Bone Fracture Mechanics

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Functions of Bones

• Support
  • Protection
  • Movement
  • Mineral Storage
  • Hematopoietic (bone marrow makes the cells of blood)

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Diagram of a sector of the shaft of a long bone, showing the different types of cortical bone, trabecular bone, and the various channels. The osteons are located between the outer and inner circumferential lamellae.¹

Microscopic observation

• Composite material
• Basic unit: Haversian system (osteon)
• Weight %
  • 2/3 inorganic material -Hydroxyapatite, \(3Ca^3(PO4)^2 Ca(OH)^2\)

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Haversian System

Picture courtesy Gwen Childs, PhD.

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Bone Remodeling

• Coupled process of bone resporption and formation
• In the first year of life, almost 100% of the skeleton is replaced.
• In adults, about 10% per year
• An imbalance in the regulation of bone remodeling results in many metabolic bone diseases, such as osteoporosis

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Bone Remodeling

• Why do we need this process?
  • Reshapes bones during growth
  • Mineral balance (Calcium)
  • Repair micro-damage
  • Response to loads (Wolff)

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Bone Multicellular Unit

Microcracks

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Bone repair

• 2 methods of bone repair
• Direct bone healing
  • Direct apposition (touching) of bone surfaces
• Indirect bone healing
  • Does not require apposition of bone surfaces

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Direct bone healing

• Surfaces are close enough together that body treats it as a remodeling process

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Credit: JBJS (br) evolution of internal fixation of long bone fractures

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Indirect Bone Healing

• Gap in fracture surfaces
• Resorption of surfaces (more to come) -

JBJS (br) Evolution of internal fixation of long bone fractures

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Indirect repair summary

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Bone Repair- response to catastrophic failure

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Bone repair: Callus

Figure from Brighton, et al, JBJS-A, 1991.

• Within days, callus begins to form
• Composed of woven bone
• Function: Gradually enlarges fracture ends and thereby fracture cross sectional area

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Collagen orientation in woven bone (Callus)

With permission http://en.wikipedia.org/wiki/File:Woven_bone_matrix.jpg

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Also Example 8.1

Figure from: Browner et al, Skeletal Trauma 2nd Ed, Saunders, 1998.

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Fracture Mechanics

• Time of Healing
  • Callus increases with time
  • Stiffness increases with time
  • Near normal stiffness at 27 days
  • Does not correspond to radiographs

Figure from: Browner et al, Skeletal Trauma, 2nd Ed, Saunders, 1998.

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Credit: JBJS (br) Evolution of internal fixation of long bone fractures

• Indirect Bone Healing
• Gap in fracture surfaces
• Resorption of surfaces

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Why does resorption take place?

• Strain theory: “tissue cannot be produced under strain conditions which exceed the elongation at rupture of the given tissue element, such as a cell”
• Either absolute stability (direct bone healing) or elastic flexible fixation of a gap is required (indirect healing) -

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Resorption at fracture sites

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Interfragmentary strain

It is easier to get a comminuted fracture to heal than a simple fracture

www.orthosupersite.com

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Bone Biomechanics

Bone is anisotropic

Ultimate Stress at Failure Cortical Bone Compression < 212 N/m2 Tension < 146 N/m2 Shear < 82 N/m2

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Bone Biomechanics

Bone is viscoelastic:

Becomes stiffer in compression the faster it is loaded.

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Bone Mechanics

Bone Density - Subtle density changes greatly changes strength and elastic modulus - Density changes - Normal aging - Disease - Use - Disuse Figure from: Browner et al: Skeletal Trauma 2nd Ed. Saunders, 1998.

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Fracture Mechanics

Figure from: Browner et al: Skeletal Trauma 2nd Ed, Saunders, 1998.

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Intramedullary Nails - Device placed in intramedullary canal of long bones - Femur - Tibia - Humerus - Radius - Ulna - Metacarpals

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IM Nails

• Moment of Inertia
  • Bending rigidity is
    • Product E*I
  • Axial rigidity
    • Product E*A

Torsional rigidity

• Product G*J where G is elastic shear modulus and J is torsional constant (for cylinder is equal to I)

Figure from: Browner et al, Skeletal Trauma, 2nd Ed, Saunders, 1998.

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Cross-Section Design

• 92% drop in torsional rigidity

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Slotting-Torsion

• Slot in nail decreases torsional rigidity by 92%

(pp268-269)

Figure from: Tencer et al, Biomechanics in Orthopaedic Trauma, Lippincott, 1994.

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IM Nail Diameter

Figure from: Tencer et al, Biomechanics in Orthopaedic Trauma, Lippincott, 1994.

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Biomechanics of Internal Fixation

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Biomechanics of Plate Fixation

Plates: - Bending stiffness proportional to the thickness (h) of the plate to the 3rd power.

Base (b)

I= bh3/12

Heigh t (h)

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Biomechanics of Plate Fixation Applied Load

Applied Load

Bone-Screw-Plate Relationship - Bone via compression - Plate via boneplate friction - Screw via resistance to bending and pull out.

Fracture Gap - Plate alone resists loads

Plate

Gap

Bone

Construct stiffness is similar however, Locking plates do not allow motion at near cortex

Biomechanics of External Fixation

Biomechanics of External Fixation

Pin Size

{Radius}4 Most significant factor in frame stability

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Biomechanics of External Fixation

SUMMARY OF EXTERNAL FIXATOR STABILITY:

Can make a fixator more stable 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 during insertion (reducing thermal necrosis).
7. Stacked frames.

**but a very rigid frame is not always good.

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Biomechanics of Screws

Screw Anatomy

Inner diameter Outer diameter Pitch

Figure from: Tencer et al, Biomechanics in OrthopaedicTrauma, Lippincott, 1994.

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Biomechanics of Screw Fixation

To increase strength of the screw, & resist fatigue: -

Increase the inner diameter

To increase pull out strength of screw in bone: -

Increase outer diameter Decrease inner diameter Increase thread density Increase thickness of cortex (of bone) Use cortex with more density (young patient).

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Biomechanics of Screw Fixation

• Cannulated Screws Increased inner root diameter required to compensate for cannulation.
• Relatively smaller thread width.
• Screw strength minimally affected
• (α r4outer core - r4inner core )

Figure from: Tencer et al, Biomechanics in OrthopaedicTrauma, Lippincott, 1994.

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