Fracture Biomechanics of the Appendicular Skeleton

Bone Structure and Function

The purpose of the skeletal system is to protect internal organs, and to provide rigid kinematic links and muscle attachment sites to facilitate body movement. These functions are supported by the unique structural and mechanical properties of bone. Bone is a hard, tough material, metabolically active, capable of self-repair, and adaptive to the mechanical demands placed upon it.

Like other connective tissues, bone consists of cells and an organic extracellular matrix. Bone is unique among mammalian tissues because of its high content of inorganic mineral salts, primarily calcium and phosphorus. This inorganic mineral accounts for 65 to 70% of bone’s dry weight and gives bone its solid consistency and rigidity. The organic extracellular matrix, composed primarily of collagen and, to a lesser extent, proteoglycans, gives bone its flexibility and resiliency. Abundant amounts of water, which also contribute to bone’s flexibility and resiliency, are also present in bone, mostly in the extracellular matrix, but also in the canals and cavities of bone.

Microscopically, bone is composed of multiple osteons or haversian systems (Fig. 108-1). In the center of the osteons are haversian canals that form the primary circulatory network in bone. Each osteon consists of concentric layers of mineralized matrix called lamellae that surround the haversian canal. Each osteon is separated from, yet bonded to, surrounding osteons by a cement line composed of a cementing ground substance consisting predominantly of glycosaminoglycans. Collagen connects one lamella to the next within an osteon, but does not cross from one osteon to the next. Interstitial lamellae, which are of the same material as the osteons but oriented differently, are continuous with the osteons and span regions between complete osteons. In long bones, osteons usually run longitudinally.

Figure 108-1. Schematic illustration of the fine structure of a section of long bone depicting multiple osteons (also called haversian systems) as the structural units. Haversian canals at the center of each osteon form the primary circulatory network. Each osteon consists of concentric lamellae interconnected by collagen. Each osteon is distinct from, yet bonded to surrounding osteons, by a cementing ground substance. Note the longitudinal orientation of the osteons.  

Biomechanical Properties of Bone

The fracture behavior of whole bones is influenced by both their material and structural properties. Mechanically, bone behaves as a biphasic, composite material with mineral (hydroxyapatite) as one phase and the collagen and ground substance as another [1]. Collagen toughens the bone, preventing the stiff mineral from undergoing brittle fracture, and the hydroxyapatite mineral prevents flexible collagen from excessive deformation and increases the bone’s elastic modulus (~stiffness) beyond that of collagen alone. Except for minor differences, all bone is formed of identical material. Two distinct macroscopic bone structures observed are cortical (compact) and cancellous (trabecular) bone. The major differences in these two structures of bone are their porosity and structural dimensions. The dense outer shell, or cortex, is made of cortical bone with 5% to 30% porosity. Inside this outer shell, cancellous bone is a fine lattice of thin bony plates with a porosity of 30% to 90% (Fig. 108-2) [1]. In either case, the hierarchical structure of bone is key to its mechanical performance and multifunctionality [2]. For example, bone’s excellent toughness (energy-absorbing capability) is due in part to its hierarchy from the level of the amino acid sequence in collagen and the coiled-coil structure of collagen up through the various haversian, lamellar, and other intermediate-sized structures, to the more macroscopic cortical shell around cancellous bone structures. The large surface area resulting from all the interfaces and levels of hierarchy enable bone to absorb energy as these interfaces, which are widely distributed throughout the structure, fail.

Figure 108-2. Longitudinal section through the proximal end of an adult canine femur. A shell of cortical bone surrounds a fine lattice of cancellous bone. Note how cancellous bone is concentrated in the irregularly shaped epiphyseal and metaphyseal segments and diminishes in the more regularly, cylindrical, thick-cortical diaphyseal segment.  

The mechanical performance of whole bones, as for any structure, is understood by measuring its deformation under the influence of externally applied forces. As increasing loads are applied to a bone, it begins to deform until finally, failure occurs. Deformation is the measured change in dimensions of the structure under conditions of known loads and can be plotted on a load-deformation curve (Fig. 108-3) [1,3-5]. Much can be revealed about a structure (such as a whole bone) by study of its load-deformation curve. Under conditions of low-level loading, a structure typically deforms in direct relation to the load applied. This linear portion of the curve is called the elastic region and reveals the elasticity of the structure, because when the load is removed the structure returns to its original shape. The point at which the applied load causes permanent deformation of shape is called the yield point. Living bone loaded to this degree will sustain microstructural damage. As applied load exceeds the yield point, the structure exhibits plastic behavior, revealed in the load-deformation curve between the yield point and the ultimate failure point. This region of the curve is called the plastic region and removal of applied loads at this point will no longer allow the structure to return to its original dimensions (structural damage has occurred). If loading is progressively increased, the structure will fail at some point (gross bony fracture), which is indicated by the ultimate failure point on the curve.

Figure 108-3. A theoretical load-deformation curve for a whole bone. Under conditions of low-level loading (elastic region, A-B), the structure deforms in direct relation to the applied load and returns to its original shape when the load is removed. Loading past the yield point (B) induces permanent deformation of shape (plastic region, B-C) even when the load is removed. If loading is progressively increased, the bone will grossly fail (fracture) at the ultimate failure point (C). The slope of the elastic region of the load-deformation curve indicates the stiffness of the studied bone. The area under the curve indicates the amount of energy absorbed by the bone prior to failure.

Functionally, two of the most important structural properties of bone are its stiffness and its load-bearing capacity. The stiffness of a structure is indicated by the slope of the elastic region of its load-deformation curve. The steeper the slope is, the stiffer the structure. Three parameters are typically used to determine the load-bearing capacity of a structure: (1) the load that the structure can sustain before failing (ultimate load), (2) the deformation that the structure can sustain before failing (ultimate deformation), and (3) the energy absorbed by the structure prior to failure. The energy-absorbed-to-failure is measured as the area under the load-deformation curve and, because it is indicative of both the load and deformation-to-failure, it provides an approximate measure of the toughness of the bone. These structural properties, from analysis of a load-deformation curve, depend on both the material composition and the dimensions of the tested bones. As an example, a large femur from a Rottweiler and a small femur from a Chihuahua are loaded in torsion to the point of gross fracture (Fig. 108-4). The larger Rottweiler femur deforms less at a given load and fractures at a larger ultimate load than does the smaller Chihuahua femur. Since both bones were from mature, healthy, nonosteoporotic animals, one can assume that the material composition of both bones is then similar. Thus, the observed differences in structural properties can be attributed to the larger size (larger outer diameter and thicker cortical wall) of the Rottweiler femur.

Figure 108-4. Idealized load-deformation curves for femora from a Rottweiler and a Chihuahua tested under torsion. The larger Rottweiler femur deforms less at given load (is stiffer) and fractures at a larger ultimate load (is stronger) than the smaller Chihuahua femur. Since both bones were from mature, healthy, non-osteoporotic animals, one can assume that the material composition of each bone is similar. Thus, the observed differences in mechanical behavior of each bone are attributed to structural differences (outer diameter, cortical thickness, etc.).

The length of the bone, the cross-sectional area, and the distribution of bone about the neutral axis (cross-sectional shape) are important geometric dimensions that influence these whole bones’ biomechanical behavior under various loading conditions. When the geometric dimensions of these whole bones are normalized, most often by testing simple-geometry samples of material cut from the bone, the load-deformation curve from mechanical testing can be converted to a stress-strain curve [1,3-5]. Bones of similar composition, like the Rottweiler and Chihuahua femurs above, have similar biomechanical characteristics as expressed in a stress-strain curve (Fig. 108-5). Thus, whereas a load-deformation curve reveals properties of structure and material composition, a stress-strain curve reveals the biomechanical properties of a material (independent of geometric dimensions). Stress is defined as load (or force) divided by cross-sectional area, and the units most commonly used for measuring stress in standardized samples of bone are Newtons per centimeter squared (N/cm2) or Newtons per meter squared (N/m2). One N/m2 is equivalent to one Pascal (Pa). Because Pascals are a small unit of measure with regard to bone testing, multiples of this unit are often employed including the kilopascal (1kPa = 1 x103 Pa), the megapascal (1mPa = 1 x 106 Pa), and the gigapascal (1gPa = 1 x 109 Pa). Bone typically fails at stresses in the megapascal range.6

Figure 108-5. Idealized stress-strain curves for simple normalized samples harvested from femora from a Rottweiler and a Chihuahua tested under torsion reveal biomechanical properties of the bones’ material (independent of geometry). Stress is the load divided by the cross-sectional area of the specimen. Strain is the measured change in dimension under the externally applied load, divided by its original dimension.

Strain is the deformation (change in dimension) that develops in response to externally applied loads, divided by its original dimension. The two basic types of strain are linear (or normal) strain, in which a stress that is applied perpendicular to the test axis of an object causes a change in length of the specimen, and shear strain in which a stress applied parallel to the test axis of an object causes a change in angular dimension within it (Fig. 108-6) [1,3-5]. Linear strain is measured as the amount of linear deformation (lengthening or shortening) of the specimen divided by its original length and is, therefore, expressed as a dimensionless number or percentage (e.g., 1cm/10cm = 0.1 strain or 10% strain). Often, although not necessarily, the units are listed (e.g., cm/cm) for clarification. Shear strain is measured as the amount of angular change in a right angle lying in the plane of interest within a specimen and is expressed in radians (1 radian equals approximately 57.3 degrees).

Figure 108-6. A. Loading of bone perpendicular to a surface (compressive or tensile force) induces normal stress and strain within the sample. Linear strain is measured as the linear deformation (shortening or lengthening) of the specimen divided by its original length, often expressed as a percentage. B. Loading of bone parallel to a surface causes one part of the bone to slide past an adjacent part, resulting in shear stress and strain within the sample. Shear strain is measured as the amount of angular change in a right angle lying in the plane of interest within the specimen, and is expressed in radians.

A stress-strain curve can be produced by placing a standardized specimen of bone tissue into a testing jig and then loading it to failure in tension, compression, shear, or bending (see Biomechanics of Bone Fracture section further in the chapter for definitions of these loading regimens). The regions of this curve are similar to those of a load-deformation curve in that the curve has elastic and plastic regions, a yield point, and an ultimate failure point. The slope of the linear elastic region of a stress-strain curve is referred to as the elastic modulus or Young’s modulus of elasticity. Stiffer materials have a higher Young’s modulus.

Mechanical Behavior of Bone

The fracture behavior of bone is influenced by its viscoelastic, anisotropic, and heterogeneous properties. Materials such as bone, the stress-strain behavior of which is dependent on the rate of loading, are viscoelastic [1,3-5]. If bone is loaded at a high rate, such as occurs with vehicular trauma or gunshot injury, its stiffness (Young’s modulus), ultimate strain, and energy-to-failure increases (Fig. 108-7). The clinical significance of the high toughness of healthy bone is that, if a high-rate loading actually causes macroscopic failure or fracture, as opposed to just distributed microscopic interfacial failures, the large release of the absorbed energy will cause marked comminution and injury to surrounding soft tissues.7 Bone is also an anisotropic material, meaning that its strength and stiffness are dependent on the orientation of the applied load relative to the bone’s microstructure and macrostructure (Fig. 108-8) [1,3-5].

Figure 108-7. Viscoelasticity of bone. Idealized stress-strain curves depicting the effect of rate of load application on bone’s stiffness and ultimate strength. The energy absorbed by the bone prior to fracture (area under the curve) is greater when it is rapidly loaded. Much of this absorbed energy is released to the surrounding soft tissues on gross fracture.

Figure 108-8. Idealized stress-strain curve depicting the anisotropic behavior of bone. Harvested samples are tested in tension in two different orientations: (a) with the longitudinal axis (parallel to the osteonal orientation) and (b) perpendicular to the longitudinal axis.

Cortical bone is stiffest and strongest when loaded parallel to the osteon long axis, rather than perpendicular to the osteon long axis. Thus, long bones are better able to resist loads applied parallel to their long axis (compression and tension) than loads applied perpendicular to their long axis (shear). As predicted by Wolff’s law, bone is generally stronger and stiffer in the direction in which the greatest loads are most commonly imposed (e.g., the long axis of the femur) [8,9]. Being a heterogeneous structure, the mechanical properties vary within a given bone. Porosity has a profound effect on the compressive stress-strain behavior of bone (Fig. 108-9). Porosity is the volume of bone occupied by non-mineralized tissue [4,5]. Apparent density, a related measurement, is the mass of bone tissue divided by the bulk unit volume of bone tissue including mineralized bone and marrow space. Apparent density of bone is directly related to its inorganic mineral content. Cortical bone is composed predominantly of inorganic mineralized matrix and, therefore, has a higher apparent density and a lower porosity (varying from 5 to 30%) than cancellous bone [1,4,5]. In contrast, cancellous bone has a lower apparent density and a higher porosity (ranging from 30 to 90%) than does cortical bone [1,4,5]. Under compressive stress, cancellous bone behaves similarly to other porous materials. Under low levels of stress, cancellous bone exhibits elastic behavior. Then, after its yield point is reached, progressive collapse of trabeculae produces a long plateau in the plastic region of the curve. With continued compression, compaction of the compressed trabeculae causes an increase in material stiffness until its ultimate failure point is reached. Under compression, highly porous cancellous bone is capable of absorbing significant amounts of energy and tolerating up to 7% strain prior to failure [4,10]. Conversely, cortical bone with its low porosity, has a more brittle behavior under compressive stress, similar to glass. Cortical bone, which undergoes little plastic deformation prior to failure, absorbs less energy and tolerates little strain (< 2%) before fracture as compared with cancellous bone. However, cortical bone has greater ultimate strength and increased stiffness and can tolerate more stress prior to fracture than can cancellous bone [4,10,11].

Figure 108-9. Idealized compressive stress-strain curve of cortical and cancellous bone samples depicting the effect of bone porosity on bone’s mechanical behavior. Note that porous cancellous bone exhibits elastic behavior prior to its yield point. Following yield, progressive collapse of the bony trabeculae produces a long plateau of plastic deformation followed by a region of increased stiffness as the fractured trabeculae are compressed. This behavior allows the cancellous bone to absorb great amounts of energy and tolerate significant strain prior to failure. Conversely, cortical bone, with its low porosity, displays brittle behavior where it is capable of tolerating great amounts of stress in the elastic region of the curve, but then fails abruptly.

There are many clinical implications of the relationship between bone’s apparent density and its mechanical behavior. Large changes in tissue strength and modulus of bone can result from small changes in its apparent density. In the clinical setting this is important because changes in apparent density may not be evident on radiographs until it is altered by 30% to 50% [4,5] Thus, minor reduction in bone density detected on radiographs is associated with greatly reduced stiffness and strength. Conversely, greatly enhanced fracture zone stiffness and strength may be present when even the most minor increases in fracture zone density are detected on radiographs.

Functional Structural Design of Long Bones

Another clinical implication of the relationship between bone porosity and its mechanical behavior is that it allows the clinician to better understand the functional design of long bones. Long bones are supremely designed structures well suited to their function as rigid kinematic links. The distinction between the mechanical behaviors of cancellous and cortical bone comes into play during weight bearing, as the ends of long bones must be able to absorb the tremendous compressive stresses and energy of weight bearing and distribute these to the diaphysis. The relatively high content of porous cancellous bone in the epiphyseal/metaphyseal regions provides bone with this unique capability. Further, the expanded cross-section of many bone ends provides additional strength and stiffness in compression because these properties are proportional to the cross-sectional area of bone. In contrast, both the cross-sectional area and the distribution of bone tissue about the neutral axis affect a structure’s resistance to bending and are quantified in the structural parameter called the area moment of inertia (AMI). In bending, one side of the bone experiences tension and the other side compression. No stresses or strains are produced at the neutral axis (Fig. 108-10).

Figure 108-10. During weight-bearing, load applied to the femoral head produces bending forces at the femoral diaphysis. Here, the concave medial side experiences compressive stresses and strains while the convex lateral side experiences tensile stresses and strains. Because the magnitude of these stresses is proportional to their distance from the neutral axis of the bone, the neutral axis is subjected to neither tensile nor compressive stresses and strains.

Bone oriented further from the neutral axis is better able to resist bending loads. This is why an I-beam is an efficient structure for resisting bending forces applied in one direction (within the plane of the height of the beam). When bending is applied within the opposite plane, however, the AMI (and thus bending stiffness) of the I-beam decreases dramatically. Diaphyseal bone, on the other hand, must endure a complex array of bending moments in many directions as a consequence of varied activities, terrains, and muscular contraction. Thus, the cylindrical shape of the diaphysis of most long bones affords resistance to bending moments in all directions (the AMI of a cylinder is proportional to the radius raised to the 4th power). The tubular shape (versus a solid cylinder) of diaphyseal bone distributes much of the bone tissue at a distance from the neutral axis, thus providing considerable resistance to bending (and torsion) with a minimum of bony mass. The factors that affect bone strength and stiffness in torsion are the same as for bending, the cross-sectional area, and the distribution of bone around the neutral axis. The polar moment of inertia (PMI) is used to calculate a structure’s resistance to torsion. The larger the PMI is (which for a cylinder is also proportional to the radius raised to the 4th power), the stronger and stiffer the bone is against torsional moments.

Biomechanics of Bone Fracture

Bones are subject to physiologic and non-physiologic forces. Physiologic forces are generated through weight-bearing and muscular contraction. Physiologic forces that are applied in a uniaxial direction (compression or tension) can give rise to torsional or bending moments in bone. Physiologic forces rarely exceed the yield point of healthy bone, or in other words they do not cause plastic (permanent) deformation of bone. On the other hand, non-physiologic forces are the result of some externally applied load (vehicular trauma, horse kick, fall from deck or pickup truck bed, gunshot) and may easily exceed the yield point and load-bearing capacity of bone, creating a fracture. Forces and moments applied to bone in various directions can produce tension, compression, bending, shear, and torsion (Fig. 108-11). Bone in vivo is subjected to all these loading modes.

Figure 108-11. Schematic illustration of tensile, compressive, bending, shear, and torsional loading modes.

Compression

During compressive loading, equal and opposite loads are applied toward the center of the structure and parallel to the axis of the structure, causing compressive stress and strain within the bone (Fig. 108-12A). Compressive loads cause most structures to shorten and widen. Maximum compressive stress occurs on a plane perpendicular to the applied load and can be thought of as many small forces directed toward the center of the bone that could potentially compact or crush the bone. Intuitively, one might expect compression fractures to develop perpendicularly to the applied compressive load and to crush or buckle the bone much like an empty soda can that is stepped on. However, compression loading also produces internal shear stresses and strains that develop oblique to the longitudinal axis and are maximal on a plane 45° from the axis of compressive loading [1,3-5 ]. Microscopically, the failure of bone loaded under compression is usually oblique cracking of the osteons created by these internal shear stresses, generated partly because of the bone’s anisotropy and the fact that bone is weaker in shear than in compression. These oblique fracture configurations produced by compressive loading are commonly seen clinically with jump-down injuries of the tibia and radius (bones that are loaded along their central axis) [3,4].

Figure 108-12. Illustration depicting stresses and strains produced by various loading modes on a cylindrical long bone. A, Compressive loading induces compressive and shear stresses and strains that, if excessive, may induce a short oblique fracture. B, Tensile loading induces tensile stresses and strains, which if excessive, induce a transverse fracture. C, Shear loading induces internal shear stresses and strains causing angular deformations. D, Bending loading induces tensile stresses and strains along the convex surface and compressive stresses and strains along the concave surface. There is a continuous gradient from maximal tensile stress, to neutral, to maximal compression. E, Torsional loading induces shear, tensile, and compressive stresses and strains, which if excessive, produce a typical spiral fracture configuration.

Tension

During tensile loading, equal and opposite loads are applied away from the center of the structure, causing tensile stress and strain within the bone. Under tensile loading, most structures lengthen and narrow (Fig. 108-12B). Maximal tensile stress occurs on a plane perpendicular to the applied load and can be thought of as many small forces directed away from the center of the bone that could potentially distract or pull apart the bone. Microscopically, the failure mechanism of bone loaded in tension is mainly debonding at the cement lines and other interfaces and pulling out of the osteons [1,3-5 ]. Grossly, bone tends to fail within a plane that is oriented perpendicularly to the applied tensile force. Clinically, fractures produced by tensile forces are typically at traction apophyses such as the tibial tuberosity, olecranon, tuber calcis, and attachment sites for ligaments.

Shear

During shear loading, equal and opposite loads are applied parallel to the surface of the bone, with the shear forces acting in opposite directions on opposing surfaces, causing shear stress and strain within the bone (Fig. 108-12C). Under shear loading, a structure deforms in an angular manner (right angles within the structure are deformed to acute or obtuse angles). Shear stress can be thought of as many small forces acting on the surface of the bone on a plane parallel to the applied load. Not so intuitive is the observation that a geometrically complex and microscopically heterogeneous structure loaded in compression or tension experiences internal shear stress (Fig. 108-12A and Fig. 108-12B). Bone is weakest when subjected to shear stresses and tends to fracture in metaphyseal regions rich in cancellous bone along the lines of maximal shear stress [1,4,5]. A clinical example is the fracture of the lateral aspect of the humeral condyle that develops when a cocker spaniel falls from a height and lands on his thoracic limbs. The compressive load applied from the radial head to the lateral aspect of the humeral condyle produces shear stress in excess of the ultimate shear strength of the humeral condyle and lateral epicondylar crest, creating fracture in these structures.

Bending

In bending, loads are applied to the surface of the bone in a manner that causes it to bend about an axis (usually the long axis of the bone). Under bending loads compression is generated on one side of the neutral axis and tension is produced on the opposite side (Fig. 108-12D). During weight bearing, eccentrically loaded bones such as the femur and humerus experience physiologic bending forces that typically produce internal compressive stresses on the concave surface of the bone and tensile stresses on the convex surface [1,3-5 ]. No stresses or strains are produced at the neutral axis. The magnitudes of the stresses are proportional to their distance from the neutral axis such that the gradation is continuous from maximal compressive stress down to no stress at the neutral axis and then increases to maximal tensile stress at the opposite bony surface. Because bone is weaker in tension than in compression, the fracture plane generally begins on the tensile surface and transversely migrates toward the compressive surface [1,3-5 ]. Clinically, these fractures tend to be transverse or short oblique configurations. The obliquity is the result of accumulated internally generated shear stresses causing fracture along the line of maximal shear stress. A large wedge-shaped "butterfly" fragment is often produced when compression is combined with bending because two oblique divergent planes of maximal shear stress cause fracture on the compression side [1,3-5 ].

Torsion

In torsion, loads are applied to the surface of the bone in a manner that causes it to twist about an axis (usually the long axis of the bone). Torsion results in shear stresses that are distributed throughout the bone (Fig. 108-12E). As in bending, the magnitude of these stresses is proportional to their distance from the central (long) axis. Under torsional loading, maximal shear stresses act on planes perpendicular and parallel to the central axis. Furthermore, the maximal tensile and compressive (normal) stresses resulting from the torsion/shear act on a plane diagonal to the central axis. The spiral fracture pattern seen under torsional loading suggests that bone fails first in shear, with formation of an initial fracture line parallel to the neutral axis. A second crack usually forms along the plane of maximal tensile stress [1,3-5 ]. Clinically, spiral fractures are commonly seen in the narrow diameters of the distal tibial and distal humeral diaphyses where the polar moment of inertia is relatively small (thus the resultant shear strain from torsional stress is relatively high).

Combined Loads

Although we have considered each mode of loading individually, non-physiologic loads-to-failure in living bone are seldom so pure. In vivo, loading of bones is complex owing to their irregular shape and the constant barrage of multiple, coincident loads. Further, the hierarchical structure of bone allows it to absorb considerable energy prior to failure, particularly under rapidly applied loads. Thus, the energy of complex, rapidly applied non-physiologic loads is rapidly dissipated through the formation of multiple fracture lines (comminution).

Stress Concentration

Alterations and defects in bony structure or density owing to such conditions as drilled holes (biopsy tract, bone graft collection, or screw removal) or neoplasia cause stress concentrations in bone that can initiate failures [12-14]. These stress concentrations can lead to local stresses in the bone near the defect that are many times higher than the nominal applied stress on the bone. One way to think of the stress concentration effect is that the applied force must "flow" through the bone and, in a defect-free, homogenous bone, it can flow equally through all regions, creating equal stress throughout. However, in bone with defects (e.g., holes from removed screws), the force cannot flow through the areas with the holes and thus must flow around the holes. This leads to a buildup of force flow (or higher stress) in the regions adjacent to defects and heterogeneities. The result is that a bone with stress concentrations fails at much lower loads or appears weaker than defect-free bones. The weakening effect of a stress concentrator is particularly marked under torsional loading where the decrease in strength may approach 90% and is proportional to the defect size [13]. Although defects smaller than 10% of the bone diameter may be of negligible significance in torsional resistance, larger holes are more problematic and remain so for an extended period of time [13,15,16]. This may be of particular concern in regions such as the distal humeral and distal tibial diaphyses where a relatively small polar moment of inertia already places these regions at risk of torsional failure (spiral fracture).

Another form of stress concentration comes from a mismatch in the elastic moduli (stiffness) of two materials (e.g., stainless steel and bone) placed in close proximity to one another and under load. The stress concentration results from the mismatch because the modulus of a material determines its response to an applied force: high moduli materials deform (strain) much less than do low moduli materials under the same load. The mismatch interrupts homogenous force flow and results in stress concentrations. Common clinical examples are cemented total joint replacement or stainless steel bone plating. As the materials are loaded, the bone exhibits greater elastic deformation, creating a shear stress at the bone-implant interface (Fig. 108-13).

Figure 108-13. Craniocaudal radiograph of a feline femur 7 days following plate fixation of a distal metaphyseal fracture. The new fracture has occurred at the junction of the proximal end of the stainless steel plate with healthy bone and is attributed to stress concentration resulting from modulus mismatch.

Biomechanics of Callus Bone Healing (Indirect Healing)

Bone union can occur by one of two different repair mechanisms, direct healing (osteonal reconstruction) or indirect healing (intermediate callus formation) [3]. Direct healing occurs primarily under conditions of anatomic alignment and rigid stability. Fracture line strain is less than 2%, and cutting cones are formed at the ends of the osteons nearest the fracture. Osteoclasts line the tip of the cutting cones for bone resorption and osteoblasts line the sides for bone formation. Resorption and formation of bone occur simultaneously as the cutting cones advance directly from one osteon to the next across the fracture line.

Indirect bone healing occurs through transformation of fibrous tissue or cartilage into osseous tissue in instances when impaired blood supply, fracture instability (deformation), or fracture-gap width do not allow direct formation of lamellar bone. Early events of indirect healing include the formation of granulation tissue in the fracture zone. This loose fibrous and vascular tissue tolerates strain as high 40%. Bone resorption at the fracture ends may be seen early in healing as this increased fracture-gap width effectively decreases fracture-gap strain (strain = change in gap dimension under load/original gap dimension). Fibrous tissue forms at the periphery of the fracture gap where blood supply is adequate, and fibrocartilage forms toward the center of the callus where blood supply is limited. Greater fracture-zone instability stimulates more abundant callus production extending further from the bone’s neutral axis. Profound increases in resistance to bending and torsional moments accompany modest increases in external callus deposition because the AMI and the polar moment of inertia are both exponentially related to the radius of a cylindrical structure. Resistance to compression and tension are also related to the cross-sectional area of the filling fracture gap.

This soft callus is able to bridge the fracture gap, but cannot decrease deformation to a level conducive to osteoblast survival. This fibrous and fibrocartilage tissue is stiffer than granulation tissue, but is also less tolerant of strain. Once the soft callus deposition is sufficient to adequately reduce fracture-gap strain, mineralization and woven bone formation begin, starting from the regions with the least motion. Once this stiffer mineralized cartilage and woven bone adequately reduce fracture-gap strain, these tissues are replaced by cancellous bone. After complete bridging by abundant cancellous bone has occurred, the fracture zone can enter into a stage of remodeling where longitudinally oriented lamellar bone and more normal bony contour are restored. In general, during callus healing, the extensive circumferential distribution of the soft callus provides structural strength and stiffness to the fracture to compensate for the relatively weak material properties of the soft callus. As the material properties of the callus strengthen and stiffen, the structural properties of callus become progressively weaker through remodeling.

Appendicular Fractures±

Fractures of the Scapula

The scapula is a thin, flat bone shaped like an I-beam through much of its body. The shape of the scapular body combined with its support by extensive musculature protect it from fracture except in the case of high-energy trauma such as vehicular and gunshot injury [15]. Many of these fractures are effectively treated non-surgically as a function of both the mechanical and biologic support afforded by the surrounding musculature. In selected scapular-body fractures with excessive displacement (folding), fixation with 1 or 2 inverted semitubular plates and screws placed adjacent to the scapular spine allows for restored alignment and maximal screw purchase in the thin bone without the need for supplemental coaptation [16]. Fractures of the acromion process and supraglenoid tuberosity are subject to pure tensile forces resulting from their musculotendinous attachments. Treatment of acute fractures in these locations should usually incorporate tension-band fixation to counter these tensile forces [17]. Fractures of the glenoid cavity are typically treated with internal fixation because rigid fixation and anatomic reduction are prerequisites for mitigation of osteoarthritis following articular fracture [17].

Fractures of the Humerus

Fractures of the humerus represent approximately 12% of long-bone fractures and most often involve the distal half of the bone [15,17-19]. Fractures of the proximal humerus, which is larger in diameter than the distal end, are relatively uncommon and are typically the result of high-energy trauma or elastic modulus mismatch inherent to physeal fractures. Low-energy trauma associated with jumping down from an elevation often causes spiral fracture configurations in the narrow distal diaphyseal region. Another common "jump down" fracture of the distal humerus is the fracture of the lateral aspect of the humeral condyle frequently seen in cocker spaniels [20-26]. On landing, axial compressive loads are transmitted from the radial head to the lateral aspect of the humeral condyle (capitulum) and the lateral epicondylar crest. The resultant shear forces in the condylar and epicondylar bone may be excessive, particularly in conditions of incomplete humeral condyle ossification, and result in fracture [24,25]. Simple supracondylar fractures and more complex "Y" fracture configurations are also relatively common and are the result of excessive compression and/or shear stresses within the narrow dimensions of the humeral condyle and epicondylar crest regions.

Fractures of the humerus can, potentially, be treated with most any surgically applied fixation system, depending on fracture location, configuration, disruptive forces, and other factors. The extensive envelope of musculature surrounding the humerus complicates application of external skeletal fixation (ESF) by itself because the connecting elements are placed extremely eccentric to the neutral axis. However, when ESF can be "tied-in" to intramedullary pin fixation, the bending resistance is dramatically increased by virtue of increased AMI [27,28].

Fractures of the Antebrachium

Fractures of the radius and/or ulna comprised 22% of all long-bone fractures in dogs and cats in one study [18]. Fractures of the diaphyseal segments of these bones are most common. As with any bone, fractures of the physes of immature dogs and cats is relatively frequent owing to the modulus mismatch at these locations. Further, the unique conical shape of the distal ulnar physis appears to predispose it to crushing injury of the resting cells of the physis. "Jump down" injury may disrupt the resting cells along the margins of the conical physis by shear forces, and compression may be focused on the resting cells at the tip of the conical distal ulnar physis. Fractures of the radius and ulna are more common in the distal diaphyseal region where the smaller diameter and lateral position of the ulna combined with the craniocaudally flattened shape of the radius (decreased AMI) may predispose it to fracture from excessive craniocaudal bending moments associated with falls, being stepped on, etc. The cross-sectional geometry of these bones may be disproportionately small in toy breeds of dogs, thereby predisposing them to distal-third antebrachial fracture [29]. Of course, high-energy trauma associated with gunshots and vehicular trauma may be more extensively distributed throughout the two bones. The olecranon is the most common location of fractures involving the proximal antebrachium [18]. Olecranon fractures should usually be stabilized using the tension-band principle because of the pure tensile load applied by the triceps muscle group insertion on the olecranon [17]. Application of a bone plate to the caudal surface of the ulna, using the tension-band principle, may be advantageous in complex olecranon fracture scenarios [30].

Fractures of the Pelvis

The pelvis (os coxae, sacrum, and first coccygeal vertebra) protects intrapelvic structures from trauma while allowing for load transmission from the pelvic limbs to the spine. Although protected by extensive surrounding musculature, fractures of the pelvis are common, representing 20% to 30% of all fractures in dogs [17]. The pelvis’ box-like shape predisposes it to fracture, most often multiple fractures. Displacement of one side of the rectangular box places stress on another side of the box. Although the blood supply provided by the surrounding musculature aids healing for most pelvic fractures even when treated non-surgically, surgical treatment is often indicated to hasten restoration of locomotor function and to ensure adequate pelvic canal dimensions when healing is complete.

Surgical stabilization is indicated for fractures involving the acetabulum, fractures causing excessive pelvic canal collapse, and many fractures in which load transmission from the pelvic limb to the lumbar spine is interrupted [17]. Anatomic reduction and stabilization of the acetabulum are paramount and can be achieved with bone plate/screw (with or without plate luting) or with screw/wire/polymethylmethacrylate fixation along the dorsal acetabular rim [31-33]. This implant placement creates a tension-band effect because the impact of the femoral head into the acetabulum creates tension along the dorsal acetabular rim. Fractures of the ilium are also commonly treated surgically. The tension surface of the canine ilium is dynamic through the gait cycle, shifting from ventromedial to neutral [34]. Standard lateral plate/screw placement for fixation of longitudinal fractures (relatively parallel to the spinal axis) of the ilium may ignore the tensile stress on the bone’s ventromedial aspect [34-36]. Use of ventral-to-dorsally oriented screws alone or in combination with bone plate fixation has been advocated to address this concern. The effects of lateral-to-medial screw purchase in the body of the sacrum are debated.34-36 Some studies of triple pelvic osteotomies show that screw migration was reduced when substantial sacral screw purchase was achieved [37,38]. Other studies suggested that sacral body screw purchase should be avoided as low-level sacroiliac joint movement may induce screw migration [35,39]. The authors of one study suggested that addition of ventral screws is a better way to increase overall screw purchase and avoids patient morbidity that may be associated with iatrogenic immobilization of the sacroiliac joint [35].

Fractures of the Femur

Fractures of the femur represent approximately 45% of all long-bone fractures in the dog and cat [18]. Approximately half of these involve the diaphysis, and the other half are evenly divided between the proximal and distal epiphyseal/metaphyseal regions [18,40]. In the proximal region, fractures of the femoral neck are most common. Weight bearing likely generates significant shear stress within the narrow diameter of the femoral neck. These shear stresses may be particularly problematic when transmitted across the physis of the femoral head and neck. Indeed, delayed closure of this physis associated with early neutering has been hypothesized as a predisposing cause of excessive and repetitive shear stress leading to physeal disruption in overweight cats [41].

Fractures of the femoral diaphysis may be of most any configuration, thus reflecting the wide array of loading leading to fracture. External rotators of the hip (gemelli, internal obturator, quadratus femoris, and iliopsoas muscles) typically produce profound external rotation of the proximal femoral segment that must be corrected during surgical stabilization. Owing to eccentric loading of the femur during weight bearing, the medial surface is the compression side and the lateral surface is the tension side. Indeed, diaphyseal fractures producing medial "butterfly" fragments are relatively common, and this fracture configuration is predictable when strong mediolateral bending forces are generated with compression loads along the medial surface. Further, surgeons must be especially aware of the impact of eccentric loading when surgically stabilizing femoral fractures, particularly with bone plates. With traditional bone-plate application on the lateral surface of the femur, defects present on the medial surface drastically reduce the AMI of the bone/plate construct, thus increasing the likelihood of fixation failure [28,42]. Simple combination of an IM pin to the plate fixation dramatically increases the fatigue life of the fixation by profoundly increasing the AMI of the composite fixation [43,44]. Common fixation methods used for femoral diaphyseal fractures include intramedullary pin plus cerclage wires, IM pin plus ESF, interlocking nail, bone plate, and plate/pin systems. The most appropriate fixation depends on a comprehensive assessment of pertinent biomechanical, biologic, and clinical factors that influence bone healing and return of locomotor function. External skeletal fixation of the femur is complicated by the extensive surrounding musculature (that shifts the ESF’s connecting elements far eccentric to the neutral axis) and adjacent body wall (that prevents utilization of many traditional frame configurations). Innovative ESF frame configurations, often in combination with an intramedullary pin "tie-in", are often advisable when applied to the femur [27,45]. Distal femoral physeal fractures are relatively common.46 This physis has a unique "4 pegs in 4 cups" configuration. Three or 4 of these metaphyseal pegs are often intact (Salter I or II fractures) in dogs and cats. Reduction of 3 or more pegs into their respective cups provides some inherent stability, particularly against torsional moments [47]. These fractures are often surgically stabilized with relatively simple single IM pin, cross-pin, or dynamic pin ("Rush-fashion") fixation.

Tibia/Fibular Fractures

Fractures of the tibia and fibula consist of 22% of all long-bone fractures in the dog and cat [18]. The majority of these fractures are located in the diaphyseal region. The smaller diameter of the distal diaphysis reduces the bones’ AMI and polar moment of inertia. Clinically, low-energy bending injury often produces short, oblique fractures or fractures with a small butterfly fragment. On occasion, in young, skeletally immature animals, the traumatic injury produces only a greenstick (incomplete) line in the tibia or a complete fracture of the tibia, but leaves the fibula intact (but sometimes plastically deformed). Low-energy trauma and torsional injury commonly produce spiral fractures in the narrow diameter of the distal tibial diaphysis where the polar moment of inertia is relatively small (thus the resultant shear strain from torsional stress is relatively high). Higher energy trauma, such as vehicular accidents, commonly produces highly comminuted fracture patterns that may extend more proximally than is typical for the lower energy fractures. Simple fractures in the distal tibial physeal region are also common and may reflect the stress concentrating effect of modulus mismatch. Fractures of the tibial crest are subject to pure tensile loading from the patellar ligament and are best treated with tension band fixation.

Fracture Assessment

The mechanical goal of fracture fixation is to provide appropriate spatial limb alignment and sufficient fracture gap stability to allow for bone healing and full restoration of limb function. In order to achieve this goal, the fixation must effectively neutralize the disruptive forces acting on the fracture. Clinically, this mechanical goal must be tempered against the biologic requirements for bone healing and inherent patient- and client-related factors.

Compression, generated by weight bearing and muscular contraction, must be neutralized in the treatment of diaphyseal fractures of all long bones. In instances in which reconstruction of the bony column is advisable, the reconstructed bony column will provide some resistance to collapse of the fracture zone. When transverse or interdigitating short, oblique fractures are purposefully compressed, the end-to-end bone contact may improve fracture stability and actually aid bone healing. In other instances, however, open anatomic reconstruction of the bony column is not advisable. In these instances, the fixation itself must resist all of the compression forces that tend to cause axial collapse via adequate purchase of the main proximal and distal fracture segments.

Tensile forces result in distraction of fracture fragments and are primarily the result of musculotendinous or ligamentous insertions on the ends of long bones. Tensile forces are best neutralized by application of the tension-band principle using a tension-band wire or tension-band plate. Tension band implants are applied opposite the direction of pull on the fragment. As an example, tensile forces from the triceps insertion on the olecranon tend to pull the proximal segment cranially and proximally. A tension-band wire is placed by initially reducing the olecranon with paired Kirschner wires. The bending force on these wires is neutralized by addition of a taut figure-of-8 tension-band wire placed on the caudal aspect of the olecranon (opposite the direction of pull). Alternatively, a plate applied on the caudal aspect of the olecranon can exert the same tension-band effect.

Bending is inherent to diaphyseal fractures of all long bones and must be neutralized if predictable, low-morbidity healing is to be realized. Bending forces in long bones result from combinations of their curvature, eccentric loading, and contraction of surrounding muscles in addition to a variety of extrinsically applied loads. Bending forces tend to cause collapse on the concave (compression) side of the bone. Loss of cortical contact on the compression side exaggerates the bending forces acting on the fracture fixation system. Neutralizing bending forces must always be a consideration in treating diaphyseal fractures of long bones.

Torsion is induced by muscular contractions, by changes in direction of the body while the foot is planted, and by extrinsic sources. Failure to neutralize torsional forces is a relatively common cause of delayed or nonunions and malunions when intramedullary pinning is used without supplementary fixation. Torsional forces are most predictably neutralized by fixation that purposefully achieves implant-bone purchase on both the proximal and distal main fracture segments. Torsional forces can seldom be adequately resisted by interdigitation of the fractured bone ends and this is only feasible in the smallest and fastest healing of patients.

Fracture Treatment

Fracture treatment must effectively address the mechanical goals stated earlier, the biologic requirements for bone healing, and the inherent clinical concerns such as patient temperament, client compliance, cost, and surgeon expertise. The following description is an overview of the inherent mechanical strengths and weaknesses of various fracture treatment methods.

Full-Cylinder Cast

External coaptation includes soft padded bandages, slings, splints, and casts. The full-cylinder cast is the most rigid form of external coaptation and is capable of effectively neutralizing bending and rotational forces when applied correctly and in the proper situations. A full-cylinder cast must span the joints above and below the fracture (note: this is not feasible for fractures of the humerus and femur), must conform to the limb, and must be sufficiently thick to withstand weight bearing. A full-cylinder cast is not capable of neutralizing axial collapse (compression) or tension. Thus, casting is not ideally indicated for fractures in which end-to-end contact of transverse diaphyseal fractures cannot be accomplished. Likewise, casts do not neutralize the pure tensile forces acting on traction apophyses.

Splints and casts encase the limb, but do not directly interact with the bony segments. Thus, an interface of soft tissue and cast padding exists between the fixation and the bony segments. More stability is provided when there is less soft interface between the cast and the bone(s) being stabilized. Clinical practicality, however, dictates that some soft interface must be present to minimize the risk and severity of cast sores. Increasing cast thickness is the easiest way to increase resistance to bending (by virtue of increased AMI), but this also increases its weight substantially. Alternatively, reinforcement of the cast in one region can be used (i.e., the I-beam effect) if unidirectional bending is anticipated.

Intramedullary Pin Fixation

Intramedullary (IM) pinning, when properly performed, effectively neutralizes bending forces because of their large AMI. Since AMI is a function of radius raised to the 4th power, the diameter of the pin greatly influences its bending strength. Furthermore, theoretically, complete fill of the intramedullary canal with an IM pin would effectively neutralize shear forces resulting from weight bearing on non-interdigitating oblique fractures. Complete (100%) filling of the intramedullary canal with an IM pin is neither realistic (because of the irregular shape of bones) nor desirable (because complete canal filling prevents intramedullary blood supply from redeveloping) [48,49]. Instead, filling of 60% to 70% of the intramedullary canal by the IM pin is frequently recommended. Pinning of the radius is seldom recommended; one reason is that the intramedullary canal is so narrow that an appropriately sized IM pin provides negligible bending strength such that the fixation must be supported with coaptation anyway. In selected instances, intramedullary pinning of small bones such as metacarpals or metatarsals is recommended, but these fixations must always be protected with suitable coaptation owing to the small diameter of the pins. Proper pinning technique also requires the IM pin to be well seated into the proximal and distal metaphyses. Unfortunately, IM pin fixation alone lacks the ability to effectively neutralize axial compression or torsion because each of these requires a system that gains purchase of the bone and the connecting element(s) of the fixation system on each side of the fracture (i.e., interlocking nails, bone plates, or external skeletal fixation). Frictional hold between the smooth surface of the IM pin and the endosteal surface of the bone is insufficient to resist torsional moments. Increasing the IM pin diameter or addition of threads does not improve torsional resistance [50]. A trilaminar fluted nail in which the flutes engage the endosteal surface to resist torsion forces has been described in the veterinary literature but has not found widespread clinical application [51]. Use of multiple, smaller diameter pins ("stack pinning") only slightly increases rotational stability and should not be relied on in fractures that are not inherently stable [52]. Supplementing the IM pin with a bone plate or an external skeletal fixator is a common strategy to complement the pin’s inherent ability to resist bending forces, with the latter systems’ abilities to resist axial collapse and rotation. Fracture fixation with only a single IM pin is seldom recommended – only in instances of interdigitating transverse fractures of very small and rapidly healing patients.

Techniques of cross pinning or dynamic pinning are commonly used for fixation of metaphyseal and epiphyseal fractures where rapidly healing, interdigitating transverse fractures are frequently encountered [47]. These fractures are inherently resistant to collapse. With each of these paired pinning methods, the pins are typically angled such that they cross on the diaphyseal side of the fracture. In this manner, the 2 pins cross the fracture in different pathways, thereby imparting some resistance to rotational moments. With cross pinning, each of the pins passes from one side of the bone and penetrates the far-cortical surface. In contrast, dynamic pins (pins placed in "Rush fashion") are placed such that they deflect off the far endosteal surface rather than penetrate it. The pins are then advanced to seat in the distant metaphyseal region. The interaction of these dynamically placed pins helps resist rotation moments, but not to the same degree as the cross-pinning technique [47].

Interlocking Nails

Interlocking nailing is an intramedullary system that addresses the axial collapse and rotational instability weaknesses of IM pin fixation while utilizing its inherent ability to resist multidirectional bending loads. By virtue of the interlock between the bone and intramedullary nail on each side of the fracture, the interlocking nail system is capable of resisting axial collapse and torsional moments [53-56]. Interlocking nails, themselves, are weakest at their screw holes (lowest AMI and a stress concentrator) [28]. Unlike bone plates, a locking screw through a nail does not reduce the stress-concentrating effects of the hole because the locking screw does not interact rigidly with the nail [56]. Therefore, these screw holes should not be placed in close proximity to the fracture zone with or without an interlocking screw. When used to span non-reconstructed fractures, the interlocking screws resist axial collapse by "tethering" the main bone segments to the level of the nail holes. As nail diameter decreases, the AMI decreases of both the nail and of the corresponding interlocking screws that can be used. When one manufacturer used a relatively large 3.5-mm screw diameter in their 6-mm nail, breakage of nails was the most common mode of clinical failure [57]. As they reduced the size of the screw hole to accept 2.7-mm screws (thus increasing the AMI of the nail), nail breakage became less common but screw failure was noted [58].

As an alternative to the use of interlocking screws, bolts are now manufactured such that positive-profile threads engage only the near-cortical surface during insertion, and the core diameter of the "tethering" portion of the bolt is maximized (Table 108-1). One does not have to be overly concerned about premature "backing out" of the bolts because they are not subjected to pull-out forces as are screws placed through a bone plate. Whereas unicortical thread engagement of the bolt is sufficient, bicortical penetration of the interlocking screws or bolts is important, particularly when functioning as a tether in non-load-sharing situations. Further, in such instances, the longer screw lengths required for use in metaphyseal regions increases their susceptibility to bending or breaking [59]. Eccentric loading of these screws, such as occurs when the nail is not centralized within the metaphyseal region, appears to improve screw fatigue life [59]. Interlocking nail systems compare favorably with bone plate and plate-pin combinations when used to stabilize gap models except with regard to torsional resistance [53,54]. The lack of a rigid interlock between the locking screw and/or bolt and the nail permits slight rotational movement [54]. One way to augment the interlocking nail system’s resistance to rotation is to use it in conjunction with external skeletal fixation [60-62]. This can be done by virtue of a connecting bar "tie-in" between the proximal extension of the interlocking nail and the ESF frame or by use of special external fixation pins designed for dual use as an ESF pin and the interlocking bolt [60,61]. One would expect such fixation to dramatically increase both bending resistance (in the plane of the frame by increasing AMI) and torsional resistance (by increasing PMI). Interlocking nails can be dynamized, if desired, by removing the interlocking devices on one side of the fracture, thus exposing the fracture zone to both axial compression and torsional stresses [60-62].

Orthopedic Wire and Cerclage

Orthopedic wire is malleable stainless steel that is formed into monofilament wire of varying dimensions. Applications in small animals typically vary from as large as 16-gauge to as little as 24-gauge wire. Full-cerclage wire is placed around the full circumference of a completely and anatomically reconstructed bony column. As the wire is tightened, the fracture lines are compressed (much like the staves of an oak barrel are compressed as the band surrounding them is tightened). If perfect anatomic reduction is not achieved, wire tightening will tend to collapse fragments into the intramedullary canal and the wire will be prone to premature loosening. Stabilization of two main fracture segments requires that the fracture line be a long oblique configuration in which the length of the fracture line is at least 2.5 times greater than the bone diameter in that location. When sufficient obliquity is present, a minimum of two properly applied wires is capable of providing excellent compression of the fracture surfaces (interfragmentary compression). When improperly applied to a short oblique fracture, full-cerclage wire creates shear stress at the fracture and, because there is only room for one wire, concentration of bending stresses. Although one should avoid the use of cerclage wire in short oblique fractures, the following "escape strategy" can be employed if alternatives are not available: use of 1 or 2 K-wires oriented perpendicularly to the plane of the fracture can minimize the shear forces created by tightening of the full-cerclage wire. The cerclage wire is placed so that, as it is tightened, the K-wire prevents its orientation perpendicular to the long axis of the bone and directs compression across the fracture line [63].

Cerclage wires can be tightened and secured in a number of ways and their relative mechanical merits are measured by comparisons of the compression achieved and the resistance to knot loosening.

Twist-knots are properly formed when each of the two ends of the wire wrap evenly around the other (improper formation is one wire wrapped around the core of the other – like a snake wrapped around a stick). Tensioning and securing the wire occur simultaneously with this method. In most instances, it is advisable to cut the knot short rather than bending it over because any manipulation of the knot decreases tension in the wire [64,65]. Resistance to knot failure under loading is determined by the frictional interface between the two wires. The number of twists to leave in the knot has not been clearly established, but cutting the knot with three twists remaining is common. If the twist-knot must be flattened, the flattening process and the final twisting should be simultaneous to minimize loss of loop tension [64,66]. Twist knots untwist when loaded past the yield point and do not exert as much loop tension as other methods [64,67]. Twist-knots sustain greater load to failure than single-loop knots, but similar load to loosening [63,64].

Single-loop knots are formed using a wire with a loop on one end. After passing the free end of the wire around the bone, it is passed through the loop. The free end is then passed into the end of a purpose-specific tightening instrument. The wire is tensioned by rotating a crank on the tightening instrument. The wire is tightened in the first phase of application; then the knot is locked in the second phase by bending the free end over the loop. This method achieves greater initial loop tension than the twist-knot, but has a similar load resistance before loosening [66]. The single-loop knot fails by unbending of the free end [67].

Double-loop cerclage is formed from a segment of wire bent 180° in the middle. The bent end is passed around the bone and the 2 free ends are passed through the loop created by the bend. The free ends are tightened with a 2-crank wire tightener. The knot is locked in a similar manner as the single-loop method. The double-strand and double-knot increase the loop tension and knot security. The double-loop knot generates 3 times as much tension as the single loop and resists twice the distracting load prior to wire loosening [64].

Bone Plates and Screws System (DCP, LC-DCP, Locking-Plate Systems)

Screws convert insertion torque into compression along their shaft such that any structures bone plate, washer, or bone fragment underlying the screw head are compressed during tightening (provided the hole diameter in that underlying structure exceeds the screw-thread diameter such that it may glide freely along the screw shaft). Individual screws may be used in positional or lag fashion. When screws are used as positional screws, their threads engage both the near and the far segments such that the position of each fragment is held in a specific location, and compression of the fracture line is not achieved. When screws are used as lag screws, their threads engage only the far bone segment. Screw tightening compresses the near segment against the far segment because the near bone segment is free to slide along the screw shaft. The amount of interfragmentary compression achieved with the lag screw method is primarily a function of the bone strength, outer-thread diameter, and insertional torque. Screws must often resist significant bending forces. The bending strength of a screw is determined by its AMI which is related to its core radius raised to the fourth power [28]. Therefore, small increases in screw core-diameter profoundly increase its bending strength. For example, a 3.5-mm cortical screw (2.5-mm core diameter) is nearly 2.5 times stronger than a 2.7-mm cortical screw (2.0-mm core diameter) (Table 108-1).

The most common use of screws is to fasten a bone plate to the bone. Unlike an ESF connecting bar, traditional bone plates are not mechanically linked to fixation screws. With traditional plating, the fixation only becomes stable when the screw is firmly tightened, thereby compressing the plate against the underlying bone. Properly applied bone plates resist compression, tension, bending, and torsional and shear forces especially when used to compress a two-piece transverse fracture of a long bone. In this instance, a dynamic compression plate (DCP) is desirable. The DCP screw hole is designed such that tightening of the screws compresses the fractured bone ends together. The DCP screw holes are oval and the surface that comes into contact with the underneath side of the screw head slopes downward and toward the fracture line (much like a playground slide). When the screw is inserted on the "high" side of the oval sloped DCP hole, the screw head comes into contact with the sloped hole as the screw is tightened. The screw is fixed in the bone and is not free to slide down the slope. Instead, the interaction between the screw head and the oval sloped DCP hole draws the plate toward the screw. Using the playground slide analogy, rather than a child sliding down a fixed playground slide, the slide is free to move and is drawn backward as the child descends. Once a traditional bone plate is secured with screws, the plate acts as the connecting element that spans the fracture.

Bone plates are most susceptible to bending forces because of their eccentric position relative to the bone’s neutral axis. Their mode of placement determines the likelihood of fixation failure. If a transverse fracture is anatomically reduced and the plate compresses the fracture segments, the plate and the bony column share the loads and their large combined AMI creates a highly rigid construct. If the bone, especially the cortex opposite the plate, is not reconstructed, the plate alone must resist considerable bending forces. The bone plate is weakest at its screw holes (lowest AMI). Further, an open screw hole centered over the fracture functions as a stress concentrator and dramatically increases the risk of failure under bending loads. Several methods can be used to increase the AMI of the fixation. Lengthening plates are available where the middle section of the plate is solid (without screw holes). Another method is to combine an intramedullary pin with bone-plate fixation [43]. The bone plate constrains axial collapse and rotational forces, while the IM pin resists bending forces. By adding the pin, the AMI of the combined fixation is greatly increased and the fatigue life of the plate is greatly extended.

The limited-contact dynamic compression plate (LC-DCP) was designed with a scalloped profile to the underneath side of the plate that contacts the bone [68]. One effect of this scalloped contour is minimized stress-concentrating effect of an open screw hole because the AMI is similar over the length of the plate [68]. Granted, the solid section (between screw holes) of the LC-DCP is significantly weaker than the solid section of a traditional DCP, however, when screw holes are left unfilled the plate is only as strong as its weakest point [69]. Another advantage of the LC-DCP is that the scalloped "footprint" of the plate against the bone may allow for improved vascular supply to the healing bone, but other factors such as bone-surface topography also influence the relative significance of this feature [70].

Whereas traditional plating depends on firm screw-insertion torque to compress the plate against the bone to ensure rigid fixation, newer locking-plate technology utilizes a locking screw mechanism to link the plate firmly to the fixation screw [71]. These locked screw-plate systems can be thought of as internal skeletal fixators. Because traditional plating does not link the plate and the screw, the screw is free to microtoggle within the plate hole. Bicortical purchase of traditional screws helps to reduce this microtoggling, which among other things, can lead to fretting failure of the plate or screw. Locking screws are rigidly fixed between the bone on one end and the plate on the other. For this reason, bicortical screw purchase is theoretically less important with locking screw-plate- systems. This may be a function of cortical bone thickness that is relatively thin in small animal patients. Pullout of locked screws is not just a function of the strength of their thread interlock in the bone, because the screw is also locked in the plate. Thus, premature screw loosening of a single locking screw is not likely. Further, the linkage between the fixation screw and the plate as a connecting element eliminates the mechanical need for compression of the plate against the bone surface. Because the threads on the screw head correspond to those in the screw hole of the plate, angling of screws is not possible and locking screw-plate systems are fixed-angle constructs. Further, dynamic compression cannot be achieved when only locking screws are used. Combined conventional and locking-screw techniques can be used, but require plate contouring on the end(s) of the plate where conventional screws are used. When conventional and locking screws are combined within a bone segment, the conventional screws are applied first to compress the contoured plate to the bone segment and to achieve the DCP effect (if desired). Locking screws are subsequently applied. If locking screws have been used to fix a plate to a fragment, subsequent insertion of conventional screws should not be performed without first loosening the locking screw (it can be retightened after insertion of all the traditional screws are in place). Dynamic compression can be achieved after one segment has been fixed with locking screws by using conventional screws in the dynamic compression portions of the plate hole.

External Skeletal Fixator

Linear ESF

The external skeletal fixation (ESF) system makes use of fixation pins, connecting bars, and pin-bar linkages. Each component of the system represents a mechanical variable that can be adjusted to the mechanical needs of the patient. Long-term stability of the pin-bone interface is foundational to success with ESF. Threaded pins provide much greater resistance to pin pullout than do non-threaded pins [72,73]. Pins with a negative-thread profile have less pullout resistance than positive-profile pins in some but not all implantation sites [74]. Negative-thread profile pins are also more prone to breakage as a result of their decreased AMI and the stress concentration at the threaded-non-threaded junction. Pin rigidity is also a function of pin diameter. As pin diameter increases, so does its AMI and flexural rigidity, but the impact of pin size on bone strength must also be considered. Proportionate loss of bone strength occurs with each increase in circular cortical defect size greater than 20% of the bone diameter [13]. ESF fixation strength and stiffness are increased by increasing the number of fixation pins in each fracture segment (unless the connecting column is the weakest component) up to a maximum of 4 pins per bone segment [75,76]. Evenly distributing pins throughout each main bone segment maximizes resistance to bending in the plane orthogonal to uniplanar ESFs [75,77]. Angling pins closest to the fracture zone in order to decrease the working length of the connecting bars may be advisable for highly comminuted, non-reconstructable fractures because the bending stiffness of the connecting bar is inversely related to its working length raised to the third power. The concept of working length and stiffness also applies to pin length. The connecting bar should be linked to the fixation pins as close as possible to the skin without causing skin irritation (usually a finger’s width) [75,76] Linkage clamps should be oriented such that the working length of the pin is minimized [75].

The rigidity of the connecting bar(s) significantly influences the strength and stiffness of the ESF-bone construct [78-80]. Elastic deformation of the connecting bar of unilateral-uniplanar (type Ia) frames places "to and fro" axial loads on the fixation pins [80]. Elastic deformation of the connecting bar can be minimized by using more rigid materials, increasing bar diameter, adding supplemental bars or plates, or utilizing more complex frame configurations [78,79]. Static strength evaluation of different configurations showed that unilateral-uniplanar (type Ia), unilateral-biplanar (type Ib), bilateral-uniplanar (type II), and bilateral-biplanar (type III) frames to be successively stronger in resisting axial compression and torsion, and bending in the plane of the ESF [78,81]. The ability of the pin-connecting bar linkage to rigidly maintain this interface is essential. In addition to clinical factors such as proper clamp assembly and tightening, clamp design also must be considered [82,83].

Circular ESF

Circular ESF (CESF), like linear ESF, consists of fasteners (tensioned wires), connecting rods and wire-connecting rod linkages. Variations in these components can be manipulated to alter the mechanical properties of the CESF-bone construct. Unlike linear ESFs, CESFs utilize small-diameter wires tensioned between clamps positioned on rings rather than using traditional fixation pins to fasten the device to the bone. This design feature accounts for a fundamental difference between the load-deformation behavior of linear ESFs and CESFs [84]. Linear ESFs using half-pins loaded in cantilever bending have a linear elastic region of their load-deformation curve followed by plastic deformation to failure with progressive loading [84,85]. CESFs using small-diameter tensioned wires loaded in three- or four-point bending show initial nonlinear elasticity with increasing rigidity followed by linear progression to yield [84,85]. This characteristic difference reveals how CESF devices allow axial micromotion of the bone segments.

Ring diameter, which dictates wire length, profoundly influences the mechanical properties of CESF. As ring diameter increases, so does the length of the tensioned fastening wires, thereby decreasing fixation rigidity [84-87]. Although ring diameter affects stability in all loading modes, its most profound influence is on axial stability [84,86]. This influence is most evident at lower axial loads because self-tensioning of the wires develops during loading, resulting in a progressive increase in stiffness [84]. The smallest diameter ring possible should be used allowing about 2 cm between the skin and the ring for pin-tract care, soft-tissue swelling, etc. Ring diameter has a greater effect on gap stiffness and gap displacement than does wire tension, and the effect of increasing wire tension decreases for larger rings [87]. Complete rings are stiffer than incomplete rings [88].

As for linear ESF, the bone fasteners (tensioned wires) should be spread over the length of each major bone segment; increasing the number of fasteners up to four per segment is advisable [85,86,89]. In CESF, tensioned wires are distributed over the bone using rings. Where possible, blocks of two rings distributed over the bone-segment length significantly increases the stability of the fixation when compared with configurations that secure individual bone segments at only one level (using a single ring) [85,86,89]. Typically, one tensioned wire is placed above each ring and another below each ring for a total of two tensioned wires per ring. When only one ring can be used owing to a short bone-segment length, "drop wires" spanned from posts extending from the ring can be used to increase the number of fasteners and increase resistance to bending [90].

Whereas much of the wire stiffness is a function of tensioning, wire stiffness is greater in larger diameter wires than in similarly tensioned smaller diameter wires. Wire diameter also influences how much a wire can be tensioned. Wire tension should not exceed 50% of its yield strength to minimize the possibility of breakage [85]. Wire tension affects the overall rigidity of the fixator construct, most notably axial stiffness during low load application. The relationship between wire tension and construct stiffness is nonlinear because of the self-tensioning effect of the wire [84,85]. Tensioning wires before loading increases the axial stiffness of a CESF at low loads, mitigating much of the displacement during physiologic loading. The practical limits of wire tensioning are associated with wire breakage, ring deformation, slippage of the wire within the clamp, and a "ceiling effect" beyond which the gain in axial stiffness is nominal [84,85]. During fixator application, sequential tensioning of wires on the same ring can cause loss of tension in the first wire owing to ring deformation. Simultaneous tensioning of wires on the same ring mitigates this effect, especially for large rings [85]. Subsequent study using 84 mm diameter rings failed to detect any differences in wire strains or construct stiffness when comparing simultaneous and sequential wire tensioning methods [91].

Ideally, tensioned wires are placed at 90° angles to one another to maximize stability and shear, but regional anatomy seldom allows this. Reducing the separation from 90° down to 45° particularly reduces the CESF’s resistance to bending in the orthogonal plane [90,91]. Reducing this separation further can also lead to plastic deformation of the ring during wire tensioning [90,92].

Hybrid linear and CESF has been used for stabilization of juxta-articular fractures. Clinically, a linear ESF is utilized on the larger main fracture segment, and the tensioned wires and ring block are used on the small juxta-articular segment. Combining fixation pins and tensioned wires within a segment is not advised because the axial motion permitted by the tensioned wires can place excessive stress on the pin-bone interfaces when few pins are used [85].

Conclusion

A basic understanding of the biomechanics of the appendicular skeleton should include the material and structural properties of bone, the generation of internal stresses caused by applied loads, and common modes of failure under these applied loads. These understandings combined with knowledge of basic biomechanics of various fixation systems enhance the surgeon’s ability to create an appropriately stable fracture zone that is conducive to rapid bone healing and restoration of patient function.