EFFECT OF LENGTH AND DIAMETER OF MINISCREW ON STRESS
DISTRIBUTIONS IN PERI-MINISCREW PALATAL BONE
Nat Saengwiwatcharoen1,*,#, Thongchai Fongsamootr2
Department of Mechanical Engineering, Faculty of Engineering, Chiang Mai University,
Chiang Mai, Thailand
*email: natsaeng2531@gmail.com
Abstract
This study aimed to evaluate the impact of thread length and diameter of orthodontic
mini-screw on the Von Mises’ stress in peri-mini-screw palatal bone, using the three
dimensional finite element method. Three dimensional models of mini-screw were designed
with thread lengths of 6.0mm, 8.0mm and 10.0mm and diameters of 1.2mm, 1.8mm and
2.0mm, each being inserted into palatal bone. Traction of force of 2 N was applied to the
neck of the mini-screw in direction parallel to the horizontal plane and overall Von Mises’
stress in peri-mini-screw palatal bone was determined. Mini-screw having the thread length
of 10mm showed least amount of stress within the bone as compared to the mini-screw with
thread length of 6mm and 8mm. and mini-screws having the diameter of 2mm showed least
amount of stresses within the bone as compared to the mini-screw with diameter of 1.2mm
and 1.8mm. The maximum stress occurred at the first thread of mini-screw located near the
neck of mini-screw. From this case study the result showed stresses in palatal bone increase
as the length of mini-screw decreases and also with diameter, stresses in palatal bone
increases as the diameter of mini-screw decreases.
Keywords : mini-screw, orthodontic anchorage, length of mini-screw, diameter of miniscrew, finite element analysis
Introduction
Efficient attainment and control of anchorage is fundamental to successful
Orthodontic treatment. Because of anchorage limitations, we may have to settle for
compromised treatment alternative, or more complicated treatment alternatives like extra-oral
traction devices (which heavily depend on patient’s compliance).1 Mini-screws have been
used as temporary anchorage in orthodontics for various purposes. They have gained
popularity over on-plants and mini-plates because of their versatility, minimal surgical
invasiveness, ease of insertion and removal, ready use after initial wound healing, and low
cost. Whereas dental s have high success rate at 81% to 100%,2 the reported success rates of
mini-screw are not satisfactory, ranging from 0% to 100% with failure rates of 10% to 30%
in most instances.3
Factors associated with mini-screw failure include screw diameter and length,4 patient
age5, cortical bone thickness,6 the amount of force application, possible damage to anatomic
structures such as dental roots, nerves and blood vessels, the possibility of screw breakage
during placement and removal, and failure due to peri-mini-screw inflammation.7
Stress analyses of mini-screw are necessary for the investigation of bone and
maximum anchorage success. Incorrect design, placement or loading of mini-screw may lead
to disturbed bone turn over and consequent loss.8Since clinical determination of stress and
strain distribution in the bone is not possible, an alternative technique should be used.
The three dimensional Finite Element Method offers a viable and non-invasive
alternative for analysis of the stress and strain distribution, which is unique because of its
ability to model geometrically complex structures.9 FEM allows predicting stress distribution
in the contact area of the mini-screw with the palatal bone, also in mini-screw.
This purposed of this study was to investigate the influence of mini-screw design
factors, including variation of screw length and diameter. Finite element analyses were
conducted for identification of the design parameters as three different lengths and diameters
of mini-screw.
Methodology
Finite element analysis was used to investigate the influence of design factors on
primary stability. The basic shapes of the finite element mini-screw and palatal bone models
were illustrated by using computer design software (SolidWorks). Titanium-alloy (Ti6V4)10
mini-screw with three different lengths, 6mm 8mm and 10mm, and three different diameters,
1.2mm 1.8mm and 2mm, were modeled. A cortical bone block 1.5mm thick bonded with
18.5-mm cancellous bone was modeled around the mini-screw with all threads imbedded in
bone. The overall dimensions of bone block were 20 mm in height, 5mm in mesiodistal
length and 5 mm in buccolingual width. Both the bone and mini-screw were assumed to be
homogeneous, isotropic and linear elastic. The material properties of elements in the models
are given in Table 1.10 The loading condition was apply 2 N horizontal traction force at the
neck of mini-screw parallel to bone surface as illustrated in fig.1. The boundary condition
was full constraint at surface of bone, no penetration contact applied for contact surface
between mini-screw and bone surface.11The equivalent stress (Von Mises) was calculated,
and the stress distribution on bone and mini-screw elements were evaluated. Von Mises
equivalent stress can be defined by the following equation:
 equivalent_Von_Mises = √(1 − 2 )2 + (2 − 3 )2 + (1 − 3 )2
where 1 , 2 and 3 are the first, second and third principal stress, respectively.
Figure 1. Finite element model of the mini-screw and bone
Each structure of cancellous bone, cortical bone and mini-screw was mesh in finite
element analysis program. The total number of elements ranged from 36,162 to 97,059 and
total number of nodes ranged from 52,769 to 138,052 with no degree of freedom. To evaluate
the effect of each parameter, length and diameter of mini-screw, one parameter had to be
fixed. To investigate the effect of screw length, mini-screw with three different lengths were
set at 6mm, 8mm and 10mm with all the same diameter (1.2mm) as shown in fig.2; lateral
loading conditions were simulated. To investigate the effect of screw diameter, mini-screw
with three different diameters were set at 1.2, 1.8 and 2mm with all the same length (6mm) as
shown in fig.3
Table 1. Properties of constituent materials10
Material
Titanium alloy
Cortical bone
Cancellous bone
Poisson’s ratio
0.3
0.3
0.3
Young’s modulus(MPa)
110,000
13,700
1,370
(a)
(b)
(c)
Figure 2. Three different lengths of screw (a) screw with length of 6.0mm (b) screw with length of
8.0mm (c) screw with length of 10.0mm
(a)
(c)
(b)
Figure 3. Three different diameters of screw (a) screw with diameter of 1.2mm (b) screw with
diameter of 1.8mm (c) screw with diameter of 2.0mm
Results
The maximum values of Von Mises equivalent stress on the palate bone of the lateralloading models for the different diameters and lengths are shown in Table 2 and Table 3.
Figures 4 and 5 describe the output of results of the finite element structural analysis.
Spectrum of different colors in figures represents the stress distribution in the cortical bone
on application of 2 N of experimental orthodontic force when each of six models of was
placed into palatal bone.
Table 2. The magnitude of maximum stress in cortical bone with three different diameters
Diameter(mm.)
Maximum stress in cortical bone
1.2
19.54 MPa
1.8
9.48 MPa
2.0
9.07 MPa
Section view of stress
distribution on entire
system
Location of maximum stress
distribution in cortical bone
Magnitude of maximum
stress in cortical bone
Diameter
1.2 mm
Diameter
1.8 mm
Diameter
2.0 mm
Figure 4.The output of result from finite element analysis simulations of three different diameters of mini-screw
Table 3. The magnitude of maximum stress in cortical bone with three different lengths
Length(mm.)
Maximum stress in cortical bone
6.0
19.54 MPa
8.0
6.87 MPa
10.0
6.77 MPa
Section view of
stress distribution
on entire system
Location of maximum stress
distribution in cortical bone
Magnitude of maximum
stress in cortical bone
Length 6 mm
Length 8 mm
Length 10 mm
Figure 5.The output of result from finite element analysis simulations of three different lengths of mini-screw
Maximum stress in cortical bone
(MPa)
We can conclude from the information in Table 2 that the increasing in length of mini-screw
will cause stress distribution in cortical bone to decrease. Also from Table 3, the increasing in
diameter of mini-screw will cause stress distribution in cortical bone to decrease as well.
Lastly, the two graphs in Fig.6 and Fig.7 are displayed reflecting the relationship between the
screw length and diameter versus the maximum Von Mises’ stresses in cortical bone when
mini-screws were subjected to the load of experimental orthodontic force 2 N.
22
20
18
16
14
12
10
8
6
4
2
0
19.54
6.87
0
2
6.77
4
6
8
length of screw (mm.)
10
12
Maximum stress in cortical bone
(MPa)
Figure 6. The relationship between length of screw and maximum stress in cortical bone
25
20
19.54
15
9.48
10
9.07
5
0
0
0.5
1
1.5
2
2.5
diameter of screw (mm.)
Figure 7. The relationship between diameter of screw and maximum stress in cortical bone
It can be noted from this two graphs that there is a tendency of maximum stress in cortical
bone to decrease when the length or diameter of screw increase.
Discussion and Conclusion
Similar studies of this type of system, Jui-Ting Hsu et al.13 conducted a study to assess
the effect of biomechanical factors, especially the length of mini-screw using three
dimensional finite element analysis. It was found the peak Von Mises stress and strain in the
cortical bone reduced as the length of mini-screw increased. Ashish Handa et al.14 in 2011
evaluated the design parameters of mini-screw using three dimensional finite element
analysis and showed that the maximum stress decreased not only as the screw length
increased but also increasing the thread pitch.
In our study, there are six different models of mini-screw and the result shows that
screw which 10mm-length and 2-mm of diameter would give the minimum value of stress on
cortical bone so from this present study we can conclude that as the length and diameter of
mini-screw increased would reduce the maximum stress in cortical bone. The results tended
to go as the same way as other researchers. However, there are many factors that would affect
maximum stress in cortical bone such as angle of insertion, site of placement, the quantity
and type of bone and orthodontic load application should be taken into consideration for the
longer survival and success of the implant.14
The finite element method has shown to be an effective tool to identify optimal design
parameters. Modification of mini-screw designs can affect the maximum stress in cortical
bone. Future research should cover on factors that affect stress distribution in cortical bone as
the author mentioned before, except length and diameter, simulating on other types of
material of mini-screw also interesting.
Acknowledgements: The author would like to appreciate to Department of Mechanical
Engineering for their aid with SolidWorks software and Department of Orthodontics and
Pediatric Dentistry, Chiang Mai University, for their any assistance.
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