Differences in heritability of craniofacial skeletal and dental characteristics between hypo- and hyper-divergent patterns using Falconer's method and principal component analysis

Both genetic and environmental factors can contribute to variations in the size and shape of the craniofacial skeletal and dental structures. If these structures are mainly influenced by genetic factors, orthodontic and/or orthopedic treatment, performed even at an early age, would not significantly change them. On the contrary, if these structures are under control of environmental factors, it would be advantageous to treat the patient from an early age. Therefore, it is necessary to verify the degree of genetic and environmental contributions to the characteristics of these structures for appropriate diagnosis and treatment planning.

Cephalometric studies of twins and their families can evaluate the relative contributions of genetic and environment factors on the size and shape of the craniofacial skeletal and dental structures.¹  However, whether vertical traits are more genetically determined than horizontal traits remains controversial. Several previous studies insisted that vertical measurements had greater heritability than horizontal measurements.^2–6  However, other researchers reported that genetic factors might contribute more to horizontal traits compared to vertical traits.^7,8  Heritability estimates should be interpreted with caution because there are possibilities for several types of bias.⁹ 

Since heritability of the craniofacial characteristics can be influenced by age, sex, ethnicity, and study design, it is necessary to adopt a study design with strict sample selection criteria. For example, the samples should be adult subjects whose growth is completed and who have the same ethnicity and sex. In addition, the samples should be divided according to the vertical and/or horizontal pattern.

Although there are some studies investigating the influence of genetic and environmental factors on the craniofacial phenotype in Korean adult twins and their siblings,^8,10  there are no twin studies comparing the heritability of the craniofacial skeletal and dental characteristics between skeletal hypodivergent and hyperdivergent subjects. Therefore, the purpose of this study was to investigate the differences in heritability of craniofacial skeletal and dental characteristics between hypodivergent and hyperdivergent patterns in monozygotic (MZ) adult twins, dizygotic (DZ) adult twins, and their adult siblings. The null hypothesis was that there was no significant difference in heritability of the craniofacial skeletal and dental characteristics between hypodivergent and hyperdivergent subjects.

The initial samples consisted of 150 Korean adult twins and their families (36 pairs of MZ twins, 13 pairs of DZ twins, and 26 pairs of their adult siblings), whose lateral cephalometric radiographs were taken in natural head position at Samsung Medical Center, Seoul, South Korea. This twin study protocol was reviewed and approved by the Institutional Review Board of the School of Public Health, Seoul National University, Seoul, South Korea (IRB 2005-08-113-027). Informed consent was obtained from all subjects.

The inclusion criteria were as follows:^8,10  (1) those who did not have an edentulous area of the anterior dental region that could affect the facial profile; (2) those who did not wear a removable prosthesis that could affect the vertical dimension of the face; (3) those who had not undergone orthodontic treatment or orthognathic surgery; (4) those whose growth was complete (over 19 years of age); and (5) those whose gender was the same in the DZ pairs and sibling pairs.

According to the vertical pattern, a total of 53 Korean adult twins and their siblings were allocated into the two groups (criteria: mean value of SN-MP angle of Korean adult twins, 35°; Table 1):⁸ Hypodivergent group (Group 1, SN-MP < 35°; mean age, 39.0 years old; 17 MZ pairs; 11 DZ and sibling [DS] pairs [three DZ pairs and eight sibling pairs]) and hyperdivergent group (Group 2, SN-MP > 35°; mean age, 41.3 years old; 16 MZ pairs; 9 DS pairs [four DZ pairs and five sibling pairs]).

The landmarks and reference lines used for cephalometric measurement are illustrated in Figure 1. A total of 56 linear, angular, and ratio cephalometric variables were measured using lateral cephalographs (Figure 2). The craniofacial structures were divided into five areas as follows: anteroposterior (AP), vertical, dental, mandible, and cranial base characteristics.⁸  All measurements were performed by a single operator (EK) using the V-Ceph 6.0 program (Cybermed, Seoul, South Korea).

All variables from 20 randomly selected subjects were remeasured by the same operator (EK) at 2-week intervals. The intra-operator measurement error was assessed using the intraclass correlation coefficient (ICC). Since there were no significant differences between the first and second measurements, the first set of measurements was used.

Although the genetic effect (A) of the MZ pairs is equal, the DS pairs of the same gender share half of their genetics.¹¹  On the assumption that the MZ and DS pairs have the same environmental effect (E),^10,12  the Pearson's correlation coefficient (r_mz, r_ds) was calculated as r_mz = A + E and r_ds = ½ 1/2 A+E, respectively (Table 2).

Falconer's method has been used to calculate genetic heritability (h²) based on the difference between the Pearson's correlation coefficients of Groups 1 and 2.^8,11–14  Heritability was calculated as h² = 2 (r_mz- r_ds).^8,10,13,14  Cultural inheritance (c²), which shows the environmental effect, was calculated as c² = 2r_ds-r_mz.^8,10,13  In the present study, an h²  value below 0.2 was considered low heritability and that above 0.8 was, high heritability.^8,10 

Principal component analysis (PCA) with Kaiser normalization varimax rotation was used to extract the dominant components for 56 cephalometric variables in Groups 1 and 2.^{6–8,10,15,16}  The components with an eigenvalue higher than 1 were selected. The mean ICC values of the cephalometric variables grouped by component were calculated. The heritability (h²) of components was also calculated in Groups 1 and 2.

All statistical analyses were performed with a significance level of 0.05 using SPSS (version 21, IBM Corp., Armonk, NY, USA).

In the AP variables, only three variables depicting the AP position of the mandible exhibited high h²  values (SNB, 1.13; SN-Pog, 0.90; facial angle, 0.91). However, among the vertical variables, numerous angular variables (ODI, 1.49; SN-PP, 1.53; FH-PP, 1.29; PP-MP, 1.11) and ratio variables (N-ANS/ANS-Me, 1.09; ANS-Me/N-Me, 1.22) exhibited high h²  values. In the dental variables, high h²  values were observed in maxillary incisor inclination (U1-SN, 1.16; U1-FH, 1.58; U1-PP, 1.39; U1-OP, 1.04; U1-NA linear, 0.93) and occlusal plane-to-mandibular plane inclination (OP-MP, 1.29). Among the mandible and cranial base variables, high h²  values were shown in the shape of the mandible and cranial base (gonial angle, 1.48; lower gonial angle, 1.40; saddle angle, 0.85).

Among the AP variables, the AP position of the maxilla and intermaxillary relationship exhibited high h²  values (SNA, 1.26; convexity of A point, 1.00; ANB, 0.82; facial convexity, 1.05). The ratio between mandibular body length and anterior cranial base length also exhibited a high h²  value (Go-Me/S-N, 0.97). However, in the vertical variables, only four angular variables had high h²  values (ODI, 0.95; SN-FH, 0.88; SN-PP, 1.53; PP-MP, 1.41). Interestingly, there was no ratio variable with a high h²  value. In the dental variables, high h²  values were observed in mandibular incisor inclination (IMPA, 0.83; L1-NB angular, 1.18; L1-NB linear 1.14; L1-OP, 1.83), occlusal plane-to-cranial base inclination (FH-OP, 1.01), and OP-MP (0.88). Among the cranial base variables, cranial base length (Ar-N, 0.95; S-N, 1.34) exhibited a high h²  value. However, the size and shape of the mandible variables did not show high h²  values.

In Group 1, the overall mean h²  value was highest at the vertical structure (0.84), followed by the dental structure (0.67), cranial base structure (0.41), mandible structure (0.39), and AP structure (0.26).

However, Group 2 did not include any structure with overall mean h²  value greater than 0.8. The AP structure exhibited the highest value (0.66), followed by the cranial base structure (0.64), vertical structure (0.41), mandibular structure (0.26), and dental structure (0.21).

In both Groups 1 and 2, the PCA derived 10 components (Tables 5 and 6) with 91.2% and 92.7% of cumulative explanation, respectively (Tables 7 and 8).

In Group 1, three PCA components showed high h²  values as follows: (1) PCA1 (0.891), which consisted of five vertical variables (SN-MP, Bjork sum, facial height ratio, FMA, PP-MP), one mandibular variable (lower gonial angle), and one dental variable (OP-MP); (2) PCA2 (1.140), which consisted of six dental variables (U1-NA angular, U1-FH, U1-PP, U1 to NA linear, U1-SN, U1-OP); and (3) PCA6 (1.325), which consisted of five vertical variables (SN-PP, N-ANS/ANS-Me, ANS-Me//N-Me, FH-PP, ODI) (Tables 5 and 7).

In Group 2, three PCA components showed high h²  values as follows: (1) PCA 3 (1.003), which consisted of three AP variables (Convexity of A point, ANB, Facial convexity) and three dental variables (L1-NB angular, L1-NB linear, IMPA); (2) PCA 9 (1.420), which consisted of two dental variables (L1-OP, FH-OP); and (3) PCA10 (1.339), which consisted of anterior cranial base length (S-N) (Tables 6 and 8).

Among the vertical facial variables, the angular measurements between the maxilla, mandible, and cranial base exhibited higher heritability values than the linear measurements in both groups (ODI, SN-PP, FH-PP, PP-MP in Group 1; ODI, SN-FH, SN-PP, PP-MP in Group 2). However, the vertical ratio of the anterior facial height had a strong genetic influence in Group 1 only (N-ANS/ANS-Me, ANS-Me/N-Me). These findings indicated that the relative ratio between the upper and lower anterior facial heights might be highly predictable in the hypodivergent pattern, which was similar to the findings of Kim et al.⁸  In contrast, Šidlauskas et al.⁷  reported low-to-moderate genetic influence in the linear and angular vertical measurements. However, these studies^7,8  did not divide their samples according to the vertical pattern.

Interestingly, posterior facial height (S-Go) and ramus height (CD-Go, Ar-Go) did not show a high heritability in either group. These results suggested that the posterior face height demonstrated a lower genetic determination compared to the anterior face height.^7,17 

Heritability of the AP position of the maxilla and intermaxillary relationship (SNA, convexity of A point, ANB, facial convexity, Go-Me/S-N) showed a strong genetic influence in Group 2. Amini et al.¹⁷  and Kim el al.⁸  demonstrated a high heritability of the AP position of the maxilla, but a low-to-moderate heritability of the intermaxillary relationships. This difference might be due to differences in the growth stage or ethnic background of the samples.

The cranial base shape (saddle angle) showed a high heritability in Group 1, while the cranial base length (Ar-N, S-N) showed a high heritability in Group 2. Amini et al.¹⁷  reported a high genetic determination of anterior cranial base length and saddle angle. However, other previous studies^6,8  reported low-to-moderate heritability values for saddle angle and cranial base length. Differences in the results might be due to the inclusion of younger twin samples before completion of growth in previous studies.^6,17 

In the mandible characteristics, although the mandibular body length (Go-Me, Go-Pog), ramus height (CD-Go, Ar-Go), and effective mandibular length (Ar-Gn, CD-Gn) showed low-to-moderate heritability values in both Groups 1 and 2, the shape and position of the mandible (gonial angle, SNB, SN-Pog, facial angle) exhibited high h²  values only in Group 1. These results were consistent with Amini et al.¹⁷  and Sidlauskas et al.⁷ , which reported a higher heritability of the shape and position of the mandible than its size. However, Carels et al.⁶  reported greater genetic determination for the linear measurements of the mandible compared to the angular measurements of the mandible (gonial angle, SNB). Since the influence of the environmental factors on linear mandibular measurements increased with age,¹⁸  differences in the results might be derived from the growth stage of the samples.

The results from this study showed high heritability values of maxillary incisor inclination (U1-SN, U1-FH, U1-PP, U1-OP, U1-NA linear) in Group 1, and of mandibular incisor inclination (IMPA, L1-NB angular, L1-NB linear, L1-OP) in Group 2. Since Carels et al.⁶  and Amini et al.¹⁷  reported high heritability of the dentoalveolar variables including mandibular incisor inclination and vertical position of the molars, the degree of dentoalveolar compensation including dentoalveolar height and incisor inclination might be significantly correlated with genetically determined skeletal parameters.

The hypodivergent pattern had a strong genetic influence on the vertical structure, while the hyperdivergent pattern did not have strong genetic control over the vertical structures. These findings indicated that genetic control on the vertical structure was more influential in Group 1 than in Group 2.

Component number and cumulative explanation in Groups 1 and 2 were 10 components with 91.2% and 92.7%, respectively. These results were relatively higher than previous twin studies using PCA, which reported five to nine components with 81.0% to 83.0% cumulative explanation.^6,7,19  Differences among these studies might be derived from different study designs and different statistical criteria (ie, eigenvalue) for determining principal components. Furthermore, those studies did not compare the heritability values of each component between hypodivergent and hyperdivergent groups.^6,7,19 

In summary, the results of the present study showed clear differences in the heritability of the craniofacial skeletal and dental characteristics between the hypodivergent and hyperdivergent patterns as follows (Tables 3 to 8): (1) In the vertical jaw position, the hypodivergent pattern had strong genetic influences on both the angular and ratio measurements; whereas the hyperdivergent pattern, only on the angular measurements; (2) In the AP jaw position, the hypodivergent pattern exhibited strong genetic influences only on the AP position of the mandible; while the hyperdivergent pattern, on the AP position of the maxilla and intermaxillary relationships; (3) In the size and shape of the cranial base and mandible, the hypodivergent pattern had a strong genetic influence on the shape of both the cranial base and mandible; whereas the hyperdivergent pattern, only on the cranial base length; (4) In terms of incisor inclination, the hypodivergent patterns exhibited strong genetic influences on maxillary incisor inclination; whereas hyperdivergent pattern, on mandibular incisor inclination; and (5) the occlusal plane inclination exhibited high heritability in both groups.

The results of this study might reveal some clinical implications in growth modification treatment for adolescent patients. In the hypodivergent pattern, growth modification treatment is favorable in changes in mandibular length and/or AP position of the maxilla. In the hyperdivergent pattern, changing the shape and/or size of the mandible is easier compared to changing the AP position of the maxilla. However, individual responses to growth modification treatment could vary even though the structures exhibited low heritability values.

Although heritability estimates of this study might be irrelevant to a different population, the study design and results of this study might be a useful guideline to compare the heritability in different populations. In future studies, three-dimensional analysis with a large sample size is necessary to investigate the heritability of transverse characteristics.

• The null hypothesis was rejected.

• Since the hypodivergent and hyperdivergent subjects exhibited different degrees of genetic influences on the AP/vertical position of the maxilla and mandible, shape of the mandible, incisor inclination, and shape and length of the cranial base, it is necessary to estimate or predict growth according to the vertical pattern for providing differential diagnosis and orthodontic/orthopedic treatment planning.