1. Figure from: Tencer. Biomechanics in Orthopaedic
Fracture Mechanics
Bending load:
Compression strength greater than tensile strength
Fails in tension
As the bone is subjected to a bending load, one side is placed under compression, the other is placed under tension.
Since the bone’s compressive strength is greater than its tensile strength, the bone fails first on the tension side.
Figure from: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 3.6 (a), (b), pg. 39.
Figure from: Tencer. Biomechanics in Orthopaedic
Trauma, Lippincott, 1994.

2. Figures from: Tencer. Biomechanics in Orthopaedic
Fracture Mechanics
Torsion
The diagonal in the direction of the applied force is in tension – cracks perpendicular to this tension diagonal
Spiral fracture 45º to the long axis
TORSION: The diagonal in the direction of the applied force is in tension – cracks perpendicular to this tension diagonal
Spiral fracture 45º to the long axis
Figures from: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 3.8 (a), pg. 41.
Figures from: Tencer. Biomechanics in Orthopaedic
Trauma, Lippincott, 1994.

3. Figure from: Tencer. Biomechanics in Orthopaedic
Fracture Mechanics
Combined bending & axial load
Oblique fracture
Butterfly fragment
Combined bending & axial loads result in oblique fractures or those with a butterfly fragment.
Figure from: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 3.7 (a), pg. 40.
Figure from: Tencer. Biomechanics in Orthopaedic
Trauma, Lippincott, 1994.

4. Biomechanics of Internal Fixation
Screw Anatomy
Inner diameter
Outer diameter
Pitch
Screw Anatomy: review screw terminology.
Inner diameter: the inner, “core” or “root” diameter determines the screw’s strength.
Outer diameter: the difference between the inner core diameter and the outer diameter of the threads is the thread width. Increasing the thread width increases the pull-out strength.
Pitch: threads per inch. Increasing pitch increases the pull out strength of the screw.
Figure from: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 6.19 (a), pg. 133.
Figure from: Tencer et al, Biomechanics in
OrthopaedicTrauma, Lippincott, 1994.

5. Biomechanics of Screw Fixation
To increase strength of the screw & resist fatigue failure:
Increase the inner root diameter
To increase pull out strength of screw in bone:
Increase outer diameter
Decrease inner diameter
Increase thread density
Increase thickness of cortex
Use cortex with more density.
Increasing the screws root diameter a factor of two allows it to withstand torques eight times greater.
The more volume of bone caught between threads, the greater the pull out strength. This can be achieved by increasing the thread width of the screw, or increasing the number of threads in contact with the bone.
Density of the bone also affect pull out strength (young> than old bone, cortical bone > cancellous bone).

6. Biomechanics of Screw Fixation
Cannulated Screws
Increased inner diameter required
Relatively smaller thread width results in lower pull out strength
Screw strength minimally affected
(α r4outer core - r4inner core )
Cannulated Screws
Increased inner root diameter of a cannulated screw is large than a comparable non-cannulated screw. This extra material is required to compensate for the cannulation (mechanical effects of converting a solid cylinder to a tube).
This results in a relatively smaller thread width and lower pull out strength.
Figure from: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 6.30 (b), pg. 140.
Figure from: Tencer et al, Biomechanics in
OrthopaedicTrauma, Lippincott, 1994.

7. Biomechanics of Plate Fixation
Plates:
Bending stiffness proportional to the thickness (h) of the plate to the 3rd power.
Height (h)
Base (b)
I= bh3/12
Bending stiffness proportional to the thickness of the plate to the 3rd power, and directly to the elastic modulus. Therefore, changing the plate thickness has more effect upon stiffness than changing the material.
This is expressed as the base (b) times the height or thickness cubed over 12.

8. Figure from: Browner et al, Skeletal Trauma 2nd Ed, Saunders, 1998.
Moments of Inertia
Resistance to bending, twisting, compression or tension of an object is a function of its shape
Relationship of applied force to distribution of mass (shape) with respect to an axis.
Resistance to bending, twisting, axial compression or tension of an object is a function of its cross-sectional shape with respect to a given axis. The relationship of resistance to applied forces to the distribution of mass (shape) with respect to an axis is related to the moment of inertia. These calculations based upon the cross-sectional shape are useful in comparing the resistance to applied forces of two different objects (solid vs. cannulated IM nails, thin vs. thick cortical bone).
Figure from: Browner B., Jupiter J., Levine A., Trafton P., Skeletal Trauma 2nd Edition, W.B. Saunders, 1998, figure 4-6, pg. 101.
Figure from: Browner et al, Skeletal Trauma 2nd Ed, Saunders, 1998.

9. Fracture Mechanics 1.6 x stronger Fracture Callus 0.5 x weaker
Moment of inertia proportional to r4
Increase in radius by callus greatly increases moment of inertia and stiffness
Effect of fracture Callus: since the moment of inertia for a cylindrical tube is proportional to r4 any small increase in the radius by callus further away from the center greatly increases moment of inertia therefore the stiffness of the structure.
Figures from: Browner B., Jupiter J., Levine A., Trafton P., Skeletal Trauma 2nd Edition, W.B. Saunders, 1998, figure 4-6, pg. 101.
Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 4.6, pg. 62.
0.5 x weaker
Figure from: Browner et al, Skeletal Trauma
2nd Ed, Saunders, 1998.
Figure from: Tencer et al: Biomechanics in
Orthopaedic Trauma, Lippincott, 1994.

10. Figure from: Browner et al, Skeletal Trauma,
Fracture Mechanics
Time of Healing
Callus increases with time
Stiffness increases with time
Near normal stiffness at 27 days
Does not correspond to radiographs
Time of Healing: Callus increases with time, therefore the stiffness increases with time. Near normal stiffness achieved at 27 days due to the callus formed further away from the axis. This increased strength does not correspond to the radiographs.
Figure from: Browner B., Jupiter J., Levine A., Trafton P., Skeletal Trauma 2nd Edition, W.B. Saunders, 1998, figure 4-15, pg. 109.
Figure from: Browner et al, Skeletal Trauma,
2nd Ed, Saunders, 1998.

11. IM Nails Moment of Inertia
Stiffness proportional to the 4th power.
Recall that for a cylindrical tube, the moment of inertia is proportional to the radius to the 4th power. Small changes in the radius can mean large changes in the stiffness.
Figure from: Browner B., Jupiter J., Levine A., Trafton P., Skeletal Trauma 2nd Edition, W.B. Saunders, 1998, figure 4-6, pg. 101.
Figure from: Browner et al, Skeletal Trauma, 2nd Ed, Saunders, 1998.

12. IM Nail Diameter
IM Nail Diameter: As the diameter of the nail increases, so does the torsional and bending moments of inertia (stiffness); a 16 mm nail is 2.5 x stiffer than a 12 mm nail. The large diameter can accommodate larger holes for larger interlocking screws. The nail size is limited by the diameter of the patient’s IM canal and the amount of reaming performed.
Figure from: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 9.21, pg. 263.
Figure from: Tencer et al, Biomechanics in Orthopaedic Trauma, Lippincott, 1994.

13. Slotting Allows more flexibility In bending
Decreases torsional strength
SLOTTING: Placing a longitudinal slot in a nail makes the nail moderately more flexible in bending (especially if slotted on the compression side), and significantly more flexible in torsion. This slot allows for radial compression of the nail during insertion into the femur. The increased bending flexibility aids in allowing an easier insertion and canal fit, but also decreases the fatigue resistance of the nail (does not seem to be a clinical problem).
Figures from: Nail cross sections: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 9.20, pg 262.
Stress diagrams: Rockwood and Green’s 4th ed.
Figure from Rockwood and Green’s, 4th Ed
Figure from: Tencer et al, Biomechanics
in Orthopaedic Trauma, Lippincott, 1994.

14. Slotting-Torsion Figure from: Tencer et al, Biomechanics
Slotting-Torsion: A slotted nail is about 2% as stiff as an intact femur in torsion, while a solid-section nail is about 50% as stiff (Tencer, Tech Orthop 1988).
Figures from: Bar graph: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippencott, 1994, figure 9.22, pg. 263.
Figure from: Tencer et al, Biomechanics
in Orthopaedic Trauma, Lippincott, 1994.

15. Interlocking Screws Disadvantages Location of screws
Controls torsion and axial loads
Advantages
Axial and rotational stability
Angular stability
Disadvantages
Time and radiation exposure
Stress riser in nail
Location of screws
Screws closer to the end of the nail expand the zone of fxs that can be fixed at the expense of construct stability
INTERLOCKING SCREWS: Control torsion and axial loads.
ADVANTAGES: The use of interlocking bolts expanded the use of IM nails to more proximal, more distal, and unstable fractures (highly comminuted, segmental), as well as adds rotational stability with the non-reamed technique.
DISADVANTAGES: Requires some technical skill to place. The holes in the nail act as stress risers (the weakest part of the nail to fatigue is at or just proximal to the most proximal distal locking screw). There is an increased rate of nail breakage if the fracture is within 5 cm of these screws (Bucholz, JBJS 1987), or if the screw hole closest to the fracture is left unfilled (Hahn, Injury 1996).
LOCATION: Screw holes closer to the end of the nail allow for the fixation of more proximal or distal fractures, but at the expense of stability of the construct.

16. Biomechanics of Internal Fixation

17. Biomechanics of Plate Fixation
Functions of the plate
Compression
Neutralization
Buttress
“The bone protects the plate”
The primary function of the plate is to maintain alignment as an internal splint, and to create compression between the fracture ends such that bone can transfer some of the applied loads itself. A compression plate, tension band, or a lag screw does this by generating compression across the fracture.
In fixation constructs in which the plate-bone system can carry load, the compressed fractured bone carries a major part of the load. “The bone, therefore, protects the implant” (B.G. Weber).

18. Biomechanics of Plate Fixation
Unstable constructs
Severe comminution
Bone loss
Poor quality bone
Poor screw technique
Unstable constructs: A construct in which compression cannot be achieved across the fracture is unstable and at risk for failure. Plates alone cannot tolerate the functional loads of a limb, and if the fracture does not heal, the construct may eventually fail due to fatigue under cyclical loading.
This situation may be due to:
Severe comminution: consider bridge plating techniques.
Bone loss
Poor quality bone
Poor screw technique
Improper choice of implants

19. Biomechanics of Plate Fixation
Applied Load
Fracture Gap /Comminution
Allows bending of plate with applied loads
Fatigue failure
Gap
A gap at the fracture site such that there is no fracture compression with applied loads allows bending or torsion of the plate with the fulcrum at the level of the fracture. All of the forces are transmitted through the plate alone instead of being shared by the bone and the plate.
Bone
Plate

20. Biomechanics of Plate Fixation
Fatigue Failure
Even stable constructs may fail from fatigue if the fracture does not heal due to biological reasons.
Fatigue Failure:
Even stable constructs may fail from fatigue if the fracture does not heal due to biological reasons (infection, soft tissue loss, periosteal stripping, smoking). The fracture surgeon must learn to balance the desire for rigid fixation with the need to preserve the soft tissue (biological fixation).

21. Biomechanics of Plate Fixation
Applied Load
Bone-Screw-Plate Relationship
Bone via compression
Plate via bone-plate friction
Screw via resistance to bending and pull out.
Screw-Plate Relationship: When load is applied to the bone, a portion of the load is transferred across the fracture line if the construct allows compression. A portion of the load is also transferred to the plate by bone-plate friction. A portion is supported by the screw resisting bending and pull out.
Lag Screw: adding a compression lag screw across the fracture site greatly increases the load transfer to the bone, further protecting the screws and plate.

22. Biomechanics of Plate Fixation
The screws closest to the fracture see the most forces.
The construct rigidity decreases as the distance between the innermost screws increases.
The screws closest to the fracture see the most forces. The screws further away experience progressively less force.
The construct rigidity decreases as the distance between the innermost screws increases.
A longer plate can increase the rigidity of the construct.
Screw Axial Force

23. Biomechanics of Plate Fixation
Number of screws (cortices) recommended on each side of the fracture:
Forearm 3 (5-6)
Humerus 3-4 (6-8)
Tibia 4 (7-8)
Femur 4-5 (8)
Through experience with failure the recommended strength of plate and number of screws in each fragment has been determined. These are general guidelines and more may be required with poor quality bone. Anatomic constraints may limit also the construct. Also it is important to note that the increased spread of screws is more important than the number of screws (provided each screw has equal purchase) for construct stability.

24. Biomechanics of Plating
Tornkvist H. et al: JOT 10(3) 1996, p
Strength of plate fixation ~ number of screws & spacing (1 3 5 > 123)
Torsional strength ~ number of screws but not spacing

25. Biomechanics of External Fixation
It is uncertain how rigid an external fixation frame should be; too rigid may be detrimental to fracture healing.

26. Biomechanics of External Fixation
Pin Size
{Radius}4
Most significant factor in frame stability
SIZE OF PINS:
RADIUS: Stiffness proportional to {radius}4, so small changes in pin diameter greatly increases stiffness. **This is the most significant factor affecting stability of the fixator.
Larger pins provide more rigid fixator, providing less bending stress at the bone-pin interface and lower rate of loosening.
However, the hole size acts as a stress riser; if the pin diameter is greater than 30% the size of the bone the risk of fracture greatly increases (McBroom, Orthop Res 88).

27. Biomechanics of External Fixation
Number of Pins
Two per segment
Third pin
NUMBER OF PINS:
1] Two pins per fragment to prevent rotation, usually in same plane.
2] A third pin in the fragment adds slightly to the resistance to bending and axial deviations, but little to rigidity. A third pin does allow the subsequent removal of a loose or infected pin without sacrificing the construct.

28. Biomechanics of External Fixation
Third pin (C) out of plane of two other pins (A & B) stabilizes that segment. B
Deformation perpendicular to the plane of two pins is best controlled with a third pin in that perpendicular plane. A third pin (C) out of plane of two other pins (A & B) stabilizes that segment.

29. Biomechanics of External Fixation
Pin Location
Avoid zone of injury or future ORIF
Pins close to fracture as possible
Pins spread far apart in each fragment
Wires
90º
PIN LOCATION:
1] Pin out of zone of injury if possible (avoid infecting fracture):
a] For stability, place pins as close to the fracture site as possible (limited by anatomy and soft tissue injury).
b] For sterility place away location of incision for any future, delayed ORIF, bone grafting, soft tissue coverage.
2] More stable if the second pin in a fragment is spread as far from the first pin to best resist motion in the perpendicular plane.
3] Wire constructs most stable when at 90 to each other.

30. Biomechanics of External Fixation
Bone-Frame Distance
Rods
Rings
Dynamization
BONE-FRAME DISTANCE:
1] ROD: The closer the frame is to the bone the more stable is the construct. Allow room for edema and wound care (2-3 cm).
2] RING: Decreasing the span that the wire travels increases the overall rigidity.
3] DYNAMIZATION: Can “dynamize” the frame easily by moving the rod further away from the bone.

31. Biomechanics of External Fixation
SUMMARY OF EXTERNAL FIXATOR STABILITY: Increase stability by:
1] Increasing the pin diameter.
2] Increasing the number of pins.
3] Increasing the spread of the pins.
4] Multiplanar fixation.
5] Reducing the bone-frame distance.
6] Predrilling and cooling (reduces thermal necrosis).
7] Radially preload pins.
8] 90 tensioned wires.
9] Stacked frames.
**but a very rigid frame is not always good.

32. Ideal Construct Far/Near - Near/Far on either side of fx
Third pin in middle to increase stability
Construct stability compromised with spanning ext fix – avoid zone of injury (far/near – far/far)

33. Biomechanics of Locked Plating

34. Conventional Plate Fixation
Courtesy of Synthes- Robi Frigg
Conventional Plate Fixation
Patient Load
Patient Load
In conventional plate fixation, as the screws are tightened, and the screws displace the bone into compression, a compressive force is generated between the plate and the bone. This compressive force must be sufficient in order to generate enough friction between the plate and the bone to maintain stability of the fracture. As long as the resultant load from body weight and muscles does not exceed what the frictional interface can support, the construct will remain stable and prevent collapse.
Patient Load
< =
Friction Force 4

35. Locked Plate and Screw Fixation
Courtesy of Synthes- Robi Frigg
Locked Plate and Screw Fixation
Here is the initial stress in the bone due to tightening (roughly 0). When the bone is loaded along the axes of the bone, the bone around the screw is compressed on the load side of the fracture.
Patient Load =
<
Compressive Strength of the Bone 5

36. Courtesy of Synthes- Robi Frigg
Stress in the Bone
Patient Load
If we compare the stresses in the bone immediately after implantation, the bone around the bi-cortical screws is already stressed from tightening whereas the bone around the locked screw is not subjected to any shear stresses. When the patient starts to weight bear, the bone in the bi-cortical screws is more highly stressed than the locked screws. +
Preload 7

37. Standard versus Locked Loading
Courtesy of Synthes- Robi Frigg
Standard versus Locked Loading
Here is the initial stress in the bone due to tightening. When the bone is loaded along the axes of the bone, the bone around the screw is compressed on the load side of the fracture.
As the load is increased, and the angle between the screw and the plate starts to change, the resultant loading vector on the screw changes from pure compression to a compressive and a tensile component. It is this additional tensile component which, when the elastic limit of the bone is exceeded, will cause toggling and eventual collapse across the fracture gap. 5

38. Pullout of regular screws
Courtesy of Synthes- Robi Frigg
Pullout of regular screws
Once the angular stability of one screw is lost [by pulling thru 2nd cortex], the cycle begins and the inherent angular stability of the construct is compromised.
by bending load

39. Higher resistant LHS against bending load
Courtesy of Synthes- Robi Frigg
Higher resistant LHS against bending load
Resistance of larger area decreases this form of pullout. Rather the next form is necessary [see next slide].
Larger resistant area

40. Biomechanical Advantages of Locked Plate Fixation
Purchase of screws to bone not critical (osteoporotic bone)
Preservation of periosteal blood supply
Strength of fixation rely on the fixed angle construct of screws to plate
Acts as “internal” external fixator
Through experience with failure the recommended strength of plate and number of screws in each fragment has been determined. These are general guidelines and more may be required with poor quality bone. Anatomic constraints may limit also the construct. Also it is important to note that the increased spread of screws is more important than the number of screws (provided each screw has equal purchase) for construct stability.

41. Preservation of Blood Supply Plate Design
LCDCP
DCP

42. Preservation of Blood Supply Less bone pre-stress
Courtesy of Synthes- Robi Frigg
Preservation of Blood Supply Less bone pre-stress
Conventional Plating
Bone is pre-stressed
Periosteum strangled
Locked Plating
Plate (not bone) is pre-stressed
Periosteum preserved

43. Courtesy of Synthes- Robi Frigg
Angular Stability of Screws
Nonlocked
Locked

44. Biomechanical principles similar to those of external fixators
Courtesy of Synthes- Robi Frigg
Biomechanical principles similar to those of external fixators
Stress distribution

45. Surgical Technique Compression Plating
Courtesy of Synthes- Robi Frigg
Surgical Technique Compression Plating
The contoured plate maintains anatomical reduction as compression between plate and bone is generated.
A well contoured plate can then be used to help reduce the fracture.
Traditional Plating

46. Surgical Technique Reduction
Courtesy of Synthes- Robi Frigg
Surgical Technique Reduction
If the same technique is attempted with a locked plate and locking screws, an anatomical reduction will not be achieved.
Locked Plating

47. Surgical Technique Reduction
Courtesy of Synthes- Robi Frigg
Surgical Technique Reduction
Instead, the fracture is first reduced and then the plate is applied.
Locked Plating

48. Surgical Technique Precontoured Plates
Conventional Plating
Locked Plating
1. Contour of plate is important to maintain anatomic reduction.
1. Reduce fracture prior to applying locking screws.

49. Unlocked vs Locked Screws
Biomechanical Advantage
1. Force distribution
2. Prevent primary reduction loss
3. Prevent secondary reduction loss
4. “Ignores” opposite cortex integrity
5. Improved purchase on osteoporotic bone
Sequential Screw Pullout
Larger area of resistance

50. Surgical Technique Reduction with Combination Plate
Courtesy of Synthes- Robi Frigg
Surgical Technique Reduction with Combination Plate
Lag screws can be used to help reduce fragments and construct stability improved w/ locking screws
Locked Plating

51. Surgical Technique Reduction with Combination Hole Plate
Courtesy of Synthes- Robi Frigg
Surgical Technique Reduction with Combination Hole Plate
Lag screw must be placed 1st if locking screw in same fragment is to be used.
Locked Plating

52. Hybrid Fixation Combine benefits of both standard & locked screws
Precontoured plate
Reduce bone to plate, compress & lag through plate
Increase fixation with locked screws at end of construct

53. Length of Construct Longer spread with less screws
“Every other” rule (3 screws / 5 holes)
< 50% of screw holes filled
Avoid too rigid construct

54. Biomechanical Advantages of Locked Plate Fixation
Purchase of screws to bone not critical (osteoporotic bone)
Preservation of periosteal blood supply
Strength of fixation rely on the fixed angle construct of screws to plate
Acts as “internal” external fixator
Through experience with failure the recommended strength of plate and number of screws in each fragment has been determined. These are general guidelines and more may be required with poor quality bone. Anatomic constraints may limit also the construct. Also it is important to note that the increased spread of screws is more important than the number of screws (provided each screw has equal purchase) for construct stability.