Vertical facial height and its correlation with facial width and depth

The fact that vertical dimension control is one of the most difficult tasks in orthodontic treatment has been recognized for a long time [15]. To thoroughly understand the vertical facial height (VFH) is therefore crucially important in orthodontic treatment. Vertical dimension, generally speaking, includes anterior (AFH) and posterior facial height (PFH). According to Björk [5] forward mandibular rotation occurs when PFH overdevelops relative to AFH; however, in many literature sources more attention was focused on the AFH and lower AFH has been confirmed as having a strong influence on the formation of vertical facial disproportions [27, 28, 34]. On the other hand some accepted terminologies used in describing vertical morphology, such as long and short face [4] or dolichofacial and brachyfacial [33] are mainly based on AFH. In the extreme case the short or long face syndrome is believed to be always characterized by low or high mandibular plane angle, respectively [32, 25]. Nanda [24] gave a similar viewpoint in a longitudinal study by differentiating the sample using the presence of anterior open bite or deep bite. However, in extreme vertical cases, muscle or organ dysfunction, such as nasal obstruction as suggested by Vig [39] is always involved. Van Spronsen et al. [38] also proposed that musculoskeletal interactions might differ between populations with normal faces and a selected group of individuals with long faces. Therefore, the orthodontic strategy on vertical control could be different between normal and extreme vertical cases. Thus it is important to study the facial height by excluding the extreme case of anterior open bite and deep bite so that the effect played by the muscle or organ dysfunction could be considerably diminished. Under the circumstances of anterior relatively normal overbite, the role played by both AFH and PFH in the formation of vertical facial type could become clear. At the same time it was also planned to verify if it is always true that the steeper the mandibular plane anteriorly inclines, the greater the AFH becomes or vice versa.

There is no doubt that longitudinal studies enable facial growth development to be understood more thoroughly than cross-sectional studies. However, fit is also necessary to know how the adult facial height, including AFH and PFH, correlates with mandibular plane angle, facial depth and width as well through the cross-sectional method.

To identify such correlations is crucial for fully understanding human craniofacial morphology and the functional interrelationship among the three dimensional (3D) structures so that orthodontic treatment strategies can be more effectively designed. Only a few studies, however, have focused on the assessment of the correlations of the 3D craniofacial structures measurements, especially on the linear measurements. Because of the well-known reason of the distortion and magnification of linear measurements in the conventional cephalometric measurements, angle measurements wherever feasible were suggested to be employed [3]. On the other hand Lundström et al. [18] evaluated facial depth and height changes by using ratio measurements. In addition to inaccuracy the traditional two-dimensional (2D) cephalometric analysis was actually based on a combination of lateral and posteroanterior films although it was referred to as a 3D method for several decades [6, 10, 16]. The same landmarks located in lateral and posteroanterior films were not always identical in these traditional studies [10]. The advent of 3D computed tomography (CT) technology allows direct visualization of the entire craniofacial structure instead of combining two projected films. Furthermore, advances in 3D software have led to actual 3D measurements becoming a reality. It is indubitable that the traditional cephalometry is still a valuable tool that can provide important information when used properly. During the past decade however, it has been verified many times in the literature that 3D CT, especially 3D cone-beam CT (CBCT) has shown to be greatly superior to the 2D approach both in the reliability of anatomical landmark identification [17, 7] and in measurement accuracy [1, 11, 23]. Therefore, in the present study in order to investigate the craniofacial structure three dimensionally accurately the 3D CBCT technique was used to preliminarily evaluate how the vertical facial height correlates with mandibular plane angle, facial width and depth in Caucasian dry skulls to deepen the understanding of vertical facial dimension and its functional interrelationships among 3D structures.

Table 3 shows the descriptive results of this study.

On the correlations among height measurements, MP-SN, S-Go/N-Me ratio (Table 4), Co-Go and S-Go moderately correlated with both MP-SN and the S-Go/N-Me ratio. The AFH, including anterior upper face height (AUFH measured between N and ANS), anterior lower face height (ALFH measured between ANS and Me) and anterior total face height (ATFH measured between N and Me) did not significantly correlate with either MP-SN or S-Go/N-Me, whereas ATFH and ALFH moderately and positively correlated with Co-Go and S-Go.

On the significant correlations between height and width (Table 5) the bizygomatic (Zyg-Zyg) distance significantly correlated with Co-Go, S-Go, S-Go/N-Me and MP-SN and Co-Go also showed low correlation with both the bicondylar (Co-Co) and the bigonial (Go-Go) width.

As for the statistically significant correlations between height and depth (Table 6), AFH, ATFH and ALFH showed moderate correlation with S-N and relatively lower correlation with ANS-PNS and S-A. On the other hand, Co-Go and S-Go correlated moderately with S-A and S-B and slightly with ANS-PNS and Go-Gn.

Although it was reasonable to find that MP-SN and PFH/ATFH showed moderate correlation with the PFH and the ramus height, it was quite implausible to discover that neither MP-SN nor PFH/ATFH correlated with any AFH measurements (Table 4 and Fig. 10). Even as the denominator of PFH/ATFH, ATFH did not correlate with this ratio. This might suggest that in normal overbite case the PFH or the ramus height rather than AFH appears to play a key role in vertical facial type.

At the same time, PFH and ramus height moderately and positively correlated with ATFH and ALFH (Table 4) which means that a face with a long PFH is normally accompanied by a relatively long AFH and vice versa. Therefore, in a normal overbite case, mandibular forward rotation cannot be simply regarded as the growth result of relatively long PFH together with relatively short AFH. In other words, the reason for mandibular forward rotation is not because of increase of PFH together with a decrease of AFH but the different increased dimension of them. These study results showed that it is the underdevelopment or overdevelopment of PFH instead of AFH that plays a key role in mandibular rotation. This agrees with Björk [5] who stated that under ideal circumstances the fulcrum point for anterior or forward mandibular growth rotation is located at the incisors. Therefore, as the result of forward rotation both the AFH and PFH increase.

On the other hand, extreme short or long face syndrome is definitely always accompanied by low or high mandibular plane angle. However, in the extreme case, muscle or organ dysfunction, such as nasal obstruction is suggested to be always involved [39]. This kind of dysfunction probably interferes with the functional capacity of adaptation that normal faces are supposed to have. Van Spronsen et al. [38] argued that musculoskeletal interactions might differ between populations with normal faces and a select group of individuals with long faces. As for the normal overbite person observed in this study, which can perfectly compensate some discrepancy within a certain extent, the mandibular plane angle was by no means associated with the anterior face height.

As for the reason why in relatively normal cases, the PFH instead of AFH plays a key role in mandibular rotation, the answer cannot be found in this study. In the literature several authors have stated that the morphology and position of the mandible should be adaptable to functional demand in the occlusal configuration [21, 31]. The posterior part of the dentition has furthermore been proposed as a main factor affecting the functional positioning of the mandible [14, 30, 8] The longitudinal growth studies conducted by Tanaka and Sato [37] revealed that continuous horizontalization of the posterior occlusal plane is accompanied by a simultaneous reduction in the mandibular plane angle during growth. They suggested that the posterior occlusal plane is the key point responsible for changes in mandibular position. If this assumption is valid, the possibility can be raised that with the horizontalization of the posterior occlusal plane, the vertical growth of mandible ramus might be obtained and as a result the mandibular plane will flatten (Fig. 11).

With respect to the correlation between face height and depth, ATFH and ALFH moderately correlated with anterior cranial base length (S-N), whereas PFH and anterior cranial base length did not correlate. As S-N is generally considered stable and reliable, environmental or functional factors seem less likely to change the S-N length. This might suggest that in normal cases, AFH is more likely to undergo relatively intrinsic growth than PFH or it is not easily influenced by functional factors such as changes in the posterior occlusal plane as noted above.

With respect to the posterior height, it weakly associated with the actual mandibular length and maxilla length and moderately and positively correlated with the anteroposterior position of the mandible and maxilla. Schudy [33] depicted the vertical and anteroposterior growth as opposing forces. That sounds reasonable with AFH being regarded as vertical height in the extreme case of long or short face type. In relative normal overbite case, however, as this study showed the vertical growth of PFH is consistent with anteroposterior growth.

In order to correct the anteroposterior discrepancy, orthodontists have tried to stimulate the capacity of adaptation to changes in mandibular position and non-human primate studies have demonstrated that the temporomandibular joint in the condylar region definitely has such functional capacity [22, 12]. According to McNamara and Bryan [21] and McNamara [19] the dentofacial complex is adaptable to the functional demands in the occlusal configuration even in young adult monkeys. Clinical studies, however, also by McNamara [20] using a functional regulator on adult humans, manifested that only minimal skeletal and dental adaptation occurred and that adaptation were considered insufficient to completely resolve patient malocclusions. It seems that for adults the protrusive function only is not enough to maintain the mandible in the forward position. Sato et al. [29], Sasaguri et al. [26] and Tanaka et al. [36] tried to maintain the mandible in the forward position by changing the occlusal configuration not only anterioposteriorly but also vertically. As a result, obvious remodelling of the condyle in adults has been found [26, 29, 36]. They suggested that the stable condyle adaptation might be available when the occlusal plane was reconstructed with either an orthodontic or prosthetic approach by increasing posterior teeth support, horizontalizing posterior occlusal plane and as a result the mandible being forward rotated. Together with the present study it can be deduced that to obtain enough mandible anteroposterior growth or forward adaptation a correct increase of posterior height might be an important factor.

As for the correlation between height and width, the ramus height together with the mandibular plane angle and the PFH/ATFH moderately correlated with the bizygomatic width and the width of Co-Co and Go-Go also correlated with ramus height to some extent, which implies that the bicondylar and bigonial width of the mandible is related to the height of the mandibular ramus. Thus, a face with a low angle, normally accompanied by a long ramus and a wide frontal region (wide bizygomatic and bigonial) can easily produce an illusion of a short face, although the anterior lower face height could be normal. This also explains why many faces with a low angle are taken for granted to be assumed as a short face, whereas a wide face and a square profile are responsible for making faces appear short.

In this study, depending on different purposes, direct or projected measurement was selected as the research method. The direct measurement method was used when the complete structure was evaluated, for instance, in measuring ramus length, mandibular corpus length and anterior cranial base length. The reason was that in this situation the study was more concerned with the real length of the structures than the projected ones and the direct measurement results could not be influenced by a poor position of the skull. In previous 2D cephalometric studies, however, as there is no way to measure the true length of any structure, observers had to make use of the projected length. The projected measurement was used here in the width measurement because only the width of identical anatomic structures on bilateral sides was made and direct measurements indicate not only width but also the vertical and anteroposterior difference between them. The larger vertical and anteroposterior difference of bilateral sides was, the more enlarged value was obtained compared with the actual result.

In this study Pearson correlation coefficients were used to find out the interrelationship among 3D structures. With these findings human craniofacial architecture and its multiple interactions among structures can be better understood but correlation studies cannot answer the cause and effect relationship among structures and also that between the skeletal morphology and jaw muscle function remain unclear. Further studies are needed to confirm some hypothesis made in this research.

Within the limitations of this 3D CBCT study on skulls of relatively normal adult Caucasian males it was concluded that low or high mandibular plane angle might not necessarily be accompanied by short or long AFH, respectively as has commonly been believed. The PFH rather than AFH is assumed to play a key role in the vertical facial type, whereas AFH seems to undergo relatively intrinsic growth.