Effect of changing various parameters on stress distribution
in mini-screws and surrounding alveolar bone :A threedimensional
finite element analysis
Ayman Mohamed Sadek1 Ibrahim MazenNegm2 KhaledAboulazm3
Aim: The purpose of the study was to clarify and
evaluate the effects of various force magnitudes
and mini-screw length, diameter and insertion angle
on the stress distribution of the mini-screw and
the surrounding bone utilizing a three dimensional
finite element analysis. Methods: We created a
three dimensional finite element model simulating
various clinical situations where mini-screws with
different diameters (1.5 and 2 mm), lengths (9, 11
and 13 mm) and insertion angles (45o and 90o) were
utilized under various force magnitudes (200 and
250gm). The resultant deformations and stresses
from the applied loading were analyzed with a 3D
FEM according to maximum values of total deformations
and Von Mises stress. Results: The Von
Mises stresses in both the mini-screw and the cortical
bone in obliquely inserted 1.5 mm diameter
screws with 200 gm and 250gm force were higher
than those with 2 mm diameter screws. The Von
Mises stresses in the spongy bone in both the vertically
and obliquely inserted 1.5 and 2 mm diameter
screws with 200gm and 250gm force were higher
with the 2 mm diameter screws. The maximum
compressive stress and equivalent micro-strain in
cortical bone was evident with screw dimensions
13mm length and 2mm diameter under an oblique
force magnitude of 250 gm. The Von Mises stresses
in the spongy bone in obliquely inserted 1.5 and 2
mm diameter screws with 200gm and 250gm force
were higher with the 2 mm diameter screws The
maximum stress (Von Mises) generated in the miniscrew
and cortical bone in all the simulated finite
element models was 72.77 and 13.52 MPa respectively.
Conclusion: Increase in the mini-screw diameter
with both vertical and oblique insertion
reduced the deformations and stresses within the
mini-screw and cortical bone but increased the deformations
and stresses within the spongy bone.
Increase in the mini-screw length with vertical
insertion had negligible effect. The deformation
and stress values within the cortical bone were
higher in oblique insertion than vertical insertion
with both (200 and 250 gm) force.
Introduction
Orthodontic mini-screws are increasingly
used by orthodontists to provide temporary
skeletal anchorage during orthodontic treatment
this is because they offer additional
advantages over conventional types of anchorage.
In traditional orthodontic treatment,
extraoral appliances such as headgear and
various intraoral appliances are utilized to
prevent anchorage loss. However lack of
patient compliance in case of extraoral anchorage,
and in some situations of missing
or periodontal affected teeth that are strategic
for intraoral anchorage, the utilization of
these appliances is compromised.
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The orthodontic mini-screws offers several advantages,
including small size, easy surgical
procedure, minimal anatomic limitations which
enable them to be placed in various sites without
damaging any anatomical structures, easy insertion
and removal with minimal trauma, and the
ability of immediate loading after implantation,
in addition to their relatively low cost.1,2
However, the mini-screw success rate in clinical
practice has been reported to range from 83.9%
to 93.3%3,4.It was found that several factors influence
their success and stability like miniscrew
length, diameter5, design (tapered or cylindrical)
6 and surface treatment in addition to
force magnitude7,8, insertion angle and torque9,10,
implantation location, root proximity, soft-tissue
characteristics.
On the other hand, factors identified as causing
failure include inflammation, infection,
nonkeratinized implant sites, and small size
mini-screws, in addition to reliance on patient
compliance in hygiene measures and
application of intermaxillary elastics when
needed.6
Kyung et al. 11 recommended mini-screw
insertion at angles of 30o to 40o in-order to
avoid root injury, rather than perpendicular
to the bone surface. Whereas previous studies
suggested an insertion angle between 50o
and 70o to achieve greater mini-screw stability
under various loading conditions.12,13
Other researches, reported that inserting
mini-screws at a 90o angle to the bone surface
decreases the stress concentration,
whereas mini-screws at angles less than 90o
to the alveolar surface did not provide advantages
as regard to anchorage resistance
force.9,10,14
Finite element analysis (FEA) is a noninvasive
computer-based numerical simulation
technique that is widely used for analyze,
predicting, and forecast the biomechanical
behavior of object movements. FEA provides
the optimal assessment for the physical
response to a mechanical stimulus and permits
the study of different loading conditions.
The successful use of mini-screws in various
applications demands a full understanding of
their biomechanical performance in conjunction
to their surrounding bone. Therefore,
the FEA was utilized to better understand
the stresses generated with different combinations
of mini-screws sizes and angles of
insertion.
The purpose of the study was to clarify and
evaluate the effects of various force magnitudes
and mini-screw length, diameter and insertion
angle on the stress distribution of the mini-screw
and the surrounding bone utilizing a three dimensional
finite element analysis.
Materials and Methods
This finite element study simulated clinical
situations where mini-screws with different
diameters (1.5 and 2 mm), lengths (9, 11 and
13 mm) and insertion angles (45o and 90o)
were utilized under various force magnitudes
(200 and 250gm).
I. Materials:
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The standard MONDEAL LOMAS (Medical
Systems, Muhlheim, Germany)mini-screw
type was chosen for this study due to the following
advantages; (i) The denser pitch design
and increased thread depth that ensured
maximum anchorage. (ii) The self-drilling
tip of the screw with its sharp threaded
flanks provided easy cutting within the bone.
In addition, to special surface treatment for
the screw called anodization process (Anodurit
®) to provide a higher bending fatigue
strength and lessen surface contamination
for screw.
A three dimensional solid modeling software
(Inventor professional version 8) was
utilized for modeling the mini-screw with its
various diameters and lengths (1.5 and
2.0mm) (9.0, 11.0, and 13.0mm) respectively.
Whereas a three dimensional finite element
analysis (FEA) software (Ansys version
14.0Inc., Canonsburg, PA, USA) was
utilized for modeling the cortical and spongy
bone assembly.The server upon which these
programs were ran was, Workstation HP
(ProLaint ML150, with Intel Xeon 3.2 GHz
processors with 1 MB L2 cache, 8 GB
RAM).
Figure 1: Sample of screw on the Inventor
screen
II. Method:
* Construction of geometrical test model incorporated
the miniscrew model which was
created on Autodesk Inventor Version (8)
(Autodesk Inc., San Rafael, CA, USA) according
to the manufacturers dimensions
and design as illustrated in figure 1.
The cortical and spongy bone model were
simulated as a parallelogram where the cortical
bone dimensions were (20 mm length,
20 mm width, and 2 mm height), whereas
the spongy bone dimensions were (20 mm
length, 20 mm width, and 13 mm height).
The assembly of the mini-screw within the
bone model was founded on subtracting the
volume of the minis-crew model from both
the cortical and spongy bone models according
to the Boolean operation. The miniscrew
model was then incorporated into the
bone model in ANSYS* environment on the
assumption of complete osseointegration. In
this study the bone model was considered a
solid type therefore the selected element
types were the tetrahedral and brick. In this
study both the mini-screw and bone (cortical
and spongy) were assumed to be linearly
elastic,homogeneous, and isotropic (thus
having identical properties in all three dimensional
directions) materials. For easier
prediction of material behavior all loadings
were in a linear range under static loading.
The material properties of each different
component representing the model were then
assigned into the program. The linear static
stress/strain analysis needed the definition of
two essential parameters the Elastic
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(Young’s) modulus and Poisson's Ratio for
each component incorporated within the assembly
which are shown in table 1. All interfaces
between the mini-screws and bone
(cortical and spongy) were assumed to be
bonded due to complete ossteoinegration
Table 1: Material properties
Material Young's Modulus Poisson's ratio
[MPa]
Screw (Titanium) 110,000 0.34
Spongy bone 13,700 0.35
Cortical bone 1300 0.35
In this study the mesh generation involved
dividing the constructed geometrical model
(mini-screw and bone) into numerous small
tetrahedral and brick finite elements. The
smaller the elements the more precise, refined
and accurate are the results. The solution
functions obtained from all the elements
compromising the mesh were combined together
to calculate a solution to the whole
body.
Twelve meshed models were required in
order to test all the possible combinations of
the mini-screws (length, diameter and insertion
angle) under the various loading (200
and 250gms), which are listed in table 2. The
following step was applying the structural
load and constraints. A full constraint was
used to simulate the boundary condition. Restriction
of the boundary condition was
mandatory in order to prevent the body from
floating, rotating, and translating. This was
performed by fixing the contouring lines of
the cortical and spongy bone geometries figure.
All the various model combinations incorporating
the screw and bone were subjected to
loads of 200 and 250 gms with a 30o angle to
the horizontal plane table 3. In order to mimic
the solution functions for the resultant
stresses a linear static analysis was made on
a work station* using commercial multipurpose
finite element software package (ANSYS
version 14.0). The resultant deformations
and stresses from the applied loadEgyptian
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ing were collected in tables and figures according
to maximum values of total deformations
and Von Mises stress.
In our study the results were based on the
total deformation (Usum) and the Von Mises
stress (Svon) values. In order to calculate the
microstrain in cortical bone the maximum
compressive stress (S3) was used. This was
calculated in accordance to the formula (microstrain
= S3×72).
Figure 2: Model components after meshing
(a) screw 1.5x9.0, (b) screw 2.0x11.0, (c)
cortical bone with vertical screw hole, (d)
cortical bone with oblique screw hole, (e)
spongy bone with vertical screw hole, (f)
spongy bone with oblique screw hole.
Figure 3: Sample of a complete longitudinal
cut section in finite element models for the
(a) vertical and (b) oblique screw.
Figure 4: Finite element mesh assembly illustrating
boundary constraints.
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Table 2 Mesh density
Volume Number of Nodes Number of Elements
Model #1: 1.5x9.0 - vertical
Cortical bone 887 8,729
Cancellous bone 8,408 59,043
Screw 5,712 45,794
Model #2: 1.5x11.0 - vertical
Cortical bone 1,347 12,119
Cancellous bone 9,784 69,192
Screw 7,007 55,954
Model #3: 1.5x13.0 - vertical
Cortical bone 938 9,140
Cancellous bone 9,976 72,097
Screw 7,652 61,094
Model #4: 2.0x9.0 - vertical
Cortical bone 819 8,242
Cancellous bone 7,782 55,196
Screw 5,353 43,266
Model #5: 2.0x11.0 - vertical
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Cortical bone 773 8,036
Cancellous bone 7,793 56,769
Screw 6,149 49,433
Model #6: 2.0x13.0 - vertical
Cortical bone 777 8,050
Cancellous bone 7,848 58,959
Screw 7,165 57,435
Model #7: 1.5x9.0 - Oblique
Cortical bone 1,599 15,039
Cancellous bone 5,086 37,418
Screw 7,357 57,449
Model #8: 1.5x11.0 - Oblique
Cortical bone 1,903 17,354
Cancellous bone 9,491 67,683
Screw 8,761 68,322
Model #9: 1.5x13.0 - Oblique
Cortical bone 1,942 18,777
Cancellous bone 9,724 74,606
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Screw 10,138 78,361
Model #10: 2.0x9.0 - Oblique
Cortical bone 2,102 19,554
Cancellous bone 9,965 76,587
Screw 11,002 79,023
Model #11: 2.0x11.0 - Oblique
Cortical bone 2,189 19,775
Cancellous bone 10,461 81,146
Screw 11,095 85,268
Model #12: 2.0x13.0 - Oblique
Cortical bone 2,304 20,087
Cancellous bone 10,723 82,214
Screw 11,134 88,573
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Miniscrew Miniscrew
Runs Load Position Diameter Length Runs Load Position Diameter Length
(gm) 90o (gm) 45o
1 200 Vertically 1.5 9 13 200 Oblique 1.5 9
2 250 Vertically 1.5 9 14 250 Oblique 1.5 9
3 200 Vertically 1.5 11 15 200 Oblique 1.5 11
4 250 Vertically 1.5 11 16 250 Oblique 1.5 11
5 200 Vertically 1.5 13 17 200 Oblique 1.5 13
6 250 Vertically 1.5 13 18 250 Oblique 1.5 13
7 200 Vertically 2 9 19 200 Oblique 2 9
8 250 Vertically 2 9 20 250 Oblique 2 9
9 200 Vertically 2 11 21 200 Oblique 2 11
10 250 Vertically 2 11 22 250 Oblique 2 11
11 200 Vertically 2 13 23 200 Oblique 2 13
12 250 Vertically 2 13 24 250 Oblique 2 13
Table 3: The twenty four finite element runs.
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Table 4: The Maximum compressive stress and equivalent micro-strain in the cortical bone in
oblique insertion both 200 and 250 gm force magnitudes
Oblique 200
gm
S3 S3 Oblique 250
gm
S3 S3
Diameter Length MPa με Diameter Length MPa με
1.5 9.0 R14 13.06 940.3 1.5 9.0 R13 16.33 1175.7
1.5 11.0 R16 12.81 921.6 1.5 11.0 R15 15.29 1100.8
1.5 13.0 R18 7.4 532.8 1.5 13.0 R17 9.39 676.1
2.0 9.0 R20 8.51 612 2.0 9.0 R19 10.63 765.4
2.0 11.0 R22 32.19 2317.6 2.0 11.0 R21 40.16 2887.2
2.0 13.0 R24 35.29 2534.4 2.0 13.0 R23 44.11 3175.2
Discussion
The success of mini-screws is influenced by
factors; length, diameter and surface characteristics
in addition to insertion angle and
torque, force magnitude, anatomic location,
soft-tissue characteristics, root proximity,
and primary stability.
Increasing the diameter of mini-screws increases
their primary stability more effectively
than increasing their lengths.5 However,
larger mini-screw diameter can limit the
placement options due to root proximity.
Thus, various tapered mini-screw designs
have been proposed to solve this problem. A
tapered mini-screw increases primary stability
through induction of a controlled compressive
force in the cortical bone.15 However,
excessive insertion torque might lead to
deformations of the surrounding bone that
would cause congestion and necrosis at the
bone interface.16 Increased deformation from
excessive stress may increase inflammatory
mediators to the site and result in bone resorption
and remodeling, which in turn
might cause mini-screw failure.9
In order to maximize the benefit of miniscrews
applications, it is thus important that
their mechanical variables become fully understood.
However, the clinical environment
proposes difficulty in determining the underlying
biomechanical mechanisms for miniscrews
via an experimental approach because
of the limited measureable mechanical
indices and imprecise parameter control.
Hence, FEA can be a suitable method for
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estimating stresses and deformations exerted
on mini-screws simulating real clinical situations.
FEA is a computer-based numerical simulation
technique that is widely utilized for predicting
the mechanical behavior of engineering
structures, in addition to solving solutions
for engineering problems. Based on
their numeric origin, the investigated parameters
can be controlled more specifically,
and many mechanical indices can also be
examined at any site on the model to reflect
the rationale of a mechanical response.
The validity of three dimensional FEA is
mainly dependent upon: 1) Similarity of the
finite element model to the real structure to
be analyzed since excessive simplifications
in the geometry would inevitably lead to
considerable inaccuracy. 2) Accurate and
precise modeling of the material properties
utilized in the case model. 3) Effectiveness
of modeling to the boundary conditions.
In our study the model consisted of the following
components: mini-screw, cortical
and spongy bone. The dimensions of the
mini-screws in our study were 1.5 mm and 2
mm in diameter, which were the most preferred
and widely used diameters. 14,17,19 According
to Miyawaki et al 3 the success rate
of mini-screws increased from 0.0% to
83.9% with the diameter increase from 1.0
to 1.5mm.
The bone geometry in this study was simplified
and simulated as a parallelogram composing
both the cortical and spongy bone.
The dimensions for the cortical bone were
(20mm length x 20mm width x 2mm high)
whereas the spongy bone dimensions were
(20mm length x 20mm width x 13mm high).
These dimensions were based on the recommendations
of Liu et al.20
The mini-screw solid modelling was created
at the Autodesk Inventor Version (8)*. This
software program provided more accurate
simulation the exact mini-screw design,
while in previous studies the mini-screw design
was simulated directly in the ANSYS†
environment software which had limited options
in accurate design simulation operations.
The subsequent operations which involved
Boolean, osseointegration and
boundary constrains were in accordance to
Perilloet al.21
Pickard et al 22recommended a 45oinsertion
angle for the mini-screws to the bone surface
to creat a larger contact area between the
cortical bone and the mini-screw. This will
increase the placement torque, resulting in a
positive effect on the mini-screw stability
during orthodontic forces application. However,
Joseph et al 23 and Choi et
al24suggested that the 90oinsertion angle of
mini-screws in order toavoid the setbacks of
oblique insertion such as potentially creating
longer lever arms and reducing the insertion
depths inside the bone. Insertion at an
oblique angle might cause slippage of the
mini-screw during its first contact with the
bone surface as well as microdamage of the
cortical bone.
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In our study the increase in length for all the
vertical mini-screw insertions with both 200
and 250 gm of force magnitude had no effect
on the deformation and Von Mises stress
within the mini-screws. Similarly this was
evident within the cortical and spongy bone.
However, in case of oblique insertion the
mini-screw length increase reduced Von
Mises stresses generated within the miniscrew
and cortical bone but increased the
Von Mises stresses within the spongy bone.
Therefore, the increase in mini-screw length
can be considered more effective with
oblique insertion this is concurrent with the
findings of Choi et al. 24 who concluded that
the maximum von Mises stresses increased
as insertion angle decreased during miniscrew.
The stresses in cortical and spongy
bone were lowest for mini-screws placed at
90o to the bone surface, irrelevant of miniscrew
design. This finding is consistent with
the results of previous studies 9,10 demonstrating
that maximum von Mises stresses in
mini-screws and cortical bone decreased as
insertion angle increased. An analysis of
stress distributions in cortical and spongy
bone revealed that the stress was absorbed
mostly by cortical bone, and small amount
was transmitted to spongy bone.9
These finding were cited by Liu et al 20 in
their FEA study. They reported that the exposed
length (the level arm of the bending
moment) was the real factor influencing
stress and displacement not the total length
of the mini-screw so longer mini-screw
might not provide extra stability if it cannot
be implanted deeply enough to reduce the
lever arm. In addition Lin et al.20 reported
that the exposed lengths of mini-screws were
significantly associated with cortical bone
stress during force application. Neither orthodontic
force direction nor the insertion
angle affect cortical bone stress significantly.
20
In our study the increase in mini-screw diameter
from 1.5 to 2mm with both 200 and
250 gm force magnitudes in both vertical
and oblique insertion of mini-screws decreased
the deformations and stresses within
the mini-screws and cortical bone. However,
these mechanical properties increased in
spongy bone. These findings were in agreement
with Wilmes et al 13 and Liu et al20who
reported that increasing the mini-screw diameter
was the mosteffective way to reduce
the stress, hence increasing the stability and
decreasing the failure rate.
Finally, it could be concluded that with both
vertical and oblique insertions the pattern of
deformations and stresses within the screw
and cortical bone decreased with increase in
length and diameter with both force magnitudes
(200 and 250 gm). However the stress
values within the cortical bone were higher
in oblique insertion.
Our results were consistent withPerillo et al
10 Woodall et al 14 and Lee et al 19 in their
studies on cadaver and finite element model.
They found that the anchorage resistance
offered by screws inserted at 90o to the alveolar
process bone was greater than the anchorage
resistance of screws inserted at 30o
or 60o. In addition to the cortical bone stress
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created via loading mini-screws inserted at
90o was less than the bone stress created via
loading mini-screws at either 30o or 60o.
They recommend insertion of the miniscrews
perpendicular (90o) to the cortical
bone as long as it did not risk root damage in
order to take advantage of the improved biological
and biomechanical stability when
applying heavy forces.
Our results also supported the outcomes of
Choi et al 24 in which they designed a threedimensional
maxilla model of a dentition
with extracted first premolars and used 2
types of mini-screws (tapered and cylindrical)
with 1.45mm diameter and 8mm length
inserted at 30o, 60o, and 90o with respect to
the bone surface. They concluded that both
cylindrical and tapered mini-screw designs,
perpendicular 90o insertion to the bone surface
is recommended to reduce stress in the
surrounding bone and offer better anchorage.
The maximum stress (Von Mises) generated
in the mini-screw and cortical bone in all the
simulated finite element models in this study
was 72.77 and 13.52 MPa respectively. Both
of these values were well below the known
yield stress of titanium (692 MPa) and cortical
bone (200 MPa) respectively.25 Therefore,
it can be concluded that mini-screws
and cortical bone had sufficient strength to
withstand force magnitudes up to 250 mg.
Frost26noted that if the peak strain exceeded
4000 micro-strain,the structural integrity of
the bone was threatened leading to pathologic
overload and micro-damage accumulation
with subsequent bone resorption and reduction
of bone strength, resulting to miniscrews
loosening.
In the current study the concept of microstrain
was considered. The maximum stress
value at the cortical bone was observed with
the oblique insertion of mini-screws. This
value (44.1 MPa) was equivalent to 3175.2
micro-strain. This calculated value was well
below the physiologic limit (4000 microstrain)
of bone integrity. Therefore, it can be
concluded that the FEA utilized in our study
is a useful tool to estimate the force effect on
stress distribution and predict the tissue reaction
against the orthodontic and orthopedic
force.
There are limitations in this study that must
be taken into consideration when interpreting
the data.
The cortical bone thickness of model was
selected according to previous studies.20,27 A
cortical bone. thickness of 1.5 mm was utilized
to simplify model construction.
Whereas the peri-screw area exhibits anisotropy
and heterogeneity during physiological
conditions, this study was performed with an
isotropic and homogeneous model that considered
physical features only.
Conclusions
Increase in the miniscrew diameter
with both vertical and oblique insertion
reduced the deformations and stresses
within the miniscrew and cortical bone but
increased the deformations and stresses
within the spongy bone.
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Increase in the miniscrew length
with vertical insertion had negligible effect.
However, in oblique insertion it reduced
the deformations and stresses within
the miniscrew and cortical bone but increased
the deformations and stresses
within the spongy bone.
The deformation and stress values
within the cortical bone were higher in
oblique insertion than vertical insertion
with both (200 and 250 gm) force.
The maximum stress (Von Mises)
generated in the miniscrew and cortical
bone were below the yield stress of pure
titanium and cortical bone. Therefore, the
miniscrews and cortical bone had sufficient
strength to withstand force magnitudes
up to 250 gm.
The maximum value of calculated
microstrain on the cortical bone was well
below the physiologic limit of bone integrity.
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