Proportional Analysis of Longitudinal Craniofacial Growth Using Modified Mesh Diagrams

For centuries, research workers in such diverse fields as art, architecture, and industry have used various grids to assess man's facial proportions. A grid method also has been used cephalometrically, namely, the mesh diagram analysis that was introduced by Moorrees in 1948.1 The conventional mesh diagram is composed of 24 rectangles overlain onto a cephalometric tracing. The vertical lines are parallel to the extracranial true vertical, which represents the natural head position,1 and the horizontal line is perpendicular to this. All the rectangles are exactly the same, arranged in six rows and four columns. The four rectangles in the middle of the face were termed the core rectangles. The vertical dimension of the core rectangle is defined by the subject's upper facial height (nasion to ANS) and the horizontal dimension by facial depth (sella to nasion), so the mesh rectangle dimensions are specific to a person at a specific age. Few proportional methods have been used to study craniofacial growth longitudinally, and even fewer incorporate “real-life” natural head position.

Subjects (n = 75) were selected from among some 900 high school students based on possession of normal occlusions (ie, Class I molar relationship with less than 3 mm of crowding, less than 3 mm overjet, and an overbite less than one-third coverage of lower incisor ). No previous orthodontic treatment and no respiratory problem have been reported. These 75 adolescents agreed to participate in the present research project, with cephalograms taken annually from 13 to 18 years of age inclusively. These data are part of a collection from the Craniofacial Growth and Development Centre at Peking University. The study protocol was reviewed and approved by the Institutional Review Board of the Stomatological School of Peking University. Just 28 subjects (15 females, 13 males) completed the study. One of the authors rotated the cephalograms to their estimated natural head positions.2,3 These oriented radiographs were then scanned and saved as digital computer files.

A modified mesh diagram was generated by a computer using preset software. The mesh diagram1,4,5 was generated using half of the nasion-ANS distance as the vertical scale and half of the sella-nasion distance as the horizontal scale. Registration was at nasion, with the vertical lines parallel to the extracranial true vertical.

The computer program then constructed 24 same-size rectangles as with the conventional technique4,5 in which only 25 landmarks had been developed. In the present study, 90 anatomic landmarks (Table 1, Figure 1A) and the other 172 interpolated points were digitized from each cephalogram (Figure 1A). Then, the total 262 points were connected with straight-line segments that produce a relatively accurate lateral cephalometric outline. This oriented cephalometric rendering, along with the mesh's 24 rectangles, is termed the elaborate mesh diagram (Figure 1B). This computer-assisted method develops a much more comprehensive and accurate picture of the person's craniofacial structures.

The computer-assisted method also lends itself to quantification. Cartesian coordinates of the 90 landmarks for each cephalogram were obtained. It should be pointed out that the coordinates here are not the absolute numbers but proportionate coordinates (ratios) scaling the absolute dimensions of each core rectangle.1 The elaborate mesh diagrams for 28 subjects were regenerated again 2 to 4 weeks later. The coordinates were also collected again. No significant mean differences between the two series of proportionate coordinates were found by using paired t-tests.

The size of measurement error was no more than 0.04, according to Dahlberg's formula (S2 = Σ D²/2N), with D being the difference between repeated measurements and N the number of double measurements. Then, the average proportionate coordinates for two ages (age 13 and age 18) were calculated. The two-tailed t-tests were used to compare them within each sex (Table 2A,B). Differences with probabilities of less than 5% (P < .05) were considered statistically significant.

The average elaborate mesh diagrams, by sex, were developed for the subjects at 13 and 18 years of age (Figure 2A–D). Then for each sex, a scaled average 18 year's diagram using the landmarks' average coordinates but scaling on the 13 year's core rectangle was constructed and was superimposed on the 13 year's average mesh diagram with registration on nasion (Figure 3A,B). This allows us to focus on only the proportionate changes of craniofacial structure by ignoring the absolute amount of growth of the mesh core rectangles.

The average elaborate mesh diagrams, by sex, at 13 and at 18 years of age are shown in Figure 2.

In girls, almost all of the coordinate changes from 13 to 18 years of age are proportional; females' faces at 18 years can be viewed essentially as scaled-up versions of their faces at 13 years. The few exceptions are the downward increase in vertical dimension of the upper first molar distal cusp, lower first molar root furcation, and soft tissue pronasale (Table 2A). In males, more dramatic changes occurred due to the disproportional increases (Table 2B), especially in the vertical direction. Among the hard tissues, the vertical coordinates of epinasale, the upper incisors, the upper first molars, lower first molars, mandibular corpus, and symphysis exhibited disproportional increases downward. Among the soft tissues, analogous accelerated vertical vectors were seen in the tip and the base of the nose and the upper lip. A few horizontal coordinates also enlarged disproportionately in males, notably the coronoid process and the anterior border of mandible ramus.

Superimposition is a graphic way of disclosing the craniofacial growth between two ages (Figure 3) in a clear, comprehensive, and detailed fashion. In females, again, most of the structures of the craniofacial complex increased uniformly across the 6 years of growth. In contrast, there was enhanced downward extension of the inferior border of mandibular corpus, symphysis, and upper and lower lips.

Disproportional changes occurred across more craniofacial structures in the males. The anterior cranial base grew upward and the inferior border of the mandibular body, symphysis, maxillary and mandibular teeth, nasal base, and upper and lower lips extended downward disproportionately. Also, the mandible exhibited downward and backward rotation. Only the posterior cranial base, condylar process, coronoid process, maxillae, orbital bones, nasal bone, and nasal bridge grew proportionately.

There are, broadly, two main methods for the study of longitudinal cephalometric data. The first consists of studying conventional angles and distances. For this, an assumedly stable reference line is relied on, which is imprecise because the locations of the bony landmarks that define the references are themselves remodeling with growth.6,7 In addition, distances and angles reflect the relative changes between specific landmarks. Also, numerous angles, lines, and ratios often are needed to characterize the complex changes of the facial structures.

A second method is serial superimpositions of cephalograms registered on stable landmarks. For example, the classical works of Björk and coworkers,8–10 using metallic implants in the two jaws, yielded unbiased views of craniofacial growth. Similarly, the best fit superimposition method11 and the structural superimpositions suggested by Björk and Skieller12–14 are graphical approaches that provide visual views of facial development. However, the perceived relationships still depend on separate intracranial structures that remodel with growth.

A mesh diagram is based on natural head position, which is an extracranial reference line. The stability and reproducibility of an extracranial reference line has been demonstrated over both short and long intervals.15–19 It can be seen in the present elaborate mesh diagram superimpositions that the profiles are quite consistent in each sex across 6 years of growth (Figure 3). Natural head position also depicts the true-life appearance of the subjects, as implied by the term natural, with the head orientated as when one is focusing on a distant point at eye level.4,5,15,20 

Another merit of the mesh diagram is that it expresses craniofacial growth changes graphically. In the present study, the elaborate mesh diagram provides a more succinct and comprehensive picture of the changing craniofacial structures than the traditional one.

It is informative to analyze the subjects by sex because males and females have such different vectors of adolescent growth.21 This graphical method shows (Figure 2) that males and females have distinctive average mesh diagrams at the same chronological ages.

The mesh diagram provides for proportional analysis. In daily life, disproportional facial changes often gain more attention. The mesh diagram scales the core rectangle that represents the size of the middle face in terms of facial depth and upper face height. It uses the growth ratio of the middle face as the basis for gauging the growth ratio of the other craniofacial structures.

The mesh core rectangles vary among individuals because the actual dimensions of the core vary. The proportional coordinates of each landmark also vary. However, there is the possibility that the average proportional coordinates of the landmarks may be the same at the two ages (age 13 and age 18 years) in each sex. And if they are the same, it means the structures are growing at essentially the same ratio as those of the average core rectangle, which is termed proportional growth. Otherwise, if they are not, it means the structures are growing faster or slower than the average core rectangle, which is termed as disproportional growth. We named the faster one an enhanced growth and the slower one a decreased growth.

More of the soft and hard tissues experienced proportional growth in females between 13 and 18 years of age. However, disproportional enhanced growth did occur in some parts, for example, the downward shift of the distal crown of the upper and lower first molars and the nose tip. Some borderline disproportional changes that have been ignored by statistical analysis are disclosed in mesh diagram superimposition, such as downward extension of the mandibular body's inferior border. It is also worth noting that purely quantitative (statistical) analysis is necessarily limited in scope—not all conceiving distances and angles among all combination of landmarks can be assessed—and whether a change is significant is modulated by sample size and amount of change. The graphical method is complementary and informative in that all of the changes are rendered in a single picture.

Males exhibited several disproportional growth changes. For example, there is a disproportionately enhanced growth of the anterior cranial base. This conflicts with the common assumption that the anterior cranial base is stable after 7 years of age.22 The reason for this disproportionately enhanced growth is that the mesh diagram is constructed using the core rectangle that is referenced on extracranial true vertical. Actually, from this, we can induce that there has been enhanced growth in the area including the anterior cranial base and middle face compared to the growth ratio of the deeper facial structures. In the mandible, the symphysis, inferior mandibular body, and gonial angle all grew downward faster than the other structures, and the mandible experienced a downward and backward rotation. This is in contrast to the traditional mandibular superimposition that emphasizes the upward-backward translation of condylion and gonion along with the downward-forward movement of menton and pogonion.8,10,23,24 

We see, then, that the two methods treat the same relationships in different ways. The traditional superimposition, orientated on an endocranial reference and registered on endocranial structures, is more suitable for a description of growth of facial components and absolute size changes. In contrast, the elaborate mesh diagram provides holistic information and a realistic sense of direction for growth of the entire craniofacial complex and helps identify disproportional size changes.

Several studies have dealt with craniofacial growth with the mesh diagram.24–27 But those data are mostly cross-sectional. Longitudinal investigation seems to provide sufficient sensibility for significant findings. But there are sometimes several difficulties in data acquisition. Apart from the present study, we are aware of just one study that has used mesh diagrams to study facial growth with pure longitudinal data.27 The subjects, not constrained to normal occlusions, were twins studies from 8 to 16 years of age. The diagrams ware based on 25 conventional landmarks, and it was found that the middle face in each sex underwent little change of the soft and hard tissue landmarks and a slight advancement of the chin and a dorsal-caudal growth of gonion.

Another possible application of results of this study is the prediction of craniofacial growth. Prediction can relate to the direction, magnitude, timing, rate of change, and/or the effects of treatment.28 Björk8 noted that growth prediction can be accomplished using three general methods: longitudinal, metric, and structural. This mesh diagram analysis is an example of the structural method. We can assume that a 13-year-old normal occlusion child is here. Can we predict the child's craniofacial growth to age 18? We could first construct the mesh diagram and compare it with the corresponding average to find the individual discrepancies. Then we could picture her predicted individual mesh diagram at the age of 18 by considering the initial discrepancy, the average diagram at 18 years of age, and growth. Precision is difficult because of each person's unique growth pattern influenced by poorly understood genetic and environmental factors. However, proportional analysis of a mesh diagram does show us a possibility.

• A proportional cephalometric method—modified elaborate mesh diagram analysis, based on mesh core rectangle and referenced on estimated natural head position—provides us a novel graphical as well as quantitative method of assessing craniofacial growth.

• From 13 to 18 years of age, two sexes with normal occlusion displayed different growth patterns referenced on estimated natural head position. In females, most craniofacial regions exhibited growth proportional to the mesh core rectangle. In males, there was an upward enhanced shift of the anterior cranial base and a downward enhanced shift of the mandibular symphysis and inferior border of the corpus.