Predictability of orthodontic movement with orthodontic aligners: a retrospective study
Lombardo et al. Progress in Orthodontics
Predictability of orthodontic movement with orthodontic aligners: a retrospective study
Luca Lombardo 0
Angela Arreghini 0
Fabio Ramina 0
Luis T. Huanca Ghislanzoni 1
Giuseppe Siciliani 0
0 Postgraduate School of Orthodontics, University of Ferrara , Via Fossato di Mortara, 44100 Ferrara , Italy
1 Department of Biomedical Sciences and Health, University of Milan , Milan , Italy
Background: The aim of this study was to evaluate the predictability of F22 aligners (Sweden & Martina, Due Carrare, Italy) in guiding teeth into the positions planned using digital orthodontic setup. Methods: Sixteen adult patients (6 males and 10 females, mean age 28 years 7 months) were selected, and a total of 345 teeth were analysed. Pre-treatment, ideal post-treatment-as planned on digital setup-and real posttreatment models were analysed using VAM software (Vectra, Canfield Scientific, Fairfield, NJ, USA). Prescribed and real rotation, mesiodistal tip and vestibulolingual tip were calculated for each tooth and, subsequently, analysed by tooth type (right and left upper and lower incisors, canines, premolars and molars) to identify the mean error and accuracy of each type of movement achieved with the aligner with respect to those planned using the setup. Results: The mean predictability of movements achieved using F22 aligners was 73.6%. Mesiodistal tipping showed the most predictability, at 82.5% with respect to the ideal; this was followed by vestibulolingual tipping (72.9%) and finally rotation (66.8%). In particular, mesiodistal tip on the upper molars and lower premolars were achieved with the most predictability (93.4 and 96.7%, respectively), while rotation on the lower canines was the least efficaciously achieved (54.2%). Conclusions: Without the use of auxiliaries, orthodontic aligners are unable to achieve programmed movement with 100% predictability. In particular, although tipping movements were efficaciously achieved, especially at the molars and premolars, rotation of the lower canines was an extremely unpredictable movement.
F22 aligner; Orthodontic movement; Movement accuracy; Predictability
Since orthodontic aligners were launched on the market,
they have been in growing demand among patients,
especially adults, thanks to their aesthetic properties and
clinical efficacy [
Although the idea of using consecutive clear
thermoplastic appliances to align the teeth was first introduced
by Kesling in 1946 [
], it was not until Align Technology
(Santa Clara, CA, USA) launched the Invisalign system
in 1998 that such appliances were prescribed on a large
scale, thanks to their introduction of CAD/CAM
technology into Orthodontics [
]. At first, aligners were
marketed as an alternative to traditional fixed appliances in
simple malocclusion cases such as slight crowding or
minor space closure [
]. Over time, however, the range
of malocclusion cases that can be treated by means of
invisible aligners has widened. Clinical research has
developed aligner-based solutions for even complex cases
involving major rotation of the premolars, upper incisor
torque, distalisation and/or extractive space closure [
That being said, there is as yet no consensus as to the
predictability of aligner treatment in such large movements;
although the aesthetic impact of aligners has been
], few studies have yet been set up to investigate the
effective capacity of aligners to achieve complex movements
]. Indeed, the majority of articles published on aligner
orthodontics have been case reports or series, reports on the
use of a particular system, and expert opinions [
3, 8, 9
Furthermore, studies have concentrated on the market leader,
Invisalign, even though many other competing systems have
been developed since Align Technology’s patent expired.
These alternative aligner systems differ from Invisalign in
terms of construction material [
], production process,
margin finishing and STL model precision, but perhaps the most
influential difference is the professionals charged with
executing treatment planning and setup (IT specialists, dental
technicians or professional orthodontists) [
As regards treatment outcomes, Align Technology
reports that roughly 20–30% of Invisalign patients require
mid-course correction or post-alignment finishing in
order to achieve the results prescribed on the setup [
This figure, however, contrasts with that reported by
orthodontists, who indicate that the number of patients
who require some unplanned correction or even
recourse to fixed orthodontics, is closer to 70–80% [
In fact, Kravitz [
] reported that Invisalign aligners had a
mean accuracy of 41% in terms of achieving planned
outcomes, with the most predictable movement being lingual
contraction (47.1%), and the least predictable, extrusion
(29.6%). In a systematic review of the literature, Rossini and
Castroflorio confirmed that the most problematic
movement for Invisalign was extrusion, followed by rotation [
However, these authors also emphasised the paucity of
reliable literature on the subject, and the aim of this
study was therefore to compare planned and achieved
tipping and rotation in patients using F22 aligners
(Sweden & Martina, Due Carrare, Italy) in order to
provide data on their effective clinical predictability.
Sixteen adult Caucasian patients (6 males and 10 females, of
mean age 28 years and 7 months) treated by means of F22
aligners at the University of Ferrara Postgraduate School of
Orthodontics Clinic were retrospectively selected. Inclusion
and exclusion criteria are reported in Table 1. Treatment
staging, i.e. the maximum movement planned for each
aligner, had been 2° rotation, 2.5° vestibulolingual and
mesiodistal tip, and 0.2-mm linear displacement. No auxiliaries of
any kind had been used (intermaxillary elastics, buttons,
chains), although the use of F22 system Grip Points
(attachments) and anterior and/or posterior stripping was allowed.
Patients were instructed to wear their aligners for 22 h per
day, excepting mealtimes and oral hygiene procedures.
Aligners were replaced every 14 days.
Pre-treatment, ideal post-treatment (according to setup)
and real post-treatment digital models of the upper and
lower jaws of each patient were analysed. Pre-treatment
and post-treatment models were acquired using a Trios
intraoral scanner (3Shape, Copenhagen, Denmark), and
setups were constructed using Orthoanalyzer software
(3Shape, Copenhagen, Denmark).
Measurement of digital models
Digital models pertaining to each patient were analysed in
.stl format by a single operator using VAM software (Vectra,
Canfield Scientific, Fairfield, NJ, USA). This enabled the
identification of anatomical reference points, planes and
axes on the digital models, required, in turn, for calculation
of the angulation, inclination and vestibular prominence of
each tooth, as well as linear and angular measurements, for
example, the intra-arch diameters [
]. Measurement was
based on a method originally involving the identification of
a total of 60 reference points per model (excluding second
molars). However, in this case, we also included the second
molars in the digital measurements, thereby expanding the
number of reference points to 100 per model (Fig. 1).
Once the 100 reference points had been marked, their
three-dimensional coordinates were extrapolated and
exported, first into a .txt file, and then onto a dedicated
spreadsheet provided with the software. This spreadsheet
enabled extrapolation of the mesiodistal and
vestibulolingual tip and rotation (Figs. 2, 3, and 4) of each tooth
with respect to a 3D Cartesian grid based on the
occlusal reference plane, which was obtained by means of the
following points: (Fig. 5):
Reference points at the mediovestibular cusps of
teeth 16 in the maxilla and 46 in the mandible
Reference points at the mediovestibular cusps of
teeth 26 in the maxilla and 36 in the mandible
The centroid of all occlusal points of the FACC (the
facial axis of the clinical crown) of teeth 15, 14, 12,
11, 21, 22, 24 and 25 in the maxilla and 35, 34, 32,
31, 41, 42, 44 and 45 in the mandible; canines were
excluded from this calculation as their occlusal
Ongoing pharmacological treatment able to influence orthodontic movement (e.g. prostaglandin inhibitors, biphosphonates)
Active periodontal disease
Treatments requiring extraction space closure
FACC point is generally outside the occlusal plane
identified by the other teeth.
One month after the 96 arches had been analysed, the
analysis was repeated on 16 randomly selected digital
models (8 upper and 8 lower arches). Dahlberg’s D was
calculated in order to quantify the measurement error,
and Student’s t test for paired data to identify any
Analysis of mean imprecision
The following calculations were made for each type of
movement of each tooth in each patient:
The absolute value of the prescription, i.e. the
difference between ideal post-treatment and
pre-treatment measurements, to identify the total
∣prescription ∣ ¼ ∣ideal posttreatment−pretreatment∣
The absolute value of the imprecision, i.e. the
difference between ideal and real post-treatment
measurements, to identify the difference between
the actual post-treatment position of each tooth and
the programmed movement:
∣imprecision ∣ ¼ ∣ideal posttreatment−real posttreatment∣
Absolute values were used for the prescription and
imprecision parameters, as the direction of movement (clockwise
vs. anticlockwise rotation, and lingual vs. vestibular or mesial
vs. distal for the tip) was not taken into consideration.
Prescription and imprecision values were grouped into eight
categories (upper and lower incisors, canines, premolars and
molars) and according to the three types of movement
(mesiodistal tip, vestibulolingual tip and rotation).
The different types of tooth (incisors, canines, premolars
and molars) were analysed separately because of the
different anatomy of the crown and the root (both in shape and
length), which inevitably results in a different response to
the application of orthodontic forces, in particular, in the
treatment with aligners. In addition, the upper jaw teeth
were divided from the mandibular ones, due to the
different type and compactness of the bone, which can greatly
influence the orthodontic movement.
Movements with a prescription of less than 2° were
excluded from the analysis. This sensitivity threshold was
determined from the mean intra-operator error
pertaining to measurements made using the VAM software,
which has been previously published in the study
validating the method [
Thus a database containing measurements of 345
teeth, subdivided into the following types, was obtained:
57 upper incisors
29 upper canines
53 upper premolars
37 upper molars
64 lower incisors
30 lower canines
52 lower premolars
23 lower molars
Fig. 5 Occlusal plane of reference
The Kolmogorov-Smirnov statistical test was used to
determine the non-normal distribution of the mean
imprecision, using the median as a measure of central
tendency and the interquartile interval as an expression of
its distribution. The Kruskal-Wallis H test (p < 0.05) was
applied in cases of an imprecision of tooth/movement
combination whose mean was different to the others.
Analysis of movement accuracy
The following formula was used to quantify the accuracy
of each movement for each tooth type with respect to
real posttreatment−initial pretreatment
movement accuracy ¼ ideal posttreatment−initial pretreatment
Thus, an index of the accuracy of each movement was
obtained: the closer the value to 1, the more precise the
dental movement achieved by the aligner series (100% of
the prescription). The mean accuracy index, standard
deviation and mean standard error were calculated for each
type of movement in each tooth category, and Student’s t
test for single samples (p < 0.05) was applied in cases in
which the predictability of any type of movement/tooth
was significantly different to 1, i.e. significantly lower than
100% of the prescription. Finally, F ANOVA (p < 0.05) and
Bonferroni’s post hoc tests were applied if there was a
statistically significant difference in the predictability among
the different types of tooth movement.
Measurement method analysis confirmed that there were
no systematic measurement errors in any of the
mesiodistal tip, vestibulolingual tip or rotation values (Table 2).
Table 3 shows the absolute values for the mean
prescription and mean imprecision of each movement of each
tooth, alongside the median, relative interquartile and
statistical significance. In the upper arch, the least precise
movement in terms of absolute values was incisor rotation
(imprecision, 5.0° ± 5.3°), while the most precise
movement was vestibulolingual tipping of the canines
(imprecision, 2.5° ± 1.5°). In the lower arch, on the other hand, the
least precision was recorded for premolar rotation
(imprecision, 5.4° ± 5.8°), while the most precise movement was
vestibulolingual tipping of the molars (imprecision,
1.3° ± 0.9°). In the upper arch, there was no statistically
significant difference in imprecision between the different
types of tooth movements, whereas in the lower arch the
canines showed a significantly greater error in terms of
rotation of the canines (6.9° ± 5.4°) with respect to the
incisors (3.4° ± 2.5°) and molars (2.0° ± 1.8°). Likewise, the
lower molar rotation imprecision was significantly more
precise than the lower incisor rotation.
Table 4 shows the mean accuracy, its standard deviation
and standard error, and the statistical significance calculated
Systematic error p level NS NS
for each type of tooth and tooth movement. In the upper
arch, the inferential statistical analysis performed showed
that neither the mesiodistal tip on the canines, premolars
and molars, nor the rotation of the molars were significantly
different from 1 (p < 0.05), chosen as the reference value to
indicate 100% achievement of the planned movement. That
being said, all other tooth movements displayed a
predictability that was significantly lower than 100%.
In contrast, in the lower arch, mesiodistal tipping and
rotation of the canines and rotation of the incisors
were significantly less accurate than 100%, while all
other tooth movements achieved were not statistically
different from the target movement.
Table 5 compares the mean accuracy among all tooth/
movement combinations. This comparison revealed only
one statistically significant difference. In other words, there
was no greater precision statistically demonstrable in terms
of one tooth movement with respect to another, with the
exception of the lower incisors, whose rotation accuracy
(0.40) was significantly lower than that of the lower
It is a common experience among clinicians that some tooth
movements can be achieved more easily than others with
aligners. However, the precise degree to which the achieved
Systematic error p level NS NS
VL tip vestibulolingual tip, MD tip mesiodistal tip, Rot. rotation, SD standard deviation, IQR interquartile range, NS not significant
*p < 0.05
movements differ from the ideal movements planned using
digital setups is difficult to quantify experimentally. First and
foremost, it is necessary to identify stable structures within
the oral cavity that can be used as reference points for
superimposition of digital images. Among these, the palatine
folds are the most frequently chosen [
], even though
several studies have shown that their position and/or
dimensions may vary in certain clinical conditions [
Furthermore, palatal structures may only be used as reference
points in the upper jaw. This is one of the reasons why
superimposition on stable teeth has been selected as the
method of choice for evaluating the accuracy of Invisalign
by several authors [
14, 19, 20
]. However, that method may
only be used in cases in which orthodontic treatment
involves the displacement of only some teeth; moreover, even
if this is the case, collateral effects on the position of other
teeth cannot be ruled out. Indeed, intrusion may occur due
to the masticatory forces exerted when wearing aligners,
and any teeth used as anchorage may be subject to
reactionary displacement [
The method of tooth position measurement proposed by
], on the other hand, is based on the occlusal
plane as a point of reference. Calculated as the plane
passing through the mesiovestibular cusps of the first molars
and the centroid of the FACC of all of the other teeth, with
the exception of canines, the occlusal plane is a reference
that enables the measurement error due to tooth
movement during orthodontic treatment to be minimised.
Moreover, it is applicable to both arches in all individuals, and
allows evaluation of orthodontic movement of all teeth,
both anterior and posterior. What is more, the reliability of
this method has been demonstrated for tooth movements
greater than 2°, at which it displays no measurement or
Using this method, we demonstrate that the mean accuracy
of orthodontic movement provided by the F22 aligner is
VL tip vestibulolingual tip, MD tip mesiodistal tip, Rot. rotation, NS not significant
*p < 0.05
73.6%, considering all movements in both anterior and
posterior teeth, while it falls to 70.6% if only the anterior teeth
are considered. Although derived from a different
methodology, these figures appear to compare favourably with the 56
and 41% predictability achieved by Invisalign for anterior
teeth reported by Nguyen and Cheng [
], and Kravitz et al.
We found that the most accurate movement achieved by
F22 was mesiodistal tipping, whose mean accuracy was
82.5% (SD = 77.4) overall, and 96.7% at the lower premolars
(SD = 96.9), closely followed by the upper molars (93.4%,
SD = 72.6) and lower incisors (87.7%, SD = 85.9%). Less
precise movements were found to be vestibulolingual
tipping of the upper molars (52.5%, SD = 53.3) and upper
canines (54.0%, SD = 57.2%) and rotation of the upper
premolars (54.0%, SD = 54.3) and lower canines (54.2%,
SD = 73.9) (Table 6, Fig. 6).
Rotation movements, especially of rounded teeth like the
canines and premolars, are notoriously difficult to achieve
with aligners. Indeed, one prospective study [
conducted on 53 canines in 31 subjects found a mean canine
rotation accuracy of 36%. Greater canine rotation accuracy
can be achieved with interproximal reduction (IPR), but
this only provides an accuracy of 43%, albeit with a lower
standard deviation (SD = 22.6%). Another study [
found a rotation accuracy of 32% at the upper canines and
even less at the lower canines (29%), as compared to the
upper central (55%) and lower lateral incisors (52%).
Moreover, there is an even further significant reduction in
the accuracy of upper canine rotation at rotations of
greater than 15° (19%; SD = 14.1%; P < .05).
Our data confirm that among the lower teeth canine
movement is the least accurate. That being said, our
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predictability percentage was higher than that reported in
the literature for other aligner systems (54.2%, SD = 73.9).
Furthermore, the F22 aligners achieved an accuracy index
not significantly different from 1, i.e. 100% of the
prescribed movement, for rotation of the upper molars (0.78,
SD = 0.61), lower premolars (0.83, SD = 1.27) and lower
molars (0.85, SD = 0.67).
That being said, comparison of all movements achieved
by F22 in all tooth categories shows that, with respect to
the prescription, the mean rotation of the upper incisors
appeared significantly more accurate than the mean
rotation of the lower premolars. This is in line with several
literature reports on other aligner systems, for example
Djeu et al.’s Invisalign study [
], in which they noted that
one of the strengths of the system was the ability to correct
the rotation of anterior teeth and level the incisor margins.
] also showed that the greatest rotation accuracy
is achieved at the upper incisors (mean accuracy 48.8% for
central and lateral incisors); Nguyen and Cheng [
confirm this finding, reporting a mean incisor rotation of
60%. This parallels our figure of 61.5% (SD = 28.5%), but
with F22 aligners, we found that the best rotation accuracy
was achieved at the lower molars (85.4%, SD = 67.4) and
lower premolars (82.7%, SD = 138)—teeth that were not
considered in Kravitz’s analysis—albeit with a high standard
Mesiodistal and vestibulolingual tipping
Kravitz’s 2009 study [
] repeated a mean accuracy of 41%
for mesiodistal tipping, which was most accurate at both
the upper (43%) and lower (49%) lateral incisors;
mesiodistal tipping of the upper (35%) and lower (27%) canines
and the upper central incisors (39%) was the least
accurate. Our F22 results are in line with these findings, in that
the least predictable movements achieved in the anterior
sector were the upper canines and incisors, although once
again, our accuracy scores were markedly higher. Indeed,
the mesiodistal tip achieved at neither the upper canines
(0.78, SD = 0.5), nor the upper premolars (0.7, SD = 0.78),
upper molars (0.93, SD = 1.02), lower incisors (0.88,
SD = 0.86), lower canines (0.87, SD = 0.82), lower
premolars (0.97, SD = 0.97) or lower molars (0.62, SD = 0.82)
was significantly different from 1, considered full
achievement of the outcomes predicted by the setup. As regards
vestibulolingual tipping, on the other hand, neither the
lower incisors (0.86, SD = 0.64), nor the lower premolars
(0.9, SD = 0.81) or lower molars (0.86, SD = 0.5) exhibited
an accuracy index not significantly different from 1.
The orthodontic movement is a multifactorial issue.
There are many parameters that can affect the ability to
reach the goal planned in the setup. The crown anatomy,
the root length and bone density were taken in
consideration in this study dividing the sample into different groups
by dental typology. Other parameters like sex and age of
the patient could also influence the response to the aligners’
application, as suggested by literature [
]. In addition, the
characteristics of the material, thickness, alignment
protocol application and staging may affect the efficiency of the
orthodontic movement. All these parameters will need to
be thoroughly investigated in future research.
There were several limitations to this study. First and
foremost, it would have benefitted from a larger sample. Only 16
patients remained after the selection process, giving a
potential 448 teeth to be analysed. However, once movements of
prescription lower than 2° were excluded, this number fell to
346. Second point, as this is a retrospective study, the cases
with complete records are more likely to be those that
completed treatment, rather than truly representative of those
who started treatment with aligners. This could overestimate
the effectiveness of the treatment.
Furthermore, we analysed only three types of tooth
movement: rotation, mesiodistal tipping and
vestibulolingual tipping; as digital models rather than radiographs were
used for measurements, there was no information
regarding root position from which to derive torque values.
Nevertheless, the method of measurement we used, with
the aid of VAM software, did enable us to analyse both
anterior and posterior teeth, relying as it did on an “average”
occlusal plane, passing through the centroids of the FACC
points of all teeth (except for the canines) as a reference.
Indeed, this plane is only minimally affected by the tooth
movements achieved during treatment. That being said, the
occlusal plane cannot be considered entirely stable and,
moreover, it is difficult to compare the results of this type
of analysis with those in the literature, which derive from
superimpositions of the palatine folds and posterior teeth.
Finally, it is worth noting that the study design did not
enable us to explore the full potential of F22 aligner
treatment. Indeed, complex movements are usually aided by
the use of auxiliaries such as elastics or chains, whereas
we evaluated outcomes achieved by the F22 Grip Points
(attachments) and stripping alone. It is conceivable that in
the hands of an experienced orthodontist, with a full array
of auxiliaries at their disposal, the accuracy percentages
we revealed could be further improved upon.
Our analysis of the predictability of orthodontic
movements that can be achieved using F22 aligners, without
auxiliaries, enables us to state that
The mean accuracy of rotation, mesiodistal tipping
and vestibulolingual tipping was 70.6% in the
anterior sector and 73.6% across both full arches.
Mesiodistal tipping was the most predictable
movement, reaching a mean accuracy of 82.5%;
vestibulolingual tipping and rotation reached 72.9
and 66.8% of the prescribed movement, respectively.
The least predictable movement was rotation of the
lower canines (54.2%), while the most predictable
movements were mesiodistal tipping of the upper molars
and lower premolars (respectively 93.4 and 96.7%).
The mean rotation error was significantly greater at the
lower canines than at the lower incisors and molars.
In the upper arch, mesiodistal tipping of the canines,
premolars and molars displayed a very high accuracy
index, not significantly different from 1. This was
also true of vestibulolingual tipping of the molars.
In the lower arch, the accuracy index was not
significantly different from 1 for mesiodistal tipping
of all teeth, vestibulolingual tipping of the incisors,
premolars and molars, and rotation of the premolars
There were no significant differences in the accuracy
index between tooth movements, with the exception
of upper incisor rotation, which was significantly
lower to that achieved at the lower premolars.
Further research on the topic using such a precise
and reproducible means of model superimposition
and measurement is required and should involve
larger samples in order to shed light on the potential
benefits and drawbacks of aligner systems.
FR analysed the dataset. AA recruited and treated the patients. LHG developed the analytical method. LL designed the study. GS supervised the research. All authors read and approved the final manuscript.
Ethics approval and consent to participate
The study was performed in accordance with the Declaration of Helsinki.
It is a retrospective analysis, and the protocol was approved by the Chairman of Postgraduate School of Orthodontics, University of Ferrara.
The authors declare that they have no competing interests.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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