morphological associations between the angle classes

8/7/2019 morphological associations between the angle classes

1/8

European Journal of Orthodontics 18 (1996) 111-118 1996 European Orthodontic Society

Morphological associations between the Angle classes

J. M. H. DibbetsDepartment of Orthodontics, Philipps University, Marburg, Germany

SUMMARY The association between the Angle classification and craniofacial form has beenanalysed with the aid of multiple linear regression analysis in a sample of 170 children,before orthodontic treatment had started. It was found that part of the differences betweenClass II, Class I, and Class III was accounted fo r by systematical var ia tion in a coherent setof midface and cranial base dimensions. These variations were in harmony with each other:the cranial base angle Ba-S-N closed and the legs S- N and S-Ba shortened systematicallyfrom Class II, over Class I, to Class III. The juvenile mandible notably was not systematicallydifferent. Because the cranial base provides the framework for the maxilla to be built upon,it is concluded that in juveniles the midface above anything else creates the characteristic

difference between the three Angle classes, not the mandible. The Angle classification ofmalocclusion, therefore, represents three arbitrary markers on a morphological continuum.

Introduction

'I n beginning the consideration of malocclusionlet us remember that it is bu t the perversion ofthe normal in growth and development ... ' thuswrote Angle in the first line of his chapter on'Malocclusion' (1907, p. 28). In the text itbecomes obvious that the Angle classificationof malocclusion is primarily based on skeletal

relationships and not so much on occlusionper se. However, the unsolved question is, arethe Angle classes three discrete groups characterized by discrepancies in size and positionof the maxilla and, notably, the mandible or,do they represent three arbit rary markers on ascale of systematic variation in anatomybetween Class II at the one end to Class III atthe other end? The fact that Angle positionedClass I before, not between, the two oppositeClasses II and III, suggests that he himselfconsidered them as being unrelated.

The association of factors such as lymphoidtissue or head posture with facial morphologyhas been explored, yet an explicit associationwith the Angle classes has no t been investigated(Bjork, 1951; Solow and Tallgren, 1976; LinderAronson, 1979; Vig et al., 1981; Solow andSiersbsek-Nielsen, 1986; Hellsing et al., 1987;Woodside et al., 1991). Cole (1988) contendsthat natural head posi tion affects the cranialbase orientation and this alone is capable ofproducing a Class II or III effect. Textbooks

depict the Angle classes as discrepancies in sizeand position of the maxilla and mandible, withou t speculation on a special role for any structure (Nanda, 1983; Moyers, 1988; Enlow, 1990;Houston et al., 1992; Proffit and Fields, 1993).Jarvinen (1980) reports that a marked part ofthe variat ion in the SN A angle is explained byvariation in the saddle angle NSAr. Only twopublications were found in which morphologicalvariation between Class II an d Class III malocclusion systematically is reduced into one singlestructure (Hopkin et al. 1968, Kerr and Adams,1988). These two studies both assign a centralrole to the cranial base and conclude that theamount of mandibular prognathism can beexplained by, or results from the cranial baseconfiguration which positions the temporomandibular (TM) joint, and thus the mandible,forward into Class III and backward intoClass II.

The opinion, however, that the Angle classesrepresent discrepancies in size and/or positionof the maxilla and mandible, explicitly or implicitly dominates the literature. Most studies compare Class II or Class III samples with a ClassI reference, and not with each other. Relativeto Class I, the Class II mandible is reported tobe shorter (Sicher and Krasa, 1920; Sicher,1947; Craig, 1951; Harris, 1965; Hunter, 1967;Wells, 1970), or almost normal (Nelson andHighley, 1948), while the cranial base angle isrepor ted to be larger (Harr is, 1975; Anderson


2/8

112

and Popovich, 1983; Bacon et al., 1992), ornormal (Wells, 1970). The TM joint in Class IIis positioned posteriorly (Sicher and Krasa,1920; Fisk et al., 1953; Maj et al., 1960; Hunter,1967; Bacon et al., 1992). Relative to Class Ithe Class III mandible is reported to be longer(Sicher and Krasa, 1920; Raynes, 1956; Majet al., 1960; Joffe, 1965; Jacobson et al., 1974;Baer, 1975; Fischer-Brandies et al., 1985; Guyeret al., 1986; Chang et al., 1992; Battagel, 1993),while the maxilla is reported to be shorter(Timmons, 1958; Gebeck, 1969; Guyer et al.,1986; Battagel, 1993), or normal (Stapf, 1940;Joffe, 1965). The cranial base angle is reportedto be smaller in Class III (Timmons, 1958;Horowitz et al., 1969; Anderson and Popovich,1983; Bacon et al., 1992; Battagel, 1993), thelinear cranial base dimensions to be smaller(Horowitz et al., 1969; Jacobson et al., 1974) orthe basicranial configuration to be different(Martone et al., 1992). The TM joint in ClassIII is positioned anteriorly (Sicher and Krasa,1920; Furlong, 1954; Maj et al., 1965; Jacobsonet al., 1974; Battagel, 1993) as is the hyoid bone(Adamidis and Spyropoulos, 1992).

Class III generally is considered to be inherited (Kantorowicz, 1915; Schwarz, 1931; Steinet al., 1956;Emrich et al., 1965;Nakasima et al.,1982). A polygenic model has been postulated(Litton et al., 1970; Bookman et al., 1974; Harriset al., 1975). Remarkable is the finding ofBookman et al. (1974) that non-Class III familymembers exhibited a definite trend towards thestatistics generated for the Class III patients intheir study, rather than to a normal population.Harris (1975) made the same observation inClass II, division I patients who were found tobe much more similar to their own immediatefamily than to a randomly selected set of unrelated Class II individuals. Yet, Harris et al.(1975) are of the opinion that the Class II andIII malocclusions cannot be considered as occu

pying opposite ends of the statistical distribution of any single variable. Also interesting isthe finding of structural differences in thecranio-vertebral junction in Class III individuals(von Treuenfels, 1981; Hirschfelder andHirschfelder, 1982a,b; Huggare, 1991). Theselatter reports suggest that at least Class III is astructural entity separated from the otherclasses.

I t is the intention of the present report toexplore if anatomical structures can be identified

J. M. H. DIBBETS

which vary systematically from Class II viaClass I to Class III. If so, the Angle classes areonly arbitrary markers in a morphological continuum. I f not, the option remains that theclassification must be considered as three morphologically discrete groups.

Subjects and methods

A total of 170children were documented beforeorthodontic treatment had started. They represent a more or less consecutively referred orthodontic sample, although effort has been madeto include some extra Class III individuals.Their mean age was 12.5 years; 45 per cent Wereboys, 55 per cent were girls. Standardized lateralcephalograms were taken, traced, digitized and

checked for errors. The 20 linear and nineangular dimensions studied are listed in Table 1.All linear dimensions have been corrected forenlargemen 1.

Angle classification

An initial Angle classification of one kind orother was necessary in order to allow furtherstatistical analysis. To that purpose the Angleclassification has been determined on plastermodels only. Deep impressions allowed theinspection of the alveolar process and the apical

area. Assessments of sagittal molar and caninerelation on the left and right side, with duerespect to mesial migration, were combined toestimate the upper to lower basal relationship.I t reflects clinical view since there is no consensus on a gold standard for the Angle classification (Rinchuse and Rinchuse, 1989; Katz,1992a,b; Kerr et al., 1994; Lowe et al., 1994) .

Regression analysis

The association between the Angle classificationand craniofacial form was analysed with the aid

of multiple linear regression analysis, whichassesses a linear relationship between independent variables (e.g. age) and a dependent variable(e.g. size). Size in this example is considered tobe dependent on age, older children typicallybeing associated with larger size. A strong pointof the regression model is the capability ofhandling multiple independent variables simultaneously, disclosing the influence of subtleindependent variables. Another strong pointis weighting the influence of independent


3/8

ASSOCIATIONS BETWEEN T HE A NG LE CLASSES 113

Table 1 The 20 linear and nine angular dimensionsstudied.

3.83.13.33.55.53.44.92.43.33.23.3

SD

7.16.55.05.83.44.27.36.03.5

5.05.13.64.04.96.33.24.93.3

Average value

110.194.767.666.431.738.7

107.161.538.6

132.0128.380.675.7

125.1126.4

8.415.534.7.

Dimension

Cranial base and maxilla linearS- N 69.3S-Ba 43.3Ba-PTM 42.2PTM-A 48.6Ar-A 79.5PNS-A 45.0Ba-Or 76.9Or-prPP 20.8N-ANS 47.6ANS-UIE 26.1S-PNS 42.6

Mandible linearS-GnAr-PgPg-GoS-GoS-ArAr-GoN-MeANS-MeLIE-Me

AngularBa-S-NOp-Ba-SS-N-AS-N-BN-S-ArGonial AngleSN/PPSN/OPSN/MP

Table 2 Average value and SD for the linear andangular dimensions, corrected for cephalometricenlargement. Note that the averages do not take intoaccount differences in the distribution of other parameters such as age, gender or the Angle classification.

Sella-GnathionArticulare-PogonionPogonion-GonionSella-GonionSella-ArticulareArticulate-GonionNasion-Menton (total face height)Anterior Nasal Spine-Menton (lowerface height)Lower Incisor Edge-Menton

Basion-Sella-NasionOpistion-Basion-SellaSella-Nasion-point ASella-Nasion-point BNasion-Sella-Articulare

Gonial AngleSella-Nasion/palatal PlaneSella-Nasion/Occlusal PlaneSella-Nasion/Mandibular Plane

Linear cranial base and maxillaS- N Sella-NasionS-Ba Sella-Basion

Ba-PTM Basion-PTMPTM-A PTM-point AAr-A Articulare-point APNS-A Posterior Nasal Spine-point ABa-Or Basion-OrbitaleOr-prPP Orbitale-perpendicular on Palatal

PlaneN-ANS Nasion-Anterior Nasal Spine (upper

face height)ANS-UIE Anterior Nasal Spine-Upper Incisor

EdgeS-PNS Sella-Posterior Nasal Spine

Linear mandibleS-GnAr-PgPg-GoS-GoS-ArAr-GoN-MeANS-Me

LIE-Me

AngularBa-S-NOp-Ba-SS-N-AS-N-BN-S-Ar

Gonial AngleSN/PPSN/OPSN/MP

variables, instead of splitting up the sample intoeven smaller sub-groups, thus avoiding substantial sample attrition and arbitrary cut-offpoints.This latter point made regression especiallyattractive since age in the three Angle classeswas far from being identical. The formulation

of an adequate model represents a problem. Incase of a linear model, linearity is not alwaysmet, as for example, size does not developlinearly with age. Yet, it can be shown bypractical examples that power outranks weakness. As a sort of post hoc test, the results havebeen verified, and found to be realistic, bycomparing the outcome for age and genderagainst public domain data (Dibbets, 1977).This approach does not replace testing of thestatistical assumptions underlying the model.

However, the comparison with data gatheredfor a different purpose provides a validverification.

One regression analysis was carried out for

each of the 29 cephalometric dimensions as thedependent variable, along with age, gender,and the Angle classification (coded II I III, seediscussion), among others, as the independentvariables. Age, gender, an d a few other independent variables, although not discussed indetail, were a necessary part of the proceduresince each of them possibly could explain aspecificamount of variance in the cephalometricdata. For all analyses, the significance level wasset at Ci = 0.05.


4/8

114

}CJ/

J. M. H. DIBBETS

Figure 1 Significant regression coefficients were incorporated as a quantitative (yet artistic) illustration of craniofacialdifferences between Class II (black) and Class III (red). The soft tissue outline and skeletal contours are estimates sinceonly hard tissue landmarks were digitized. The structure central to these differences apparently is formed by the cranialbase, when angle Ba-S-N closes and legs S-N and S-Ba shorten from Class II over Class I to Class III. Note t ha t themandible was not systematically different.

Results

Angle classification and age

The distribution of the Angle classification was14 per cent Class I; 69 per cent Class II; and 17percent Class III. The average age was 14.2years in Class I, 12.8 years in Class II, and 10.0years in Class III.

The average age of the sample was 12.5years,SD 3.0 years. With exception of the skeweddistribution for Class III, (see Subjects andmethods), these figures reflect the referring pattern from the regional dental practitioners.

Regression analysis

The results are presented in Tables 2 and 3 andin Fig. 1. Table 2 depicts the average value andSD of the cephalometric dimensions withouttaking into account age, gender or Angle classification. Table 3 depicts the results from theregression analysis. The regression coefficientmay be interpreted as estimated mm or degreesdifference between Class II and Class I or ClassI and Class III. The difference between Class II

and Class III, however, equals two steps ordouble the regression coefficient, because ClassI has been positioned between the two. Forexample, a regression coefficient of - 1.7 forSella-Nasion may be interpreted such that theSella-Nasion dimension in Class I is 1.7mmshorter than in Class II and that the Class IIIdimension is 1.7 mm shorter than in Class I(from Class II to Class I and from Class I toClass III it ' shortens' each time by 1.7mm). Inother words, Sella-Nasion is 3.4 mm shorter inClass III compared with Class II, or, conversely,Sella-Nasion in Class II is 3.4 mm longer than

in Class III. The significant findings have beenincorporated in Figure 1.

Discussion

The Angle classification has been determinedon plaster models in an attempt to capture theclinical situation and because the method is freefrom cephalometric bias (Jarvinen, 1988). Thejustification to enter the Angle classification asan independent variable in a regression model


5/8

ASSOCIATIONS B ET WE EN T HE ANGLE CLASSES 115

Table 3 Significant regression coefficients* for Angle classification and cephalometric dimensions. The coefficient may be interpreted as estimated difference in millimeters or degrees between the Classes II and I or theClasses I and III. The sign represents direction of the difference.

Dimension

Cranial base and maxilla linearS-NS-BaB a ~ P T M

PTM-AA r ~ A

P N S ~ A

Ba-OrOr-prPPN-ANSANS-UIES-PNS

Mandible linearS-GnAr-PgPg-GoS-GoS-ArAr-GoN-MeANS-MeLIE-Me

AngularBa-S-NOp-Ba-SS-N-AS-N-BN-S-Ar

Gonial AngleSN/PPSN/OPSN/MP

Regression coefficient

-1 .7-1 .2-1 .7-1 .9-3.3-2 .0-2.7-0 .5-0 .7-1 .2-0.7

NSNSNS-0 .9-1 .3NS-1 .6-1.6-1 .1

-1 .5NS-0 .8+2.7-1 .1

NSNSNS-1 .0

Estimated difference betweenClass II and Class rn-

-3.4-2.4-3.4-3 .8-6.6-4.0-5.4-1 .0-1.4-2.4-1.4

-1 .8-2 .6

-3.2-3.2-2 .2

-3.0

-1.6+5.4-2 .2

-2.0

*P


6/8

116

Jarvinen, 1988; Lowe et al., 1994) or the determination on plaster models. Another explanation could be age differences between thereported studies. From the presented literatureit seems that differences in mandibular sizebetween Class I and Class II or Class I andClass III emerge later during development andtherefore these differences are more likely to befound in adult samples (Jacobson et al., 1974).A third explanation finds its origin in datahandling and will be elucidated with one publication, in which cephalometric dimensions inchildren with a Class I were compared to aClass II sample (Harris, 1965). Initially a largermean Sella-Nasion dimension in the Class IIindividuals was found, but no differences werenoticed between the means of the mandibularparameters, as becomes evident from a table.Because the cranial base probably was considered to be independent from the Angle classification, the author must have been puzzled bythe unexpected discrepancy in anterior baselength and decided to compensate for theassumed head size differences of the twosamples. A covariance analysis with regressionon Sella-Nasion was performed, producingidentical Sella-Nasion means and smallerArticulare-Pogonion means in Class II relativeto Class I as a result. Thus, a smaller mandiblein the Class II sample relative to Class I wasreported in the discussion and summary.Apparently, comparison of the outcome ofdifferent studies calls for great care and a merereplication of numbers leads to erroneousconclusions.

The findings in this study quantitativelymatch those of Hopkin et al. (1968) and Kerrand Adams (1988) and also agree that thestructure pivotal to the differences between theAngle classes is the cranial base. Both studiescited, however, interpret their findings from aperspective of an immutable anterior cranial

base. The cranial base angle in that view affectsthe position of the spheno-occipital part of thebase and, consequently, results in a relocationof the TM joint forward or backward. However,sagittal relocation of the spheno-occipital bonenecessarily includes relocation of the cervicalspine. In addition from being impractical, thisview ignores the impact of size and shape ofthe cranial base on the maxilla (Koski, 1960;Birch, 1968; Knowles, 1963; Baer and Nanda,1976; Enlow, 1990). The deepness of the

1. M. H. DIBBETS

pharynx and the horizontal and vertical maxillary dimensions are entirely accounted for bythe sizeand shape of the cranial base. Thereforeit is concluded that the size and configurationof the cranial base, and therefore the size andposition of the midface, created the characteristic difference between the Angle classes asestablished on plaster models. The juvenilemandible was not systematically different. Thus,the Angle classification of malocclusion represents three arbitrary markers in a morphologicalcontinuum.

Address for correspondence

Prof. Dr J. M. H. DibbetsMZ ZMK Department of OrthodonticsGeorg-Voigt-Strasse 3

D-35033 Marburg Germany

Acknowledgements

Dr C. Sessler, University of Marburg, Germany,and Priv. Doz. Dr A. Jager, University ofGottingen, Germany, discussed the manuscript.L. Th van der Weele, University of Groningen,Netherlands, provided indispensable statisticalcounselling.

References

Adamidis I P, Spyropoulos M N 1992 Hyoid bone positionand orientation in Class I and Class III malocclusions.American Journa l of Orthodont ics and DentofacialOrthopedics 101: 308-312

Anderson D, Popovich F 1983 Relation of cranial baseflexure to cranial form and mandibular position.American Journal of Physical Anthropology 61: 181-187

Angle E H 1907 Treatment of malocclusion of the teeth.Angle's system. 7th edition. S.S. White, Philadelphia

Bacon W, Eiller V, Hildwein M, Dubois G 1992The cranialbase in subjects with dental and skeletal Class II.European Journal of Orthodontics 14: 224-228

Baer L D 1975 A cephalometric study of patients with theWiedemann-Beckwith syndrome and subjects with ClassIII malocclusion. Master's Thesis, University ofWashington, Seattle

Baer M J, Nanda S K 1976 A commentary on the growthand form of the cranial base. In: Bosma J F (ed.)Development of the basicranium. U.S. Department ofEducation, Health and Welfare Publication No. (NIH)76-989, Bethesda, pp.515-536

Battagel J M 1993 The aetiological factors in Class IIImalocclusion. European Journal of Orthodontics 15:347-370

Birch R H 1968 Foetal retrognathia and the cranial base.Angle Orthodontist 38: 231-235


7/8

ASSOCIATIONS B E T W E E N T HE A NG LE CLASSES

Bjork A 1951 Some biological aspects of prognathism andocclusion of the teeth. Angle Orthodontist 21: 3-27

Bookman D J et al. 1974 Inheritance of the craniofacialcomplex in Class III malocclusion. Master' s Thesis,University Michigan, Ann Arbor

Chang H-P, Kinoshita Z, Kawamoto T 1992 Craniofacial

pattern of Class III deciduous dentition. AngleOrthodontist 62: 139-144

Cole S C 1988 Natural head position, posture , and prognathism. British Journal of Orthodontics 15: 227-239

Craig C E 1951The skeletal patterns characteristic of ClassI and Class II, Division 1 malocclusions in norma lateralis.Angle Orthodontist 21: 44-56

Dibbets J M H 1977 Juvenile temporomandibular jointdysfunction and craniofacial growth. A statistical analysis. Stafleu and Tholen, Leiden

Emrich R E, Brodie A G, Blanley J R 1965Die Verbreitungvon Anomalien der Klassen I, II und III bei einerstadtischen Population. Deutsche ZahnarztlicheZeitschrift 20: 87-94

Enlow D H 1990Facial growth, 3rd edition. W B Saunders,Philadelphia

Fischer-Brandies H, Fischer-Brandies E, Dielert E 1985Ober die Gesamtlange und den Achsenwinkel desUnterkiefers. Eine Analyse seitlicher Fernrontgenbilder.Fortschritte der Kierferorthopadie 46: 241-246

Fisk G V, Culbert M R, Grainger R M, Hemrend B,Moyers R E 1953 The morphology and physiology ofdistocclusion. A summary of our present knowledge.American Journal of Orthodontics 39: 3-12

Furlong F J 1954 A radiographic investigation of thetemporomandibular joint in Class III malocclusion.Master's Thesis, Northwestern University of Chicago

Gebeck T R 1969 A cephalometric study of moderate ClassIII malocclusion . . Master's Thesis, University ofMichigan, Ann Arbor

G uyer E C, Ellis E E, M cN am ara J A, Behrents R G 1986Components of Class III malocclusion in juveniles andadolescents. Angle Orthodontist 56: 7-30

Harris J E 1965 Cranio-facial growth and malocclusion.Transactions of the European Orth odo nti c Society,pp. 103-119

Harri s J E 1975 Genetic factors in the growth of the head.Inheritance of the craniofacial complex and malocclusion.Dental Clinics of North America 19: 151-160

Harris J E, Kowalski C J, Walker S J 1975 Dentofacialdifferences between 'normal ' sibs of Class II and ClassIII parents. Angle Orthodontist 45: 103-107

Hellsing E, McWilliam J, Reigo T, Spangfort E 1987 Therelationship between craniofacial morphology, head posture and spinal curvature in 8, 11 an d IS-year oldchildren. European Journal of Orthodontics 9: 254-264

Hirschfe1der H, Hirschfelder U 1982a Die Halswirbelsauleim seitlichen Fernrontgenbild aus orthopadischer Sicht.Fortschritte der Kierferorthopadie 43: 52-56

Hirschfe1der U, Hirschfe1der H 1982b Veranderungen deroberen Ha1swirbe1sau1e bei Patienten des progenenFormenkreises. Deutsche Zahnarztliche Zeitschrift 37:691-698

117

Hopkin G B, Houston W J B, James G A 1968The crania lbase as an aetiological fac tor in malocclusion. AngleOrthodontist 38: 250-255

Horowitz S L, Converse J M, Gerstman L J 1969Craniofacial relationships in mandibular prognathism.Archives of Oral Biology 14: 121-131

Houston W B J, Stephens C D, Tulley W J 1992A textbookof orthodontics. 2nd edition. Wright, Oxford

Huggare J 1991 Association between morphology of thefirst cervical vertebra, head posture, and craniofacialstructures. European Journal of Orthodontics 13:435-440

Hunter W S 1967 The vertical dimensions of the face andskeletodenta1 retrognathism. American Journ al ofOrthodontics 53: 586-595

Jacobson A 1975 The 'Wits ' appraisal of jaw disharmony.American Journal of Orthodontics 67: 125-138

Jacobson A, Evans W G, Preston C B, Sadowsky P L 1974Mandibular prognathism. American Journal ofOrthodontics 66: 140-171

Jarv inen S 1980 Relat ion of the SNA angle to the saddleangle. American Journal of Orthodontics 78: 670-673Jarvinen S 1988 Relat ion of the Wits appraisal to the ANB

angle: a statistical appraisal. American Journal ofOrthodontics and Dentofacial Orthopedics 94: 432-436

Joffe B M 1965 Cephalometric analysis of mandibularprogna thi sm II. Journa l of the Denta l Association ofSouth Africa 20: 173-180

Kantorowicz A 1915 Die Progenie und ihre Vererbung.Deutsches Monatsschrift fu r Zahnheilkunde 33: 105-128

Katz MI 1992a Angle classification revisited. 1: is currentuse reliable? American Journal of Orthodont ics andDentofacia1 Orthopedics 102: 173-179

Katz MI 1992b Angle classification revisited. 2: a modified

Angle classification. American Journal of Orthodonticsand Dentofacial Orthopedics 102: 277-284Kerr W J, Adams C P 1988 Crania l base and jaw relation

ship. American Journal of Physical Anthropology 77:213-220

Kerr W J S, Miller S, Ayme B, Wilhelm N 1994Mandibularform and position in 10-year old boys. American Journalof Orthodontics an d Dentofacial Orthopedics 106:115-120

Knowles C C 1963 The influence of cranial base structureon the orientation of the middle third of the face. DentalPractitioner 13: 531-542

Koski K 1960 Some aspects of the growth of the cranialbase and the upper face. Odontologisk Tidskrift 68:

344-358Linder-Aronson S 1979 Naso-respiratory function andcraniofacial growth. In: McNamara J A (ed.)Nasorespi ra tory function and craniofacial growth.Monograph No 9, Craniofacial Growth Series, Centerfor H um an Grow th and Development, University ofMichigan, Ann Arbor, pp. 121-147

Litton S F, Ackermann L V, Isaacson R J, Shapiro B L1970 A genetic study of Class III malocclusion. AmericanJournal of Orthodontics 58: 565-577

Lowe B F, Phillips C, Lestrel P E, Fields H W 1994Skeletaljaw relationships: a quantitative assessment using elliptical Fourier functions. Angle Orthodontist 64: 299-310


8/8

118

Maj G, Luzi C, Lucchese P 1960A cephalometric appraisalof Class II and Class III malocclusions. AngleOrthodontist 30: 26-34

Martone V D, Enlow D H, Hans M G, Broadbent B H,Oyen 0 1992 Class I and Class III malocclusion subgroupings related to headform type. Angle Orthodontist62: 35-44

Moyers R E 1988Handbook of orthodontics. 4th edition.Year Book Medical Publishers, Chicago

Nakasima A, Ichinose M, N aka ta S, Takahama Y 1982Hereditary factors in the craniofacial morphology ofAngle's Class II and Class III malocclusion. AmericanJournal of Orthodontics 82: 150-156

Nanda S K 1983The developmental basis of occlusion andmalocclusion. Quintessence, Chicago

Nelson W E, Highley B 1948 The length of mandibularbasal bone in normal occlusion and Class I malocclusioncompared to Class II, division I malocclusion. AmericanJournal of Orthodontics 34: 610-617

Proffit W R, Fields H W 1993Contemporary orthodontics.2nd edition. Mosby Year Book, St. Louis

Raynes J G 1956 A study of facial pat terns of individualswith class III malocclusions. Master's Thesis, Universityof Washington, Seattle

Rinchuse D J, Rinchuse D J 1989 Ambiguities of Angle'sclassification. Angle Orthodontist 59: 295-297

Schwarz A M 1931 Die Ontogenese des menschlichenGebisses in ihren Beziehungen zur Orthodontik.Fortschritte der Orthodontie I: 8-21

Sicher H 1947 The growth of the mandible. AmericanJournal of Orthodontics and Oral Surgery 33: 30-35

J. M. H. DIBBETS

Sicher H, Krasa F C 1920 Anatomische Untersuchungenan Schadeln mit Stellungsanomalien der Zahne.Osterreichische Zeischrift fur Stomatolgie 18: 375-403

Solow B, Siersbeek-Nielsen S 1986Growth changes in headposture related to craniofacial development. AmericanJournal of Orthodontics 89: 132-140

Solow B, Tallgren A 1976 Head posture and craniofacialmorphology. American Journal of Physical Anthropology44: 417-436

Stapf W C 1940A roentgenographic appraisal of the facialpattern in Class III malocclusion (Angle). Master'sThesis, University of Illinois, Chicago

Stein K F, Kelley T J, Wood E 1956 Influence of heredityin the etiology of malocclusion. American Journal ofOrthodontics 42: 125-141

Timmons L S 1958 Integration of certain variants as adeterminant of facial morphology in Class III malocclusion (Angle). Master's Thesis, University Illinois, Chicago

Treuenfels von H 1981 Die Relation der Atlasposition beiprognather und progener Kieferanomalie. Fortschritteder Kierferorthopadie 42: 482-491

Vig P S, Sarver D M, Hall D J, Warren D W 1981Quantitat ive evaluation of nasal airflow in relation tofacial morphology. American Journal of Orthodontics79: 263-272

WellsD L 1970A multivariate cephalometric study of ClassII, division 2 malocclusion. Master's Thesis, Universityof Michigan, Ann Arbor

Woodside D G, Linder-Aronson S, Lundstrtm A,McWilliam J 1991 Mandibular and maxillary growthafter changed mode of breathing. American Journal ofOrthodontics and Dentofacial Orthopedics 100: 1-18

Documents

morphological associations between the angle classes