Prevalence of unexpected tooth movements
In the present study sample, 27% of the patients showed unwanted tooth movements despite intact bonded retainers in the upper and/or lower jaw. Unwanted tooth movements exclusively in the mandible were seen in 14.1% of the subjects. In the literature, this complication has only been described for the lower jaw with prevalence rates ranging between 1.1 to 43.3% [11, 16, 19]. Thus, our patient sample is in the lower span of the reported prevalence.
The study describing the highest prevalence of 43.3%  categorized the samples into "stable," "moderate" and "severe" cases based on the amount of rotational position changes. They found that 30% of the patients were moderately affected and 13.3% were severely affected, justifying retreatment for the severe group. In comparison, all patients in the present study completed the entire retention period without unwanted tooth movements being classified as severe enough to justify retreatment. The severely affected cases corresponding to the 13.3% of the sample by Wolf et al.  were initially excluded in the present study because of retreatment during the retention phase. Taking this into account, the prevalence rate in the present study underestimates the phenomenon.
In the present sample, the maxillary retainers were affected more often (20.9%) than the lower ones. To date, there are no other studies in the literature analyzing upper retainers. This may be due to the fact that bonded retainers are not used that commonly in the upper jaw, as indicated by questionnaire-based survey studies [2, 3, 7]. Furthermore, survey studies and survival studies regarding upper bonded retainers show a large variety in different retainer extensions for the upper jaw: 1–1 retainers (only the central incisors), 2–2 retainers (central and lateral incisors) and 3–3 retainers (canines, central and lateral incisors) [4, 6, 27,28,29,30]. If maxillary retainers are extended to the canines as in the present study, a higher incidence of retainer losses and wire breakages is reported [25, 27, 30], especially in deep bite cases. Although all upper retainers in the present study were initially placed out of occlusion, a gradual bite deepening during the retention period is often observed clinically, whether caused by settling of the occlusion or an initial relapse of deep bite correction [31,32,33]. Potentially, such a contact of the lower canines on the retainer wire between the upper laterals and the canines could have resulted in distorting the retainer wire, explaining some of the observed unwanted tooth movements in the upper jaw.
Direction and amount of unexpected tooth movements
In the vertical plane, predominantly extrusive movements occurred in both arches, though the upper teeth were more frequently and more severely affected than the lower ones. In the current literature, only Wolf et al.  measured the amount of unexpected movements in the lower arch, but due to methodological differences, the comparability to the present results is limited. Wolf et al.  present a mean apicocoronal movement for the severely affected lower canines of 0.52 ± 0.35 mm, which is larger than the median values of the present samples (Fig. 3). However, the present samples did not comprise severely affected cases requiring retreatment as mentioned above and could thus underestimate the amount of tooth movement. Especially for the vertical dimension, the extrusive movements could also have been caused by post-orthodontic settling alone. Theoretically, a distinction of post-orthodontic settling and unwanted extrusive tooth movements for the upper jaw could be investigated by measuring extrusive movements of the premolars and molars and subtracting the amount of extrusion of the lateral teeth from the amount of extrusion of the retained teeth, because the jaws were superimposed using the stable structures of the hard palate. Due to the lack of stable structures in the mandible and the necessity for superimposition on dental structures, a distinction between post-orthodontic settling and unwanted tooth movements in the lower jaw is not possible.
In the transverse dimension, clockwise movements prevailed. Again, the upper jaw was more frequently and more severely affected than the lower jaw. Furthermore, the teeth of the patient´s first and fourth quadrant seemed to be more affected than the teeth of the second and third quadrant. As previously suspected by Kucera and Marek , asymmetric unwanted tooth movements could possibly be due to the winding/unwinding direction of multistranded retainer wires. However, this hypothesis remains scientifically untested.
In the sagittal plane, the upper teeth showed mainly protrusive movements, which were more frequent and more severe in the incisors compared to the canines. This could be due to a transverse relapse, resulting in an extension of the dental arch. However, the analysis of treatment-related factors revealed no association between alterations of the intercanine distance and unintentional tooth movements. In the lower jaw, the movement pattern of the present sample shows similarities to the twist effect previously described in the literature [11, 19, 22, 23].
Pretreatment or treatment-related factors
In contrast to Kucera and Marek , neither the mandibular plane angle nor the incisor proclination before treatment was correlated to unintentional tooth movements. Wolf et al.  found patients with larger amounts of intercanine expansion and greater overjet reduction during orthodontic treatment to be more affected by severe posttreatment tooth movements in the lower jaw. This could not be confirmed by the results of the present study.
In the present sample, affected patients presented oral dysfunctions or habits prior to orthodontic treatment more often. Additionally, for all time points, a significant association with the interincisal relationship was observed: affected patients presented an incisor overlap without interincisal contact more frequent, while unaffected patients presented an interincisal contact more often. This factor has not been investigated previously. Theoretically, the inability to establish an interincisal contact even during MB treatment could be due to an abnormal resting position of the tongue and tongue thrust swallowing, which could result in orovestibular-directed forces created by the tongue, and in turn, unintentional tooth movement of the retained segment.
Another possible explanation for unwanted tooth movements despite bonded retainers could be an iatrogenic activation of the retainer during bonding, as proposed by some authors [17,18,19, 22, 23]. However, in that case, tooth position changes should occur within a few weeks after bonding. In contrast, in the present sample as well as in other study samples [11, 16, 18, 22], later onsets of tooth position changes are reported. These changes could be the result of wire fatigue or deformation caused by masticatory forces or hard food particles [16, 18, 22].
Some in-vitro studies investigated the mechanical properties of retainer wires: Sifakakis et al.  simulated intrusive-extrusive and labio-lingual bite forces. They found even small wire displacements of 0.2 mm could exert forces of approximately 1 N on the teeth, which would be sufficient to cause unwanted tooth movements. Another in vitro study  investigated retainer wires loaded with intrusive forces, which resulted in residual forces and moments in all retainer types, thus demonstrating that retainer wires are not passive after loading and may induce tooth movements.
Limitations of the study
In the present study, 46.6% of the patients had to be excluded because of unsuitable plaster casts. Due to the methodology, perfectly intact plaster casts for further scanning, superimposition and measurement were necessary to prevent method errors. Furthermore, patients with bonded retainers including teeth other than the canines, lateral and central incisors as well as patients with adhesive or prosthetic restorations were excluded. Especially regarding the prevalence of unexpected tooth movements found in the present study, the high drop-out rate has to be taken into account.
Additionally, the retainers were not bonded by one single operator but by all orthodontists and residents of the department following the same protocol. While two investigations found operator experience to be a significant factor regarding detachments of bonding sites [30, 36], Lie Sam Foek et al.  could not detect any association. Due to the fact that operator experience has not been studied in cases of unwanted tooth movements despite intact bonded retainers, the impact can only be hypothesized. Nevertheless, further prospective studies should aim at the highest possible standardization for retainer bonding.
Complications during the supervised retention period (detachments of bonding sites, wire breakages) showed no statistically significant association to unexpected tooth movements, however they occurred only in some patients, limiting the statistical power. Nevertheless, their impact on the registered unwanted tooth movements cannot be totally ruled out. In some cases, patients were unaware of detached bonding sites until these were observed by the practitioner at the control appointment. During such a period, tooth movements may occur. To overcome this limitation, affected patients should have been excluded from the study. Unfortunately, this was not possible due to the fact that the exact time points of detachment were not documented.
Another possible limitation could be seen in the method of digital superimposition. In the maxilla, the hard palate area around the third rugae has been used as a stable structure for digital superimposition in several studies [26, 38,39,40,41,42]. Despite the fact that this area is not absolutely stable due to growth and remodeling [43, 44] as well as orthodontic treatment using rapid maxillary expansion or maxillary protraction headgear , stability seems acceptable for intervals comprising up to two years , especially during a retention period as in the present sample. Furthermore, a recently published systematic review confirms that this area is the most accurate one for maxillary superimposition to date . For mandibular superimposition, the most actual approaches use CBCT data [47,48,49,50], which is however ethically unacceptable for orthodontic retention surveillance. Only one study  investigated the superimposition of different anatomic mandibular areas depicted on digital casts and found acceptable accuracy in patients with bilateral mandibular tori only. Due to the fact that the prevalence of mandibular tori is only about 25% and varies with ethnicity [52, 53], to date there is no reliable methodology for superimposition using stable structures in the mandible . Therefore, as in the study by Wolf et al. , a dental superimposition was used. The limitations arising from a dental superimposition, such as changes in tooth position due to post-orthodontic settling and dentofacial growth as well as changes in the tooth morphology due to abrasion, attrition and/or erosion, must be acknowledged.
Digital dentistry, and especially the possibilities of model superimposition and measurement, is a fast-growing field and current subject of research. Due to the present limitations of superimposition discussed above and the fact that the topic of unwanted tooth movements despite intact bonded retainers is not yet well investigated, to date there are no scientifically based thresholds or cut-off values identifying unwanted tooth movements. Therefore, the present pilot study approach used a visual inspection of plaster casts initially, as visually recognized tooth movements could also be recognized by patients, general dentists or orthodontists during routine appointments and therefore may be considered clinically relevant.
In the present study, all measurements in the sagittal, vertical and transverse dimension were performed manually using the software GOM Inspect. Despite the excellent ICCs, the manual identification of landmarks bears a risk for errors and operator bias, especially if only one investigator performs all measurements, as in the present study. Other studies used software-aided measurement algorithms, which can express rotational and translational tooth movements along the x-, y- and z-axes of a coordinate system [19, 42]. To minimize individual errors and enhance comparability to other studies, the use of an alternative software that allows for superimposition and automated measurements could be beneficial.
In summary, the phenomenon of unintentional tooth movements despite bonded retainers still lacks a solid research background. To our knowledge, the present study is only the third systematic retrospective study on the topic and the first one including the upper jaw. Prevalence, extent and etiology remain to be elucidated by further research projects.