Biomechanics

BIOMECHANICS

DEPARTMENT OF ORTHODONTICS AND DENTO FACIAL ORTHOPEDICS

SEMINAR ON

BIOMECHANICS

Submitted by: GURINDER SINGH

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CONTENTS 1)Introduction

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2) What Is Biomechanics 3) Center Of Gravity 4) Center Of Resistance 5) Moment 6) Centre Of Rotation 7) Couple 8) Moment To Force Ratio 9) Stateof Equilibrium 10) Begg Mechanotherapy 11) Objectives Of Stage-I 12) Biomechanics Of Incisor Intrusion

A) Degree Of Anchor Bend B) Role Of Class II Elastics C) Role Of Class I Elastics 13) Biomechanics Of Rotation 14) Biomechanics Of Incisor Tipping 15) Objectives Of Stage-II 16) Biomechanics Of Space Closure 17) Conclusion 18) Bibliography

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INTRODUCTION The physical concepts that form the foundation of orthodontic mechanics are the key in understanding how orthodontic appliances work. The principles are not unique to orthodontics but are basic to the science of static mechanics.

With the objective of achieving predictable results based on predetermined treatment goals, the basic mechanics underlying orthodontic appliance activation must be thoroughly understood.

BIOMECHANICS: Biomechanics is the study of mechanics as it affects the biologic systems. It is the application of mechanics to the biology of tooth movement.

Physical properties such as distance, weight, temperature and force are treated mathematically as either scalars or vectors.

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• Scalars include temperature and weight, these have a definite magnitude but do not have a direction.

They are completely

described by their magnitude. • Vectors include force, these have both magnitude and direction. In case of force, along with magnitude and direction, point of application must be taken into account. BIOMECHANICS:

Biology + Mechanics = Biomechanics Various terminologies and laws:  Force  Moments  Couple  Moment to force ratio

FORCE: It is defined as an act upon a body that changes or tends to change the state of rest or motion of the body.

Force is a vector it has both

magnitude and direction. Direction consists of two properties – a line of action and a sense. In case of understanding of tooth movement along

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with magnitude and direction, point of application of force is important. The forces are indicated by straight arrows.

CENTER OF MASS: Each body has a point in its mass, which behaves as if the whole mass is concentrate at that single point, which we call the center of mass in a gravity free environment.

The same is called center of gravity in an environment where gravity is present.

Since the tooth is partially restrained as its root is embedded in bone its center of gravity moves apically and this is known as Center of resistance.

• In case of single rooted tooth center of resistance is on the long axis of tooth between one third and one half of the root length apical to alveolar crest.

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• For a multirooted root, the center of resistance is probably between the roots 1-2 mm apical to furcation.

Center of Resistance Varies (CRES): 1) Length of root: Maxillary canine have long root than maxillary lateral incisor. Thus center of resistance of canine will be more apically placed as compared with center of resistance of lateral incisor. 2) Alveolar bone height: Center of resistance shifts apically as with the alveolar bone loss. 3) Periodontal status: The center of resistance shifts apically in periodontally compromised patients.

The center of resistance for a single rooted tooth estimated by different authors are as; a) At 50% of root length – Proffit, Nikoli b) Between 50% to 3% of root length – Smith and Burstone. c) At 33% of root length – Burstone d) Between 25% to 33% root length – Nanda 6

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MOMENT: It is defined as a tendency to rotate. Moment is a measure of the turning tendency produced by a force. Moments can be symbolized by curved arrows.

MOMENT OF FORCE:

When a force is applied at any point other than through the center of resistance in addition of moving the center of resistance in direction of the force, a moment is created.

In case of tooth, since it is embedded in the alveolar bone, we cannot apply force directly on CRES, but can apply force on the exposed part of the tooth, which is at a distance from C RES. Therefore with a single force we invariably create a moment called as moment of force. A moment may be referred as, Rotation, Tipping or Torquing.

Moment is the product of the force times the perpendicular distance from the point of force application to the center of resistance. M=FXD It is measured in grams – millimeters. 7

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This changing magnitude of force or changing the perpendicular distance from the line of action to center of resistance has an effect on magnitude of moment. The direction of a moment can be determined by continuing the line of action of the force around the center of resistance.

CENTER OF ROTATION:

It may be defined as a point about which a body appears to have rotated as determined from its initial to final positions.

A simple method of determining a center of rotation. Draw the long axis of the tooth in its initial and final positions; we will see that both these lines intersect at a point. This is the point around which the tooth rotates and is called center of rotation.

Center of rotation could be at the center of resistance, apical or incisal to CRES or at infinity.

Its position will determine the type of tooth

movement.

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The moment to force ratio controls the center of rotation for the intended displacement.

UNCONTROLLED TIPPING: In this situation, when force is applied the crown moves in one direction and root moves in the opposite direction. Here Center of rotation lies near to center of resistance. This is referred as uncontrolled tipping. CONTROLLED TIPPING: In this situation, crown moves in the direction of force but the root position remains the same or gets minimally displaced. Here Center of rotation lies at apex of the root. TRANSLATION: In this situation tooth moves bodily i.e. both crown and root portion of tooth moves bodily in the direction of force. Here Center of rotation lies at infinity. All the points in the tooth move by same distance in the same direction in translation. ROOT MOVEMENT: In this situation, root moves in the direction of force but the crown position remains the same or gets minimally displaced. Here Center of rotation lies at Incisal edge of the crown. COUPLE: Two equal and opposite, non - collinear forces are called a couple. Couple consists of two forces of equal magnitude, which are parallel to each other but not coincident and they face in opposite direction. 9

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The moment of this couple is equal to the magnitude of one of the forces multiplied by the perpendicular distance between the two lines of actions. If the two forces of the couple act on opposite sides of the center of resistance, their effect is additive. However, if they are on the same side of the center of resistance, their effect is subtractive. MOMENT TO FORCE RATIO: In terms of direction, the counter-balancing moment is always going to be in the direction opposite the moment of force It seems that type of movement exhibited by a tooth is determined by ratio between the magnitude of the couple (M) and the force applied at the bracket. In terms of direction the moment of couple is always going to be in the direction opposite the moment of force. The ratio of the counter moment to the force applied determines the type of tooth displacement, brought about by the combined application of a force and counter moment. As the counter balancing moment increases, the center of rotation moves apically. At one specific level of M/F the moment which arises from the force and the applied counter movement cancel out each other i.e. there is no rotational component, and hence only a translation takes place under the effect of force. M/F Ratio values normally quoted of various types of displacements are; M/F ratio less than 5:1 causes uncontrolled tipping in which the crown and the root apex move in opposite directions. M/F ratio between 5:1 and 8:1 causes controlled tipping in which the root apex remains stationary and only the crown moves. M/F ratio of 10:1 causes translation. The crown and the root apex move to same extent in the same direction of force. 4) M/F ratio of 12:1 causes root movement. The crown remains stationary while only the root moves. It is important to note that the differences between the M/F Raito for controlled tipping, translation and root movement are small. In other words, even small alterations in the magnitude of the applied force or the counter movement will alter the type of movement brought about. STATE OF EQUILIBRIUM:

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When an appliance is fitted in the mouth, it assumes a state of equilibrium. The active elements in the appliance generate certain forces or moments. Other forces or moments arise automatically in the system to balance these forces or moments. Some of them may be beneficial while others may be undesirable. Whenever state of equilibrium is established in the system the sum of all forces and moments (together) present must be zero in all three planes. For example, tip back bend (like the bite opening bend in Begg appliance) generates a moment which tends to tip the molar tooth crown distally. This is balanced by an automatic creation of another moment in the overall system in opposite direction comprising of two forces an intrusive force at the anterior end and on extrusive force on the molar.

BEGG MECHANOTHERAPY Begg mechanotherapy is very efficient in opening the deep anterior overbites. It is generally agreed that Begg mechanics bring about bite opening by a combination of molar extrusion (especially of lower molars) and some intrusion of lower anteriors. Upper anteriors may not change in their position in vertical direction (i.e. they are prevented from erupting) or may intrude slightly or may even extrude slightly. There are three basic movements in the Begg mechanotherapy Incisor intrusion Tipping of teeth Root uprighting. The mechanism of intrusion is understood by considering the net intrusive force magnitude and direction in relation to Centre of resistance of tooth. While tipping of teeth and root uprighting is explained on the basis of M/F ratio. OBJECTIVES OF STAGE I: Open the anterior bite : Proper amount of bite opening bends or curves in the arch wire. Continual wearing of Class II intermaxillary elastics as required. 2) Eliminate anterior crowding: 11

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Vertical loops between crowded anterior teeth, with bracket areas modified for desired overcorrection. 3) Close anterior spaces: - Plain arch wire with latex elastic or elastomeric chain from cuspid to cuspid. Over correct rotated cuspids and bicuspids : Rotating springs Elastomeric traction into the arch wire Over correct the mesiodistal relationship of the buccal segments Continued wearing of class II elastics. Proper bite opening bends in both upper and lower arch wires. Attaining edge to edge anterior tooth relationship and correction of deep overbite are main objectives of stage I.

BIOMECHANICS OF STAGE-I As we understand today the Begg appliance is a good example of single couple system. The orthodontic environment created during stage I is conducive to rapid movement of anterior teeth under the light forces generated by the arch wires and intermaxillary elastics Bite opening has been reported as a result of; Primarily increased eruption of the mandibular molar (According to Cadman, Swain et al). Intrusion of the mandibular incisors (Sims, Levin et al) A combination of mandibular incisor intrusion and mandibular molar extrusion (James, William and Thompson). Mainly by intrusion of upper and lower anterior teeth (Begg and Kesling). The preference during bite opening is for incisor intrusion and avoid for molar extrusion because of the following reasons. Incisor intrusion reduces or prevents gummy smile. In case of adults, bite opening should not be done by molar extrusion as it is not a stable result and at the same time can increase the mandibular plane angle thereby worsening the Class II profile. MECHANISM OF INTRUSION: Lack of true intrusion of the maxillary incisors was one of the major weaknesses of traditional Begg. Bite opening occurred mainly on account of molar extrusion and some intrusion of the lower incisors. Whether the upper incisors are intruded is a debated issue. The round arch wire derives bite opening force from the anchor bends. A clockwise moment generated by the anchor bend in the molar tube (upper) is automatically balanced by the generation of anticlockwise moment in the 12

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anterior segment along with intrusive force on the anterior and extrusive force on the molars in order to establish state of equilibrium. This anticlockwise moment generated in the anterior segment bring about labial flaring of the upper anteriors. This flaring tendency of upper incisors can be resisted by using Class II elastics during stage I. But class II force along with horizontal component have vertical component of force which reduces the magnitude of the intrusive force of the arch wire on the upper anteriors. Thus the interplay between the intrusive force from the arch wire and the retractive force from the elastics determines both the magnitude and direction of the net resultant force acting on anterior teeth. VARIOUS TYPES OF BITE OPENING BENDS: The Anchor bend the conventional bite opening bend causes more intrusion of canines while the lateral and central incisors progressively lag behind. A Gable bend causes a progressively more intrusion of central and lateral incisor, as compared to canine Mollenhouer’s bite opening curve – Mollenhouers especially recommends it with use of 0.018 wire. Swain modification: Mild gingival curve is incorporated in the anterior section, from mesial of cuspid to mesial of other side cuspid. CONSIDERATION OF THE MAGNITUDE OF INTRUSIVE FORCE. OPTIMAL INTRUSIVE FORCE VALUE: Many authors have suggested optimum intrusive force values ranging from 15-30 grams per upper incisor and slightly higher values for upper canines. In 1985 Kesling stated that upper and lower bite opening bends generate intrusive forces of approximately 1.5 Oz and 1.2 Oz magnitude respectively at upper and lower midlines. The extrusive component of the light Class II elastics on the upper incisors is approximately 1ounces. Hence the net intrusive force n the upper incisors is approximately .5 ounces. Probably this force is enough to prevent their normal eruption and to maintain their height, but insufficient to intrude them. For active intrusion the upper anteriors should receive approximately 60 grams net force in the midline in after negating the extrusive component of Class II elastics. ROLE OF LIGHT CLASS II ELASTICS: 13

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Hocevar stated 120 grams of archwire generated intrusive force in conjunction with 60 grams of Class II elastics pull on either side for efficient for intrusion. According to Dr.Jayade net intrusive force of 60 grams can be obtained by a combination of 75 grams of intrusive force generated by arch wire and some modification in wearing of elastics that is by using light elastic forces for longer periods from 2-5 days. Very light Class II force is delivered as the elastic force diminishes rapidly in oral environment. Sims states the use of 3/8” ultra light elastics instead of routinely used 5/10” light elastics. He said continue the same elastic for 4-5 days till they break. ROLE OF CLASS I ELASTICS: Modifying the force system to achieve simultaneous intrusion and retraction using Class I elastic instead of Class II elastics was first illustrated by Shin Yang Liu (1981). He summarized that the direction of resultant force should pass through the center of resistance of anterior teeth (or close to it). Therefore, substituting Class II elastic forces by Class I elastic forces would orient the resultant force more vertically passing nearer to the center of resistance of anterior teeth. In traditional begg technique the direction of the intrusive vector of the maxillary arch wire and the extrusive vector of the class II elastics are opposite. This accounts for the difficulty in obtaining anterior maxillary teeth intrusion In this technique modification, of using Class I elastics, it solves the problem of lack of intrusion of the maxillary anteriors. In this arrangement the vectors are in the same direction as the elastic pull and the arch wire force are unidirectional and hence synergistic. Dr. Jyothindra Kumar introduced concept of power arms as a point of attachment high up in the vestibule for the engagement of Class I elastics. Dr. Jayade has been using Class I elastics, which were worn from transpalatal arch (TPA) to the canine hooks/loops. It is impossible to precisely calculate the required intrusive force every time, for every patient since therefore it is dependent on various variables. Different root sizes and tooth inclination.

Different arch sizes, which affect the length of the wire spans and stretch of the elastics. Individual biomechanical response

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Difference in the archwire sizes. Normally .018” wire will produce more intrusive force as compared to 0.016” wire when some degree of anchor bend is given.

The conclusion is too use higher intrusive forces in combination with very light Class II elastic forces for active upper incisor intrusion. CONSIDERATION OF THE DIRECTION OF THE RESULTANT FORCE: Teeth respond only to the resultant of the forces which are applied and not to the individual components of the force system. During Stage I, the upper anteriors are subjected to two forces i.e. the retractive force of class II elastics and the intrusive force generated by the anchor bend in the arch wire. The resultant of these two will determine how the upper anterior teeth respond to the intrusion.

The direction and magnitude of resultant force both depend upon the interplay between.  Magnitude of Intrusive Force: Whose direction remains constant i.e. tangential to the arc that the anterior segment of the arch wire would subscribe, if released from the brackets.  Magnitude and the direction of the elastic force.

Different

inclinations of the anterior teeth would require different combinations of the intrusive and elastic forces. 15

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Hocevar states, that the teeth are not affected by the magnitudes of various components of force systems, they experience only the total resultant force

For example, in case of severely proclined upper anteriors a low magnitude of intrusive force along with high class II force would give a desired resultant force, passing palatal to Cres; this will help correcting the proclination of incisors. Once the inclination of upper incisors is corrected then the class II elastics force is reduced helping in keeping the resultant force close to Cres.

In Class II Division 2 cases, where the upper centrals are retroclined, only intrusive force should be used (Avoiding the Class II elastics). The intrusive force acts labial to Cres and corrects the retroclination. Once the inclination is corrected then we can use Class II elastics.

MECHANISM OF ROTATION

For correction of rotation of incisors one can do anti rotational adjustment in the incisor bracket consisting of a small piece of .010” ligature wire

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welded to mesh depending on rotation. If the incisor is rotated distopalately, then weld the ligature on the mesial side of the bracket.

For correction of rotation of canines and premolars one can go for - Rotating springs - Elastomeric traction into the arch wire

Rotating spring works on the principal of couple. Since in rotating spring the couple generated is acting on one side of Cres of tooth so it is less effective as compared to couple acting on either side of Cres

MECHANISM OF TIPPING: Generally, uncontrolled tipping is undesirable because it leads to root resorption as stated by Reitan. There is more resorption when uncontrolled tipping is in labio-lingual direction. Intrusion and tipping are intimately related not only because they are carried out simultaneously but also, when both are balanced judiciously it help in overcoming uncontrolled tipping of incisors.

This is achieved by manipulating the intrusive force generated by wire and retractive component of force from the elastics. Both the anchor bend 17

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in the wire and class II elastics produce moments in the same labiolingual plane but act in opposite directions. The intrusive force produces crown labial-root lingual moment i.e. anticlockwise moment on the upper anteriors. While the retractive force produced the Class II elastics generates clockwise moment i.e. crown lingual-root labial moment

The moment from the intrusive force can act as the counter balance moment against the moment produced by the elastic force. The ratio of the former to the retraction component of the elastic force is the M/F ratio which governs the type of tipping while retracting the anterior teeth. The most important consideration is to keep light Class II elastic and use adequate amount of intrusive force so that correct M/F ratio (8:1) is obtained to have a controlled tipping.

PREVENTING UNCONTROLLED TIPPING OF UPPER INCISORS

In the refined Begg mechanics, use of MAA (Mollenhauer’s Aligning Auxillary) which provides a moment in the labio-lingual plane by creating a couple. In case of MAA, the moment of couple generated in upper anteriors is in anticlockwise direction in X – Axis. While the 18

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moment produced by the anchor bend is again in the anticlockwise direction but in the Y – Axis.

Both the moments generated by the anchor bend and the MAA are in the anticlockwise direction thus gets summed up. Once the bite is opened in the first stage, the intrusive force level is reduced which inturn reduces M/F ratio. This leads to greater likelihood of uncontrolled tipping of upper anterior teeth during later part of the first stage and whole of second stage.

Thus the anticlockwise moment produced by anchor bend on anterior is supplemented by the moment of couple produced by MAA

PREVENTING UNCONTROLLED TIPPING OF LOWER INCISORS:

In case of lower anterior the anchor bend the intrusive force generated by anchor bend can alone can flare the teeth.

Flaring occurs as lower

incisors are subjected to crown labial root lingual moment from the

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intrusive force in arch wire, while there is no restraining force on these teeth as similar to Class II force on Upper incisors.

The flaring can be avoided by two means; 1) Minimizing the clockwise force moment by reducing the intrusive force. 2) Secondly, cinching tightly the distal ends of the arch wire. 3) Lastly by producing counter moment using a MAA for labial root torque or a reverse torquing auxiliary. In case of severely lingually tipped lower anteriors, Cres will be lying buccal to the point of application of the intrusive force generated by the anchor bend so there are more chances to tip the lower anteriors more lingual So in that case we give a By pass arch wire in order to upright the lower incisors. When we activate the By pass arch wire by pulling from the mesial end of molar tube, the direction of resultant force is basically in labial direction , thus correcting the inclination of incisors by moving the crown of incisors labially .

BEGG STAGE II

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Amongst the traditionally described stages of Begg technique, the second stage of treatment involves closure of extraction spaces. This is thought to be the easiest phase of treatment

When all the objectives of Stage I are met stage II mechanics can be instituted. The sole or main purpose of II stage is closure of extraction spaces. The extraction space can be closed by either retraction of the anteriors or protraction of the posteriors or combination of both. During Stage II all the corrections achieved during first stage should be maintained.

1) Maintain edge to edge relationship of anterior teeth:  Reduced anchor bend in archwire and wearing of intermaxillary elastics as required.

2) Maintain anterior space closure :  To tie cuspid ties either elastomeric rings or steel ligatures.

3) To maintain overcorrected or normal mesiodistal molar relationship :  Keep wearing of intermaxillary elastics as required during posterior space closure. In addition to the above, the stage II of the refined Begg aims are 21

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In addition to the above, the stage II of the refined Begg aims are Controlled tipping of the incisors, when space closure is to be mainly achieved by the anterior retraction.

OBJECTIVES OF STAGE II:

When all the objectives of Stage I are met stage II mechanics can be instituted. The sole or main purpose of stage II is closure of extraction spaces. The extraction space can be closed by either retraction of the anteriors or protraction of the posteriors or combination of both

1) To maintain all the corrections achieved during the stage I. 2) To close all the extraction spaces, this is done by further retraction of the anterior teeth or by protraction of the posterior teeth or combination of both.

In addition to the above, the stage II of the refined Begg aims are 1) Controlled tipping of the incisors, when space closure is to be mainly achieved by the anterior retraction. 22

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2) Preventing excess tipping of the anteriors when space closure is mainly achieved by protracting the posteriors. 3) If the molar relation is not fully corrected at the end of Stage I, this correction is to be achieved during the stage II.

BIOMECHANICS OF STAGE II

The anchor bend should be sufficient enough as to produce a counter clockwise moment slightly less than the clockwise moment produced by the Class I elastics in anterior section of upper arch. The M/F ratio should be sufficient around 8/1 so as to have a controlled tipping movement.

Same way in lower arch the clockwise moment produced by anchor bend should be slightly lesser than anticlockwise moment produced by Class I elastics, so as to have controlled tipping movement.

Normally 0.016 upper and lower arch wires with reduced bite opening bends are used. Some authors say use of heavy arch wire 0.020 as it will 23

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function as retainers to maintain arch form and bite opening achieved during stage I. Dr. Swain advocated the use of lingual attachments on molars and cuspids to allow the use of lingual space closing elastics to aid the traditionally used buccal vector of intra maxillary elastic force during stage II known as half strength elastics. Two distinct advantages in using intra maxillary (Half strength) space closing elastics  It gives a better positional control over the anchor molar thus obviating the need for a mandatory compensate toe in bend when  using elastic force only from buccal side.  Closure of extraction spaces becomes easier.

This needs an additional adaptation demands on the patients tongue and calls for greater patient cooperation in terms of elastic wear. As an alternative, elastomeric modules can be put to use. But the use of fixed elastomeric modules is best done in those patients who have good oral hygiene status.

USE OF BRAKING MECHANICS:

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When further retraction of anterior teeth into the remaining space is deemed undesirable, then the posterior teeth are brought forward, posterior teeth are mesialized.

To achieve mesialization of posterior teeth heavy elastic forces are required with concurrent use of brakes in the anterior region.

Various brakes are - Using uprighting springs (passive springs) - Reverse torque to incisor roots (Udder arch and MAA)

-

Using T pins

The brakes reverse the anchorage site from the posterior to anterior segment by allowing bodily movement rather than the tipping of anterior teeth; this bodily movement provides more resistance hence acting as a anchorage.

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CONCLUSION The importance of biomechanics is well understood in clinical orthodontics. Applications of biomechanical principles improve the efficacy of our appliance system as well as orthodontic technique.

A common misconception is that the application of biomechanical properties would make the technique too cumbersome. On the contrary, biomechanically designed appliance gives a predictable tooth movement, optimal biologic tissue response and minimal side effects.

In the lighthearted note - One can say that on the average, an orthodontist spends half the treatment time on problems presented by the patient and other half on problems resulting from treatment side effects 26

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ORTHODONTICS COULD BE IN OUR HAND IF WE USE EFFICIENT

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BIBLIOGRAPHY  Nanda

Ravindra.

Biomechanics

in

clinical

orthodontics.Philadelphia: W.B Saunders Company ;1997  Begg, P. R.: Begg orthodontic theory and technique, Philadelphia, 1965, W. B. Saunders Company.  Swain, B. F., and Ackerman, J. L.: An evaluation of the Begg technique, AM. J. ORTHOD. 55: 668-687, 1969.  Hocevar RA: Orthodontic force systems: Technical refinements for increased efficiency. AM J ORTHOD 81: 1-11, 1982.  Hocevar RA: Understanding, planning, and managing tooth movement: Orthodontic force system theory. AM J ORTHOD 80: 457-477, 1981.

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 Reitan K: Tissue behavior during orthodontic tooth movement. AM J ORTHOD 46: 881-900, 1960.  Cadman, G. R.: Nonextraction treatment of Class II, Division 1 malocclusion with the Begg technique, AM. J. ORTHOD. 68: 481498, 1975  Sims, M. R.: Anchorage variation with the light wire technique, AM. J. ORTHOD. 59: 456-469, 1971.  Marcotte MR: Prediction of orthodontic tooth movement. AM J ORTHOD 69: 511-523, 1976.  Thompson, W. J.: Current application of Begg mechanics, AM. J. ORTHOD. 62: 245-271, 1972.  Begg, P. R., and Kesling, P. C.: The differential force method of orthodontic treatment,AM.J. ORTHOD. 71: 1-39, 1977.  Shin-Yang Liu and C.W Herschleb: Controlled movement of maxillary incisors in the Begg technique AM.J. ORTHOD.79 : 300-315, 1981.  Smith and Burstone: Mechanics of tooth movement AM.J. ORTHOD.105: 294-307, 1984.

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