A novel method for superimposition and measurements on maxillary digital 3D models—studies on validity and reliability

A novel method for superimposition and measurements on maxillary digital 3D models—studies on... Summary Background Serial 3D models can be used to analyze changes, but correct superimposition is crucial before measurements can be assessed. Earlier studies show that every palatal structure changes due to growth or treatment. Here, we describe a new method that uses an algorithm-based analysis to perform superimpositions and measurements in maxillary 3D models. This method can be used to identify deformations. In a second step, only unchanged areas are used for superimposition. Objectives This study investigates the validity and reliability of this novel method. Methods Digital 3D models from 16 cases were modified by an independent 3D engineer to simulate space closure and growth. True values for tooth movements were available as reference. Measurements and repeated measurements were performed by four observers. Results The total tooth movement had an absolute mean error of 0.0225 mm (SD 0.03). The intraclass correlation coefficient (ICC) was 0.9996. Rotational measurements had an absolute mean error of 0.0291 degrees (SD 0.04 degrees) and an ICC of 0.9999. Limitations Serial models need to be taken with a moderate interval (1 to 2 years). Obvious changed areas in the palate need to be cropped before processing the models. Conclusion The tested method is valid and reliable with excellent accuracy and precision even when changes through growth or orthodontic treatment occur. Introduction Traditionally, orthodontists have used lateral cephalograms and study casts to establish diagnoses and to develop treatment plans. Changes as the result of growth or treatment are commonly evaluated through superimposition in order to describe what changes have taken place between the two registrations (1, 2). When superimposition is made on study casts, the palatal rugae have been used as references (3). Study casts, however, are rapidly being replaced by digital 3D-models, a technique that has proven to be valid and reproducible for linear measurements such as overjet, overbite, arch width, and tooth width (4–8). Consequently, measurements on digital 3D models are generally considered comparable to measurements using study casts, making 3D models a viable replacement for traditional study casts (9). As with any superimposition, stable anatomical structures are required as references. Because the medial points of the third palatal rugae were found to be stable enough in untreated patients and in patients treated with premolar extractions and en masse retraction (10), the palatal rugae have been used as reference landmarks even for the first attempts to superimpose 3D models. This principle of manually selecting a few corresponding points giving a rough initial alignment is called ‘coarse’ or ‘raw matching’ (11). Although raw matching is used in most software packages for orthodontic treatment planning and analysis, the manual selection and measurement of matchings can be a source of error. The next generation of superimposition approaches used the palatal vault or parts of it as a reference by using a best-fit method (12–15). This technique of ‘fine matching’ uses thousands of reference points instead of a few landmarks and is based on ‘iterative closest point algorithms’ (ICP) (16). The effect of outliers is reduced while accuracy and reliability markedly improves for superimposition of serial 3D models. A five-year follow-up study found that even the position of the third rugae is changed slightly in the vertical plane, a finding that was true for both adolescents and adults due to growth and remodelling (17). Moreover, a trial in patients treated with rapid maxillary expansion and maxillary protraction headgear reported significant changes in the vertical plane due to orthodontic treatment (18). In addition, it has been shown that palatal height changes several millimetres due to growth in adolescents (19, 20). Therefore, it remains unclear whether parts of the palatal vault can be considered stable enough to be used as a reference landmark for superimposition. There is evidence that in adolescents the palatal vault changes in the sagittal, transversal, and vertical planes, so there is no anatomical structure that in general can be considered stable. However, this instability does not mean that there are no structures at all that can be used for superimposition. Computer programs detect morphological changes in a series of models. By using this ‘deformation analysis’, all structures that have changed can be filtered out, leaving only unchanged structures for superimposition. Through several series of test-measurements, we found that the best results came from a combination of ‘raw matching’, ‘fine matching’, and ‘deformation analysis’. This novel method, that we call RFD-superimposition, can handle variations in local point resolution, can differentiate outliers from morphological changes, and can use several techniques for sample size reduction. We hypothesized that RFD-superimposition introduces minimal measurement error. The aim of this study was to analyse the validity and reliability of measurements on serial 3D models that use the RFD-superimposition method. Material and Methods Materials Sample size requirements were determined based on data from Choi et al.(12); they reported standard deviations between 0.12 and 0.2 mm for the mean differences between digital and manual point-to-point measurements. Assuming the within-case standard deviation to be within that range and the between-case standard deviation to be approximately 0.75 mm, based on clinical experiences within the research group, the value of the intraclass correlation coefficient (ICC) lies between 0.93 and 0.96. A power analysis using the programming language ‘R’ (21) and the ‘ICC.Sample.Size’ package (22) showed that including 16 cases would give 80% power with an anticipated ICC of 0.95 when testing the null hypothesis that the ICC is equal to 0.80. A list of 16 randomly selected cases was generated using ‘R’. These cases were derived from a randomized controlled trial on anchorage (23). Ethical approval was obtained from the Uppsala University′s ethics committee. All patients and their parents gave written informed consent. Study casts of these 16 cases were fabricated from alginate impressions at the in-clinic laboratory within 24 hours. These casts were then digitalized with a R700 desktop scanner (3Shape, Copenhagen, Denmark). The 3Shape system has been validated in earlier studies (24, 25). The 16 digital models served as start models. Specimen To simulate an orthodontic treatment and growth, the 16 start models were modified by an independent 3D engineer. This modification was used to simulate space closure after extraction of the first premolars. Since tooth movements were performed artificially, the true value for translation and rotation of the right maxillary first molar (tooth 16) could be used as a reference. The palatal vault was then changed morphologically to simulate growth and to challenge the matching process. Superimposition The RFD-superimposition is based on a series of matchings. A matching places one object on top of another object using as many corresponding points as possible from both objects. To improve the accuracy, the matching process is repeated several times. For every repetition, the starting position is improved although matching two different objects cannot result in 100% congruence. Therefore, the matching result does not improve after a certain number of repetitions. Since every repetition needs time for calculation, it is crucial to choose a balanced number of repetitions: As many times as necessary, as few times as possible. The same principle applies for the number of points included in the calculation. The part of the palate that was included in the matching process contains about 11000 points. If deformation analysis is performed for each point, the calculation will take hours and the influence of outliers will increase. By reducing the number of points included, calculation times are shortened and outliers are excluded. The number of repetitions and points mentioned in the following description was found suitable in the test series. When matching two objects, one of the objects has a fixed position and it is called the ‘master object’; the other object (the object to be superimposed) is called the ‘slave object’. Superimposition of maxillary 3D models was accomplished in three steps: raw matching, fine matching, and deformation analysis. Raw matching Since the median point of the third rugae was considered most stable, the superimposition started with a coarse positioning of the models according to six corresponding points in this area (Figure 1). The corresponding points were individually selected for every case. The selection was based on clear and characteristic surfaces that could be found in both models. Figure 1. View largeDownload slide Palatal vault of start (blue, master model) and specimen (red, slave model) with corresponding reference points. Figure 1. View largeDownload slide Palatal vault of start (blue, master model) and specimen (red, slave model) with corresponding reference points. Fine matching The fine matching, performed using Final Surface® software, uses a point to triangle best fit method, a technique that is less sensitive to variations in the local point resolution. To minimize the effect of outliers, the maximum number of reference points was limited to 1000. From these 1000 reference points, the best 900 of these were used for the matching. Beyond this, the convergence method was used – i.e., the fine matching was repeated until a certain level of agreement between the matching objects was reached. The level of agreement was defined as 0.000001 mm. The maximum number of repetitions was 50. Deformation analysis with the ICProx algorithm An algorithm is a predefined set of operations. The main task of the ‘Iterative closest proximity algorithm’ (ICProx) is to detect deformations (26). Deformations can generally be detected by associating corresponding points from master to slave model. The ICProx algorithm puts a grid of regularly distributed points onto the master model. After these so-called candidate points are estimated, the median distances between the candidates and their adjacent points are calculated. Next, a surface with a radius of this distance is created that surrounds every candidate point. For the slave model, candidate points are estimated in the same way. Every candidate point from the slave model has a corresponding surface on the master model. This point-to-surface approach gives the algorithm a robust tolerance against point resolution variations since the corresponding point is matched somewhere on the surface and not exactly on the corresponding candidate. Deformations are then detected by applying an octree cell structure onto the model. Octrees are used to subdivide 3D space into cubes. A grid of cubes with an edge length of 0.5 mm was put into the model and the algorithm identified one candidate point per cube. The candidate points were then filtered by merging cubes into cells with 1.5 mm edge lengths (Figure 2). Cells where the distances between the candidate surface and the corresponding point exceed a certain threshold are understood as containing morphological changes and are excluded from the following matching. Figure 2. View largeDownload slide Palatal vault after deformation analysis. Used reference points are marked red. The 3D grid consisting of filter cubes is shown in light grey. Figure 2. View largeDownload slide Palatal vault after deformation analysis. Used reference points are marked red. The 3D grid consisting of filter cubes is shown in light grey. This three-step process is repeated 15 times to minimize the distance between the corresponding points and surfaces. The final result of the superimposition is shown in Figure 3. The ICProx algorithm was originally developed in order to monitor morphological changes in terrestrial laser scans (26). With this algorithm point clouds with large inherent deformation zones can be matched (27). RFD-superimposition is the result of an interdisciplinary approach to transfer this knowledge to the dental field. The ICProx (iterative closest proximity) algorithm is not to be confused with ICP (iterative closest point) algorithms. ICP algorithms match corresponding points from two objects. The ICP fails to conduct a correct superimposition as soon as the two objects differ too much in their morphology. Best-fit methods are usually based on ICP algorithms. Figure 3. View largeDownload slide Distance analysis with true values showing an unchanged area (white coloured) in the centre of the palatal vault. Figure 3. View largeDownload slide Distance analysis with true values showing an unchanged area (white coloured) in the centre of the palatal vault. Measurements Four senior consultant orthodontists independently conducted the superimpositions followed by the measurements. Repeated superimpositions and measurements were performed by all four observers after at least two weeks. The observers were blinded to the true value until the repeated measurements were completed. After the initial exercise program, measurements could be performed within ten minutes per case. 3D-model analysis All 3D models were imported as. stl-files into the Final Surface® software including the DefoScan++ Plugin (v 6.0.2, Society for the Promotion of Applied Computer Science, Berlin, Germany). Superimposition and measurement are presented in ‘Supp1–InstructionVideo.mov’ and were performed as follows (the start model is the master and the specimen is the slave): Cropping of the palatal vault: In a first step, both the start and the specimen model were cloned. The clones were named ‘start palatum’ and ‘specimen palatum’. All areas known to be unstable were removed leaving the palatal vault from distal of the second premolar to the papilla incisiva. Raw matching through six individually chosen corresponding points near the median point of the third rugae. Fine matching with up to 50 iterations. Deformation analysis and superimposition with the DefoScan ++ Plugin with 15 iterations. Collector parameter was set to octree cell size 0.5 mm edge length and filter parameter to octree cell size 1.5 mm edge length. Superimposition of the uncropped models was performed by loading the transformation matrix of ‘specimen palatum’ into the ‘specimen’ model, transferring the result of the RFD-Superimposition of the palatal vault to the original models. Measurements were then executed as follows: The superimposed models ‘start’ and ‘specimen’ were cloned. The clones were named ‘start 16’ and ‘specimen 16’. Then the occlusal surfaces of the right maxillary first molar in both models were selected and cropped. The weight centres were centralised and the position of ‘start 16’ was measured (PreTX x-, y-, z-coordinates). ‘Start 16’ was then cloned again and named ‘start 16a’. This new clone was moved towards the position of ‘specimen 16’. This was done through an initial raw matching followed by repeated fine matchings until the number of iterations was fewer than ten. The position and rotation angles of the occlusal surface 16 were measured. The position of the two objects ‘start 16’ and ‘start 16a’ are shown in Figure 4. Figure 4. View largeDownload slide Pre- and post-treatment position of tooth 16′s occlusal surface. Figure 4. View largeDownload slide Pre- and post-treatment position of tooth 16′s occlusal surface. Variables Tooth movement was calculated by subtracting the PreTX coordinates from the PostTX coordinates, giving a translation for x (transversal), y (mesio-distal), and z (vertical). The total movement, d, was calculated as d=(x2+y2+z2). In addition to translation, the rotation was measured. Measurements of tooth 16 were separated into rotations around the three principal axes. Statistics For the purpose of examining the relationship between measured total movement and true total movement, a mixed effects model was fitted with ‘measured total movement’ as the dependent variable, ‘true total movement’ as a fixed covariate, and ‘cases’ and ‘observer’ as random factors. A variance components structure was used in the model. The mixed model can be explained as a simple linear regression model of the relationship between measured and true total movement, but this also accounts for dependence between observations made on the same case and by the same observer. As a measure of relative reliability, ICCs were estimated for the following variables: ‘total movement; x-, y-, z-translations’; and ‘x-, y-, z-rotations’. Random effects models were estimated with each of these as a dependent variable and ‘case’ and ‘observer’ as random effects. The ICCs were estimated as follows: σ2bs/ (σ2bs + σ2bo + σ2e), where σ2bs is the between-cases variance component, σ2bo is the inter-observer variance component, and σ2e is the residual variance of the model. This ICC estimates the correlation between two repeated measurements on the same case performed by the same observer. Confidence intervals (CI) with 95 % confidence levels for the ICCs were estimated using parametric bootstrapping with 2000 iterations. The R-Code that was used for statistical analysis can be found in ‘Supp2-RCode.R’. The raw data is presented in ‘Supp3–RawData.csv’. Results The differences between ‘measured total movements’ and ‘true total movements’ are presented in Figure 5. The mean absolute error for ‘total movement’ was 0.0225 mm (SD 0.03 mm). The arithmetic mean error was -0.0017 mm. The range of total movements was from -0.07 mm to 0.08 mm. The ICC for measured total movement was 0.9996. Figure 6 shows the measured total movements plotted against the corresponding true total movements. Thus, the distribution of the measurements is generally very close to the line of identity. This indicates that this technique is as accurate for measuring small distances as it is for measuring longer distances. Figure 5. View largeDownload slide Differences between measured total movements and true total movements. Each of the four observers is represented by a unique colour. Figure 5. View largeDownload slide Differences between measured total movements and true total movements. Each of the four observers is represented by a unique colour. Figure 6. View largeDownload slide Measured total movement versus True total movement. Figure 6. View largeDownload slide Measured total movement versus True total movement. Estimated parameters from the mixed model, describing the relationship between measured and true total movement, are presented in Table 1. The intercept (−0.007) and the slope for the true movement (1.003) were very close to the line of identity (intercept = 0, slope = 1), indicating that any systematic errors of the measurements were very small. Random measurement errors (i.e. the variability of the random effects) were dominated by the residual error (56.9% of total variance), variability due to cases (32.4%), and variability due to observer (13.7%). However, the random measurement errors were also small; the standard deviation of the random effects due to cases, observer, and residuals were 0.0177 mm, 0.0115 mm, and 0.0229 mm, respectively. Table 1. Estimated parameters for total tooth movement of the mixed model. Fixed effect  Estimate  Standard error   Intercept  −0.007  0.01   True value (slope)  1.003  <0.01  Random effect  Variance  Standard deviation   Cases  0.0003142  0.018   Observer  0.0001327  0.012   Residual error  0.0005228  0.023  Total variability  0.0009697  0.031  Fixed effect  Estimate  Standard error   Intercept  −0.007  0.01   True value (slope)  1.003  <0.01  Random effect  Variance  Standard deviation   Cases  0.0003142  0.018   Observer  0.0001327  0.012   Residual error  0.0005228  0.023  Total variability  0.0009697  0.031  View Large The results of translational and rotational measurements are presented in detail in Table 2. Table 2. Mean absolute errors, arithmetic mean errors, range of errors, and ICC with estimated 95% CI.   Abs mean error  Mean error  Range  ICC (95% CI)  Total tooth movement [mm]  0.0225 (SD 0.03)  −0.0017  −0.07 to 0.08  0.9996 (0.9990, 0.9998)  Translation [mm]   X (mesio-distal)  0.0152 (SD 0.02)  −0.0049  −0.06 to 0.09  0.9994 (0.9985, 0.9997)   Y (transversal)  0.0208 (SD 0.03)  −0.0033  −0.09 to 0.06  0.9996 (0.9991, 0.9998)   Z (vertical)  0.0240 (SD 0.04)  0.0020  −0.21 to 0.15  0.9902 (0.9762, 0.9951)  Rotation [degree]   X (disto-mesial tipping)  0.0291 (SD 0.04)  −0.0241  −0.35 to 0.11  0.9999 (0.9998, 1.0000)   Y (buccal-palatal tilting)  0.0134 (SD 0.02)  0.0021  −0.13 to 0.06  0.9999 (0.9999, 1.0000)   Z (around the tooth axis)  0.0215 (SD 0.03)  0.0098  −0.12 to 0.13  0.9999 (0.9999, 1.0000)    Abs mean error  Mean error  Range  ICC (95% CI)  Total tooth movement [mm]  0.0225 (SD 0.03)  −0.0017  −0.07 to 0.08  0.9996 (0.9990, 0.9998)  Translation [mm]   X (mesio-distal)  0.0152 (SD 0.02)  −0.0049  −0.06 to 0.09  0.9994 (0.9985, 0.9997)   Y (transversal)  0.0208 (SD 0.03)  −0.0033  −0.09 to 0.06  0.9996 (0.9991, 0.9998)   Z (vertical)  0.0240 (SD 0.04)  0.0020  −0.21 to 0.15  0.9902 (0.9762, 0.9951)  Rotation [degree]   X (disto-mesial tipping)  0.0291 (SD 0.04)  −0.0241  −0.35 to 0.11  0.9999 (0.9998, 1.0000)   Y (buccal-palatal tilting)  0.0134 (SD 0.02)  0.0021  −0.13 to 0.06  0.9999 (0.9999, 1.0000)   Z (around the tooth axis)  0.0215 (SD 0.03)  0.0098  −0.12 to 0.13  0.9999 (0.9999, 1.0000)  View Large Model diagnostics were performed using various graphs of residuals and fitted values. QQ-plots of the residuals showed somewhat heavy tails for some of the mixed effects models but were considered to be within the limit of what could be acceptable. More details can be found in the supplementary material. Discussion The combination of raw matching, fine matching, and deformation analysis (RFD) superimposition delivers accuracy and precision in a dimension far beyond measurements on cephalometric X-rays, plaster casts, or 3D models with point-to-point measurements. The RFD superimposition delivers results that describe tooth movements not only as translation but also in terms of tipping, tilting, and rotation. This technique takes measurements by matching objects rather than by manually selecting measurement points. The identification of points is difficult and has been reported as a source of error (28, 29). Nalcaci et al., comparing manual point measurements of molar distalization on cephalometric X-rays, photographs, and 3D models, found a standard deviation of about 1.3 mm for all three techniques (30). No statistical significant difference was found. Therefore, it can be assumed that this new technique can eliminate the error associated with manual selection of measurement points. Although earlier validation studies have analysed different techniques for superimposition and reported measurements with high accuracy and precision, these studies compared measurements on digital 3D models with measurements on plaster casts or on lateral cephalograms (12, 15, 18). Hoggan et al., comparing measurements on plaster casts with cephalometric X-rays, found no statistically significant differences in measurements of movement of the maxillary first molar, but they did find that the standard deviation for measurements on plaster casts was between 1.6 and 2.1 mm and on cephalometric X-rays it was 2.0 mm (3). Because RFD-Superimposition has a standard deviation of 0.03 mm, it can be assumed that these techniques, although widely used, suffer from more measurement errors than measurements gathered from digital 3D models. Therefore, these techniques may no longer be considered the gold standard. Chen et al., using unloaded miniscrews as reference points, conducted measurements on 15 adult patients (13). Although unloaded miniscrews are regarded as stable in this study, they reported changes in miniscrew positions of up to 0.5 mm. This movement indicates that miniscrews might not be suitable as a reference for a technique with minimal measurement errors. Thiruvenkatachari et al. actually used a setup where the true values for translation were used as reference (14). This study was a source of inspiration for our current work. The use of specimen is an elegant way to avoid a situation where measurements assessed with a new technique have to be compared to another technique that obviously has more measurement error. However, in their study both master and slave models were identical in the palate. Technically, this validation matched identical surfaces. It would have been surprising if the matching process had failed. Moreover, their study did not measure rotational movement. Unlike earlier studies, our study used true values as reference and the master and slave model did not have identical surfaces in the palate (12–14, 18, 30). Consequently, our results showed that our new technique was robust for changes in the palate, implying that this new method can be used in growing patients subjected to orthodontic treatment. The measurements were performed by senior consultant orthodontists with different computer skills. After thorough instruction, any orthodontist would be capable of performing these measurements. The time needed per case (10 minutes) was comparable or even shorter for the time needed and duration to carry out, for example, tracing and superimposition of cephalometric X-rays. If the RFD superimposition is applied, the lateral head radiographs are not needed for evaluation of tooth movements. That is, an added benefit of the technique is that patients are not exposed to X-ray radiation. Limitations Despite the impressive accuracy and precision of the assessed RFD superimposition found in this study, there are three important circumstances to note: First, there has to be at least some structure that in fact is unchanged. Since differences correlate with time, it is important to keep the interval between the two registrations short enough. In adolescents, an interval of one to two years is appropriate. Second, one basic assumption in the workflow of this technique is that the area surrounding the median point of the third rugae is somehow stable (10, 18). Use of this area during the raw-matching is therefore crucial. Impression or scanning errors could give an inaccurate 3D model. Local swelling of the gingiva after treatment with, for example, a Nance-appliance or palatal miniscrews could generate an inaccurate 3D model. Therefore, areas that obviously have been changed need to be cropped before the superimposition process is started. Third, sometimes growth or treatments like rapid maxillary expansion follow an asymmetric pattern. This asymmetry needs to be taken into account when corresponding points are picked during the raw-matching. Thus, for raw-matching one would only use the median point of the third ruga on the non-effected side. It is important that this technique has to be used under the conditions discussed above. The algorithm will always process the models that are put in. If there is an asymmetry or other abnormal growth pattern that is visible to the naked eye, one has to check whether the result of the superimposition is feasible or reasonable. The morphological changes caused by growth and treatment are very complex. Therefore, this technique is far from a one-click-solution and it is performed in specialised 3D software. Consequently, for correct RFD superimposition it can be advisable to involve serial models taken with a moderate interval (1 to 2 years), to remove obvious changed areas in the palate, and to consider clinical information about asymmetric treatment effects. We believe that deformation analysis will be a key-element in future superimposition-techniques. There may be several algorithms that could do the trick. However, these algorithms will probably be more complex than a simple best-fit method. Conclusions The novel RFD-Superimposition method is a valid and reliable tool for measuring tooth movements in the maxilla. This method can tolerate morphological changes in the palate and gives excellent precision and accuracy. In addition, this method is robust for variances in the local point resolution and may also be used in growing subjects who undergo orthodontic treatment. Supplementary material Supplementary data are available at European Journal of Orthodontics online. Conflict of interest All authors have completed the ICMJE Conflict of Interest Disclosure form and declare the following: Niels Ganzer reports grants and nonfinancial support from the Centre for Research and Development, Uppsala University/Region Gävleborg, Sweden, and grants from the Swedish Dental Associations Scientific Funds during the conduct of the study; Ingalill Feldmann reports grants from the Thuréus Foundation for the Promotion of Dental Science, Uppsala University, Sweden, during the conduct of the study. The funding sources had no influence on study design, collection, analysis, or interpretation of the data, writing the article, or in the decision to submit the article for publication. There are no financial relationships with any organizations that might have interests in the submitted work in the previous three years. There are no other relationships or activities that could appear to have influenced the submitted work. 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Google Scholar CrossRef Search ADS PubMed  © The Author(s) 2017. Published by Oxford University Press on behalf of the European Orthodontic Society. All rights reserved. For permissions, please email: journals.permissions@oup.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The European Journal of Orthodontics Oxford University Press

A novel method for superimposition and measurements on maxillary digital 3D models—studies on validity and reliability

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Abstract

Summary Background Serial 3D models can be used to analyze changes, but correct superimposition is crucial before measurements can be assessed. Earlier studies show that every palatal structure changes due to growth or treatment. Here, we describe a new method that uses an algorithm-based analysis to perform superimpositions and measurements in maxillary 3D models. This method can be used to identify deformations. In a second step, only unchanged areas are used for superimposition. Objectives This study investigates the validity and reliability of this novel method. Methods Digital 3D models from 16 cases were modified by an independent 3D engineer to simulate space closure and growth. True values for tooth movements were available as reference. Measurements and repeated measurements were performed by four observers. Results The total tooth movement had an absolute mean error of 0.0225 mm (SD 0.03). The intraclass correlation coefficient (ICC) was 0.9996. Rotational measurements had an absolute mean error of 0.0291 degrees (SD 0.04 degrees) and an ICC of 0.9999. Limitations Serial models need to be taken with a moderate interval (1 to 2 years). Obvious changed areas in the palate need to be cropped before processing the models. Conclusion The tested method is valid and reliable with excellent accuracy and precision even when changes through growth or orthodontic treatment occur. Introduction Traditionally, orthodontists have used lateral cephalograms and study casts to establish diagnoses and to develop treatment plans. Changes as the result of growth or treatment are commonly evaluated through superimposition in order to describe what changes have taken place between the two registrations (1, 2). When superimposition is made on study casts, the palatal rugae have been used as references (3). Study casts, however, are rapidly being replaced by digital 3D-models, a technique that has proven to be valid and reproducible for linear measurements such as overjet, overbite, arch width, and tooth width (4–8). Consequently, measurements on digital 3D models are generally considered comparable to measurements using study casts, making 3D models a viable replacement for traditional study casts (9). As with any superimposition, stable anatomical structures are required as references. Because the medial points of the third palatal rugae were found to be stable enough in untreated patients and in patients treated with premolar extractions and en masse retraction (10), the palatal rugae have been used as reference landmarks even for the first attempts to superimpose 3D models. This principle of manually selecting a few corresponding points giving a rough initial alignment is called ‘coarse’ or ‘raw matching’ (11). Although raw matching is used in most software packages for orthodontic treatment planning and analysis, the manual selection and measurement of matchings can be a source of error. The next generation of superimposition approaches used the palatal vault or parts of it as a reference by using a best-fit method (12–15). This technique of ‘fine matching’ uses thousands of reference points instead of a few landmarks and is based on ‘iterative closest point algorithms’ (ICP) (16). The effect of outliers is reduced while accuracy and reliability markedly improves for superimposition of serial 3D models. A five-year follow-up study found that even the position of the third rugae is changed slightly in the vertical plane, a finding that was true for both adolescents and adults due to growth and remodelling (17). Moreover, a trial in patients treated with rapid maxillary expansion and maxillary protraction headgear reported significant changes in the vertical plane due to orthodontic treatment (18). In addition, it has been shown that palatal height changes several millimetres due to growth in adolescents (19, 20). Therefore, it remains unclear whether parts of the palatal vault can be considered stable enough to be used as a reference landmark for superimposition. There is evidence that in adolescents the palatal vault changes in the sagittal, transversal, and vertical planes, so there is no anatomical structure that in general can be considered stable. However, this instability does not mean that there are no structures at all that can be used for superimposition. Computer programs detect morphological changes in a series of models. By using this ‘deformation analysis’, all structures that have changed can be filtered out, leaving only unchanged structures for superimposition. Through several series of test-measurements, we found that the best results came from a combination of ‘raw matching’, ‘fine matching’, and ‘deformation analysis’. This novel method, that we call RFD-superimposition, can handle variations in local point resolution, can differentiate outliers from morphological changes, and can use several techniques for sample size reduction. We hypothesized that RFD-superimposition introduces minimal measurement error. The aim of this study was to analyse the validity and reliability of measurements on serial 3D models that use the RFD-superimposition method. Material and Methods Materials Sample size requirements were determined based on data from Choi et al.(12); they reported standard deviations between 0.12 and 0.2 mm for the mean differences between digital and manual point-to-point measurements. Assuming the within-case standard deviation to be within that range and the between-case standard deviation to be approximately 0.75 mm, based on clinical experiences within the research group, the value of the intraclass correlation coefficient (ICC) lies between 0.93 and 0.96. A power analysis using the programming language ‘R’ (21) and the ‘ICC.Sample.Size’ package (22) showed that including 16 cases would give 80% power with an anticipated ICC of 0.95 when testing the null hypothesis that the ICC is equal to 0.80. A list of 16 randomly selected cases was generated using ‘R’. These cases were derived from a randomized controlled trial on anchorage (23). Ethical approval was obtained from the Uppsala University′s ethics committee. All patients and their parents gave written informed consent. Study casts of these 16 cases were fabricated from alginate impressions at the in-clinic laboratory within 24 hours. These casts were then digitalized with a R700 desktop scanner (3Shape, Copenhagen, Denmark). The 3Shape system has been validated in earlier studies (24, 25). The 16 digital models served as start models. Specimen To simulate an orthodontic treatment and growth, the 16 start models were modified by an independent 3D engineer. This modification was used to simulate space closure after extraction of the first premolars. Since tooth movements were performed artificially, the true value for translation and rotation of the right maxillary first molar (tooth 16) could be used as a reference. The palatal vault was then changed morphologically to simulate growth and to challenge the matching process. Superimposition The RFD-superimposition is based on a series of matchings. A matching places one object on top of another object using as many corresponding points as possible from both objects. To improve the accuracy, the matching process is repeated several times. For every repetition, the starting position is improved although matching two different objects cannot result in 100% congruence. Therefore, the matching result does not improve after a certain number of repetitions. Since every repetition needs time for calculation, it is crucial to choose a balanced number of repetitions: As many times as necessary, as few times as possible. The same principle applies for the number of points included in the calculation. The part of the palate that was included in the matching process contains about 11000 points. If deformation analysis is performed for each point, the calculation will take hours and the influence of outliers will increase. By reducing the number of points included, calculation times are shortened and outliers are excluded. The number of repetitions and points mentioned in the following description was found suitable in the test series. When matching two objects, one of the objects has a fixed position and it is called the ‘master object’; the other object (the object to be superimposed) is called the ‘slave object’. Superimposition of maxillary 3D models was accomplished in three steps: raw matching, fine matching, and deformation analysis. Raw matching Since the median point of the third rugae was considered most stable, the superimposition started with a coarse positioning of the models according to six corresponding points in this area (Figure 1). The corresponding points were individually selected for every case. The selection was based on clear and characteristic surfaces that could be found in both models. Figure 1. View largeDownload slide Palatal vault of start (blue, master model) and specimen (red, slave model) with corresponding reference points. Figure 1. View largeDownload slide Palatal vault of start (blue, master model) and specimen (red, slave model) with corresponding reference points. Fine matching The fine matching, performed using Final Surface® software, uses a point to triangle best fit method, a technique that is less sensitive to variations in the local point resolution. To minimize the effect of outliers, the maximum number of reference points was limited to 1000. From these 1000 reference points, the best 900 of these were used for the matching. Beyond this, the convergence method was used – i.e., the fine matching was repeated until a certain level of agreement between the matching objects was reached. The level of agreement was defined as 0.000001 mm. The maximum number of repetitions was 50. Deformation analysis with the ICProx algorithm An algorithm is a predefined set of operations. The main task of the ‘Iterative closest proximity algorithm’ (ICProx) is to detect deformations (26). Deformations can generally be detected by associating corresponding points from master to slave model. The ICProx algorithm puts a grid of regularly distributed points onto the master model. After these so-called candidate points are estimated, the median distances between the candidates and their adjacent points are calculated. Next, a surface with a radius of this distance is created that surrounds every candidate point. For the slave model, candidate points are estimated in the same way. Every candidate point from the slave model has a corresponding surface on the master model. This point-to-surface approach gives the algorithm a robust tolerance against point resolution variations since the corresponding point is matched somewhere on the surface and not exactly on the corresponding candidate. Deformations are then detected by applying an octree cell structure onto the model. Octrees are used to subdivide 3D space into cubes. A grid of cubes with an edge length of 0.5 mm was put into the model and the algorithm identified one candidate point per cube. The candidate points were then filtered by merging cubes into cells with 1.5 mm edge lengths (Figure 2). Cells where the distances between the candidate surface and the corresponding point exceed a certain threshold are understood as containing morphological changes and are excluded from the following matching. Figure 2. View largeDownload slide Palatal vault after deformation analysis. Used reference points are marked red. The 3D grid consisting of filter cubes is shown in light grey. Figure 2. View largeDownload slide Palatal vault after deformation analysis. Used reference points are marked red. The 3D grid consisting of filter cubes is shown in light grey. This three-step process is repeated 15 times to minimize the distance between the corresponding points and surfaces. The final result of the superimposition is shown in Figure 3. The ICProx algorithm was originally developed in order to monitor morphological changes in terrestrial laser scans (26). With this algorithm point clouds with large inherent deformation zones can be matched (27). RFD-superimposition is the result of an interdisciplinary approach to transfer this knowledge to the dental field. The ICProx (iterative closest proximity) algorithm is not to be confused with ICP (iterative closest point) algorithms. ICP algorithms match corresponding points from two objects. The ICP fails to conduct a correct superimposition as soon as the two objects differ too much in their morphology. Best-fit methods are usually based on ICP algorithms. Figure 3. View largeDownload slide Distance analysis with true values showing an unchanged area (white coloured) in the centre of the palatal vault. Figure 3. View largeDownload slide Distance analysis with true values showing an unchanged area (white coloured) in the centre of the palatal vault. Measurements Four senior consultant orthodontists independently conducted the superimpositions followed by the measurements. Repeated superimpositions and measurements were performed by all four observers after at least two weeks. The observers were blinded to the true value until the repeated measurements were completed. After the initial exercise program, measurements could be performed within ten minutes per case. 3D-model analysis All 3D models were imported as. stl-files into the Final Surface® software including the DefoScan++ Plugin (v 6.0.2, Society for the Promotion of Applied Computer Science, Berlin, Germany). Superimposition and measurement are presented in ‘Supp1–InstructionVideo.mov’ and were performed as follows (the start model is the master and the specimen is the slave): Cropping of the palatal vault: In a first step, both the start and the specimen model were cloned. The clones were named ‘start palatum’ and ‘specimen palatum’. All areas known to be unstable were removed leaving the palatal vault from distal of the second premolar to the papilla incisiva. Raw matching through six individually chosen corresponding points near the median point of the third rugae. Fine matching with up to 50 iterations. Deformation analysis and superimposition with the DefoScan ++ Plugin with 15 iterations. Collector parameter was set to octree cell size 0.5 mm edge length and filter parameter to octree cell size 1.5 mm edge length. Superimposition of the uncropped models was performed by loading the transformation matrix of ‘specimen palatum’ into the ‘specimen’ model, transferring the result of the RFD-Superimposition of the palatal vault to the original models. Measurements were then executed as follows: The superimposed models ‘start’ and ‘specimen’ were cloned. The clones were named ‘start 16’ and ‘specimen 16’. Then the occlusal surfaces of the right maxillary first molar in both models were selected and cropped. The weight centres were centralised and the position of ‘start 16’ was measured (PreTX x-, y-, z-coordinates). ‘Start 16’ was then cloned again and named ‘start 16a’. This new clone was moved towards the position of ‘specimen 16’. This was done through an initial raw matching followed by repeated fine matchings until the number of iterations was fewer than ten. The position and rotation angles of the occlusal surface 16 were measured. The position of the two objects ‘start 16’ and ‘start 16a’ are shown in Figure 4. Figure 4. View largeDownload slide Pre- and post-treatment position of tooth 16′s occlusal surface. Figure 4. View largeDownload slide Pre- and post-treatment position of tooth 16′s occlusal surface. Variables Tooth movement was calculated by subtracting the PreTX coordinates from the PostTX coordinates, giving a translation for x (transversal), y (mesio-distal), and z (vertical). The total movement, d, was calculated as d=(x2+y2+z2). In addition to translation, the rotation was measured. Measurements of tooth 16 were separated into rotations around the three principal axes. Statistics For the purpose of examining the relationship between measured total movement and true total movement, a mixed effects model was fitted with ‘measured total movement’ as the dependent variable, ‘true total movement’ as a fixed covariate, and ‘cases’ and ‘observer’ as random factors. A variance components structure was used in the model. The mixed model can be explained as a simple linear regression model of the relationship between measured and true total movement, but this also accounts for dependence between observations made on the same case and by the same observer. As a measure of relative reliability, ICCs were estimated for the following variables: ‘total movement; x-, y-, z-translations’; and ‘x-, y-, z-rotations’. Random effects models were estimated with each of these as a dependent variable and ‘case’ and ‘observer’ as random effects. The ICCs were estimated as follows: σ2bs/ (σ2bs + σ2bo + σ2e), where σ2bs is the between-cases variance component, σ2bo is the inter-observer variance component, and σ2e is the residual variance of the model. This ICC estimates the correlation between two repeated measurements on the same case performed by the same observer. Confidence intervals (CI) with 95 % confidence levels for the ICCs were estimated using parametric bootstrapping with 2000 iterations. The R-Code that was used for statistical analysis can be found in ‘Supp2-RCode.R’. The raw data is presented in ‘Supp3–RawData.csv’. Results The differences between ‘measured total movements’ and ‘true total movements’ are presented in Figure 5. The mean absolute error for ‘total movement’ was 0.0225 mm (SD 0.03 mm). The arithmetic mean error was -0.0017 mm. The range of total movements was from -0.07 mm to 0.08 mm. The ICC for measured total movement was 0.9996. Figure 6 shows the measured total movements plotted against the corresponding true total movements. Thus, the distribution of the measurements is generally very close to the line of identity. This indicates that this technique is as accurate for measuring small distances as it is for measuring longer distances. Figure 5. View largeDownload slide Differences between measured total movements and true total movements. Each of the four observers is represented by a unique colour. Figure 5. View largeDownload slide Differences between measured total movements and true total movements. Each of the four observers is represented by a unique colour. Figure 6. View largeDownload slide Measured total movement versus True total movement. Figure 6. View largeDownload slide Measured total movement versus True total movement. Estimated parameters from the mixed model, describing the relationship between measured and true total movement, are presented in Table 1. The intercept (−0.007) and the slope for the true movement (1.003) were very close to the line of identity (intercept = 0, slope = 1), indicating that any systematic errors of the measurements were very small. Random measurement errors (i.e. the variability of the random effects) were dominated by the residual error (56.9% of total variance), variability due to cases (32.4%), and variability due to observer (13.7%). However, the random measurement errors were also small; the standard deviation of the random effects due to cases, observer, and residuals were 0.0177 mm, 0.0115 mm, and 0.0229 mm, respectively. Table 1. Estimated parameters for total tooth movement of the mixed model. Fixed effect  Estimate  Standard error   Intercept  −0.007  0.01   True value (slope)  1.003  <0.01  Random effect  Variance  Standard deviation   Cases  0.0003142  0.018   Observer  0.0001327  0.012   Residual error  0.0005228  0.023  Total variability  0.0009697  0.031  Fixed effect  Estimate  Standard error   Intercept  −0.007  0.01   True value (slope)  1.003  <0.01  Random effect  Variance  Standard deviation   Cases  0.0003142  0.018   Observer  0.0001327  0.012   Residual error  0.0005228  0.023  Total variability  0.0009697  0.031  View Large The results of translational and rotational measurements are presented in detail in Table 2. Table 2. Mean absolute errors, arithmetic mean errors, range of errors, and ICC with estimated 95% CI.   Abs mean error  Mean error  Range  ICC (95% CI)  Total tooth movement [mm]  0.0225 (SD 0.03)  −0.0017  −0.07 to 0.08  0.9996 (0.9990, 0.9998)  Translation [mm]   X (mesio-distal)  0.0152 (SD 0.02)  −0.0049  −0.06 to 0.09  0.9994 (0.9985, 0.9997)   Y (transversal)  0.0208 (SD 0.03)  −0.0033  −0.09 to 0.06  0.9996 (0.9991, 0.9998)   Z (vertical)  0.0240 (SD 0.04)  0.0020  −0.21 to 0.15  0.9902 (0.9762, 0.9951)  Rotation [degree]   X (disto-mesial tipping)  0.0291 (SD 0.04)  −0.0241  −0.35 to 0.11  0.9999 (0.9998, 1.0000)   Y (buccal-palatal tilting)  0.0134 (SD 0.02)  0.0021  −0.13 to 0.06  0.9999 (0.9999, 1.0000)   Z (around the tooth axis)  0.0215 (SD 0.03)  0.0098  −0.12 to 0.13  0.9999 (0.9999, 1.0000)    Abs mean error  Mean error  Range  ICC (95% CI)  Total tooth movement [mm]  0.0225 (SD 0.03)  −0.0017  −0.07 to 0.08  0.9996 (0.9990, 0.9998)  Translation [mm]   X (mesio-distal)  0.0152 (SD 0.02)  −0.0049  −0.06 to 0.09  0.9994 (0.9985, 0.9997)   Y (transversal)  0.0208 (SD 0.03)  −0.0033  −0.09 to 0.06  0.9996 (0.9991, 0.9998)   Z (vertical)  0.0240 (SD 0.04)  0.0020  −0.21 to 0.15  0.9902 (0.9762, 0.9951)  Rotation [degree]   X (disto-mesial tipping)  0.0291 (SD 0.04)  −0.0241  −0.35 to 0.11  0.9999 (0.9998, 1.0000)   Y (buccal-palatal tilting)  0.0134 (SD 0.02)  0.0021  −0.13 to 0.06  0.9999 (0.9999, 1.0000)   Z (around the tooth axis)  0.0215 (SD 0.03)  0.0098  −0.12 to 0.13  0.9999 (0.9999, 1.0000)  View Large Model diagnostics were performed using various graphs of residuals and fitted values. QQ-plots of the residuals showed somewhat heavy tails for some of the mixed effects models but were considered to be within the limit of what could be acceptable. More details can be found in the supplementary material. Discussion The combination of raw matching, fine matching, and deformation analysis (RFD) superimposition delivers accuracy and precision in a dimension far beyond measurements on cephalometric X-rays, plaster casts, or 3D models with point-to-point measurements. The RFD superimposition delivers results that describe tooth movements not only as translation but also in terms of tipping, tilting, and rotation. This technique takes measurements by matching objects rather than by manually selecting measurement points. The identification of points is difficult and has been reported as a source of error (28, 29). Nalcaci et al., comparing manual point measurements of molar distalization on cephalometric X-rays, photographs, and 3D models, found a standard deviation of about 1.3 mm for all three techniques (30). No statistical significant difference was found. Therefore, it can be assumed that this new technique can eliminate the error associated with manual selection of measurement points. Although earlier validation studies have analysed different techniques for superimposition and reported measurements with high accuracy and precision, these studies compared measurements on digital 3D models with measurements on plaster casts or on lateral cephalograms (12, 15, 18). Hoggan et al., comparing measurements on plaster casts with cephalometric X-rays, found no statistically significant differences in measurements of movement of the maxillary first molar, but they did find that the standard deviation for measurements on plaster casts was between 1.6 and 2.1 mm and on cephalometric X-rays it was 2.0 mm (3). Because RFD-Superimposition has a standard deviation of 0.03 mm, it can be assumed that these techniques, although widely used, suffer from more measurement errors than measurements gathered from digital 3D models. Therefore, these techniques may no longer be considered the gold standard. Chen et al., using unloaded miniscrews as reference points, conducted measurements on 15 adult patients (13). Although unloaded miniscrews are regarded as stable in this study, they reported changes in miniscrew positions of up to 0.5 mm. This movement indicates that miniscrews might not be suitable as a reference for a technique with minimal measurement errors. Thiruvenkatachari et al. actually used a setup where the true values for translation were used as reference (14). This study was a source of inspiration for our current work. The use of specimen is an elegant way to avoid a situation where measurements assessed with a new technique have to be compared to another technique that obviously has more measurement error. However, in their study both master and slave models were identical in the palate. Technically, this validation matched identical surfaces. It would have been surprising if the matching process had failed. Moreover, their study did not measure rotational movement. Unlike earlier studies, our study used true values as reference and the master and slave model did not have identical surfaces in the palate (12–14, 18, 30). Consequently, our results showed that our new technique was robust for changes in the palate, implying that this new method can be used in growing patients subjected to orthodontic treatment. The measurements were performed by senior consultant orthodontists with different computer skills. After thorough instruction, any orthodontist would be capable of performing these measurements. The time needed per case (10 minutes) was comparable or even shorter for the time needed and duration to carry out, for example, tracing and superimposition of cephalometric X-rays. If the RFD superimposition is applied, the lateral head radiographs are not needed for evaluation of tooth movements. That is, an added benefit of the technique is that patients are not exposed to X-ray radiation. Limitations Despite the impressive accuracy and precision of the assessed RFD superimposition found in this study, there are three important circumstances to note: First, there has to be at least some structure that in fact is unchanged. Since differences correlate with time, it is important to keep the interval between the two registrations short enough. In adolescents, an interval of one to two years is appropriate. Second, one basic assumption in the workflow of this technique is that the area surrounding the median point of the third rugae is somehow stable (10, 18). Use of this area during the raw-matching is therefore crucial. Impression or scanning errors could give an inaccurate 3D model. Local swelling of the gingiva after treatment with, for example, a Nance-appliance or palatal miniscrews could generate an inaccurate 3D model. Therefore, areas that obviously have been changed need to be cropped before the superimposition process is started. Third, sometimes growth or treatments like rapid maxillary expansion follow an asymmetric pattern. This asymmetry needs to be taken into account when corresponding points are picked during the raw-matching. Thus, for raw-matching one would only use the median point of the third ruga on the non-effected side. It is important that this technique has to be used under the conditions discussed above. The algorithm will always process the models that are put in. If there is an asymmetry or other abnormal growth pattern that is visible to the naked eye, one has to check whether the result of the superimposition is feasible or reasonable. The morphological changes caused by growth and treatment are very complex. Therefore, this technique is far from a one-click-solution and it is performed in specialised 3D software. Consequently, for correct RFD superimposition it can be advisable to involve serial models taken with a moderate interval (1 to 2 years), to remove obvious changed areas in the palate, and to consider clinical information about asymmetric treatment effects. We believe that deformation analysis will be a key-element in future superimposition-techniques. There may be several algorithms that could do the trick. However, these algorithms will probably be more complex than a simple best-fit method. Conclusions The novel RFD-Superimposition method is a valid and reliable tool for measuring tooth movements in the maxilla. This method can tolerate morphological changes in the palate and gives excellent precision and accuracy. In addition, this method is robust for variances in the local point resolution and may also be used in growing subjects who undergo orthodontic treatment. Supplementary material Supplementary data are available at European Journal of Orthodontics online. Conflict of interest All authors have completed the ICMJE Conflict of Interest Disclosure form and declare the following: Niels Ganzer reports grants and nonfinancial support from the Centre for Research and Development, Uppsala University/Region Gävleborg, Sweden, and grants from the Swedish Dental Associations Scientific Funds during the conduct of the study; Ingalill Feldmann reports grants from the Thuréus Foundation for the Promotion of Dental Science, Uppsala University, Sweden, during the conduct of the study. The funding sources had no influence on study design, collection, analysis, or interpretation of the data, writing the article, or in the decision to submit the article for publication. There are no financial relationships with any organizations that might have interests in the submitted work in the previous three years. There are no other relationships or activities that could appear to have influenced the submitted work. 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The European Journal of OrthodonticsOxford University Press

Published: Feb 1, 2018

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