Keywords palatal slope bone-borne expander - miniscrew positions - stress distribution - nasomaxillary
area - finite element
Introduction
One typical problem in orthodontic practice is maxillary transverse discrepancy, which
affects patients with diverse individual characteristics such as posterior crossbite,
crowded teeth, broad buccal corridor, and uneven dental attrition.[1 ] A technique utilized to address transverse maxillary discrepancy is maxillary expansion,
with the objective of optimizing impact of transverse dentofacial orthopaedics while
minimizing dentoalveolar adverse effects.[2 ] Traditionally, conventional tooth-borne palatal expanders are used to expand maxillary
arch width; however, adverse effects on anchored teeth may have occurred.[3 ]
In order to create an appropriate posterior occlusion for long-term stability, orthopaedic
expansion of the basal bone is essential.[4 ]
[5 ]
[6 ] Miniscrew-anchored palatal expanders or bone-borne rapid palatal expanders (B-RPE)
have been beneficial to late adolescent or adult patients undergoing maxillary expansion
because of their ability to dissipate expansion force directly through basal bone,[7 ] which reduces undesirable side effects compared to conventional tooth-borne expanders
and the need to perform surgery in many cases.[8 ] Generally, B-RPE is composed of four anchored miniscrews placed at paramedian area
or at palatal slope, called palatal slope bone-borne expander, which has been deemed
effective and secure regarding anchorage support and success rate.[3 ]
[6 ]
[9 ] Even though satisfying outcomes have been achieved clinically using palatal slope
bone-borne expanders in some studies,[5 ]
[10 ]
[11 ]
[12 ] variations in miniscrew positions were addressed, and the mechanical information
regarding variation in appliance design, especially anchored miniscrew position, is
not sufficient to describe clinical scenario.
Three-dimensional finite element analysis (FEA) is a computerized technique that is
used to investigate the impact of mechanical stimuli in biological subjects, and it
has been used to investigate the mechanical effect of maxillary expansion.[3 ]
[4 ]
[6 ]
[13 ] Thus, this study focuses on investigating the stress distribution pattern of palatal
slope bone-borne expander on maxillary area according to a different anteroposterior
position of anchored miniscrews using FEA that might provide additional mechanical
data for explaining possible correlation to clinical outcome of this appliance.
Materials and Methods
Three-Dimensional Virtual Nasomaxillary Model and Palatal Slope Bone-Borne Expander
Three-dimensional (3D) nasomaxillary model in this study was acquired from computed
tomography (CT) images of an artificial human skull (QS 7/9-E artificial human skull)
(SOMSO Modelle GmbH, Coburg, Germany) of Sermboonsang et al studies.[14 ]
[15 ] Dolphin 3D imaging software (Patterson Dental Supply, Chatsworth, United States)
was used to build up the model. The outer cortical layer of maxilla was obtained by
extracting outer boundary of each maxillary cross-sectional CT image. The aforementioned
boundaries were used to build up the 3D stereolithography (STL) exterior model of
maxilla. All maxillary tooth models were also segmented to separate from the maxilla
model, which included incisors, canines, premolars, and molars. All models generated
from CT images were recorded in STL file format. STL models of cortex were subtracted
from teeth to build up maxilla with teeth cavity. Then, the cancellous layer was created
by 1.6 mm internal offsetting of cortical layer to achieve a cortical bone thickness
distribution between 1.2 and 2.0 mm.[16 ] All STL models, that is, cortex layer, cancellous layer, and teeth, were converted
into nonuniform rational basis spline models prior to being completed as computer-aided
design (CAD) solid models using CAD software (VISI, Hexagon AB, Stockholm, Sweden).
The cortical layer of maxilla was completed by subtracting the outer boundary of maxilla
with cancellous layer. Periodontal ligaments (PDL) were constructed by offsetting
tooth root surface by 0.2 mm.[3 ] The intersection volume between offset model and cortical bone was defined as PDL.
Suture was modeled by creating a 0.5 mm width of midpalatal segment.[3 ] This was performed by separating the CAD model of maxilla in both cortex and cancellous
layers using “cut bodies” function. The separated cortex and cancellous layers were
then united together as partly ossified one null straight functional unit in approximately
posterior one-third of palate geometry to represent the suture,[17 ]
[18 ] and the combined model was assigned material property of suture, stage D maturation.[19 ] The model was selected to obtain only nasomaxillary area as an area of interest,
which facilitates computational calculation and reduces time-consuming process of
creating a comprehensive model of entire skull with all of the sutures.[4 ] The components of geometric nasomaxillary models were displayed in [Fig. 1A ].
Fig. 1 (A ) Components of three-dimensional virtual nasomaxillary model. (B ) Three-dimensional virtual nasomaxillary model with palatal slope bone-borne expander
in occlusal and sagittal view: Model A, two anterior miniscrews were located between
maxillary canine and first premolar, and two posteriors between second premolar and
first molar; Model B, two anteriors were located between maxillary lateral incisor
and canine, and two posteriors between second premolar and first molar; Model C, two
anteriors were located between maxillary canine and first premolar, and two posteriors
were distal to first molar.
Basically, palatal slope bone-borne expanders consist of a stainless steel jackscrew
expander or expansion screw, self-cured acrylic resin plate, and stainless steel miniscrews.
Hyrax expanders (Dentaurum, Ispringen, Germany) and miniscrews (Bio-Ray, New Taipei
City, Taiwan) were employed as the prototype for modeling. The expander screws have
a 0.1 mm transverse widening on each side with every turn of expansion. Expander screw
position was determined at the center of the model's palate area between second premolar
and first molar, and was linked to four supported miniscrews with 2 mm in diameter
and 12 mm in length on acrylic plate.
The palatal slope bone-borne expander appliance was designed in three different anteroposterior
miniscrew placement locations, which were designated as model A, B, and C, respectively,
and shown in [Fig. 1B ]. Miniscrews were set approximately 8 mm vertically from alveolar ridge[3 ] and were engaged bicortically.[9 ]
[14 ] Model A: two anterior miniscrews were located between maxillary canine and first
premolar, and two posterior miniscrews between second premolar and first molar.[3 ]
[12 ] Model B: two anteriors were located between maxillary lateral incisor and canine,
and two posteriors between second premolar and first molar.[6 ] Model C: two anteriors were located between maxillary canine and first premolar,
and two posteriors were distal to first molar.[5 ]
[13 ]
Element Generation
FEA meshing or discretization is the process of transforming a continuous solid region
into a discrete computational domain including a finite number of elements that enables
the numerical calculation of structural equations using FEA.[20 ] The assembled geometric models for mathematical analysis were transformed and imported
into a FEA pre-processing program (Patran, MSC Software Corp., California, United
States) to generate the desired finite element volumetric mesh, prior analysis in
FEA program (Marc Mentat, MSC Software Corp., California, United States).
Three distinct values of the element were produced, and the corresponding equivalent
von Mises stress experienced by miniscrews was examined in the convergence test. According
to the convergence results ([Fig. 2A ]), a four-node tetrahedral mesh-size of 1.0 mm was used for all portions, except
for teeth, PDL, and components of the palatal slope expander, whose 0.5 mm element
size was set. Model A consists of 1,278,617 total elements and 364,482 nodes. Model
B consists of 1,264,475 total elements and 362,418 nodes. Model C consists of 1,284,717
total elements and 370,408 nodes. The simulated materials were assumed to be elastic,
isotropic, and homogeneous, and the model structures were characterized by particular
properties listed in [Table 1 ].[2 ]
[3 ]
[14 ]
[15 ]
Table 1
The material properties of each component[2 ]
[3 ]
[14 ]
[15 ]
Component
Elastic modulus (MPa)
Poisson's ratio
Cortical bone
13,700
0.30
Cancellous bone
7,900
0.30
Suture
0.667
0.40
Stainless steel
200,000
0.33
Acrylic resin
2000
0.30
Tooth
20,700
0.30
PDL
0.68
0.49
Abbreviation: PDL, periodontal ligaments.
Fig. 2 (A ) Convergence test and (B ) the boundary condition of a three-dimensional virtual nasomaxillary model with palatal
slope bone-borne expander.
Boundary Condition
The boundary condition was displayed in [Fig. 2B ]. The node of geometric model was set to zero displacement and rotation and was confined
in the posterosuperior region and in the middle of facial bone at the superior region
of zygomatic process of zygomatic bone.[14 ]
[15 ]
[18 ]
Contact Condition
All bony parts of geometric model, expander screws, acrylic resin plate, and miniscrews
were set as having no relative displacement and assumed that miniscrews and bone contact
were fully anchoring.[14 ]
[15 ]
Mechanical Simulation and Parameter Measurement
Simulation of the expansion effect was created by enforced displacement toward the
center of expansion screw transversely for 0.1 mm on each side. Maximum principal
stress, equivalent elastic strain distribution on the maxilla, von Mises stress on
appliance's component, and displacement of teeth were evaluated. The magnitude of
each parameter measurement was presented visually using a gradient color column, where
a light gray color means the highest value and a deep blue color means the lowest
value of each parameter, respectively.
Results
Maximum Principal Value of Stress
In occlusal view, the maximum principal stress of the cortex bone was mostly found
at the bone-miniscrew interface for all models (models A–C), and the stress distribution
patterns were displayed in [Fig. 3A ]. The stress was not only concentrated at miniscrew-supported area but also noticed
the stress accumulation at buccal bone of posterior teeth, lateral wall of nasal cavity,
and superior surface of the zygomatic bone, which was obviously seen in lateral and
frontal views.
Fig. 3 Maximum principal value of stress: (A ) Stress distribution pattern of cortex bone in occlusal, lateral, and frontal view;
(B ) Stress distribution pattern of cancellous bone in occlusal view.
Stress of cortex bone produced by model B had the highest amount with values above
140 MPa, which were observed in areas of two anterior miniscrew engagements, and model
A had the lowest amount of stress ([Table 2 ]). However, stress in model A apparently showed the intersecting area between anterior
and posterior miniscrews and was diffused via palatal vault directed through the midline,
with the largest area of stress dispersion along dental arch from canine to first
molar. The stress distribution pattern had a uniformly similar pattern in models B
and C, which mostly accumulated around anchored miniscrews.
Table 2
The maximum principal value of stress of cortical and cancellous bone (MPa)
Model
Maximum principal value of stress of cortical bone (MPa)
Maximum principal value of stress of cancellous bone (MPa)
A
33.28
6.22
B
149.12
5.80
C
48.11
4.97
For all models, stress on cancellous bone was primarily concentrated in the anterior
region near incisive foramen and then dissipated through palate in a posterior and
lateral direction; however, model A revealed notable area of stress concentration
along midpalatal line. Models A and C exhibited the highest and lowest values of stress,
respectively; nevertheless, model C showed a more uniform distribution pattern and
dispersed evenly all over the palatal contour than other models ([Fig. 3B ]).
Equivalent Elastic Strain
The elastic strain value of all models was shown in [Table 3 ]. Equivalent elastic strain distribution pattern was similar to the principal stress
pattern for all models. Model A had the lowest value of strain both in cortex and
cancellous bone. The highest amount of strain values was 11,222.23, which was detected
in areas of two anterior miniscrews of model B and correlated with the highest value
of stress in this area, whereas model C has the most consistent strain pattern, which
was consonant with the stress distribution pattern ([Fig. 4A ], B).
Fig. 4 Equivalent elastic strain: (A ) Strain distribution pattern of cortex bone in occlusal view. (B ) Strain distribution pattern of cancellous bone in occlusal view.
Table 3
The equivalent elastic strain of cortical and cancellous bone (µε)
Model
Equivalent elastic strain of
cortical bone (µε)
Equivalent elastic strain of
cancellous bone (µε)
A
2,733.20
4,476.00
B
11,222.23
8,867.86
C
4,721.58
6,530.13
Equivalent von Mises Stress
The highest value of equivalent von Mises stress was located on the expander screw
for all models. Force was mainly concentrated at expander screw body-acrylic resin
plate interface and transmitted via the acrylic resin plate to supported miniscrews.
Model A had the highest value of the equivalent von Mises stress at the expander screw,
while model B had the lowest value. Anteriorly supported miniscrews had a higher equivalent
von Mises stress value than posteriorly supported miniscrews in all models. The value
of equivalent von Mises stress on the appliance's component was indicated in [Table 4 ].
Table 4
The equivalent von Mises stress of palatal expander appliance (MPa)
Model
Anterior miniscrews
Posterior miniscrews
Expander screw
Acrylic resin plate
A
468.86
418.81
701.5
202.70
B
397.06
233.71
523.5
108.16
C
445.70
269.42
655.9
460.78
Displacement
Teeth displacement was principally evaluated in the transverse plane; however, anteroposterior
and vertical directions were also evaluated. Model A displayed the greatest amount
of transverse displacement of teeth, with a shallow bell-shaped displacement pattern,
while model C displayed the least amount of transverse displacement. However, model
C displayed a very shallow curve line, which indicates a more consistent transverse
displacement pattern when compared to other models, as shown in [Fig. 5A ]. Anteroposterior tooth displacement was only noticed at maxillary central incisor
of all models, and the amounts of displacement were 0.003, 0.004, and 0.008 mm in
model A, B, and C, respectively. Vertical displacement was mainly found at buccal
cusp of posterior teeth. Model A had the largest amount of vertical displacement (0.005 mm),
and it was on buccal cusp of the maxillary canine and posterior teeth. The least amount
of vertical displacement was in model C (0.002 mm), while model B's vertical displacement
(0.003 mm) was nearly equal to that of model C's.
Fig. 5 Displacement: (A ) Transverse teeth displacement in occlusal view and graph plot of transverse teeth
displacement; (B ) Overall transverse displacement area in occlusal view, pterygomaxillary junction
(black arrowhead), maxillary tuberosity (red arrowhead), and pterygoid plate of sphenoid
bone (blue arrowhead); (C ) The V-shape (green arrow) transverse displacement pattern of all models in frontal
view.
The overall transverse displacement of all models was displayed in [Fig. 5B ]. Model B showed the shortest area of displacement in anteroposterior direction;
the displacement was confined posteriorly at maxillary tuberosity. The longest area
of displacement was in model C; the displacement pattern dispersed to pterygoid plate
of the sphenoid bone, while the area of displacement in model A was close to pterygomaxillary
junction. In frontal view ([Fig. 5C ]), it exhibited V-shape transverse displacement pattern for all models, where the
tip of V was located above vomer bone and the base of the V was located in area of
alveolar bone and teeth. This pattern indicated that the more superior the model,
the less transverse displacement showed.
Discussion
This study utilized FEA to primarily investigate and compare stress distribution patterns
on the maxillary bone structure with different anteroposterior miniscrew positions
of palatal slope bone-borne expander. Several studies[3 ]
[4 ]
[6 ]
[9 ]
[17 ]
[21 ] have shown that FEA is a beneficial method for analyzing stress, strain, and force
distributions pertinent to orthodontic treatment of maxillary transverse discrepancy.
Moreover, FEA is also an alternative, noninvasive, and convenient tool to study how
maxillary bone and teeth respond to transverse force from maxillary expander.[22 ] Within the context of limitations of our study, the findings suggested that there
was a variation in stress distribution and outcome pattern depending on the position
of the miniscrew. This finding was in the same manner as previous investigations,
which was also interested in the effect of miniscrew positions of bone-borne expander.[13 ]
Adult patient skeletal expansion has been demonstrated to be successful when using
bone-borne palatal expanders with a variety of appliance designs.[7 ]
[8 ]
[23 ] According to available scientific studies,[3 ]
[6 ]
[10 ] palatal slope bone-borne expanders had superior advantages over other types of B-RPE
because of their versatility in allowing the positioning of anchor screws in a variety
of positions, ease of fabrication and adjustment, and less stress accumulation at
the area around anchored miniscrews compared to other designs. Expanders can be employed
for the purpose of retention once the expansion process has been completed and simply
offer direct or indirect absolute anchorage. Despite the fact that B-RPE has been
utilized in orthodontic specialty for many years, few studies[6 ]
[13 ] examined the impact of different anchor screw positions of B-RPE on stress distribution,
which may be related to treatment outcome.
Many factors, especially the modeling process, affected the stress distribution pattern.
It is important in the field of biomechanics to incorporate all contributing factors
because reliable results can possibly be obtained if the FEA model reflects the actual
skull shape and form. However, the model was partially selected into an interesting
nasomaxillary area and simplified some anatomical structures in our study and reduced
the time-consuming phase of modeling process. Hence, interpretation of results for
clinical application must be approached with caution. The bone thickness of the model
may affect stress and strain values.[2 ]
[24 ] Even though a plastic human skull was used as the prototype for reverse engineering
in our study, the cortical bone thickness was then modified to achieve a more realistic
model.[14 ] Stress distribution to other areas, not only the palate, was close to what was found
by MacGinnis et al[22 ]; therefore, a further study including the whole skull with all sutures would demonstrate
a more realistic clinical scenario.
The ability of the nasomaxillary model to endure stresses applied during expansion
is largely dependent on the material properties and conditions that make up the model.
However, there was inconsistent material property value addressed in several studies;
it was technically challenging to assign the suitable material properties for each
situation, and small changes in these values might not have a meaningful impact on
the patterns of stress, strain distribution, and the final displacement results.[25 ]
A report by Boryor et al[4 ] indicated that stress distribution on maxillary bone is determined primarily by
palatal expander design. Different B-RPE designs showed unique stress distribution
characteristics.[5 ] The range of stress values and distribution patterns of the present study coincided
with several previous FEA reports.[3 ]
[17 ]
[22 ]
[26 ] Stress and strain color map gradients or distribution patterns were directly correlated
to expansion outcomes. Efficient force transmission to the resistance area as a suture
and low stress around the anchorage site are necessary for successful maxillary expansion.[25 ] Because model A had the lowest value of stress concentration around miniscrews,
the residual force was possibly able to transmit along the midline and palatal contour
more pronouncedly than in models B and C.[22 ]
The procedure for attaching miniscrews to alveolar bone and acrylic resin connector
may affect the force distribution from expander screws through the resin plate and
miniscrews.[25 ] Because there was a difference in the orientation and line of force of the two anterior
miniscrews from the expander screw body in model B, this may be the reason why model
B had the highest value of force concentration around miniscrews when compared to
models A and C.[9 ] The short distance between each support miniscrew and expander screw of model A
may explain why the stress distribution of the cortex bone of model A not only had
a unique width with a superimposed area of stress distribution from maxillary canine
to second premolar but also exhibited the largest amount of overall transverse displacement.
While miniscrews of models B and C had approximately similar distances between anterior
and posterior support miniscrews, the stress distribution pattern of cortex bone,
where force was mainly concentrated around miniscrews, was fairly indistinguishable.
In addition to the load-bearing region, force also affected buccal bone of maxillary
posterior teeth and the distant midface structuress.[22 ] This could be related to findings from previous clinical studies[6 ]
[12 ]
[23 ] which indicated that buccal tooth tipping, buccal alveolar bone height reduction,
and aching around the nose area could possibly occur after using a palatal slope bone-borne
expander. Interestingly, the stress distribution pattern of cancellous bone was related
to the distribution of cortex bone, but in the opposite direction. This circumstance
may be because a portion of the energy delivered into the mechanical system by the
applied transverse displacement at expander screws was converted into strain energy
and compressive strain inside the device's components rather than being transmitted
to the sutural and bony structures.[17 ] Thus, the difference in stress value between cortex and cancellous bone was apparently
shown, especially in model B. Anyhow, the stress value of cancellous bone in each
model had a little difference in a range of 4 to 6 MPa.
In compliance with the study by Frost,[27 ] strains valued above 3,000 µε be able to increase the number of microfractures in
bone, but the remodeling process normally repairs them, while strains valued above
25,000 µε can cause bone fractures. When stress values and accumulative strain surpass
physiological thresholds, the bone remodeling process may enter the pathologic overload
phase. This is characterized by a predominance of stress fractures and bone resorption
over new bone formation, marginal bone loss, and overstressed and loosening anchored
miniscrews.[9 ]
[11 ]
[17 ]
[27 ] The amount of equivalent elastic strain was approximately between 2,500 and 11,000
µε, which was much smaller than the previous B-RPE FEA study,[14 ] which exhibited more than 50,000 µε. This may be implied by the fact that palatal
slope bone-borne expanders demonstrated less possibility of miniscrews loosening compared
to paramedian bone-borne expanders, in accordance with 2014 research conducted by
Lee et al.[3 ]
Equivalent von Mises stress is usually used for ductile materials to determine if
they will yield or fracture.[2 ] The study by Lee et al[28 ] informed us that the cortical bone thickness of the anterior palate is thicker than
that of the posterior palate, which may explain why equivalent von Mises stress value
at anteriorly supported miniscrews was higher than that at posteriorly supported miniscrews
in all models.
The pattern of transverse displacement of both bone and teeth apparently corresponded
to the stress distribution pattern. The overall displacement color map indicated that
the location of the miniscrews most likely contributed to the suture separation, in
addition to the different degrees of ossification the midpalatal suture encountered
along its entire length.[17 ] According to previous studies,[6 ]
[12 ]
[23 ] center of resistance and center of rotation of the zygomaticomaxillary complex are
present during palatal expansion. The unavoidable V pattern of maxillary halves displacement
in frontal view was consistent with previous FEA studies.[14 ]
[28 ] This may be the result of bone splitting at two centers of rotation: one was located
at the superior boundary condition of this model or above at frontomaxillary area,
and the other was at pterygomaxillary area.
This study was presumed to have isotropic qualities at specific healing time, whereas
skull bone is anisotropic and mechanical properties at suture line can be changed
over time. The influence of soft tissue effects, bone deformations or remodeling,
or individual characteristics such as tooth position and arch form were not taken
into consideration in this study. Therefore, these elements should be used in future
studies to determine a more accurate scenario.[25 ]
[28 ]
Conclusion
In the scope of this investigation limitations, the study identified differences in
stress distribution patterns based on the anteroposterior position of miniscrews in
palatal slope bone-borne expander, as determined through computational calculations.
In model A, the results suggested favorable miniscrew positions for achieving optimal
expansion, including (1) placement sites with a short distance between the anterior
and posterior anchored miniscrews to facilitate force transfer from the expander screw,
(2) placement sites allowing for a short distance between the expander screw and miniscrews,
and (3) placement sites where the orientation of miniscrews aligns with the line of
force. On the other hand, in model C, an equally considerable distance between anchored
miniscrews and expander screws had an advantage in terms of consistent biomechanics.
