Assessment of maxillary position: Implant vs cephalometric methods

The maxilla grows downward and forward relative to the cranium and cranial base, which is accomplished in two ways: by a push from behind created by cranial base growth, and by growth at the sutures.1 The maxilla becomes larger as the result of bone apposition at the sutures, whereas almost the entire anterior surface is an area of resorption.2 In orthodontics, the degree of maxillary prognathism is commonly assessed by the position of point A in relation to the skull base or a reference plane.3 

In many cephalometric methods, the SNA angle describes the degree of maxillary prognathism in relation to the anterior skull base. The anterior skull base is considered to be stable from the age of 7,1,4 but the landmark nasion (N) is not stable during growth.5 Subsequently, the forward position of the maxilla will not be fully expressed in the change in the SNA angle, because the N also moves forward with growth. Moreover, the SNA angle is limited to express sagittal changes only. To overcome the shortcomings of the SNA angle, cephalometric methods have been devised that are based on reference grids related to the stable part of the anterior skull base.6–8 

A recent study9 compared the accuracy of superimposition on metallic implants and the lingual curvature of the palatal plane as advocated by the American Board of Orthodontists; samples of serial head films from an implant study were used.10 Study results9 showed that the American Board of Orthodontists method underestimated the vertical displacement and overestimated the forward movement of maxillary landmarks. In a previous study,11 in which mandibular growth achieved with the aid of implants was compared with growth attained through conventional cephalometric linear measurements of the mandible, it was found that the cephalometric figures obtained were not proportional to the actual condylar growth as assessed from two-dimensional lateral cephalograms. Because of significant growth changes in the maxilla, defining point A at different time points is not identical, whereas maxillary implants express the full movement of the “maxillary body.”12 

The aim of this study was to compare changes in maxillary position assessed from maxillary implants and three cephalometric methods based on linear measurements on lateral cephalograms.

The material comprised series of tracings of the maxilla obtained from the implant study by Björk and Skieller.13 Tracings of the anterior skull base and maxilla representing 5 to 6 years of growth around puberty from 19 subjects were included in the present study. These tracings had been obtained at 3 years before (T₁) and 3 years after pubertal maximum (T₃), respectively. However, five subjects were followed for 5 years only; cases 4, 5, 7, and 8 were followed from 2 years before the pubertal maximum, and case 13 was followed to 2 years after pubertal maximum. In this study, the two maxillary tracings superimposed at the sella and along the nasion-sella line (NSL) were used: T₁, at the start of the study, and T₃, at the end of the study (Figure 1). Before any measurements were made, the tracings were enlarged to their original size. The grid devised for the respective cephalometric method was defined for each subject on the tracing obtained at T₁. For each cephalometric method, subsequent measurements of the position of the A-point at T₁ (A₁) and T₃ (A₃), respectively, were made using a grid defined at T₁, superimposed on the anterior skull base at T₃ (NSL at S). The NSL had been transferred from film T₁ to film T₃ in accordance with the structural method.13 In this study, all measurements were taken by one examiner.

The “absolute” displacement of the maxilla in relation to the anterior skull base was assessed by measuring the distance between the most anterior implant at T₁ and T₃ (Figure 1).

The sagittal reference planes devised by three cephalometric methods were the NSL (Bergin et al.6; Figure 2), the upper occlusal plane (Pancherz7; Figure 3), and the constructed horizontal line drawn 7 degrees down to the NSL at N (Hack et al.8; Figure 4). The vertical reference planes devised by the three cephalometric methods were defined by a perpendicular plane, which was drawn to the respective sagittal reference plane at the sella (Figures 2 through 4). Subsequently, the sagittal (H₃-H₁), vertical (V₃-V₁), and absolute (A₃-A₁) changes in point A, representing the maxillary position assessed by conventional cephalometric methods, were measured along the respective reference planes, separately for each method (Figures 2 through 4).

Identification of point A consisted of the point at the deepest midline concavity of the maxilla oriented along the perpendicular axis to the NSL (Bergin et al.6; Figure 2), to the upper occlusal plane (Pancherz7; Figure 3), and to the constructed “true horizontal line” drawn 7 degrees down to the NSL at N (Hack et al.8; Figure 4).

The angle between the extrapolated implant line (I₁-I₃) and each of the three sagittal reference planes was measured (Figures 2 through 4).

By calculation, the displacement of the most anterior implant in relation to the sagittal reference plane of each of the three cephalometric methods was formulated as follows (Figures 2 through 4): horizontal displacement (y or ΔIH)  =  x cos θ, and vertical displacement (z or ΔIV)  =  x sin θ, when θ is the angle between the extrapolated implant line and each of the sagittal reference planes of the three cephalometric methods (Figures 2 through 4).

Comparisons of the absolute, horizontal, and vertical displacement of the maxilla were assessed from the implant and point A, respectively, using the three different cephalometric methods (Figures 1 through 4).

Data were analyzed with statistical analysis computer software (Statistical Package for the Social Sciences [SPSS] 15.0 for Windows, SPSS Inc, Chicago, Ill). Ten randomly selected cases were used for method error analysis calculated by Dahlberg's formula, ME  =  ⁠, where d was the difference between the two measurements of a pair and n was the number of double measurements. Paired t-tests were also performed to compare the double measurements. No difference was found to be statistically significant.

Two independent measurements were made and averaged. Because the normality (Kolmogorov-Smirnoff test) and variance homogeneity assumptions (Levene's test) of the data appeared to be valid, one-way analysis of variance and Bonferroni multiple comparisons tests were used to compare the absolute displacement of the maxilla measured by the implant method and three cephalometric methods, and the difference between implant displacement and point A displacement was assessed with three cephalometric methods in horizontal and vertical directions. Paired t-tests were applied to compare the mean changes between the implant method and point A displacement with the three cephalometric methods in horizontal and vertical directions. The level of significance was defined as P < .05.

The 10 paired measurements were not statistically significant, and the method error was 0.05 mm. The direction of maxillary growth was assessed as the change in position of the most anterior implant from T₁ to T₃ relative to each of the three sagittal reference planes, superimposed on the NSL at S (Table 1). Results showed that the maxilla moved downward and forward in all subjects except one (case 5), irrespective of the method used. The average direction of maxillary growth assessed with the implant method in relation to the respective reference plane was 40.2 degrees (Bergin et al.6), 33.9 degrees (Hack et al.8), and 21.8 degrees (Pancherz7), respectively; the differences among the three methods were statistically significant (P < .01) (Table 1).

Displacement of the maxilla was assessed as the change in position of the maxilla from T1 to T3 in terms of absolute, horizontal, and vertical displacement obtained by the implant method (I₃-I₁) and three cephalometric methods (A₃-A₁). Results showed that the average estimation of the displacement of the maxilla by three cephalometric methods (point A) was larger than that by the implant method in absolute magnitude and in horizontal and vertical directions (Tables 2 and 3). During T₁ to T₃, the average absolute displacement of the implant was 6.3 mm, and that of point A was 9.4 mm (Bergin et al.6), 8.9 mm (Hack et al.8), and 8.7 mm (Pancherz7), respectively; the difference among the three cephalometric methods was not statistically significant (Table 2). Maxillary growth assessed by cephalometric methods and expressed in the percentage of maxillary growth estimated by the implant method varied from 98.0% to 241.1% (Bergin et al.6), from 88.8% to 180.4% (Pancherz7), and from 96.1% to 212.5% (Hack et al.8) (Table 2).

Total and annual rates of absolute displacement of the maxilla assessed by the implant and that of point A are presented in Table 2.

Significant differences in horizontal and vertical movements of point A were found with use of the three cephalometric methods compared with the implant method (Tables 3 and 4). Average differences in the horizontal plane were 1.6 mm (P < .001; Pancherz7), 1.2 mm (P < .01; Hack et al.8), and 0.7 mm (P < .05; Bergin et al.6), respectively. However, in cases 11 and 20, the horizontal movement of point A was less than that of the implant (Table 4). Average differences in the vertical plane were 3.6 mm (P < .001; Bergin et al.6), 2.5 mm (P < .01; Hack et al.8), and 2.2 mm (P < .001; Pancherz7), respectively. However, in cases 8 and 14, the vertical movement of point A was less than that of the implant (Table 4). The difference in the movement of point A vs the implant was greater for vertical movement than for horizontal movement, irrespective of the method used; the difference was statistically significant (P < .001) for the Bergin et al.6 method only.

This study aimed to compare the assessment of maxillary position during puberty in relation to the anterior skull base through the implant method13 and three conventional cephalometric methods based on linear measurements, using their devised reference planes.6–8 It has been shown that implants inserted in the maxilla are stable and can be used to define the displacement of the maxilla in relation to the anterior skull base,1 whereas the results of this study confirm that it is not possible to accurately assess displacement of the anterior part of the maxilla with conventional cephalometric methods, because the location of point A was affected.

Subsequently, the purpose of this study was to quantify to what extent the three selected conventional cephalometric methods based on linear measurements describe “actual” changes in the position of the maxilla assessed from an implant. It has been demonstrated that linear measurements used in cephalometric methods are more valid than angular measurements.14,15 Descriptions of any changes in forward maxillary positioning by the angle SNA are compromised by the change in position of the N-point in growing individuals.5,13 

The reference planes used in those three cephalometric methods were the NSL (Bergin et al.6), the line drawn 7 degrees down from the NSL at the nasion (Hack et al.8), and the upper occlusal plane (Pancherz7). The directions of all three reference lines were significantly different from that of maxillary displacement assessed by the implant line; average differences were 40 degrees, 34 degrees, and 22 degrees, respectively, with very large individual variation (Table 1). The difference was statistically significant (P < .01) between the methods used by Bergin et al.6 and Pancherz,7 and those of Hack et al.8 and Pancherz,7 respectively. In conclusion, the inclination of none of the three investigated reference planes or that of their respective perpendicular was close to the “actual” displacement of the maxilla. In only three cases, the direction of true maxillary displacement was close to the reference lines (Table 1).

The change in position of the maxilla was significantly larger (Table 2) when assessed by cephalometric methods compared with the implant method, expressed in percentage of the difference of 141.5% (Pancherz7) to 152.0% (Bergin et al.6), respectively. The change in position of the implant was due to displacement of the maxillary body only. The significantly larger change in the position of point A (Table 2), independent of the conventional cephalometric method used, indicated that the positioning of point A changed as the result of an increase in maxillary height and some apposition of bone in the anterior part of the maxillary alveolar process,12 when superimposition was made on the implant inserted in the maxilla (Table 2). Point A moved significantly more forward and downward than the implant, independent of the cephalometric method used (Table 4). Movement of point A relative to the implant was greater in the vertical plane than in the sagittal plane, but the difference was statistically significant for one method6 only. Subsequently, the position of point A changed, not only because of displacement of the maxillary body, but also considerably in both the sagittal and vertical planes as the result of growth of the alveolar process; this finding is consistent with previous observations.16–18 The change in positioning of the body of the maxilla can be assessed only by inserting fixed markers,12 not by the commonly used maxillary cephalometric landmark point A. The annual absolute displacement interpolated from the data obtained over a 6-year period showed that the displacement of point A was 36% to 45% larger than that of the implant (P < .001; Table 2). However, this study was based on the assumption that the reported changes were linear over the 6-year observation period when they rather have a steady curve-linear course, which required annual data.9 However, one study17 showed a relatively uniform downward displacement of point A over a 7-year period of observation.

With all three conventional cephalometric methods, a statistically significant overestimation of the maxillary position was seen on average in both horizontal and vertical planes (Table 4). The average overestimation was five times larger in the vertical plane than in the horizontal plane for one of the cephalometric methods (Bergin et al.6); this finding was in close agreement with findings of a recent study based on a smaller sample, which also used NSL as a reference plane.9 For the other two methods (Pancherz,7 Hack et al.8), the average amount of overestimation was larger in the horizontal plane but less in the vertical plane compared with the method used by Bergin et al.6 However, the range of underestimation and overestimation of maxillary positioning over a 6-year period was considerable in this selected sample of 19 subjects, and varied from an underestimation of about −3 mm to an overestimation of about +4 mm in the horizontal plane, and from about −4 mm to +9 mm in the vertical plane (Table 4).

Consequently, the findings of this study indicate that any evaluation of changes in positioning of the maxilla over a longer observation period using any of the three investigated conventional cephalometric methods was likely to be inaccurate, especially that of an individual subject. If the observation period was brief (eg, about a year), the results of this study indicate that the level of underestimation/overestimation of changes in maxillary position did not usually exceed 0.5 mm in the horizontal plane and 1 mm in the vertical plane. However, this was not taken into account in the inherent method errors of conventional cephalometric methods,3 which makes the validity questionable for almost any cephalometric variable used for evaluation of treatment and growth changes in individual subjects.18 

Maxillary growth in height takes place by periosteal apposition of the alveolar process in combination with resorptive lowering of the nasal floor (ie, a substantial amount of maxillary bone has disappeared and been formed, respectively, during a 6-year period around puberty). Seemingly, no part of the maxillary contour remains totally stable, which means that the cephalometric landmark, such as point A, often is likely to change location.

• The cephalometric landmark, point A, could not be used to describe “actual” changes in the position of the maxillary body, as it was located on the anterior part of the maxillary alveolar process, which had undergone changes during growth.

• On average, the use of point A with any of the three investigated cephalometric methods resulted in an overestimation of the change in position of the maxilla in both horizontal and vertical planes.

We thank the late professor A. Björk for his kind permission to use material from his classical paper.13