Tornetta Rockwood Adults 9781975137298 V2

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CHAPTER 1 • Biomechanics of Fractures and Fracture Fixation

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Figure 1-4.  Influence of cross-sectional geometry on bending stiffness for basic implant shapes. A: Doubling the plate thickness increases bending stiffness eightfold. B: Doubling the diameter of a Kirschner wire will increase bending stiffness 16-fold. C: For a hollow cylinder such as a diaphysis, increasing the outer diam- eter from 10 mm to 12 mm while retaining a wall thickness of 2 mm increases bending stiffness by 82%.

stiffer and more brittle but giving it a higher ultimate strength. 140 It becomes apparent that material properties of anisotropic and viscoelastic biologic tissues are far more complex than those of implant materials, and the reader is referred to other sources for more detailed information. 93,152,197 STRUCTURAL PROPERTIES Structural properties depend on both the material properties and the shape and size of the object. In fracture surgery, one must consider the structural properties of two different objects, the fixation device and the bone. Because of their relatively simple geometries, the structural properties of fixation devices such as plates and intramedullary nails can readily be calculated. The stiffness and strength of fracture fixation plates depend on their material property and cross-sectional geometry. For an osteo- synthesis plate of width w = 10 mm and thickness t = 4 mm, the bending stiffness ( EI ) can be calculated as the product of its E-modulus and the second moment of inertia I = ( w × t 3 )/12 (Fig. 1-4A). In this formula, bending stiffness correlates linearly with plate width but relates to the third order with plate thickness. Therefore, doubling the plate width increases plate stiffness two- fold, while doubling the plate thickness will increase plate stiff- ness eightfold (2 3 ). The effect of plate geometry is evident when one evaluates the flexibility of a 1/3 tubular plate and a 3.5-mm compression plate. The width of both plates is relatively similar, but the 3.5-mm plate is thicker, resulting in a far greater bending

stiffness. Similar calculations can be performed to understand the differences in bending stiffness of a solid cylinder such as a k-wire, which increases to the fourth power of the diameter (Fig. 1-4B). Doubling the diameter of a k-wire increases its stiff- ness 16-fold (2 4 ). Hollow cylinders are common in orthopedic applications, such as cannulated screws and intramedullary nails (Fig. 1-4C). Hollow cylinders represent weight-optimized struc- tures, whereby coring out 50% of the tube diameter will remove 25% of material, but will reduce bending stiffness and strength by only 6%. For example, a solid intramedullary nail with a diam- eter of 10 mm has a bending resistance of I = 490 mm 4 , while a hollow nail with an outer diameter of 10 mm and an inner diam- eter of 3 mm has a similar bending resistance of I = 487 mm 4 . This demonstrates that removing the core of an intramedullary nail to accommodate guide wire placement does not significantly affect its bending resistance. Diaphyseal bone also resembles the principal structure of a hollow cylinder. As an individual ages, the diameter of the femo- ral diaphysis increases and the thickness of the cortex decreases. Using the principle of the second moment of inertia discussed earlier in this section, the bending stiffness of a tubular bone increases as the outer diameter increases, even as the cortical thickness and material properties of the bone decrease. The aggregate increase in strength realized by increasing the diameter of the shaft is enough to protect the elderly from osteoporotic diaphyseal femur fractures. In contrast, trabecular thinning in the vertebrae cannot be compensated by structural changes of the

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