INTRODUCTION

Computed tomography (CT) has been widely used for clinical diagnosis, and it has also been applied to orthodontic treatment and orthognathic surgery.1–8 It allows us to evaluate 3-dimensional (3D) morphology of the maxillofacial skeleton, which is difficult to identify with cephalometric radiography.1–3679–12 On the other hand, use of CT increases radiation exposure, and this should not be ignored.

Several 3D reconstructed CT (3D-CT) systems have been proposed for maxillofacial skeletal measurements.391113–18 We have also proposed a 3D-CT system for evaluating the facial asymmetry, in which landmarks are plotted on axial slice images.1415 Measurement accuracy depends on the image resolution of individual machines and is generally reported to be sufficient for linear measurements with recently available CT apparatuses.910 Although reproducibility has been evaluated for 3D-CT, most of the evaluations dealt with linear measurement of the length between two landmarks. When reproducibility in the length measurement is evaluated using relative indices, such as coefficient of variance, it appears higher as longer length is analyzed. Moreover, when the reproducibility of the length measurement is not sufficient, it cannot be determined which of the two landmarks that creates the line is unstable.

Although various coordinate systems have been proposed for 3D-CT based on the anatomic landmarks that are traditionally used for cephalometric measurements to identify the location of skeletal indices and to clarify their changes after treatment, there are few studies regarding the reproducibility of the coordinates of a certain landmark. The plotting reproducibility of landmarks that are referred to for creating a coordinate system should be verified before the system is set up.

A method using scatterplots and the 95% confidence ellipse is an alternative for evaluating the coordinate reproducibility19 and has been used to evaluate plotting reproducibility of cephalometric landmarks.20 The method can be modified for 3D evaluations.21

The purposes of the present study were to assess the plotting reproducibility of landmarks on 3D-CT images through use of the 95% confidence ellipse and to propose sufficiently stable coordinate systems for 3D-CT measurements.

MATERIALS AND METHODS

CT Data Acquisition and Image Processing

An acrylic head phantom with an embedded human dried skull (Kyoto Kagaku, Kyoto, Japan) was scanned parallel to the Frankfort horizontal plane at the dorsal position using a CT machine (HiSpeed NX/i Pro, GE Yokogawa Medical Systems, Tokyo, Japan). Referring to the scout view, scans were performed from 1 cm superior to the nasion (N) to 1 cm inferior to the menton (Me) at 120 kV and 200 mA. The sequential axial slice data were acquired at 1 mm, 2 mm, and 3 mm slice thickness. The image matrix was 512 × 512, field of view was 170 mm, and the size of 1 pixel was approximately 0.33 mm. Nineteen landmarks were selected and defined for 3D-CT images with references to landmarks in cephalometric measurements (Table 1).

Table 1.  Definitions of Anatomic Landmarks for 3-Dimensional Computed Tomography

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Sice data were transferred to a notebook PC (VAIO PCG-NV99M/BP, Sony, Tokyo, Japan) in DICOM (digital imaging communications in medicine) format via a portable hard disc (HD-D120U2, Buffalo, Nagoya, Japan) and were converted to 8-bit images in tagged image file format (TIFF) using image analysis software VG Studio Max 1.1 (Networking Visualization Science, Tokyo, Japan). The TIFF images were moved to image-processing software (Adobe Photoshop 6.0, Adobe Systems, San Jose, Calif), and a landmark was plotted as a circle of 7-pixel diameter on the axial slices images (Figure 1). After the landmarks were plotted, the TIFF images were imported again to VG Studio Max 1.1, and a 3D image was created using a volume rendering method. The plotted landmarks were also displayed on the created 3D-CT image (Figure 2).

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Using this software, a corner of a cubic 3D matrix was automatically set as the origin (0, 0, 0), and the X-axis was determined roughly parallel to the right-left direction of the phantom's maxillofacial skeleton. The Y-axis and Z-axis corresponded to the posterior-anterior and superior-inferior directions, respectively. The coordinates (x, y, z) could be determined for each voxel (Figure 2) and were expressed as the actual size that was calculated by converting the “number of voxels” to millimeters.

RESULTS

The areas of 95% confidence ellipses on three planes (the XY, YZ, and ZX planes) and in images with three-slice thicknesses were calculated for each landmark evaluated (Table 2). Consequently, nine confidence ellipses were produced for each landmark. Generally, the areas increased as the slice thickness increased. The basion (Ba) and the bilateral coronoid processes (CPs) showed small areas (under 2 mm²) in all nine ellipses. The tooth-related landmarks had relatively small areas, indicating high reproducibility.

Table 2.  Area of 95% Confidence Ellipse for 19 Landmarks (mm²)^a

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For five landmarks (the sella [S], N, Ba, orbitale [Or], and true porion [Po]) that are frequently used as reference points on cephalograms, the ellipses were displayed on three planes (Figure 3). The plotting reproducibility showed characteristic features for each landmark. Among the five landmarks, the Ba showed the smallest ellipses in all planes on 3D-CT images, regardless of the slice thickness. As for the S and N, the ellipses for the image of 1-mm slice thickness were smaller than those for other slice thicknesses on all three planes (the XY, YZ, and ZX planes). The ellipses for 2-mm and 3-mm slice images were expanded along the Z axis (the superior-inferior direction); no enlargements were found along the X- and Y-axes compared with those of the 1-mm slice image. These findings indicated relatively higher reproducibility in the right-left (X-axis) and anterior-posterior (Y-axis) directions.

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The ellipses of Or in 1-mm and 3-mm thickness images expanded along the right-left direction (the X-axis) with small variation along the Y- and Z-axes. In the 2-mm slice image, enlargement was also seen in the superior-inferior direction (Z-axis). These results indicated that the Or showed good reproducibility in the superior-inferior direction (Z-axis) on 1-mm or 3-mm thickness images.

Regarding the Po, the reproducibility for the 1-mm slice was good in the superior-inferior (Z-axis) and anterior-posterior (Y-axis) directions. For 2-mm and 3-mm slices, the reproducibility was still stable along the Y-axis but became worse along the Z-axis.

DISCUSSION

Various coordinate systems for 3D-CT measurements have been proposed.37911 Many include at least one of three landmarks, namely the S, N, and Ba, as the points that are referred to when the coordinate axes are determined. Based on the results of the present study, use of these landmarks is considered to be reasonable for 3D-CT because of their high plotting reproducibility. Moreover, orthodontists are familiar with these landmarks because they are well accepted as reference points on cephalograms.

We have previously proposed a 3D coordinate system with the S, N, and Ba as references for evaluating facial asymmetry.1415 In that system, the sagittal plane (YZ plane) is initially determined with reference to these three landmarks. Kitaura et al22 have also proposed a coordinate system using the S as the origin and the N and Ba as references. They have applied it to patients of different ages and have 3-dimensionally determined the age-related changes in various landmarks of the maxillofacial skeleton. They examined the accuracy and reproducibility of 29 types of length measurements between two landmarks. They concluded that the reproducibility of length measurement decreased when the slice thickness increased.

The present study verified that the coordinate axes proposed in these two studies were established with sufficiently stable landmarks, although they did not examine the reproducibility of the S, N, and Ba measures. Park et al3 plotted 19 landmarks five times on 3D-CT images and determined the standard deviations (SDs) of the coordinates of the landmarks. The SD was determined for the XYZ axis components for each landmark. Although their method of determining the coordinate axes was not described in detail, the coordinate axes were established with the N as the origin and the anterior, superior, and left directions as positive for the Y-axis, Z-axis, and X-axis, respectively. Therefore, the directions of these axes roughly matched those in the present study. According to their results, the Po on the 2-mm thickness image had larger SD in the Z-axis direction than in the directions of other axes. As for the Or, the SD in the Z-axis direction was not increased, indicating only a small variability in the superior-inferior direction. Although they did not propose new coordinate axes, their results are consistent with the results of the present study.

Generally, the reproducibility became higher as a thinner slice thickness was used for 3D reconstruction. However, for some landmarks, such as the Or, the reproducibility in the Z-axis was poorer for the 2-mm slice thickness image than for the 3-mm image. This discrepancy may be due to the difference in morphology surrounding the landmark between the adjacent slices. The difference may be more easily identified on the 3-mm thickness image than on the 2-mm thickness image. Therefore, one could determine the landmarks on axial CT images with much confidence.

Among several methods for identifying landmarks on 3D-CT images, we have chosen the method of plotting them on axial slice CT images and then creating 3D images by means of a volume rendering procedure.1415 Because CT data are traditionally stored in the form of sequential slice data, the method is considered to be useful for establishing a system independent of the model of CT machine and software used. Recently, however, it has become easy to obtain and manipulate volume data with the development of multi-slice CT or cone-beam CT.623 Therefore, it should be possible to modify and improve the method used in the present study in the near future. Eventually, we might obtain better reproducibility than that in the present study.

It is noteworthy that the reproducibility was determined here in three directions (X-, Y- and Z-axes) by means of the 95% confidence ellipse. For the Or on the 1-mm and 3-mm images, the confidence ellipse showed small variability in the Z-axis, indicating high reproducibility in this direction. This means the Or can be used to determine the axial plane (XY plane). On the 1-mm thickness image, the Po was stable in the directions of the Y- and Z-axes but was unstable in the X axis. Therefore, the Po is suitable for determining the axial plane (XY plane) and the coronal plane (ZX planes) on 1-mm images.

Based on these results, we propose a new coordinate system using the Ba, Po, and Or (Figure 4). For example, using a 1-mm thickness image, a plane is initially determined with reference to the bilateral Po and the left Or, and then the XY plane is defined as the plane including the Ba as the origin of the coordinate axes and parallel to the initially determined plane. Next, the ZX plane is determined as the plane including the Ba and parallel to the plane that includes the bilateral Po measures and is perpendicular to the XY plane. Finally, the YZ plane is determined as the plane that is perpendicular to both the XY and ZX planes and includes the Ba. As shown here, if we establish a stable coordinate system with use of these three landmarks (Ba, Po, and Or), which are situated in a relatively low part of the maxillofacial skeleton, there is no need to scan the superior region where the N and S are located. This could significantly reduce the radiation exposure to patients, especially for the dose to the lens.

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CONCLUSION

• The methods of the present study could be used to evaluate the plotting reproducibility of the anatomic landmarks for 3D-CT and to provide a suitable coordinate system for different treatments or studies in accordance with their objectives and subjects.