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progress in orthodontics 1 3 ( 2 0 1 2 ) 154–163
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journal homepage: www.elsevier.com/locate/pio
Original article
Three-dimensional finite-element analysis of a central
lower incisor under labial and lingual loads
Luca Lombardo a,∗ , Filippo Stefanoni b , Francesco Mollica c , Attoresi Laura d ,
Giuseppe Scuzzo e , Giuseppe Siciliani f
a
Research Assistant, Department of Orthodontics, University of Ferrara, Italy
Post-doctoral Researcher, Department of Engineering, University of Ferrara, Italy
c Assistant Professor, Department of Engineering, University of Ferrara, Italy
d Resident, Department of Orthodontics, University of Ferrara, Italy
e Adjunct Professor, Department of Orthodontics, University of Ferrara, Italy
f Chairman, Department of Orthodontics, University of Ferrara, Italy
b
a r t i c l e
i n f o
a b s t r a c t
Article history:
Introduction: The aim was to evaluate the differences between labial and lingual application
Received 8 June 2011
of an orthodontic force. This was achieved using a three-dimensional CAD design software
Accepted 28 October 2011
model of a real lower incisor surrounded by a prismatic representation of the mandibular
bone. This model was subjected to various loading conditions, with finite-element analysis.
Materials and methods: Cone-beam computed tomography scanning was used to create a
three-dimensional geometric model of a lower incisor, together with its simulated periodontal ligament. This model was then meshed and analysed with commercial finite-element
code. Various single and combined forces and moments were applied to each side of the simulated lower incisor at the centre of the clinical crown. To evaluate the effects of the various
forces considered, the instantaneous displacement and stress generated in the bone and
the periodontal ligament were measured, as a comparison of the labial and lingual loading
sites.
Results: Dental movement was only influenced by the side of the force application when
an intrusive component was present. The simulations showed larger displacement when
a vertical force was present at the lingual surface. In general, this movement was of the
tipping type when the combined forces were applied, while there was greater intrusion
upon application of combined forces and an anticlockwise moment to the labial surface.
Conclusions: Application of an intrusive lingual force to a lower incisor appears to generate
bodily movement, while the same intrusive labial force appears to lead to labial tipping.
Subject to further study, this should be taken into consideration when devising treatment
plans for fixed appliances.
© 2012 Società Italiana di Ortodonzia SIDO. Published by Elsevier Srl. All rights reserved.
Corresponding author. Contrada Nicolizia, 92100 Licata, Agrigento, Italy.
E-mail address: [email protected] (L. Lombardo).
1723-7785/$ – see front matter © 2012 Società Italiana di Ortodonzia SIDO. Published by Elsevier Srl. All rights reserved.
doi:10.1016/j.pio.2011.10.005
∗
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progress in orthodontics 1 3 ( 2 0 1 2 ) 154–163
1.
Introduction
Continuous application of an orthodontic force to a tooth
triggers remodelling in the surrounding bone, which eventually leads to tooth displacement. On a biological level,
dental displacement appears to be brought about by catabolite
recruitment, as deformation of the trabecular bone generates
a change in its metabolism.1
From a biomechanical perspective, numerous studies have
sought to characterise how this dental movement is brought
about. In particular, Sandstedt2 noted that different types of
force lead to different types of dental movement, and hypothesised that bone tissues react differently according to whether
they are subjected to compression or tension. Specifically,
Sandstedt2 documented the formation of new tissue on the
side of the tooth where the periodontal fibres were under tension, whereas bone resorption occurred in the same fibres on
the side of the tooth where compression was applied. On the
other hand, Ren et al.,3 explored continuous application of
orthodontic forces of various intensities, and reported that the
rate of dental displacement over time in response to these
forces shows considerable individual variation. Therefore,
according to the speed of the dental displacement, patients
can be classified as ‘fast movers’ or ‘slow movers’.4
This is particularly important when planning orthodontic treatment that involves fixed appliances. Indeed, following
many more recent advances in the field, clinicians now have
access to a wide variety of high-quality techniques. In particular, the growing emphasis on aesthetics means that the lingual
technique has reached a similar level of application and
development as the more conventional labial orthodontics. In
addition to their relative unobtrusiveness, lingual appliances
obviate the need for etching the labial enamel, and the displacement of each tooth can be observed more clearly, with
respect to the labial technique.5,6 However, the typical greater
variability in tooth anatomy on the lingual side of the dental
arch can make the positioning of the bracket difficult,7 which
can have a profound influence on the biomechanics of this
lingual approach. In this respect, the main difference between
the labial and lingual techniques is the distance between the
point of application of the force that is transmitted through
the bracket and the centre of resistance of the tooth.7 Consequently, the displacement and stress induced in bone by these
two techniques will also differ, and these need to be evaluated so that useful comparisons can be made between these
techniques.
Although biomechanical forces are relatively difficult to
measure directly, analysis using the finite-element method
(FEM) can provide useful estimates. Indeed, as an example, the
FEM has already been successfully used to evaluate the state
of stress generated by palatal miniscrews, to determine their
ideal implantation sites.8 Furthermore, the FEM approach has
been used to provide a convincing evaluation of the stress distribution in tooth roots, the periodontal ligament,9–15 and the
trabecular bone upon the application of different loads.16–25
However, to the best of our knowledge, no FEM studies
have been carried out on lower incisors to compare the effects
of such forces on lingual and labial bracket-placement sites.
Despite this, some studies have assumed that there are indeed
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differences here.7–26 We therefore designed a FEM geometric
model of a lower incisor, its supporting trabecular bone, and
its surrounding periodontal ligament, to evaluate and compare the biomechanical responses to forces mimicking those
generated by both lingually and labially positioned brackets.
To create this workable model, we used an actual ex-vivo lower
incisor, with cone-beam computed tomography scanning of
its anatomy to obtain a digital three-dimensional rendering.
To obviate interference from the actual soft tissues, the surrounding bone was generated using three-dimensional CAD
design software. This model was subjected to FEM simulations
to evaluate the effects of loads that would be generated by
a bracket positioned on each side of the crown of the lower
incisor.
Initially, each force was analysed individually, to better
compare the effects for the two sides of the force application.
Subsequently, however, to better approximate the complex
reality of bracket loading conditions, combinations of several
simultaneous forces were analysed. We thus report here on
the considerations relating to the mechanical effects of each
type of simulated treatment.
2.
Materials and methods
A whole lower incisor that was sterile and devoid of caries
was mounted on a wax support and scanned by cone-beam
computed tomography using a NewTom 3G (QR Srl, Verona,
Italy). The following settings were applied: 110 kV, 0.50 mA,
12-inch field-of-view, and 5.4-second exposure time. According to the manufacturer specifications, the voxel was an
isometric cube with an edge length of 0.3 mm. To maintain
optimum image clarity and to minimise interference produced
by the surrounding soft tissues, an experimental model was
chosen for this initial investigation, rather than a real patient.
Mimics (Materialise, Leuven, Belgium) and SolidWorks CAD
(DS SolidWorks Corp., Massachusetts, USA) three-dimensional
design software were used to create a solid model of the lower
incisor from the cone-beam computed tomography images.
The CAD software was also used to construct a simulated prismatic bony region of 20 × 15 × 10 mm around the lower incisor
comprising both the trabecular and cortical bone, as well as
the periodontal ligament and alveolus. The compact bone and
the periodontal ligament layers were designed to be irregular
in shape, so as to conform to the shape of the lower incisor.
The compact bone layer was 0.5 mm thick on average, while
the periodontal ligament layer had a thickness ranging from
0.1 mm to 0.5 mm. The lower incisor was placed virtually in
the alveolar cavity, with an angle of 110◦ created with respect
to the occlusal plane, to reflect a typical clinical case. The geometric model was then imported into the ANSYS Workbench
platform (ANSYS, Inc., Canonsburg, Pennsylvania, U.S.A.) for
the FEM simulations (Fig. 1).25
Due to the irregular geometry, the geometric model was
discretised with non-linear tetrahedral elements, each of
which had ten nodes (i.e. the TET10 element). The mesh was
refined at the points where gradients were expected (e.g. at
the material interfaces) and was left coarse elsewhere, to
avoid unnecessary use of computation time. The final mesh
had a total of 35,684 elements and 67,133 nodes. All of the
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Fig. 1 – The geometric model. The different colours correspond to the tissues simulated, i.e. cortical bone (yellow),
trabecular bone (green), periodontal ligament (dark grey) and dentine (light grey). Z is the labiolingual axis.
Table 1 – Material properties.
Material
Dentine
Cortical bone
Trabecular bone
Periodontal ligament
Young’s Modulus
[MPa]
19600
13700
1370
0.667
Poisson
Coefficient
0.31
0.3
0.3
0.45
materials were considered isotropic and linearly elastic, with
their respective properties as reported in Table 1.
For the boundary conditions, the lower and lateral surfaces
of the simulated bone region holding the lower incisor were
kept fixed, and the various orthodontic loads were applied to
the surfaces of the lower incisor as nodal forces. The point of
application of each force was designed to coincide with the
centre of the exposed coronal surface, first on the labial side,
and then on the lingual side. The application site was chosen
on a purely anatomical basis, without taking variables such as
the type of bracket or the slot size into consideration.
To evaluate the effects of single forces, different types of
load were applied. It should also be noted that the complete
loading on a tooth will also depend on the position of the adjacent teeth, and therefore will differ from patient to patient.
Each single force that was applied was assumed to have
a modulus of 0.3 N (ca. 30 gf ). This was based on Proffit and
Fields,27 where the ideal force for tipping, rotation, intrusion
or extrusion is given as ca. 35 g for a monoradicular tooth.
Five cases were considered for each force that was applied,
which included different directions and orientations (Fig. 2):
labiolingual (case 1) and linguolabial (case 2) directions; mesial
(case 3) and distal (case 4) rotations; and intrusion (case 5). The
same force modulus and direction were considered in each
case, with the only variable being the point of application.
Combinations of several forces acting together were also
considered. Here, the intrusive component was added to both
the linguolabial and labiolingual forces, to provide two additional loading conditions (cases 6 and 7), which were applied
to the labial and lingual sides in turn (Fig. 3). In these cases,
the resultant force had a modulus of 0.42 N (42 gf ) and was
directed at an angle of 45◦ with respect to the occlusal plane.
A complex system of forces was also applied to the lower
incisor. As considered by Liang et al.,24 a labiolingual force of
Fig. 2 – Forces applied to the lingual and labial sides of a lower incisor: 1) labiolingual; 2) linguolabial; 3) mesial rotation;
4) distal rotation; 5) intrusion.
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157
Fig. 3 – Combination of the single forces considered previously: 6) linguolabial + intrusion; 7) labiolingual + intrusion.
1 N (100 gf ), an intrusive force of 0.64 N (64 gf ), and an anticlockwise moment of 0.5 N mm were used (Fig. 4), which were
applied to both the labial and lingual sides (case 8).
To quantify the dental movement in response to these
forces, the instantaneous displacement of the lower incisor
in the labiolingual direction was considered, i.e. the displacement immediately after the loading was applied. It is
important to notice that this is different from the final displacement of the tooth, as it occurs before the remodelling
of the surrounding bone tissue and it will necessarily be
much smaller. Nevertheless, we hypothesised in this initial
study that although different in magnitude, this immediate
displacement will be proportional to the final displacement,
thereby allowing considerations for the total movement of
the lower incisor and comparisons of the various loading
conditions.
As the state of stress that would be generated in the ligament and the surrounding bone by the movement of the
lower incisor is a determining factor for bone remodelling,
the stress in the labiolingual direction was also evaluated. The
benchmark value of 3.3 kPa, which corresponds to a pressure
of 25 mmHg, is given in all the figures, as this is believed to be
essential for the triggering of the processes of bone remodelling. Indeed, the well-known theory of Schwarz,28 which
confirmed the discoveries of Sandstedt,2 defined the optimal
force as that which causes pressure variations in the periodontal ligament without occluding the capillaries. As the capillary
pressure is from 20 gf /cm2 to 26 gf /cm2 , this is considered to
be optimal. However, it should be noted that Ren et al.,3 could
not define an optimal orthodontic force in their study of the
application of continuous forces of various intensities.
3.
Results
The maximum instantaneous displacement vectors caused
by the application of forces to the lower incisor in cases 1-5
were in the direction of the forces themselves, and these are
reported in Table 2. These values were very similar in cases 1-4,
irrespective of the application site (lingual or labial), while
there was a marked difference in case 5, although the values
are very small in all cases.
Considering case 1, Figure 5 shows the comparison of
the dental displacement in the labiolingual direction upon
Fig. 4 – Complex system of forces applied to the incisor (Case 8): a) linguolabial, intrusion and anticlockwise moment
applied to the labial surface; b) labiolingual, intrusion and anticlockwise moment applied to the lingual surface.
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Table 2 – Absolute values for the maximum
displacement in the direction of the force applied in the
scenarios considered.
Maximum displacement in the direction
of the force applied [!m]
Labial application
Case 1
Case 2
Case 3
Case 4
Case 5
0.15
0.15
0.25
0.25
0.08
Lingual application
0.15
0.15
0.26
0.26
0.04
Fig. 5 – Displacement [mm] in a labiolingual direction in
Case 1. Left: Labial application. Right: Lingual application.
application of the single force to the labial or lingual sides
of the lower incisor. The normal stress in the same direction
("Z ) in the alveolar region for the same case 1 is shown in
Figure 6. In both of these analyses, the lower incisor displacement is concentrated in the crown of the lower incisor, with
virtually none in the apical region, which indicates a tipping
movement. Moreover, Figure 6 shows a trend in the stress generated that conforms to this type of dental movement, i.e. it
shows two regions of compression, in the upper and lower
thirds of the apical region.
In the interest of brevity, the results obtained for cases 2-4
are not reported individually, as they all showed maximum
displacement as localised at the incisal border of the crown of
the lower incisor, with far lower, and almost negligible, values
at the apex. Thus, the fulcrum of the displacement is again at
the apex, in proximity to the centre of displacement, and this
also causes a rotational, i.e. tipping, movement in these cases.
Likewise, the tensional states are analogous, irrespective of
the side of the force application to the lower incisor.
Interestingly, the results for case 5, i.e. intrusion, reveal
a different distribution between the two sides of application
(Fig. 7). Indeed, when the force was applied labially, the trend
was similar to that reported for case 1, albeit to a lesser extent.
However, the lingual application resulted in the displacement
of the upper and lower thirds of the lower incisor in the
same direction as the force, while the central portion of the
lower incisor moved in the opposite direction. In this case,
the displacement trend in the direction of the force applied
(downwards) can provide useful information about the dental displacement. Indeed, the labial force application led to
regional differences in the downwards movements, which is
suggestive of tipping. However, upon lingual application, only
two areas were displaced, and to very limited degrees, thereby
indicating that this lingual application of the force induces
only limited bodily intrusion.
Figure 8 shows a comparison of the stress states in case
5, upon labial (Fig. 8, left) and lingual (Fig. 8, right) application of the force. When the force was applied labially, zones of
compression were evident in the upper and lower thirds of the
apical region of the lower incisor, confirming its tipping. The
lingual application of the force, on the other hand, generated
a more generalised compression throughout the alveolar area
of the lower incisor, thereby indicating bodily intrusion.
For the cases with combined forces, Figure 9 shows the
immediate displacement of the lower incisor for case 6. When
the forces were applied to the labial side of the lower incisor,
the displacement was greater, thereby leading to more pronounced rotation. Figure 10 shows the stress states in a
labiolingual direction in the bony region for the lower incisor.
In both cases, the stress trends are very similar, although
Fig. 6 – Stress ("Z ) in a labiolingual direction [MPa] in Case 1. Left: Labial application. Right: Lingual application.
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159
Fig. 9 – Displacement in a labiolingual direction [mm] in
Case 6. Left: Labial application. Right: Lingual application.
Fig. 7 – Tooth displacement [mm] in labiolingual (Z, above)
and downward (Y, below) directions upon application of the
force on the labial (left) and lingual (right) sides.
larger regions of compression are seen when the force is
applied lingually; here, rotation was impeded by the anatomical features that blocked the movement of the lower incisor,
thereby generating greater stress in the surrounding areas.
Figure 11 shows the instantaneous displacement of the
lower incisor for case 7. Here, the displacement indicated
a tipping movement, irrespective of the side of application,
although it was seen to be greater for the lingual force application. This is confirmed by the trend in stress shown in
Figure 12, where there are larger regions of stress when the
forces were applied labially and the displacement of the lower
incisor was impeded.
Figure 13 shows the immediate displacement of the lower
incisor in case 8. The movements observed, which apparently
included tipping, were very similar. Figure 14 shows the stress
state in the labiolingual direction in the bony region, which
reveals compression of the entire area due to the intrusion
of the lower incisor following the labial force application, and
an apparent rotation when the force was applied lingually, as
seen by the zones of compression.
4.
Discussion
The objective of the present initial study was to compare the
biomechanical responses to labial and lingual application of
Fig. 8 – Stress ("Z ) in a labiolingual direction [MPa] in Case 5. Left: Labial application. Right: Lingual application.
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Fig. 10 – Stress ("Z ) in a labiolingual direction [MPa] in Scenario 6. Left: Labial application. Right: Lingual application.
Fig. 11 – Displacement in a labiolingual direction [mm] in
Case 7. Left: Labial application. Right: Lingual application.
Fig. 13 – Displacement in a labiolingual direction [mm] in
Case 8. Left: Labial application. Right: Lingual application.
Fig. 12 – Stress ("Z ) in a labiolingual direction [MPa] in Case 7. Left: Labial application. Right: Lingual application.
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Fig. 14 – Stress ("Z ) in a labiolingual direction [MPa] in Case 8. Left: Labial application. Right: Lingual application.
an orthodontic force on a lower incisor. To this end, we evaluated the instantaneous displacement of the lower incisor
through the FEM. To complete the picture, the stress distribution within the surrounding bony support was also calculated,
to identify regions of tension and compression. As these
measurements in actual patients would be hampered by the
variability in their tissue responses and by the dental anatomy
itself, a bespoke three-dimensional FEM model was created
that featured both the lower incisor and the alveolus.
To perform the FEM analysis, some simplifying assumptions were made. In this respect, perhaps the most critical
point is that the result of the FEM simulations is not the final
displacement of the lower incisor at the end of the orthodontic treatment, but rather the immediate displacement after
the application of the forces. It is clear that the final tooth
displacement depends heavily on the remodelling phenomena that occur within the bone tissue that supports the lower
incisor, but these were not considered in the present study.
Indeed, these are still considered to be unresolved issues in
biomechanics. Although precise quantification of the final
movements of the lower incisor cannot be obtained with the
present approach, useful comparisons under the various loading conditions can be drawn on the assumption that the final
lower incisor displacement is proportional to this initial displacement.
Secondly, the simulated lower incisor was embedded in a
bone block that is just a rough representation of an authentic alveolar site, even though it was designed according to the
material properties of the trabecular and cortical portions, and
of the periodontal ligament. This approach clearly simplifies
the numerical analysis, as the geometry is easier. However, it
does not consider the possible interactions between different
teeth during this orthodontic treatment, which will undoubtedly be an important factor. Nonetheless, it must be borne in
mind that the stress state in an elastic solid that is loaded
in a relatively small region (like the bone tissue holding the
lower incisor in our analysis) decays with distance according
to the cube of the distance.29 We therefore assumed that the
dimensions of the simulated bone block were large enough to
provide significant results, within certain limits.
Finally, all of the materials were assumed to be linearly
elastic, thereby simplifying the numerical analysis. While
such a hypothesis may be appropriate for bone, dentine and
enamel, the periodontal ligament, as a soft tissue, should be
considered a non-linear, perhaps even viscoelastic, material.
Nevertheless, for the purpose of the present initial analysis,
the hypothesis of linearity appears to be reasonable due to
the small strains in the periodontal ligament which never
exceeded 0.07% to 0.10%.
When this model underwent various simulations to highlight the differences according to the side of application of
the force to the lower incisor, the findings showed substantial differences in four of the cases. For the cases in which
single forces were applied (cases 1-5), the only differences
were noted for an intrusive force (i.e. case 5): there was a
more bodily dental displacement when the force was applied
to the lingual surface of the lower incisor. This confirms
the findings documented in the literature, and particularly
those reported of Ryoon et al.,30 in their prospective clinical
study: i.e. intrusion of the lower incisors is more effective
when the lingual mechanics are exploited. Furthermore, in
the same study,30 and in agreement with Schudy et al.,31 it
was confirmed that the correction of labial overbite using
continuous wire occurs through the extrusion of the posterior sectors and the labial displacement of the incisors,
with minimal incisor intrusion. This demonstrates that the
application of a force with an intrusive component to the lingual surface of an incisor will bring it closer to the centre of
resistance.
Different displacements did, however, result from labial
and lingual application of the combined forces to the lower
incisor. Indeed, with the loading towards the exterior in case
6, this resulted in greater rotation when the combined force
was applied labially to the lower incisor, while in case 7, with
the loading towards the interior, there was greater rotation
when the combined force was applied lingually to the lower
incisor.
Finally, for consideration of the most complex case in
which the lower incisor was subjected to forces and moments
acting in labiolingual, downwards and anticlockwise
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directions, the labial application mainly caused a bodily
retrusive movement of the lower incisor, whereas the lingual application generated tipping, with an apical centre of
resistance.
Among others, Liang et al.,24 also reached the same conclusions. i.e. that bodily (translatory) displacement of a tooth
is favoured by the application of the force to the labial side.
5.
Conclusions
In the present study, various FEM simulations were used
to evaluate the differences in the mechanical responses to
various types of force-loading conditions. These conditions
parallel the application of an orthodontic bracket on the lingual or labial side of an anatomical system that comprises
a lower incisor and its corresponding alveolar region. The
results were the following:
– When single forces are applied to the lower incisor, a tipping displacement is generated, irrespective of the point of
application, except when an intrusive force is applied to the
lingual side.
– When combined linguolabial and intrusive forces are
applied to the lower incisor, it is displaced in a labial direction, irrespective of the side of application.
– When combined labiolingual and intrusive forces are
applied to the lower incisor, the tooth displacement is
essentially reminiscent of tipping, irrespective of the side of
application. This finding is confirmed by the trend in stress
observed around the dental surface.
– For a plausible system of forces acting on a lower incisor,
bodily retrusion occurs when the force is applied labially,
whereas a force applied lingually creates a tipping movement of the lower incisor that is accompanied by a greater
loss of torque.
The intrusion of lower incisors is one of the most common movements in fixed appliance orthodontics. This is used,
for example, during bite opening or for the flattening of the
curve of Spee. The present FEM simulation demonstrates that
lingual orthodontic appliances are more efficient than labial
appliances for bodily intrusion of a lower incisor.
Conflict of interest
The authors have no conflicts of interest.
Riassunto
Obiettivi: Lo scopo di questo studio è di valutare le differenze meccaniche nell’applicazione di una forza ortodontica sulla superficie
vestibolare o linguale di uno stesso dente. Lo studio è stato realizzato
mediante un software di design CAD tridimensionale con il quale è
stato creato un modello di un incisivo inferiore circondato dalla rappresentazione prismatica dell’osso mandibolare. Questo modello è
stato soggetto a vari condizioni di carico con l’analisi a modelli finiti
(FEM).
Materiali e metodi: Un’acquisizione mediante tomografia volumetrica è stata usata per creare un modello geometrico tridimensionale
di un incisivo inferiore, insieme al suo legamento parodontale. Varie
forze singole (orizzontali, verticali e laterali) e momenti (orizzontali
e verticali; orizzontali, verticali e antiorari) sono stati applicati
durante diverse simulazioni al centro della corona clinica della superficie vestibolare e linguale dell’ incisivo inferiore. Per valutare gli
effetti delle varie forze considerate, sono stati considerati la dislocazione immediata e gli stress generati nell’osso e nel legamento
parodontale.
Risultati: Il movimento dentale era influenzato dalla superficie di
applicazione della forza solo quando erano presenti forze intrusive.
Le simulazioni hanno evidenziato movimenti più grandi quando la
forza verticale era applicata sul lato linguale. In genere, il movimento
era di tipping quando erano applicate forze combinate, mentre c’era
più intrusione in seguito all’applicazione di forze combinate e di un
momento antiorario sulla superficie vestibolare.
Conclusioni: L’applicazione di una forza intrusiva su un incisivo
inferiore sembra generare un movimento corporeo, mentre la stessa
forza intrusiva applicata sulla superficie vestibolare determina tipping. Questo dovrebbe essere preso in considerazione ogni volta che
viene fatto un piano di trattamento che prevede l’impiego di apparecchiature fisse.
Résumé
Objectifs: Le but de cette étude a été d’évaluer toutes les différences mécaniques entre l’application labiale et linguale d’une
attache orthodontique par le biais d’une simulation virtuelle qui
comprend une incisive inférieure entourée de son support osseux et
soumise à de différentes conditions de charge.
Matériels et méthodes: L’imagerie par tomographie volumique à
faisceau conique (CBCT) d’une incisive inférieure a été utilisée pour
créer un premier modèle géométrique tridimensionnel et ensuite un
modèle éléments finis de la dent, avec son support osseux et son ligament alvéolo-dentaire. Des forces et des moments individuels
(dans les sens horizontal, vertical et latéral) et combinés (sens horizontal et vertical; horizontal, vertical et antihoraire) ont été appliqués
à ce modèle sur chaque côté de la dent au milieu de la couronne
clinique.
Résultats: Dans le but d’évaluer l’effet des différentes forces prises
en examen, le déplacement instantané dans le sens labiolingual et le
stress engendré sur l’os et le ligament parodontal, suite à ce mouvement, ont été mesurés et utilisés pour comparer les deux sites de
mises en charge.
Conclusions: Le côté où la force a été appliquée n’a influencé le mouvement dentaire que lorsqu’une composante intrusive était présente.
Par voie de conséquence, c’est le résultat souhaité qui devra déterminer le site de placement d’une attache. Les simulations réalisées
ont mis en relief aussi un mouvement en corps supérieur lorsqu’une
force verticale est présente sur la surface linguale. En général, ce
mouvement a été du type oscillatoire lorsque des forces combinées
ont été appliquées; toutefois, une intrusion en corps supérieure a été
enregistrée après application de forces combinées et d’un moment de
force antihoraire sur la surface labiale.
Resumen
Objectivo: El objetivo de este estudio es valorar cualquier
diferencia mecánica entre la aplicación labial y lingual de un
bracket ortodóntico, mediante la creación de un simulacro virtual que
contempla un incisivo inferior rodeado de su soporte óseo, sometiéndolo a condiciones diferentes de carga.
Materiales y métodos: Realización de una imagen por tomografía
de haz de cono (CBCT) en un incisivo inferior para crear, primero, un
Author's personal copy
progress in orthodontics 1 3 ( 2 0 1 2 ) 154–163
modelo geométrico tridimensional y luego un modelo de elementos
finitos del diente, completo con su soporte óseo y ligamento periodontal. Fuerzas y momentos individuales (horizontal, vertical y lateral)
y combinados (horizontal y vertical; horizontal, sentido antihorario)
han sido aplicados a este modelo, en ambos lados del diente, en el
centro de la corona clínica.
Resultados: Para valorar el efecto de las diferentes fuerzas
consideradas, fueron medidos tanto el desplazamiento instantáneo,
en el sentido labiolingual, y el estrés engendrado en el hueso y el
ligamento periodontal, a raíz de este movimiento. Lo anterior sirvió
para comparar los dos lados sometidos a carga.
Conclusiones: El lado en que se aplicó la fuerza influyó en el
movimiento dentario únicamente cuando estaba presente un componente intrusivo. Por consiguiente, en estos casos, el lugar de
colocación del bracket debería depender del resultado que se quiere
lograr. Los simulacros realizados también destacaron un movimiento
en cuerpo superior cuando estaba presente una fuerza vertical en la
superficie lingual. En términos generales, este movimiento fue de tipo
oscilatorio cuando se aplicaron fuerzas combinadas, pero se observó
una intrusión en cuerpo superior en el caso de aplicación de fuerzas
combinadas y un momento antihorario en la superficie labial.
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