A comparative analysis of commonly used retraction loops

A COMPARATIVE ANALYSIS OF
COMMONLY USED RETRACTION LOOPS
IN EDGEWISE SYSTEMS- A FINITE
ELEMENT STUDY
www.indiandentalacademy.com

INTRODUCTION

FEM VS EXPERIMENTAL

Ideal Loop Characteristics
1) Sufficiently high Moment/Force
(M/F) ratio to bring about desired
tooth movement.
2) Low Load Deflection (F/D) rate to
maintain a low rate of force decay.

Aims and Objectives
a) Compare the Moment Force ratio
and Load deflection rates from the
FEM with those of Burstone’s
findings.
b) To seek an explanation for
different findings, if any.

AIMS AND OBJECTIVES

Aims and Objectives
c) Provided FEM was validated, to
apply it to different loop
configurations, which are routinely
used.

Materials and Methods
EMRC NISA Ver. 7.0 Finite element
software.
2-D beam elements used.
Elements ranged from 67 to 107.
Boundary conditions applied to
restrain one end of the wire;
force of known magnitude applied
at the other end in an increment of
0.5 N. www.indiandentalacademy.com

MATERIALS AND METHOD

A MODELLED STANDARD LOOP
FR

Materials and Methods
• Large deflection Non-Linear Static
Analysis carried out.
• Resultant moment and displacement
values obtained from the computer
analysis.
• M/F and F/D ratios calculated from
this data.

DISPLACED SHAPE OF THE LOOP

PHASE I - VALIDATION WITH
BURSTONE’S FINDINGS

Stage I - Validation with Burstone’s
findings
• The same parameters as employed
by Burstone were used, namely
• Wire dimensions of 0.016” with
properties of
E = 2.1 x 10 4
N/mm2
Yield strength = 40,000 psi

Stage I- Validation of FEM with
Burstone’s study (Contd)
Variations in Moments and
displacements calculated due to
alteration in loop parameters like
• Loop Height & Diameter
• Horizontal Loop length
• Centred loop or Eccentric
placement

LOOP OF
HEIGHT
4mm
F M D
6.84 12.94 .7
6.84 8.96 .7
LOOP OF
HEIGHT
6 mm
F M D
4.85 16.02 1.44
4.85 10.60 1.38
LOOP OF
HEIGHT
10 mm
F M D
3.11 19.47 3.62
3.11 12.60 3.32
RESULTS
FEM
B
VARIATION IN LOOP HEIGHT

LOOP OF
DIAMETER
0.5 mm
F M D
4.69 13.99 1.2
4.69 9.70 1.3
LOOP OF
DIAMETER
1 mm
F M D
4.85 16.02 1.44
4.85 10.60 1.38
LOOP OF
DIAMETER
2 mm
F M D
5.17 20.22 2.01
5.17 12.48 1.90
RESULTS
FEM
B
VARIATION IN LOOP DIAMETER

VARIATION IN LOOP LENGTH
HORIZONTAL
LOOP LENGTH
7mm
F M D
4.85 16.02 1.44
4.85 10.60 1.38
HORIZONTAL
LOOP LENGTH
14 mm
F M D
4.15 8.04 1.40
4.15 6.99 1.56
HORIZONTAL
LOOP LENGTH
21 mm
F M D
3.83 4.62 1.34
3.83 5.31 1.68
RESULTS
FEM
B

Stage I- Validation with Burstone’s
findings INFERENCES
I) The trends in the variations of the
moments and displacement values
obtained from the FEM and the
findings of Burstone are similar.
Hence, there is a valid place for using
FEM in understanding Loop
mechanics.

findings INFERENCES
II) The numerical values for
displacements are very close to the
ones observed by Burstone.
III) The values for moments from the
FEM are, in general, on the higher side.
This is probably on account of the
boundary conditions in the FEM and
other material properties like elasticity.

findings INFERENCES
IV) The numerical values for the
moments , though higher initially ,
showed a rapid drop when the
horizontal loop length was increased
from 7-14 and then 14-21 mm.

STAGE II - COMPARATIVE
ANALYSIS OF COMMON LOOPS

Stage II - Comparative analysis of
Common loops
Keeping in mind these differences
between the FEM and the Experimental
approach, the second stage was
carried out.
Material was modelled as a rectangular
stainless steel wire of dimensions
0.018” X 0.025”.

Common loops
The other material properties were as
defined by Siatowsky, namely
E = 3 X 10 4
N/mm2
Poisson’s ratio= 0.3
Forces ranging from 0.5 - 5N were
applied at one end of the wire of
horizontal loop length of 17.25 mm.

Common loops
The Moment, Displacement, M/F and
F/D values were calculated for the
following configurations :

i) Standard vertical loop with varying
height and diameter.

ii) Vertical loop with arms crossing each
other in two designs
a) Flattened top b) Curved top

Iii)Vertical loop with
difference in height iv) Curetton’s loop
of the two legs

v)Tear drop loop

vi) L loop

viii) Asymmetric T loop

vii) T loop

ix) L loop with angulated legs

LOOP BY TYPE
T LOOP
ASYMMETRIC
T LOOP
L LOOP WITH
ANGULATION
L LOOP
VERTICAL LOOP
TEAR DROP LOOP
BOX LOOP
REVERSE LOOP
M/F
5.0988
4.850
4.946
3.914
3.618
3.548
3.330
3.163
F/D
6.642
6.793
8.216
8.092
11.006
10.678
9.432
10.295

LOOP TYPE
VERTICAL LOOP
CURETTON’S
LOOP
VERTICAL LOOP
WITH A SHORT
LEG
M/F
3.618
3.650
2.833
F/D
11.006
10.909
15.770

INFERENCES

INFERENCES
I) Of all the loops studied, T loop has
the most ideal properties in terms of
M/F and F/D.

INFERENCES
II) The L loop with angulated legs and
the Asymmetric T loop come close to
the T loop in terms of M/F alone in
certain conditions. However, their F/D
rate is considerably higher.
III) The tear drop loop and the box loop
with differing tops are not very different
to the standard vertical loop in terms of
M/F or the F/D. www.indiandentalacademy.com

INFERENCES
IV) A change in the height of one loop
leg does alter the M/F ratio
considerably; however the Curetton’s
modification does not significantly
alter the M/F ratio or the F/D rate.

LOOP
HEIGHT
8
8
8
8
8
4
6
10
LOOP
DIAMETER
2
3
4
5
6
2
2
2
M/F
3.618
3.928
4.108
4.340
4.570
1.217
2.383
4.954
F/D
11.006
10.420
9.820
9.440
9.147
64.400
22.970
6.190

INFERENCES
V) The increase in the M/F of a
standard vertical loop when the height
or the diameter are increased is not
strictly proportionate.
Although a vertical loop with a 10 mm
height or a 6 mm diameter do give high
M/F ratios, the anatomic constraints
come in the way of clinically
employing them.

A NEW FINDING

INFERENCE
A kink like deformation in the Z plane
(1mm) of a tear drop or a vertical loop
showed a drastic rise in the values of
the M/F.
If this could be verified, it could give
us an additional tool to enhance the
M/F of any loop by a very simple
manipulation.

Shortcomings of FEM
1) It is not possible to exactly simulate
the clinical conditions.
2) It is quite difficult to duplicate the
wire bracket relationship.
3) Boundary conditions need to be
altered at times, which is not possible
in the current software.

CONCLUSION
Finite Element Method is a useful tool for
studying Loop mechanics.At the present
juncture it cannot entirely replace
experimental methods.
Software refinements shall help in using this
numerical procedure increasingly more in
Orthodontic research

CONCLUSION SAYING

A comparative analysis of commonly used retraction loops

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