Abstract | | |
**Aim:** To measure the vertical linear cephalometric dimensions of the anterior and posterior segments of the craniofacial complex and establish ratios between vertical linear dimensions in subjects with normal occlusion, pleasing profile, and facial harmony. **Setting and Sample Population:** Department of Orthodontics, Saveetha University. Lateral cephalograms of 120 subjects of both sexes in the age group of 17-28 years with normal occlusion belonging to Chennai, India. **Materials and Methods:** The vertical segments measured are anterior maxilla, posterior maxilla, and ramus-cranial floor vertical. The facial heights were measured in the anterior and posterior region of the craniofacial complex. Establish ratios and proportions between the vertical segments and different facial heights. **Results:** In both the sexes, the ratio between anterior maxilla, posterior maxilla, and ramus-cranial floor vertical is 1:1:1, PTFH:ATFH is 1:1, AUFH:ATFH is 2:5, ALFH:ATFH is 3:5, PUFH:PTFH is 1:2, PLFH:PTFH is 1:2, AUDH:ALDH is 2:3, and facial depth is 2:1. PUDH:PLDH is 7:9 in females and 3:4 in males. There was a statistically significant difference in posterior total facial height:anterior total facial height ratio between the two sexes with a "*P*" value of 95%. **Conclusion:** Thus, the anterior maxilla, posterior maxilla, and cranial floor-ramus vertical composite are in dimensional balance in subjects with normal occlusion and facial harmony. This analysis helps to identify skeletal deviations in size and position in the vertical dimension and allows the clinician to outline an appropriate treatment.
**Keywords:** Facial depth, facial heights, vertical anatomical segments
**How to cite this article:** Felicita A S, Chandrasekar S, Shanthasundari K K. Determination of craniofacial relation among the subethnic Indian population: A modified approach (vertical evaluation). Indian J Dent Res 2013;24:456-63 |
**How to cite this URL:** Felicita A S, Chandrasekar S, Shanthasundari K K. Determination of craniofacial relation among the subethnic Indian population: A modified approach (vertical evaluation). Indian J Dent Res [serial online] 2013 [cited 2021 Oct 18];24:456-63. Available from: https://www.ijdr.in/text.asp?2013/24/4/456/118396 |
Lateral roentgenographic cephalometry has extensive use in clinical orthodontics to quantify skeletal, dental, and soft tissue relationships of craniofacial complex. Sagittal and vertical cephalometric evaluation of the craniofacial complex is a prerequisite to effective diagnosis and treatment planning. Lateral cephalometry has varied applications in orthodontics such as morphological analysis and growth analysis. Morphological analysis is used to evaluate the facial skeleton, the dentition and the soft tissue profile. Growth analysis evaluates serial radiographs taken at different intervals and compares their relative changes. Cephalometric analysis can also evaluate changes during and after treatment and assesses posttreatment stability.
Cephalometric analysis can be classified into various categories.
- Normative analysis:
^{[1],[2],[3],[4],[5]} It consists of comparing the patient's linear and angular measurements to a set of mean values or norms established through cross-sectional or longitudinal studies for a given population or ethnic group. - Proportionate analysis:
^{[6],[7],[8],[9],[10],[11]} It is based on the comparison of various angular or linear measurements between separate parts of the facial skeleton. Individual, angular, or linear measurements of a given patient are compared with measurements from the same patient to evaluate skeletal discrepancy or harmony without referring to an established norm. - Analysis based on templates or coordinates compare the patient's profile with a template or Cartesian coordinate system or mesh diagram of an ideal profile established through cross-sectional or longitudinal studies.
^{[12],[13],[14],[15]} - Lateral cephalometric analysis is formulated for specific purposes like cephalometric analysis for orthognathic surgery,
^{[16]} growth prediction, ^{[17]} superimposition analysis for treatment evaluation, ^{[18],[19],[20]} and so on. - Cephalometric analysis based on mathematical models likes Tensor analysis,
^{[21]} finite element analysis, ^{[22]} Fourier analysis, ^{[23],[24]} and so on. Among these methods, proportionate evaluation of man's face with establishment of proportions and ratios dates back to ancient records from China, Eygpt, and India.
One of the early works on facial proportion in human is that of Hellman. ^{[25]} Hellman determined facial proportion by direct head measurements.
D'Arcy West worth Thompson ^{[26]} conducted a comparative study of growth and form of primate skulls in comparison with human skulls based on a proportional analysis by means of transformations of Cartesian coordinate system.
De Coster of Belgium ^{[27]} advocated transformation of mesh coordinate system for analysis of radiographs in normal lateralis of orthodontic patients.
Benjamin ^{[28]} conducted a study to ascertain the changes that occur with age in certain craniofacial proportions in the horizontal and vertical planes.
Broadbent ^{[29]} evolved an analysis to determine the proportional relationship between vertical, facial, and dentoalveolar heights, and thereby establish vertical abnormalities. The data for the study was derived from lateral cephalograms of children comprising of Bolton's standards.
Moorrees *et al*., ^{[13]} created a mesh analysis which is a proportionate cephalometric method of graphically assessing craniofacial disharmonies. The patient serves as his own control, thus providing an individualized form of craniofacial evaluation without comparison with population norms.
Accurate diagnosis, proper treatment planning, and a good prognosis involves a clear understanding of dentofacial harmony, balance, and association of anatomical entities. Analysis based on proportions or ratios establish a cause and effect between anatomical entities. This concept of facial balance and harmony was expressed by Enlow *et al*., ^{[30]} in their analysis of intrinsic facial form and growth. This cephalometric analysis evaluates individuals based on their own particular morphological and morphogenetic facial pattern.
They were of the opinion that most conventional cephalometric planes and angles do not coincide with actual sites and fields of growth and remodeling and are not appropriate for evaluation of the craniofacial complex. Therefore, if planes are constructed to directly represent growth and remodeling fields, a built in and morphologically natural set of standard is identifiable for evaluation of craniofacial form and pattern.
Considering the clinical usefulness of this concept of intrinsic facial form and growth, a lateral cephalometric study was undertaken to evaluate the vertical skeletal relationship of the craniofacial complex. A craniofacial analysis based on ratios and proportions was developed for cephalometric evaluation of subjects with normal occlusion, pleasing profile, and facial harmony who belonged to the local population in Chennai.
The aims of the present study are as follows:
- To measure the vertical, linear, cephalometric dimensions of anterior and posterior segments of the craniofacial complex.
- To establish ratios and proportions between the vertical, linear dimensions in subjects with normal occlusion, pleasing profile, and facial harmony.
Materials and Methods | | |
The sample for the present study consists of 120 patients, 60 males and 60 females from the local population staying in Chennai city, within the age group ranging from 17 to 28 years with Tamil as their mother tongue.
The previous paper ^{[31]} explains the inclusion and exclusion criteria used in the study, method of standardization of lateral cephalograms, and the reference points and reference planes used. Linear dimensions of specific anatomical segments were measured parallel to the posterior maxillary plane vertical with the mandibular plane, palatal plane, functional occlusal plane, and cranial base reference plane as limiting planes [Figure 1]. A single operator measured all the parameters.
The vertical segments are anterior maxilla (A1), posterior maxilla (A2), and ramus-cranial floor vertical (A3) [Figure 2]. | Figure 2: Showing the vertical anatomic segments used in the study. A1-Anterior maxilla, A2-Posterior maxilla, A3-Composite ramus-cranial floor vertical used in the study
**Click here to view** |
Measure these linear vertical parameters between the functional occlusal plane and cranial base reference plane parallel to the PM vertical.
Measure the following facial heights to evaluate the anterior and posterior region of the craniofacial complex [Figure 3]. | Figure 3: Showing the facial heights evaluated in the study. ATFH-FMN to mandibular plane, PTFH-SE point to mandibular plane, AUFH-FMN to palatal plane, ALFH-palatal plane to mandibular plane, PUFH-SE point to palatal plane, PLFH-palatal plane to mandibular plane, AUDH-palatal plane to occlusal plane, ALDH-occlusal plane to mandibular plane, PUDH-palatal plane to occlusal plane, PLDH-occlusal plane to mandibular plane (All the posterior vertical heights are measured on PM vertical and all the anterior vertical heights are measured on line parallel to PM vertical through FMN)
**Click here to view** |
- Total facial height-Anterior and posterior
- Anterior facial height (ATFH)-Upper and lower
- Posterior facial height-Upper and lower
- Upper dental height and lower dental height-Anterior and posterior.
Correct all the linear measurements to the nearest 0.5 mm. Alphabetical and numerical code are given to the various parameters measured in the vertical direction as given below [Table 1]:
- A1-A3-Vertical anatomic segments
- F1-F10-Various facial and dental heights.
| Table 1: Showing the various vertical cephalometric parameters and facial heights used in the study
**Click here to view** | Tabulate the measurements in a form analysis sheet. To find out whether a dimensional balance exists between the different segments, establish ratios between the different anatomic segments separately for males and females. Statistical evaluation of the various ratios reveals the presence or absence of sexual dimorphism.
Randomly select 10 cephalograms (five each from males and females) and retrace after 3 weeks to evaluate intraexaminer variability in measurements. Statistical evaluation of these values shows reliability of measurement.
**Statistical analysis**
Dahlberg's method of error determination shows intraoperator error in measurement. Establish ratios between the different vertical parameters. Assess the level of significance for sexual dimorphism with independent 't' test. "*P*" value less than 0.05 is 95% significant, "*P*" value less than 0.01 is 99% significant, and "*P*" value less than 0.001 is 99.9% significant. The results obtained from the statistical evaluation were tabulated in [Table 2] and graphically represented in Graphs 1-9. | Table 2: Showing the ratios of the various vertical cephalometric parameters studied
**Click here to view** |
Results | | |
[Table 1] and Graph 1-9 show the results obtained from statistical evaluation. Statistical evaluation of intraoperator error shows a ''*r*'' value in the range of 0.000689-0.0792. This value indicates that the evaluation by the operator was consistent. "*r*" value nearing 1 indicates inconsistency.
Vertical evaluation of the craniofacial complex consists of evaluation of vertical, anatomical segments, evaluation of facial heights and facial depth.
**Evaluation of vertical anatomical segment**
The ratio between anterior maxilla, posterior maxilla, and composite ramus-cranial floor (A1:A2:A3) was in the ratio of 1.00056:1:1.05726 (1:1:1) for males and 1.00528:1:1.02687 (1:1:1) for females [Table 2] and Graph 1].
**Evaluation of facial heights**
The ratio between anterior upper facial height (AUFH) and anterior total facial height (ATFH) was 0.41205:1 (2:5) for females and 0.40350:1 (2:5) for males [Table 2] and Graph 2].
The ratio between the anterior lower facial height (ALFH) and ATFH was 0.58488:1 (3:5) in females and 0.59307:1 (3:5) in males [Table 2] and Graph 3].
The ratio between the posterior upper facial height (PUFH) and posterior total facial height was found to be 0.51377:1 (1:2) in the females and 0.49878:1 (1:2) in males [Table 2] and Graph 4].
Similarly, the ratio between the posterior lower facial height and posterior total facial height was found to be 0.48379:1 (1:2) in the females and 0.49444:1 (1:2) in males [Table 2] and Graph 5].
The ratio between the posterior total facial height and ATFH was 0.91021:1 (1:1) in the females and 0.93812:1 (1:1) in the males. The "*P*" value was 0.010 and there was a statistically significant difference between males and females at a level of 99% [Table 2] and Graph 6].
The ratio between the anterior upper dental height and anterior lower dental height is 0.67360:1 (2:3) in females and 0.66730:1 (2:3) in males [Table 2] and Graph 7].
The ratio between the posterior upper dental height and posterior lower dental height was 0.77887:1 (7:9) in females and 0.76032:1 (3:4) in males [Table 2] and Graph 8].
**Evaluation of facial depth**
The ratio between the total ATFH and facial depth at point B was 1.92527:1 (2:1) in females and 1.83943:1 (2:1) in males. There was no statistical significance between the males and females [Table 2] and Graph 9].
Discussion | | |
The rationale behind this analysis is that the vertical size of one bony segment can be compared with another specific bony segment of the same individual. In most of the conventional analysis, ATFH is measured between nasion and gnathion or menthon anteriorly and posterior facial height is measured between sella and gonion. These landmarks were excluded from the present study as sella and nasion are subject to anatomical variation. The vertical heights were measured anteriorly and posteriorly at the points of intersection of the cranial base, palatal, and mandibular plane with the anterior maxillary reference line and PM vertical reference line, respectively. It is evident from [Table 2] and Graph 1 that the vertical segments of the craniofacial complex evaluated in the present study had a mean ratio of 1.00528:1:1.02687 (1:1:1) in females and 1.00056:1:1.05726 (1:1:1) in males. This indicates that anterior maxilla, posterior maxilla, and cranial floor-ramus vertical composite are in dimensional balance. Any alteration in this ratio will help the clinician to locate whether the structural imbalance is in the anterior region in the nasomaxilla or in the posterior region in the posterior cranial floor/ramus composite.
Evaluation of facial heights reveals various ratios for the different vertical parameters measured in the study. It can be seen from [Table 2] and Graph 2 that in the anterior region, the upper facial height with respect to total facial height had a proportional ratio of 2:5 in both males and females. A proportion of 3:5 was noted in both males and females between the ALFH and ATFH [Table 2] and Graph 3]. In the posterior segment, both the upper facial height to total facial height and lower facial height to total facial height was expressed as a proportion of 1:2 in both the sexes [Table 2] and Graphs 4 and 5]. These heights will help to localize the cause of vertical skeletal discrepancy between the anterior and posterior region. They also help to localize the deficiency to either the anterior or posterior part of maxillary skeletal base or the anterior or posterior part of the mandibular skeletal base.
The ratio between ATFH and posterior facial height was 0.93812:1 (1:1) in females and 0.91021:1 (1:1) in males. Sexual dimorphism was noted with a statistical significance of 99.9% [Table 2] and Graph 6].
Evaluation of dentoalveolar relation in the vertical dimension revealed a ratio of 2:3 between anterior upper dental height to anterior lower dental height in both sexes [Table 2] and Graph 7]. The ratio of posterior upper dental height to posterior lower dental height was found to be 0.77887:1 (7:9) and 0.76032:1 (3:4) in males and females, respectively [Table 2] and Graph 8].
The ratio of ATFH to the facial depth at point B was found to be 1.92527:1 (2:1) in females and 1.83943 (2:1) in males [Table 2] and Graph 9]. An alteration in this ratio would suggest the retrusive or protrusive position of the mandible.
These ratios established in the present study for the above-mentioned vertical heights are not comparable to the values expressed by other investigators ^{[8],[32],[33],[34],[35],[36]} due to the difference in the anatomic landmarks chosen and the method of expression of the values.
Di Paolo ^{[8],[9],[10],[11]} measured ALFH from the point of projection of A point on the palatal plane to the projection of B point on the mandibular plane. The posterior facial height was measured between projection of J point onto the mandibular plane and projection of Pterogomaxillary fissure to the palatal plane. He reported a ratio of 1:1.21 for ALFH:AUFH and 1:1.52 for PLFH:ALFH.
Scheideman *et al*., ^{[37]} analyzed facial profile and proportionality of 56 adult Caucasians with class I skeletal and dental relationships and good vertical facial proportion with a computerized craniofacial model. Measurements were made relative to Sella-Nasion registered at nasion. He reported that the lower facial height (ANS-Me) was 55.5% of the total facial height (N-Me). These measurements were very close to the values of Goldman 54.6% (ANS-Gn), Weinberg and Kronman ^{[32]} 54.8% (ANS-Gn), Schudy ^{[33]} 56.5%(ANS-Gn), and Broadbent ^{[34]} 54.6%(ANS-Me). Scheideman observed that the main source of difference is because of the manner in which the lower facial height was expressed (ANS-Me vs. ANS-Gn). Further, the ratio between N-ANS/ANS-Me was found to be 0.80 and 0.81 for males and females, respectively. In terms of facial proportion index (FPI), the values were 11% and 10% for males and females. This finding agreed with that of Opdebeeck *et al*. ^{[35]}
Jarabak and Fizzell ^{[36]} reported a percentage relationship between anterior and posterior facial height 62%-65% to indicate horizontal and vertical growth patterns.
Wylie ^{[38]} devised a method of rapid evaluation of vertical facial dysplasia. They devised transparencies for the evaluation of profile roentgenograms without actually measuring the films. In the group with good facial pattern, the upper facial height (nasion-anterior nasal spine) is 45% and lower facial height (anterior nasal spine-menton) is 55% of the total facial height (nasion-menton).
Wylie and Johnson ^{[39]} conducted a cephalometric evaluation of facial dysplasia in the vertical plane. He reported the mean values for upper facial height (50.65 ± 0.38 mm), total facial height (113.02 ± 0.6 mm) and ratio of upper facial height as a percentage of total facial height (43.84 ± 0.32). He was of the opinion that though these proportions do make a well-balanced face, one of the measurements may vary from mean without causing a major imbalance if the appropriate compensating area adjusts itself to the required degree. He was one of the first to consider malocclusion or dysplasia as a random combination of craniofacial parts which are by themselves neither large nor small but when taken together produce an undesirable combination of parts.
Schwarz ^{[7]} noted a ratio of 4:3 or 3:2 for anterior to posterior jaw height for males and females, respectively. He also reported that the ratio of average length of ramus to the length of corpus is 5:7.
Broadbent ^{[34]} evolved an analysis to measure vertical facial and dentoalveolar heights to assess vertical abnormalities based on the data derived from lateral cephalogram of children comprising of Bolton's standards. SN plane was used as reference plane to describe three sets of measurements and for desired proportional relationships. The ATFH was measured from N to Me perpendicular to SN plane. This was divided into AUFH (AUFH-N to ANS) and ALFH (ALFH-ANS to Me), measured at right angles to SN plane. It was in a ratio of 45:55.
Similarly, the posterior total facial height (SN to Go was divided into PUFH and PLFH). PUFH was measured at right angles to SN as far as PNS. The PLFH was measured at right angles to SN as far as gonion. The dentoalveolar vertical segments were divided into anterior and posterior upper and lower dental components. The mean values (in mm) of various vertical measurements are used as a comparison to evaluate vertical disproportions.
Opdebeeck *et al*., ^{[35]} introduced the FPI to express the proportions of AUFH to total facial height and ALFH to total facial height (ATFH). FPI is calculated by subtracting AUFH expressed as a percentage of TFH from ALFH expressed as percentage of TFH. In a balanced face, the FPI value is 10 regardless of absolute measurements. The FPI is less than 10 in short faces and more than 10 in long faces.
Ricketts ^{[40]} conducted studies to establish the relative proportion of facial components and dentition. Measurements of facial photographs, frontal and lateral cephalograms, and plaster models of teeth of subjects with normal occlusion were made. He noted that the various anatomical relationships in the face, skull, and dentition were related by a mathematical ratio of 1:1.618.
Di Paolo *et al*., ^{[8],[9],[10],[11]} formulated the quadrilateral analysis to provide an individualized skeletal, dental, and soft tissue assessment of patients requiring treatment especially orthognathic surgery. He found that a ratio of 1:1 exists between maxillary base length and mandibular length. Further, the average of anterior and posterior lower facial height was also found to be equal to the maxillary and mandibular bony base length.
Lundstrom and Cooke ^{[41]} evaluated lateral cephalograms of 172 adult patients for eight horizontal and two vertical namely upper to lower facial heights and upper to lower jaw heights and one vertical and horizontal proportion (facial height to depth).
Lundstrom *et al*., ^{[42]} in another lateral cephalometric study analyzed three facial indices namely facial depth to facial height, lower facial height to total facial height, and horizontal lower and upper apical base relationships. Correlation between facial depth to height index and mandibular plane was found to be highly significant. Facial depth to height and lower facial height relationships were also found to be strongly correlated at each age between 10 and 16 years. The index between maxilla and mandible increased continually between 10 and 16 years in boys and 10-14 years in girls by about 0.3 units per year.
Most of the values in previous studies are presented in percentages, whereas in the present study it is expressed as ratio. The earlier analyses ^{[30],[43],[44],[45],[46],[47],[48]} done based on the analysis of intrinsic facial form and balance does not measure vertical facial heights although dimensional balance between the vertical anatomic segments have shown results similar to the present study.
Evaluation of vertical facial proportion is of utmost importance in the comprehensive analysis of a patient. This is very true if the patient has a skeletal discrepancy in the vertical plane. The present analysis measures the relationship between the facial heights anteriorly and posteriorly and the relation between facial height and depth and enables the clinician to perform a thorough evaluation of the face in the vertical direction.
Conclusion | | |
Thus, the anterior maxilla, posterior maxilla, and cranial floor-ramus vertical composite are in dimensional balance in subjects with normal occlusion and facial harmony.
The ratios established for the various vertical facial height measurements can be used as a guide to localize any vertical skeletal contribution to malocclusion.
This analysis helps to identify skeletal deviations in size and position in the vertical dimension and allows the clinician to outline the appropriate orthodontic procedures as deemed necessary.
This analysis along with evaluation of sagittal relation and cranial base inclination can be used to determine a comprehensive treatment plan for different type of malocclusions.
References | | |
1. | Steiner CC. Cephalometrics for you and me. Am J Orthod 1953;39:729-55. |
2. | Downs WB. Variation in facial relationship: Their significance in treatment and prognosis. Am J Orthod 1948;34:812-84. [PUBMED] |
3. | Holdaway RA. A soft tissue cephalometric analysis and its use in orthodontic treatment planning: Part I. Am J Orthod 1983;84:1-28. [PUBMED] |
4. | McNamara JA. A method of cephalometric evaluation. Am J Orthod 1984;86:449-69. |
5. | Ricketts RM, Bench RW, Gugino CF, Hilgers JJ, Schulhof R. Bioprogressive therapy. Denver: Rocky Mountain Orthodontics; 1979. |
6. | Koski K. Analysis of profile roentgenogram by means of a new circle method. Dent. Rec. 1953;73:704-13. |
7. | Schwarz AM. Roentgenostatics. A practical evaluation of the x-ray headplate. Am J Orthod 1961;47:561-85. |
8. | Di Paolo RJ. The quadrilalteral analysis. Cephalometric analysis of the lower face. JPO J Pract Orthod 1969;3:523-30. [PUBMED] |
9. | Di Paolo RJ. Cephalometric diagnosis using the quadrilateral analysis. J Clin Orthod 1970;4:30-5. [PUBMED] |
10. | Di Paolo RJ, Philip C, Maganzini AL, Hirce JD. The quadrilateral analysis: An individualized skeletal assessment. Am J Orthod 1983;83:19-32. [PUBMED] |
11. | Di Paolo RJ, Philip C, Maganzini AL, Hirce JD. The quadrilateral analysis: A differential diagnosis for surgical orthodontics. Am J Orthod 1984;86:470-82. [PUBMED] |
12. | Moorrees CF. Normal variation and its bearing on the use of cephalometric radiographs in orthodontic diagnosis. Am J Orthod 1953;39:942-50. |
13. | Moorrees CF, van Venrooij ME, Lebret LM, Glatky CB, Kent RL Jr, Reed RB. New norms for mesh diagram analysis. Am J Orthod 1976;69:57-71. |
14. | Moorrees CF, Efstratiadis SS, Kent RL Jr. The mesh diagram for the analysis of facial growth. Proc Finn Dent Soc 1991;87:33-41. [PUBMED] |
15. | Moorrees CF, Kean MR. Natural head position, a basic consideration in the interpretation of cephalometric radiographs. Am J Phys Anthrop 1958;16:213-34. |
16. | Burstone CJ, James RB, Legan H, Murphy GA, Norton LA. Cephalometrics for orthognathic surgery. J Oral Surg 1978;36:269-77. [PUBMED] |
17. | Ricketts RM. Orthodontic Diagnosis and Planning. Denver: Rocky Mountain Orthodontics; 1982. p. 283-8. |
18. | Ricketts RM, Bench RW, Gugino CF, Hilgers JJ, Schulhof R. Bioprogressive therapy. Denver: Rocky Mountain Orthodontics; 1979. p. 55-70. |
19. | Ricketts RM. A four step method to distinguish orthodontic changes for normal growth. J Clin Orthod 1975;9:208-28. [PUBMED] |
20. | Pancherz H. The nature of class II relapse after Herbst appliance treatment: A cephalomertic long term investigation. Am J Orthod Dentofacial Orthop 1991;100:220-33. [PUBMED] |
21. | Bookstein FL. The geometry of craniofacial growth invariants. Am J Orthod 1983;84:384-98. |
22. | Sameshima GT, Melnick M. Finite element-based cephalometric analysis. Angle Orthod 1994;64:343-50. [PUBMED] |
23. | Lu KH. Harmonic analysis of the human face. Biometrics 1965;21:491-505. [PUBMED] |
24. | Lestrel PE, Kimbel WH, Prior FW, Fleischmann ML. Size and shape of the hominoid distal femur: Fourier analysis. Am J Phys Anthropol 1977;46:281-90. [PUBMED] |
25. | Hellman M. Morphology of face, jaws and dentition in class III malocclusion. J Am Dent Assoc 1931;18:2150-73. |
26. | Alexander Jacobson and Richard L. Jacobson Radiographic Cephalometry: from basics to 3D. 2 ^{nd} edition. IL, USA: Quintessence Publishing Company, Inc.; 2006. |
27. | De Coster L. The network method of orthodontic diagnosis. Angle Orthod 1939;9:3-29. |
28. | Williams BH. Craniofacial proportionality in a horizontal and vertical plane, a study in norma lateralis. Angle Orthod 1953;23:26-33. |
29. | Broadbent BH. A new X ray technique and its application to orthodontia. Angle Orthod 1931;1:45-66. |
30. | Enlow DH, Moyers RE, Hunter WS, McNamara JA Jr. A procedure for the analysis of intrinsic form and growth. An equivalent-balance concept. Am J Orthod 1969;56:6-23. [PUBMED] |
31. | Sumathi FA, Shyamala C, Shanthasundari KK. Determination of craniofacial relation among the subethnic Indian population: A modified approach-Part I (sagittal relation). Indian J Dent Res 2012;23:305-12. |
32. | Weinberg H, Kronman JH. Orthodontic influence upon anterior face height. Angle Orthod 1966;36:80-8. [PUBMED] |
33. | Schudy FF. Vertical growth versus antero-posterior growth as related to function and treatment. Angle Orthod 1964;34:75-93. |
34. | Broadbent JM. Essence of the beautiful face. CDS Rev 1989;82:31-42. [PUBMED] |
35. | Opdebeeck H, Bell WH, Eisenfeld J, Mishelevich D. Comparative study between SFS and LFS rotation as a possible morphogenetic mechanism. Am J Orthod 1978;74:509-21. [PUBMED] |
36. | Jarabak JR, Fizzell JA. Technique and treatment with lightwire edgewise appliance. St. Louis: CV Mosby; 1972. |
37. | Scheideman GB, Bell WH, Legan HL, Finn RA, Reisch JS. Cephalometric analysis of dentofacial normals. Am J Orthod 1980;78:404-20. [PUBMED] |
38. | Wylie WL. The assessment of anteroposterior dysplasia. Angle Orthod 1947;17:97-109. |
39. | Wylie WL, Johnson EL. Rapid evaluation of facial dysplasia in the vertical plane. Angle Orthod 1952;22:165-81. |
40. | Ricketts RM. Divine proportion in facial esthetics. Clin Plast Surg 1982;9:401-22. [PUBMED] |
41. | Lundstrom A, Cooke MS. Proportional analysis of the facial profile in natural head position in Caucasian and Chinese children. Br J Orthod 1991;18:43-9. |
42. | Lundstrom F, Leighton B, Richardson, Lundstrom A. A proportional analysis of some facial height and depth variables in 10 to 16 year old children. Br J Orthod 1998;42:99-115. |
43. | Enlow DH, Takayuki K, Arthur L. The morphological and morphogenetic basis for craniofacial form and pattern. Angle Orthod 1971;41:161-88. |
44. | Enlow DH, Takayuki K, Arthur B. Intrinsic craniofacial compensations. Angle Orthod 1971;41:271-85. |
45. | Enlow DH, Pfister C, Richardson E, Kuroda T. An analysis of Black and Caucasian craniofacial patterns. Angle Orthod 1982;52:279-87. [PUBMED] |
46. | Bhat M, Enlow DH. Facial variations related to headform type. Angle Orthod 1985;55:269-80. [PUBMED] |
47. | Cevidanes LH, Franco AA, Scanavini MA, Vigorito JW, Enlow DH, Proffit WR. Clinical outcomes of Fränkel appliance therapy assessed with a counterpart analysis. Am J Orthod Dentofacial Orthop 2003;123:379-87. [PUBMED] |
48. | Trouten JC, Enlow DH, Rabine M, Phelps AE, Swedlow D. Morphologic characteristics in deep bite and open bite. Angle Orthod 1983;53:192-211. [PUBMED] |
**
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**Correspondence Address**: A Sumathi Felicita Department of Orthodontics, Saveetha Dental College, Chennai India
**Source of Support:** None, **Conflict of Interest:** None
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**DOI:** 10.4103/0970-9290.118396
[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2] |