Biomechanics in orthodontics / /certified fixed orthodontic courses by Indian dental academy


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Biomechanics in orthodontics / /certified fixed orthodontic courses by Indian dental academy

  5. 5. INTRODUCTION The biologic cascade of events that ultimately results in boneremodeling and orthodontic tooth movement begins with the mechanicalactivation of an orthodontic appliance. The force systems produced byorthodontic appliances, consisting of both forces and moments, displaceteeth in a manner that is both predictable and controllable. By varying theratio of moment to force applied to teeth, the type of tooth movementexperienced can be regulated by the orthodontist. Orthodontic appliancesobey the laws of physics and can be activated to generate the desired forcesystems to achieve predetermined treatment goals for individual patients.Likewise, any orthodontic appliance can be analyzed to define themechanical force systems it produces. Understanding the biomechanicalprinciples underlying orthodontic appliance activations is essential forexecuting efficient and successful orthodontic treatment.
  6. 6. Mechanics is the discipline thatdescribes the effects of forces on bodiesBiomechanics refers to the science ofmechanics in relation to biologic system.
  7. 7. MECHANICAL CONCEPTS IN ORTHODONTICS An understanding of severalfundamental mechanical concept isnecessary to understand clinicalrelevance of biomechanics inorthodontics.
  8. 8. Scalar: When a physical property ( Weight, temperature ,force) has onlymagnitude , its called a scalar quantity.( E.g.. A force of different magnitude such as 20gm,50gm etc)Vector: When a physical property has both magnitude and direction its calleda vector quantity.(E.g.. A force vector characterized by magnitude, line of action, point of originand sense)
  9. 9. Force Force is equal to mass times acceleration F= ma Forces are actions applied to
  10. 10. RESULTANTS AND COMPONENTS OF ORTHODONTICFORCE SYSTEMS Teeth are often acted upon by more than one force. Since the movement of atooth (or any object) is determined by the net effect of all forces on it, it isnecessary to combine applied forces to determine a single net force, orresultant. At other times there may be a force on a tooth that we wish to break up intocomponents. For example, a cervical headgear to maxillary molars will movethe molars in both the occlusal and distal directions. It may be useful to resolvethe headgear force into the components that are parallel and perpendicular tothe occlusal plane, in order to determine the magnitude of force in each ofthese directions.
  11. 11. h a ø bsin ø= a/h a = h sin øcos ø = b/h b = h cos ø
  12. 12. Resultant of forces F1 F1 ø F1 cos ø + F2 cos ø F2 F 2 The parallelogram method of determining the resultant of 2 forces having common point of application
  13. 13. Components of a force F sin ø F ø F cos ø
  14. 14. The resultant of 2 force with different point of application can bedetermined by extending the line of action to construct acommon point of application
  15. 15. Center of mass Each body has a point on its mass ,which behaves as if the whole mass isconcentrated at that single point. Wecall it the center of mass in a gravityfree environment.Center of gravity The same is called the centre ofgravity in an environment whengravity is present.
  16. 16. Center of resistanceCenter of mass of a free body is the point through which anapplied force must pass to move it linearly without any rotation. Thiscenter of mass is the free objects “Balance Point”The center of resistance is the equivalent balance point of arestrained body.Center of resistance varies depending up on the - Root length & morphology - Number of roots - Level of alveolar bone support
  17. 17. Center of resistance of Center of resistance of maxilla 2 teethCenter of resistance of Maxillarymolar AJO DO 90: 29-36, 1986
  18. 18. Center of resistance depending upon the level of alveolar bone.
  19. 19. Center of resistance during anterior teeth retraction Center of resistance of 6 anterior teeth- ± 7mm apical tothe interproximal bone Center of resistance of 4 anterior teeth- ±5mm apical tothe interproximal bone Center of resistance of 2 anterior teeth- ±3.5mm apical tothe interproximal bone The location of the instantaneous center of resistanceshifted apically as the number of dental units consolidated(2, 4, and 6) increased.Clinical implication: They suggest that little difference in the moment/forceratio (M/F) is required to translate a two- or four-teeth unit.However, for the retraction of a six-teeth segment, the M/Fratio of a retraction spring should be calibrated for a highervalue to facilitate translation. AJO DO 91(5):375-384,1987
  20. 20.
  21. 21. Center of resistance during anterior teeth intrusion For an anterior segment comprising two central incisors, thecenter of resistance was located on a projection line parallelto the midsagittal plane on a point situated at the distal half ofthe canines For an anterior segment that included the four incisors, thecenter of resistance was situated on a projection lineperpendicular to the occlusal plane between the canines andfirst premolars. For a rigid anterior segment that included the six anteriorteeth, the center of resistance was situated on a projectionline perpendicular to the occlusal plane distal to the firstpremolar. AJO DO 90(3):211-220,1986
  22. 22. The center of resistance was found in different occlusoapicalpositions, depending on the direction of the force. Thus thelocation of the center of resistance cannot be considered to beconstant, independent of the direction of loading, for a tooth with agiven support. A force always acts to displace the center of resistance in thedirection the force is acting (support being the same) . www.indiandentalacademy.comAJO DO 1993 May (428 - 438) AJO DO 99(4):337-
  23. 23. JCO28(9):539-546,1994
  24. 24. JCO28(9):539-546,1994
  25. 25. Center of rotation If a model of a tooth is attached to a piece of paper by a pin, the point with thepin in it cannot move, and this point becomes the center of rotation about whichthe tooth can spin. If the pin is placed at the incisal edge, only movement of theroot is possible if it is placed at the root apex, movement is limited to crowntipping. In each case, the center of rotation is determined by the position of thepin. Thus, in two dimensional figures, the center of rotation may be defined as apoint about which a body appears to have rotated, as determined from its initialand final positions.
  26. 26. The more nearly translational the movement, the farther apically the center ofrotation would be located. In the extreme case, with perfect translation, thecenter of rotation can be defined as being an infinite distance away. A simple method for determining a center of rotation is to take any two points on the tooth and connect the before and after positions of each point with a line. The intersection of the perpendicular bisectors of these lines is the center of rotation AJO DO 85(4):294-307,1984
  27. 27. Burstone stated in his simple formula:y × (M/F) = 0.068 h2 where y = Distance from center of resistance to center of rotation M/F = Distance from center of resistance to point of force application h = Root lengthThus, in this special case of a two-dimensional parabolic root, 0.068 is aconstant for a given root length. AM J ORTHOD 1969;55:351-69.
  28. 28. Two important parameters σ2 and γ, which measure theresistance of the tooth to tipping, were found to be constantsfor loading in one plane of space, independent of the position ofocclusoapical force. Using experimental σ2 or γ values, one can calculate thelocation of the center of rotation of the tooth for a given forceposition or, conversely, when a center of rotation is desired, theposition of the force (or the equivalent moment/force ratio at thebracket) can be calculated. Because the γ values differed as the load was changed fromone plane to another through the long axis of the tooth, it wasshown that different centers of rotation would be produced for agiven force location if the direction of loading was changed. The center of rotation located more apically to the center ofresistance with forces directed labiopalatally than mesiodistally. AJO DO 99(4):337-345,1991
  29. 29. More is the value of σ2 & γ more is the resistance to tipping or rotation www.indiandentalacademy.comAJO DO 99(4):337-345,1991
  30. 30. Sign ConventionsA universal sign convention is available for forces & moments in dentistry &orthodontics.Forces are positive when they are in :-Anterior direction-Lateral direction-Mesial direction-Buccal direction-Extrusive forces Moments are positive when they move the crown in a mesial, buccal orlabial direction.
  31. 31.
  32. 32. Moment of the force :-It is the tendency of a force to produce rotation.The force is not acting through the CresIt is determined by multiplying the magnitude of force by the perpendiculardistance of the line of action to the center of resistance.Unit– Newton . mm ( Gm. mm)
  33. 33. The direction of moment of force can be determined by continuing the lineof action around the Cres
  34. 34. Couple A couple consists of two forces of equal magnitude, with parallel butnoncolinear lines of action and opposite senses.The magnitude of a couple is calculated by multiplying the magnitude of forcesby the distance between themUnit :- Newton . mm (Gm . mm)
  35. 35. Moment of a couple The tendency of a couple to produce pure rotation around the CresDirection of rotation is determined by following the direction of either forcearound the Cres to the origin of opposite force. Cres
  36. 36. Irrespective of where on a rigid object a couple is applied; the external effectis the same. 50g 50gm 50gm 50gm
  37. 37. The moment of force is always relative to a point of reference. Themoment of a force will be low relative to a point close to the line of actionand high for a point with a large perpendicular distance to the line of action. A couple is no more than a particular configuration of forces which have aninherent moment. This moment of couple is not relative to any point.
  38. 38. In orthodontics depending up on the plane in which the couple is acting theyare called as Rotation-1st order Tipping- 2nd order Torque- 3rd order
  39. 39. TorqueTorque is the common synonym of moments Moments of forces moments of couples
  40. 40. Systems Equivalent force A useful method for predicting the type of tooth movement that will occur withthe appliance activation is to determine the “ equivalent force system at tooth’scenter of resistance.It’s done in three stepsFirst- Forces are replaced at the Cres maintaining its magnitude and directionSecond- The moment of force is also placed at the Cres.Third- Applied moment ( moment of couple in bracket wire combination) is alsoplaced at Cres.
  41. 41. MC-MF F FMC MF
  42. 42. Moment to force ratio & types of tooth movement The type of movement exhibited by a tooth is determined by the ratio betweenthe magnitude of the couple (M) and the force (F) applied at the bracket. The ratio of the two has units of millimeters (this represents the distance awayfrom the bracket that a single force will produce the same effect). www.indiandentalacademy.comAJO 85(4):294-307,1984 AJO DO 90: 127-131, 1986
  43. 43. Tipping -Greater movement of crown of the tooth than of the root Uncontrolled tipping: -Movement of the root apex and crown in opposite direction -Crot – Between Cres and apex -Mc/F ratio 0:1 to 5:1 -0<Mc/MF<1 Controlled tipping: -Movement of the crown only - Crot – At the root apex -Mc/F ratio 7:1 -0<Mc/MF<1 www.indiandentalacademy.comJCO13:676-683,1979 AJO 85(4):294-307,1984
  44. 44. Translation -Bodily moment occurs -Crot – At infinity -Mc/F ratio 10:1 -Mc/MF=1 -Root movement -Root movement occurs with the crown being stationary -Crot – at the incisal edge or the bracket -Mc/F ratio 12:1 - Mc/MF>1 Pure rotational movement -Root & crown move equally in opposite direction - Crot – Just incisal to Cres - Mc/F ratio 20:1 - Mc/MF>1 www.indiandentalacademy.comJCO13:676-683,1979 AJO 85(4):294-307,1984
  45. 45. Newton’s Laws :First Law: The Law Of Inertia Every body continues in its state of rest or uniform motion in a straight lineunless it is compelled to change by the forces impressed on it.Second Law :The Law Of Acceleration The change in motion is proportional to the motive force impressed & ismade in the direction of straight line in which the force is impressed.Third Law :The Law Of Action & Reaction To every action there is always opposing & equal reaction. When a wire is deflected or activated in order to insert it into poorly alignedbrackets the 1st & 3rd laws are apparent.
  46. 46. Static Equilibrium It is a valuable application of Newton’s Laws of motion to the analysis of theforce system delivered by an orthodontic appliance. Static Equilibrium implies that, at any point within a body , the sum of forces &moments acting on a body is zero; i.e., if no net force or moments are acting onthe body the body remains at rest (static).The analysis of equilibrium can be stated in equation formΣ Horizontal forces = 0Σ Vertical forces = 0Σ Transverse forces = 0 ANDΣ Moments ( Horizontal axis ) = 0Σ Moments ( Vertical axis )= 0Σ Moments ( Transverse axis ) = 0
  47. 47. Intrusion
  48. 48. Centered ‘V’ AJO DO 98(4):333-339 1990
  49. 49. Off Centered ‘V’ AJO DO 98(4):333-339 1990
  50. 50. Step bend It is easy to understand that the forces generated in this type of situation are stronger than those generated in an off- center V bend. Indeed, for a given angle between the wire and the brackets, the two moments, C1 and C2, add up in the step bend, yielding a stronger reactional moment, as well as stronger vertical AJO DO 98(4):333-339 1990
  51. 51. No Couple System d d F F MF
  52. 52. One Couple System (Determinate force system)
  53. 53. Two Couple System (Indeterminate force system)
  54. 54. Leveling & Aligning Wider bracket Narrower bracket More Mc Less Mc Less contact angle More contact angle More the play more is the Mc It was found that a predictable ratio of the moments produced between twoadjacent brackets remained constant regardless of interbracket distance or thecross section of the wire used if the angles of the bracket remained constant to www.indiandentalacademy.comthe interbracket axis. AJO DO 1988 Jan (59 – 67)
  55. 55. We put thinner wires at the beginning of alignment i.e. more play - less appliedcouple - less M:F - no root moment only crown moment (tipping)
  56. 56. MC MC MC MC MCAm J Orthod www.indiandentalacademy.com1974;65:270-289
  57. 57. The 2 central incisors are rotatedmesial in creating a symmetric Vgeometry. Thedesired corrective force systeminvolves 2 equaland opposite moments as illustrated Semin Orthod 2001;7:16-25.
  58. 58. The force system developed by inserting a straight wire into the brackets ofthe 4 anterior teeth will create counterclockwise moments on the 2 centralincisors as well as lingual movement of the left central incisor and labialmovement of the right central incisor. The initial geometry is not favorable foralignment. Semin Orthod 2001;7:16-25.
  59. 59. shows a lingually placed right lateral incisor. In this case, the geometricrelationship between the right lateral and central incisors is a step geometryand the placement of a straight wire into the brackets of the 4 anterior teeth willalign the teeth and also shift the midline to the right side Semin Orthod 2001;7:16-25.
  60. 60. In the maxillary arch shown in Figure, the relationship between the centralincisors is a step geometry and an asymmetric V geometry is observedbetween the central and lateral incisors on the right side. Analysis of the forcesystem shows that, although correction of the 2 central incisors will occur asa result of straight wire placement, the right lateral incisor will be displacedlabially, which is undesirable side effect . Semin Orthod 2001;7:16-25.
  61. 61. The relationship between the right lateral and central incisors isrecognized as an asymmetric V geometry. Analysis of the force systemshows that, although the left lateral incisor will be corrected by rotating mesialout and moving labially, the right lateral incisor will move further lingually Semin Orthod 2001;7:16-25.
  62. 62. The relationship between the right lateral and central incisors isrecognized as an asymmetric V geometry. Analysis of the force systemshows that, although the left lateral incisor will be corrected by rotating mesialout and moving labially, the right lateral incisor will move further lingually Semin Orthod 2001;7:16-25.
  63. 63. During extrusion of a high canine unilaterally. Figure A shows the force system generated by the placement of a straight wire through a high maxillary right canine. The canine will extrude as desired, but the lateral incisor and first premolar on that side will intrude and tip toward the canine space. An open bite may result on that side of the arch, and the anterior occlusal plane will be canted up on the right Semin Orthod 2001;7:16-25.
  64. 64. Molar Rotations- absence of maxillary molar rotation is highly desirable inobtaining class-I occlusion of the molars, premolars, & canines.B/L Molar rotations:Palatal Arch Mc Mc
  65. 65. HeadgearF F MF MF
  66. 66. U/L Molar Rotations:D M MF MF Mc Mc
  67. 67. Simultaneous Intrusion & Retraction:
  68. 68.
  69. 69. Cres MF MF MF MFCross bite elastics Cres
  70. 70. Force vectors in Cl-III elastics Force Vectors in Cl-II elasticsFavorable in low angle deep bite Favorable in low angle cases www.indiandentalacademy.comcases
  71. 71. Space ClosureGroup A AnchorageGroup B AnchorageGroup C Anchorage
  72. 72. Force system for Group B space closureM/F Ratio 10/1in anterior & posterior – Translation of anterior & posterior Mc Mc
  73. 73. Force System for Group A space closureM/F ratio 12/1 or more in posterior & 7/1 or 10/1in anteriors – Root moment ofposteriors & tipping or bodily moment of anteriors IDEAL
  74. 74. Forces Differ
  75. 75. Moments Differ
  76. 76. Force system for Group C space closure mirrors that of groupA.The anterior teeth becomes the effective anchor teeth.The anterior moment is of greater magnitude & the vertical force sideeffect is an extrusive force on the anterior teeth.
  77. 77. TORQUING WITH THE MOMENT OF A COUPLE System equilibrium Torquing arch Incisor movements AJO DO1993 May (428 – 438)
  78. 78. TORQUING WITH THE MOMENT OF A FORCE System equilibrium Base arch Incisor movements AJO DO1993 May (428 – 438)
  79. 79. CONCLUSION Various mechanics can often be used to achieve the tooth movementsdesired for orthodontic treatments. It is important however to understandthe mechanics involved and to recognize when the appliance will not achieveadequate results or may result in undesirable side effects. This can help usto prevent prolonged overall treatment time and/or compromise in the finalorthodontic outcome. The ultimate result will be a happy post treatment patient , with abeautiful smile leaving your clinic.
  80. 80. REFFERENCES1. Smith RJ, Burstone CJ: Mechanics of tooth movement. AJO 85:294- 307,1984.2. Burstone CJ, Koenig HA: Creative wire bending- The force system from step & V bends. AJO DO 93(1):59-67,1988.3. Burstone CJ, Koenig HA: Force system from the ideal arch. AJO 65(3):270- 289,1974.4. Demange C: Equilibrium situations in bend force system. AJO DO98(4):333- 339,1990.5. Issacson RJ, Lindauer SJ, Rubenstein LK: Moments with edgewise appliance e: Incisor torque control. AJO DO 103(5):428-438,1993.6. Koing HA, Vanderby R, Solonche DJ, Burstone CJ: Force system for orthodontic appliances: An analytical & experimental comparison. J Biomechanical Eng102(4):294-300,1980.7. Kusy RP, Tulloch JFC: Analysis of moment/force ratio in the mechanics of tooth movement. AJO DO 90; 127-131,1986.8. Nanda R, Goldin B: Biomechanical approaches to the study of alteration of facial morphology. AJO 78(2):213-226,1980.
  81. 81. 9. Vanden Bulcke MM, Burstone CJ, Sachdeva RC , Dermaut LR: Location ofcenter of resistance for anterior teeth during retraction using the laser reflectiontechnique. AJO DO 91(5):375-384,1987.10. Vanden Bulcke MM, Dermaut LR, Sachdeva RC, Burstone CJ: The centerof resistance of anterior teeth during intrusion using the laser reflectiontechnique & holographic interferometry. AJO DO 90(3): 211-220,1986.11. Mulligan TF: Common sense mechanics 2 . Forces & moments. JCO13:676-683,1979.12. Siatkowski RE: force system analysis of V-bend sliding mechanics. JCO28(9):539-546,1994.13. Tanne K, et al: Moment to force ratios & the center of rotation. AJO 94:426-431,198914. The basics of orthodontic mechanics. Semin Orthod 2001;7:2-1515. Leveling & aligning: Challenges & Solutions Semin Orthod 2001;7:16-25.16. Biomechanics in clinical Orthodontics. Ravindra Nanda, 1 st Edition17. Biomechanics in Orthodontics. Michael R. Marcotte, 1st Edition
  82. 82. 18. Modern Edgewise Mechanics & Segmented Arch Technique, Dr C JBurstone, 1st Edition19. Contemporary Orthodontics. W R Proffit 3 rd Edition20. Orthodontics Current Principles & Techniques. T M Graber, R lVanersdal. 3rd Edition21. Systemized Orthodontic Treatment Mechanics. R P McLaughlin, J CBennet, H J Trevisi
  83. 83.