration is untrans-formed (see the Table for de-scription of abbreviated terms).D) Graphical display of finalmandibular configurationshowing mandibular shapechanges as total spline.

Table. Homologous mandibular landmarks used in this study

Landmark Definition

Condylion (Cd) Most superior point on mandibular condyleAnterior border of ramus (Ab) Intersection of functional occlusal plane with anterior border of ramusLower incisor lingual bony contact (Lib) Lingual contact of alveolar bone with mandibular central incisorInfradentale (Id) Most anterosuperior point on labial aspect of mandibular alveolusB point or supramentale (B) Deepest point on mandibular alveolusProtuberance menti or Most superoposterior point on mandibular symphysis changes from

suprapogonion (Pm) concave to convexPogonion (Pog) Most anterior point on mandibular symphysisGnathion (Gn) Most anteroinferior point on mandibular symphysisMenton (Me) Most inferior point on mandibular symphysisGonion (Go) Midpoint of mandibular or gonial anglePosterior border of ramus (Pb) Intersection of functional occlusal plane with posterior border of ramusArticulare (Ar) Posterior intersection of condylar head and posterior cranial base

A B

C D

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prognathic patients in late deciduous dentition orearly mixed dentition [10]. The girl in this reportbegan treatment with 150 to 300 g of force per side ofthe chin cup. This force was increased to a minimum of450 g per side over a 2-month period. She was in-structed to wear the chin cup for a period of 10 to 12hours per day. In cases of more severe malocclusion oruncooperative patients, the period of requested wear isincreased to 12 to 16 hours daily. After resolution of theintermaxillary skeletal imbalance, both the amount ofchin-cup force and the duration of wear are reduced.The appliance is then used as a retainer for the remain-der of the treatment period. The appliance is fabri-cated so that the pull on the chin cup is oriented alonga line from the mandibular symphysis (chin) to themandibular condyle.

In successfully treated cases, the generalized effectof chin-cup therapy on mandibular structures can beinterpreted as a forward direction of condylar growthassociated with a restriction in sagittal advancement ofthe symphysis [10, 14]. On the other hand, untreatedprogression of Class III growth presents as an overalldeformation of the mandible with extension in theregions of the mandibular condyle and the antero-inferior portion of the mandibular symphysis [14]. Inthis study, TPS analysis demonstrated that the patientwith untreated Class III malocclusion with self-correctionof the original malocclusion (Case 1) showed a com-pression in the region of the antero-inferior portion ofthe mandibular symphysis, a counter-clockwise rotationof the mandibular body, and forward compression ofthe mandibular condyle and neck. This is similar to

Fig. 2. Case 2. Mandibular prognathism in a girl receiving chin cup therapy. A) Pretreatment cephalometric roentgenogram. B)Posttreatment cephalometric roentgenogram. C) Follow-up cephalometric roentgenogram. D) Graphical display of pretreatment mandibularconfiguration is untransformed (see the Table for description of abbreviated terms). E) Graphical display of posttreatment mandibularconfiguration showing mandibular shape changes as total spline. F) Graphical display of follow-up mandibular configuration showingmandibular shape changes as total spline.

A B C

D E F

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cases of successfully treated Class III malocclusion withchin-cup therapy [14]. Although there was a counter-clockwise rotation of the inferior portion of the man-dibular symphysis, the relapse of skeletal Class IIImalocclusion in this patient was treated with a chincup, which revealed a forward extension in the regionof the anterior portion of the mandibular symphysis.This result is the same as in a previously reporteduntreated growing case of Class III malocclusion [14].The follow-up cephalograph in Case 2 with relapseshowed a posterior extension of the mandibular condyleand ascending ramus, an extension in the region of theanterior portion of the mandibular symphysis, andclockwise rotation of the mandibular body as in theuntreated case of growing Class III malocclusion. Thisexplains why the girl developed severe skeletal Class IIImalocclusion. Clinically, this may be related to theduration of treatment, level of force used, wearing timeof the appliance, and/or the age of the patient [9].Thus, TPS graphical analysis demonstrated differentshape changes in the mandibular configuration ofchildren with Class III malocclusion with or withouttreatment and with or without correction of the origi-nal malocclusion.

The ultimate treatment goal for skeletal Class IIIpatients should not only be the correction of the jawrelationship and negative incisal overjet related tomesial occlusion at that stage, but also the stabilizationof the intermaxillary skeletal and dental relationshipsresulting from orthopedic appliance treatment. Thus,close observation and follow-up of mandibular growthduring adolescence, particularly during the second orthird stage of orthodontic treatment, is essential.

Using dried human skulls with strain gauges, Omatsuand Kawamoto investigated the effects of a chin cup onthe pediatric craniofacial skeleton [15]. This includedconsideration of different directions of traction forceimparted by the chin cup. They found that when thedirection of traction was 20° more vertical than thechin-condyle line, i.e., through the occlusal surfaces ofthe molars, the chin cup produced strong verticalcompression stress on the maxillary molars, suggestiveof induction of counter-clockwise rotation of themandible. Therefore, this treatment strategy mayprevent the relapse of treated skeletal Class III mal-occlusion. The effects of orthopedic force produced bya vertical chin cup are correlated with the cephalomet-ric and histologic observations during use of this appli-ance in animal studies [16, 17].

In conclusion, TPS analysis may show the degree oftransformation within the mandibular geometric con-figuration due to treatment effects and/or growthchanges, as seen on lateral cephalometric roent-genograms. Further research into the growth changesand/or treatment effects of the vertical chin cup with

the direction of traction of 20° more vertical than thechin-condyle line on a large number of patients withskeletal Class III malocclusion using TPS graphicalanalysis is warranted.

ACKNOWLEDGMENTS: This study was supported by aresearch grant from the National Science Council,Taiwan (NSC 91-2320-B-037-022).

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