Sample Selection

A total of 256 human dry skulls of Chinese ethnicity from the Faculty of Dentistry of the University of Hong Kong were analyzed and those with documented sex and age >20 years were included. Skulls with fractures, missing parts, or severe deformities (cleft palate or hemifacial microsomia), were excluded. The protocol was approved by the Institutional Review Board (UW-18112), and the study was registered in the HKU Clinical Trials Registry (HKUCTR-2383).

Image Analysis

Cone beam computed tomography scans (CBCTs) were acquired (ProMax 3D Mid, Planmeca, Helsinki, Finland) with field of view of 20 × 17 cm, exposure of 36 s, 19 mGy, 90 kV, 14 mA, and voxel size of 200 μm. Images were analyzed using a computer software (Planmeca Romexis 5.0, Planmeca) with slice thickness of 200 μm. Skulls were oriented starting from the axial view and positioning the coronal slice passing through the maxillopalatal suture, and the parasagittal slice aligned to ans-pns. In the coronal view, the para-axial slice was aligned with the hard palate. In the sagittal view, the para-axial slice was aligned to ans-pns (Figure 1, Appendix Table 1).

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Table 1.  Descriptive Statistics of the Measurements of the Low-Length Group, of the High-Length Group, of the Difference Between the Two Groups (Δ), and of the Total Sample. Grouping Was Based on Absolute APMCL, ie, the Length of the Maxillary Complex (ans-pns)^a,b

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Table 2.  Linear Regression Models, One With Outcome Variable the Absolute Anteroposterior Length of the Maxillary Complex (ans-pns) (Upper), and the Other With the Relative Anteroposterior Length of the Maxillary Complex With Respect to the Anterior Cranial Base (ans-pns/SN) (Lower)^a,b

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Table 3.  Descriptive Statistics of the Measurements of the Low-Length Group, of the High-Length Group, of the Difference Between the Two Groups (Δ), and of the Total Sample. Grouping Was Based on Relative APMCL, ie, the Length Ratio of the Maxillary Complex Relative to the Anterior Cranial Base (ans-pns/SN)

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Group Allocation

On the parasagittal slice, the anterior cranial base length (SN, mm) and the maxillary complex length (ans-pns, mm) were measured (Figure 1). The length ratio of the maxillary complex relative to the anterior cranial base was measured (ans-pns/SN). Based on absolute APMCL, the mean ans-pns value among the whole sample was used as the cut-off for identifying a low- and a high-length group. Based on relative APMCL, the mean ans-pns/SN value was used, instead, to identify the two groups.

Sample Size Calculation

The sample size was calculated based on a collective decision between absolute and relative APMCL. Ten skulls not included in the final study were included in a pilot study, showing a standard deviation (SD) of 5.7 mm for ans-pns and 6% for ans-pns/SN, which were the primary parameters for each criterion, respectively. Setting a clinically significant difference of 5.0 mm^11,17–20 and 5%^15,18 between the two groups, respectively, a significance level α = 0.05, and a power β = 90%, the required sample size was 30 skulls for each group.

Experimental Variables

On the para-axial slice, the length of the premaxilla (PM, mm), maxilla (MA, mm), and palatine bone (PA, mm) were measured to quantify the contribution of each segment to the maxillary complex length (Figure 1, Appendix Table 1). Their length ratios relative to the maxillary complex were calculated and expressed in percentage (PM% = PM/ans-pns, MA% = MA/ans-pns, and PA% = PA/ans-pns).

On the parasagittal slice, the maxillary complex alveolar protrusion (SNA, °) and the maxillary complex basal protrusion (SNans, °) were measured to quantify its anteroposterior position (Figure 1, Appendix Table 1).

Data Analysis

Measurements were taken by a primary (FM) and a secondary assessor (FS), after calibration on five skulls. The primary assessor repeated all measurements after a washout period of one month, and the mean between the repeated measurements was used for data analysis. The secondary assessor repeated 50% of the measurements. The intraclass correlation coefficient (ICC) was used to calculate intra and inter-assessor agreement (“poor” if <0.5, “fair” from 0.5 to 0.7, “good” from 0.7 to 0.8, “excellent” if >0.8).²¹ The method error was estimated with Dahlberg's formula.²²

Normality of data distribution was assessed with Shapiro-Wilk test. Two independent analyses were carried out based either on maxillary complex length (ans-pns, absolute APMCL), or on the length ratio of the maxillary complex relative to the anterior cranial base (ans-pns/SN, relative APMCL). Student's t-tests were used to assess differences between high- and low-length groups. Two linear regression models were developed: one with ans-pns and one with ans-pns/SN as outcome variables, to assess their correlation with the length of each segment of the maxillary complex, with the length ratio of each segment relative to the maxillary complex, and with the maxillary complex position.

Data analysis was performed using SPSS (V23.0, IBM, Armonk, New York) with a significance level α = .05.

Sample

Among 246 skulls available, 90 fulfilled the inclusion criteria, 18 were further excluded because sutures were not clearly visible on CBCT, and 60 were randomly selected. By using either absolute APMCL or relative APMCL, half were assigned to the low-length group and the other half to the high-length group.

The sample consisted of 49 males and 11 females, ranging from 20 and 86 years (mean 61.0 ± 14.9 years). Most subjects were dentate (73%), few had complete dentition (21%), and medical conditions were unknown.

Method Error and Reliability

The method error was ≤0.6 mm for linear measurements and ≤1.1° for angular measurements. The intra-assessor agreement was excellent for all measurements (0.93 to 0.98). The inter-assessor agreement ranged from good to excellent (0.70 to 0.93) for all variables apart from the premaxillary (0.54) and maxillary (0.53) segment length, for which it was fair.

Grouping Based on Absolute Measurements

By grouping based on absolute APMCL, the length of the anterior cranial base (Δ = −2.1 ± 4.3 mm, P = .003) and of the maxillary complex (Δ = −5.0 ± 1.8 mm, P < .001) were both shorter in the low-length group. The length of the premaxilla (Δ = −1.6 ± 4.1 mm, P = .026), palatine bone (Δ = −1.7 ± 3.1 mm, P = .004), and maxilla (Δ = −0.8 ± 3.7 mm, P = .197) were also shorter in the low-length group, although the maxilla did not show a significant difference. Nevertheless, no significant differences were present when the length ratio of each segment relative to the maxillary complex was considered, showing that the proportions of the segments were similar between groups (Table 1, Figures 2 and 3). The maxillary complex basal protrusion was smaller in the low-length group (Δ = −2.5 ± 5.7, P = .019), but the alveolar protrusion was similar (Table 1).

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The maxillary complex length was correlated to both the length of each segment and to the length ratio of each segment relative to the maxillary complex (β = 0.449 to 1.125, P ≤ .003). No correlation was found between the maxillary complex length and its protrusion (Table 2).

Grouping Based on Relative Measurements

By grouping based on relative APMCL, the low-length group showed a shorter maxillary complex (Δ = −3.8 ± 3.1 mm, P < .001) and a longer anterior cranial base (Δ = 1.8 ± 3.3 mm, P = .014). In particular, the maxilla was shorter (Δ = −1.5 ± 3.3 mm, P = .014), but the length of the premaxilla and the palatine bone were similar in both groups. However, when the length ratios of each segment relative to the maxillary complex were measured, the premaxilla was longer in the low-length group (Δ = 3 ± 9%, P = .047) (Table 3, Figures 2 and 3). The maxillary complex alveolar protrusion (Δ = −3.7 ± 5.5°, P = .001) and basal protrusion (Δ = −3.6 ± 5.5°, P = .001) were smaller in the low-length group (Table 3).

The regression model showed that the length ratio of the maxillary complex relative to the anterior cranial base was positively correlated to the maxillary length (β = 1.968, P < .001) but negatively correlated to the relative length of the premaxilla compared to the maxillary complex (β = −2.118, P < .001). No correlation was found between the maxillary complex length and its protrusion (Table 2).

Maxillary Anteroposterior Length

Anteroposterior maxillary complex hypoplasia is particularly relevant in patients with skeletal Class III,¹² Down syndrome,⁸ and obstructive sleep apnea,²⁰ and cephalometry is used for both skeletal diagnosis and upper airway assessment.²³ However, the criteria to identify this condition are not well defined, and both the maxillary complex length^8,14,20 and its ratio relative to the anterior cranial base^15,18 have been used. In fact, absolute measurements showed that subjects with a shorter anterior cranial base had a shorter maxillary complex (Figure 3), and the length of the maxillary complex was correlated to the length of each bone of which it was constituted, suggesting limitations of absolute parameters for the identification of disproportions (Table 2). In addition, despite that a shorter maxillary complex presented shorter premaxillary bones and palatine bones, no difference was present in the percentages in which each of these contributed to its total length, confirming that the proportions among the parts were maintained (Figure 3).

It is worth noting that the discrimination between “absolute” and “relative” measurements has been applied to other medical conditions such as “macroglossia,” in which diagnosis may be based either on the tongue absolute size, or on its ratio relative to the oral cavity.¹³ In agreement with the present findings, the same study concluded that the relative criterion should be preferred.¹³

When relative APMCL was adopted, the low-length group had a significantly longer cranial base, suggesting that disproportions were identified (Figure 3). Accordingly, relative measurements through counterpart analysis can show treatment-induced remodeling compensations of the craniofacial skeleton that may be missed using conventional cephalometrics.¹⁶

In the present study, the maxillary complex length was measured relative to the anterior cranial base, since the growth of this structure is related to the growth of the midface,²⁴ and it is also counterpart of the nasomaxillary complex.²⁵ In particular, despite having a longer cranial base, the short maxillary complex group had significantly shorter maxillary bones. Hence, a reduced length of the maxilla, and not the premaxilla or palatine bones, was associated with a relatively shorter maxillary complex. Conversely, the length ratio of the premaxilla relative to the maxillary complex in the short-length group (35%) was higher than in the long-length group (32%). Interestingly, the premaxillary length in the low-length group (15.9 ± 3.1 mm), which was expected to be shorter, resulted to be as long as in the high-length group (15.7 ± 2.5 mm) (Figure 3). Accordingly, the regression model based on relative APMCL showed a positive correlation with the maxillary length (β = 1.968), confirming the maxilla to be associated with a shortening of the maxillary complex. On the contrary, a negative correlation was present with the length ratio of the premaxilla (β = −2.118) (Table 2). The premaxilla may have implications in the onset of midfacial deformities,² and such greater premaxillary length ratio could be resulting either from an active compensatory sutural growth stimulated by homeostatic forces acting on the septopremaxillary ligament,³ or from a passive mechanism involving reduction of the subperiosteal resorption on the anterior premaxillary surface,²⁶ both aiming at counterbalancing the deficient maxillary growth to maintain adequate proportions.²⁴

With regard to norms to identify relative maxillary hypoplasia, previous authors reported a normal maxillary complex to anterior cranial base ratio of 65 ± 3%.¹⁸ However, that sample consisted of Caucasian children and may not be comparable to the present results as the anterior cranial base is shorter in Asians compared to Caucasians.²⁷ Furthermore, other authors reported no differences in the maxillary complex to anterior cranial base ratio between Class III subjects (127.8 ± 4.1%) and controls (130.5 ± 4.5%).¹⁵ However, the cited study adopted the distance between condylion and anterior nasal spine, which is not the actual length of the maxillary complex. That said, the present study did not aim at providing norms for maxillary hypoplasia, since the sample did not represent a random selection from the general population as it was evident from the higher proportion of males. Furthermore, even if such a norm were identified, its diagnostic value and range of normality would be widely debatable due to age, sex, and race variations.²⁸ Still, given the variety of methods proposed in the literature,^{11,14,15,17–20} a critical analysis of the criteria to assess the maxillary complex anatomy is a requisite for achieving consistent diagnosis of its deformities.

Maxillary Anteroposterior Position

The literature refers to “maxillary retrusion” as a condition in which the maxillary complex is normal in size but retropositioned with respect to the anterior cranial base.²⁹ This condition has clinical relevance since, for example, it has been associated with obstructive sleep apnea in adults.³⁰ Even though maxillary “retrusion” and “hypoplasia” have been sometimes used interchangeably, the present results showed the presence of an association (Tables 1 and 3) but not a correlation (Table 2) between the anteroposterior maxillary complex length and its protrusion. Furthermore, although the basal protrusion was smaller in the low-length group, both by using absolute APMCL (Δ = −2.5 ± 5.7) and relative APMCL (Δ = −3.6 ± 5.5°), the findings related to the alveolar protrusion were less consistent (Table 1). Previous authors reported that the size of the maxilla may not influence its prognathism,¹⁷ and it is suggested to differentiate retrusion from hypoplasia. The present study did not aim at providing norms for maxillary retrusion, as the prevalence of skeletal Class III in Chinese is about 13%,³¹ and only a subgroup of the present sample may belong to that category. In addition, the diagnosis of midface deformities is based on a comprehensive assessment of the relationship among skeletal components, which include the whole cranial base, maxillary complex, and mandible.^8,11,15

Limitations

Although human dry skulls offer the advantage to acquire high resolution CBCTs thanks to the absence of soft tissues and no risk of radiation exposure, the premaxillomaxillary suture was difficult to identify^6,32 as it undergoes progressive ossification postnatally.³³ The inter-assessor agreement for premaxillary and maxillary length was fair, showing variations in the interpretation between clinicians. For this reason, and because of controversies related to the premaxilla in humans,^1,2 a further comparison between the high-length and the low-length group based on relative APMCL was performed considering the premaxilla and maxilla as a single bone, confirming the presence of a shorter premaxillomaxillary segment in the low-length group (P = .044) and no differences in the length of the palatine bones.

Despite that size anomalies of the maxillary complex may be three-dimensional,¹² only the anteroposterior dimension was analyzed because of the already complex study design and the lack of reliable references for latero-lateral and supero-inferior measurements of such structures. Overall, the present study did not investigate the characteristics of subjects with maxillary hypoplasia or retrusion, which would require a case control study. Furthermore, demonstrating the etiology of the presented anatomical findings and their underlying growth mechanisms, including allometry and differential growth among the parts,²⁴ would require longitudinal investigations in growing subjects.