In: Textbook of Small Animal Orthopaedics, C. D. Newton and D. M. Nunamaker (Eds.) Publisher: International Veterinary Information Service (www.ivis.org), Ithaca, New York, USA.

Biomechanics Pertinent to Fracture Etiology, Reduction, and Fixation ( 1-Jan-1985 ) G. K. Smith

! Bone as a Material

! Bone Function Versus Bone Failure

! Mechanical Concepts

! Fracture Etiology Tension Compression Shear Bending Torsion Failure Under Combined Loading Energy to Failure

! Biomechanics of Fracture Reduction

! Biomechanics of Fracture Fixation External Immobilization External Skeletal Fixation Internal Fixation Intramedullary Fixation Mathematical Modeling Plate-Induced Osteopenia Biomechanics of Surgical Screws

! Biomechanics of Fracture Healing

The Role of Functional Weight Bearing Internal Fixation Comparative Biomechanical Studies: Healing Relative to Treatment Modality

Biomechanics is defined as mechanics applied to biology. Mechanics, in turn, is the analysis of any dynamic system, be it the relative motion of quanta and subatomic particles or the motion of galaxies. The term mechanics was used as early as 1638 by Galileo in a treatise describing force, motion, and the strength of materials. (1,2,38,89) Galileo and his colleagues Harvey, Santorio, and Descartes were unknowingly the early pioneers in biomechanics, basing their biologic discoveries on physical principles, astute observation, and quantitative analysis. Briefly, their most notable contributions include the discovery of blood circulation, development of the microscope, theoretic mathematical modeling of animal structure, and early studies on metabolism. Since its inception, the scope of biomechanics has expanded immensely, now incorporating all of continuum mechanics in physiology and the mechanics of medical application in the health sciences: from clinical problems in the cardiovascular system to quantitative physiology and rheology of biologic tissues to orthopaedic implants and the kinematics of the musculoskeletal system. It is the purpose of this chapter to focus on some of the more important biomechanical principles relating to fracture etiology, reduction, and repair.

BONE AS A MATERIAL Before discussing the mechanical properties of bone and the influence of forces thereon, it is important to have a solid understanding of the anatomy of bone. This topic has been covered elsewhere in this book (Chapter 1) and should be reviewed. Compact (or cortical) bone is a "composite" material in the true sense of the word. Two thirds of the weight (and approximately one half of the volume) of compact bone consists of an inorganic material having a composition similar to the formula for hydroxyapatite, namely, 3Ca3 (PO4)2Ca (OH)2. The remainder is composed of organic material, mainly collagen. Collagen molecules band together in an orderly sequence to form collagen fibrils, which in turn run parallel to each other to form collagen fibers. Inorganic hydroxyapatite crystals (approximately 200 nm long and 50 nm x 50 nm in cross section) attach at specific sites along the collagen fibril. Collagen fibers are found to have a characteristic orientation relative to bone type. That is, in woven fiber bone, collagen fibers are arranged in a randomly tangled array, whereas in lamellar bone collagen fibers run parallel within any given lamella. The parallel collagen fibers in successive lamellae are oriented approximately at right angles to each other (see Fig. 1-16). A concentric, cylindrical arrangement of lamellae constitutes the haversian system or osteon (see Fig. 1-16). Circumferential lamellae form the bone adjacent and parallel to the bone surface, while interstitial lamellae represent remnants of old haversian systems with typical osteonal characteristics. Virtually all bone is microscopically lamellar in nature. However, the degree of porosity yields two macroscopically distinct types. Figure 12-1 shows a light photomicrograph of cortical bone in transverse section and, on the right, an electron photomicrograph of cancellous bone.(35) The major difference between the two is the relative porosity, which for cortical bone varies from 5% to 30%, whereas that for cancellous bone is 30% to over 90%. In general, bone is a good composite material, having a strength higher than either of its components, apatite or collagen. The softer (low-modulus) collagen prevents the stiff (high-modulus) apatite from undergoing brittle fracture, while apatite acts as a rigid scaffold to prevent collagen from yielding. Not surprisingly, the mechanical properties of bone are as complex and varied as the anatomy and composition. Seemingly simple properties such as bone strength, stiffness, and energy absorption to failure depend not only on material properties of bone (e.g., inherent composition, microscopic morphology of bone components, bonds between fibers and matrix and bonds at points of contact of fibers) but also on structural properties (e.g., geometry of whole bone, bone length, and bone curvature). Furthermore, it is well known that the material strength of bone varies with the age, sex, and species of animal under investigation and with the location of bone, such as femur versus humerus. In attempting to assess structural and material properties of bone using mechanical testing techniques, additional variation in bone strength may result from factors such as the orientation of load applied to the bone (since bone is anisotropic), strain rate (rate of deformation), and testing conditions, including tension versus compression, bending versus torsion, wet bone versus dry bone. Mechanical testing may yield even wider dispersion in results when specifically applied to the material and structural properties of healing bone. Amount of callus, type of callus, and degree of callus reorganization all affect the mechanical assessment of bone healing. Clearly, these complexities (compositional, anatomical, mechanical, and experimental) necessitate careful scrutiny on the part of the orthopaedist in extracting clinical relevance from the available literature on bone and bone-healing biomechanics.

BONE FUNCTION VERSUS BONE FAILURE Bones are linked together in an orderly array to form the skeletal system and in this regard have three primary biomechanical functions: to encase or partially surround vital internal organs, thus affording protection; to act as rigid kinematic links and attachment sites for muscles (intrinsic force generators); and to facilitate body movement by means of well-lubricated (low-friction) joints. Given the importance of these functions to survival, bone, through evolution, has developed two unique

FIG. 12-1 (A) Reflected light photomicrograph of cortical bone from a human tibia. (original magnification x 40) (B) Scanning electron photomicrograph of cancellous bone from a human tibia demonstrates marked porosity relative to cortical bone. original magnification x 30) (Frankel VH, Nordin M Basic Biomechanics of the skeletal System. Philadelphia Lea & Febiger, 1980)

properties: bone remodels to meet functional need, so-called Wolff's law(100) (1884); and bone has the capacity for repair. It is the biomechanical optimization of this latter property that has most relevance to the practice of veterinary orthopaedics and therefore will receive further elaboration in the sections that follow. Bone, in performing its function, must withstand a complex pattern of imposed forces. In a static situation, bone acts largely to resist the forces of gravity, supporting the weight of the body and the attendant muscular activity necessary to maintain a given static posture. In a dynamic mode, however, such as during locomotion or athletic activity, these forces may be magnified many fold and may be omnidirectional. Bone, in function, experiences two types of imposed forces. In general, intrinsic forces may be considered physiologic and are imparted to bone through articular surfaces by means of ligaments surrounding joints and at tendinous sites of muscle insertion. Under normal circumstances such forces sustain ground reaction forces during posture and gait and only under unusual circumstances do they approach the inherent breaking strength of bone. Extrinsic forces, on the other hand, originate from the environment and, unlike the intrinsic system, have no limitation on magnitude or direction of application, for example, automobile impact. Clearly it is these nonphysiologic forces that have the greatest potential to result in catastrophic bone failure (fracture) and that must be understood to evaluate the biomechanics of fracture etiology. Intrinsic and extrinsic forces act to cause microscopic deformations of bone. The degree of deformation is dependent on the magnitude of the imposed force, the geometry of the bone (size, shape, diameter, curvature), and the material properties of bone (cortical versus cancellous). It is intuitive that should the magnitude of imposed forces on bone exceed the ultimate strength of that bone, catastrophic failure will result. More specifically, bone fracture occurs at the point at which the energy-absorbing capacity of bone is exceeded (KE = I/2 mv2). This point will be discussed further in the section to follow.

MECHANICAL CONCEPTS The biomechanics of bone in its normal and healthy state are integral to an understanding of fracture etiology and to the development of optimum repair modalities. The purpose of the following section is to introduce some mechanical concepts that were developed for evaluation of inanimate materials systems but that may appropriately be applied to bone. Hopefully this information will engender a biomechanical vocabulary common to both engineers and surgeons. As stated previously, bone is a solid material and as such experiences forces and resultant deformations in performing its function. In this context, force and load are used synonymously to define the magnitude of the vector quantity (force) that acts to deform the structure, for example, the whole bone. In contrast, stress refers to the distribution of applied force over the cross-sectional area of whole bone specifically.

STRESS=FORCE/AREA The relationship of force to stress will receive further attention shortly. However, it should be recognized that the two parameters (force and stress), although related, are not synonymous. The measure of a material's deformation (e.g., elongation) can be expressed either as an absolute change in length (delta L) or as normal strain, the change in length per unit initial length (delta L/Li). In contrast to normal strain, shear strain is the measure of the amount of angular deformation, alpha, in response to the application of shear force. Stress is usually expressed in units of newtons per centimeter squared (N/cm2), newtons per meter squared (N/m2), pascals (1 Pa= 1 N/m2) or megapascals (1 mega Pa= 1 x 10^6 Pa). Normal strain is a dimensionless unit; for example, centimeters/centimeter, and is expressed as a percentage while shear strain is expressed in radians (1 radian is approximately 57.3¡). Stress and strain having been defined, it is possible to introduce the two most important mechanical properties of bone as a material, namely, strength and stiffness. First, however, it is important to recognize the distinction between structural parameters and material parameters. For example, consider the situation depicted in Figure 12-2 in which a tibia and its corresponding fibula are loaded independently to failure in tension. It is obvious that the fibula will exhibit failure at a lower load (force) than the tibia because of its reduced cross-sectional dimension. Under such a circumstance the tibia is said to have a higher structural strength than the fibula. If, however, the applied loads at failure are normalized relative to cross-sectional area of bone (F/A = stress) and if instead of absolute deformation (delta L), the strain (delta L/ Li) is measured, the

material strength of the tibia and fibula can be shown to be comparable. This distinction is graphically illustrated by examining a plot of the pertinent data on a "load-deformation" curve relative to a "stress-strain" curve (Fig. 12-3). It is apparent from the idealized stress-strain curve that per unit bone volume, the tibia and fibula have similar material strength in spite of their obvious structural differences. Such concepts must be appreciated when making comparative assessments of bone strength, such as dog bone versus human bone, cortical bone versus cancellous bone, or cortical bone versus fracture callus.

Strength, then, as a material parameter is defined as the ultimate stress at which failure occurs, whereas strength defined structurally is the ultimate load (or force) at which failure of the system occurs. This distinction becomes extremely important when discussing fracture healing. For example, on a materials basis (per unit volume) fracture callus has a strength far inferior to normal bone yet on a structural basis, because of its abundant volume (cross section), may have structural strength approaching that of whole intact bone. To adequately define stiffness as a mechanical property, the stress-strain curve requires further elaboration. Figure 12-4 is an idealized stress-strain curve of a machined specimen of a ductile metal having known cross section loaded in tension. As the specimen is loaded in tension from point A, its stress strain behavior proceeds in a linear fashion to point B, the yield point. If the load were removed at point B, the metal would return to its original undeformed length along path B-A; this is termed "elastic" behavior. The slope of the stress-strain curve in the elastic region is defined as the material's stiffness or modulus (in tension, Young's modulus). If the sample is stressed beyond point B, yielding or plastic deformation ensues such that if at point C the load were again removed, the sample would return its elastic component of deformation along line C-C' but not the plastic portion. At C' the unloaded specimen is permanently elongated a distance A-C' and by convention the specimen is said to have a permanent strain, C'; expressed in percent. Loading beyond point C continues to plastically deform the sample until the ultimate tensile strength of bone is reached and failure occurs. Stiffness or modulus is an important material parameter relating degree of deformation to applied load. As an example, consider the stress-strain curves of three very dissimilar materialsÑ soft metal, glass, and boneÑin Figure 12-5. Metal has the highest stiffness (elastic modulus) and at stresses beyond its yield point exhibits typical ductile behavior (large plastic deformations before failure) in the nonelastic region. Glass also has a much higher modulus than bone; however, as a material it readily undergoes brittle failure, having no discernible nonelastic (plastic) region. Bone has a much lower modulus than either metal or glass, but in terms of failure mechanics bone behaves similar to glass, fracturing in a brittle (low-deformation) mode. Brittle materials fracture into two or more pieces that have very little permanent plastic deformation and therefore have the potential to be nicely pieced together into the original prefracture conformation. In the case of bone, this behavior facilitates accurate anatomical fracture reduction and reconstruction using internal fixation. A fractured metal plate, in contrast, does not conform to its original prefractured shape, owing to the permanent plastic deformation that occurred prior to fracture. However, the ductile behavior of the plate is desirable for internal fixation purposes, allowing the surgeon, within limits, to plastically contour the plate to bone without incurring brittle fracture.

FIG. 12-2 Tibia and fibula loaded to failure independently in tension to evaluate mechanical properties. It is intuitive that the fibula will fracture at a lower load than the tibia.

FIG. 12-3 (A) Idealized force/elongation plot of the relative mechanical behaviors of the tibia and fibula depicted in Figure 12-2. The fibula experiences failure at a lower force, Ff, than the tibia, Ft. This graph represents the structural parameters of the tibia and fibula. (B) In contrast, material parameters are represented on a plot of stress versus strain where the failure loads in A are divided by the corresponding bone cross-sectional areas, thus yielding the relative tensile strengths (stress). Additionally, elongation (delta L) is converted to strain (delta L/Li). Under such conditions the bone of the fibula and the bone of the tibia (as a material) can be shown to have approximately equivalent strength (Sf = St).

The relative stiffness or modulus of bone versus metallic plate is an important consideration in fracture healing under conditions of internal fixation. There exists an obvious modulus difference, or modulus mismatch, between stainless steel and bone. This modulus mismatch will be discussed more fully in another section; however, the higher stiffness and strength of the metal plate relative to bone in a bone/plate reconstruction result over time in a well-recognized bony resorption under the plate, so- called stress protection, or plate-induced osteopenia. That is, the bone under the plate atrophies from disuse: the metal plate acts as a stiff bridge protecting the underlying bone from experiencing forces either axial, bending, or rotational. This phenomenon warrants precaution when removing metallic plate and screws based solely on radiographic evidence of fracture healing. The "stress- protected" bone, once free of the metal plate, must be gradually introduced to weight-bearing loads. Impact forces are to be avoided. Controlled loads over time allow the bone to remodel and to gradually reassume its initial strength.

FRACTURE ETIOLOGY Force is defined as a vector quantity having magnitude and direction. The forces and moments (rotational forces) applied to bone result in loading modes that require understanding to appreciate the biomechanics of fracture etiology. Bone as a structure may be loaded in tension, compression, bending, shear, torsion, or a combination of these modes. If the magnitude of applied load does not exceed the bone's elastic limits, fracture does not occur, and the bone, elastically deformed, returns to its prestrained state. Shortly beyond the elastic limit, however, catastrophic failure takes place. The failure mode of bone under circumstances of catastrophic overload is directly related to the loading mode of the bone. That is, from an evaluation of the fracture characteristics, it is possible to speculate what loading modes produced the fracture. Following is a discussion of loading modes, pure and combined, with corresponding clinical examples of failure modes produced by overload.

TENSION Tensile loading, schematically depicted in Figure 12-6, A, produces an elongation and narrowing of a structure. Maximal tensile forces in the structure are generated on a plane perpendicular to the applied load, and by definition these are termed normal forces. Consequently, failure typically occurs along this plane. In bone the tensile failure mechanism has been shown to be mainly one of debonding at bone cement lines and pulling out of osteons. (35) There are relatively few bones in the

FIG. 12-4 Stress strain curve for a ductile metal of known cross section. sigma u, is the ultimate strength of the material while sigma y is the yield point that marks the transition between elastic and plastic behavior. The area under the stress strain curve reflects the energy stored by the material prior to failure. The slope of the plot in the linear elastic region is known as the modulus and reflects the material's stiffness.

FIG. 12-5 Idealized stress strain behavior for three materials: metal, glass, and bone. Note the relative differences in stiffness (slope) and ultimate strength. Bone, although exhibiting some plastic deformation (deviation from linearity), behaves more like the brittle glass than the ductile metal. (Frankel VH, Nordin M: Basic Biomechanics of the Skeletal System, p. 19 Philadelphia, Lea & Febiger, 1980)

FIG. 12-6 Patterns of deformation.

body that experience pure tensile forces over their cross-sectional area. Most notable are the traction apophyses, including the olecranon process, tuber calcis, and tibial tuberosity, as well as ligamentous attachment sites. Figure 12-7 is an illustration of a common fracture of the tibial tuberosity produced under conditions of tensile loading. Because bone as a structural component of the musculoskeletal system must withstand large axial loads (both compressive and tensile) to sustain weight bearing and locomotion, it, by adaptation, exhibits greater strength when subjected to tension directed longitudinally versus tension directed transversely. This observation is essentially a restatement of Wolff s law and helps to explain bone's anisotropic mechanical behavior (i.e., varying strength as a function of load direction). Figure 12-8 demonstrates the relative strength of cortical bone tested

COMPRESSION Compressive forces on a structure tend to shorten and widen it as shown in Figure 12-6B. As in pure tension, maximal stresses occur on a plane perpendicular to the applied load; however, the stress distribution and resultant fracture mechanics in compressive failure are often very complicated, particularly for an anisotropic material such as bone. Unlike failure in tension, compressive failure in bone does not always proceed along the theoretic perpendicular plane of maximum stress, but rather once a crack is initiated it may propagate obliquely across the osteons(35) following the line of maximum shear stress. Clinical examples of this type of fracture mode are the compressive fractures commonly seen in vertebral bodies. On occasion, axial loading of long bones may produce compression fractures, particularly at the growth plate in young dogs.

SHEAR Tensile and compressive forces act perpendicular or normal to a structure's surface. In contrast, shear forces act parallel to the surface as shown in Figure 12-6C and tend to deform a structure in an angular manner; thus, squares or rectangles under shear loading become parallelograms. In contrast to normal forces (tension and compression) where deformation or strain is related to stress by the relationship where:

sigma= E x epsilon where sigma=stress, epsilon=strain, E=modulus

Shear strain is related to stress in terms of angle change tau= G tan alpha where tau=shear stress,alpha=shear strain angle, G=modulus of rigidity (shear modulus)

Shear loading is described graphically by a load- angle-change plot instead of by a load-deformation plot as in the case of tension and compression. All other considerations, such as stiffness, yielding, and elastic and nonelastic behavior, are interpreted similarly from the plots regardless of loading mode. Pure shear fractures are frequently encountered in veterinary orthopaedics; the most common is the lateral condylar fracture of the distal humerus. Less frequently the tibial plateau, femoral condyles, glenoid cavity, vertebral bodies, and carpal and

FIG. 12-7 Radiograph of an injury produced by tensile forces imposed on the tibial tuberosity by the quadriceps musculature. (Courtesy of RB Hohn, DVM) in tension as a function of stress orientation. Clearly, cortical bone loaded longitudinally is stronger, stiffer, and absorbs far more energy to failure than any other load orientation.

FIG. 12-8 Anisotropic behavior of cortical bone specimens machined from a human femoral shaft and tested in tension. The orientation of load applicationÑlongitudinal (L), tilted 30¡ with respect to the bone axis, tilted 60¡, and transverse (T)strongly influences both the stiffness and the ultimate strength. (Frankel VH Nordin M Basic Biomechanics of the Skeletal System, p. 22 Philadelphia, Lea & Febiger, 1980)

tarsal bones are prone to shear fractures. Figure 12-9 is a schematic diagram showing the biomechanics of a lateral condylar fracture of the distal humerus. This fracture typically results from an animal falling or jumping from a height. Owing to the anatomy of the elbow and particularly the distal humerus, axial compressive forces transmitted up the radius are imparted largely (80%) to the lateral condyle, producing shear forces in the intercondylar and epicondylar areas. In Figure 23-2A a radiograph shows a typical lateral condylar fracture resulting from shear forces exceeding the shear strength of bone in the intercondylar and epicondylar areas.

It is important in describing fracture etiology to understand the mechanical behavior of bone under these three primary modes of loading. It has been shown that cortical bone strength is strongly dependent on the mode of loading, being strongest in compression and weakest in shear (Fig. 12-10).(77) Thus, bone strength is a function not only of load orientation within any given mode as shown in Figure 12-8, but it is also a function of loading modeÑtension, compression, or shearÑat a given load orientation. This observation helps to explain why fracture lines do not follow precisely the line of maximum stress (e.g., in compressive failure in which maximum stress occurs perpendicular to applied load). Rather, owing to mechanical anisotropy cracks may propagate obliquely along lines of maximum generated shear stress and reduced bone strength. This consideration applies also to failure under conditions of bending and torsion yet to be discussed.

BENDING Bending is a loading mode schematically illustrated in Figure 12-6D and results in the generation of maximum tensile forces on the convex surface of the bent member and maximum compressive forces on the concave side. Between the two surfaces, that is, through the cross section of the member, there is a continuous gradient of stress distribution from tension to compression (Fig. 12- 11). An imaginary longitudinal plane corresponding to the transition from tension to compression, approximately in the center and normal to applied force, is designated the neutral surface. Along this surface there is theoretically no tensile or compressive load on the material. Another useful designation is the neutral axis, which is the line formed by the intersection of the neutral surface with a cross section of the beam, perpendicular to its longitudinal axis (Fig. 12-11).

FIG. 12-9 Biomechanics of a lateral humeral condyle fracture. Forces transmitted proximally along the radius impact largely on the lateral humeral condyle, thus creating shear forces in the intercondylar and epicondylar areas, where failure is prone to occur.

FIG. 12-10 Ultimate stress for human adult cortical bone specimens tested in compression, tension, and shear. For comparative purposes the shaded area represents the ultimate stress in tension and compression for human adult cancellous bone with a density of 0.35. (Frankel VH Nordin M Basic Biomechanics of the Skeletal System. Philadelphia, Lea & Febiger, 1980; data from Reilly D, Burstein A: The elastic and ultimate properties of compact bone tissue J Biomech 8:393, 1975)

FIG. 12-11 (Top) A beam subjected to pure bending shows the relative orientation of the neutral surface and the neutral axis. (Bottom) Distribution of stresses around the neutral axis in a transverse section of the beam subjected to bending. Tensile stresses are maximum on the top surface, and compressive stresses are maximum on the bottom surface of the beam The neutral surface theoretically experiences no tension or compression.

During normal function bone is subjected to large bending forces both intrinsic and extrinsic (termed moments). The act of locomotion, for example, results in alternating tension and compression on the cortex of weight-supporting bones during the gait cycle.(19,35) The introduction of large extrinsic forces (e.g., automobile trauma) perpendicular to the diaphysis of long bones may generate enough tension on the convex surface of the bent bone to exceed its inherent tensile strength, resulting in crack initiation and failure. Clinically, fractures produced by bending forces are commonly transverse or short oblique, as shown in Figure 12-12. The mechanism of failure in bending is one of crack initiation at the point of maximum tensile stress on the convex (tension) surface of bone with crack propagation along a line of maximum tensile stress or minimal material strength (e.g., in shear) resulting in transverse or short oblique fractures, respectively. Because mature healthy bone is stronger in compression than in tension, failure usually begins on the tension surface. In very young animals or severely osteoporotic bone, however, folding or buckle fractures are sometimes noted on the concave or compression side of the bone, indicating failure in a compressive mode subsequent to bending.

Structurally, in a bending mode of loading, bone strength and stiffness are dependent not only on cross-sectional area as in tension and compression but also on the arrangement or distribution of bone mass about the neutral axis (shape). This strength parameter is termed the area moment of inertia and is an important concept in understanding the strength of a specific shape or geometry under conditions of bending. For example, it is intuitive that a 2" x 4" piece of lumber is "stronger" in bending when placed on its edge (2" side) than on its flat (4") side, yet cross-sectional area remains constant. From the beam theory, formulas have been derived to express area moment of inertia as a function of geometry. The formula to compute the area moment of inertia, I, for a rectangular cross section is

I= base(height)^3 /12 From Figure 12-13 one can appreciate, therefore, that a 2" x 4" on its edge has an area moment of inertia four times greater than on its side and accordingly demonstrates a fourfold increase in rigidity. More simply put, the area moment of inertia takes into account the fact that in bending, a structure gets stronger (and stiffer) as its mass is moved further from its neutral axis. In engineering applications this concept is demonstrated nicely by the design of the "I" beam, which affords maximum resistance to bending with minimum weight. Long bone, in its tubular shape, is aptly designed to uniformly resist bending in all directions and in addition has its mass located circumferentially at a distance from the neutral axis, thus providing a high area moment of inertia and high resistance to bending.

TORSION Torsional loading as depicted in Figure 12-6C is a geometric variation of shear and acts to twist a structure about an axis (the neutral axis). The amount of deformation is measured in terms of shear angle, alpha. As in bending, in which maximum tensile and compressive stresses occur on the surface and distant from the neutral axis, torsional loading produces maximum shear stresses over the entire surface, and these stresses are proportional to the distance from the neutral axis (Fig. 12-14).

FIG. 12-12 Radiograph of a short oblique long-bone fracture probably produced by bending forces imposed on the midshaft humerus.

FIG. 12-13 The area moment of inertia, 1, for a rectangular beam loaded in bending is I = bh^3/ 12. The calculation for a 2" x 4" beam yields a moment of inertia approximately four times greater when the beam is loaded on its edge than on its side. This corresponds to a fourfold increase in rigidity. Moreover, the maximum bending stress in the cross section of the beam considered is proportional to the distance from the neutral axis and inversely proportional to 1, indicating that the 2" x 4" beam on its edge when compared to loading on its side can withstand roughly twice the load necessary to cause failure.

The fracture mechanics in torsional failure are more complicated than those in any of the other loading modes previously described. A material under torsional loading experiences maximum shear stresses on planes perpendicular and parallel to the neutral axis, while maximum tensile and compressive stresses are generated normal to each other and on a diagonal to the neutral axis. This is more clearly demonstrated in Figure 12-15 where the square finite element drawn on the surface of the cylinder undergoes shear-type deformation with torsional forces applied to the cylinder. The diamond-shaped element experiences a deformation in torsion analogous to simple tension and compression; that is, it elongates and narrows, with maximum tensile stresses acting on a plane perpendicular to the axis of elongation and maximum compressive stresses orthogonal to this. Considering the stress distribution in areas other than the principal axes of tension and compression, it is apparent from Figure 12-16 that on planes perpendicular and parallel to the neutral axis maximum shear stresses are manifested in this material. In torsion, then, as in other loading modes, the location of crack initiation and the direction of its propagation are dependent on the inherent strength of the material in any given loading mode and on the magnitude of the imposed stresses within the material. In dog bone subjected to pure torsional loading, it has been suggested that failure begins with crack initiation in a shear mode,(35) that is, parallel to the neutral axis, followed by crack propagation generally along the line of maximum tensile stress (30¡ to the neutral axis). The net effect of this fracture mechanism is to produce a so-called spiral fracture of the long bone as shown schematically in Figure 12-17. Figure 12-18 is a radiograph showing a spiral fracture of a humerus as observed in clinical practice.

As in bending, in which strength and stiffness of bone are determined by the area moment of inertia, that is, the size and shape of the bone, the analogous structural quantity in torsional loading that takes into account size (cross-sectional area) and shape (distribution of bone about the neutral axis) is the polar moment of inertia. This quantity provides an explanation for the observed "structural" strength of healing fractures in which abundant callus has formed a cuff around the fracture ends.

FIG. 12-14 Cross section of the cylinder loaded in Figure 12-6, E in torsion shows the shear stress distribution about the neutral axis Shear stress increases as a function of distance from the neutral axis.

FIG. 12-15 Torsional deformation of a square-shaped and a diamond-shaped element drawn on the surface of a cylinder. The elongation of the diamond-shaped element with torsion indicates that maximum tensile stresses are acting on a plane perpendicular to the axis of elongation and, conversely, that compressive stresses act orthogonal to this. The square element undergoes shear-type deformation similar to that shown in Figure 12-6,C.

FIG. 12-16 Maximum shear stresses on the surface of a cylinder subjected to torsional forces occur on planes perpendicular and parallel to the neutral axis. Spiral fractures of bone are produced by torsional forces applied to the overall structure; failure of the material, however, typically occurs in tension along the line of maximum generated tensile stress.

FIG. 12-17 Schematic illustration of a two-piece spiral fracture of the femur drawn from a radiograph of a clinical case Note the orientation of the fracture line relative to the long axis of the bone. In this example both shear and tensile failure modes are represented.

Obviously fracture callus does not have the material strength of organized lamellar bone; however, the net effect of large cross-section and callus distribution distant from the neutral axis gives fracture callus a polar moment of inertia approaching the strength and stiffness of whole intact bone. The polar moment of inertia also explains why cortical bone at the isthmus of long bones (small diameter) must perforce be thicker than in the wider metaphyseal areas to produce equivalent resistance to torsional and flexural loading.

FAILURE UNDER COMBINED LOADING Tension, compression, shear, bending, and torsion rep- resent simple and pure modes of loading. Examples of failure under these loading modes have been presented. In clinical practice, however, fractures encountered are more commonly a product of a combination of the aforementioned modes. This is not surprising when one considers that the mode of loading is determined by the direction of load application and that in the case of bone fracture produced by trauma (e.g., automobile) there is virtually no constraint on applied load orientation (or magnitude).

ENERGY TO FAILURE As shown in Figure 12-4, the area under the stress-strain or load deformation curve corresponds to the energy absorbed by the bone while undergoing deformation. Since bone behaves largely like a brittle material, exhibiting very little permanent plastic deformation to failure, most of this absorbed energy is returnable upon unloading. When bone is loaded to failure, however, the stored energy is released or dissipated at a very rapid rate through the formation and propagation of one or more cracks. The number and pattern of cracks formed depend largely on the rate at which load is applied. Bone has been shown to have a higher modulus (stiffness) and to absorb more energy to failure the more rapidly it is loaded,(80) that is, it is stiffer and tougher. A single crack, however, has a finite threshold energy for initiation and a finite capacity to dissipate stored or applied energy. Thus, under conditions of high loading rate, if the stored energy in the structure exceeds that which can be dissipated via the formation of one crack, multiple cracks will form and energetically less favorable fracture mechanisms may initiate. This situation results clinically in fracture comminution. Stated in another way, bone has a finite capacity to absorb energy that increases significantly with load rate. When the energy extrinsically imparted to bone (kinetic energy) exceeds the energy- storage capacity of bone, fracture occurs. Kinetic energy is defined by the formula

KE= 1/2mv2 where m = mass v = velocity From this formula it is clear that the effect of increasing load rate, that is, the velocity, plays a bigger role in determining the ultimate fracture (and fracture potential) than does mass alone. (This point will be discussed in the chapter on ballistics.) Fractures are arbitrarily grouped into three general categories based on the energy required to produce them: low-energy, high-energy, and very high energy fractures. An example of a typical low-energy fracture would be the lateral humeral condyle fracture that results when a Yorkshire terrier falls from its owner's arms. High-energy fractures are commonly observed following automobile trauma (Fig. 12-19), and very high energy fractures are associated exclusively with gunshot injuries produced by missiles having high muzzle velocity

FIG. 12-18 Radiograph of a spiral fracture of the humerus shows the spiral fracture surface and a fissure extending proximally along the line of maximum tensile stress.

FIG. 12-19 Radiograph of a high-energy fracture shows marked comminution resulting from trauma sustained in an automobile accident.

FATIGUE FRACTURES Fatigue fractures are infrequently encountered in the practice of small animal orthopaedics. They are, however, a common occurrence in human and equine practice and also in certain dog sporting events, such as dogsled racing, for which dogs must be trained to the limits of their endurance. Fatigue fracture is a phenomenon observed in many materials systems including bone. In contrast to the bone fractures previously mentioned, in which failure followed static loading of bone beyond its ultimate stress, fatigue fractures result from repetitive loading of bone at magnitudes below the ultimate strength of bone. Clinically, fatigue fractures occur after prolonged periods of strenuous activity in which cyclic loads coupled with muscular fatigue (exhaustion) are predisposing factors.

The fatigue behavior of a material is classically represented on a plot of the peak stress per cycle (S) versus number of cycles (N) to failure as shown in Figure 12-21. The quantity sigma u, represents the ultimate strength of the idealized material under a load frequency of N = 1. Points on the curve represent the S-N conditions that produce fracture of the material. At low frequency and high stress, fracture occurs by mechanisms other than fatigue, that is, failure due to repetitive loading of a material beyond or near its yield point. At high frequency, however, and well below a materials yield point, fracture occurs by fatigue mechanisms, namely, microcrack formation and crack coalescence. The dotted line corresponds to a so-called endurance limit that many materials display. A material can be cycled virtually endlessly at stresses below this limit. Carter and Hayes,(20) however, have studied fatigue properties of cortical bovine bone and have demonstrated by flexural testing that microdamage is prevalent even at low-frequency cycling and at loads well below the ultimate flexural strength of bone. Based on these results, Carter(18) suggested a mathematical relationship to predict the number of cycles to failure under fatigue conditions. Interestingly, the formula does not make provision for an endurance limit as occurs in various other inanimate materials. This information would imply that dead bone is susceptible to microdamage and fatigue failure even under small-load magnitudes given adequate cycling. In living bone, however, it is theorized that microdamage may be a stimulus to bone remodeling and that catastrophic fatigue failure occurs only when the rate of damage outpaces the rate of biologic repair (7,20,25,28,37)

BIOMECHANICS OF FRACTURE REDUCTION Biomechanical principles of fracture reduction are simple but, unfortunately to date, are not quantifiable. Each surgeon with time develops an individualized assortment of fracture reduction techniques specific to fracture type. Whether the reduction is performed open or closed, manually or with skeletal traction, with or without instruments, the objectives remain the same:

FIG. 12-20 Radiograph of a very high energy fracture produced by a bullet fired from a gun at high muzzle velocity. The energy of the projectile imparted to the soft tissue and bone upon impact results in extensive tissue destruction and very fine bony comminution. associated exclusively with gunshot injuries produced by missiles having high muzzle velocity (Fig. 12-20)

FIG. 12-21 S-N curves for an idealized metal and for cortical bone show a marked difference in fatigue behavior. At stresses below the endurance limit, the metal can be cycled endlessly without experiencing failure. Dead cortical bone, however, has been shown to be susceptible to microdamage and ultimate fatigue failure at small load magnitudes well below the ultimate strength of bone sigma u and therefore is thought not to demonstrate a recognizable endurance limit. (Carter DR The Fatigue Behavior of Compact Bone. PhD dissertation, Stanford University, 1976)

1. The fractured bone ends and fragments must be brought into close enough proximity to optimize the fracture-healing process.

2. The reconstructed fracture must approximate normal anatomy well enough to provide for optimum function after healing.

3. The preceding must be accomplished with minimal additional trauma to vital structures and surrounding tissue. These requirements necessitate a mechanical means of applying force either remotely or locally to mobilize the fracture ends and move them into acceptable orientation. The resultant force to achieve reduction is largely tension (traction) along the axis of the long bone and must be sufficient to overcome gravitational forces (limb weight); forces of muscle contracture; hydrostatic forces due to edema; and in the case of long-standing fractures, forces due to granulation tissue and fibrous callus at the fracture site. The mechanical effect of edema as an impediment to fracture reduction is often not fully appreciated. Postfracture edema and hematoma in the course of achieving a hydrostatic equilibrium fill interstitial spaces and create fluid-filled voids along tissue planes surrounding the fracture site. The effect is to impart lateral forces circumferentially to the soft tissue overlying the fracture. The process stops, that is, equilibrium is achieved, when the hydrostatic pressure from edema is counteracted by tension in the walls of soft tissue compartments and skin. The expansile forces act to shorten the fractured extremity and resist reduction, thereby freezing the fracture orientation in its shortened position (Fig. 12-22). An attempt at fracture reduction during the phase of edema is both difficult and hazardous. Without an option for protracted skeletal traction, it is often judicious, if not necessary, to apply a temporary compression wrap to the limb for 24 to 48 hours to combat the lateral expansile forces and minimize edema before fracture reduction is attempted. Forces necessary to overcome muscle contracture and fibrous callus increase with time (days/weeks), and therefore to facilitate fracture reduction it is advisable to attempt a reduction as early in the postfracture period as is clinically feasible. (See Chapter 14.)

For closed nonsurgical realignment of long-bone fractures, reduction entails grasping through the skin, the joints, and bony prominences proximal and distal to the fracture. The tension necessary to effect reduction at the fracture site can be achieved only by exerting compressive, tensile, and shear forces on the soft tissues overlying or remote from the fracture site. Soft tissues, however, like bone, are materials having yield points and failure limits, and the surgeon must therefore use care not to exceed these ultimate biologic limits to avoid additional tissue damage in reducing a fracture. Typically biologic strength is a small percentage (10%) of the tissue's material strength, and therefore considerable iatrogenic tissue damage in the process of fracture reduction is not inconceivable.

The most effective closed technique for achieving reduction of transverse or short oblique long-bone fracture is "toggling," as shown in Figure 12-23. It must be recognized, however, that digital pressure exerted over sharp fracture ends creates very high concentrations of stress that are potentially injurious to soft tissues and may result in the creation of an open fracture. Accordingly, digital pressure over sharp fracture ends should be avoided if possible. If attempts at closed reduction yield poor results, open surgical reduction is indicated. This topic is discussed more fully elsewhere (Chapter 16). The mechanical act of open reduction necessitates an assortment of instruments, the purpose of which is to allow the surgeon to grasp and localize distraction forces in proximity of the fracture ends. Ideally a bone-holding forceps should satisfy the following requirements: (1) securely grasp bone via self-retaining mechanism without causing further comminution; (2) cause minimal soft tissue injury and periosteal stripping during application; (3) facilitate anatomical realignment of fracture fragments; and (4) have the

FIG. 12-22 Idealized model of fracture edema leading to compression and shortening of the extremity. To achieve fracture reduction in the presence of significant edema, forces must be applied to overcome the lateral expansile forces of edema filling tissue compartments and interstitial spaces. Alternatively a compressive wrap can be used prior to fracture reduction to minimize or reverse the extent of edema formation.

FIG.12-23 Illustration of the method of "toggling" to achieve fracture reduction. Bone fragments must be placed in correct rotational orientation and angled to provide edge-to-edge cortical contact. Gradual straightening of the bone is accomplished by digital pressure applied away from sharp fracture ends.

capacity to maintain this reduction without obstructing the application of primary internal fixation. Obviously no single bone-holding instrument can satisfy these requirements under all fracture conditions, and therefore an assortment is indicated. At times it may be necessary to use additional aids in maintaining reduction, such as full cerclage wires (which, if made of stainless steel 316L, may be left permanently in place) or temporary full cerclage nylon bands (normally used as collars for bundles of electrical wires; the latter must be removed prior to closing). The surgeon should be aware of some mechanical limitations to achieving an adequate intraoperative reduction. First, bone, having limited ultimate strength, will undergo further fracture if excessive force, either in grasping the bone or in physically distracting fragments, is imprudently exerted. Second, the use of orthopaedic instruments gives the surgeon a large mechanical advantage that must be used judiciously in accordance with the ultimate biologic strength of surrounding vital structures (e.g., nerves and vessels). Exceeding the biologic limits of these tissues can result in purposeless surgery. Finally, forces necessary to achieve reduction may exceed the surgeon's inherent physical strength. This situation can potentially arise from fractures in very large dogs, fracture of long-standing duration (2 weeks), or fractures having relatively inaccessible location, such as ilial shaft fracture.

BIOMECHANICS OF FRACTURE FIXATION In veterinary orthopaedics there exist two major objectives of fracture fixation: first, fracture fixation must provide for early if not immediate ambulation and weight bearing, and second, it should optimize the bone-healing process such that the need for fracture fixation is supplanted in a minimum period of time by recovery of strength and stiffness of the healed bone. Unfortunately, these two objectives at times run counter to each other. For example, the rigidity of fracture fixation achieved through the use of internal fixation with plate and screws satisfies the first objective and provides for early weight bearing. However, the overwhelming strength and stiffness of the device is thought to shield the bone from normal weight-bearing stresses and therefore short circuit the biomechanical stimuli necessary to attain optimum strength and rigidity of bone. It is thus likely that the choice of fracture-fixation methodÑinternal, external, or transfixationÑmust represent a trade-off of these two conflicting objectives. The choice, however, is not very clear-cut. The surgeon in the morass of confusing animal experimentation, subjective reporting, and as yet poorly understood fracture-fixation biomechanics, by necessity practices orthopaedics with those fracture-fixation techniques that work best in his hands. Fortunately, encouraging developments in biomechanical experimentation are providing quantitation and means of optimization of the fracture-healing process. As discussed, the specific mechanical aims of fracture fixation regardless of method are to provide stability of fracture reduction, namely, maintain axial alignment and prevent rotation, and to support the fracture in this manner until the completion of fracture healing. Correspondingly, the topic of biomechanics of fracture fixation can be divided into two sections: biomechanics of fracture stability in the immediate postfixation phase and biomechanics of healing relative to method of fracture fixation. The discussion to follow will attempt to cover pertinent information in each of these areas.

EXTERNAL IMMOBILIZATION The objective of external immobilization is to stabilize fracture fragments internally by application of rigid material externally. The process necessitates interposing soft tissue between two relatively rigid materials, bone and splint. The fracture stability achieved with external fixation, unlike that of internal fixation, is not rigid per se but relative, that is, dictated by the limits of compressibility or strain tolerance of interposed soft tissue. Thus, by definition external immobilization in the immediate postfixation period can at best approach but not equal the stability of rigid internal fixation or transfixation. Nevertheless, fracture healing can proceed toward so-called secondary bony union if the applied external fixation provides limits to fracture fragment displacement compatible with specific biologic processes of repair, particularly revascularization. Owing largely to technical difficulties in biomechanically evaluating fracture stability under conditions of external immobilization, this topic has received surprisingly little attention in the literature. Moreover, the necessities of veterinary orthopaedics (in contrast to human orthopaedics) dictate that all forms of external fixation be functional, that is, weight bearing. Therefore the information extractable from human literature is reduced even further. Two areas, however, deserve mention: functional bracing and the material properties of casts. Functional bracing was first introduced in the late 1960s by Sarmiento,(81-83) a human orthopaedist. The original concept applied to tibial fractures incorporated a below-the-knee cast that hypothetically transmitted ground reaction forces to the straight patellar tendon, bypassing the fracture. Further investigation, however, including accounts from patients who

experienced pressure over the calf area during ambulation, pointed toward a more plausible mechanism. Plastic braces were instrumented with pressure transducers and evaluated during ambulation. Results revealed significantly greater pressures over the gastrocnemius muscle group than the tibial tuberosity, suggesting that perhaps the original hypothesis was invalid. Additionally, the plastic brace itself was found to carry only 15% of the axial load during weight bearing, indicating that the constrained bone and soft tissue were withstanding greater than 80% of the ground reaction forces. Further studies of anesthetized patients having tibial fractures demonstrated a 75% reduction in bone overriding of braced fractures versus nonbraced fractures when subjected to 25-pound axial loads. These findings led Sarmiento(49,84,85) to postulate a multifactorial mechanism operating to prevent shortening and angulation during functional bracing. First, the calf musculature, owing to its incompressible nature and conical shape, when constrained by a conforming plaster brace develops large hydrostatic pressures during weight bearing that act to prevent shortening. Second, the elastic properties of soft tissue structures in the area of the fracture prevent excessive overriding. Third, the interosseous membrane between the tibia and fibula further resists fracture displacement. The principle of functional bracing has been adapted for use in tibial fractures in dogs by Nunamaker. A two-part thermoplastic splint consisting of an cranial half cast from stifle to toes and a cranial conforming brace from stifle to just above the hock is applied using elastic bandage. Experimental and clinical results to date for fractures involving the proximal two-thirds of the tibia are encouraging. Specific techniques of splint application will be covered in Chapter 15. For reasons of economy and acceptable performance, plaster casts find widespread application in veterinary orthopaedics. Biomechanical studies on the properties and stresses in orthopaedic walking casts have been carried out by Schenck and co-workers.(88) Although their work involves lower-leg walking casts for human application, the results are in part applicable to weight-bearing casts in animals. Several findings are of interest. First, the ultimate strength of plaster is finite and in tension is one third that in compression (700 psi versus 1800 psi). This would suggest in general that areas of a cast subjected to large tensile stresses or large resultant moments about joints such as occur during walking may require buttressing with extra layers of plaster. Examples in the dog would include the caudal surface of the carpus in an extension cast of the forelimb, or in the case of a lower hind-leg cast, the cranial surface of the hock, which in humans at least is prone to failure owing to high tensile forces in plantar flexion. Second, the strength of plaster casting material is dependent on setting and drying time. Schenck and co-workers(88) have shown that after 24 hours (the recommended drying time), a 1/4" plaster cast will achieve only about one third of its ultimate strength.. The authors suggested at least 48 to 60 hours drying time before the casts are subjected to weight-bearing forces. To the veterinary orthopaedist, these findings would indicate that plaster casts be constructed with optimum strength using the minimum amount of materials to facilitate drying, lightness of weight, and early weight-bearing. A heavy, cumbersome cast is just as contraindicated as one that is too weak. To facilitate the drying process the fresh plaster cast should not be wrapped with occlusive dressing (including adhesive tape and elastic bandage) for a period of at least 24 hours (for 1/8'' cast). Until the cast is completely dry, it is recommended that the patient be cage rested.

EXTERNAL SKELETAL FIXATION External skeletal fixation (also termed transfixation or fixateur externe) is a fixation method consisting of multiple percutaneous, transcortical pins proximal and distal to the fracture site incorporated into a surrounding external frame. The system facilitates easy management of fracture-associated, soft tissue injuries while providing adequate skeletal fixation without the physical presence of metal at the fracture site. Accordingly, external skeletal fixation is suitable for the treatment of compound fractures and infected nonunions as well as for stabilization of joint fusions, osteotomies, and limb-lengthening procedures. Owing to renewed interest in this method by human orthopaedists, several external fixators have been commercially introduced in various frame configurations (Fig. 12-24). High cost, however, has largely precluded their practical use in veterinary orthopaedics. The system most frequently used in veterinary practice has been the Kirschner-Ehmer (K-E) apparatus. The K-E instrumentation is readily adaptable for application at various skeletal locations (tibia, femur, humerus, radius, and ulna) and can, with practice, be constructed into appropriate frame configurations, the more common of which are shown in Figure 12-25. The type and location of fracture and the condition of soft tissues will of course determine the final frame configuration. As with other fixation methods, the successful application of external skeletal fixation depends on an understanding of the mechanics of fracture reduction and fixation, as well as an awareness of the structural integrity of the bone-fixator composite.

Research both theoretic and experimental is ongoing and has provided useful information in this regard.(22) The clinical performance of external skeletal fixation is dependent on fixator stiffness, which has been shown to be related to the geometric arrangement of pins, including their direction of orientation and their diameter, the length of pins between bone and clamp, the distance between clamps, the lengths of sidebars, and the design and system of assembly of the frame. Many of these factors are determined by the surgeon at the time of fracture fixation, and therefore surgical technique has a profound influence on both the stability of the fixator and motion at the fracture site.(45)

As discussed in Chapter 16, the two most common fixator configurations used in veterinary practice are the half frame (unilateral configuration; Fig. 12-25, A) and the full frame (or bilateral configuration; Fig. 12-25, B). The K-E half frame is most similar to the Hoffmann half-frame system, the mechanics of which have been extensively studied.(13) Lindahl,(54,55) in a series of investigations in the early 1960s, examined the rigidity of various kinds of osteosynthesis for transverse and oblique fractures; he concluded that the rigidity of the half-frame configuration was unsatisfactory from a clinical view- point. In contrast, Burny and co-workers(13) conducted theoretic and experimental studies to determine the optimum conditions of half-frame fixation and concluded that the connecting sidebar length should be minimized; clamps must be as close to the bone as possible; and better stability is achieved with three pins than two, maximally spaced in each fragment. Under optimum conditions, however, the half-frame fixator provides "elastic" rather than rigid skeletal fixation. The authors contend that this "controlled mobility" acts to enhance clinical fracture healing through exuberant periosteal callus formation.(13) Although it is common practice in veterinary orthopaedics to use two or more angled pins in each fracture fragment in conjunction with the half-frame K-E, the Hoffmann apparatus uses parallel transfixation pins, and therefore a comparative assessment of fixator rigidity is not possible. Minimally, the angled pins would seem to act as a desirable impediment to the apparatus being pulled out by the animal. In this vein, Evans(31) has demonstrated improved rigidity of the Oxford apparatus by angling the outer pins inward by 20¡, while Boltze(8) angled and elastically bent the pins in opposite directions in each proximal and distal segment and obtained greater fixator stiffness. In general, however, the unilateral frame (half-pin) has been shown to yield only 20% to 50% of the fracture stiffness obtained by a standard full-pin bilateral configuration,(14,24,33) and therefore its use has significant mechanical limitations. The full-frame external fixator (bilateral configuration) uses through-and-through pins and provides superior bone-fixator stability as well as improved longevity for prolonged clinical application. By manipulating pin size and pin number, a spectrum of fracture stabilities can be achieved from elastic to rigid. Also, since the full frame is symmetric in configuration, it is conducive to applying either compression or distraction forces to the fracture ends. The relative rigidity of the full-frame external fixator depends on several important geometric variables. The number of pins in proximal and distal fracture segments has been shown to influence fixator stiffness directly, with three pins per segment yielding 50% to 100% more stiffness in compression, bending, and torsion than two pins per segment.(22) Interestingly, the addition of more pins (more than four) per segment results in an insignificant increase in overall fixator stiffness, particularly

FIG. 12-24 Common geometric shapes used in the design and application of external fixators: (a) The unilateral configuration; (b) the bilateral configuration; (c) the quadrilateral configuration; (d) the triangular configuration (half-pin); (e) the triangular configuration (full- and half-pin); (f) the semicircular configuration; (g) the circular configuration. (Chao EY, Kasman RH, An KN: Rigidity and stress analyses of external fracture fixation devices: A theoretical approach. J Biomech 15:971, 1982)

FIG. 12-25 Configurations of Kirschner-Ehmer apparatus commonly used in veterinary practice. (A) Double-clamp (half-pin) configuration. (B) Single connecting-bar (half-pin) configuration. (C) Double connecting-bar (full-pin) configuration. (D) Triangular (half-pin) configuration.

in the most critical anteroposterior (AP) bending mode. Pin placement within each pin group is also important. In general, a comparison of various pin numbers used and their placement in bone has demonstrated that fixator stiffness can be improved by increasing pin separation within each group; minimizing pin length; and reducing pin-group separation.(9-11,21,23,58) The determination of optimum pin separation, however, must take into account the obvious regional differences in bone stiffness. For example, Egkher(29) has suggested that better overall stability may be achieved by firm placement of pins "closer" together within diaphyseal cortical bone, away from the thinner and weaker cortical and cancellous bone of the metaphysis. Increasing the transfixation pin diameter can greatly improve the rigidity of the composite bone-fixator. For example, a 2-mm increase in pin diameter (from 4 mm to 6 mm) results in a fivefold increase in rigidity of a standard Hoffmann-Vidal frame (bilateral).(24) This is attributable to the area-moment inertial properties of the larger pin; that is, rigidity is a function of the fourth power of the diameter. Clearly, however, pin diameter must be balanced against the weakening (stress raiser) effect of the associated hole in the bone. Optimally, pin diameter should not exceed 30% of the bone diameter. (11) The diameter and stiffness of the sidebars are typically much greater than those of the transfixation pins. The sidebars, therefore, are not a limiting factor in the overall fixator rigidity; however, to minimize the total weight of the external fixation apparatus the surgeon should select the minimum diameter and length of rod to achieve an optimum combination of strength and weight.

The content of the foregoing discussion has been neatly summarized by Chao in an analysis of the rigidity and stresses in external fixation devices by means of the finite element method.(23) Figure 12-26 shows parametric plots of the effects of geometric variations on bone fixation stiffness in axial compression, torsion and AP and lateral bending. Although these theoretic plots were derived using the standard Hoffmann-Vidal (bilateral) configuration as a model, the results can be applied to the stiffness characteristics of a full-frame (bilateral) K-E apparatus with reasonably good approximation. In Figure 12-26, C, it is important to note the reduced frame stiffness when loaded in the AP mode of bending (< 160 N/cm). This relationship was experimentally substantiated in a comprehensive comparative study of various fixator designs conducted at the Mayo Clinic.(58) Figure 12-27 summarizes these findings along with similar results from the standard Hoffmann,s4 the Hoffmann- Vidal,(22) and the Oxford fixator.(31) It is clear from Figure 12-27 that all external skeletal fixation devices tested are relatively weak under AP bending conditions.

Chao, in a comparative study, evaluated the relative fracture stiffness of prepared tibias fixed by eight-hole AO compression plate or common Kuntscher nail and compared these findings with results obtained from similar loading conditions of the

FIG. 12-26 Parametric diagrams illustrate the effects of geometric variables on the stiffness property of the standard Hoffmann-Vidal external fixation device. (d, pin diameter; h, pin separation; l, sidebar separation [pin length]; s, pin group separation; n, pin number) (Chao EY, Kasman RH, An KN: Rigidity and stress analyses of external fracture fixation devices A theoretical approach. J Biochem 15:971 1982)

FIG.12-27 Overall relative stiffness comparison for various fixators in the tibia. (Chao EY, Kasman RH, An KN Rigidity and stress analyses of external fracture fixation devices: A theoretical approach. J Biomech 15:971, 1982)

FIG. 12-28 Comparison of fracture fixation stiffness produced by internal and external fixation devices: 8 full-pin (8F-PIN) Hoffmann-Vidal splint; 6 full-pin (6F-PIN), Vidal-Adrey splint; 6 half:pin (6H-PIN) Hoffmann-Vidal splint. (Chao EY8, Pope MH: The mechanical basis of external fixation In Seligson D Pope MG (eds): Concepts in External Fixation, p 13. New York Grune & Stratton, 1982)

Hoffmann-Vidal fixator in a plastic bone model.(24) For comparative purposes the results appear in the compound diagram shown in Figure 12-28. It is noteworthy that the composite stiffness characteristics of external fixators and internal fixation devices differ markedly. The plate demonstrates superior stiffness behavior in all but the "bending open" loading mode, whereas the nail, as might be expected, performs relatively well in bending, AP, and lateral, but has minimal ability to withstand axial loading and torsion. The very rigid eight full-pin quadrilateral fixator (8 F-pin, Hoffmann-Vidal), except in AP bending as discussed, exhibits rigidity approximating plate fixation. The six full-pin (6 F-pin, Vidal-Adrey) fixator, however, has significantly reduced stiffness, yet in axial and torsional loading is still superior to nail fixation. Not surprisingly, the six half-pin fixator (6 H-pin, Hoffmann-Vidal) demonstrated the least stiffness of all fixation systems evaluated and accordingly has been termed "elastic external fixation."(13)

INTERNAL FIXATION Internal fixation in veterinary orthopaedics is readily divided into two distinct treatment modalities: intramedullary (IM) fixation (pins, wires, and nails) and screw and plate fixation. The former category, though little studied in a biomechanical sense, is widely used on an empirical basis in veterinary orthopaedics. Screw and plate fixation, on the other hand, has received more complete investigation, yet because of technical complexities in application and the increased cost has not received widespread use in veterinary practice.

INTRAMEDULLARY FIXATION IM fixation as applied to small animals is limited to four basic techniques: single IM Steinmann pin; single IM Kuntscher nail; single IM Steinmann pin with hemicerclage wiring; and multiple IM Steinmann pins with full cerclage wiring. To date few reports appear in the literature addressing the biomechanical principles of IM fixation.(3) Moreover, none of the reports pertain to IM fixation using Steinmann pins alone or in combination with antirotational wires. In a study by Allen and co- workers(3) focusing on IM rod fixation, the most important mechanical characteristics determining device performance of rod fixation in humans were identified as bending strength, bending rigidity, and torsional rigidity. In this report bending strength and bending rigidity represent "device" properties that, if exceeded either by excessive static load or fatigue, result in implant failure. By contrast, in veterinary orthopaedics, failure of IM fixation rarely occurs as a result of material strength limitations. Rather, failures more commonly stem from inadequate torsional rigidity; that is, the fracture site becomes rotationally unstable while the rod remains intact. Allen and co-workers have shown that a Kuntscher nail, when optimally placed in a reamed cadaver femur and torsionally tested, has only about 15% of the torsional rigidity of the contralateral unosteotomized side.(3) Even the best designed fluted femoral IM rod yielded a torque capability of only one third the control side. Mensch and co-workers,(59) using similar methodology, added polymethylmethacrylate (PMMA) to fill in a created middiaphyseal bony deficit and found torsional rigidities to be approximately 39% of control for a Kuntscher nail embedded in PMMA and approximately 18% of control for multiple Steinmann pins embedded in PMMA. Obviously, a single IM Steinmann pin in an unreamed femoral medullary canal devoid of PMMA would have even less contact and mechanical interlock than the Kuntscher nail or stacked pins and would likely yield very low torsional resistance, depending of course on the fracture type. The torque capabilities of multiple (stacked) IM Steinmann pins conceivably could approach but not surpass the performance of the Kuntscher nail for transverse long-bone fractures. With an understanding of these mechanical limitations, it is clear that to optimize fracture stability using IM fixation with Steinmann pins, ancillary fixation may be indicated to provide rotational stability. In the case of a closed pinning with a single IM Steinmann pin, this necessitates using an external splint or cast, which of course in combination may predispose to "fracture disease." For open single IM pinning the addition of one or more hemicerclage wires potentially can afford adequate torsional resistance. Similarly, for multiple stacked pinning of oblique fractures, full cerclage wires provide essential rotational support. Because of the relatively low torsional resistance of IM fixation even under conditions of optimum wire and pin or nail placement, it is advisable to enforce strict confinement of the orthopaedic patient, particularly in the immediate postoperative period and for one month following or until there exists radiographic evidence of healing. By virtue of location axially in the marrow cavity of long bones, IM fixation is excellently suited to resist bending forces imposed on the bone and by this means maintains axial alignment. An IM device, however, has no capacity to sustain axial compressive loads, and therefore the method should be reserved for those fractures that can be reconstructed to transmit axial forces through the surrounding bone, that is, good end-to-end contact. As might be expected, the two major potential complications to the use of IM fixation are rotational instability and fracture shortening. Moreover, resultant motion at the fracture site predisposes to pin migration and may ultimately lead to nonunion

or malunion. Additionally, should the migrating pin penetrate the skin, the fracture site may become infected, thereby introducing the serious complication of osteomyelitis.

COMPRESSED PLATE FIXATION The need for early postoperative weight bearing in treating fractures of all types in animals has led the veterinary surgeon to pursue fixation techniques that afford maximum postsurgical rigidity. In the 1960s Lindahls(54-56) investigated the relative stabilities of various forms of internal fixation applied to oblique and transverse fractures of long bone. His conclusions, based on results from flexural and torsional testing, were the following: no form of internal fixation could match the flexural and torsional strength of intact bone; and of the methods available, plate and screw fixation provides the maximum rigidity. Hayes and Perren(42) advanced the concept of "interfragmentary compression" to increase the rigidity of the composite plate-bone system. By torsional testing of sheep tibia before and after osteotomy with compression-plate fixation, they established a torsional rigidity of the plate bone composite approximately 60% of the control intact tibia and significantly greater than the plate-bone composite without interfragmentary compression. Results also showed that torsional rigidities were optimized by placing screws close to the fracture or osteotomy site so as to increase the length over which the bone and plate act as a composite system. Similar studies(40,71) were extended to quantitation of the flexural rigidity of the plate-bone composite system. Four-point bending was performed on osteotomized and plated human cadaver femora and tibias, with and without interfragmentary compression, and results were com- pared with the intact control. Bending forces were applied in two distinct configurations, one that tended to open the osteotomy line opposite the applied plate and one that tended to close the osteotomy site. Results from a typical test specimen appear in Figure 12-29, in which bending force is plotted against midspan deflection. Clearly, the plate-bone composite does not duplicate the flexural rigidity (stiffness) of the original intact tibia, confirming the results of Lindahl in an earlier study.(54) In the bending mode, which tends to open the osteotomy site, the results indicate a greater stiffness of the compressed fracture than the noncompressed fracture in the early phase of deflection. With increasing deflection, as bone-to-bone contact is lost, both compressed and non-compressed tibias demonstrate similar stiffness (slopes) corresponding to the bending resistance of the plate alone. In the opposite mode, with bending tending to close the osteotomy site, the plate and bone as a composite become mechanically operational having an area moment of inertia approximately equal to intact bone. Not surprisingly then, the compressed plate-bone composite has mechanical behavior and stiffness approaching that of the intact tibia. The noncompressed fracture experiences an initial low stiffness corresponding to plate bending alone, followed by a slope similar to that of the intact tibia at deflections beyond that necessary to close the osteotomy line. To minimize or eliminate this low stiffness portion of the curve, the authors, following Bagby and Jones,(6) advanced the concept of "prebending or over- bending" of the stainless steel plate in a concave configuration just over the osteotomy line. This technique, upon screw tightening and subsequent compression, results in maximum contact of the cortical bone diametrically opposite the plate (a preload), producing in- creased flexural rigidity. Aeberhard' extended these studies to torsional loading and demonstrated a marked improvement in torsional rigidity using compression with prebending of the plate.

From these studies the authors concluded that for maximum mechanical stability of a transverse fracture, bone contact is optimized by prebending the plate prior to application. In addition, since the bone-plate composite showed greater flexural rigidity in the "bending closed" loading mode, it was recommended that these devices be applied such that the acting forces in the system tend to close the fracture or osteotomy site. Usually this necessitates applying the plate on the convex or "tension band" surface of the bone. These tension band surfaces have been determined to a reasonable degree of accuracy by direct measurements in vitro and in vivo(47,48,92)and by theoretic mechanical analyses.(24,30,62,71) Along the same vein as Hayes and Perren, Bynum and co-workers(17) investigated the biomechanical capacity of installed commercial bone

FIG. 12-29 Plot of bending force versus midspan deflection for compressed and noncompressed osteotomies relative to intact bone. Results suggest that plates should be applied in such a way that the forces acting on the bone tend to close the fracture site. (Hayes WC: Biomechanics of fracture treatment. In Heppenstall B (ed): Fracture Treatment and Healing, p 124. Philadelphia, WB Saunders 1980)

fixation plates applied to the dorsal surface of equine third metacarpal bones. Bone specimens, having midshaft osteotomies and compression plating, were loaded to failure in compression, torsion, and flexure. Flexural loads were applied in the bending open and bending closed modes as well as from the side, or lateral loading. Results of testing, although lacking statistical analysis, demonstrated a range of plate-bone composite strengths from 16% to 67% of whole intact bone. As expected, the lowest strength corresponded to the bending open loading mode and the highest, to the bending closed mode. The authors concluded that plate- bone composite strength is dependent on the type of fracture and the mode of loading and that state-of-the- art plate fixation per se lacks the necessary mechanical requirements for successful equine fracture stabilization. Obviously, in long-bone fractures of small animals and humans in whom transmitted loads are significantly smaller and for whom confined rest or restricted activity is more simply enforced, the margin of safety in the use of plate and screw fixation is markedly improved. The same authors,(76) in a subsequent investigation, performed parametric studies with varying plate length, plate width, and screw diameter, again using the osteotomized equine metacarpus but in flexural loading only. Results suggested that with optimized experimental parameters of plate length, width, and screw diameter the strength of the reconstructed osteotomy does not exceed 60% of the intact bone. Additionally, it was demonstrated that plate width (from 0.5 inch-1 inch) and screw diameter (from No. 8 to No. 14) did not significantly influence the strength of the plate-bone system. Increasing plate length, however, from 3 inches to 6 inches improved the flexural strength of the fixation approximately twofold. The finding emphasizes the need to select plate length such that bending forces can be more uniformly distributed along the length of the plate-bone composite. The question of optimum plate placement for long-bone fractures has long been a topic of discussion among orthopaedists. Hayes and Perren(4l,7l) suggested positioning plates on the convex or tension band surface of long- bone fractures to provide maximum resistance to bending of the plate-bone composite. Minns and co-workers(61) pursued this concept further, hypothesizing that plate placement on the tension surface (of the tibia) is mechanically more stable in both flexural and torsional testing than placement on the compression surface. Theoretic calculations drawn from gait analysis data by Paul(68) plus inherent geometric properties of human tibia supported the contention that the anterolateral surface of the tibia experiences the maximum tensile stresses during gait. Subsequent studies to test their hypothesis and the validity of their theoretic calculations were performed using physiologic loads and various plate configurations. Results indeed confirmed that plate placement on the anterolateral surface of the tibia provided more resistance to physiologic load than on the anteromedial surface. In addition, it was concluded that tibial osteotomies fixed with compression plating were more rigidly stabilized than those without compression. Further, in comparing plate-bone rigidity in relation to plate size, it was found, not unexpectedly, that a thicker plate resists bending and torsion better than a thinner plate. Whether these biomechanical findings in human tibias find practical application in veterinary orthopaedics depends on factors such as the increased complexity of plate application on the anterolateral side of the tibia and the extent of improved clinical performance of this plating configuration. After discussion with many veterinary surgeons in clinical practice, it is apparent that the large majority of clinicians do not feel justified in abandoning the anteromedial placement of plate fixation of tibial fractures.

MATHEMATICAL MODELING The high expenditure of time and money in conducting scientific biomechanical experimentation has led investigators to pursue theoretic mathematical models that can be fitted to the various mechanical and material conditions of internal fixation. Very simply, the technique utilizes available information from experimentation pertaining to internal fixation combined with mathematics of theoretic mechanics to approximate or predict the biomechanics of internal fixation relative to various specific parameters. The most popular method to this end has been in use since the early 1970s and is termed the "finite" element method. The following is a brief review of information derived from this method relevant to fracture fixation biomechanics. Finite element modeling of transversely osteotomized and compression-plated equine third metacarpals led to the early realization that axial loads, mathematically applied, had predictable results on the plate-bone composite; namely, tensile forces tend to open the osteotomy line while compressive forces tend to close the osteotomy site.(78)These results supported the purely experimental findings cited previously.(17,24,26,71) The analysis also predicted that under conditions of axial compressive loads the plate carries approximately 18% of the load, thereby protecting the underlying bone from experiencing the total force transmitted.

In similar modeling of an oblique fracture of the equine third metacarpus, the stress distribution of the contacting fracture ends was investigated as a function of plate tension, bone screws, and axial forces.(79) Application of axial compressive force was found to increase the area of contact as well as the magnitude of contact stresses at the osteotomy site. Plate tension alone, however, in the absence of axial compressive loads on the bone resulted in very high stress concentrations beneath the plate with distraction and loss of contact of cortical bone opposite the plate. The insertion of a single interfragmentary screw perpendicular to the bone axis tended to antagonize these unwanted effects of compression plating. Askew and co-workers(5) used photoelastic and mathematical analyses to quantitate the phenomenon of bending caused by the eccentric placement of a compression plate on a long bone. In the case of a straight plate applied to a straight bone subjected to physiologic axial bending loads, eccentric compression plating resulted in extremely high stress concentrations beneath the plate in the order of 107 N/m2 and a decrease in bone cross- sectional contact to 8% to 20% of normal. Based on their analysis the authors supported the prebending of compression plates prior to application as advanced by Perren and Hayes.(4l) Plant and Bartel mathematically evaluated the bending effect of compression plating as a function of plate modulus.(74) Results of analyses of metallic plate-bone composites corroborated the above conclusions of Askew and co-workers: high stress concentration beneath the plate and fragment distraction of the "trans" cortex. Moreover, with plate modulus matching that of bone, compression was found to further exaggerate the bending effect, producing even larger osteotomy distraction than observed with metallic plates. These results were further substantiated by Hayes and co-workers, who showed through an idealized bone-plate model that overbending plates even minimally (approximately 0.2¡) produces more nearly uniform compressive contact stresses across the osteotomy site(4l)(Fig. 12-30). Clearly, then, experimental and mathematical evidence strongly supports the clinical practice of overbending compression plates for application on transverse or short oblique long-bone fractures. The resultant plate-bone composite demonstrates increased bone contact at the fracture site, more uniform end-to-end stress distribution, and less cyclic bending of the metallic plate.

PLATE-INDUCED OSTEOPENIA As mentioned in the introduction to this chapter, compression-plate fixation shares with the bone the job of force transmission across the fracture line. This phenomenon, so-called stress protection of bone, results from the large mismatch of modulus between bone and metallic plate. Because mechanical stress is integral to bone remodeling and form (Wolff's law), a shielding of the bone from stress is postulated to cause a phenomenon termed plate-induced osteopenia. This topic has been the subject of several investigations, theoretic (mathematical) as well as experimental.(2,26,76,91,93,99)

Woo and co-workers(103) used finite element analysis to evaluate the effect of plate modulus on long-bone remodeling. Earlier quantitative histologic studies(2) demonstrated gradations of plate-induced osteopenia in the lateral cortex of canine femora subjected to lateral compression-plate fixation. The degree of osteopenia was postulated to correspond to the modulus of the compression plate applied such that high modulus, for example conventional stainless steel, produces marked cortical thinning while lower modulus plates are associated with less osteopenia. Subsequent finite element analysis modeling of the human femur has yielded the theoretic magnitude of stress protection directly beneath the plate. In a comparison of bone stress beneath plates having elastic moduli differing by an order of magnitude (vitallium versus graphite-fiber-reinforced composites) it was determined that the vitallium plated bone experiences only 7% of the stress of weight bearing when compared with the control unplated femur while composite-plated bone experiences 53% of weight bearing stress. The authors used this calculated stress reduction to explain the observed relative osteopenias in the canine femora of the previous study. These theoretic calculations were confirmed experimentally by Cochran(76) and by Schatzker and co-workers(87) using in vitro strain gauge measurements of plated canine femora subjected to axial loads. Cochran demonstrated an 84% reduction in bone strain immediately beneath an anterolaterally placed, four-hole AO plate and a 22% reduction on the medial side. Schatzker and colleagues evaluated bone strain as a function of plate type: four-hole semitubular plate versus four-hole AO dynamic compression plate. Strain measurements beneath the semitubular plate were reduced 64% on the laterally plated

FIG.12-30 Contact stresses at an osteotomy site for straight and prebent plates. For straight plates, the stresses are highly compressive directly beneath the plate. Prebending the plate results in a more nearly uniform distribution of contact stresses. ( Hayes WC: Biomechanics of fracture treatment. In Heppenstall B (ed): Fracture Treatment and Healing, p 124. Philadelphia, WB Saunders. 1980)

surface and 20% on the medial cortex relative to the measured strains in intact bone. The dynamic compression plate, on the other hand, reduced bone strain even more-77% in the lateral cortex and 34% on the medial cortex. The results, both theoretic and experimental, document the potential of internal fixation via plating to protect the underlying bone from normal physiologic stresses of muscle activity and weight bearing. The absence of sufficient mechanical stimuli may perhaps explain the osteopenia observed by Akeson and co-workers(2) beneath the plate in canine femora. A plausible alternative explanation, however, may be that the plate acts as an impediment to vascular supply to the bone beneath the plate or simply as a foreign body producing secondary or chemical osteopenia unrelated to mechanical stimuli. Obviously the possibilities require further investigation. In summary, internal fixation using plates and screws yields the most stable form of fixation immediately post-operatively,(50,59) although no means of fixation is mechanically capable of achieving the strength and stiffness of whole intact bone. Whether or not this rigid fixation is detrimental to the subsequent development of late-stage fracture strength will be discussed in a section to follow.

BIOMECHANICS OF SURGICAL SCREWS Surgical screws in veterinary orthopaedics are commonly employed in fracture management to secure internal fixation plates to bone or to appose bony fragments pursuant to the principles of interfragmentary compression. Less commonly, screws may be used as anchoring points to attach synthetic ligaments or tendon for joint reconstruction. The biomechanics of surgical screws have received considerable attention in the literature, yet owing to the many variables involved in determining optimum screw design, the present armamentarium of commercially available screws has resulted as much from empirical trial and error as pure scientific endeavor. Factors to consider relative to strength and holding power in bone include screw diameter (both core and outside diameter), thread type (angle, cross-sectional configuration), technique of application (pretapped versus self-tapping, pilot hole size) and of course inherent bone characteristics (thickness of cortex, bone damage upon screw introduction, and cortical versus cancellous holding strength at the time of screw introduction and later in the healing phase). Optimization of all parameters clearly would necessitate a parametric study of enormous complexity. Fortunately in clinical veterinary orthopaedic practice, assuming the tenets of internal fixation are closely observed, failures of internal fixation, when they occur, rarely are due to screw deficiencies either in inherent structural strength or holding force in bone. Surgical screws are used to compress plate to bone or bone to bone and therefore by design experience large tensile loads. To achieve optimum tension, however, a screw during the process of insertion undergoes a complex set of forces, including axial compression to maintain mechanical interlock between screwdriver and screw and torsion to drive the screw and manifest compression of components. Torsional force can be specifically subdivided into the force necessary to cut threads (in the case of self-tapping screws); to overcome thread friction; to overcome friction at the screwhead/countersink interface; and ultimately to achieve the desired tensile force in the screw(40,43) (holding power in bone). Hughes and Jordan have shown that as little as 5% of the total applied torque upon insertion is converted into screw tension under the adverse conditions of no pretapping of the pilot hole and no lubrication. To optimize the efficiency of torque conversion to screw tension, the authors suggested using the largest practicable pilot hole, pretapping the screw hole, and irrigating with saline as a lubricant.(43) Using these measures a 65% conversion of applied torque to useful screw tension can be achieved. Furthermore, they suggested, from the results of their testing of screw insertion forces, that the maximum torque necessary to drive a screw should not exceed 65% of the screw's ultimate strength. This figure was determined after appreciahng that screw failure under the influence of multiple loading modes, such as torsion plus tension, may occur at torsional loads well below the screw's ultimate strength in pure torsion. The orthopaedist must acquire the surgical judgment to select the proper screw size based on the mechanical demands placed on the screw in performing its intended function and the size and quality of the bone into which the screw is to be inserted. Hughes and Jordan have shown that screw holding power is dependent on the shear strength of the surrounding bone and is independent of the mechanical properties of the screw.(43) Not surprisingly, cortical bone demonstrates the highest holding power,(17) reported by Gotzen to be approximately 400 N/mm bone thickness for the AO 4.5-mm screw.(39) Cancellous bone is much weaker, yielding a holding power of 4 N/mm7 of surface.(70) Accordingly, to optimize pullout strength in cancellous bone it is recommended that screws have a wide, deep thread and high thread pitch.(70) A useful concept in describing screw-to-bone contact is the parameter termed interference. Interference is defined as the difference between the major diameter of the screw and the pilot hole diameter divided by the major diameter minus minor (core) diameter. For example, for the AO 4.5-mm cortical screw,

Interference = (4.5-3.2)/ (4.5-3.0) x 100 = 87% For practical purposes, interference can be thought of as the degree of interdigitation of screw thread with bone. Interestingly, studies to evaluate pullout strength in cortical bone as a function of interference have shown a poor correlation,(17,26,43,47) confirming the work of Hughes and Jordan(43) that holding power is proportional to the surface area of cortical bone subjected to shear stress and therefore the major diameter of the screw. Screws having small core diameter and high interference, although appropriate for cancellous bone, are subject to torsional failure on insertion into dense bone as a result of high torsional forces due to increased thread-bone friction. Bynum and co-workers(17) have suggested interference values of 35% to 50% for optimum pullout strength of pretapped machine-type screws in cortical bone. Nunamaker and Perren evaluated screw holding power in bovine cancellous bone and concluded that screw core diameter should be as large as conditions allow for maximum screw strength and that the major screw diameter should be maximized to achieve the optimum holding strength.(65) Recognizing that screw pullout strength is a function of the shear properties of the surrounding bone and that these properties may potentially change with time from the trauma of insertion or with healing, Schatzker and co-workers(86) conducted an in vivo study of screw holding power in mongrel dogs for periods of up to 12 weeks. At no time did holding power drop below the time "0" value, and at 6 and 12 weeks, pushout strength exceeded the initial postoperative values. Not unexpectedly, the 4.5- mm AO screw, having the largest major diameter in the series of screws tested, exhibited the greatest holding power. Subsequent histologic evaluation of the thread-bone interface revealed no impairment of the bone-healing process although lacunae within 1 mm of the screw threads were found to be devoid of nuclear material in the early (6 weeks) healing phase. Although results of this study must be tempered by the fact that the screws were only minimally loaded during the experiment, it is apparent that the trauma of the screw insertion was not deleterious to holding power over a 12-week period. In an investigation of screw tension associated with plate fixation, Laurence and co-workers(50) reported on engineering considerations related to the internal fixation of fractures of the tibial shaft in humans. Osteotomized human tibias were fixed with plates and specially instrumented screws and taken to failure in a bending "open mode." Results indicated that the maximum tension generated in the screws was only about one half the potential pullout strength of the screw and much less than the ultimate strength of the screw. The authors concluded that four screws (eight cortices) were sufficient to provide adequate stability to a plated transverse tibial fracture at the moment of implantation but that more screws may be necessary to ensure optimum stability over time. This work supports the empirical impression in veterinary orthopaedic practice that inherent screw deficiencies are rarely responsible for the failure of internal fixation of fractures.

BIOMECHANICS OF FRACTURE HEALING The biomechanics of fracture-fixation methods have been discussed with particular emphasis on immediate post-fixation stability. Although of extreme value, this information requires interpretation in light of the biomechanics of the subsequent fracture healing process. That is, the rate (indeed ultimate extent) at which a fractured bone unites is determined in large part by mechanical factors in and near the fracture environment. The process of fracture healing has been thoroughly covered in a preceding chapter. (See Chapter 3.) The orthopaedist's responsibility is to reconstruct the normal anatomy of a fractured bone and to provide at least the minimum stability necessary for healing to proceed. This entails limiting fracture fragment motion sufficiently to maintain the viability of the interposed tissue. The presence or absence of motion determines the type of tissue that can survive between fracture ends, which in turn dictates the type of bony union to be expected: primary, secondary, or nonunion. Whether or not a tissue type survives in the face of motion depends on its inherent ability to withstand strains both normal and angular. Perren has reported(69,70) that granulation tissue, cartilage, and bone can withstand normal strains of 100%, 10%, and 2%, respectively, and angular strains of 40¡, 5¡, and 0.5¡, respectively. In a poorly immobilized fracture in which large tissue strains are to be expected, the mechanical properties of granulation tissue make it more suited to survive, thus constituting a nonunion. In the sequence of endochondral ossification leading to secondary bony union, a continuum of increasing stiffness (low strain tolerance) and strength is observed in tissue types from granulation tissue to cartilage and finally to bone. Thus, "the precursor tissues prepare the fracture gap mechanically and biologically for solid bone union."(70) In the case of rigid internal fixation in which deformations between fracture ends are limited to less than 2% strains, bone can form directly along vascular elements to a so-called primary bone union with no interposed fibrous granulation or cartilaginous phases. This phenomenon has been demonstrated by Perren and co-workers in an evaluation of cortical bone healing in sheep using instrumented compression plates.(72) Histologic results as shown in Figure 3-8 reflect the mechanical stability at the osteotomy site. Remodeling osteons are seen directly traversing the fracture line without the presence of fibrous or cartilaginous components.

Traditionally the clinical progress of fracture healing has been documented by radiographic evaluation and clinical empiricism. Experimentally the stages of fracture healing have been classified based on biochemical observations, histologic appearances, and radiographic criteria. White and co-workers(94) were the first investigators to correlate histologic and radiographic stages of fracture healing with objective measurements of the mechanical properties of healing bone tested to failure. The methodology utilized external skeletal fixation and was originally developed in an attempt to quantitate the effect of cyclic loading on the rate of fracture healing. To this end the investigation fell short of its mark. Nevertheless, results of torque-angle measurements and radiographs made after mechanical testing of tibial osteotomy sites in rabbits afforded a clear delineation of four biomechanical stages of fracture repair. Figure 12-31 is a composite torque-angular displacement curve of six representative rabbit tibias at various fracture healing times. Stage I repair corresponds to short fracture healing times (< 26 days) in which ultimate loading of partially healed bones results in failure through the original experimental fracture site with a low-stiffness, rubbery pattern. Stage II healing is marked by failure through the osteotomy site as in Stage I but with progressive development of a high-stiffness, hard-tissue pattern as shown at 27 days in Figure 12-31. Stage III repairs undergo torsional failures partially through the original experimental fracture site and partially through the previously intact bone with a high-stiffness, hard-tissue pattern (49 days, Fig. 12-31). Stage IV fracture healing again displays a high-stiffness pattern upon mechanical testing (56 days, Fig. 12-31); however, failure occurs radiographically at sites unrelated to the original osteotomy site.

Statistical analysis of data demonstrated the four stages to correlate closely with fracture strength and healing time. The authors emphasized the need for a nondestructive means of assessing the clinical progression of fracture healing. For the present, the veterinary orthopaedist must rely on radiography, clinical judgment, and the empirical passage of time to monitor fracture healing. On the horizon, however, are promising non- destructive, fracture strength assessment techniques including ultrasound, stress wave propagation, and resonant vibration.(49) In a later study White and co-workers(95) used a similar rabbit model to investigate temporal changes in physical properties of healing fractures. Pertinent results indicate that the maximum torque to failure at 3 weeks is 25% of intact bone, progressing to 75% at 9 weeks. Angular deformations prior to failure are understandably very large at 3 weeks and diminish to slightly less than intact bone at 9 weeks. This finding can likely be explained by the large polar moment of inertia associated with callus formation. It should be recognized that the testing methodology employed in this series of investigations involved the use of a transfixation apparatus and various fixed and cyclical compressive loads. Also, rabbits were not permitted normal weight bearing on their hind limbs. Whether these results then can be extrapolated to a comparative assessment of clinical fracture healing using standard internal, external, or transfixation is open to question. Minimally, the significance of these reports would support the continued use of radiography as an indicator, albeit crude, of fracture strength and fracture healing progress. Along a similar vein, Whiteside and co-workers(98) investigated the biochemical characteristics of fracture callus temporally and correlated these findings with biomechanical data and the radiographic stage of fracture healing. Specifically, osteotomized rabbit tibias repaired with IM pins were subjected to tensile testing at various stages of fracture repair (determined temporally and radiographically), and results were correlated with the biochemical composition of callus. As might be expected, in the early stages of callus formation the observed large total strain to failure was positively correlated with high mucopolysaccharide level (hexosamine) and low calcium level. As callus matures, however, tensile strength increases progressively and the callus becomes stiffer and therefore can endure less strain to failure and correspondingly less energy to failure. Associated with these changes the biochemical picture is one of diminishing hexosamine level (particularly in the callus-bridging phase) and increasing calcium content of the callus. Interestingly, in the final stage of callus maturation no biochemical changes were observed, yet mechanical properties changed markedly toward increased strength and stiffness.

FIG. 12-31 A composite torque-angle graph of six bones representative of the entire bone-healing period. The numbers on the graph indicate days of healing time. As healing progresses, there is increase in the strength of union as shown by the changes in the torque-angle graphs. (White AA, Panjabi MM, Southwick WD: The four biomechanical stages of fracture repair. J Bone Joint Surg 59A:188, 1977)

It is likely that this phenomenon is a result of the internal remodeling process that works to optimize the structural characteristics of the healing fracture. Additional and often underestimated factors in determining the rate of fracture callus formation and maturation are the extent of soft tissue trauma in the vicinity of the fracture and the type of surgical approach used to achieve fracture reduction and stabilization. For example, soft tissue trauma and extraperiosteal dissection have been shown to retard the formation and strength of fracture callus when compared with control fractures approached subperiosteally.(97) Clearly it is important to be aware of such an influence when designing or interpreting comparative experiments of fracture healing.

THE ROLE OF FUNCTIONAL WEIGHT BEARING It has long been theorized that fracture healing rate and ultimate fracture strength may be profoundly influenced by mechanical factors in the fracture environment. In recent years several experimental investigations have been conducted to elucidate these mechanical factors with the intent of optimizing the fracture healing process(32,44,51-53,66,67,75,91,95,101) White and co-workers, using a rabbit osteotomy model previously described,(67) attempted to demonstrate significant mechanical differences between fractures healed under conditions of constant compression and fractures subjected to constant compression and a superimposed cyclic load. Constant and dynamic loading was implemented by means of a specially designed external fixator. Previous investigations had been unsuccessful in demonstrating a significant effect.(95) In their most recent study, by imposing more dissimilar mechanical environments, they (99) were able to demonstrate at 6 weeks of healing significantly increased torque and energy absorption to failure (as well as lower stiffness) in fractures exposed to cyclic loading versus pairmates treated with constant compression alone. No significant differences, however, were noted at 4 or 8 weeks. There was a "suggestion" that compression-treated bones may be stronger than load-cycled bones in the earlier phases of fracture healing. This finding had also been reported in an earlier study by Sarmiento and co-workers.(85) Apparently, in the early phase of fracture healing, cyclic loads and the resultant tissue strains retard the normal and delicate process of vascular repair and granulation tissue formation,(27) thus delaying creation of an early fibrous callus. However, in the interval between 4 and 6 weeks cyclically loaded fractures demonstrate superior mechanical behavior in both torsional testing(72,99) and three-point bending.(85) Again, this is probably due to the more extensive strain-induced callus and attendant increased inertial properties. The positive correlation between motion and increased fracture callus and cartilage is compatible with the findings of a number of previous noteworthy investigations.(36,57,60,104) In 8 weeks, however, the effect disappears. It is conceivable from these studies that the optimum fracture-fixation method would incorporate rigid immobilization in the early revascularization stage of fracture healing followed at 2 to 6 weeks by the introduction of small interfragmentary strains (via controlled weight bearing) to maximize callus formation and thereby speed the return of strength and stiffness. At 8 weeks and beyond it appears that the process of fracture reorganization and remodeling leads to the same mechanical end point regardless of function and immobilization history. Cyclic loading, therefore, may be useful in hastening the return of fracture strength add stiffness but does not have a significant effect on ultimate fracture strength of the remodeled fracture site. It remains unclear whether this accelerating effect is attributable to motion at the fracture site, the variable applied force, or perhaps a strain-induced biologic signal (e.g., bioelectrical). Additional information on the influence of motion on the formation of fracture callus and the resultant rate and strength of fracture healing was presented by Piekarski and co-workers.(73) Their original objective was to test biomechanically the effects of delayed IM internal fixation versus immediate internal fixation. In evaluating results from the delayed fixation of osteotomies of the radius of rabbits, no significant mechanical difference was observed within the 6-week experimental period between fractures fixed immediately and those fixed one week following a created fracture. There was, however, a noticeable increase in callus cross section and callus volume in the delayed-fixation group, particularly in the early stages (up to 3 weeks) of fracture healing. Not surprisingly this cross section diminished in size with the added support of the IM device; however, this was not evident until 2 weeks following insertion. Although callus was more exuberant in the delayed-fixation group, its material strength was less than that of the control (immediately fixed) group at 3 weeks as a result of the discovery of an increased callus porosity. This porosity was found to diminish slowly from 3 to 6 weeks, and in conjunction with the observed reduction in cross section in this period the delayed-fixation group demonstrated reduced failure loads and tissue strengths. Therefore, although delayed fixation appears to enhance early callus formation and thereby increase fracture stability, the poor quality of callus and the rapid reduction in cross section over time would suggest that its use has no particular advantage over immediate fracture fixation. In correlating mechanical behavior with radiographic fracture appearance, Sarmiento and co-workers(85) found that the

radiographic disappearance of the fracture line in the rat tibial osteotomy model did not necessarily indicate completed fracture healing based on biomechanical criteria. That is, tibias subjected to functional weight bearing in which a radiographic fracture line was visible were mechanically stronger than immobilized rat tibias in which the fracture line had disappeared. Again this is undoubtedly due to the superior structural properties in the exuberant noncalcified fracture callus. The finding, however, would warrant caution in assessing fracture strength solely on the basis of the presence or absence of a fracture line. In summary, biomechanical information is accumulating to support the functional loading of fractures, except perhaps in the immediate postfracture phase. Fractures treated with functional loading demonstrate a more rapid return of strength and stiffness when compared with immobilized fractures, although the biomechanical end point to fracture healing (after remodeling has occurred) is the same regardless of fixation technique. An additional advantage of functional weight bearing, of course, is the maintenance of normal muscle mass and freedom of joint motion. Weight bearing and the consequent fracture motion appear to correlate positively with the size of the fracture callus. Some investigators suggest that the continued mechanical stimulation of weight bearing accelerates the subsequent callus ossification process; however, the validity of this impression awaits rigorous scientific proof. These theoretic and experimental findings are perhaps not too surprising to the veterinary orthopaedist who historically has been managing fractures in animals in the face of an overwhelming desire on the part of the animal to ambulate. Functional weight bearing is and always has been recognized, at least empirically, as an integral part of successful fracture management in animals. Studies that advocate limited though appreciable motion at the fracture site to enhance callus formation would be difficult if not impossible to implement in animals owing to lack of patient cooperation. Although theoretically, functional weight bearing results in an earlier return of strength and stiffness in a controlled situation in experimental animals, in clinical animals there is no such control. Accordingly the veterinary practitioner must tailor the fixation method to the type of fracture and the type, size, and expected activity level of the animal. Although rigid internal fixation with plate and screws may inherently antagonize the desirable callus formation process, it nevertheless is clearly the treatment of choice in the extremely active animal whose physical activity would exceed the mechanical constraints of any alternate form of fracture treatment. It must be remembered that in time the reorganization and remodeling process yields mechanically the same result regardless of function and immobilization, and therefore the appropriate choice of fixation and activity level is that which has the capacity to provide adequate stability for the minimum duration from fracture organization to callus reorganization.

INTERNAL FIXATION The mechanical influence of internal fracture fixation on the biologic healing process has been the subject of considerable investigation, yielding valuable information to the orthopaedic surgeon. Fortunately for the veterinarian, most of these studies have been performed in experimental animals and therefore the results (particularly in the canine) are directly applicable to veterinary orthopaedic practice.

PLATE AND SCREW FIXATION It has been stated previously that compression-plate fixation facilitates rigid internal stability, leading to primary bone union and absence of callus. What, however, are the biomechanical effects of compression on bone over time? Perren and co-workers,(72) using strain gauge, instrumented compression plates in sheep, characterized the time-dependent decay of interfragmentary compression forces postsurgically and evaluated subsequent radiographic and histologic changes attributable to the compression. Strain gauge results indicated that post-surgical interfragmentary compressive forces of 60 kilo- ponds to 140 kiloponds diminished with time but did not drop to zero over the 1 2-week experimental period. Interestingly, similar results were obtained when instrumented compressive plates were applied to intact (non- osteotomized) bone. This finding would suggest that the positive stabilizing effects of interfragmentary compression are manifested, albeit in declining magnitude, throughout the critical first 3 months of healing. Also, histologic and radiographic results confirmed that in the force range of 60 kiloponds to 140 kiloponds, no "pressure necrosis" of bone could be demonstrated at the fracture site. This finding ran counter to many popular beliefs at the time (1969). With the introduction of rigid plate fixation much practical concern has been voiced by orthopaedists regarding the phenomenon of stress protection and the attendant plate-induced osteopenia. Particular concern stemmed from the practice at that time of double-plating femoral fractures, which resulted in an unacceptably high incidence of refracture following plate removal. The topic of plate-induced osteopenia has been covered in a previous section on mathematical modeling, however, pertinent experimental studies will be discussed below.

Investigations on plate-induced osteopenia have radiographically demonstrated the existence of cortical thinning beneath the plate for at least the first 6 months following application.(93) Histologic follow-up has pointed to a mechanism of increased periosteal resorption of cortical bone with associated increased bony porosity. These changes have been shown to be virtually completely reversible within 3 months after plate removal.(93) Increased bone porosity was a common finding in a study by Akeson and co-workers,(2) who demonstrated a relationship between the degree of cortical porosity and the modulus of the applied plate (i.e., decreasing plate stiffness results in decreased bony porosity). Similar findings were reported by Tonino and associates(91) in a comparison of stainless steel and plastic plates. Plastic-plated bones were shown to have superior mineral mass and mechanical properties. On the other hand, stainless steelplated bones exhibited massive endosteal resorption as determined by microradiography. In contrast to these findings, Woo and co-workers(102) were unable to demonstrate significant mechanical differences between 16 healed radial fractures treated with stainless steel plates and those treated with low-modulus graphite-PMMA composites. A later study by this group(101), however, revealed a significantly increased amount of bony atrophy associated with healed fractures treated with stiff stainless steel plates in comparison with those treated with less stiff stainless steel plates. Interestingly, the material properties of healed fractures from both experimental groups were found to be indistinguishable. A detectable cortical thinning in the stiff-plated group was thought to be responsible for the significantly inferior structural properties observed. The effects of plating (with and without compression) on intact bone morphology were investigated by Slatis and associates(90) using the rabbit tibia model. Histologically the application of a plate on an intact tibia was found with time to result in the formation of subperiosteal new bone and a concomitant resorption of subendosteal cortical bone. Point counting of cross-sectional areas of bone revealed no significant difference between compressed and noncompressed tibia by the end of the 9- months experiment. The net result, however, of plating intact bone regardless of compression was to increase the area of the medullary canal and at the same time to increase the total cross-sectional area of bone, creating a larger diameter, thinner walled tube. Thus it appears that the application of a metallic plate to bone has the potential to produce significant morphologic changes in the bone, including widening of endosteal haversian canals (increasing porosity), widening of the medullary canal, and enlargement of the overall outside diameter. The precise mechanism or mechanical stimulus for these changes is unclear, but it is probably related to the stress-protection phenomenon described previously. Of extreme importance is the realization that similar morphologic alterations are to be anticipated along the length of bone exposed to an overlying plate. This plate-associated weakening of bone warrants careful discretion in removing metallic plates following radiographic evidence of fracture healing. Considering the weak correlation between radiographic assessment of fracture healing and the actual mechanical strength of the healed bone, optimum timing of plate removal is very difficult to determine clinically. It has been shown in the dog that the mechanical and morphologic changes associated with plate-induced osteopenia are completely reversible within 3 months of plate removal.(63,93) Based on these findings, it is advisable to suggest several months of restricted activity (if not temporary splinting) for the veterinary orthopaedic patient following plate removal. Contrary to the generally held views on plate-induced osteopenia, Noser and co-workers(64) have shown that plated osteotomized canine femora increase in torsional strength up to 6 months post implantation to a strength in excess of normal unoperated bone and thereafter decrease in strength apparently as a result of stress-protection phenomena. This would suggest that if peak mechanical maxima were identifiable clinically, the timing of plate removal could be determined to minimize the risk of refracture. Presently such nondestructive noninvasive mechanical testing methods are not available to the veterinary practitioner. The existence of open screw holes following plate removal raises the question of the consequent mechanical weakening of bone. It has been shown that the mechanical influence of a freshly drilled screw hole is relatively independent of size (if less than 30% of bone diameter) and for 2.8- and 3.6-mm screw holes a 1.6-fold increase in stress is generated around a screw hole relative to the surrounding bone.(11) When freshly drilled bone is torsionally loaded, fracture typically occurs through the drillhole and at approximately a 50% reduction in torque relative to the contralateral control side(14) Burstein and associates(l4) histologically demonstrated dense woven bone filling screw holes in dogs within 4 weeks of screw removal, but despite this finding they reported the radiographic existence of prominent radiolucent defects in bone even months after screw removal. Apparently there exist significant density differences reflecting variation in calcium content between normal bone and the plug of bone filling a screw hole. After 4 weeks and the formation of a dense woven bone plug, however, torsional loading to failure produced fracture lines not localized to screw holes. Conceivably the stress concentration effect of freshly drilled holes reported by Brooks(11) may serve as a stimulus for

adaptive bone changes in the area of the screw hole such that with healing, stress concentration is eliminated. This impression was confirmed by a related experiment in rabbit femora that indicated that bone adapts to reduce stress concentrations regardless of whether the defect is an empty screw hole, a screw hole with screw in situ, or a screw hole filled with silastic plug. By 8 weeks of healing, all femora so treated had similar torsional strength. If, however, after 8 weeks of healing with a metal screw in situ the screw is removed, a significant (25%) decrease in mechanical properties is observed. Again, this information would suggest that following plate and screw removal serious consideration should be given to limiting the activity of the patient to allow the adaptive processes of the bone to reach completion.

IM ROD FIXATION As stated earlier, single IM rod fixation does not provide the rigid internal stability of plate and screw fixation. Therefore more motion is to be expected at the fracture site, resulting in increased callus formation and healing by secondary bony union. Curiously, very few investigations have been undertaken with the goal of optimizing the healing process relative to the many parameters of IM fixation. Of note is a study by Brown and Mayor, who investigated the biomechanical effect of IM rod fixation relative to rods of differing composition having vastly different moduli.(12) Rods were fashioned from stainless steel, titanium, Delrin, and nylon with respective moduli relative to bone at 10-, 6-, 0.1- and 0.003-fold, respectively. Osteotomized tibias in rabbits were fixed using the above rods and allowed to heal for 16 weeks. Torsional testing with the rods in situ demonstrated a 30% greater strength and 36% greater stiffness of fractures treated with plastic rods versus those treated with metal rods. No mechanical differences were noted between fractures fixed with the two types of metal rods nor between fractures fixed with either type of polymer. From histologic and radiographic comparisons the authors correlated these mechanical differences with associated morphologic changes of the healed tibial fracture. Stiff metallic rods were found to elicit the formation of bony caps at the ends and a sleeve of bone along their length, while flexible polymeric rods caused no such changes. It was postulated that the metal rods, as a result of the formation of bony caps and sleeves, were capable of protecting the tibia from stress, thus explaining the observed lack of remodeling and loss of cortical density relative to the polymer-treated fractures. Fifty percent of the plastic-treated fractures achieved strengths within 10% of the control unoperated side within the 16-week healing period. Although rabbit tibial fractures without associated fibular fracture may represent a rare clinical occurrence and may impart a significant component of rotational stability to the reconstructed fracture site, the results of this investigation would warrant continued study into the feasibility of flexible IM devices. Fracture healing associated with IM fixation has been shown to be influenced by the extent of soft tissue trauma as well as by the type of surgical approachÑsubperiosteal or extraperiosteal. Whiteside and Lesker investigated the rate of fracture healing and ultimate tensile strength of healed osteotomized rabbit tibia at 3 weeks following subperiosteal or extraperiosteal dissection or complete muscle transection at the osteotomy site.(97) All osteotomized tibiae were internally fixed using a single IM pin. Of the tibia exposed subperiosteally, 71% healed within 3 weeks, while of those exposed extraperiosteally only 7% had solid union. Muscle transection resulted in a marked retardation in fracture healing of all tibiae whether exposed subperiosteally or extraperiosteally. This finding, in combination with earlier work that demonstrated the adverse effect of extra- periosteal dissection on the collateral circulation to traumatized muscle,(96) would strongly support a subperiosteal approach for both severely traumatized and untraumatized extremities. Although not specifically studied, this conclusion would likely apply to all forms of internal fixation.

COMPARATIVE BIOMECHANICAL STUDIES: HEALING RELATIVE TO TREATMENT MODALITY Few investigations appear in the literature that attempt to quantitate mechanically the relative merits of the various internal fracture-fixation techniques in terms of associated fracture healing. Furthermore, virtually no information in this regard is available on external means of fracture fixation. Clearly such information is of utmost importance to the orthopaedist who desires a knowledge of the relative mechanisms, strengths, and rates of healing to facilitate appropriate selection of fracture-fixation method. Anderson,(4) in the mid-1960s, performed midfemoral osteotomies in dogs and histologically followed the fracture-healing process as a function of fixation technique. Five separate fracture-treatment groups were defined in increasing order of fracture stability: series 1, no fixation; series 2, loose-fitting medullary nails; series 3, tight-fitting medullary nails; series 4, plate and screw fixation without compression; and series 5, compression plates. Results, as one might expect, indicate that the mode of osteogenesis and the vascular and cellular response of healing were largely dependent on the stability and reduction of the fracture fragments. Furthermore, eventual fracture-callus size was shown to be directly proportional to fracture instability. As an extension of this study, attempts at mechanical testing of fracture strength were performed in a crude

fashion on plated femora with and without compression. A three-point bending load was applied gradually to healing excised femora by suspending a bucket from one end of the bone and slowly adding water. Although after 6 weeks the authors reported a union rate of 100% for the compression-plated group versus 91% for the plated group having no compression, they could not demonstrate a statistically significant difference in fracture strength using their mechanical testing methodology. Nevertheless, from their results they suggested that the beneficial influence of compression on fracture healing is to increase the rigidity of fixation by impacting the bone ends and thereby reducing the interfragmentary space for bone bridging. A somewhat more sophisticated comparative study of fracture fixation relative to fracture healing was performed by Braden and associates(9) also using the dog midshaft femoral osteotomy model. Fractured femora were treated with three different fixation methods applied over three different intervals: IM pin in place for 6 weeks, IM pin with supplementary one half Kirschner apparatus removed at 4 and 6 weeks, respectively, and bone plates removed at 10 weeks. All animals were killed at 10 weeks and the excised femora were tested in torsion to failure to determine ultimate strength and stiffness (normalized to the contralateral unoperated femur). Results demonstrated the femora with IM pin and one half Kirschner apparatus to have the highest strength (80.2% of the normal side) compared with IM pin alone and bone plate (61.9% and 36%, respectively). Stiffness results followed a similar pattern. The authors concluded that the two techniques of IM pin fixation and IM pin fixation with supplementary one half Kirschner apparatus are mechanically superior to bone plating for fracture fixation in the experimental time period of 10 weeks. Furthermore, they went on to attribute these mechanical differences to a relative lack of functional loading (stress protection) associated with femoral plating (see section on plate osteopenia, above). Although these conclusions appear plausible based on the experimental results, the authors' interpretations are subject to criticism in several areas. First, for a strictly comparable study, the various types of fixation should have remained in situ for equivalent periods of time. Indeed, subsequent data reported by the same group'¡ indicated a rapid increase in strength and stiffness of plated femora following removal of the device and resumption of weight bearing. It remains unclear, then, whether the biomechanical differences reported here are solely dependent on fixation technique, on postfixation functional loading, or on a combination of the two. Second, no mention was made of callus type, size or geometry, raising the question of whether motion at the fracture site and exuberant callus formation may have contributed more to the obvious mechanical differences than the postulated concept of stress protection. Third, the described mechanical testing methodology adds numerous variables to the determination of ultimate torsional strength and stiffness when compared with standardized torsional testing in the absence of cycling.(15) Specimens were subjected to extremely complex, if not uncertain, stress fields and therefore endured disparate failure modes not easily normalized to the control femur nor necessarily comparable from one group with another. The validity of these criticisms was borne out in a study by Mullis and co-workers(63) in a quantitative and comparative analysis of fracture healing under the influence of compression plating versus closed weight-bearing treatment. Results indicated that fractures treated by closed reduction experienced large periosteal callus formation and after 1 month regained superior strength and stiffness compared with 1-month, compression-plated fractures (immediately after plate removal). This difference, however, was virtually eliminated at 3 months when the strength of fractures previously compression- plated was shown to approach that of fractures uniting by periosteal callus. The influence of stress protection as postulated by Braden to explain the inferior torsional properties of plated femora at 10 weeks was modified subsequently by the same group of investigators in a continuation study of the effect of time on healing strength of plated bone.(64) Indeed, in marked contrast to the earlier 10-week results, plate removal from osteotomized femora at 6 months was associated with torsional properties actually exceeding the strength and stiffness of the contralateral control femur. Curiously, this effect was reversed at 9 months when healed fractures immediately post-plate removal demonstrated significant reductions in torsional strength and stiffness of 34% and 18%, respectively. The authors attributed the improved strength at 6 months to selective osteonal activation stimulated by the fracture-healing process, while the 9-month reduction in mechanical properties was again related to stress protection phenomena. No attempt, however, was made to explain the earlier 10-week strength data in light of this new information. It was concluded that timing of plate removal should optimally coincide with the observed mechanical maxima but that these findings are preliminary and clearly more research is necessary. Perhaps the recognized weakening influence of screw holes on bone strength represents a more plausible explanation for the 10-week strength data.(11) In a well-controlled comparative study of various fracture-fixation techniques, Burstein and associates measured the corresponding return of torsional strength and stiffness of osteotomized femora using standardized torsional testing methodology. (16) The primary purpose stated was to describe and evaluate a new fixation technique of pericortical clamping designed to provide initial fracture reduction and stability comparable to compression plating but without the need for

cortical screw holes and the associated cortical weakening. Clamp fixation devices consisted of two interlocking halves made of cobalt-chromium alloy that were secured to the bone by a system of embedded spikes and maintained by two screws in the device itself. For comparative purposes, three other internal fixation devices were used in this study: a standard four-hole rigid AO plate; a similar plate machined to yield a tenfold decrease in bending rigidity; and a Kuntscher IM rod appropriately sized to fit the unreduced femoral canal. Devices were applied to transverse femoral osteotomies in adult mongrel dogs and torsionally tested at specified time intervals of 0 (device in place), 10, 16, and 20 weeks (device removed). A corresponding group of dogs had devices applied similarly but without osteotomy. Half of these animals had their femora removed and tested at 10 weeks while the remainder had the devices removed at 10 weeks and their femora tested at 18 weeks. Results of mechanical testing were expressed as percentages of the values from the contralateral control femur. Figure 12-32 shows the rate of recovery of torsional strength, stiffness, and energy to failure of osteotomized femora from the four experimental groups. Similarly Figure 12-33 demonstrates the recovery of torsional strength, stiffness, and energy absorption to failure at 18 weeks (after removal of the fixation devices at 10 weeks). Consistent with studies already discussed, the torsional strength of freshly plated osteotomized femora reflects the stress concentration effect of the screw holes, producing a 50% reduction in strength.(14) In subsequent tests at 10, 16, and 20 weeks immediately following plate removal, this effect persisted for both the rigid and flexible plate and is in marked contrast to the results of Noser and associates(64), who, as discussed, found torsional strengths at 6 months to exceed the normal contralateral bone. From Figure 12-33 it is apparent that the cortical- weakening effect of screw holes was eliminated by the healing process within 8 weeks of plate and screw removal from unosteotomized femora. In addition, unosteotomized plated bones at 10 weeks showed a significant reduction in torsional strength and energy to failure as a function of plate rigidity as previously shown by Woo and co- workers. (101) However, the postulated stress protection effect between rigid and flexible plate in this case accounted for only 16% of the loss in strength, implying that the weakening effect of screw holes is the major controlling factor. In fact, throughout the experiment, the strength of bone fixed by internal fixation plates never varied significantly from the value predicted from a consideration of the screw holes alone, suggesting that stress protection although real, may be an overly emphasized concept.

The clamp and Kuntscher nail, although demonstrating low initial mechanical properties, were associated with progressive improvement of torsional strength, stiffness, and energy absorption of bone over the 20-week course of the experiment. Moreover, compared with plate fixation, these two cortical-sparing devices did not produce as marked a reduction in the mechanical properties of the fixed unosteotomized femora and therefore would be less susceptible to refracture upon device removal. Of the fixation methods tested, the proposed clamp system clearly exhibited superior performance. Disadvantages include the need for a wide variety of clamp sizes to ensure adequate fixation of all size dogs and the difficulty in fixing severely

FIG.12-32 Rate of recovery of torsional strength stiffness, and energy to failure of osteotomized canine femora relative to fixation method In plot A, mean torsional strength was determined at "O" time with fixation devices in place All other data in A B, and C correspond to testing immediately following plate removal. Note the negligible torsional strength at "O" time of intramedullary Kuntschner-nail fixation. (Data adapted from Burstein AH, Moseley CF, Robinson RP et al: Comparative mechanical performance of a new clamp fracture fixation device. Personal Communication, 1983)

FIG.12-33 Rate of recovery of torsional strength stiffness, and energy to failure of intact (nonosteotomized) canine femora exposed to four different fixation devices for 10 weeks. The cortical-weakening effect of screw holes at 10 weeks is almost completely eliminated 8 weeks following plate and screw removal. (Data adapted from Burstein AH, Moseley CF, Robinson RP et al: Comparative mechanical performance of a new clamp fracture fixation device. Personal Communication, 1983)

comminuted, nonunion, or metaphyseal fractures. The obvious advantages are adequate, immediate fracture reduction and stability without the weakening effects of screw holes or disruption of the medullary blood supply. The information from this study is extremely helpful in evaluating the relative merits of various fracture fixation techniques, particularly for application in veterinary orthopaedic practice. It is probably the only investigation to date having sufficient control to yield statistically significant differences among fixation methods.(40)

REFERENCES 1. Aeberhard HJ: Der Einfluss der Plattenuberbiegung auf die Torsionsstabililtat der Osteosynthese. Thesis. Bern, Switzerland, 1973 2. Akeson WH, Woo SL Y, Coutts RD et al: Quantitative histologic evaluation of early fracture healing of cortical bones immobilized by stainless steel and composite plates. Calcif Tissue Res 19:29, 1975 3. Allen WC, Piotrowski G, Burstein AH et al: Biomechanical Principles of Intramedullary Fixation. Clin. Orthop. Rel. Res., 60:13, 1968 4. Anderson LD: Compression plate fixation and the effect of different types of internal fixation on fracture healing. J Bone Joint Surg 47A: 191, 1965 5. Askew MT, Mow VC, Wirth CR et al: Analysis of the intraosseous stress field due to compression plating. J Biomech 8:203, 1975 6. Bagby GM, Jones JM: The effect of compression on the rate of fracture healing using a special plate. Am J Surg 95:761, 1958 7. Baker J, Frankel VH, Burstein AH: Fatigue fractures: Biomechanical considerations. J Bone Joint Surg 54A:1345, 1972 8. Boltze WH, Chignet C, Niederer PG: Der Fixateur externe (Rohr system). Stabilitat pruhing. Bern, AO Bulletin, 1978 9. Braden TD, Brinker WO, Little RW et al: Comparative biomechanical evaluation of bone healing in the dog. J Am Vet Med Assoc 163:65, 1973 10. Brinker WO, Flo GL, Braden TD et al: Removal of bone plates in small animals. J Vet Med 11:577, 1975 11. Brooks DB, Burstein AH, Frankel VH: The biomechanics of torsional fractures: The stress concentration of drill holes. J Bone Joint Surg 58A:506, 1976 12. Brown SA, Mayor MB: The biocompatibility of materials for intemal fixation of fractures. J Biomed Mater Res 12:67, 1978 13. Buray F, Bourgois R, Donkerwolkcke M: Elastic external fixation: Concepts in external fixation: A biomechanical study of the half-frame. In Seligson D, Pope MH (eds): Concepts in External Fixation, p. 67. New York, Grune & Stratton, 1982. 14. Burstein AH, Currey J, Frankel VH et al: Bone strength: The effect of screw holes. J Bone Joint Surg 54A: 1143, 1972 15. Burstein AH, Frankel VH: A standard test for laboratory animal bone. J Biomech 4:155, 1971 16. Burstein AH, Moseley CF, Robinson RP et al: Comparative mechanical performance of a new clamp fracture fixation device (personal commu- nication, 1983.) 17. Bynum D, Ray DR Jr, Boyd CL et al: Capacity of installed commercial bone fixation plates. Am J Vet Res 32:783, 1971 18. Carter DR: The Fatigue Behavior of Compact Bone. PhD dissertation, Stanford University, 1976 19. Carter DR: Anisotropic examination analysis of strain rosette information from cortical bone. J Biomech 11:199, 1978 20. Carter DR, Hayes WC: Compact bone fatigue dam- age: A microscopic examination. Clin Orthop 127:265, 1977 21. Chao EYS, An K: Stress and rigidity analysis of external fracture fixation devices. In Simon BR (ed): Finite Elements in Biomechanics, vol 2. International Conference Proceedings. University of Arizona, 1980 22. Chao EYS, Briggs BT, McCoy MT: Theoretical and experimental analyses of Hoffmann-Vidal external fixation system. In Brooker AF, Edwards CC (eds): External Fixation: The Current State of the Art. Baltimore, Williams & Wilkins, 1979 23. Chao EYS, Kasman RH, An KN: Rigidity and stress analyses of external fracture fixation devices: A theoretical approach. J Biomech 15:971, 1982 24. Chao EYS, Pope MH: The mechanical basis of external fixation. In Seligson D, Pope MH (eds). Concepts in External Fixation, p 13. New York, Grune & Stratton, 1982 25. Charnay A, Tschantz P: Mechanical influences in bone remodeling: Experimental research on Wolffschan. J Biomech 5:173, 1972 26. Cochran GVB: Effects of internal fixation plates on mechanical deformation of bone. Surg Forum 20:469, 1969 27. Cruwess RL, Dumont J: Current concepts, fracture healing. Can J Surg 18:403, 1975 Fractures and Dislocations 28. Currey JD: Stress concentrations of bone. J Micro Sci 103:161, 1962 29. Egkher E, Martinek H, Wielke B: How to increase the stability of external fixation units: Mechanical tests and theoretical studies. Arch Orthop Trauma Surg 96:35, 1980 30. Evans FG: Stress and strain in the long bones of the lower extremity. Am Acad Orthop Surg 9:264, 1952 31. Evans M: The Oxford external fixateur. The 6th Annual Report of the Oxford Orthopaedic Engineering Centre, 1979

32. Falkenburg J: An experimental study of the rate of fracture healing: As assessed from the tensile strength and Sr55 activity of the callus with special reference to the effects of intramedullary nailing. Acta Orthop Scand (Suppl 50), 1961 33. Fischer DA, Chao EYS, Cabanela ME: Cortical bone union in external fixators: A clinical and biomechanical analysis. Scientific exhibit. Ameri- can Academy of Orthopaedic Surgeons Annual Meeting, Atlanta, Georgia, 1980 34. Frankel VH, Burstein AH: Orthopaedic Biome- chanics. Philadelphia, Lea & Febiger, 1971 35. Frankel VH, Nordin M: Basic Biomechanics of the Skeletal System. Philadelphia, Lea & Febiger, 1980 36. Freidenberg FB, French G: The effects of known compression forces on fracture healing. Surg Gynecol Obstet 94:743, 1952 37. Frost HL: Bone Dynamics in Osteoporosis and Osteomalacia. Springfield, IL, Charles C Thomas, 1966 38. Fung YC: Biomechanics: Mechanical Properties of Living Tissue. New York, Springer-Verlag, 1981 39. Gotzen L, Muhr C, Anna O: Biomechanische Untersuchungen zur Vorbiegung von AO-Osteosyntheseplatten, Hefte Z. Unfallheilkunde 126:387, 1976 40. Hayes WC: Biomechanics of fracture treatment: In Heppenstall B (ed): Fracture Treatment and Healing, p 124. Philadelphia, WB Saunders, 1980 41. Hayes WC, Girens WB, Murch SA et al: Effects of plate modulus, thickness, and pre-bending on the mechanics of compression plate fixation. Transactions of the 24th Annual Orthopaedic Research Society, Dallas, Texas, February 1978 42. Hayes WC, Perren SM: Plate-bone fixation in the compression fixation of fractures. Clin Orthop Rel Res 89:236, 1972 43. Hughes AN, Jordan BA: The mechanical properties of surgical screens and some aspects of insertion practice. Injury 4:25, 1972 44. Hutzschenreuter R, Perren SM, Steinemann S et al: Some effects of rigidity of internal fixation on the healing pattern of osteotomies. Injury 1 :77, 1969 45. Jorgensen TE: Measurements of stability of crural fractures treated with Hoffmann osteotaxis: Parts 1-4. Acta Orthop Scand 43: 188, 1972 46. Lanyon LE, Hampson WGJ, Goodship AE et al: Bone deformation recorded in vivo from strain gauges attached to the human tibial shaft. Acta Orthop Scand 46:256, 1975 47. Lanyon LE, Smith RN: Measurements oI bone strain in the walking animal. Res Vet Sci 10:93, 1969 48. Lanyon LE, Smith RN: Bone strain in the tibia during normal quadrapedal locomotion. Acta Orthop Scand 41 :238, 1970 49. Latta LL, Sarmiento A, Tarr RR: The rationale of functional bracing of fractures. Clin Orthop Rel Res 146:28, 1980 50. Laurence M, Freeman MAP, Swanson SAV: En- gineering considerations in the internal fixation of fractures of the tibial shaft. J Bone Joint Surg 51B:754, 1969 51. Lettin AWF: The effects of axial compression on the healing of experimental fractures of the rabbit tibia. Proc R Soc Med 58:882, 1965 52. Lettin AWF: The biological effect of rigid internal fixation on the healing of cortical bones: Proceed- ings of the British Orthopaedic Association. J Bone Joint Surg 50B, 1:227, 1968 53. Lettin AWF: Effect of rigid internal fixation on the mechanical properties of healing cortical bone: Proceedings of the British Orthopaedic Association. J Bone Joint Surg 51 B, 1: 177, 1969 54. Lindahl O: Rigidity of immobilization of transverse fractures. Acta Orthop Scand 32:237, 1962 55. Lindahl O: Rigidity of immobilization of oblique fractures. Acta Orthop Scand 35:39, 1964 56. Lindahl O: The rigidity of fracture immobilization with plates. Acta Orthop Scand 38:101, 1967 57. Lindholm RV, Lindholm TS, Toikkanen S et al: Effect of forced interfragmental movements on the healing of tibial fractures in rats. Acta Orthop Scand 40:721, 1969 58. McCoy MT, Briggs BT, Chao EYS: A comparative study of external factors based on bone fracture stiffness. Proceedings of the 26th Orthopaedic Research Society, Atlanta, Georgia, 1980 59. Mensch JS, Mankoff KL, Roberts SB et al: Experimental stabilization of segmental defects in the human femur. J Bone Joint Surg 58A:185, 1976 60. Mindell ER, Rodbard S, Kuasman BG: Chondrogenesis in bone repair: A study of healing fracture callus in the rat. Clin Orthop Rel Res 79:187, 1971 61. Minns RJ, Brimble GR, Campbell J: A biomechanical study of internal fixation of the tibial shaft. J Biomech 10:569, 1977 62. Muller ME, Allgover M, Willenegger H: Manual of internal fixation. New York, Springer-Verlag, 1970 63. Mullis DL, Latta LL, Alvarez R et al: A quantitative, comparative analysis of fracture healing under the influence of compression plating versus closed weight-bearing treatment. Proceedings of the Orthopaedic Research Society, Dallas, Texas, February 1978. J Bone Joint Surg 60A:99, 1978 64. Noser GA, Brinker WO, Little RW et al: Effect of time on strength of healing bone with bone plate fixation. J Am Anim Hosp Assoc, 13:559, 1977 65. Nunamaker DM, Perren SM: Force measurements in screw fixation. J Biomech 9:669, 1976

66. Olerud S, Danckwardt-Lilliestrom G: Fracture healing in compression osteosynthesis in the dog. J Bone Joint Surg 50B, No. 4:844, 1968 67. Panjabi MM, White AA III, Southwick WO: Temporal changes in the physical properties of healing fractures in rabbits. J Biomech 10:689, 1977 68. Paul JP: Bioengineering studies of the forces transmitted by joints. In Kenedi RM (ed): Biomechanics and Related Bioengineering Topics. London, Pergamon Press, 1965 69. Perren SM: Biomechanical basis for fracture healing. Veterinary Orthopedic Society, 5th Annual Meeting, Snowmass, Colorado, February, 1978 70. Perren SM: Physical and biological aspects of fracture healing with special reference to internal fixation. Clin Orthop Rel Res 138:175, 1979 71. Perren SM, Hayes WC: Biomechanik der Platenosteosynthese. Med Orthop Tech 94:56, 1974 72. Perren SM, Huggler A, Russenberger M et al: Cortical bone healing. Acta Orthop Scand (Suppl)125:19, 1969 73. Piekarski K, Wiley AM, Bartels TF: The effect of delayed internal fixation on fracture healing. Acta Orthop Scand 40:543, 1969 74. Plant RE, Bartel DL: Finite element analysis of bone plate screw system: Paper presented at Annual Meeting of American Society of Engineers, New York, November 1974 75. Rahn BA, Gallinaro P, Baltensperger A et al: Primary bone healing: An experimental study in the rabbit. J Bone Joint Surg 53A: 783, 1971 76. Ray DR, Ledbetter WB, Bynum D et al: A parametric analysis of bone fixation plates on fractured equine third metacarpal. J Biomech 4:163, 1971 77. Reilly D, Burstein AH: The elastic and ultimate properties of compact bone tissue. J Biomech 8:393, 1975 78. Rybicki EF, Simonen F, Mills EJ et al: Mathematical and experimental studies on the mechanics of plated transverse fractures. J Biomech 7:377, 1974 79. Rybicki EF, Simonen FA: Mechanics of oblique fracture fixation using a finite element model. J Biomech 10:141, 1977 80. Sammarco T, Burstein AH, Davis W et al: The biomechanics of torsional fractures: The effect of loading on ultimate properties. J Biomech 4:113, 1971 81. Sarmiento A: A functional below-the-knee cast for tibial fractures. J Bone Joint Surg 49A:855, 1967 82. Sarmiento A: A functional below-the-knee brace for tibial fractures: A report on its use in one hundred thirty-five cases. J Bone Joint Surg 52A:295, 1970 83. Sarmiento A: Functional bracing of tibial and femoral shaft fractures. Clin Orthop Rel Res 82:2, 1972 84. Sarmiento A: Functional bracing of tibial fractures. Clin Orthop Rel Res 105:202, 1974 85. Sarmiento A, Schaeffer JF, Beckerman L et al: Fracture healing in rat femora as affected by func- tional weight-bearing. J Bone Joint Surg 59A:369, 1977 86. Schatzker T, Sanderson R, Murnaughan TP: The holding power of orthopaedic screens in vivo. Clin Orthop Rel Res 108:115, 1975 87. Schatzker T, Sumner-Smith G, Clark R et al: Strain gauge analysis of bone response to internal fixation. Clin Orthop Rel Res 132:244, 1978 88. Schenck T, Somerset TH, Porter RE: Stresses in orthopaedic walking casts. J Biomech 2:227, 1969 89. Singer CJ: A Short History of Scientific Ideas to 1900. New York, Oxford University Press, 1959 90. Slatis P, Karaharjn E, Holmstrom T et al: Structural changes in intact tubular bone after application of rigid plates with and without compression. J Bone Joint Surg 60A:516, 1978 91. Tonino AJ, Davidson C L, Klopper PJ et al: Protection from stress in bone and its effects: Experiments with stainless steel and plastic plates in dogs. J Bone Joint Surg 58B, No. 1: 107, 1976 92. Turner M, Mills GT, Gabel AA: In vivo measure- ments of bone strain in the horse. Am J Vet Res 36:1573, 1975 93. Uhthoft HK, Dubue FL: Bone structure changes in the dog under rigid internal fixation. Clin Orthop Rel Res 81:165, 1971 94. White M, Panjabi MM, Southwick WO: The four biomechanical stages of fracture repair. J Bone Joint Surg 59A: 188, 1977 95. White AA, Panjabi MM, Southwick WO: Effects of compression and cyclical loading on fracture healing: A quantitative biomechanical study. J Biomech 10:223, 1977 96. Whiteside LE, Lesker PA: The effects of extraper- iosteal and subperiosteal dissection: I. On blood flow in muscle. JBJS 60A:23, 1978 97. Whiteside LE, Lesker PA: The effects of extraperiosteal and subperiosteal dissection: II. On fracture healing. JBJS 60A:26, 1978 98. Whiteside LA, Lesker PA, Sweeney RE: The relationship between the biochemical and mechanical characteristics of callus during radiographically determined stages of fracture healing. Transactions of the 24th Annual Orthopaedic Research

Society, Dallas, Texas, February 1978 99. Wolf JW, White AA, Panjabi MM et al: Comparison of cyclic loading versus constant compression in the treatment of long-bone fractures. J Bone Joint Surg 63A: 805, 1981 100. Wolff J: Sitz. Ber. Preuss. Akad. Wiss. 22. Sitzg., phsik-math, KI, 1884 101. Woo SLY, Akeson WH, Coutts RD et al: A comparison of cortical bone atrophy secondary to fixation with plates with large differences in bending stiff: ness. J Bone Joint Surg 58A: 190, 1976 102. Woo SLY, Akeson WH, Levenetzky B et al: Potential application of graphite fiber and methyl methacrylate resin composites as internal fixation plates. J Biomed Mater Res 8:321, 1974 103. Woo SLY, Simmon BR, Akeson WH et al: An interdisciplinary approach to evaluate the effect of internal fixation plate on long bone remodeling. J Biomech 10:87, 1977 104. Yamagiski M, Yoshinurn Y: The biomechanics of fracture healing. J Bone Joint Surg 37A: 1035, 1955

All rights reserved. This document is available on-line at www.ivis.org. Document No. B0013.0685.