FINITE ELEMENT STUDY OF INTRUSION SPRING DESIGNS

“A FINITE ELEMENT STUDY OF DIFFERENT
CANTILEVER INTRUSION SPRING”
Department of Orthodontics & DentofacialDepartment of Orthodontics & Dentofacial
OrthopedicsOrthopedics
www.indiandentalacademy.com

CONTENTS
• INTRODUCTION
• AIMS AND OBJECTIVES
• MATERIALS AND METHOD
• RESULTS
• DISCUSSION

INTRODUCTION
Correction of the anterior deep bite in a
patient can present challenges to the
clinician.
It requires thoughtful application
of diagnostic knowledge as well as skillful
application of the mechanical principles.

• There are basically two approaches that
can be used to apply the force system
necessary to trigger the biologic
phenomena that results in correction of
the anterior deep bite:
– True intrusion of the upper and/or lower
anteriors, and
– Relative intrusion i.e. allowing the
posterior teeth to erupt while the
anteriors are withheld from further
eruption www.indiandentalacademy.com

• However, simultaneously a moment is
generated within the posterior segment
which adds to the anteroposterior
anchorage.
• Likewise addition of a curvature to the
posterior part of the wire (commonly
referred to as “Reverse Curve of Spee”)
should presumably perform exactly in the
same way as with anchor bend.

• Some of these designs have been tested
using analytic equations and/or
sophisticated experimental methods;
• However, since these methods are very
lengthy and required a lot of precision they
were restricted to study of one or two
designs at the most.

• In recent times, the Finite Element
Method has been used by some
researchers in orthodontics for studying
the different cantilevers especially of loop
characteristics.
• Some of these trials, however, were aimed
at developing newer archwire / loop
configurations.

• Relatively few studies, however, have
compared the commonly used intrusion
archwire designs.
• Therefore, this study is planned, to carry
out a comprehensive evaluation of the
physical characteristics of various
intrusion archwire designs.
• An evaluation of the archwire properties
and physical characteristics are also
considered. www.indiandentalacademy.com

Aims & Objectives :

• To study the deformation pattern of
activated cantilever intrusion spring.
• To describe the force system developed by
cantilever with different configuration
when activated

Material & Methods

• The study was done in the Department
of Orthodontics and Dentofacial
Orthopedics, Bapuji Dental College
and Hospital, Davangere, in
association With Bapuji Institute of
Engineering Technology, Davangere,
Karnataka, India.

Six different cantilever
configurations were analyzed

TIP BACK UTILITY

LOOPCOMPOSITE LOOP

FLAT CURVE DEEP CURVE

• Young’s Modulus and Poisson’s ratio
for various materials used in this study.
• Stainless Steel 170GPa 0.3
• Blue Elgiloy 160GPa 0.3
• T.M.A. 75 GPa 0.3
• NiTi 35GPa 0.3

Activation in
% or mm
0% = 20mm
10% = 18mm
20% = 16mm
30% = 14mm
40% = 12mm
50% = 10mm
60% = 8mm
70% = 6mm
80% = 4mm
90% = 2mm
100% = 0mm
External loading was applied as a forced
displacement of the right end tip of the wire in 10
increments of 2 mm.

• A comparison of all these forces,
moments and displacement were
performed for all the four materials
(Stainless Steel, Cobalt Chromium,
T.M.A. and Nickel Titanium wires).
• The results were then tabulated and
shown as graphs.

RESULTS

Horizontal Displacement
0
1
2
3
4
5
6
7
8
9
10
0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection (mm)
HorizontalDeflection(mm)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
TMA
0
1
2
3
4
5
6
7
8
9
10
0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
SS
0
1
2
3
4
5
6
7
8
9
10
0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
CCr
0
1
2
3
4
5
6
7
8
9
10
0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
NiTi

Activation Force
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16 18 20
ActivationForce(cN)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
0 2 4 6 8 10 12 14 16 18 20
ActivationForce(cN)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
0 2 4 6 8 10 12 14 16 18 20
ActivationForce(cN)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
0
10
20
30
40
0 2 4 6 8 10 12 14 16 18 20
ActivationForce(cN)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
TMA SS
Ccr NiTi

Moment at Tube
0
250
500
750
1000
1250
1500
1750
2000
2250
2500
0 2 4 6 8 10 12 14 16 18 20
MomentatTube(cNmm)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
TMA
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection
MomentatTube(cNmm)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
SS
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection
MomentatTube(cNmm)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
Ccr
0
100
200
300
400
500
600
700
800
900
1000
0% 0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection
MomentatTube(cNmm)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
NiTi

Intrusion Force
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16 18 20
IntrusionForce(cN)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
TMA
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection
IntrusionForce(cN)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
SS
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection
IntrusionForce(cN)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
Ccr
0
10
20
30
40
0 2 4 6 8 10 12 14 16 18 20
Vertical Deflection
IntrusionForce(cN)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve
NiTi

ACTIVATION FORCE (cN)
At 100% activation
0
20
40
60
80
100
120
140
160
180
TIP BACK UTILITYARCH LOOP COMPOSITE
LOOP
ActivationForce(cN)
TMA
NiTi
STEEL
BLUE ELGILOY

MOMENT AT THE TUBE (cNmm)
At 100% activation
0
1000
2000
3000
4000
5000
TIP BACK UTILITY ARCH LOOP COMPOSITE
LOOP
Momentatthetube(cNmm)
TMA
NiTi
STEEL
BLUE ELGILOY

Deactivation-Intrusion Forces (cN)
At 100% activation
0
20
40
60
80
100
120
140
160
180
TIP BACK UTILITY ARCH LOOP COMPOSITE
LOOP
IntrusionForces(cN)
TMA
NiTi
STEEL
blue elgiloy

Intrusion : Moment Ratio
At 100% activation
0
0.01
0.02
0.03
0.04
TMA NiTi STEEL BLUE ELGILOY
Intrusion:MomentRatio
TIP BACK UTILITY ARCH LOOP
COMPOSITE LOOP FLAT CURVE DEEP CURVE

DISCUSSION

• For the purpose of simplification the
discussion can be carried out under two
parts:
• Part One: Investigation of the six different
cantilever configurations considering
material property of T.M.A. wire only.
• Part Two: Comparison between the six
cantilevers employing different archwire
materials.

Part One
• Here the investigation of the six different
cantilever configurations considering
material property of T.M.A. wire was
carried out.
• The material i.e. TMA was kept as a
constant in order to ensure that the results
obtained would not vary due to the
differences in the material of the wire.

• The purpose of this part of the study was to
evaluate the effects of the different
cantilever configurations on the force-
deflection characteristics viz.
– horizontal displacement,
– activation force,
– moment at the tube,
– vertical (intrusive) and horizontal
(retraction / protraction) deactivation
forces. www.indiandentalacademy.com

a) Horizontal Displacement
• The largest forward horizontal displacement in
Y-axis was found for the deep curved bend and
lowest for the utility arch.
• It is interesting to note that the maximal
forward horizontal displacement in Y-axis value
for different cantilever designs except for the
two curved bends occurred at either 60%
(utility) or 80% (tip-back, loop and composite
loop) of activation, while that of deep curve
bend and flat curve bend occurred at 100%.

All trajectories, except for the two curved
bends, showed a maximal forwar horizontal
displacement in Y-axis before reaching their
final activation.

Horizontal Displacement
0
1
2
3
4
5
6
7
8
9
10
0 2 4 6 8 10 12 14 16 18 20
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve

b) Activation Force
When comparing the activation forces it was
found that the tip back bend requires the highest
forces in the y axis.
The curved bends too needed high forces (almost
like the tip-back bend) followed by the utility
arch and composite loop.
The loop configuration exhibited the least
amount of requirements for its activation in the
y axis.

Activation Force
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16 18 20
ActivationForce(cN)
Tip-
Back
Utility
Loop
Comp
Loop
Flat
Curve
Deep
Curve

d) Deactivation forces
• The force system generated during deactivation was
largely dependent on the activation force. It should also
be noted that the deformation of various configurations
during activation has a significant influence on the direction
of the intrusion forces.
• As can be seen in each one of the configurations has a
different deformation pattern, especially at the free end of
the cantilever that can be measured easily. This positioning of the
free
end of the cantilever will determine the direction of the intrusion
force
(i.e. either intrusion-protrusion or intrusion-retrusion forces).

TIPBACK
UTILITY
LOOP
COMPOSITE LOOP
FLAT CURVE
DEEP CURVE

• In the considered loading mode for the FE analysis
the activation force was directed purely vertically.
This force can be resolved into a force component
perpendicular to the wire and a pulling force in the
wire itself.
• After fixing the wire in its deformed state only the
reaction force the Fperp can be used during the de-
activation process. Consequently, the vertical and
horizontal components of Fperp represent the
intrusion/extrusion and protrusion/retraction
components respectively. The nature of the
horizontal component of force depends on the
deformed shape of the cantilever.

The force system was separated into intrusive and
retraction / protraction components.
F intrusion
F perp
F protraction
D

for example for a tip back configuration, the Fperp (the force
perpendicular to the arch wire) is further resolved into two forces. One
force, which acts in vertical plane considered as true intrusion force
(F intrusion) & another smaller force in horizontal plane. This horizontal
force, depending on its direction, could be either a retractive force
(F retraction – when arrow facing towards the tube) or a protrusive
force (F Protrusion – when arrow facing away from the tube).
• It is interesting to note that the horizontal forces may be retractive (-
ve value) or protrusive (+ve value) at different levels of activation. The
tip-back bend, for example, at 100% activation shows an intrusive force
of 69.1 cN and a protrusion force of 24.3 cN. However, it takes only
four increments of upward displacement before protrusion turns into
retraction.

• This shift also occurs for the other bends with the exception of
the
curved bends, which have solely retraction forces the magnitude of
this
retraction forces, however, is strongly dependent on the amount of
curvature. The magnitude of protrusion at 100% activation is
highest
with tip-back, followed by utility, composite loop and then loop
configuration.
• The utility arch has the least amount of retraction forces for at
any
given level of deactivation when compared to other cantilever
configuration. The deep curve has the maximum amount of
retractive
forces at any level of deactivation.

e) Intrusion : Moment (I:M)
A three piece intrusion arch can be considered one couple
appliance system. Here a couple is generated within the tube,
where
the spring makes contact at the mesial and distal ends. At the
mesial end of the spring there is a single point contact and there
by
no couple is generated. Whenever true intrusion is intended it is
always preferable to minimize the extrusion of the posteriors.
This
extrusion is directly proportional to the amount of moment
created in
the auxillary molar tube. Thus it would be said that a design
which
gives maximum intrusive forces with least amount of moment
created posteriorly would be the most favorable one. Therefore
the
design that has the highest intrusive to moment (I:M) ratio wouldwww.indiandentalacademy.com

• It was found that of all the designs at 100%
activation utility arch shows the highest I:M
ratio followed by composite loop. The least
desirable I:M ratio was seen with deep curve.
The tip-back and flat curve, showed almost a
similar I:M ratio which was slightly less than
the loop design. This pattern was seen up to
the 30% of activation .The pattern, however,
changes at 20% and 10% which is clinically
not significant.

Part Two
• Here, comparison between the six
cantilevers employing different archwire
materials was carried out.
The materials employed are those
which are most commonly used as arch
wires, i.e. Stainless steel, Blue Elgiloy,
T.M.A (B-titanium), Nickel Titanium.

Horizontal Displacement :
• For a given design the horizontal
displacement remained the same,
irrespective of the material used. It could
be, therefore, said that the deformation
characteristic of a given cantilever is
independent of the material. In other words,
whether a utility arch is fabricated with
stainless steel or Niti, it will show the same
amount of horizontal displacement at every
level of activation / deactivation.

Activation Force:
• Activation force was maximum for stainless steel,
followed by Blue Elgiloy, TMA and NiTi` for any
given configuration.
• The activation forces for that of the TMA was
almost half of SS, while the activation forces of the
NiTi was almost half of the TMA wire. Blue Elgiloy
was showing a slightly lower forces than that of the
SS.
• In conformation of the first part of the study each
material required maximum activation force for the
tip back bend and minimal for the utility arch.

Moment at the Tube:
• Moment at the tube followed a similar
pattern to the activation force, i.e. stainless
steel generates the highest moment
followed by Blue Elgiloy, TMA and NiTi in
descending order.
• The highest moment generated was
recorded for the SS wire with the tip-back
design (5030.76 cNmm) and least was for
the NiTi wire with composite loop
configuration (428.85 cNmm).

Deactivation
• This deactivation force (F
perpendicular), as explained in the first
part of the discussion, can be resolved
into two components. These are F
intrusion and F protrusion /F retraction.

• These force vectors generated depend
on two things:
• Activation force: Greater the activation
force, greater will be the deactivation
force.
• Configuration: The design of the
cantilever

• For any given configuration, the activation force required for
stainless steel is the greatest and so the reactionary force
generated is the highest when compared to the other materials
used in this study. The deactivation force kept on decreasing in
Blue Elgiloy, TMA, NiTi, in descending order.
• However, the forces generated by the SS wire were much
higher than those considered as desirable in the literature.
• For example, the tip-back configuration which was made up of
the stainless steel generated an intrusion force of 156.1 cN
(roughly 160 gms). In other words, it means that lateral and
central incisor in a 3 piece intrusion arch, will receive an
intrusion force of approximately 80 cN each.

• Though the least intrusion force value among the
various designs in stainless steel material was shown
by composite loop configuration, it generated an
intrusive forces of 70.2 cN (i.e. central and lateral
incisors each will experience 35 cN of force).
• The desirable intrusion forces, however, was shown
by both the loop configurations when made up of the
TMA material and when tip-back, utility, flat and deep
curve configuration made up of the NiTi wire (the
intrusion forces ranged from approximately 40 to 25
cN i.e. central and lateral each would experience only
12 to 20 cN).

• Different cantilever designs showed a shift
from protractive to retractive forces at
different levels of deactivation.
• This shift does not vary with different
materials using the same design. Similarly in
deep curved bends the initial horizontal
vector is retractive in all the four materials.
• Because of the inherent property of the
material the horizontal vector of force
generated would decrease significantly from
stainless steel to NiTi.

e) Intrusion: Moment (I:M)
Ratio
• As mentioned previously, whenever true intrusion is
intended it is always preferable to minimize the
extrusion of the posteriors. This extrusion is directly
proportional to the amount of moment created in the
auxillary molar tube. Thus it would be said that a
design which gives maximum intrusive forces with
least amount of moment created posteriorly would be
the most favorable one. Therefore the design that
has the highest intrusive to moment (I:M) ratio would
be the most suitable.
• In the present study we compared the I:M ratio
generated for all the materials. With this we were
able to study the best combination of the material and
archwire design for an intrusion arch.

• It was found that of all the materials, the utility arch
showed the highest I:M ratio at 100% activation. For
the next positions, there was no proper sequence as
different materials showed different ratios for different
designs. However the variation between the loop,
comp. loop, tip-back and flat curve designs were
small (0.031 and 0.035). Irrespective of the material,
the least ratio was seen with the deep curve,
especially with NiTi wires which showed only 0.0079.
• In short a clinical situation may demand retraction or
protrusive forces be generated along with the
intrusive forces. Thus, it can be seen that using a
combination of different materials and cantilever
designs we can get the desired vector of forces.

In summary following conclusions
can be listed:
• The configuration of the cantilever is crucial for the direction of
the force delivered.
• The results demonstrated that the curved cantilevers behaved
fundamentally differently from other designs.
• When fully activated (100%) the cantilevers with a curvature
would be capable of delivering a retractive force in combination
with intrusion.
• In all other configurations, the tip back, utility, loop and
composite loop the horizontal force component at 100%
activation was generating a forward directed force, leading to a
protrusion of the anterior unit, however after some deactivation,
it reversed into a retraction force. The turning point between
protrusion and retraction forces depended on the configuration.

• The addition of length to the wire by bending
a loop or a step, in a utility shaped cantilever
lowers the stiffness of the configuration and
results in lower deactivation forces.
• Of all the materials, the force generated by
stainless steel was almost more than the
double of those of TMA wire. And the forces
generated by TMA wire were slightly more
than the double of the NiTi wires. The force
generated by blue elgiloy wires were 10%
less than SS wires.

• The forces generated by the SS wire for all the six
configurations were much higher than those
considered as desirable in the literature.
• The desirable intrusion forces, however, was shown
by both the loop configurations when made up of the
TMA material and when tip-back, utility, flat and deep
curve configuration made up of the NiTi wire.
• When the intrusion forces were compared to the
amount of the moment generated at the molar tube
and I:M ratio was considered, it was found that the
utility design generated the best ratio, where as the
deep curve showed the worst I:M ratio.

• In patients where a combined retraction and intrusion
is desired, the use of a curved cantilever made up of
NiTi wire can be recommended, as this design further
contributes an additional horizontal force component.
If protrusion is desirable then a tip-back design of
NiTi wire should be used, as it can deliver the desired
combination of protrusive and intrusive forces
efficiently.
• If extrusion of posterior teeth is desired the deep
curve design should provide the right combination of
maximum intrusion of the incisors and high moment
at the molar tubes. However, the best combination of
the material and design for intrusion of incisors would
be a utility arch constructed with a NiTi wire.

THANK YOU

FINITE ELEMENT STUDY OF INTRUSION SPRING DESIGNS

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