Biomechanics of torque control

1
BIO-MECHANICS OF
TORQUE
A Finite Element Investigation
Dr. Vijay P. Jayade
Prof. And Head,
Department Of Orthodontics,
S.D.M. College of Dental Sciences,
Dharwad.

3
 Angle’s achieved a quantum leap in orthodontic
mechanics by introducing root control in his
appliances.
 ( “All that one can do is to push, pull or twist”).
 This “twist in the tale” has dramatically
changed the script of orthodontic mechanics.

4
Torque
 Torque control is essential for
1. Esthetic, functional and health outcome of
the treatment,
2. Stability of the results.
It is commonly attained by manipulating third
order relationship of a rectangular archwire -
rectangular slot.

5
What prompted the present
study
Writings of
 Isaacson et al, - mechanics of torque using
rectangular wires, more specifically the
complex reactions on the adjacent teeth,
 DeAngelis and Davidovitch - biologic
considerations of torque application.

6
Reciprocal reactions on adjacent
teeth during torque application with
rectangular wires
 These were mentioned by Brodie (1931)
and subsequently by others like Strang,
Thurow and Andreasen.
 However, their complexity was not given
due attention till recently.

7
Theory V/s Practice of Torque
Isaacson et al (1993)
“The equal and opposite reciprocal reactions
(which generally cause undesirable opposite
movements of adjacent teeth) are commonly
disregarded”.
“On the basis of theoretical mechanics, this
approach is conceptually flawed”.

8
What happens with incremental
torque?
1,2,3 progressively
torqued more and
more?
Some other
response?
All torqued
equally?

10
Relevant Clinical situation
 Incremental
twisting bends
between 13, 12,
11 also 21, 22, 23.
X
X
X
X

11
Ineffectiveness of Progressive
Torque in Clinical Practice?
 This situation for torquing the incisors, is
analogous to the one discussed by Isaacson.
 It does appear to work clinically.
 HOW DOES IT HAPPEN?

12
Possible explanation
 What Isaacson mentioned are the initial effects
and not all the actions and reactions, which
keep on fluctuating till the twist in the wire
expresses itself completely.

13
Possible explanation
 Perhaps, as the end teeth start moving, the
torquing moments on them gradually diminish,
and so also the reactionary moments on the
middle teeth. The twist in the wire would then
start acting on the middle teeth.
 The changing sequence of actions and
reactions needs to be worked out.
 IS THERE ANY ROUND TRIPPING?

14
Biologic implications
(DeAngelis and Davidovitch)
 Root resorption possibility increases due to :
a) “round tripping” and “jiggling” of roots,
b) excessive torquing forces / moments.

15
Optimum Torquing moments
10 to 20 N mm for rectangular wire torque
(Burstone, Nikolai, and Meiling and Odegaad) for
bodily translation (M/F ratio 10:1)
Are the moments, which are generated in
clinical practice, within this range?.

16
Aims and objectives
1. To verify the hypothesis of Isaacson
regarding the initial effects of
progressive root torque.
2. To work out how the effects of root
torque in various situations might
gradually be altering over a period of
time.

17
Aims and objectives
3. To explore the effects of different amounts
of built-in torque on adjacent teeth in the
PAE appliances.
4. To estimate the quantum of moments
generated by different archwires.

18
Methodology
 Finite Element Method (FEM) – Excellent tool in
analyzing problems of mechanical nature (in
this instance, moments and displacement
behavior).

19
Methodology
 The FEM software employed was Nastran-
Patran.
 A rectangular wire in edgewise mode was
modeled initially as straight length and later
as anterior part of an archwire on Autocad
software
 175 nodes in the anterior curvature

21
Methodology
 Appropriate torquing moments were applied at
the correct locations :
 a) from presumed twists in the archwire OR
 b) from in-built torque in the brackets.
 Then reciprocal reactions were derived from the
software (both initial, as also over time from
wire relaxation).

23
Some Assumptions
 The software assumes that the archwire
fits precisely in the bracket slot without any
play (e.g., a slot height of 0.019” was
assumed for the archwire having the
dimension of 19x25).

24
Some Assumptions
 Will this affect its reliability in application to the
clinical practice?
 No, because what it depicts is the clinically
effective torque that acts on the teeth after the
archwire-bracket play has been overcome.
 The play is uniform for all the brackets for any
given archwire.

25
Validation of force values
 Any numerical study must be validated by
comparing with a laboratory study.
 A laboratory set up, as used by Meling,
Odegaard and Meling, was simulated on FEM,
and moments generated were compared.

26
Validation of force values
Wire
Size
Range
of
play
Mean
play
Expt.
Range
Mean
value
FEM
18 x25
mil
2.98o -
6.31o 4.6o
3.24-
4.79
Nmm
3.86
Nmm
3.39
Nmm
Wire twisted by 1 degree -

27
I. Verification of Isaacson’s hypothesis
for Straight length of wire
Tooth 1 Tooth 2 Tooth 3 Tooth 4
Tooth 1 : 0
Tooth 2 : 10
Tooth 3 : 20
Tooth 4 : 30
-19.5 0 0 19.5
Tooth 1 : -2
Tooth 2 : 10
Tooth 3 : 20
Tooth 4 : 28
-15.3 -3.8 4 15.1
Torque on teeth (N mm)

28
Activation Torque on teeth (N mm)
Left
Lateral
Left
Central
Right
Central
Right
Lateral
R. Lateral : 0
R. Central : 10
L. Central : 20
L. Lateral : 10
33.1 -1.68 8.97 -19.46
Verification of Isaacson’s
hypothesis -for curved anterior
segment

29
Verification of Isaacson’s
hypothesis
 Thus the clinical picture may be slightly
different because of curvature in the
archwire and different inter-bracket
distances.

30
II. Stepwise resolution of anterior
Torque
 Incremental
twisting bends
between 13, 12,
11 also 21, 22, 23.
X
X
X
X

31
Amount of
torque
(Degrees)
Torque on each tooth
(Nmm)
Central Lateral Canine
Central : 20
Lateral : 10
30.74 -6.53 -13.76
Central : 18
Lateral : 12
Canine : -2
22.53 -0.23 -8.11
Central : 16
Lateral : 12
Canine : -4
17.62 -0.14 -0.08
Central :14
Lateral :12
Canine :-4
12.91 3.69 -0.06
Central :12
Lateral :12
Canine :-4
8.11 7.58 -0.08
Central :10
Lateral :10
Canine :-4
6.8 4.97 2.64
Stepwise resolution of anterior
progressive torque

32
Other situations studied
 Torquing two incisors
in the same direction
X
X
X
X
Torquing four incisors,
with twists only
between 13 & 12 and
22 & 23.

33
Lingual Root Torque for Central Incisors
Amount of
torque
(Degrees)
(Nmm)
10 23.94 -19.46
8 15.8 -9.15 -2.76
6.5 9.49 -1.22 -4.8
5 3.4 6.43 -6.9
cent-5
latr-3.5
5.8 1.71 -4.84

34
Lingual Root Torque on Four Incisors
Amount of
torque
(Degrees)
(Nmm)
cent and
lat – 10
canine 0
6.81 12.93 -13.76
cent and
lat - 8
canine -2
5.51 6.26 -2.64
cent and
lat - 6
canine -2
4.1 3.6 0.17

35
Individual Root Torque – Right central
incisor
Wire
size/
alloy
Act.
Torque on each tooth (Nmm)
L.
Lateral
L.
Central
R.
Central
R. Lateral
R.
Canine
19x25/
ss
10 -15.37 39.19 -19.29
19x25/
ss
8 -3.81 -4.1 24.68 -9.14 -2.82
17x25/
ss
10 -11.97 30.21 -14.96
17x25/
ss
8 -2.96 -3.24 19 -7.11 -2.2

36
III. The effect of built-in torque using
MBT prescription
 The results are different depending on the
torque in cuspid bracket (-7, 0 or +7)

37
MBT Actual Clinical moment
values
 The high FEM values do not apply (for
untorqued arch wire) in clinical practice
because of about 10 degrees of wire-slot
play. But the trends seen are important.
 However, if the 19x25 SS wire is given
additional torque that overcomes the play,
then the FEM values would be close to the
Clinical.

38
MBT Cuspid -7
Amount of
torque
(Degrees)
Central Lateral Canine Premolar
Central: 17
Lateral: 10
Canine:-7
23.42 13.4 -42.56 (13.93)
Central: 15
Lateral: 8
Canine:-5
22.12 6.89 -31.79 (10.4)

39
MBT Cuspid 0 and +7
Amount of
torque
(Degrees)
Central: 17
Lateral: 10
Canine: 0
23.42 -0.58 -13.76
Central: 17
Lateral: 10
Canine:7
23.42 10.22 15.05 (-13.93)

40
MBT Inverted lateral bracket
Amount of
torque
(Degrees)
Central: 17
Lateral: -10
Canine: 7
57.67 -79.35 42.56 (-13.93)
Central: 17
Lateral: -10
Canine: 0
57.67 -65.37 13.76 ---
Central: 17
Lateral: -10
Canine: -7
57.67 -51.39 -15.05 (13.93)

41
 IS IT A GOOD IDEA TO INVERT THE
LATERAL BRACKET ( especially alongside a
cuspid bracket with +7 torque)?
 Even after discounting 40 N mm moment
due to 10 degrees play, the moments
generated are high.
 Use Niti rectangular wires before SS wires.

42
IV. Torquing Moments from various
wires
 The torsional stiffness ratio of SS : TMA :
NiTi is 10 : 3 : 1.
 Torquing moments from heavy SS wires
are high and often above, those from TMA
generally within and those from NiTi below
the physiologic limit.

43
Clinical recommendations
 Twists in the rectangular archwire seem to be
appropriate only when reciprocal torque is
required on the adjacent teeth, but beware of
high moments. (‘Use undersize wires’- Thurow)
 In other situations, this method to cause active
root torque appears mechanically and
biologically unsound (often high moments
which drop suddenly, also round tripping)

44
For active torquing with twists in the rectangular
wires, TMA wires should be considered.
The rectangular near full size SS wires can be
used thereafter for holding the teeth in their
corrected torque positions.

45
 The moments generated by the NiTi
archwires even in 19x25 are too low to
bring about active torquing of teeth over
long periods.
 However, they may prove beneficial when
reciprocal torque is needed on adjacent
teeth.

46
Alternate methods proposed by authors like
Thurow, DeAngelis and Burstone/Isaacson
deserve a serious attention when reciprocal
torque on adjacent teeth is not needed, and
round tripping is to be avoided.
The reciprocal reactions of these are spread
on many (often distant) teeth, and are
controlled more easily.

47
Alternate torquing methods
(Thurow)

48
(DeAngelis)
Warren Spring

49
(Burstone, Isaacson)

50
Twist in the wire v/s Torque of teeth
 Angle’s torque control concept is inseparable
from good orthodontic practice.
 However, his “twists” in the rectangular wire
for attaining torque should be employed
judiciously, and not indiscriminately.

51
THANKS TO
Co-Authors:
Prof. Satish Annigeri (B.V.B. Engineering
College, Hubli),
 Dr. Chetan V. Jayade,
 Dr. Punit Thawani.

56
Young’s modulus and Poisson’s
ratio
Young’s
Modulus
Poisson’s
Ratio
Stainess Steel 179000 N/mm2 0.3
TMA 71700 N/mm2 0.3
Nitinol 41400 N/mm2 0.3

57
Moments generated by SS
Wires
Clinical Situation
Amount of
torque
(Degrees)
Lingual root torque
on two central
incisors
10 23.94 -19.46
Lingual root torque
on two all 4
incisors -
progressive root
torque - like
Isaacson's
Central : 20
Lateral : 10
30.74 -6.53 -13.76
Pre adjusted
Edgewise
Prescription - MBT
Central: 17
Lateral: -10
Canine:7
57.67 -99.17 83.43

58
Individual Root Torque – Right central incisor
Wire
size/
alloy
Act.
L.
Lateral
L.
Central
R.
Central
R. Lateral
R.
Canine
19x25/
TMA
10 -6.16 15.71 -7.73
19x25/
TMA
8 -1.53 -1.64 9.89 -3.66 -1.13
17x25/
TMA
10 -4.79 12.1 -6
17x25/
TMA
8 -1.19 -1.31 7.61 -2.85 -0.88

59
Ineffectiveness of Progressive
Incremental Torque (Isaacson)

60
Some Assumptions
 The differences in the sizes and shapes of
roots of various teeth were generally
disregarded. Also, the periodontal and
alveolar bone support to all the teeth were
considered as uniform.
 All the archwire materials viz. stainless steel,
T.M.A. and Niti were considered to have
linear elastic properties (hence, applicable
only to work hardened NiTi).

61
Basic Premise of the Edgewise
Appliance
An ideally shaped rectangular archwire,
would move the teeth to the desired final
positions because of its close fit in the
rectangular bracket slots.
Is this movement a direct translation of the
teeth along the shortest route, or does it
involve “round tripping” of some of the
teeth, if not all?

62
P.A.E. Appliances
 Same implicit understanding of P.A.E.
appliances also (which use continuous
archwires) : the archwire bracket
relationship would cause the teeth to
move from their malaligned positions to
the correct positions.
 Again, is there a possibility of some
amount of round tripping?

63
Aims and objectives
6. To study the possible actions and
reactions generated by alternative
torquing mechanism such as a Warren
spring, and compare these with those
from the conventional archwire twist.

64
Some Assumptions
 All brackets perfectly leveled and aligned.
 Root apices of teeth undergoing torque
move by 1.5 to 2 degrees per month
(based on what is commonly observed in
the clinical practice, and also from
Creekmore’s interview).

68
 “Orthodontic practice is nothing but push, pull and
twist”.
 Angle introduced the “twist” in the tale that
dramatically changed the script of orthodontic
mechanics.

70
Advantages of FEM
When properly applied
 It could obviate the need for the use of
elaborate laboratory (often invasive)
procedures.
 Its accuracy is very high.
 It can segregate the effects of bending from
those of twisting in curved members (e.g.,
Archwire).

71
Methodology
 Appropriate values for Young’s Modulus and
Poisson’s ratio were given.
 As per the expert advice, it was not necessary
to model the brackets, since applying
appropriate boundary conditions at the location
of the brackets simulates wire-bracket inter-
face.

72
Optimum Torquing moments
 A light torquing spring with 3 to 4 N mm moment
was shown to cause no tissue damage by Reitan.

Biomechanics of torque control

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