Biomechanics in Orthodontics E-Book

Ram S. Nanda

• Herausgeber: Quintessence Publishing Co, Inc
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 332

Veröffentlichungsjahr: 2019

Beschreibung

Correct application of the principles of biomechanics leads to highly efficient and successful orthodontic treatment; a lack of proper understanding produces ineffectual systems that may even lead to collateral tissue damage. In addition, knowledge about the properties of the latest wire, bracket, and bonding materials and designs is a key factor in the configuration of successful orthodontic appliances. This essential book introduces students of orthodontics to the evolution of orthodontic technology and the properties of orthodontic materials and outlines the essential mechanical principles behind successful orthodontic treatment.

Leseprobe

Ram S. Nanda, BDS, DDS, MS, PhDProfessor Emeritus Department of Orthodontics College of Dentistry University of Oklahoma Oklahoma City, Oklahoma

Yahya S. Tosun, DDS, PhDPrivate Practice Dubai, United Arab Emirates Former Professor Department of Orthodontics University of Aegeaİzmir, Turkey

Library of Congress Cataloguing-in-Publication Data

Nanda, Ram S., 1927-

Biomechanics in orthodontics : principles and practice / Ram S. Nanda, Yahya Tosun.     p. ; cm. Includes bibliographical references. ISBN 978-0-86715-505-1 1. Orthodontic appliances. 2. Biomechanics. I. Tosun, Yahya. II. Title. [DNLM: 1. Biomechanics. 2. Orthodontic Appliances. 3. Malocclusion—therapy. 4. Orthodontic Appliance Design. WU 426 N176b 2010] RK527.N366 2010 617.6'430284—dc22

                                                      2010013547

© 2010 Quintessence Publishing Co, Inc

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Contents

Preface

1 Physical Principles

2 Application of Orthodontic Force

3 Analysis of Two-Tooth Mechanics

4 Frictional and Frictionless Systems

5 Anchorage Control

6 Correction of Vertical Discrepancies

7 Correction of Transverse Discrepancies

8 Correction of Anteroposterior Discrepancies

9 Space Closure

Glossary

Preface

Once comprehensive diagnosis and treatment planning have set the stage for initiating treatment procedures, appliance design and systems have to be developed to achieve treatment goals. Correct application of the principles of biomechanics assists in the selection of efficient and expedient appliance systems.

Over the last three decades, there has been an explosion in the development of technology related to orthodontics. New materials and designs for brackets, bonding, and wires have combined to create a nearly infinite number of possibilities in orthodontic appliance design. As these new materials are brought together in the configuration of orthodontic appliances, it is necessary to understand and apply the principles of biome-chanics for a successful and efficient treatment outcome. Lack of proper understanding may not only set up inefficient force systems but also cause collateral damage to the tissues. The path to successful treatment is through good knowledge of biomechanics.

This book is written with the purpose of introducing a student of orthodontics to the evolving technology, material properties, and mechanical principles involved in designing orthodontic appliances.

Physical Principles

Movement of teeth in orthodontic treatment requires application of forces and periodontal tissue response to these forces. Force mechanics are governed by physical principles, such as the laws of Newton and Hooke. This chapter presents the basic definitions, concepts, and applicable mechanical principles of tooth movement, laying the groundwork for subsequent chapters.

Newton’s Laws

Isaac Newton’s (1642–1727) three laws of motion, which analyze the relations between the effective forces on objects and their movements, are all applicable to clinical orthodontics.

The law of inertia

The law of inertia analyzes the static balance of objects. Every body in a state of rest or uniform motion in a straight line will continue in the same state unless it is compelled to change by the forces applied to it.

The law of acceleration

The law of action and reaction

The reaction of two objects toward each other is always equal and in an opposite direction. Therefore, to every action there is always an equal and opposite reaction.

Vectors

When any two points in space are joined, a line of action is created between these points. When there is movement from one of these points toward the other, a direction is defined. The magnitude of this force is called a vector, it is shown by the length of an arrow, and its point of application is shown with a point. For example, in Fig 1-1, the line of action of the force vector, which is applied by the labial arch of a removable appliance on the labial surface of the crown of the incisor, is horizontal. The direction is backward (ie, from anterior to posterior), and its amount is signified by the length of the arrow.

Fig 1-1 Force is a vector. The force applied to the incisor is signified by the length of the arrow, and the point of application is on the crown. Its line of action is horizontal, and its direction is from anterior to posterior.

Addition of vectors

Vectors are defined in a coordinate system. The use of two coordinate axes can be sufficient for vectors on the same plane.

In Fig 1-2a, the resultant (R) of the vectors of different forces (x and y), which are on the same line of action and in the same direction, equals the algebraic sum of these two vectors (x + y). The resultant of two vectors on the same line of action but in opposite directions can be calculated as (x + [–y]) (Fig 1-2b).

The resultant of two vectors that have a common point of origin is the diagonal of a parallelogram whose sides are the two vectors (Fig 1-3a). The resultant of the same vectors can also be obtained by joining the tip of a vector parallel to vector y drawn from the tip of vector x to the point of origin of vector x (Fig 1-3b).

Fig 1-3 (a) The resultant (R) of the x and y vectors that have the same point of origin is the diagonal of the parallelogram with these vectors used as the sides. (b) R can also be obtained by drawing a vector parallel to vector y and extending from the tip of vector x, then drawing a line joining its tip to the origin of vector x.

Sum of multiple vectors

The sum of multiple vectors is calculated in the same system as the calculation of two vectors. Therefore, the third vector is added to the resultant of the first two vectors, and so on (Fig 1-4).

Subtraction of two vectors

To define the difference between two vectors, a new vector (–y) is drawn in the opposite direction from the tip of vector x and parallel to vector y, and the point of origin of vector x is joined to the tip of vector –y (Fig 1-5). Thus, the resultant (R) is from the point of origin of vectors x and y toward the tip of vector –y.

Fig 1-5 The difference between x and y vectors having the same point of origin can be obtained by drawing a vector (–y) starting from the tip of vector x that runs parallel to the y vector but in the opposite direction; then the tip of vector –y is joined to the point of origin of vectors x and y.

Separating a vector into components

To separate a resultant vector (R) into components, two parallel lines are drawn from the point of origin of that vector toward the components that are searched. By drawing parallels from the R vector’s tip toward these lines, a parallelogram is obtained. The sum of the two components obtained by this method is exactly equal to vector R.

The separation of a resultant vector into components is generally (at the elementary level) realized on x and y reference axes for ease of presentation and trigonometric calculations (Fig 1-6). In fact, for complicated calculations, vectors can be separated into unnumbered directions. Therefore, the x-axis is generally accepted as the horizontal axis, and the y-axis is accepted as the vertical axis. Thus, the component x of vector R can be defined as horizontal and the component y as vertical.

Fig 1-6 The separation of a resultant vector into components on an x- and y-axis coordinate system.

Force

Force is the effect that causes an object in space to change its place or its shape. In orthodontics, the force is measured in grams, ounces, or Newtons. Force is a vector having the characteristics of line of action, direction, magnitude, and point of application. In the application of orthodontic forces, some factors such as distribution and duration are also important. During tipping of a tooth, force is concentrated at the alveolar crest on one side and at the apex on the other (Fig 1-7a). During translation, however, the force is evenly distributed onto the bone and root surfaces (Fig 1-7b).

Fig 1-7 Distribution of force on the bone and root surfaces in tipping (a) and translatory (b) movements. During tipping, the possibility of indirect bone resorption is high because the forces are concentrated in small areas. Therefore, the forces must be kept as low as possible.

Forces according to their duration

Constancy of force

Clinically, optimal force is the amount of force resulting in the fastest tooth movement without damage to the periodontal tissues or discomfort to the patient. To achieve an optimum biologic response in the periodontal tissues, light, continuous force is important.1Figure 1-8 compares the amount of loss of force occurring over time on the force levels of two coil springs of high and low load/deflection rates.2

Continuous forces A continuous force can be obtained by using wires with low load/deflection rate and high working range. In the leveling phase, where there is considerable variation in level between teeth, it is advantageous to use these wires to control anchorage and maintain longer intervals between appointments. Continuous force depreciates slowly, but it never diminishes to zero within two activation periods (clinically, this period is usually 1 month); thus, constant and controlled tooth movement results3 (Fig 1-9a). For example, the force applied by nickel titanium (NiTi) open coil springs is a continuous force.

Interrupted forces Interrupted forces are reduced to zero shortly after they have been applied. If the initial force is relatively light, the tooth will move a small amount by direct resorption and then will remain in that position until the appliance is reactivated. After the application of interrupted forces, the surrounding tissues undergo a repair process until the second activation takes place3 (Fig 1-9b). The best example of an active element that applies interrupted force is the rapid expansion screw.

Intermittent forces During intermittent force application, the force is reduced to zero when the patient removes the appliance3 (Fig 1-9c). When it is placed back into the mouth, it continues from its previous level, reducing slowly. Intermittent forces are applied by extraoral appliances.3

Fig 1-8 The loss of force, with time, in springs with high (a) and low (b) load/deflection rates. In the same period (4 weeks), the loss of force in the spring with a high load/deflection rate was approximately 225 g, compared to only 75 g in the spring with a low load/deflection rate. (Reprinted from Gjessing2 with permission.)

Fig 1-9 The effects of continuous (a), interrupted (b), and intermittent (c) forces on the periodontal tissues. (Reprinted from Proffit3 with permission.)

Center of Resistance

The point where the line of action of the resultant force vector intersects the long axis of the tooth, causing translation of the tooth, is defined as the center of resistance. Theoretically, the center of resistance of a tooth is located on its root, but the location has been extensively investigated. Studies show that the center of resistance of single-rooted teeth is on the long axis of the root, approximately 24% to 35% of the distance from the alveolar crest.4–10

The center of resistance is sometimes confused with the center of mass. The center of mass is a balance point of a free object in space under the effect of gravity. A tooth, however, is a restrained object within the periodontal and bony structures surrounded by muscle forces. Therefore, the center of resistance must be considered a balance point of restrained objects.

The center of resistance is unique for every tooth; the location of this point depends on the number of roots, the level of the alveolar bone crest, and the length and morphology of the roots. Therefore, the center of resistance sometimes changes with root resorption or loss of alveolar support because of periodontal disease (Fig 1-10). For example, in the case of loss of alveolar support, this point moves apically.11

Fig 1-10 The in response to a loss of alveolar bone or periodontal attachment.

Center of Rotation

The center of rotation is the point around which the tooth rotates. The location of this point is dependent on the force system applied to the tooth, that is, the moment-to-force (M/F) ratio. When a couple of force is applied on the tooth, this point is superimposed on the center of resistance (ie, the tooth rotates around its center of resistance). In translation it becomes infinite,meaning there is no rotation. This subject is explained in greater detail in the M/F ratio section later in the chapter.

Moment

Fig 1-12 A force having a line of action passing through the center of resistance (CRes) causes translation of the tooth. During this movement, the center of resistance moves along the line of action of the force.

Couple

A couple is a system having two parallel forces of equal magnitude acting in opposite directions. Every point of a body to which a couple is applied is under a rotational effect in the same direction and magnitude. No matter where the couple is applied, the object rotates about its center of resistance—that is, the center of resistance and the center of rotation superimpose12 (Fig 1-13). For example, a torque (third-order couple) applied to an incisor bracket causes tipping of the tooth about its center of resistance. This phenomenon is explained in detail in the equivalent force systems section later in the chapter. The calculation of the moment of a couple can be performed by multiplying the magnitude of one of the forces by the perpendicular distance between the lines of action.

Fig 1-13 A couple causes an object to rotate around its center of resistance regardless of the point of application, thereby superimposing the center of resistance (CRes) and the center of rotation (a). Two examples of fixed appliances in which the couple is applied are torque in the third order (b) and antitip in the second order (c). In calculating the moment (M) of a couple, it is sufficient to multiply the magnitude of one of the forces (F) by the perpendicular distance (d) between the lines of action of these forces.

Transmissibility of a Force Along Its Line of Action

Forces can be transmitted along their line of action without any change in their physical sense. Provided that the line of action is the same, any force acting on a tooth would be equally effective if it were applied by pushing distally with an open coil or pulling distally with a chain elastic. The principle of transmissibility states that the external effect of a force acting on a tooth is independent of where the force is applied along its line of action.13

Static Equilibrium and the Analysis of Free Objects

The rules of static equilibrium are applied similarly for every object or mechanical system and for every part of that object or system. Therefore, to make it easier to understand the forces applied on a mechanical system, it is sufficient to analyze only a part of the system as a free object. For instance, to define all the forces applied on a dental arch, it may be sufficient to analyze the relations between only 2 teeth instead of analyzing all 14 teeth. Of course, the forces applied in this system of 2 teeth must be in balance. Briefly, the analysis of a free object is the study of an isolated part of a system or an object in a state of static equilibrium, enabling us to get an idea about the whole system.

Fig 1-14 On a scale in a state of static equilibrium, the moments around all the points must be in balance. The algebraic total of the moments on the O, A, B, and C points on the bar that tend to rotate the system clockwise and counterclockwise must equal zero.

The book in Fig 1-15 is in a state of rest. The factor that enables this book to remain still is the fact that a force (A), the weight of the book, has an equal and opposite force (N), the table, working against it. Because the system is statically balanced, there is balance between the forces acting on it. For an object to be in a state of static equilibrium, the foremost condition is that there must be no motion in the system.

Fig 1-15 The book on the table is in a state of rest. For the book to remain statically balanced, a force (N) of the same magnitude as the weight of the book (A) but in the opposite direction must act on the book.

Tooth Movement

Tipping

Controlled and uncontrolled tipping

Tipping, in practice, is the easiest type of tooth movement. When a single force is applied to a bracket on a round wire, the tooth tips about its center of rotation, located in the middle of the root, close to its center of resistance. This single force causes movements of the crown and apex in opposite directions. This movement, caused by the moment of force (M1), is called uncontrolled tipping13 (Fig 1-16a), and it is usually clinically undesirable. In this movement, the M/F ratio can vary from approximately 0:1 to 1:5 (see the M/F ratio section later in the chapter).

If a light, counterclockwise moment (M2; torque) is added to the system with a rectangular wire while the single distal force is still being applied, the tooth tips distally in what is called controlled tipping, which is clinically desirable. In this movement, the center of rotation moves apically, and the tooth tips around a circle of a greater radius. In controlled tipping, the M/F ratio is from approximately 6:1 to 9:1 (Fig 1-16b).

When the counterclockwise moment (M2; torque) is increased to equal the moment of force (M1), the moments neutralize each other, and there is no rotation in the system. In this case, the center of rotation no longer exists (it is infinite) and the tooth undergoes translation, or bodily movement (Fig 1-16c). In translation, the M/F ratio is approximately 10:1 to 12:1. Clinically, translation is a desirable movement, but it is hard to achieve and maintain. If the counterclockwise moment (M2; torque) is increased even more to an M/F ratio of approximately 14:1, then the moment becomes greater than M1, and the tooth undergoes root movement. In root movement, the center of rotation is located at the crown (Fig 1-16d).

Translation (bodily movement)

Theoretically, translation of a body is the movement of any straight line on that body, without changing the angle with respect to a fixed reference frame (see Fig 1-12). During translation, all the points on the body move the same distance, and they therefore have the same velocity.

Rotation

Rotation of a body is the movement of any straight line on that body by a change in the angle with respect to a fixed reference frame. If the body rotates about its center of resistance, it is called pure rotation.

Equivalent Force Systems

Fig 1-17 (a) Because translating an incisor by applying a force that passes directly through the center of resistance is not practical, this movement can be achieved by setting up an equivalent force system on the crown that gives the same result. (b) When a force (F) of 150 g is applied to the crown, a clockwise moment (M1) of 1,500 g-mm occurs. (c) If this moment is balanced with an equal and opposite moment (M2), only a net force of 150 g remains in the system. (d) Even though it is applied to the crown, this force causes translation as if it were being applied to the center of resistance. d, distance.

Moment-to-Force Ratio

If a counterclockwise moment (M2) of 900 g-mm is applied on the bracket with palatal root torque, the M/F ratio becomes 6:1 (see Fig 1-16b). In this case, the center of rotation moves apically, so the tooth moves as a pendulum around its apex (or a point close to it). This is a case of controlled tipping. If the M2 moment is increased to 1,500 g-mm, then the M/F ratio becomes 10:1. The moments balance each other, and only 150 g of single force remains on the system, causing the tooth to translate. In this case, the center of rotation of the tooth is infinite (see Fig 1-16c). If the magnitude of the M2 moment is increased even more, up to 2,100 g-mm, the M/F ratio becomes 14:1. In this case, the center of rotation moves to the crown. This is root movement (see Fig 1-16d).

Everything explained above is also valid in the transverse plane. A canine moving distally with a segmented arch acting on the bracket at a point away from the center of resistance rotates distolingually. This rotation can be controlled with an antirotation bend. In this plane, the M/F ratio is also equal to the distance between the center of resistance and the line of action of the force (Fig 1-18).

Fig 1-18 The type of tooth movement in the sagittal direction in Fig 1-17 is also valid in the transverse direction. The only difference is that a couple (antirotation) is applied in the first order. d, distance; F, force.

In the second order, as a result of distal force, the canine tips distally. This moment is balanced with an an-titip bend (counterclockwise moment). The magnitude of this moment depends on the amount of the bend and the width of the bracket. Note that for the same amount of couple, forces applied on the wings of a narrow bracket are higher compared with the wide bracket in the second order. This is basically because of the difference in distance between parallel forces of the couple. The greater the distance, the less the force and vice versa. Because the distance on the narrow bracket is less than that of the wide bracket, the magnitude of forces is higher. For example, assuming the width of the brackets (d) is 3.4 mm, the amount of force applied on the bracket wings can be calculated (Figs 1-19a and 1-19b) as

If a narrow bracket (2 mm) is used, the amount of force effective on the bracket wing is 750 g. During application of a third-order couple (torque), because the interbracket distance is very small, the magnitude of force on the bracket wings is that much more (Fig 1-19c). This is one of the main reasons ceramic bracket wings break when torqued.

Fig 1-19 For the same moment (M), the force applied to the wings of the brackets decreases as the width increases. Because the distance (d) on the wide bracket is larger (3.4 mm) (a) than that of the narrow bracket (2 mm) (b), the force is low. In torque (c), the magnitude of force on the bracket wings is high because the distance (0.63 mm) is very small.

M/F ratios of teeth with loss of alveolar support

The center of resistance of a tooth depends on the length, number, and morphology of the roots and the level of alveolar bone support. In root resorption, the root shortens, causing the center of resistance to move occlusally, but with loss of alveolar bone support, the center of resistance moves apically (Fig 1-20; see also Fig 1-10). This is particularly important in the treatment of adult patients, who often have periodontal problems.

As the distance (d) between bracket and center of resistance increases, the M/F ratio also increases. To obtain a higher M/F ratio, two options can be considered:

• Place the bracket gingivally. If this is done, the bracket base may no longer adapt well to the tooth surface.15 Furthermore, it will be more difficult to insert a straight wire for leveling. An adaptive step-up bend may be needed on the archwire, but this might affect the precision of alignment.

• Increase the moment, decrease the force, or a combination of both.15 Clinically, the moment applied to the bracket is predictable only if a segmented archwire is used. The moment generated by an antitip or torque bend cannot be measured accurately. It is therefore difficult to accurately adjust the M/F ratio by changing the moment. Adjusting the amount of force according to the type of movement obtained seems to be more practical.

Braun et al15 have stated that the M/F ratio depends basically on the location of the center of resistance, and they have determined coefficients of moments and forces to be used in cases with loss of alveolar bone support (Table 1-1).

Fig 1-20 In the case of alveolar bone loss (a), the center of resistance (CRes) moves apically, thus the distance (d) increases (b). For translation, the M/F ratio should also be increased. Clinically, it is better to reduce the force (F) to control tooth movement. This is particularly important in adults who may have alveolar bone loss owing to periodontal disease. In the case of root resorption (c), the center of resistance moves occlusally. (Reprinted with permission from Braun et al.15)

Table 1-1Moment and force values that can be applied to a tooth with alveolar bone loss*Loss of alveolar support for offset increase (mm)Moment multiplying factor to compensate for offset increaseForce multiplying factor to compensate0--11.060.9421.130.8931.190.8441.250.8051.320.76*Reprinted with permission from Braun et al.15

Clinically, determining the position of the center of resistance and the exact value of the M/F ratio to be applied and keeping it stable throughout the movement is fairly difficult. Tanne et al5 have stated that because of a very small change in the M/F ratio and the exponential relationship between the center of rotation of the tooth and this ratio, the center of rotation can change drastically. The amount of force is key to controlling the M/F ratio (ie, tooth movement). If undesired tipping occurs as a result of an overactivated loop, one should let the wire work until root movement has been accomplished.

Effect of loop configuration on M/F ratio

The objective of a loop is to decrease the load/deflection rate of the wire (ie, increase the elasticity); thus, to apply force in a wider range within physiologic limits. Because of spring characteristics, loops are commonly used in space closure with differential mechanics. During space closure, it is important to obtain controlled tooth movement in both anterior and posterior segments. Uncon-trolled tipping is usually undesirable because side effects such as anchorage loss and root resorption may occur in uprighting. For example, with the Begg appliance, extraction spaces are usually closed in a relatively short time by uncontrolled tipping of the anterior teeth, using a combination of round wires and Class II elastics. Uprighting excessively tipped incisors, however, takes longer and requires a high level of anchorage support.16

The configuration of the loop has a significant effect on the M/F ratio. Studies have shown that the M/F ratio generated by a vertical loop is approximately 2:1.17 Increasing the length of the loop can increase the M/F ratio to 4:1,18 but increasing the height of the loop is not practical because it may cause irritation and discomfort.

Figure 1-21 shows the changes in the M/F ratio of a vertical loop 6 mm high and having 20 degrees of antitip. Note that the M/F ratio generated by a 1-mm activation is less than 3:1, which produces uncontrolled tipping. The M/F ratio increases as the loop deactivates. When it has deactivated to 0.1 mm, the M/F ratio approaches 7:1, which approximates controlled tipping. The M/F ratio increases to approximately 20:1 when the deactivation goes from 0.1 to 0 mm.

Fig 1-21 The M/F ratios of a 6-mm-high vertical loop with a 20-degree gable bend. During deactivation of the loop, the M/F ratio shows a relatively stable curve throughout a distance of 0.9 mm, then increases dramatically up to 19:1 at the last 0.1 mm. (Reprinted with permission from Burstone.17)

It is evident that 0.1 mm of activation is clinically significant. A minor error in activation could change the location of the center of rotation dramatically. In clinical terms, with a 1.0-mm activation, the tooth undergoes uncontrolled tipping during the first 0.7 mm of deactivation (M/F ratio, 5:1). The center of rotation shifts to a point between the center of resistance and the apex. Thereafter, the tooth sustains controlled tipping from 0.3 to 0.12 mm. The M/F ratio becomes 7:1 and the center of rotation moves to a point between the apex and infinity. As the loop deactivates from 0.12 mm to 0.03 mm, the M/F ratio becomes 10:1, the center of rotation disappears (goes to infinity), and the tooth translates. At the final deactivation between 0.03 and 0 mm, the M/F ratio rises to 20:1, and the center of rotation moves occlusally to a point close to the crown. In this case, the tooth undergoes root movement.17

The amount of force produced by vertical loops per unit of activation can be relatively high. For example, the force produced by a Bull loop of 0.018 × 0.025–inch stainless steel (SS) wire delivers approximately 500 g.19 Such a large force produces uncontrolled tipping, and it may cause root resorption. If we need only 100 g of force, then the activation of the loop would be only 0.2 mm, which is clinically impractical. After activation, the legs of a vertical loop close rapidly, which initially produces uncontrolled tipping. If one lets the wire work, the tooth uprights slowly with root movement. The duration of uprighting depends on the amount of tipping and the M/F ratio. The more the tooth tips, the longer the uprighting will take.

Clinically, a good space-closing loop should generate an M/F ratio high enough to produce controlled tipping at maximum activation. The M/F ratio increases progressively as the loop deactivates and produces root movement. As mentioned earlier, increasing the length or adding a helix to the vertical loop decreases its load/deflection rate but has little effect on the M/F ratio.16 Putting more wire at the top of the loop to increase the M/F ratio is recommended.17,18 There are two reasons for incorporating more wire in a loop:

• To increase the M/F ratio (if placed gingivally)

• To decrease the load/deflection rate

A T-loop made from β-titanium (β-titanium alloy, or β-Ti; also titanium-molybdenum alloy, or TMA) wire is capable of generating a higher M/F ratio at a larger activation than a vertical loop. To do so, a T-loop should be “preactivated” before bracket engagement (Fig 1-22). The preactivation (gable) bend can sometimes reach 180 degrees from the horizontal, according to the anchorage needs of the case. A 0.017 × 0.025–inch TMA T-loop preactivated 180 degrees and activated 7 mm horizontally delivers approximately 350 g.13 A 0.016 × 0.022–inch TMA T-loop with the same activation generates 243 g,18 while a 0.017 × 0.025–inch and an 0.018–inch TMA composite T-loop deliver 333 g.17 To obtain 150 g for canine distalization, a T-loop on a 0.016 ×0.022–inch archwire requires only 4 mm of activation.

Fig 1-22 The activation (a) and neutral (b) positions of a T-loop.

Figure 1-23 shows an M/F ratio generated by a T-loop on a 0.016 × 0.022–inch TMA wire.18 An M/F ratio at 7 mm activation is 7.6:1, which produces controlled tipping. The average force per unit of activation (1 mm) of the T-loop is 34.5 g, which is relatively low. An error of 1 mm in activation of the loop applies 34.5 g more force to the periodontal tissues.

Fig 1-23 M/F ratios achieved by 7-mm activation of a T-loop on a 0.016 × 0.022–inch TMA wire. The M/F ratio generated by the T-loop activated 1 mm is approximately 7 times more (21.6:1) than that of a vertical loop (3:1). At full activation (7 mm), a T-loop generates an M/F ratio of 7.6:1, which produces controlled tipping. (Based on data from Manhartsberger et al.18)

The M/F ratio increases as the loop deactivates. When it has deactivated to 2.7 mm, the M/F ratio approaches 12:1, which approximates root movement. The M/F ratio increases to approximately 27:1 when the deactivation goes from 2.7 to 0.5 mm.

Conclusion

The laws of mechanics governing forces and motion in the context of orthodontics concern material properties (eg, the stress, strain, stiffness, springiness, and elastic limit of wires). Concepts such as moments and couples, center of resistance and center of rotation, and the moment-to-force ratio are likewise essential to understand in order to control tooth movements. This basic knowledge of the physical principles behind orthodontics allows the practitioner to design appliances and plan treatment that will provide optimal results.

References

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2. Gjessing P. Biomechanical design and clinical evaluation of a new canine-retraction spring. Am J Orthod 1985;87:353–362.

3. Proffit WR. Contemporary Orthodontics. St Louis: Mosby, 1986:235,237,238.

4. Burstone CJ, Pryputniewicz RJ. Holographic determination of centers of rotation produced by orthodontic forces. Am J Orthod 1980;77:396–409.

5. Tanne K, Koenig HA, Burstone CJ. Movement to force ratios and the center of rotation. Am J Orthod Dentofacial Orthop 1988;94:426–431.

6. Tanne K, Nagataki T, Inoue Y, Sakuda M, Burstone CJ. Patterns of initial tooth displacements associated with various root lengths and alveolar bone heights. Am J Orthod Dentofacial Orthop 1991;100:66–71.

7. Tanne K, Sakuda M, Burstone CJ. Three-dimensional finite element analysis for stress in the periodontal tissue by orthodontic forces. Am J Orthod Dentofacial Orthop 1987;92:499–505.

8. Vanden Bulcke MM, Burstone CJ, Sachdeva RJ, Dermaut LR. Location of centers of resistance for anterior teeth during retraction using the laser reflection technique. Am J Orthod Dent-ofacial Orthop 1987;91:375–384.

9. Pedersen E, Andersen K, Gjessing P. Electronic determination of centres of rotation produced by orthodontic force systems. Eur J Orthod 1990;12:272–280.

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