“A FINITE ELEMENT STUDY OF DIFFERENT CANTILEVER INTRUSION SPRING”

Dissertation by – Dr. Abdul Wahab.Md.

Guide- Dr.T.Ramanujulu,Associate prof.,Department of orthodontics,Bapuji dental college & hospital.

Dr. K. Sadashiva Shetty,Dr. K. Sadashiva Shetty,Professor & head,Professor & head,Department of orthodontics,Department of orthodontics,Bapuji dental college & hospital.Bapuji dental college & hospital.

Department of Orthodontics & Dentofacial Department of Orthodontics & Dentofacial OrthopedicsOrthopedics

CONTENTS

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

• DISCUSSION

• SUMMARY AND CONCLUSION

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

• 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.

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 20Vertical Deflection (mm)

Horiz

onta

l Def

lect

ion

(mm

)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveTMA

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection

Hor

izon

tal D

efle

ctio

n (m

m)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveSS

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10 12 14 16 18 20

Vertical Deflection

Hor

izon

tal D

efle

ctio

n (m

m)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveCCr

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection

Hor

izon

tal D

efle

ctio

n (m

m)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveNiTi

Activation Force

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection (mm)

Activ

atio

n Fo

rce

(cN)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurve

0102030405060708090

100110120130140150160170180

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection (mm)

Activ

atio

n Fo

rce

(cN)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurve

010

20304050

607080

90100110

120130140150

160170

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection (mm)

Activ

atio

n Fo

rce

(cN)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurve

0

10

20

30

40

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection (mm)

Activ

atio

n Fo

rce

(cN)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurve

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 20Vertical Deflection (mm)

Mom

ent a

t Tub

e (c

N m

m)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveTMA

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection

Mom

ent a

t Tub

e (c

N m

m)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurve

SS

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection

Mom

ent a

t Tub

e (c

N m

m)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveCcr 0

100

200

300

400

500

600

700

800

900

1000

0% 0 2 4 6 8 10 12 14 16 18 20Vertical Deflection

Mom

ent a

t Tub

e (c

N m

m)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveNiTi

Intrusion Force

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection (mm)

Intru

sion

For

ce (c

N)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveTMA

0102030405060708090

100110120130140150160

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection

Intr

usio

n Fo

rce

(cN

)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveSS

0102030405060708090

100110120130140150160

0 2 4 6 8 10 12 14 16 18 20Vertical Deflection

Intr

usio

n Fo

rce

(cN

)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveCcr

0

10

20

30

40

0 2 4 6 8 10 12 14 16 18 20

Vertical Deflection

Intru

sion

For

ce (c

N)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurveNiTi

ACTIVATION FORCE (cN)At 100% activation

0

20

40

60

80

100

120

140

160

180

TIP BACK UTILITY ARCH LOOP COMPOSITELOOP

FLAT CURVE DEEP CURVE

Activ

atio

n Fo

rce

(cN)

TMA

NiTi

STEELBLUE ELGILOY

MOMENT AT THE TUBE (cNmm)At 100% activation

0

1000

2000

3000

4000

5000

TIP BACK UTILITY ARCH LOOP COMPOSITELOOP

FLAT CURVE DEEP CURVE

Mom

ent a

t the

tube

(cNm

m)

TMANiTiSTEELBLUE ELGILOY

Deactivation-Intrusion Forces (cN)At 100% activation

0

20

40

60

80

100

120

140

160

180

TIP BACK UTILITY ARCH LOOP COMPOSITELOOP

FLAT CURVE DEEP CURVE

Intru

sion

For

ces

(cN)

TMANiTiSTEELblue elgiloy

Intrusion : Moment RatioAt 100% activation

0

0.01

0.02

0.03

0.04

TMA NiTi STEEL BLUE ELGILOY

Intru

sion

: M

omen

t Rat

io

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.

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 curvedbends, 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 20Vertical Deflection (mm)

Horiz

onta

l Def

lect

ion

(mm

)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurve

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 20Vertical Deflection (mm)

Activ

atio

n Fo

rce

(cN)

Tip-Back

Utility

Loop

CompLoop

FlatCurve

DeepCurve

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 protractionD

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.

• The results obtained in this study were in agreement with the study done by Melsen and Dalstra.

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 would be the most suitable.

• 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.

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