Validity and reliability of a trigonometry-based method for the measurement of tooth movement on digital models

Abstract

Objective: The objectives of the present study were to develop a method for longitudinally measuring tooth rotation, inclination and angulation on digital models, and to test the method validity and reliability. Methods: The initial and final planned models of 14 patients treated with Invisalign® (386 teeth) were exported from ClinCheck®. The rotation, inclination and angulation values were assessed for the incisors, canines, premolars and molars, in both models, using trigonometry. An application was developed in Python 2.7 to automate the measurements. The ∆planned (variation in the position between the initial and final planned models) was obtained for each tooth and each type of movement. To test the validity, the degree of agreement between the ∆planned and the values available in the Invisalign® Table of Movements was assessed using the Intraclass Correlation Coefficient (ICC) and Bland-Altman analysis. For intra and inter-rater reliabilities, the ∆planned was obtained again. Results: Excellent ICCs (> 0.9) and limits of agreement with narrow and clinically acceptable discrepancies were obtained for the rotation of all teeth (except maxillary canines, which had broader limits: -3.47 - 5.43) and for the inclination of premolars and molars. The inclination of anterior teeth and angulation of all teeth had ICCs and limits that were not indicative of great agreement. The reliability was high for the three movements (discrepancy <2°). Conclusions: The method developed is reliable and suitable for longitudinally measuring inclination (posterior teeth) and rotation (except maxillary canines). It has limited value for the other movements measurements.

Accuracy of Invisalign® aligners in adult patients: a retrospective study of angular tooth movements

“…To the best of our knowledge, this is the first study to assess tooth movement predictability with aligners using a previously validated method. 15 Although this method has been shown to have limited validity for mesio-distal tip and buccal-lingual tip of specific teeth, it was applied to calculate the predicted and achieved movements in all teeth, as, by using the same technique, the error maintenance principle tends to minimize the problem. In other words, if both deltas are measured by the same method, any presumed error will likely be kept in the same proportion for both measurements, making the comparison valid.…”

“…Following the previously described methodology of Santos et al, 15 .STL models were imported into Geomagic Control ® (3D Systems, Rock Hill, SC, USA) software. Five points (lingual gingival, mesial, distal, occlusal, and vestibular gingival) were marked on each tooth of Model 1 ( Fig 1 ).…”

“…Rotation was defined as the angle between the line formed by the mesial and distal points of each tooth and the Y axis ( Fig 3 A). For the measurement of mesio-distal and buccal-lingual tip ( Figs 3 B and 3 C), in order to fully capture the movement and not just one vector component, it was necessary to reorient the Cartesian space of each tooth with the aid of a rotational matrix, as described by Santos et al 15 and Huanca et al 1 6 …”

Accuracy of orthodontic movements with 3D printed aligners: A prospective observational pilot study

“…Models were compared using trigonometry, placing six points for each tooth according to the disposition described by Huanca et al 13 and well resumed by Santos et al 15 …”

“…Points were placed on patient-wise morphologically recognizable spots of the palatal rugae for the T0, T1, and Tp STL files to overlap the casts based on stable structures. 14 Models were compared using trigonometry, placing six points for each tooth according to the disposition described by Huanca et al 13 and well resumed by Santos et al 15 • Mesial point of the occlusal surface (MO)…”