Introduction
Setups of the dental arches play a key role in orthodontic diagnostics and treatment planning [
5]. After decades of use of plaster casts, application of digital dental-arch models for orthodontic diagnosis and virtual treatment planning has recently increased [
8,
34]. Although commercial dental software packages provide digital setup tools, the underlying methods are unable to predict the final clinical dental arch position relative to the initial malocclusion and jaw base. This constitutes a major limitation because the actual position of the dental arch affects the occlusal relationships and the final incisor position influences the facial soft-tissue profile. This is particularly relevant if large orthodontic tooth movements (OTM) are required, as in premolar extraction.
In 1998, Alcañiz et al. [
2] presented a concept for computer-aided orthodontic treatment simulation. Their analogical model for OTM has not, however, been validated. More sophisticated OTM simulations based on finite element analysis are usually applied for research purposes [
19,
23]; however, time-consuming preprocessing and computation impede broad clinical application of such simulations in individual treatment cases. More efficient and realistic approaches for visualization and quantification of therapeutically required OTM may rely on superimposition of pretreatment and virtual setup models. Previous approaches [
7,
28] registered models via surface alignment at the tooth crowns, which either limits applicability to very small OTM [
7,
13] or disregards concomitant movement of reference teeth due to anchorage loss [
20,
33] and physiological drift of teeth [
27]. The frequently proposed surface alignment of jaw models in relation to attached soft tissue such as the hard palate and palatal rugae [
9,
10,
18,
22,
36,
38] is only applicable to the maxilla. In the mandible, only the (rarely available) mandibular tori provide a reliable reference [
3]. The use of mini-implants as markers [
9,
15] is invasive and, therefore, not applicable in clinical routine. A general limitation of structures further away from the teeth [
14,
17,
25] is related to morphological changes over time [
29,
31], which not only occur during tooth eruption and the main growth period, but also in adults [
11,
35]. Generally, treatment simulation should primarily focus on treatment-induced changes. Other factors such as growth should be considered separately.
We recently introduced a novel biomechanical approach for dental-arch model superimposition [
31], called “equilibrium of forces and moments” (EFM), for OTM monitoring during the levelling and alignment phase of fixed appliance therapy. Results were validated against several established surface registration methods (SRM) using palatal soft-tissue regions. The present study aims to investigate the applicability of EFM for monitoring and simulating premolar extraction treatments that implement large OTM. First, OTM during the space-closure phase of clinical cases was determined by EFM. Accuracy was validated against results from conventional SRM in the maxilla. Second, a case study demonstrates how EFM may be used for simulation and decision-making in treatment planning.
Discussion
The investigated method for dental-arch model superimposition called EFM is based on biomechanical principles and allows monitoring and simulation of effective 3D OTMs of individual teeth within subgroups of teeth as well as the complete dental arch. An important precondition for EFM is that the orthodontic appliance does only have an effect on teeth within the same dental arch, without any support on the opposite arch or external structures such as orthodontic mini-implants. Unlike EFM, conventional superimposition approaches depend on stable gingival or dental surfaces or both. Stable gingival surfaces with sufficient distance from the tooth crowns are predominantly found in the hard palate. In the mandible, such structures are only rarely available. Hence, the application of gingivae-dependent methods is usually restricted to the maxillary arch. Conventional superimposition methods that purely rely on dental surfaces may theoretically be applied to both arches. Orthodontic therapy, however, usually results in movement of all teeth of the respective dental arch because, even for large anchorage units, reactive forces and moments induce at least minor reactive OTM [
26,
37]. Moreover, even teeth which are not included in the appliance show passive OTM, e.g., due to load transmission via soft-tissue structures and interproximal contacts (also apparent in our results; Fig.
3). Hence, the registration of dental-arch models from different treatment stages purely based on superimposition of dental surfaces will arguably always be compromised.
For validation, OTMs derived from 3 EFM variants were compared with those obtained from conventional SRM using palatal surface registration. Previous studies [
6,
9] found significant changes in the position of the first two palatine rugae during treatment of extraction cases and, consequently, proposed omission of this region for SRM. Nevertheless, we used the entire palatal vault surface for superimposition, to increase registration reliability [
31]. This was reasonable because the monitored treatment period ended before the retraction of anterior teeth might have induced changes in the rugal region.
Generally, OTM values derived from the investigated EFM strategies deviated only slightly from the SRM results. This particularly concerns the 3 rotational components (median deviations < 0.5°) as well as the transversal and sagittal translations (median deviations < 0.08 mm). Considering the large translational movements observed for the retracted teeth, with median values > 3 mm, these small deviations may be considered clinically negligible. One might speculate that the somewhat larger, yet clinically insignificant deviations between EFM and SRM observed for vertical translations (median for EFM3: 0.14 mm) are related to the considerable tipping movements of adjacent teeth into the extraction space, leading to occlusal precontacts which might have induced intrusive forces. The EFM method does not take the latter into account. Another explanation might be the imbalanced sex distribution of the evaluated patients. Morphological data from literature used in EFM may overestimate the root size of women [
21], which, in turn, may overestimate the resistance of tipping teeth against vertical movements. We therefore suppose that among the simplifications introduced in the EFM model [
31], the implementation of average morphological data is a major source of remaining inaccuracies of EFM model superimposition. This limitation could be addressed by individualization of tooth geometries, e.g., on the basis of panoramic radiographs [
30].
The greater accuracy in EFM2 and even greater accuracy in EFM3 indicates that EFM superimposition gains stability from including teeth that are not involved in the appliance. However, in clinical treatment, the largest OTM usually occur in the sagittal and transversal directions, where EFM provided very accurate results (Fig.
3). Since there is no apparent reason why the application of EFM should be more inaccurate in the mandible than in the maxilla, one might extrapolate the remarkably high accuracy demonstrated for maxillary OTM to mandibular OTM.
The separate evaluation of OTM for quadrants with PM1-Ex and PM2-Ex exemplifies the great clinical potential of dental-arch model superimposition based on EFM. It allows quantification of mesial and distal shares of OTM required for space closure. Assuming that an extracted premolar provides approximately 6.7 mm [
32] space in the dental arch, space-closure ratios of 80.6% (PM1-Ex) and 65.5% (PM2-Ex) mean that extraction of the first or second premolar would provide approximately 5.4 mm or 4.4 mm space per quadrant, respectively, for alignment and uprighting of the frontal segment. These values are relevant for helping clinicians to decide between both extraction options. Another clinically interesting finding was a significant tipping and rotation of the first molars, canines and first premolars into the extraction space. Counter-tip (15°) and counter-rotation (30°) preactivations of the T‑Loop wires were apparently insufficient to compensate for these concomitant collateral movements. Furthermore, the quantitative information provided by this study regarding passive OTM of anterior teeth excluded from the appliance (a well-known phenomenon during extraction-space closure or other large OTMs) is of clinical interest.
As demonstrated by our case study, EFM may be applied both retrospectively to quantify OTM after orthodontic treatment, or prospectively to simulate treatment. Regarding the latter, application of EFM may considerably improve the accuracy and informative value of diagnostic setups because feasibility and treatment effort can be assessed more realistically. In a conventional setup procedure, positioning of individual teeth and tooth segments with respect to the dentoalveolar base is somewhat arbitrary. Especially the chosen anteroposterior position of teeth may vary considerably between clinicians due to the lack of suitable references. In contrast, superimposition of the malocclusion and setup models using EFM interrelates the dental arches according to objective and widely accepted biomechanical criteria. The added value of such EFM-aided treatment planning is exemplified by the presented case study results.
First, superimposition of the pretreatment models with setup models reflecting the treatment goal enabled prediction of total therapeutic OTM. It is noteworthy that such target setups may easily be revised to run through alternative treatment scenarios. An obvious benefit of such simulations is an estimation of the incisors’ final positions relative to the jaws and facial soft-tissues. Such information is of utmost importance in treatment planning because these positions substantially affect esthetic and functional outcomes as well as treatment stability [
1,
16]. The variation of the sagittal changes of the central incisors’ positions for the 3 simulated treatment options in the maxilla (range: 1.0 to 5.1 mm) and mandible (range:−1.9 to 2.5 mm) indicate the considerable potential influence of sagittal changes on the lip profile because the lip contour follows 70–80% of these changes [
16]. With respect to the sagittal central incisor position for PM2-Ex, the actual treatment outcome differed from the simulation by only 0.48 mm on average, which can be considered reasonably accurate. Another clinically highly relevant benefit of EFM-aided treatment simulation is the prediction of differential sagittal OTM of posterior teeth in the maxillary and mandibular arches. Such data may reveal the influence of different therapeutic strategies on the occlusal relationship. Unsatisfactory results after EFM superimposition may indicate the need for additional skeletal or intermaxillary anchorage to achieve neutral occlusion in the buccal segments. Such considerations are part of most orthodontic treatments.
The included simulation study further demonstrates that particularly in premolar extraction cases, further applications of EFM-aided treatment simulation are conceivable. This not only concerns the comparison of the provided and required space after premolar extraction (as exemplified here), but also the optimal timing of inclusion of the front teeth in the appliance or deactivation of the T‑Loop once the retracted tooth has reached its final position. Detailed explanation of these options, however, are beyond the scope of this paper.
Besides the predictive accuracy of the superimposition method, treatment simulations based on orthodontic setups are fundamentally limited by the degree of agreement between simulated and therapeutically achieved tooth positions, which mainly depends on realistic planning and the professional skills of the orthodontist. This particularly applies for sagittal root positions and inclinations of the incisors, which substantially affect the final anteroposterior position of the dental arch.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.