4 Biomechanics of Internal Fracture Fixation

10.1055/b-0040-176945

4 Biomechanics of Internal Fracture Fixation

Jason A. Lowe, Hannah L. Dailey, and Jason Wild

Introduction

A proper discussion of biomechanics necessitates knowledge and understanding of key concepts. Since the definitions are complex, the concepts in this chapter will prove difficult without a command of the language of biomechanics.

I. Definitions

Stress is a force applied to an object distributed over the area that bears the load and is measured in Newtons per meter squared N/m² (pascal).
Strain describes a change in shape in response to an applied stress. In axial loading, strain is the change in length of an object over the original length. In fracture management, multiplanar motion at the fracture site gives rise to complex three-dimensional strains.
A stress–strain curve is the experimentally observed relationship between applied load (stress) and deformation (strain) for a given material (see ▶ Fig. 4.1 ). This curve also defines other material properties.

Fig. 4.1 Representative material stress–strain graph showing Young’s modulus of elasticity (E), proportional limit (P), yield strength (σ_{_Y )}), and ultimate strength (σ_{_U )}).
Young’s modulus of elasticity (E) describes the stiffness of a material and is defined by the slope of linear portion on a stress–strain curve. The modulus E is measured in megapascals (MPa) and is intrinsic to the material, so it does not depend on material geometry. The more stress it takes to deform an object, the steeper the curve (higher E).
Proportional limit (P) of a material is the point on the stress–strain curve of a material after which any additional applied stress will cause nonelastic permanent deformation. For many materials, including implant-grade metals, the proportional limit is equal to the elastic limit.
Elastic deformation is the change in shape that is completely reversible when the applied stress is removed.
Plastic deformation or permanent set is deformation that does not completely resolve when stress is removed. When plastic deformation occurs, the object’s shape is permanently altered because of damage to the material microstructure.
Strength is the ability of a material to withstand applied loading without failure (breakage) or plastic deformation.
Yield strength (σ_{_Y}) is the stress at which a material starts to experience plastic deformation and it typically coincides with the proportional limit (P).
Ultimate strength (σ_{_U}) is the stress in a material when catastrophic failure occurs following a one-time overloading event and corresponds to point UF of the stress–strain curve.
Fatigue strength (σ_{_N}) is the maximum stress a material can withstand for N cycles of repeated loading. Trauma implant components are typically designed to withstand at least several hundred thousand cycles of weight bearing loading before fatigue failure (▶ Fig. 4.2 ).

Fig. 4.2 Representative fatigue life curves for metals. Higher applied loads (higher cycle stress amplitude, σ_{_a}) are associated with earlier fatigue failure.
Endurance limit (σ_E) is the stress at which a ferrous material, such as stainless steel, can experience infinite cyclic loading without failing. Nonferrous metals including implant-grade titanium alloys have a fatigue limit , which is the stress corresponding to failure at a defined limit such as 500 million loading cycles.
Stiffness describes the ability of a material or of a manufactured part to resist deformation in response to an applied load. The material stiffness, or Young’s modulus E, does not depend on part geometry. The part stiffness is a function of the part geometry, the material’s Young’s modulus E, and the mode of loading (e.g., axial tension/compression, bending, or torsion). Choosing a larger part (e.g., thicker plate, larger-diameter nail or screw) always increases construct stiffness.
Flexural rigidity is a measure of the force required to bend an object and is the product of the material Young’s modulus of elasticity (E) and a geometric factor. For a plate with rectangular cross section, the flexural rigidity is proportional to the plate thickness to the third power (h ³). For a screw or pin with a circular cross section, the flexural rigidity is proportional to the radius to the fourth power (r ⁴).
Stress concentration or a stress riser describes the local high stresses that arise near a defect such as a notch or hole. Locally high stresses also occur around loading contact points, such as near bone screws or where a nail contacts the endosteal cortex.
Fracture working length is the length between fracture ends.
Implant working length is the distance between the closest fixation points (▶ Fig. 4.3 ).

Fig. 4.3 (a) Six-month follow-up anteroposterior distal femur with plate osteosynthesis with a large fracture gap (malreduction). The working length (WL, distance between screws immediately adjacent to the fracture) is small creating a rigid implant. While the plate length (greater than 3 × WL) and screw density (< 50%) are appropriate, the screw very close to the fracture site limits the WL of the plate. The absence of callous at 6 months is due to the low-strain environment at the fracture site. The plate is experiencing high stress concentration right at the fracture site and may be subjected to failure. (b) Comminuted fracture fixed with a more flexible implant with longer WL. Callus formation is present at 3 months. Plate has stress spread across entire WL therefore minimizing strain and stress concentration. Interfragmentary screw may increase strain at main fracture site and may also cause formation of hypertrophic nonunion due to excessive strain at fracture site.

II. Implant Construct Design and the Mechanobiology of Fracture Healing

These definitions are important to clinical practice because the mechanics of fracture fixation are an exercise in modulating strain (fracture motion) to promote the desired mode of fracture healing (primary vs. secondary).

Primary bone healing
1. Occurs in the presence of bony contact and the absence of fracture motion.
2. This is classically observed with simple fractures and is accomplished with interfragmentary compression.
3. Strain must be less than 2%, which is achieved with compression and the absence of a fracture gap.
Secondary bone healing
1. Any gap at the fracture line or flexibility in the fixation construct will allow some relative motion between the bone fragments and result in secondary healing.
2. Characterized by the formation, ossification, and later remodeling of a bridging cartilaginous callus.
3. Preferred for comminuted fractures as well as simple long bone fractures treated with intramedullary implants.
4. The magnitude and direction of the micromotion occurring at the fracture site are known to influence the speed and course of secondary healing. In general, moderate axial strains (approximately 2–10%) support callus formation maturation, whereas shear or torsional strains may disrupt callus and delay healing.
5. Excessive strain (motion) at the fracture gap may lead to nonunion.
Modulating strain
1. Given the absence of intraoperative “strain gauges,” the surgeon must try to anticipate the postoperative demands on the construct as a result of the fracture’s natural stability, patient body mass, and weight bearing restrictions.
2. Surgeons attempt to control interfragmentary strain by modulating construct stiffness. This concept bears clinical significance because a mismatch between desired healing mode and construct stiffness will lend itself to nonunion, and a fixation construct that is not strong enough or has a significant amount of strain concentrated over a small working length will fatigue prior to osseous union.
Example of excessive stiffness
1. Comminuted distal femur fracture with large original length where secondary bone healing is desired.
2. Application of an excessively stiff implant limits movement in a fracture that requires micromotion for callus formation.
3. In the presence of a large fracture gap or complex fracture, interfragmentary strains may be too low to allow secondary healing to occur. This can be observed clinically in locked plating constructs where no callus forms or asymmetrical callus forms only at the far cortex where some motion occurs as a result of plate bending.
4. In the absence of callus formation to support load sharing, the implant experiences high stresses during weight bearing and the construct may experience early fatigue failure.
5. To avoid this outcome, the surgeon would choose to apply implants that are less stiff/more flexible to allow some interfragmentary motion, and would design a construct that spreads the stress over a greater length.
Example of excessive strain
1. A simple fracture stabilized with a relatively flexible construct.
2. A very small gap such that even small relative motions between the bone ends can cause large strains because the original length across the gap is small (▶ Fig. 4.3a ).
3. The excessive tissue strains may induce some resorption at the bone ends to effectively lengthen the gap and reduce the strain to more optimal levels for secondary healing.
4. However, if this does not occur, the fracture may go on to nonunion as the strain is too high for bone to bridge the gap.
5. To avoid this situation, the surgeon should be particularly wary of the simple fracture that has been compressed and stabilized with a plate that is too thin, too short, or has insufficient number of screws.
6. This situation may lead to motion at the fracture site resulting in secondary rather than primary bone healing and a greater likelihood of the construct failing before union.
Given the importance of interfragmentary strain for controlling the healing outcome, how then can construct stiffness be modulated to produce the desired response? The following sections provide a series of simple and intuitive guidelines to follow when considering the implant configuration and may serve as a guide to understanding and applying the biomechanical principles of fracture fixation.