Twenty adult patients (10 male, 10 female),aged 18 to 30 years, were searched and selected from the patient database in the Department of Orthodontics at our hospital and enrolled in this study. Patients had common pretreatment orthodontic records of plaster dental casts, panoramic radiograph and lateral and frontal cephalograms, and took additional craniofacial CBCT examinations within one month because of the need of orthognathic surgery. The study procedure was shown in Fig. 1.
Plaster dental casts were scanned by a laser scanner (3Shape R700, 3Shape A/S, Copenhagen, Denmark), the scanned images were reconstructed into 3D digital dental casts. Lateral and frontal cephalograms were obtained from the same Cephalostat (OC-100, Instrumentarium Imaging Co., Finland); the patient turned 90° while the Cephalostat was fixed between two scans. Craniofacial CBCT images were acquired using a CBCT unit (NewTom VG, Quantitative Radiology, Verona, Italy) with the following parameters: 15×15 cm FOV, 110 kVp, 10.8 mA, 3.6 s, and 0.3-mm slice thickness.
The cephalograms were digitally traced using Adobe Photoshop CS 5.0 (Adobe Systems Corporation, San Jose, CA, USA) on a hand-writable liquid crystal display (Cintiq DTK-1300, Wacom, Saitama, Japan) (Fig. 2a). The tracings were saved in BMP format. By using the Matlab 10.0 (Math Works Inc., Mass., USA) with a self-edited code (see Additional file 1), the tracings were adjusted by magnification, extracted as 2D points, and then transformed into 3D points by adding an additional Z value of zero to the lateral cephalogram tracing and an additional X value of zero to the frontal cephalogram tracing. The final 3D tracings were saved in TXT format and imported into the Rapidform 2006 software (Inus Techonology, Seoul, Korea), where the lateral and frontal cephalogram tracings were presented in the XY and YZ planes respectively, and intersected with each other at the facial midline of the frontal tracing.
Then, the maxillary digital dental cast was imported into the Rapidform software to integrate with the cephalogram tracings. First, the midsagittal plane of the maxillary digital dental cast, generated as the mirror symmetry plane of the palatal vault region, was coincided with the XY plane; subsequently, the inferior outline of the palate (Outline_P) was generated by slicing the digital cast with the XY plane. The labial outline of the anterior incisor (Outline_I) and the occlusal outline of the dentition (Outline_O1) were generated by projecting the cast onto the XY plane, while the buccal outline of the second molar (Outline_M) and the occlusal outline of the dentition (Outline_O2) were generated by projecting the cast onto the YZ plane (Fig. 2b). Thereafter, the maxillary dental cast was registered with lateral and frontal cephalogram tracings through 3D translation and rotation, where the digital dental cast was first aligned laterally, then frontally, going back and forth between two cephalograms until radiographic tracings and dental cast outlines of teeth and palate were best-fit registered . The best-fit registration was defined as follows: (i) on the XY plane, Outline_I and Outline_O1 coincided with corresponding lateral cephalogram tracings, Outline_P was just below the corresponding palatal tracing; (ii) on the YZ plane, Outline_M and Outline_O2 coincided with corresponding frontal cephalogram tracings (Fig. 2c).
Figure 2d shows the final integration of the maxillary dental cast and the cephalograms. The mandibular dental cast could be integrated through its occlusion with maxillary dental cast. Subsequently, measurements were recorded to evaluate the accuracy and reproducibility of this method. Nasion (N), ANS, and PNS points were selected on the lateral cephalogram, and PP line was constructed by connecting ANS and PNS. The mesiobuccal cusps of bilateral second molars (UMR and UML) and midpoint of the incisal edge of the right central incisor (UIR) were selected on the dental cast (Fig. 3a). The N point was set as the origin of coordinates and the PP line as the direction of the X-axis, the 3D coordinate values (X, anteroposterior; Y, vertical; Z, mediolateral) of UMR, UML, and UIR points were recorded, and their distance from N point and PP line were measured as UMR-N, UML-N, and UIR-N and UMR-PP, UML-PP, and UIR-PP, respectively. The integration process and measurements were repeated two times at a 2-week interval by two examiners.
As the standard reference, CBCT images were processed using the Dolphin imaging software (Version 11.7, Dolphin Imaging & Management Systems, CA, USA). First, the skull was oriented with the Frankfort horizontal plane parallel to the ground and the midsagittal plane passing through the N, sella, and basion points . Subsequently, the landmarks of N, ANS, and PNS were located on the midsagittal plane (Fig. 3b), whereas those of UMR, UML, and UIR were identified on the three orthogonal planes (Fig. 3c); the original coordinates of the six points were exported and this was followed by the same measurements of distances and point coordinates as recorded in the integrated images. The distance measurement and point coordinate transformation were completed using the Matlab with a self-edited code (see Additional file 2).
To evaluate the angular error of the integration method, the pitch, roll and yaw  of the dental cast in the integrated images compared with the CBCT were measured. First, 3D surface skeletal model was generated from CBCT scans using Dolphin software. Second, the skeletal model was imported into the Rapidform software and registered with the integrated images, where the midsagittal plane (mirror symmetry plane) of the skeletal model coincided with the XY plane initially (Fig. 4a) and then the sliced and projected outline curves conincided with the lateral and frontal cephalogram tracings through 3D translation and rotation (Fig. 4b-c). Subsequently, a copied dental cast was superimposed with the skeletal model through registration of crown surfaces of all teeth (Fig. 4d-e). Thereafter, the deviation of the cephalogram-integrated dental cast from the CBCT-superimposed dental cast in terms of pitch, roll and yaw was measured as rotation angle around Z, X and Y axes respectively (Fig. 4f).
We performed the statistical analysis using SPSS software (version 26.0; IBM, Armonk, NY). Intra- and inter-examiner reproducibility of the method for integration of the digital dental cast and cephalograms were tested using intraclass correlation coefficients (ICCs) with a 95% confidence interval. All data were determined to have normal distributions as assessed with the Kolmogorov-Smirnov test. Comparsions of linear distance and coordinate values (X, Y and Z) between the integrated and the CBCT images were conducted with paired t test; comparsions of angular measurements (pitch, roll and yaw) were conducted with one sample t test. The difference and the absolute value of the difference were both described as mean ± standard devitation.