The ability to measure the amount of tooth movement in both horizontal and vertical directions is important when assessing orthodontic treatment outcomes related to molar anchorage loss, incisor retraction, intrusion and the extrusion of teeth. An analysis of orthodontic tooth movement enables the assessment of the magnitude, rate and type of movement as well as the efficiency of treatment intervention and anchorage conservation. Cephalometric analyses such as the Pancherz, Bjork, Steiner, Ricketts and the McNamara analysis have commonly been used to measure dental and skeletal changes related to orthodontic treatment. The Pancherz analysis has two components which are a vertical occlusal (VO) and a sagittal occlusal (SO) assessment which makes it possible to measure vertical and horizontal tooth movements.1,2
The availability and use of 3D scanners in dentistry have provided an alternative method of measuring tooth changes which are non-invasive as it does not subject the patient to radiation exposure. Measurements on digital casts have been validated and are comparable to direct measurements taken on plaster casts.3,4 Furthermore, a 3D cast rendition from most scanners has also been found to be accurate and reliable.3,5 Methods of measuring tooth movement on digitised casts, however, depend on accurately identifying intraoral landmarks for the superimposition of the dental models. Various landmarks and methods of superimposition have been reported and discussed but are still not fully established.6–10
Digitised maxillary study casts are more commonly used for measuring tooth movement due to the suitability of the palatal rugae as stable reference points.6,7 Some researchers have suggested the use of medial points6,9 or the medial two-thirds of the third palatal rugae7,10 as reference landmarks for maxillary cast superimposition. These points have been shown to remain stable even after orthodontic tooth movement.9,11 Additional studies have found using the ‘best fit’ and the regional palatal area just as reliable.12,13 The mandibular arch, however, lacks stable landmarks and requires surface superimposition of digitised study casts on mandibular basal bone structures using a combination of cone beam computed tomography (CBCT) images.8,14
Most of the stable points on the maxillary casts are based on the anterior segments of the palate. To improve roll and pitch control, some authors have recommended additional posterior landmarks.15 This suggested that authors had noted problems with the control of positions of the superimposed casts without the added reference landmarks (Figure 1). However, these methods used regional posterior extensions and cannot be applied when using point registration-based software.6,7,10 Therefore, the present study aimed to assess the validity and reproducibility of measuring maxillary orthodontic tooth movement on 3D digital study casts superimposed using a tripoding method. Tripoding locates three positions that could accurately reposition the 3D casts in a pre-defined spatial orientation. The null hypothesis is that there is no significant difference in tooth movement measurements between the digital superimposition using a tripoding method and the Pancherz cephalometric analysis.
The investigation was a method comparison study to assess the validity and reproducibility of linear measurements of tooth movements measured using a tripoding reference method for 3D digital casts compared to a cephalogram. Ethical approval for this study was obtained from the Medical Ethics Committee of the Faculty of Dentistry, Universiti Malaya (Reference number: DF CD1809/0044(L)).
The sample size was calculated using G*Power software version 3.1.9.4 and based on a previous study by Cha et al.12 A minimum of 27 cases were required for a power of 80%, an effect size of 0.57 at the 5% level of significance with 30 cases finally selected for the present study. The initial and final maxillary study casts and cephalograms (9 males and 21 females, participants’ age ranged between 13 and 34 years with a mean age at the start of treatment of 19.3 ± 4.7 years and a mean age at the end of treatment of 21.9 ± 4.5 years) were collected from the Faculty of Dentistry, Universiti Malaya.
The cases were selected if they fulfilled three inclusion criteria: (1) well-defined stable structures on the cephalograms and study casts, (2) a full permanent dentition from first molar to contralateral first molar, and 3) bilateral premolar extractions. However, the cases were excluded if the cephalograms were of poor quality, the study casts were broken, or had poorly defined palatal structures, cases showing dental anomalies related to tooth number and/or orthognathic cases or cleft cases.
The maxillary casts were scanned using Einscan-Pro+ Fixed Scan (with turntable) (SHINING 3D®, Zhejiang, China) with scanning software Einscan-Pro series V3 (SHINING 3D®, Zhejiang, China). Superimpositions of pre- and post-treatment digital study casts were conducted using Materialise 3-matic Research 12.0 (Materialise N.V., Leuven, Belgium.) software by a two-step technique, the first of which involved point registration. Six points (three on each side) were located within the area of the anterior palate (Figure 2) as described by Vasilakos et al.10 This area is limited anteriorly by the medial two-thirds of the third palatal rugae and laterally by two lines parallel to the midpalatal suture and extending posteriorly 5 mm from the third rugae (Figure 3a). The bilateral central depressions of the greater palatine foramen were used as the posterior reference points. These bilateral landmarks are commonly used for greater palatine local anaesthesia16 and are easily identifiable. Each depression was located at the palatal border of the maxillary tuberosity (Figure 3b) and, in total, eight points were identified. The second step involved global registration that applied an iterative closest point algorithm which was employed to minimise the difference between two clouds of points of the 3D superimpositions. A modified co-ordinate system12 was set on the pre-treatment digital cast and identified by the junction of the incisive papilla and palatine raphe as the origin (0, 0, 0), resulting in an
Pre- and post-treatment digital cephalograms were traced and superimposed on the Sella-Nasion (SN) line registered at Sella using OPAL software (COGSoft OPAL version 2.4, Bristol, United Kingdom). The superimposed images were then printed with the aspect ratio preserved.
The Pancherz sagittal (SO)1 and vertical occlusal (VO)2 analyses were used to measure changes in the sagittal and vertical direction, respectively. The landmarks and reference planes are shown in Figure 4. The respective study cast was used to aid identification of the left molar on the cephalogram. The differences (d) between the pre- and post-treatment landmark positions for each variable were calculated.
Horizontal and vertical dental changes were obtained by applying the following calculations: is/OLp (d) minus sp/OLp (d)—horizontal change in the position of the incisal tip of the most prominent central incisor in relation to the occlusal line perpendicular. ms/OLp (d) minus sp/OLp (d)—horizontal change in the position of the left permanent first molar in relation to the occlusal line perpendicular. is/NL (d)—vertical change in the position of the incisal tip of the most prominent central incisor in relation to the nasal line. msc/NL (d)—vertical change in the position of the left permanent first molar in relation to the nasal line.
Ten sets of maxillary casts and cephalograms were used to assess operator reliability for both methods. A single operator was trained and the first measurements were compared against a second experienced examiner (N.N.Z) for the assessment of inter-operator reliability. The measurements to determine intra-operator reliability were conducted after an interval of 2 weeks.
Data analysis was performed using the Social Package for the Social Sciences (SPSS) version 25. The Shapiro-Wilk test was carried out on all data of the cephalometric and 3D digitised measurements. All of the data were found to be normally distributed. The intra-operator and inter-operator reliability for both methods were assessed using the intraclass correlation coefficient (ICC).
A paired
A repeatability test was performed after an interval of two weeks from the first measurements using ICC (two-way mixed effects model with absolute agreement) and the paired
The intra-operator and inter-operator ICC values, for measurements using the cephalogram, had excellent agreements of 0.92 and 0.97, respectively. For measurements using the 3D cast method, the intra-operator and inter-operator ICC values had excellent agreement of 0.96.
The paired
Bland-Altman analysis and paired
Paired |
Bland–Altman | |||||||
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Tooth movement | Mean (SD) | Standard Error mean | 95% CI of difference | Mean difference (SD) | Lower Limit | Upper limit | ||
0.41 (1.30) | 0.24 | (-0.07,0.89) | 1.72 (29) | 0.096 | 0.41 (1.30) | -2.14 | 2.95 | |
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-0.51 (1.90) | 0.35 | (-1.21,0.20) | -1.46 (29) | 0.156 | -0.51 (1.90) | -4.23 | 3.22 |
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0.10 (1.54) | 0.28 | (-0.47,0.68) | 0.37 (29) | 0.712 | 0.10 (1.54) | -2.91 | 3.13 |
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0.03 (1.35) | 0.25 | (-0.48,0.53) | 0.11 (29) | 0.916 | 0.03 (1.35) | -2.62 | 2.67 |
Figure 5, illustrating the Bland-Altman plots, generally showed well-distributed differences. In Table I of the Bland–Altman analysis, the 95% limits of agreement were beyond the cutoff points of acceptable clinical difference (greater than 2 mm). The 95% limits of agreement were between -2.14 and 2.69 mm for the horizontal incisal movements and between -4.23 and 3.21 mm for the vertical incisal movements. The 95% limits of agreement were between -2.92 and 3.12 mm for the horizontal molar movements and between -2.62 and 2.68 mm for the vertical molar movements.
The ICC is presented in Table II. Based on the results, the reproducibility of the measurements was good to excellent. The paired
Data analysis for incisor and molar movements measured from 3D models and cephalometric radiographs, each on two separate occasions (in mm).
Intraclass correlation (ICC) | Paired |
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Tooth movement | Measurement method | 95% CI | ICC | Mean (SD) | Standard Error mean | 95% CI of difference | |||
Incisor Horizontal | 3D | (0.88, 0.97) | 0.94 | <0.001 | 0.02 (0.65) | 0.11 | (-0.23,0.26) | 0.13 (29) | 0.90 |
Ceph | (0.67, 0.91) | 0.83 | <0.001 | 0.01 (1.50) | 0.27 | (-0.55,0.57) | 0.05 (29) | 0.96 | |
Incisor Vertical | 3D | (0.89, 0.97) | 0.95 | <0.001 | -0.06 (0.48) | 0.09 | (-0.24,0.12) | -0.68 (29) | 0.50 |
Ceph | (0.69, 0.92) | 0.84 | <0.001 | 0.23 (0.93) | 0.17 | (-0.12,0.58) | 1.33 (29) | 0.19 | |
Molar Horizontal | 3D | (0.89, 0.97) | 0.94 | <0.001 | 0.13 (0.46) | 0.08 | (-0.04,0.30) | 1.56 (29) | 0.13 |
Ceph | (0.63, 0.90) | 0.81 | <0.001 | 0.18 (1.18) | 0.21 | (-0.26,0.62) | 0.82 (29) | 0.42 | |
Molar Vertical | 3D | (0.86, 0.97) | 0.93 | <0.001 | -0.03 (0.33) | 0.60 | (-0.16,0.09) | -0.56 (29) | 0.58 |
Ceph | (0.76, 0.94) | 0.88 | <0.001 | -0.05 (0.87) | 0.16 | (-0.37,0.28) | -0.31 (29) | 0.76 |
Validation measures how well a new method, in this case 3D superimposition using a tripoding method, performs against a criterion method, which is represented by cephalometric superimposition. The measurement of dental and skeletal changes is valuable to determine the effectiveness of an intervention and to assess overall post-treatment outcome. Several authors have suggested that the clinically relevant differences in measuring anchorage loss are in the range of 1.5 mm19 to 2 mm.17 Therefore, it was proposed that a difference of less than 2 mm was an appropriate threshold to indicate a clinically acceptable difference between the conventional cephalometric and an alternative method for measuring tooth movements.
Measuring software using surface-based registration has the advantage of allowing regional superimposition without the need for manually locating landmarks which, in turn, is less time-consuming.8 It was also considered more accurate because there is less variability compared to a point registration-based method.20 Nonetheless, measuring software that depends on a point registration-base can still be used for superimposition provided that the fiducial points or landmarks are valid.
The medial two-thirds of the third rugae and a small distal area have high anatomical form stability and have been established as a structural reference for maxillary arch superimposition. However, few studies have included posterior extensions to the palatal rugae area for superimposition references.6,7,10 Garib et al.15 added lateral and posterior landmarks to those of stable regions to provide roll and pitch controls, respectively. This suggested that the authors had experienced problems with control of the positions of the superimposed casts without the added reference landmarks. Unlike regional-based software, this issue is particularly relevant in point registration-based software used for superimposition.10 However, past studies have used arbitrary margins as posterior references and not from recognisable anatomical landmarks. The replication of the arbitrary posterior extensions using point registration-based software is subjective and susceptible to errors because there is no specific landmark that can be identified within the recommended distance of the posterior extension to the midpalatal suture.15
The current study introduced a tripoding method using recognisable anatomical landmarks as references for point registration-based software to superimpose digitised maxillary dental casts. It is recommended that posterior reference points are added to avoid cast rotation in the sagittal plane (pitch) during the superimposition. By using three distanced co-ordinates, this method would concurrently allow for control of roll and yaw during superimposition. The current study found that the method showed no significant differences in the conducted measurements when compared to measurements of dental movements based on cephalograms. The method was also found to be reproducible. Therefore, it is a valid process to measure dental changes using 3D casts but the system is currently only applicable to the maxilla because stable references in the mandible, such as the chin, symphysis and the mental foramen, cannot be clinically identified by a 3D surface scanner and require CBCT imaging. Future studies are recommended to compare the validity of measuring orthodontic tooth movement using a 3D method that applied these reference landmarks to cephalograms.14,21
In the present study, the mean differences between both methods for incisal and molar movements were very small, being less than 0.51 mm. The paired
The ICC and paired
There are several limitations related to the present study. The pre- and post-treatment casts were of non-growing subjects less than 5 years apart, which was considered a stable interval to account for palatal rugae changes.15 Although the palatal rugae structures are considered stable, they are also subject to change over a long period, and therefore need to be carefully considered when comparing study casts of more than five years.6,15 Furthermore, although the bilateral depressions of the greater palatine foramen13 can be clinically identified and are reliably used for local anaesthesia blocks, there are no published studies on the stability of these foramen. Therefore, it is recommended that future studies investigate the stability of these posterior landmarks.
The tripoding method using the medial two-thirds of the third palatal rugae, and the bilateral depressions of the greater palatine foramen is a valid and reliable method to superimpose maxillary study casts for measuring incisor and molar orthodontic movements but is not interchangeable with the Pancherz cephalometric analysis.
The authors declare that there is no conflict of interest.