Abstract
Fracture biomechanics can be tough-going for most candidates and yet it is definitely an A-list topic. Textbook chapters can be too complicated and detailed to understand whilst short note sections may appear incomplete as biomechanical assumptions have not been fully explained or the brevity of the notes makes them difficult to fully understand, never mind encouraging any higher-order thinking.
We hope this chapter uncomplicates a difficult area of the syllabus that a lot of candidates find offputting.
Introduction
Fracture biomechanics can be tough-going for most candidates and yet it is definitely an A-list topic. Textbook chapters can be too complicated and detailed to understand whilst short note sections may appear incomplete as biomechanical assumptions have not been fully explained or the brevity of the notes makes them difficult to fully understand, never mind encouraging any higher-order thinking.
We hope this chapter uncomplicates a difficult area of the syllabus that a lot of candidates find offputting.
Structured oral examination question 1
IM nail biomechanics
EXAMINER: This is a radiograph of a broken femoral nail that was used to fix a distal femoral shaft fracture (Figure 9.1). How can you prevent nail breakage?
CANDIDATE 1: I would insert the largest diameter solid nail that is available for use.
COMMENT: Not a good start. The answer isn’t particularly well thought out and is not scoring the candidate any marks.
EXAMINER: Why would you use a solid nail? Most nails used in orthopaedics are hollow.
CANDIDATE: Because a solid nail will be stronger than a hollow nail.
COMMENT: This is continuing on with a poor choice of imprecise terms and more importantly the candidate is missing scoring opportunities.
EXAMINER: What do you mean by the term ‘stronger’?
CANDIDATE: Strong is the ability of a material to resist deformation.
COMMENT: This is an incorrect definition and the viva is going nowhere.
EXAMINER: How does this relate to ultimate tensile strength (UTS)?
COMMENT: UTS is the highest stress observed on the stress versus strain diagram while the failure strength is the stress value at which the material eventually fails.
Strong is an imprecise biomechanical term.
A strong material has a high ultimate tensile strength.
CANDIDATE: [Silence …] Can I retract my last few statements and say that the torsional and bending rigidity of a solid nail will be greater than that of a hollow nail?
COMMENT: The candidate is not getting past the opening questions. Better to discuss factors predisposing to nail breakage. This will then lead onto discussions about area and polar moments of inertia, the biomechanical benefits of using larger-diameter nails for long bone fractures, the solid versus hollow nail dialogue, benefits of IM reaming, etc. Another road to journey down is patient factors that could predispose to non union and eventual nail breakage(smoking, alcohol, malnutrition etc)
(Score 4.)
CANDIDATE 2: An unstable fracture pattern (segmental or comminuted) or the use of a small unreamed diameter nail increases the risk of nail breakage.
Distal femoral fractures have a high incidence of intramedullary nail breakage, especially if the fracture has been produced by high-energy trauma and the patient encouraged to weight bear early. Early weight bearing with delayed fracture healing increases the time over which cyclic stress may act to cause fatigue failure and nail breakage.
Technical errors in nail insertion, such as scoring the nail during locking, may weaken the nail or create stress risers. Excessive impaction during nail insertion due to under-reaming of the medullary canal may also weaken the nail.
Intramedullary nails rarely break when no locking screws are used. Statically locked nails can produce high concentrations of stress at the proximal or distal end of the nail, predisposing it to breakage. Nail design changes such as increased material thickness around screw holes, cold forming which increases material strength reduce risk of nail breakage.
(Score 6.)
CANDIDATE: Failure of a material with repetitive loading below the ultimate tensile strength.
CANDIDATE: As mentioned, cyclic loading of an object can result in fatigue failure. An S-N curve gives information about the number of cycles a material can endure for a given stress level.
EXAMINER: Can you draw out an S-N curve?
CANDIDATE: (Figure 9.2)
EXAMINER: What makes fatigue failure more likely?
CANDIDATE: In the presence of stress risers such as a hole, a sharp edge, an indentation, notch or scratch, the loads can go beyond the normal limit that is localized in that area. This can lead to crack propagation.
EXAMINER: Why?
CANDIDATE: Crack propagation.
EXAMINER: What do you mean by this?
CANDIDATE: Sorry, I am not sure.
COMMENT: Score 6.
For a score 8: The applied stress concentrates on residual material beneath a stress riser and means the number of cycles to failure is much lower than the fatigue strength.
All stress risers greatly weaken a structure, stress risers (stress concentrators) produce increased local stresses that may be several times higher than those in the bulk of the material and may lead to local failure. Methods to produce a shorter working length(reaming for larger nail). Using a stainless steel rather than titanium nail (higher Youngs modulus) but long list of pros and cons for each material.
Figure 9.2 S-N curve.
Structured oral examination question 2
Area and polar moment of inertia
CANDIDATE: The second moment area of inertia provides a measure of how the material is distributed in the cross-section of an object relative to the load applied to it. The further away the material is from the centre of a beam, the greater its bending stiffness.
The polar moment of inertia applies to a cylindrical structure and its ability to resist torsion.
EXAMINER: How do the second moment area and polar moment area differ between a solid and a hollow nail?
CANDIDATE: For a solid nail the second moment area or second moment of inertia is directly proportional to the fourth power of the radius.
I = πr4/4
For a hollow nail the second moment of area or second moment of inertia is directly proportional to the fourth power of the outer radius minus the fourth power of the inner radius.
I = π(rO4 – rI4)/4
Nail wall thickness is equal to the difference between r0 = outer radius and r1 = inner radius.
Controversial topic
The assumption that if a nail has a thin wall then the inner radius is roughly equal to the outer radius, so the bending rigidity approximates to the third power of the outer radius, is inaccurate.
Hollow orthopaedic implants do not approximate to rO3.
In engineering, approximations are made for ‘thin’ cylinders, which is when the inner radius (r1) approaches the outer radius (r0). The rO4 – rI4 term approaches rO3 as rO~ rI, hence the approximation.
However, in the case of orthopaedic implants, using the r03 approximation is inaccurate. Using a cylinder that thin has no practical use because of the forces it must resist. The wall thickness of a hollow nail must be optimal to be able to withstand bending stress and avoid sudden failing by buckling (local concentrated deformations). The implant also starts behaving as a curved sheet rather than a hollow cylinder .
A Synthes 13 mm nail (6.5 mm radius) has a 1.2 mm wall thickness. r0 = 6.5 mm, rI = 5.3 mm (which is 6.5 – 1.2). So (rO4 – rI4) = 1785 – 789 = 996. That’s the true value of the (rO4 – rI4) term, the true coefficient for moment of inertia. Approximating rO3 is 6.53 = 275. 996 is 3.6 × 275, so to estimate a hollow nail to rO3 is a 360% underestimate, which is quite significant.1
For a solid nail the polar moment of inertia (polar moment area) varies with the fourth power of its radius.
Jo = πr4/2
For a hollow nail the polar moment of inertia varies with the fourth power of the outer radius minus the inner radius.
Jo = π(rO4 – rI4)/2
EXAMINER: Which type of nail, solid or hollow, biomechanically do we prefer to use?
CANDIDATE: A hollow nail is more efficient as less material can be used for equivalent values of bending and torsional rigidity.
EXAMINER: Why?
CANDIDATE: The further the material is spread away from the neutral axis of the nail, the greater its rigidity against bending and torsional forces.
(For score 7 candidates.)
EXAMINER: Why are spiral fractures of the tibia more common in the lower third of the tibia even though the cortex is much thicker there?
CANDIDATE: The tibia resembles a cylinder. This site has a low polar moment of inertia; even though the cortex is especially thick at this point, it has less resistance against torsional forces because of its smaller radius compared to the upper segment. Under a specific load the lower third segment will deform more than the upper segment of the tibia. The further a material is distributed away from the neutral axis of the structure, the greater the polar moment and therefore greater strength and rigidity against torsional stress.
(For score 8 candidates.)
EXAMINER: What about the bending and torsional rigidity of a hollow nail with an open section?
CANDIDATE: There is very little difference in bending rigidity between a solid hollow nail and an open nail section of the same diameter. For torsional rigidity the situation is different and is a much greater affect. The difference in behaviour of open and closed nails against torsional stress is created by the circumferential discontinuity. Stress is transmitted uniformly through the entire thickness of the cross-section of a closed-section hollow nail without any change in direction. There is a change is stress direction in an open nail when its gap is reached with a significant fall in the magnitude of polar moment (Figure 9.3).
EXAMINER: What about differences between the cross-sectional shape of a nail?
CANDIDATE: A clover leaf cross-section nail improves torsional and bending rigidity compared to a round cross-section.
EXAMINER: Why?
Figure 9.3 With the open-section nail there is reversion of the direction of torsional stress as shown by the arrows. In a closed hollow nail, the nail stress lines are in the same direction because of the continuity and therefore the nail is stronger against torsion.
Structured oral examination question 3
IM nail
EXAMINER: What does the picture show (Figure 9.4)?
CANDIDATE: This is a clinical picture showing an intramedullary nail. It looks as though this is a femoral antegrade nail as it has an anterior bow, it has multiple locking options proximally and it is cannulated distally. They are usually made of titanium.
COMMENT: Be able to describe the typical features of an IM nail.
EXAMINER: How does an IM nail function?
CANDIDATE: IM nails stabilize a fracture by acting as internal splints with load-sharing characteristics.
EXAMINER: What do we mean by an internal splint?
CANDIDATE: Splintage is defined as a construct in which micromotion can occur between bone and implant, providing only relative stability without interfragmentary compression. Callus forms at the fracture site.
EXAMINER: Do nails always act as a load-sharing device?
CANDIDATE: It depends on how it is used.
COMMENT: Candidate waffle.
EXAMINER: How is it used?
CANDIDATE: [Silence …]
COMMENT: In more comminuted fracture patterns that are not axially stable, a nail will have to transmit all the forces applied to the limb, so-called load-bearing.
Ideally, a nail should be used as a load-sharing device, but in certain situations will be used as a load-bearing device.
EXAMINER: Which is stiffer, a solid or a hollow nail?
COMMENT: Be careful with this question as it is poorly explained in some textbooks.
The bending stiffness of a cylindrical cross-section is proportional to the fourth power of its radius as described by the second moment of area.
In the case of a hollow cylinder, the bending stiffness is proportional to the fourth power of the outer radius minus the fourth power of the inner radius. As such, for any given material a hollow cylinder is less stiff than a solid cylinder of the same outer diameter.
If, however, a constant volume of material is used for construction of an IM nail of fixed length, then the use of a hollow nail would allow a greater outer radius to be used, resulting in a stiffer nail.2
CANDIDATE: I would need to decide if I want to achieve primary or secondary bone healing.
If the fracture was significantly comminuted I would ideally choose to plate in bridging mode with fracture healing by indirect or secondary fracture healing with callus formation.
Simple fractures could be treated with interfragmentary compression.
Ideally, plate position should be on the tension side of the fracture. I would need to decide the length of plate itself, the number and relative position of screws needing to be inserted and the type of screws to be used (standard cortical screws, cancellous screws, locking screws, etc.).
The plate length should be 2–3 times higher than the overall fracture length in comminuted fractures and 8–10 times higher in simple fractures.
The plate screw density should be kept below a value of 0.5, indicating that less than half of the plate holes are occupied by screws.
Two screws (monocortical or bicortical) on each main fragment is the minimum number of screws needed to keep the plate bone construction stable. Such a construct will fail if one screw breaks due to overload or if the screw loosens, so it is generally advised to add another screw to each side of the fracture construct.
Plating offers two different fixation concepts – splinting and interfragmentary compression. Comminuted fractures are best treated using a splinting technique, because local bone and soft tissue devascularization can be minimized; while in simple fractures interfragmentary compression is preferred as a stabilization tool.
When nailing the position, the length and diameter of the nail as well as the position of the locking bolts are more or less given and standardized by the local anatomy of the broken bone segment as well as the implant design (Table 9.1).
EXAMINER: What is the working length of a plate?
CANDIDATE: The working length of a plate is defined as the distance across a fracture site between the two nearest points where the bone is fixed to the plate, e.g. the distance between the two screws closest to the fracture.
EXAMINER: How is the working length of a plate altered?
CANDIDATE: The working length of a plate can be altered by changing screw position. Screws placed close to a fracture create a short working length, which increases a plate’s construct stiffness. Screws placed further from the fracture site increase the working length and produce a less-stiff construct that permits more motion at the fracture gap.
EXAMINER: What problems may arise if screws are placed too close to the fracture site?
CANDIDATE: There is the potential to create stress concentration with the risk of plate fracture. Placing screws further from the fracture site can better distribute the stress the plate experiences and decrease the risk for plate fatigue failure.
The addition of more than three screws per fragment does not significantly impact on a plate’s construct stiffness in axial loading. Adding an additional screw nearest to the fracture site provides the greatest increase in axial stiffness.
EXAMINER: Why do we want to avoid over-torqueing of screws?
CANDIDATE: Over-torqueing of the screws should be avoided during insertion.
The screw head can be destroyed.
It may cause screw–bone interface failure (i.e. stripping torque).
EXAMINER: What else?
CANDIDATE: As a screw is inserted into bone, the screw head compresses the plate against the bone with a force proportional to the torque applied to the screw.
If the screw is tightened beyond the ultimate strength of the bone–screw interface, the screw threads will lose purchase in the bone and the screw will spin with little resistance. Although pull-out strength is related to the depth of the screw thread and quality of the bone, stripping the screw reduces the pull-out strength of the screw by more than 80%.
EXAMINER: Why do we retighten screws before closure?
CANDIDATE: Before wound closure, all screws should be retightened to allow time for stress relaxation of the screw–bone interface.
Table 9.1 Characteristics of fixation.
| Plating | IM nailing | |
|---|---|---|
| Concept of fixation | Splinting Compression | Splinting |
| Load transfer | Locking Friction | Locking |
| Position | Tension side Compression side | Intramedullary |
| Insertion | Open MIPO | Intramedullary |
| Length | To decide | Whole length of bone |
| Dimension | In relation with bone and bone segment | Inner diameter of bone |
| Number of screws | Minimum 4 | Minimum 0 |
| Maximum? | Maximum 6 | |
| Position of screws | To decide | Given by nail design |
| Design of screws | Bicortical | Monocortical |
| Bicortical | ||
| Self-tapping | ||
| Self-drilling | ||
| Standard cortical | ||
| Locking |
Structured oral examination question 4
Biomechanics IM nail
CANDIDATE: Working length is defined as the length of a nail spanning the fracture site from its distal point of fixation in the proximal fragment to its proximal point of fixation in the distal fragment. More simply, it is the distance between the two points on either side of the fracture where the bone firmly grips the metal.
Thus, working length is the unsupported portion of the nail between the two major bone fragments and reflects the length of a nail carrying the majority of the load across the fracture site.
CANDIDATE: The bending rigidity of a nail is inversely proportional to the square of its working length.
CANDIDATE: Torsional rigidity is inversely proportional to a nail’s working length.
COMMENT: If all else fails, a shorter working length means the greater the bending and torsional rigidity of a nail, i.e. a stronger fixation.
EXAMINER: What factors affect working length?
CANDIDATE: The working length of a nail can be very variable depending on:
Type of force (bending, torsion). When the bone bends at the fracture site the nail may become fixed to the bone by 3 point fixation.
Type of fracture (fracture pattern) and if the fracture is reduced.
Interlocking. This modifies the working length of a nail and increases torsional stability.
Reaming. This prepares a uniform canal, allows a larger diameter nail to be used, improves nail/bone fixation and reduces the working length of the nail.
A nail has a shorter working length in bending with fixation of a transverse fracture than when used to stabilize a comminuted fracture.
EXAMINER: What affects bending rigidity?
CANDIDATE: Bending rigidity is affected by:
1. Material properties (Young’s modulus of elastic).
A cobalt chromium nail has twice the bending stiffness as that of titanium.
2. Structural properties.
(a) Length.
(b) Second moment area (SMA) of the nail, which is a variable that describes the spatial distribution of a material within a structure. The SMA is affected by the organization and shape of the material.
For a solid circular nail, the bending rigidity is proportional to the fourth power of the nail’s radius.
SMA = π.r4/4
For a hollow nail the bending rigidity is very roughly proportional to the third power of the nail diameter.
EXAMINER: Are you sure (see above)?
CANDIDATE: It is more accurate to say the bending rigidity is directly proportional to the fourth power of the outer radius minus the fourth power of the inner radius.
SMA = π. (r40 – r14)/4 where r0 is the outer radius and r1 is the inner radius.
CANDIDATE:
1. Material properties.
2. Structural properties.
Torsional rigidity is proportional to the fourth power of the nail diameter.
A slotted nail has a torsional rigidity of 1/50 that of a non-slotted nail.
EXAMINER: And?
CANDIDATE: A nail with sharp corners or fluted edges resists torsional forces to a greater degree than a smooth-walled nail.
EXAMINER: What is the difference between second area moment and polar moment for a nail?
CANDIDATE: The second moment area and polar moment area represent the relationship between bending and torsional rigidity of a nail and its cross-sectional dimensions.
The greater the material is distributed away from the neutral axis of the structure, the greater is its area and polar moment and thus the strength and rigidity against bending and torsional stress.
COMMENT: This may lead on to the examiners asking about the differences in second area moment and polar moment for a solid and hollow nail (see above). As mentioned previously, this is often poorly or inaccurately described in books or short notes bullet revision texts.
EXAMINER: What happens to polar moment of inertia when a nail has a slot?
CANDIDATE: The polar moment of inertia is greatly reduced.
CANDIDATE: The length of the nail between the forces working to bend it determines the length of the moment arm and therefore the magnitude of the bending moment. A similar situation applies in cases of torsional forces.
EXAMINER: How is bending and torsional stiffness related to working length?
CANDIDATE: The bending stiffness of a nail is inversely proportional to the square of its working length.
The torsional stiffness is inversely proportional to its working length.
The shorter the working length, the greater is the bending and torsional stiffness (rigidity) of the nail in the construct and the stronger the fixation.
CANDIDATE: Medullary reaming prepares a uniform canal and improves nail–bone fixation towards the fracture, thus reducing the nail’s working length.
CANDIDATE: Stiffness is defined as the slope of the curve in the elastic range on a stress–strain curve.
EXAMINER: Are you sure?
CANDIDATE: Yes.
COMMENT: The slope of the curve in the elastic range on a stress–strain curve is Young’s elastic modulus for a material. Stiffness is defined as the slope of a force versus displacement graph. Elastic modulus is the corresponding slope, but of a stress versus strain graph. Load is converted to stress and displacement to strain.
EXAMINER: What material are IM nails made of?
CANDIDATE: They are made of either titanium or stainless steel. IM nails can be solid or hollow.
EXAMINER: How can we reduce the stiffness of a nail?
CANDIDATE: One way of reducing stiffness is to put a longitudinal slot in the wall of a nail. This makes it much more flexible, but does so at the cost of the nail losing overall bending and torsional strength. The slot allows the cross-section to be compressed when inserted into the medullary canal.
Very stiff nails may damage the bone if there is any discrepancy between the shape of the nail and that of the bone.
EXAMINER: What factors alter a nail’s axial, bending and torsional rigidity?
CANDIDATE: This can be divided into material and structural properties. Parameters include cross-sectional geometry, nail length, the presence of a longitudinal slot and the elastic modulus of the material.
Structured oral examination question 5
IM nails
Initial questions on area and polar moment of inertia, bending and torsional rigidity (see above).
EXAMINER: How does the presence of a slot affect bending and torsional rigidity of a nail?
CANDIDATE: The presence of a slot reduces both the bending and torsional stiffness of a nail. A slot significantly affects torsional rigidity, but has much less effect on bending stiffness.
EXAMINER: Why do we use slotted nails?
CANDIDATE: It makes the nail easier to insert.
EXAMINER: What else?
CANDIDATE: Err …
COMMENT: When a solid nail is introduced into the medullary canal it makes room for its entry by compression of the surrounding bone tissue. Bone tissue exerts an equal and opposite force on the nail (Newton’s third law).
EXAMIMER: What about hoop stresses?
CANDIDATE: Sorry?
COMMENT: Hoop (expansion) stresses are generated in the bone when an IM nail is inserted. Hoop stresses are much higher when a solid or closed-section nail is introduced when compared to a slotted nail. If hoop stresses are too high they can cause comminution or splintering of the bone.
EXAMINER: What is the difference between stiffness and rigidity?
CANDIDATE: [Long silence …] Sorry, I don’t know.
COMMENT: Rigidity and stiffness are very similar concepts often used interchangeably to denote overall performance of a structure. There are however important distinctions between the two.
Stiffness is a material property, a materials ability to resist deformation, force divided by displacement.
Rigidity is a structural property, a structures ability to resist deformation. Depends on a materials stiffness and geometry construct. Rigidity incorporates both the type of material and its shape and size.
CANDIDATE: Interlocking screws help control torsion and axial loads placed on the nail. They provide rotational and longitudinal stability.
EXAMINER: Historically, why were they introduced?
CANDIDATE: The use of interlocking screws expanded the indications for use of IM nails to include more proximal, more distal, and more unstable (highly comminuted, segmental) fractures.
EXAMINER: What are the disadvantages of using interlocking screws?
CANDIDATE: Insertion requires reasonable 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, or if the screw hole closest to the fracture is left unfilled. The closer the fracture is to the distal locking screws, the less cortical contact the nail has, which leads to increased stress on the locking screws and greater chance of screw breakage.
The further the distal locking screw is from the fracture site, the more rotationally stable the fracture becomes because of friction of the nail within the medullary cavity and less chance of screw breakage.
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.
EXAMINER: When nailing a long bone, how do you decide on how many locking screws to use?
CANDIDATE: The number of interlocking screws used is based on fracture location, amount of fracture comminution, and the fit of the nail within the canal.
Midshaft transverse femoral fractures have the greatest fixation stability because of isthmic cortical contact. Oblique and comminuted fractures rely on interlocking screws for stability, as do very proximal and very distal metaphyseal fractures, where the medullary canal widens and is filled with weaker cancellous bone.
In general, one screw is sufficient for stable fractures.
EXAMINER: How are locking screws (bolts) different to other screws used for fracture fixation?
CANDIDATE: Locking bolts have a wide core diameter and smaller outer thread diameter. The screw functions to reduce torsional stresses acting on the nail and is not designed to maximize pull-out strength.
EXAMINER: What may occur if you place too many screws in multiple planes through a nail?
CANDIDATE: An IM nail allows fracture healing with relative stability even if a nail is statically locked. Minor movements occur between the nail and screw even in a static mode of nail fixation. Placing screws in multiple planes may lead to a reduction of this fragment toggle and hinder fracture healing.
EXAMINER: What is the biomechanical effect of the orientation of the locking screw?
CANDIDATE: There are some studies that suggest oblique tibial locking screws increase the stability of proximal tibial fractures compared to transverse locking screws. Distally, however, there is little difference.
In the femur, studies suggest no difference in biomechanical behaviour with locking screw orientation.
EXAMINER: What effect does multiple locking screw breakage have on fracture stability?
CANDIDATE: Premature failure of locking screws especially with unstable fracture patterns may lead to angulation, shortening, malunion and IM nail migration.
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